ECLIPSE Pre- and Post-Processing Suite ECLIPSE* reservoir simulation software Reference Manual Proprietary notice Copyright © 2014 Schlumberger. All rights reserved. Reproduction or alteration without prior written permission is prohibited, except as allowed under applicable law. Use of this product is governed by the License Agreement. Schlumberger makes no warranties, express, implied, or statutory, with respect to the product described herein and disclaims without limitations any warranties of merchantability or fitness for a particular purpose. Trademarks & service marks "Schlumberger," the Schlumberger logotype, and other words or symbols used to identify the products and services described herein are either trademarks, trade names, or service marks of Schlumberger and its licensors, or are the property of their respective owners. These marks may not be copied, imitated, or used, in whole or in part, without the express prior written permission of their owners. 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Table of Contents List of Figures ..... ...................................................................................................................................................................7 List of Tables ...... ...................................................................................................................................................................8 Chapter 1 - Developments................................................................................................................ 9 Product Maintenance..............................................................................................................................................................9 Developments for 2004A ......................................................................................................................................................10 Chapter 2 - The Most Asked Questions About PVTi.................................................................... 13 Introduction ......... .................................................................................................................................................................13 Chapter 3 - Introduction ................................................................................................................. 25 General information ..............................................................................................................................................................25 Chapter 4 - Getting started............................................................................................................. 29 Starting PVTi ...... .................................................................................................................................................................29 Chapter 5 - Tutorials ....................................................................................................................... 31 Overview............. .................................................................................................................................................................31 Fluid Properties Estimation...................................................................................................................................................33 Creating a fluid system .........................................................................................................................................................36 Simulating experiments ........................................................................................................................................................42 Fitting an equation of state to experimental results ..............................................................................................................49 Exporting ECLIPSE Black Oil PVT tables.............................................................................................................................53 Converting a black oil run to compositional ..........................................................................................................................58 Workflow Tutorial .................................................................................................................................................................61 Multiphase Flash .................................................................................................................................................................69 Exporting an ECLIPSE Thermal model ................................................................................................................................73 Data analysis and quality control ..........................................................................................................................................77 Removing contamination from samples................................................................................................................................84 Converting old projects to the current version ......................................................................................................................87 Chapter 6 - Reference section ....................................................................................................... 89 General information ..............................................................................................................................................................89 Main PVTi window ................................................................................................................................................................90 The PVTi main module .........................................................................................................................................................91 The fluid model ... .................................................................................................................................................................98 COMB - Compositional Material Balance ...........................................................................................................................112 Simulation using PVTi ........................................................................................................................................................117 Regression in PVTi .............................................................................................................................................................126 Exporting keywords ............................................................................................................................................................133 VFP module ........ ...............................................................................................................................................................138 Utilities ................ ...............................................................................................................................................................144 Batch system and keywords ...............................................................................................................................................152 Error handling ..... ...............................................................................................................................................................165 Chapter 7 - Keywords ................................................................................................................... 167 PVTi keywords.... ...............................................................................................................................................................167 Keywords A-D..... ...............................................................................................................................................................168 ACF: Acentric factors......................................................................................................................................................... 169 ACHEUH: A-coefficient for Cheuh-Prausnitz BICs ............................................................................................................ 170 ALLDRY: Dry Gas Tables for Each Sample ...................................................................................................................... 171 PVTi Reference Manual Table of Contents 3 BIC: Binary interaction coefficients .................................................................................................................................... 172 BLACKOIL: Start of the BLACKOIL section....................................................................................................................... 174 CALVAL: Specify calorific values....................................................................................................................................... 175 CHARACT: Components to be characterized.................................................................................................................... 176 CNAMES: Component names ........................................................................................................................................... 177 COATS: Blackoil tables...................................................................................................................................................... 178 COMB: Start of the COMB section .................................................................................................................................... 179 COMBINE: Group existing components ............................................................................................................................ 180 CORRACF: Splitting correlation for ACFs ......................................................................................................................... 181 CORRCP: Splitting correlation for critical properties ......................................................................................................... 182 DRYGAS: Dry gas tables................................................................................................................................................... 183 DEADOIL: Dead oil tables ................................................................................................................................................. 184 DEBUE: Select output to debug file ................................................................................................................................... 185 DEBUG: Select output to debug file................................................................................................................................... 186 DEFBIC: Default binary interaction coefficients ................................................................................................................. 187 DEGREES: Temperature convention ................................................................................................................................ 188 DIFFERENTIAL: Blackoil tables ........................................................................................................................................ 189 DREF: Reference densities ............................................................................................................................................... 190 Keywords E-K ..... ...............................................................................................................................................................191 ECHO: Insert PVI file into PVP file..................................................................................................................................... 192 EOS: Defines the required Equation of State .................................................................................................................... 193 EOSOUT: EoS data for ECLIPSE 300............................................................................................................................... 194 EXP: Experiments.............................................................................................................................................................. 195 EXPIND: Set Status of Experiments .................................................................................................................................. 200 FIT: Perform fit by regression ............................................................................................................................................ 201 FRAC: Specify plus fraction data ....................................................................................................................................... 202 FRAGOR: Blackoil tables................................................................................................................................................... 203 FVFREF: FVF reference conditions................................................................................................................................... 204 GI: Define GI nodes for E200 tables .................................................................................................................................. 205 GROUP: Start of the GROUP section................................................................................................................................ 206 GRBYALL: Start of the GROUP section ............................................................................................................................ 207 GRBYMIX: Start of the GROUP section ............................................................................................................................ 208 GRBYSAM: Start of the GROUP section........................................................................................................................... 209 GRPBYWGT: Grouping by molecular weight .................................................................................................................... 210 HYDRO: Define component as hydrocarbon or non-hydrocarbon..................................................................................... 211 KVTABLE: Request K-value table for ECLIPSE 300 output .............................................................................................. 212 Keywords L- O .... ...............................................................................................................................................................213 LBC: Lohrenz-Bray-Clark viscosities ................................................................................................................................. 214 LBCCOEF: Set non-default LBC coefficients..................................................................................................................... 215 LIVEOIL: Live oil tables ..................................................................................................................................................... 216 LNAMES: Specify library names........................................................................................................................................ 217 MAXIT: Max. number of regression iterations.................................................................................................................... 218 MAXSTEP: Maximum step size allowed in regression ........................................................................................................ 219 MDP: Data for Whitson splitting ......................................................................................................................................... 220 MESSAGE: Echo message to file and screen ................................................................................................................... 221 MINDELP: Minimum pressure difference........................................................................................................................... 222 MINSTEP: Minimum step limit allowed in regression ........................................................................................................ 223 MIX: Mix samples............................................................................................................................................................... 224 MODSPEC : Denotes start of the run specification section ............................................................................................... 225 MODSYS : Start of the MODSYS section......................................................................................................................... 226 MOSES : Blackoil tables................................................................................................................................................... 227 MW : Specify molecular weights....................................................................................................................................... 228 MWS : Define plus fraction mole weight for CMF splitting................................................................................................ 229 NCOMPS : Specify number of components ..................................................................................................................... 230 NEWPVI : Request new output PVI file ............................................................................................................................ 231 NEWPVO : Request new output PVO file......................................................................................................................... 232 NOECHO : No insertion of PVI file into PVP file ................................................................................................................ 233 OBS : Specify observations .............................................................................................................................................. 234 OBSIND : Specify observation weights ............................................................................................................................ 235 4 PVTi Reference Manual Table of Contents OMEGAA/B: Specify EoS omega values........................................................................................................................... 237 OPTIONS : Set various program options ......................................................................................................................... 238 OUTECL3 : Start of the OUTECL3 section ...................................................................................................................... 240 Keywords P- S .... ...............................................................................................................................................................241 PARACHOR : Define parachors ........................................................................................................................................ 242 PCRIT : Critical pressures ................................................................................................................................................ 243 PEARCE : Blackoil tables................................................................................................................................................. 244 PEDERSEN : Specify Pedersen viscosities ..................................................................................................................... 245 PRCORR : Peng-Robinson correction ............................................................................................................................. 246 PSEUCOMP : Start of the PSEUCOMP section.................................................................................................................. 247 RECOVERY : Liquid production for recovery estimates................................................................................................... 248 REGRESS: Start of the REGRESS section....................................................................................................................... 249 REGTARG : Regression target ........................................................................................................................................ 250 RTEMP : Reservoir temperature for ECLIPSE Compositional ......................................................................................... 251 RUNSPEC : Denotes start of the run specification........................................................................................................... 252 SALINITY : Specify sample salinity ................................................................................................................................. 253 SAMPLE : Specify fluid sample ........................................................................................................................................ 254 SAMPLES : Specify fluid samples.................................................................................................................................... 255 SAMPLES : Specify fluid samples.................................................................................................................................... 256 SAMTITLE : Specify titles of fluid samples....................................................................................................................... 257 SAVCOMP : Save compositions ...................................................................................................................................... 258 SCT : Defines Semi-Continuous Thermodynamics split................................................................................................... 259 SG : Specify specific gravity ............................................................................................................................................. 260 SIMULATE : Start of the SIMULATE section.................................................................................................................... 261 SPECHA-D: Specify specific heat capacity coefficients .................................................................................................... 262 SPLIT : Start of the SPLIT section................................................................................................................................... 263 SSHIFT : Dimensionless volume shifts for PR3 ................................................................................................................ 264 STCOND : Standard conditions......................................................................................................................................... 265 SYSTEM : Start of the SYSTEM section ........................................................................................................................... 266 Keywords T - Z ... ...............................................................................................................................................................267 TBOIL : Specify boiling points .......................................................................................................................................... 268 TCRIT : Specify critical temperatures............................................................................................................................... 269 THERMX : Thermal expansion coefficient for volume shifts............................................................................................... 270 TITLE : Specify run title ................................................................................................................................................... 271 TLOW : Define lowest temperature for VFP tables ............................................................................................................ 272 TREF : Specify reference temperatures............................................................................................................................ 273 UNITS : Specify unit conventions ..................................................................................................................................... 274 VAR : Specify regression variables ................................................................................................................................... 275 VCRIT : Specify volumes.................................................................................................................................................. 278 VCRITVIS : Specify volumes for LBC viscosity calculations ........................................................................................... 279 VERSION : Version of PVTi .............................................................................................................................................. 280 VFP : Start of the VFP section .......................................................................................................................................... 281 WAT100 : Output water properties .................................................................................................................................... 282 WAT200 : Output water properties .................................................................................................................................... 283 WAT300 : Output water properties .................................................................................................................................... 284 WATVFP : Output water properties .................................................................................................................................... 285 WETGAS : Wet gas tables.................................................................................................................................................. 286 WHIT : Defines Whitson splitting....................................................................................................................................... 287 WHITSON : Blackoil tables ................................................................................................................................................ 288 X/YMFVP: XMFVP and YMFVP ECLIPSE tables .............................................................................................................. 289 ZCRIT : Specify critical Z-factors...................................................................................................................................... 290 ZCRITVIS : Specify critical Z-factors for LBC calculations .............................................................................................. 291 ZI : Specify sample composition...................................................................................................................................... 292 ZMFVD : Composition versus depth table ......................................................................................................................... 293 Chapter 8 - Technical Description ............................................................................................... 295 Overview............. ...............................................................................................................................................................295 Theoretical background of PVT ..........................................................................................................................................296 PVTi Reference Manual Table of Contents 5 Equation of state . ...............................................................................................................................................................317 Basic laboratory experiments..............................................................................................................................................339 Regression ......... ...............................................................................................................................................................348 Output for ECLIPSE simulators ..........................................................................................................................................354 Analysis techniques ............................................................................................................................................................371 Recommended PVT analysis for oil reservoirs ...................................................................................................................372 Recommended PVT analysis for gas condensate reservoirs .............................................................................................377 Consistency tests and correlations .....................................................................................................................................381 Fluid Properties Estimation .................................................................................................................................................384 Regression in PVT analysis ................................................................................................................................................386 Wax and asphaltene precipitation in PVTi ..........................................................................................................................394 Cleaning samples contaminated with oil-based mud..........................................................................................................398 Mixing and recombination of samples.................................................................................................................................400 ECLIPSE Thermal Export Module ......................................................................................................................................401 Appendix A - Units........................................................................................................................ 409 Units.................... ...............................................................................................................................................................409 Appendix B - Symbols.................................................................................................................. 413 Symbols .............. ...............................................................................................................................................................413 Appendix C - Bibliography........................................................................................................... 415 Appendix D - Index ....................................................................................................................... 421 6 PVTi Reference Manual Table of Contents List of Figures Figure 5.1 .......... Figure 5.2 .......... Figure 5.3 .......... Figure 5.4 .......... Figure 5.5 .......... Figure 5.6 .......... Figure 5.7 .......... Figure 5.8 .......... Figure 5.9 .......... Figure 5.10 ........ Figure 5.11 ........ Figure 5.12 ........ Figure 6.1 .......... Figure 6.2 .......... Figure 6.3 .......... Figure 6.4 .......... Figure 6.5 .......... Figure 6.6 .......... Figure 6.7 .......... Fingerprint Plot .......................................................................................................................................39 Phase Plot ..............................................................................................................................................40 The plotted simulation results .................................................................................................................45 Plot of Oil FVF, Viscosity and Rs versus pressure for the output black oil property tables ....................55 Phase Diagram for Schrader Bluff Fluids ...............................................................................................70 The phase envelope plot. .......................................................................................................................78 The main display shows messages indicating the quality of the data.....................................................79 The main plot window after zooming in ..................................................................................................80 The plot of k values versus pressure. .....................................................................................................81 The Hoffman-Crump plot ........................................................................................................................82 Hoffman-Crump-Hocott plot. ...................................................................................................................83 The original sample, the cleaned sample and the estimated contaminant. ............................................85 The main PVTi window ...........................................................................................................................91 Fingerprint Plot .....................................................................................................................................109 Phase plot.............................................................................................................................................110 Ternary Plot .........................................................................................................................................111 Main display after performing material balance ....................................................................................113 COMB module - vapor versus pressure plot ........................................................................................114 The VFP module...................................................................................................................................138 PVTi Reference Manual List of Figures 7 List of Tables Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 6.1 Table 6.2 Table 6.3 Table 6.4 Table 6.5 Table 6.6 Table 6.7 Table 6.8 Table 6.9 Table 6.10 Table 6.11 Table 6.12 Table 6.13 Table 6.14 Table 6.15 Table 6.16 Table 6.17 Table 7.1 Table 7.2 Table 7.3 Table 7.4 Table 7.5 Table 7.6 Table 7.7 Table 7.8 Table 8.1 Table 8.2 Table 8.3 Table 8.4 Table 8.5 Table 8.6 Table 8.7 Table 8.8 Table 8.9 Table 8.10 Table 8.11 Table 8.12 Table A.1 Table A.2 Table A.3 8 The Fundamentals panel .........................................................................................................................34 Component and fluid definitions...............................................................................................................36 Program Options data ..............................................................................................................................38 Constant Composition Expansion experiment at 220o F (* indicates bubble point pressure)..................43 Differential Liberation Experiment at 220o F (* indicates bubble point pressure).....................................46 List of library components ........................................................................................................................95 Observation data....................................................................................................................................123 Set PVTi Program Options panel ...........................................................................................................145 Keywords for introducing sections .........................................................................................................156 RUNSPEC keywords .............................................................................................................................156 SYSTEM keywords ................................................................................................................................157 SPLIT keywords .....................................................................................................................................158 GROUP keywords..................................................................................................................................159 COMB keywords ....................................................................................................................................159 SIMULATE keywords .............................................................................................................................160 REGRESS keywords .............................................................................................................................160 BLACKOIL keywords .............................................................................................................................161 PSEUCOMP keywords ..........................................................................................................................162 OUTECL3 keywords ..............................................................................................................................162 VFP keywords ........................................................................................................................................163 APITRACK keywords .............................................................................................................................163 Error codes ............................................................................................................................................165 Output indices ........................................................................................................................................185 Output indices ........................................................................................................................................186 Required data for experiments...............................................................................................................195 Keyword arguments ...............................................................................................................................196 Restrictions for EXP keyword arguments...............................................................................................198 Component Types..................................................................................................................................211 Equation of State omega values ............................................................................................................237 Default limits for variables ......................................................................................................................276 Alkanes ..................................................................................................................................................298 Napthenes..............................................................................................................................................299 Aromatics ...............................................................................................................................................299 Physical properties.................................................................................................................................300 Multi-component (ii) mixtures .................................................................................................................300 CVD Report............................................................................................................................................309 Equation of State coefficients ................................................................................................................319 Equation of State constants ...................................................................................................................320 Parameter estimation data. N is the number of experimental points .....................................................335 Parameter Values for Pure Component Viscosity Correlation ...............................................................336 Physical Properties of Methane and Decane .........................................................................................337 PVTi defaults for Fluid Property Estimation ...........................................................................................385 Units .......................................................................................................................................................410 Constants ...............................................................................................................................................411 Conversion factors .................................................................................................................................411 PVTi Reference Manual List of Tables Developments Chapter 1 Product Maintenance Maintenance of this application is continuing until further notice. PVTi Reference Manual New developments Product Maintenance 9 Developments for 2004A ECLIPSE Thermal Export facility For the 2003A version of PVTi a new ECLIPSE Thermal support module was available where you were able to interactively develop a correlation which accurately predicted K-values for each component in a given fluid. For the 2004A version this module has been extended to a full export facility where you can write out files that are suitable for use as PVT input for ECLIPSE Thermal. The motivation behind this is so that, just as you can export files to use as PVT input for ECLIPSE BlackOil and ECLIPSE Compositional, they will now be able to do the same for ECLIPSE Thermal. PVTi will export a series of keywords when an export for ECLIPSE Thermal is performed. For a workflow description and brief summary of these keywords see "Compositional Data for ECLIPSE Thermal" on page 366. For a more technical outline of how the exported keywords are used in ECLIPSE Thermal see "ECLIPSE Thermal Export Module" on page 401. Export for API Tracking option in ECLIPSE BlackOil The API Tracking facility enables ECLIPSE BlackOil to model the mixing of different types of oil, having different surface densities and PVT properties. Without the API Tracking facility, the presence of different types of oil in the reservoir could be handled with the aid of PVT region numbers. Oil in PVT region 1 would have its properties determined from PVT table number 1, and so on. However, this method cannot model the mixing of oil types. Oil flowing from region 1 into region 2 would appear to take on the properties associated with region 2. The API Tracking facility essentially replaces the concept of PVT regions for oil. The PVT tables used for determining the oil properties are selected at each time step according to the average API of the oil in each grid block (or to be more precise, its average surface density). For a overview of the workflow involved to export PVT tables suitable for use in ECLIPSE BlackOil with the API Tracking option turned on see "Export for API Tracking option in ECLIPSE BlackOil" on page 134. For a more technical description of the API Tracking model in ECLIPSE as well as an explanation of how PVTi calculates suitable PVT tables see "Model for API Tracking option in ECLIPSE BlackOil" on page 363. Batch Mode For the 2004A version of PVTi the batch mode has undergone a significant revamp. Over the last few years the user interface of PVTi has evolved rapidly and the existing batch mode facility no longer adequately supports more recent functionality. There have been 3 significant modifications to the PVTi batch mode: 1 10 The way a batch mode is executed has changed. The new way to launch a batch mode run on a PC is to use the command $pvti -batch filename where filename is the name of your PVTi project. See "General information" on page 152 for more details on running batch mode with other platforms. New developments Developments for 2004A PVTi Reference Manual 2 The new batch mode now supports the majority of the functionality available in interactive mode - namely splitting, grouping, regression, experiment simulation and export. Export for ECLIPSE Thermal, PNA splitting and material balance checks are not currently supported. For more details on the functionality constraints of the batch mode see "Constraints on the workflow" on page 154. 3 It was felt that a more user friendly way of constructing the .PVI files suitable for batch mode was needed since a batch mode file requires some extra sections than a standard interactive mode PVI file does. A new option called Write Keywords for Batch Mode is available on the Options panel. If this is turned on and a workflow is performed in interactive mode and then the file saved, PVTi ensures that this file is then suitable for use in a batch mode run. The batch mode run then reproduces the workflow and results that were obtained in interactive mode. See"Preparing Batch Mode Files in Interactive Mode" on page 153 for a detailed explanation of this facility. For an overview of all aspects of the new batch mode facility see "Batch system and keywords" on page 152. Panel Addition/Modification 1 There is a new LBC Viscosity Coefficients panel available under the menu option Edit | Fluid Model | LBC Viscosity Coefficients.... This panel shows, if using the LorentzBray-Clark (LBC) viscosity model, the current values of the five coefficients. 2 The Thermal Properties panel has been modified to include the new properties introduced as a result of the new ECLIPSE Thermal export functionality. Specifically, the properties Heat Cap. A and Heat Cap. B have been changed to Heat Cap. A/G and Heat Cap. B/H. There is also a new property called Heat of Vaporization which corresponds to the HEATVAPS keyword exported for ECLIPSE Thermal. Component Constraints 1 It is now possible to read in projects where fluid samples can have up to 100 components. However, no functionality involving the EoS flash can be used until a group operation has been performed in order to reduce the number of components in all samples to <=50. 2 Two new components are available in the PVTi library - Benzene (C6H6) and Toluene (C7H8). The short names for use in the fundamentals or components panel are BEN for Benzene and TOL for Toluene. See "Library" on page 95 to view the components in the PVTi library. To view the library within PVTi itself use the View | Library option. New Keywords and sections Keywords There are two new keywords in PVTi 2004A. 1 EXPIND. This is a list of integers - one for each experiment defined in the project - which specify whether an experiment should be used (‘turned on’) or not used (‘turned off’) when performing a regression. PVTi Reference Manual New developments Developments for 2004A 11 2 HEATVAPS. This keyword is used to store the Heat of Vaporization at the standard temperature for each component. Sections There is a new section called APITRACK. This is used when preparing batch files if the API Tracking export facility is to be made use of in batch mode. It is essentially the same as the BLACKOIL section but has an extra keyword called SAMPLES, which records the samples for which PVT tables will be exported. Manual 12 1 The section "The Most Asked Questions About PVTi" on page 13 has been updated with questions regarding the Batch Mode, ECLIPSE Thermal Export and API Tracking functionality. 2 A number of the tutorials have been amended - in particular the tutorial entitled “Using the ECLIPSE Thermal Support Module” has been replaced by a tutorial called "Exporting an ECLIPSE Thermal model" on page 73. New developments Developments for 2004A PVTi Reference Manual The Most Asked Questions About PVTi Chapter 2 Introduction This section has been designed as a reference section so that you can quickly access information about common problems encountered with PVTi without having to spend time looking through the manual for the relevant section. The questions in this section have been constructed using the most common support issues and also the InTouch database. Cross-references are provided where necessary so that readers can access the appropriate parts of the manual for more detailed information on a particular topic if required. The questions are: • "What is PVTi used for? Why do we need it?" on page 14 • "Where do I start? How do I set up a project within PVTi?" on page 14 • "How do I create an experiment along with a series of observations?" on page 15 • "What are the data limitations in PVTi?" on page 16 • "What is the Fluid Properties Estimation facility in PVTi?" on page 17 • "How do I perform regression on multiple fluid samples?" on page 17 • "What regression parameters should I choose?" on page 19 • "What is the difference between normal regression, special regression and automatic (PVTi selects) regression?" on page 18 • "How does PVTi support gas condensate simulation?" on page 20 • "Can Black Oil tables be extended above the liquid bubble point in PVTi?" on page 20 • "Can PVTi be used if you know the composition of a fluid but do not have any observations? And vice-versa?" on page 20 • "What black oil correlations are available in PVTi?" on page 21 • "How do I generate the asphaltene phase envelope using PVTi?" on page 21 • "How does PVTi support ECLIPSE Thermal?" on page 22 • "How do I Use PVTi’s Batch Mode?" on page 23 PVTi Reference Manual The Most Asked Questions About PVTi Introduction 13 • "How Can I Export PVT Tables to use the API Tracking Functionality in ECLIPSE BlackOil?" on page 23 What is PVTi used for? Why do we need it? PVTi is a compositional PVT equation-of-state based program used for characterizing a set of fluid samples for use in our ECLIPSE simulators. We need PVTi because it is vital that we have a realistic physical model of our reservoir fluid sample(s) before we try to use them in a reservoir simulation. PVTi can be used to simulate experiments that have been performed in the lab on a set of fluid samples and then theoretical predictions can be made of any observations that were performed during a lab experiment, in order that we can test the accuracy of our fluid model. Any differences between the measured and calculated data are minimized using a regression facility which adjusts various Equation of State parameters. This ‘tuned’ model is then exported in a form suitable for one of our ECLIPSE simulators. What is especially important to note when using the ECLIPSE Compositional simulator is that PVTi and ECLIPSE Compositional use the same flash algorithm. This is vital as the flash has been used to simulate the experiments and predict values for experimental observations and is therefore inherent within the fluid model itself which has been exported by PVTi. If ECLIPSE Compositional used a different flash then the fluid model exported by PVTi would no longer be valid. Where do I start? How do I set up a project within PVTi? Defining a Fluid Sample If you want to open a new project then start PVTi as instructed in "Getting started" on page 29 for your machine-type and choose a filename. PVTi starts; recognizes that it has a new project and immediately opens the Fundamentals panel. This panel has been specifically designed to make setting up a new project as easy as possible. Simply fill in the Components and ZI columns with the component names and mole fractions respectively, which is the minimum required to have a project within PVTi. To fill in the component names simply type the standard shorthand names for the components in your fluid, for example, C1, N2, CO2, H2S, IC5, etc. For more information on shorthand names and component types see "Component types" on page 102. The mole fractions can be entered as fractions or percentages by selecting the appropriate option on the panel. Also, weight fractions/percentages can be entered for the components instead of mole fractions/ percentages. Your Mole/Weight data must add up to 1 if entering as fractions and up to 100 if entering as percentages. If they do not then PVTi asks you if you want it to renormalize your data when you close the Fundamentals panel. If you want to add some components then select No,- otherwise select Yes. Warning 14 If you try to perform operations on a fluid with incorrectly normalized mole/ weight fractions then the operation may fail. The Most Asked Questions About PVTi Introduction PVTi Reference Manual Once the Fundamentals panel has been completed you will see have a sample called ZI on the tree view on the left-hand side of the main window.This is the fundamental sample for the project and the name ZI cannot be changed. Creating Other Fluid Samples Other fluid samples can be created in a project by selecting Edit | Samples | Name... . Simply type in the name of the new fluid sample you want to create. The composition information can then be entered for this fluid by selecting the Edit | Samples | Compositions... option. Additional fluid samples to the project must always be subsets of the ZI sample in terms of the component names, for example you cannot have a C8 component in an additional fluid sample called OIL if C8 was not defined in the ZI sample. If you open the Edit | Samples | Compositions... panel you can see why this has to be the case in PVTi. Note Just because a component is defined in the ZI sample it does not mean there has to be any of it there. It only has to be defined in the ZI sample to be used in other fluid samples. If the mole fraction of a C8 component in the ZI sample is set to be 0.0 then the C8 component can then be use in the OIL sample and the mole fractions set as required. Once at least one fluid sample (the ZI sample) has been defined then any experiment supported within PVTi can be simulated as well as operations such as phase plots, fingerprint plots and splitting. For more information on creating fluid samples see "Defining Samples" on page 107. How do I create an experiment along with a series of observations? Creating Experiments To create an experiment select the Edit | Experiments... option and the experiment Entry panel opens. The existing experiments are listed and you can edit them by selecting one of them and clicking the next button. To create a new experiment click add in the top left of the panel and select the experiment you wish to create. Choose the fluid sample you want to perform the experiment on and then navigate through the panels by filling in the required information and then clicking next, which takes you to the next panel. The information generally consists of temperature and/or pressure information but not always, it depends on the experiment. Once an experiment has been created an experiment button, along with an experiment name, appears below the fluid sample which the experiment was performed on. Creating Observations If there are no observations at all for a particular experiment then to create one you need to select the Edit | Observations... option and the Observations panel appears. On the Experiments column on the left-hand side there is a list of all the experiments that are available within PVTi and * symbols are next to the ones that you currently have defined within your project. PVTi Reference Manual The Most Asked Questions About PVTi Introduction 15 If one of these experiments is selected then in the Experiment List column a list of all the names of the experiments of that type in your project appears for example, BUBBLE5, DEW3, DL1. If one of these is selected then all the possible observations available within PVTi for that type of experiment are displayed in the Observation Type column. Again observation types with a * next to them means that there are values already defined for this particular experiment in your project. Simply click on one to see and edit the values. To create a new observation select the one you want and then click on the + button on the top left of the panel. Values and weights can then be entered for the observation. Note Currently defined observations for an experiment can be edited in the Observations folder on the experiment Entry panel. For more information on creating and editing experiments/observations see "Simulation using PVTi" on page 117 and/or the tutorial "Simulating experiments" on page 42. What are the data limitations in PVTi? Pre-2003A Up to and including the 2002A_1 release (pre-2003A) the following data constraints were present in PVTi: • 50 fluid samples • 50 components per fluid sample* (see below) • 50 experiments per fluid sample • 300 observations per experiment Note *When a splitting operation was performed it was possible to have more than 50 components (up to 100 in fact) but the components had to be grouped back so that there were less than 50 before any experiment simulation could take place. 2003A These pre-2003A data constraints have been present in PVTi for 4 to 5 years and, in-line with the huge increase in computing power in the last few years, we have decided to enhance the data constraint capability of PVTi so that the following is now available: • 100 fluid samples • 100 components per fluid sample* (see below) • 100 experiments per fluid sample • 300 observations per experiment Note 16 It is now possible to read in, save, split and group with fluids containing up to 100 components. However, the limit is still 50 components for any functionality involving the EoS flash. The Most Asked Questions About PVTi Introduction PVTi Reference Manual What is the Fluid Properties Estimation facility in PVTi? The Fluid Properties Estimation (FPE) facility in PVTi is designed so that it can be used when you have minimal data at your disposal, at the well-site for example. In this scenario, a full lab analysis of multiple fluid samples from the reservoir has not yet been performed. Typically, just a single sample would be available and minimal fluid behavior known for example, saturation pressure at a particular temperature. Specifically, the FPE facility assumes that a single fluid sample with compositional information is available which includes a single plus fraction (for example C7+) component of which the weight fraction is known. Typically, this weight fraction data is fairly accurate but the mole weight, which is used to characterize the critical properties of the plus fraction, is not. The FPE functionality allows you to perform a quick look simulation that regresses on the mole weight of the plus fraction, and keep the weight fraction constant, in order to fit to a saturation pressure observation at a particular temperature. The FPE facility is available in the top right-hand corner of the fundamentals panel whenever a new project is created. Alternatively it can be accessed using the Edit | Properties Estimation (FPE)... option. For more information on this facility see "Fluid Properties Estimation" on page 384. For an example of how it works see the tutorial "Fluid Properties Estimation" on page 33. How do I perform regression on multiple fluid samples? General The fluid samples that PVTi performs regression on is determined by the structure of the tree view on the left-hand side. By default, PVTi performs a regression on every experiment which has observations defined, even if there are multiple fluid samples, each with their own experiments. The reason for this is that, within a project, all fluid samples are considered to be relevant to each other and so the same fluid model should be applied to all samples, even if the compositional make-up of each sample is different Note If two of your fluid samples are not relevant to each other for example they come from different wells/reservoirs then a separate project should be created for each one. Disabling Experiments/Observations You can prevent PVTi from including an experiment in the regression by right-clicking on the experiment and selecting Don’t use in Regression. A cross appears on the experiment indicating it is not currently available within the regression facility. You can disable an observation so that it is not used within the regression by again right-clicking and selecting Don’t use in Regression. Alternatively, by right-clicking and selecting Set Weight and then entering zero the observation is also not included in the regression. PVTi Reference Manual The Most Asked Questions About PVTi Introduction 17 Note If an experiment is disabled then, as you would expect, all the observations are automatically disabled. Regression Weights In general there will be a set of values in an observation. For example, if we have a differential liberation (DL) experiment defined then a viscosity observation would have a value for each pressure. We have two types of weight: there are single weights for each value of an observation and global weights that apply to every value in an observation. By right clicking on an experiment observation the global weight can be set. As mentioned above, by setting this to zero none of the values in the observation would be used. Alternatively, you may want to set a global weight for an experimental observation particularly high, for example, matching the bubble point of a fluid is normally very important if one wants to ensure that it is a single-phase liquid at the temperature and pressure of the reservoir. Or maybe you do not trust the accuracy of a particular observation value, for example an oil formation volume factor (FVF) value in a DL experiment.You may then not want to use a global weight as all the other observation values look ok. In this case setting a single-value weight to a very low value helps you match all the other values in the observation during regression as the rogue, inaccurate value no longer inhibits convergence. Both the single-value and global weights for an experimental observation can be set in the Observations panel by selecting the Edit | Observations... option, highlighting the appropriate observation and then simply typing in your chosen weights. For a good example of how to use the regression facility, see the tutorial "Fitting an equation of state to experimental results" on page 49. What is the difference between normal regression, special regression and automatic (PVTi selects) regression? There are 3 types of regression: normal, special and automatic. The difference between them depends entirely on what kind of variables are being regressed on. Normal regression parameters are equation of state variables relating to a particular component, for example, critical pressure, P c , critical temperature, T c , acentric factor, ω . and the binary coefficients. The full set of normal regression variables can be viewed using the regression panel using the Run | Regression... panel. Select normal as the regression type and then click variables - the upper table shows the single-valued normal regression parameters for each component and the lower panel shows the binary coefficients table. For more information on setting normal regression see "Setting normal variables" on page 127. Special regression parameters are global Equation of State variables, for example, the thermal expansion coefficient or the Cheuh-Prausnitz A factor for binary coefficients. There may also be some splitting parameters available as special regression variables depending on whether a multi-feed split has been performed on the plus fraction. See "Multi-feed Split (also called semicontinuous thermodynamic (SCT) split)" on page 106 for more details on this facility. For more information on setting special regression variables see "Setting special variables" on page 128. 18 The Most Asked Questions About PVTi Introduction PVTi Reference Manual The automatic regression facility or PVTi Selects as it is called on the Regression panel attempts to choose the best normal variables to regress on for you before actually doing the regression and reporting the answer. It should be noted that there is no substitute for a good engineer in the sense that one should not just use this automatic facility all the time in the belief that PVTi will do all the work. For example, the automatic facility will not use special variables to regress on and so it is up to you to decide whether this would be necessary or not. However the automatic facility can still be a useful tool in obtaining a good match to PVT data. The way the algorithm chooses the regression parameters is essentially based on 2 criterion. No parameters are allowed to have more than a 90% correlation on any other parameter. Secondly, no parameter is allowed to have less than 1% of the sensitivity of the most sensitive parameter For a detailed discussion of the automatic regression algorithm see "A consistent methodology that can be applied automatically" on page 389. For more general information on the regression facility see "Regression in PVTi" on page 126. What regression parameters should I choose? It should be noted that there are no concrete rules for getting a good match to observations relating to multiple fluid samples, but there are some general guidelines of what is often a good idea, and what you should definitely not do. Library components tend to have properties that are very well known and any of these will not normally be good choices of regression variables. Properties of non-library components and characterized components are much less well known and these are often good choices. In general, the following set of variables are normally good things to initially regress on: • P c, T c and ω of any non-library component. • P c, T c and ω of any component with mole weight of C7 or heavier (as these are effectively mixtures of different molecule types and so may differ from library values). • Ω A and Ω B of any component with mole weight C7 or heavier. Again because these are mixtures. • No binary inter-active coefficients because of the risk of over-fitting. • No viscosity-specific parameters, again because of the risk of over-fitting. The variables mentioned above are all normal regression variables. The following set of special regression variables can also often prove useful to get a match between samples: • Do a multi-feed split to split the plus fraction into 2 or 3 pseudo-components. The α , SCTMW and Kw parameters, which control the splitting are then very good choices. • The Cheuh-Prausnitz A binary parameter if using Cheuch-Prausnitz binaries. • The mole weight of a plus fraction (if no split on the plus fraction has been performed). For a detailed explanation of why some of the above are good and bad choices for regression parameters, see "Regression in PVT analysis" on page 386. There are also more specific guidelines for choosing regression parameters depending on whether one is dealing with an oil reservoir, see "Recommended PVT analysis for oil reservoirs" on page 372 - or a gascondensate reservoir, see "Recommended PVT analysis for gas condensate reservoirs" on page 377. Finally, for a tutorial illustrating the use of the normal and special regression facilities in a typical workflow see the new "Workflow Tutorial" on page 61. PVTi Reference Manual The Most Asked Questions About PVTi Introduction 19 How does PVTi support gas condensate simulation? Gas condensate simulation is modeled in PVTi using the Constant Volume Depletion (CVD) experiment. In most gas condensate reservoirs liquid does reach a high enough saturation to become mobile as the pressure drops. Thus, gas and oil, to a good approximation, do not move with respect to each other and so the CVD experiment models this behavior very well. Other experiments that tend to be used for gas condensates are the dew point and constant composition expansion experiments. For more information see "Gas condensate systems" on page 341. A common failing when analyzing gas condensate reservoirs is to attempt to establish an equation of state representation without a through examination of the data on which it is to based. Things to check in the data are the characteristics of the heavy components (use a fingerprint plot), material balance information and other information such as K-values and Zfactors. Once you are happy with the data that you will try to match there is a recommended procedure, in terms of regression, which will work for most gas condensates. For a detailed description on how to model gas condensates see the section entitled "Recommended PVT analysis for gas condensate reservoirs" on page 377. Can Black Oil tables be extended above the liquid bubble point in PVTi? Yes. You should make sure that the DL/CVD experiment you simulate in PVTi covers the full range of pressure values you are likely to encounter within your reservoir. If ECLIPSE BlackOil encounters a pressure outside the range in the black oil table you exported from PVTi then it will have no choice but to try to extrapolate to estimate properties such as gas-oil ratio (GOR) and formation volume factor (FVF). The extrapolation used is linear and uses the appropriate quantities at the two highest pressures in the exported black oil table. However, this extrapolation can sometimes run into difficulties as is common in any problem when you are trying to gain information about unexplored parameter space. The normal error is that ECLIPSE throws up negative compressibilities for your fluid. If this happens then be sure to check your black oil tables covered the appropriate range of pressures. For a thorough description of the black oil model used by PVTi and how the tables are extended above the bubble point see "Blackoil model" on page 354. Can PVTi be used if you know the composition of a fluid but do not have any observations? And vice-versa? You know the fluid composition If you have compositional information about the fluid, but no observations, then you can do anything you want within PVTi except use the Regression facility. This is because the Regression facility tries to minimize the differences between lab observations and PVTi’s theoretical predictions and this is not a sensible operation if no observations are defined. 20 The Most Asked Questions About PVTi Introduction PVTi Reference Manual In fact, in PVT laboratories engineers tend to use the default fluid model (one that has not been regressed on) for a given equation of state in PVTi to give them a ‘ball-park’ answer for their particular experimental observation. This can give them some idea as to how to set their experiment up as they now have information on the kind of answers they might expect to measure. You have observations If you have observations but no compositional information at all then PVTi does have the facility to convert black oil tables into a fully compositional model. To do this you must have black oil tables that were exported by PVTi using the 2002A release or later. The tutorial entitled "Converting a black oil run to compositional" on page 58 will explain this workflow in more detail. Note If you have black oil tables exported from before and including 2001A_2 PVTi, or you have no black oil tables at all then, unfortunately, PVTi will not be able to construct the compositional model for you. ! What black oil correlations are available in PVTi? PVTi is a compositional PVT program and at the moment does not support black oil correlations within its functionality. It can however export a black oil model, using the compositional model tuned by the user within PVTi to a DL or CVD experiment, for the ECLIPSE BlackOil simulator by generating tables of Rs, FVF, etc. as a function of pressure for a given reservoir temperature. To export a black-oil model select File | Export Keywords... . If you want to export a black oil table from a DL experiment then you generally use the Oil Reservoir... menu option and if you have a CVD experiment then the Gas Reservoir...option is appropriate. For more information on exporting keywords see the section entitled "Exporting keywords" on page 133. How do I generate the asphaltene phase envelope using PVTi? Just like a phase curve has single phase regions for the vapor and liquid and a 2-phase region an asphaltene phase envelope may exist for your fluid. The asphaltene phase envelope partitions off a region in pressure-temperature space where an asphaltene phase exists, analogous to the two-phase region in a standard phase curve. The upper line partitioning a region in pressure-temperature space where an asphaltene phase does and does not exist is called the Asphaltene Disappearance Pressure (WDP) line. The lower line is called the Asphaltene Appearance Pressure (WAP) line. In PVTi 2003A both curves are supported, whereas in PVTi 2002A/2002A_1 just the functionality for the appearance line is available. Unlike a standard phase curve though where, as long as you do not have a fluid consisting of a single pure component, there will always be a two-phase region, this is not the case in terms of an asphaltene phase envelope. Asphaltene may never be present no matter what temperature and pressure your fluid is at. PVTi Reference Manual The Most Asked Questions About PVTi Introduction 21 In order to try to generate one of the asphaltene curves a PNA split must first be performed on the heaviest component/pseudo component. To do this select Edit | Fluid Model | Split | PNA Distribution..., which does this split for you using correlations from within PVTi. Now, to create the curve an asphaltene appearance/disappearance experiment must be performed. This can be done using the instructions in this section on "How do I create an experiment along with a series of observations?" on page 15. In the experiment entry panel tick the appropriate box depending on whether you want the asphaltene disappearance/appearance curve and enter the temperature values where you want the curve generated. Caution You cannot plot theoretical predictions from PVTi of an experimental unless at least one observation has been defined. Make sure there is at least one observation defined for this experiment and then right click on the experiment and select plot. You can super-impose your curve onto a standard phase plot by using the super-impose button on the toolbar. Hint There is a shortcut for doing standard phase plots. This is accessed by clicking and holding the left mouse button down on the appropriate fluid sample icon and then dragging the cursor into the plot viewer. There is a more detailed section on the theory behind how PVTi models the presence of wax and asphaltene phases in "Wax and asphaltene precipitation in PVTi" on page 394. How does PVTi support ECLIPSE Thermal? The 2004A release of PVTi contains a new module that is capable of exporting a series of keywords in a file suitable for use in an ECLIPSE thermal simulation. Therefore, just as you were previously able to export PVT files suitable for use in ECLIPSE BlackOil and ECLIPSE Compositional they can now do the same for ECLIPSE Thermal. In PVTi and ECLIPSE Compositional we deal with an isothermal flash. This means that, for a particular cell in a simulation, we know the composition of the fluid and the pressure and temperature. We try to minimize the Gibbs Free Energy in order to determine how each component splits across the different phases present. In other words we try to find the K-values, which are the unknown variables. In fact, in ECLIPSE Compositional, the temperature of each cell in a particular PVT region is assumed not to change over time. In ECLIPSE Thermal this is not the case. The temperature is a free parameter, which needs to be determined by way of a different type of flash - one at constant energy. What we are saying here is that we know the pressure, functional form of the K-values (K=K(P,T)), and the total energy of the system and the temperature is unknown. The new ECLIPSE Thermal Export facility allows you to export one of two keywords (KVCR or KVWI) to model the functional form of the K-values for each component. Since, as just explained, isothermal flashes are not performed in ECLIPSE Thermal, PVTi also provides support in this export facility in terms of calculating density and enthalpies in the oil and gas phases. In ECLIPSE Thermal the keywords PREFT, TREFT, DREFT and ZFACTOR are used to calculate oil/gas densities and the keywords STCOND, SPECHA, SPECHB, SPECHG, SPECHH and HEATVAPS are used to calculate oil and gas phase enthalpies. For a brief summary of all the keywords exported for use in ECLIPSE Thermal see "Outline of keywords for ECLIPSE Thermal" on page 367. 22 The Most Asked Questions About PVTi Introduction PVTi Reference Manual For more detailed information on the new thermal module see "ECLIPSE Thermal Export Module" on page 401. For workflow information and a summary of the exported keywords see "Compositional Data for ECLIPSE Thermal" on page 366. How do I Use PVTi’s Batch Mode? The batch mode facility is accessed from the command line (if using a PC) using the command ‘$pvti -batch filename.pvi’ where filename is the rootname of your project. If using a UNIX machine then use the command ‘@pvti -batch filename.pvi’. The recommended way to prepare a file for use in the batch mode is as follows: 1 Open the project file in interactive mode which you wish to use. 2 Save the file using the File | Save (concise)... menu option. 3 Load this new ‘concise’ file back into PVTi and open the Set PVTi Program Options panel by doing Utilities | Program | Options.... Set the last option Write Keywords for Batch Mode to Yes. 4 Now perform the required workflow in interactive mode that you wish the batch mode to reproduce e.g. simulation of experiment, splitting, grouping, export, etc. 5 When you have performed the workflow save the file using File | Save... 6 The saved file is now suitable for running in batch mode. For a comprehensive review of the new batch mode functionality see "Batch system and keywords" on page 152. How Can I Export PVT Tables to use the API Tracking Functionality in ECLIPSE BlackOil? PVTi now has the capability to export multiple PVT Tables for use in ECLIPSE BlackOil’s API Tracking. Without the API Tracking facility, the presence of different types of oil in the reservoir could be handled with the aid of PVT region numbers. Oil in PVT region 1 would have its properties determined from PVT table number 1, and so on. However, this method cannot model the mixing of oil types. Oil flowing from region 1 into region 2 would appear to take on the properties associated with region 2 Just like exporting a standard black oil table a depletion experiment must be defined in order to do API Tracking export. The workflow is as follows: 1 Use the File | Export Keywords | API Tracking option in ECLIPSE BlackOil... menu option to open the Export Panel for API Tracking. 2 Select the samples you wish to use in the export and move them to the Use box. 3 Choose the keywords you wish to export. Normally the Live Oil (PVTO) and Dead Gas (PVDG) keywords are used with the API Tracking option. 4 Select whether you wish to export a gas table for each sample or just a single gas table. 5 Select whether you wish to plot the tables in PVTi. 6 Select whether you wish to write to tables using full double precision numbers. 7 Select the separator you wish to use for the export. 8 Select the units you wish to export the table in. PVTi Reference Manual The Most Asked Questions About PVTi Introduction 23 PVTi should then write the tables to a file and show them in the output display. This file is then suitable to use as the PVT input for an API Tracking run in ECLIPSE BlackOil. For a similar description of the API Tracking workflow see "Export for API Tracking option in ECLIPSE BlackOil" on page 134. For a technical description of the API Tracking model in ECLIPSE as well as an explanation of how PVTi calculates suitable PVT tables see "Model for API Tracking option in ECLIPSE BlackOil" on page 363. 24 The Most Asked Questions About PVTi Introduction PVTi Reference Manual Introduction Chapter 3 General information The PVTi program is an Equation of State based package for generating PVT data from the laboratory analysis of oil and gas samples. The program may be used through an interactive menu system or run in a batch mode. An interactive session can be saved as a batch input file, which contains commands to reproduce the interactive operations. Alternatively, a batch input file can be run from an interactive session. Equations of state and viscosity correlation Four equations of state are available, implemented through Martin’s generalized equation. This enables the Redlich-Kwong, Soave-Redlich-Kwong, Peng-Robinson and Zudkevitch-Joffe equations to be used. Two 3-parameter extensions of the Peng-Robinson Equation of State are also available, one based on a Peneloux et al. volume shift, the other being an implementation of the Schmidt-Wenzel Equation of State 2-parameter Peng-Robinson. The Soave-RedlichKwong Equation of State similarly has a three-parameter extension. Viscosities may be calculated using a method by Pedersen et al. based upon a corresponding states comparison with methane, or by the Aasberg-Petersen model based upon a corresponding states comparison with methane and decane, or by the Lohrenz-Bray-Clark method. Fluid definition Multiple fluid samples can be defined by specifying components as one of three types. Library components require only that the appropriate component mnemonic be entered. Characterized components define properties of plus fractions from a limited set of information. Finally all the properties of a component can be defined, a facility which can be used selectively to edit the properties of existing components. PVTi Reference Manual Introduction General information 25 It is possible to group the components to reduce or pseudoise the fluid system (make a fluid definition of the system using pseudo components), or to split the plus fraction into more components, preserving molecular weight and mole fraction. Multiple samples having different plus fraction properties, say mole weight and specific gravity, can be characterized by splitting the plus fraction into two or more pseudo-components of fixed properties but variable composition. Fingerprint plots of mole fraction against molecular weight, or phase diagrams, are available. Material balance checks A compositional material balance can be performed on any gas condensate or volatile oil for which a laboratory constant volume depletion or differential liberation experiment has been performed. This can be used to estimate liquid compositions and hence K-values. The calculated quantities can then be used to estimate the quality and consistency of the laboratory data. Additionally, tests on recombination of separator data can be performed and estimates of reservoir recovery can be made. Simulation of experiments Experiments may be performed on the fluid systems defined using the equation of state model. Possibilities are: • saturation pressures • flash calculations • constant composition expansions • constant volume depletions • differential liberations • swelling tests • multi-stage separator simulations. Other experiments available are: 26 • composition versus depth • vaporization test • multiphase flash • critical point • saturation temperature • first contact miscibility • multiple contact miscibility (condensing and vaporizing). • wax appearance temperature • asphaltene appearance pressure Introduction General information PVTi Reference Manual Regression of equation-of-state to measured data The equation of state model may be tuned by regression. The critical state data, Ω a and Ω b values, interaction coefficients, δ ij , and volume shift parameters, s i (for the three-parameter volume shift equations of state), may be matched to experimental data from the first eight of the experiments mentioned in the previous paragraph. Additionally, depending on the use of certain facilities and options, five special regression parameters are also available. These are the A coefficient in the Cheuh-Prausnitz Bids, the thermal expansion coefficient in the modified Peneloux et al. volume shift method, and three variables associated with the Modified Whitson splitting technique (denoted Semi-Continuous-Thermodynamics), being the mole weight and distribution skewness parameter (on a sample-by-sample basis) and the characterization factor of the plus fraction. Hint Almost any result from the experiments mentioned can be used as an observation against which to regress. PVT data for ECLIPSE simulators Black oil and equilibration tables for ECLIPSE can be prepared, using the liquid and gas compositions obtained from constant volume depletion or differential liberation experiments passed through a separator system using the Coats or Whitson and Torp methods. Gas injection schemes can be modeled using the ECLIPSE pseudo-compositional model which modifies the ECLIPSE black oil tables as a function of the volume of injected gas. For use in ECLIPSE Compositional, either pseudoised/regressed equation of state data or tabular data (either K-values or liquid and vapor mole fractions as a function of pressure) can be output. Black oil tables can also be generated for the Vertical Flow Performance (VFPi) program, simulating the phase and volumetric change in the wellstream fluid by a constant composition expansion experiment at two temperatures, the highest (reservoir) and lowest in the production string. Water properties may also be output for use in any of the above programs. Default values for formation volume factor, compressibility, etc., are constructed using well-known correlations from specification of the pressure, temperature, salt and gas content of the water, though these may be changed. PVTi Reference Manual Introduction General information 27 28 Introduction General information PVTi Reference Manual Getting started Chapter 4 Starting PVTi Windows platforms ECLIPSE Program Launcher 1 Start the ECLIPSE Program Launcher. 2 Click on the PVTi button. 3 Select the version and working directories as required. Command line 1 Type the command $PVTI in a command prompt window. UNIX platforms 1 PVTi Reference Manual Type the command @pvti at the command prompt. Getting started Starting PVTi 29 30 Getting started Starting PVTi PVTi Reference Manual Tutorials Chapter 5 Overview The tutorials provide a step-by-step introduction to the functionality of PVTi. Note These tutorials are not intended to teach PVT analysis, but instead concentrate on illustrating typical work-flows for PVTi. Each tutorial is divided into a number of distinct sections intended to highlight a specific aspect of the analysis process. To avoid repetition, later tutorials assume familiarity with some used in the first tutorials, so it is strongly recommended that you work through them in the order they are presented. Available tutorials The following tutorials are available: • "Fluid Properties Estimation" on page 33 • "Creating a fluid system" on page 36. • "Simulating experiments" on page 42. • "Fitting an equation of state to experimental results" on page 49. • "Exporting ECLIPSE Black Oil PVT tables" on page 53. • "Converting a black oil run to compositional" on page 58. • "Workflow Tutorial" on page 61. • "Multiphase Flash" on page 69. • "Exporting an ECLIPSE Thermal model" on page 73. • "Data analysis and quality control" on page 77. • "Removing contamination from samples" on page 84. PVTi Reference Manual Tutorials Overview 31 • 32 Tutorials Overview "Converting old projects to the current version" on page 87. PVTi Reference Manual Fluid Properties Estimation This tutorial describes how to use PVTi for Fluid Properties Estimation. The data for this tutorial is provided with the standard installation of PVTi in the directory: $ECL/2014.1/pvti/tutorials and you should copy the files from this directory to your local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 33 • "Basic Information - Fundamentals" on page 33 • "Flash calculations" on page 35 • "Discussion" on page 35 Introduction Fluid properties estimation can provide quick-look PVT tables at the well site. A saturation pressure (bubble or dew-point) together with a reservoir composition are sufficient inputs to provide a quick-look simulation, giving an initial estimation of fluid properties in advance of a full fluid analysis in the lab. After completing this tutorial you should be able to use PVTi as a simulation tool for fluid properties estimation. Basic Information - Fundamentals 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 Enter FPE.PVI as the file name for the new project. Hint When a new, empty project is created in PVTi, the Fundamentals panel opens automatically. To re-enter this panel at any later time, select PVTi: Edit | Fundamentals... The Fundamentals panel allows you to enter the minimum information required to create a complete equation of state model. 3 Click on the Enter Weight Fractions check box. Hint PVTi Reference Manual The mole fractions that you see in lab reports are derived from weight fractions and the mole weights of the components. It is weight fractions that are actually measured. PVTi allows a choice of either form in the Fundamentals panel. Tutorials Fluid Properties Estimation 33 4 Right-click in the table and select Table Import | From File. a Import the file FUNDAMENTALS.TXT . b In the Text Import Wizard switch on Ignore Records and set the number of records to ignore to 2 (since we want to ignore the column headings). The Fundamentals panel should now look like Table 5.1. Table 5.1 Components CO2 The Fundamentals panel ZI Weight Frac. (percent) (percent) 0.05 C1 6.25 C2 3.10 C3 3.27 IC4 0.89 NC4 2.44 IC5 1.11 NC5 1.09 C6 3.88 C7+ 77.49 5 Spec Gravity 0.43 N2 Hint Mol Weight 218 Only enter mole weights for components whose properties will be characterized, the other components come from the library. Also, specific gravity is an optional additional parameter that can be used in the characterization, if it is not specified it is calculated using a correlation. Click Apply PVTi adds the mole fractions and the specific gravity of the plus fraction. 6 Click on the Fluid Properties Estimation (FPE) check box The temperature and pressure fields are now active. a Enter a Temperature of 220 F. This is the temperature of the saturation pressure (dew or bubble point) and the temperature that is used in the generated depletion experiments. b Hint c 34 Enter a Saturation Pressure of 2800 psia. PVTi uses this saturation pressure to fit the fluid model. The weight of the plus-fraction is varied, the weight fraction being constant, until the saturation pressure predicted by the equation of state matches the entered pressure. Enter a Maximum Pressure of 5000 psia. Tutorials Fluid Properties Estimation PVTi Reference Manual Hint This is the maximum pressure in the depletion experiments that are created. 7 Set the Project Units to Field, this sets the units that are used on the plots. 8 Click OK. This is all the information required to fit the equation of state and to generate the Constant Composition Expansion (CCE), depletion experiment (either differential liberation or constant volume depletion) and the optimized separator. After fitting the equation-of-state and creating the experiments, default plots from the depletion experiments are drawn along with the phase curve for the fitted fluid. The methods used in Fluid Properties Estimation are explained in "Fluid Properties Estimation" on page 384. 9 PVTi: Run | Simulate This opens a complete report for the project including the results from all the created experiments. Hint By clicking on one of the experiments in the sample tree with the right mouse button, and selecting Report..., you can view the reports for individual experiments separately. Flash calculations 1 2 Right-click on ZI in the project tree-view and select Properties Estimation (FPE)... a Enter a temperature of 60 F b Enter a pressure of 15 psia c Click OK. Right-click on the newly created Flash simulation (FLASH1) and select Report to see the results of flashing the reservoir fluid to standard conditions. This allows you to attempt any Flash calculation on the reservoir fluid. Hint The Properties Estimation panel can also be used to create additional separators, saturation pressure or depletion experiments, for example at other temperatures. Discussion Fluid Properties Estimation is a useful tool, particularly in situations where full lab analysis of the fluid is not available for a complete equation-of-state matching project. For full details of the operations performed during fluid property estimation see "Fluid Properties Estimation" on page 384. During fluid properties estimation, the project created is a complete PVTi project. This means that a more experienced user has access to the rich range of features within the product. At the same time, the less experienced user can use PVTi for Fluid Properties Estimation without requiring in-depth knowledge of equation-of-state methods or PVT analysis. PVTi Reference Manual Tutorials Fluid Properties Estimation 35 Creating a fluid system This tutorial describes how to specify fluid properties in PVTi. It covers the basic functionality of PVTi; knowledge of this tutorial is assumed in the later tutorials, so you are advised to work through them in order. The data for this tutorial is provided with the standard installation of PVTi in the directory: $ECL/2014.1/pvti/tutorials and you should copy the files from this directory to your local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 36 • "Defining a fluid" on page 36 • "Selecting an equation of state" on page 38 • "Program options" on page 38 • "View fluid attributes" on page 39 • "Saving the SYSTEM section for future use" on page 40 • "Discussion" on page 41 Introduction The PVT report for this fluid contains details of three experiments: a Constant Composition Expansion experiment, a Differential Liberation experiment, and a Bubble Point experiment. The later tutorials describe how the experimental results may be used to fit an equation of state to the experimental behavior, and how this fitted equation of state can be used to generate PVT tables for use in reservoir simulations. This tutorial shows how to set up basic fluid properties in PVTi and how to display the phase envelope for the defined fluid. Defining a fluid PVT analysis involves fitting an Equation of State to experimental data and then using this Equation of State to produce PVT tables for use in reservoir simulations. The first step is to start up PVTi, and import the component and fluid definitions. Table 5.2 shows the component and fluid definitions that are used in this tutorial. Table 5.2 36 Component and fluid definitions Component % Mole Fraction CO2 0.91 N2 0.16 C1 36.47 Tutorials Creating a fluid system Mole Weight Specific Gravity PVTi Reference Manual Table 5.2 Component and fluid definitions Component % Mole Fraction C2 9.67 C3 6.95 IC4 1.44 NC4 3.93 IC5 1.44 NC5 1.41 C6 4.33 C7+ 33.29 Mole Weight Specific Gravity 218.0 0.8515 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 Select PVTi: File | New... 3 Enter BLACK.PVI as the project name in the file selection window. 4 Click on Open on PC or OK on UNIX platforms. Note This has defined BLACK as the prefix for any files that are written by PVTi. The Fundamentals panel opens so that basic project information can be entered. 1 Enter CO2, N2, C1 and C6 into the Components column. 2 Click Apply. 3 Click Yes so that PVTi fills in the library component names. 4 Enter the mole fractions from Table 5.2 and the details for the C7+ component into the Fundamentals panel and click OK. Note The components for which no mole weight or specific gravity has been specified are automatically set to use the PVTi component properties library (see "Component types" on page 102.) Hint The component properties can be examined by selecting PVTi: Edit | Fluid Model | Components.... This panel can also be used to add additional components, the select alternative characterization methods and to manually defined component properties. Hint Only one sample, ZI, is defined in the Fundamentals panel. Additional samples can be created using PVTi: Edit | Samples | Names... and mole fractions can be entered using PVTi: Edit | Samples | Compositions... PVTi Reference Manual Tutorials Creating a fluid system 37 Selecting an equation of state In this tutorial, the three-parameter Soave-Redlich-Kwong equation of state (see "Equation of state formulation" on page 318) is fitted to the results of experiments carried out on the fluid defined in "Defining a fluid" on page 36. The Lohrenz-Bray-Clark correlations (see "Lohrenz, Bray and Clark" on page 330) is used for viscosity. 1 PVTi: Edit | Fluid Model | Equation Of State... This opens the Equation of State and Viscosity Correlation panel. 2 Select the 3-parameter Soave-Redlich-Kwong equation of state (SRK3). 3 Click on OK. 4 Click on OK to change the parameters to SRK3 defaults. Program options 1 PVTi: Utilities | Program | Options... This opens the Program Options panel. 2 Set the Separator GOR calculation to use Liquid at Stock Tank Conditions. 3 Set the Temperature-dependence for volume shifts to be calculated by Polynomial correlations. (See "Shift parameters" on page 322.) 4 Set Treatment of Volume Shifts to Independent Variables and click on OK. The Program Options panel should now contain the following data: Table 5.3 Program Options data Field Data Definition of Liquid Saturation in CCE Sliq=Vliq/Vsat Treatment of volume shifts Independent variables Separator GOR Calculation Liquid at Stock Tank Conditions Temperature-dependence for volume shifts Polynomial correlations Specify/Calculate density & molar volume units user units Binary Interaction Coefficients for EoS Katz-Firoozabadi Specific Heat Capacity Coefficients and Calorific Values 38 Calculated compositions No Save to samples Component Library Katz-Firoozabadi Experimental Compositions Output to Screen/PVP Experimental Results Always Output to PVP Plot Vectors No Output to file Print file output A4 format Definition of GOR in Diff Lib Normal Definition of Oil relative volume in Diff Lib Oil FVF = Voil(p)/Voil(stc) Black Oil Table Output All Data LBC viscosity coefficients Keep Fixed Tutorials Creating a fluid system PVTi Reference Manual Table 5.3 Program Options data (Continued) Field Data Flash Calculations E300 Flash Sample mole fractions when regressing Keep Fixed Phase plot algorithm New Phase Plots Write Keywords for Batch Mode No 5 Click Yes in answer to the question Set volume shifts to the default values for this dependence. View fluid attributes Now that a fluid has been defined, there are two plots available to review the fluid we have entered. First is the fingerprint plot of mole fraction versus molecular weight; the second is a phase plot. 1 Right-click on ZI in the project tree-view and select Fingerprint Plot from the pop-up menu. The plot should look like Figure 5.1. Figure 5.1 Fingerprint Plot 2 PVTi: View | Samples | Phase Plot... 3 Request Sample ZI, 5 quality lines. 4 Click on OK. PVTi Reference Manual Tutorials Creating a fluid system 39 The plot should look like Figure 5.2. Figure 5.2 Phase Plot Note A default phase plot with a single quality line can be generated by dragging ZI from the tree-view of the project (in the left pane of the main window), and dropping it on to the main plot workspace. Saving the SYSTEM section for future use The fluid sample definition can output as the RUNSPEC and SYSTEM sections of a PVI file. 1 PVTi: File | Save (Concise)... 2 Call the file FLUID_DEF.PVI. Hint The complete project can be saved using PVTi: File | Save... This, effectively, saves a history of the project. The original fluid description is saved, along with SPLIT or GROUP sections for split and group operations you perform. By choosing to save current modifications, the system is saved in its current state, after all splits, groups, etc., have been performed. For work in progress it is usually better to use Save so that past steps can be recovered. For a final fluid model, the Save (Concise) option allows a complete description of the final model to be saved, without the steps taken to get there. This file can now be read in using the PVTi: File | Import | SYSTEM... option. 40 Tutorials Creating a fluid system PVTi Reference Manual Discussion In this tutorial a fluid was defined from data and an Equation of State was selected to describe that fluid. This fluid definition provides the basic building blocks for further PVT analysis. The fluid definition can be used in simulation studies to compare it with experimental results from the reservoir fluid; see "Simulating experiments" on page 42. This definition can then be adjusted so that it describes the experimental results; see "Fitting an equation of state to experimental results" on page 49. The fitted fluid definition is finally used to generate PVT tables for ECLIPSE ; see "Exporting ECLIPSE Black Oil PVT tables" on page 53, ECLIPSE pseudo-compositional, VFPi and ECLIPSE Compositional. PVTi Reference Manual Tutorials Creating a fluid system 41 Simulating experiments This tutorial illustrates how experiments are simulated in PVTi. It covers the basic functionality of PVTi. Knowledge of this tutorial is assumed in later tutorials, so you are advised to work through them in order. The data for this project are provided in the standard installation of PVTi in the directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 42 • "Defining experiments for simulation" on page 43 • "Plotting simulation results" on page 45 • "Defining further experiments and observations" on page 45 • "Defining further experiments and observations" on page 45 • "Simulating all the experiments" on page 47 • "Discussion" on page 48. Introduction This tutorial describes how experimental observations can be entered into PVTi and how the experiments can then be simulated from an existing fluid definition. 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 File | Open... 3 Open the file FLUID_DEF.PVI that was created in the last tutorial. (Alternatively open the supplied tutorial file FLUID_CORRECT.PVI). Setting units 42 1 Utilities | Units... 2 Set the Unit Type to Field 3 Set the Temperature Unit Type to Fahrenheit 4 Set Mole Fraction or Percentage to Percentage 5 Set Absolute or Gauge Pressure to Gauge. 6 Click on OK. Tutorials Simulating experiments PVTi Reference Manual Defining experiments for simulation In this part of the tutorial, the experimental results from the PVT report are brought into PVTi ready for simulation. In this section data from a constant composition expansion experiment are brought into PVTi. If you do not have access to a spreadsheet, type the numbers from the tables into the data entry forms in PVTi at the appropriate points. Table 5.4 Constant Composition Expansion experiment at 220o F (* indicates bubble point pressure) Pressure Relative Volume (PSIG) (V(p)/V(pb) 5000.0 0.9453 4500.0 0.9541 4000.0 0.9638 3500.0 0.9746 3000.0 0.9867 2900.0 0.9893 2800.0 0.9920 2700.0 0.9948 2620 0.9970 2605 0.9974 2591 0.9978 2516.7* 1.0000 2401 1.0243 2253 1.0599 2090 1.1066 1897 1.1750 1698 1.2655 1477 1.4006 1292 1.5557 1040 1.8696 830 2.2956 640 2.9457 472 3.9877 1 PVTi: Edit | Experiments... 2 Experiment Entry: Add | Pressure Depletion | Constant Composition Expansion... PVTi Reference Manual Tutorials Simulating experiments 43 Hint The constant composition expansion or CCE experiment can sometimes be known as a constant mass study in PVT Reports. The differential liberation or DL experiment is also known as a differential vaporization experiment in PVT Reports. The multi-stage separator or SEPS experiments can also be called a separation test in PVT Reports. The Experiment Entry window now shows three folders: General, Observations and Components. These folders are used to define the experiment entry form. 3 Select the Observations folder. 4 Click in the top left cell of the table and select Pressure from the drop-down list in that cell. 5 In the second column select Relative Vol. from the drop-down list. Hint 6 By making the column headings the same as those in Table 5.4, the task of data entry is simplified. The ability to tailor the table means that data entry can then be further accelerated by importing observations from a text file or the clipboard. Click on Next. The table now shows two folders. The Components folder has disappeared as there were no component observations selected; the General folder now shows an entry field to select fluid type and another to enter the temperature of the experiment. 7 In the General folder, enter the temperature from Table 5.4 (220 F). 8 Select the Observations folder. The Observations folder now shows a two-column table with the columns selected previously. The table resembles Table 5.4. Table 5.4 is provided in the file CCE_TABLE.TXT 9 Right-click in the table and select Table Import | From file... 10 Select CCE_TABLE.TXT and click on Open. 11 In the Text Import Wizard turn on Ignore Records and set the number of records to ignore to 1 (since we want to ignore the column headings). The view of the table should no longer contain the first row. 12 Click on OK. Note The error message “Cannot delete rows from this table” appears This is because the table has a fixed length and the file we are importing from has fewer rows than the table. This message can be safely ignored. 13 Click on OK to remove the message “Cannot delete rows from this table”. The table now contains the same information as Table 5.4. As the experiment information is complete, the experiment can be created. 14 Click on Next to create the experiment. 44 Tutorials Simulating experiments PVTi Reference Manual Hint The data tree now shows the created experiment (CCE1). The asterisk (*) next to the experiment’s name means that it is active. CCE1 has one observation node, for the relative volume measurements. 15 Click Close to shut the panel. Plotting simulation results 1 Click on the Relative Vol. observation in the Data Tree and drop it over the Main Plot Window. The Main Plot Window should now look like Figure 5.3. Figure 5.3 The plotted simulation results Defining further experiments and observations In this section of the tutorial the other experiments are defined, along with their observations. The equation of state is later fitted to these observations, and then the fitted equation is used to generate tables for a fully compositional ECLIPSE simulation. PVTi Reference Manual Tutorials Simulating experiments 45 Differential liberation experiment The first experiment to be added is a differential liberation experiment (Table 5.5), as in "Defining experiments for simulation" on page 43. Table 5.5 Differential Liberation Experiment at 220o F (* indicates bubble point pressure) Gas Gas Volume Relative Factor Density (rb/Mscf) Pressure (PSIG) Oil Volume Factor Gas Solution Deviation GOR Factor (Mscf/stb) Z Reservoir Oil Density (lb/ft3) 2516.7* 1.7493 1.1342 45.110 2350 1.7095 1.0526 0.8686 45.6688 0.7553 1.2574 2100 1.6535 0.9378 0.8692 46.5022 0.7547 1.4070 1850 1.6013 0.8309 0.8719 47.3311 0.7565 1.6006 1600 1.5523 0.7307 0.8767 48.1595 0.7614 1.8586 1350 1.5057 0.6361 0.8836 48.9920 0.7704 2.2164 1100 1.4609 0.5460 0.8926 49.835 0.7859 2.7411 850 1.4171 0.4591 0.9036 50.6992 0.8121 3.5773 600 1.3726 0.3732 0.9167 51.6076 0.8597 5.1050 350 1.3234 0.2824 0.9324 52.6319 0.9618 8.7518 159 1.2720 0.1960 0.9481 53.6731 1.1726 18.6846 0 1.1228 0.0 56.3229 1.8901 1 PVTi: Edit | Experiments... 2 Experiment Entry: Add | Pressure depletion | Differential Liberation... 3 In the Observations folder, set the table headings to match those in Table 5.5: Pressure, Oil Rel. Vol., Gas-Oil ratio, Vapor Z-factor, Liquid Density, Gas Gravity, Gas FVF. 4 Click on Next 5 Enter 220 F as the temperature in the General folder. The file DL_TABLE.TXT provides the table in Table 5.5. 6 Import the file DL_TABLE.TXT into the table in the Observations folder, remembering to ignore the first line, which contains column headings. 7 Click on Next to create the experiment. The Experiment Entry panel now shows that there are 2 experiments defined. Defining the bubble point experiment Finally, there is a bubble point experiment at 220o F to be added. 46 1 Experiment Entry: Add | Single Point | Bubble Point... 2 In the Observations folder set the first column heading to Sat. Pressure and the second to Liquid Density 3 Click on Next Tutorials Simulating experiments PVTi Reference Manual 4 Enter the temperature, 220o F in the General folder. 5 Select the Observations folder. 6 Enter the saturation pressure as 2516.7 psig and the liquid density as 45.11 lb/ft3. 7 Click on Next to create the experiment. 8 Click Close. Simulating all the experiments All the experiments have now been entered. In summary, then, the project should now contain the following: • A fluid description (component properties and a sample defined by mole fractions of components). • A Constant Composition Expansion experiment with observations of relative volume. • A Differential Liberation experiment with observations of: relative oil volume, solution gas-oil ratio, Z-factors, oil density, gas gravity and gas formation volume factor. • A Bubble Point experiment at 220o F with observations of bubble point pressure and liquid density. Hint 1 The information about which experiments have been defined, and for which observations have been entered for those experiments, is contained in the Data Tree. PVTi: Run | Simulate A simulation report, showing information on all the experiments, is displayed in the Output Display panel. 2 Output Display: File | Close Plotting all observations for an experiment 1 PVTi: View | Observations... 2 Select the Differential Liberation (DL1) experiment. 3 Click OK. This plots each observed data set (as points) for the differential liberation experiment and each calculated data set (as lines) generated by simulation. Hint 4 Examine each of the plots and note how well (or badly) the simulation has matched the data. Hint PVTi Reference Manual Double-clicking on one of the small plots swaps it with the large plot. You can right-click on an axis and select Show Edit Box from the drop-down menu. This opens the Axis Property Editing panel. In this panel you can customize the axes, for example by changing the units used in plotting. Tutorials Simulating experiments 47 In the next section, the match between calculated and observed data values are improved by regression. Saving the project for future use The fluid sample definition can be output as the RUNSPEC, SYSTEM and SIMULATE sections of a PVI file. 1 PVTi: File | Save (concise)... 2 Call the file SIMULATE_SECTION.PVI. Discussion In this tutorial an existing project was extended to include experiments. Constant Composition Expansion, Bubble Point and Differential Liberation experiments were imported and simulated for the defined fluid. The match between the experimental observations and the simulated results was examined using the plotting facilities in PVTi. The fluid model can then be adjusted so that it provides the best fit (in a least-squares sense) to the experimental observations (see "Fitting an equation of state to experimental results" on page 49). The fitted fluid definition is finally used to generate PVT tables for ECLIPSE (see "Exporting ECLIPSE Black Oil PVT tables" on page 53). 48 Tutorials Simulating experiments PVTi Reference Manual Fitting an equation of state to experimental results This tutorial shows how a fluid definition can be fitted, by regression, to describe experimental results. This tutorial covers basic functionality of PVTi and knowledge this tutorial is assumed in later tutorials, so you are advised to work through them in order. The data for this project are provided in the standard installation of PVTi under the directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 49 • "Fitting an equation of state by regression" on page 49 • "Discussion" on page 52 Introduction This tutorial illustrates the fitting of the fluid definition to the experimental observations. The fluid definition and experiments are read in from an existing PVI file and the regression facilities in PVTi are used to generate an improved fit between the two. Fitting an equation of state by regression 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 File | Open... 3 Open the file SIMULATE_SECTION.PVI created in the last tutorial. (Alternatively you can use the file SIMULATE_CORRECT.PVI.) Hint The Data Tree shows the contents of the opened project. Fitting an equation of state by regression In this part of the tutorial, the equation of state is fitted to the observation data to produce a better representation of the fluid. A sensitivity analysis is carried out to determine which attributes of the fluid components improve the solution by the smallest change. The most sensitive attributes are then adjusted slightly by regression to improve the equation of state model of the fluid. The first step in designing any regression is to determine the parameter set that will be used. There are certain steps an engineer can take to improve the performance of a regression. The first step is to try to make all regression variables have similar sizes. This is done to prevent a minor constituent of the fluid having its properties varied extensively to achieve a mathematical fit, which is not a reasonable physical solution. 1 PVTi Reference Manual Examine the fluid component data in "Component and fluid definitions" on page 36. Tutorials Fitting an equation of state to experimental results 49 Note The idea here is to look for consecutive components that have small mole fractions. These can be grouped together and treated as a single regression variable, forcing the solution to be physically realistic. Hint The properties of C1 and C2 are well known and generally do not differ significantly from the library properties. Grouping the C3, IC4, NC4, IC5, NC5 and C6 components into a single regression variable preserves monotonicity between the components, in addition to creating a variable that accounts for 19.5% of the total composition. Hint The plus fraction (C7+) contains a mixture of components C7+ and higher, so its properties may not be so well-determined. This makes the plus fraction an ideal candidate for regression to fit the equation of state to the experimental results. C7+ is the second regression variable. Sensitivity analysis Sensitivity analysis is used to establish which fluid properties most affect the difference between the observed and simulated values. The sensitivities are calculated for critical temperature and pressure for each experiment, for both regression variables. Finally the most sensitive properties will be selected for use in the regression. Hint In any regression, having a few very sensitive parameters is preferable to having hundreds of insensitive ones. Always look for parameters that can be discarded (this is called conditioning the problem - an ill-conditioned problem is difficult to solve). 1 PVTi: Run | Regression... opens the Regression panel. 2 Select Normal as the Type of regression variables in the Variables section of the panel. 3 Click Variables. The regression variables are numbered for each property. Entering 1 in the critical pressure (Pcrit) column in the rows corresponding to C3, IC4, NC4, IC5, NC5 and C6 groups those components into the first regression variable. 4 50 Fill in the table in the Select EOS parameters for regression panel with the following data: Mnem Pcrit Tcrit C3 1 1 IC4 1 1 NC4 1 1 IC5 1 1 NC5 1 1 C6 1 1 C7+ 2 2 Tutorials Fitting an equation of state to experimental results PVTi Reference Manual 5 Leave the second part of the Select EOS parameters for regression panel blank. 6 Click on OK. Hint 7 The second part of the Select EOS parameters for regression panel relates to binary interaction coefficients. Click Regression in the Report section of the panel The Regression Report panel provides several views of the regression problem, designed to give the best possible insight into creating a fluid model. For a description of the Regression Report panel see "Regression Report" on page 130. a Select the Sensitivities folder. The sensitivities for the first Pcrit parameter are generally lower than for the other regression variables. b Select the Hessian folder. The values in the leading diagonal dominate the matrix, except in the first row, the row relating the first Pcrit parameter. c Select the Covariance folder In this table the largest value is for the first Pcrit parameter, indicating that it is the least well determined by the regression. d Select the Correlation folder. There is a strong negative correlation between the two Pcrit parameters, indicating that the regression would proceed better if only one of those two parameters were used. From an examination of the information in the Regression Report panel, it can be seen that the first Pcrit parameter is not likely to aid the regression, and it may hinder it. Consequently that regression variable is removed before regression is started. 8 Close the Regression Report panel. 9 Click Variables in the Regression panel. 10 In the Select EOS parameters for regression panel click on Reset to clear all the cells in the table. 11 Fill in the columns to describe the reduced set of regression variables with the following data: Mnem Pcrit Tcrit C3 1 IC4 1 NC4 1 IC5 1 NC5 1 C6 1 C7+ 1 2 12 Click on OK. PVTi Reference Manual Tutorials Fitting an equation of state to experimental results 51 Viewing the regression progress The results of regression are viewed in a similar way to the results of simulation. 1 Right-click on experiment DL1 in the project tree-view and select Plot from the pop-up menu. 2 Click Run in the Regress section of the Regression panel. This starts the regression. 3 Click on Regression in the Report section of the Regression panel. a Select the Modifiers folder. The difference between the final and initial value of each regression variable is displayed. b Select the Details folder. An observation-by-observation breakdown of the final fit is shown, along with the total fit to all data (both unweighted and incorporating the observation weights). 4 Examine the plots in the main window. The observed data are plotted as points and the simulated data before and after regression are plotted as lines. The regression has improved the equation of state model, so the regression results can be accepted. Hint Right-clicking on an experiment allows you to choose to turn off that experiment during the regression process. 5 Click Accept in the Regress section of the Regression Panel. 6 Close the Regression Report and Regression panels. Saving the project 1 PVTi: Save (concise)... 2 Call the file REGRESS_SECTION.PVI The results of regression are the fluid definition (that is the SYSTEM section) of the newly created PVI file. They can now be read in using the PVTi: File | Import PVI Section | SYSTEM... option. Discussion In this tutorial a fluid definition, an Equation of State and some experiments along with their observations were imported from an existing PVI file (the file created in "Simulating experiments" on page 42). The definition was adjusted so that it provided the best fit (in a leastsquares sense) to the experimental observations ("Fitting an equation of state to experimental results" on page 49). This fitted fluid definition can now be used to generate PVT tables for ECLIPSE (see "Exporting ECLIPSE Black Oil PVT tables" on page 53). 52 Tutorials Fitting an equation of state to experimental results PVTi Reference Manual Exporting ECLIPSE Black Oil PVT tables This tutorial provides a typical workflow for PVTi: producing PVT tables that are then used in an ECLIPSE BlackOil simulation. The data for this project are provided with the standard installation of PVTi under the directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 53 • "Exporting water properties" on page 53 • "Generating ECLIPSE Black Oil PVT tables" on page 53 • "Importing the keywords into ECLIPSE Office" on page 56 • "Discussion" on page 57 Introduction Once the fluid description has been fitted to the experimental observations, it may be used in a reservoir simulation. PVTi facilitates the transition between a fluid description and the PVT keyword description required by the ECLIPSE family of simulators. In this tutorial PVT tables are created for the fluid definition developed in the tutorials 2, 3 and 4. The output tables are then used in an ECLIPSE simulation. 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 Open REGRESS_SECTION.PVI created in the last tutorial (alternatively, open REGRESS_CORRECT.PVI). Exporting water properties The water properties exported from PVTi are generated by correlation. This is effectively separate from the fluid model. 1 2 PVTi: File | Export Keywords | Water... a Enter a reservoir temperature of 220 F and an initial reservoir pressure of 2500 psig. b Click on OK c Enter the filename PVTW.PVO for the water keyword Close Output Display panel. Generating ECLIPSE Black Oil PVT tables In order to generate ECLIPSE BlackOil simulation PVT tables, PVTi requires either a Differential Liberation experiment or a Constant Volume Depletion experiment to be simulated from the fitted equation of state. The PVT tables are generated off either of these experiments. PVTi Reference Manual Tutorials Exporting ECLIPSE Black Oil PVT tables 53 1 Right-click on experiment DL1 in the sample tree and select Export Keywords... from the drop-down menu Hint 2 PVTi: File | Export Keywords | Oil reservoir... produces an export panel for all available Differential Liberation experiments. Select PVTO and PVDG (Live oil and dry gas) on the radio button menu. The Separators drop-down menu becomes active. This is because the produced fluid from the Differential Liberation experiment must be passed through a surface separator to calculate, for example, surface gas-oil ratios. The default is a separator at Standard Conditions. If any separator experiments were defined for this sample, they would also appear here. 3 Click OK 4 In the File Selection box, enter ECLIPSE100 as the name of the export file. The keywords are generated and the Display Output module shows the generated keywords. Note The comments prefixed with --PVTi that appear before each keyword are the concise version of the current PVTi project. This is the minimum information PVTi requires to create the tables. This information can be used to rapidly convert an ECLIPSE BlackOil data-set to an ECLIPSE Compositional data-set. Caution Note Avoid editing the --PVTi prefixed comments. Any changes may invalidate the file, preventing PVTi from reading it. If the sample has had to be swelled, the sample SWELLSAM will have been added to the sample tree. This sample is the swelled sample that was obtained by swelling the original sample with vapor that was split off just below the bubble-point of the fluid. PVTi automatically swells the sample with the vapor from the bubble-point so that the table can be extended to values above the original bubble point. The information in the keywords is also shown in the main plot space, keyword PVTO is shown in Figure 5.4. 54 Tutorials Exporting ECLIPSE Black Oil PVT tables PVTi Reference Manual Figure 5.4 Plot of Oil FVF, Viscosity and Rs versus pressure for the output black oil property tables Generating ECLIPSE Black Oil equilibration keywords This is similar to the generation of PVT tables. To generate equilibration tables, a composition versus depth experiment is required. 1 PVTi: Edit | Experiments... 2 Edit Experiments: Add | Composition with depth... 3 Click Next 4 In the General panel enter the reference properties for the sample: a Enter 220 F as the Temperature. b Enter 3580 psig as the Pressure. c Enter 9200 ft. as the Depth 5 In the Observations panel enter the depths 9000 ft. and 9400 ft. 6 Click Next 7 Click OK to allow PVTi to add extra points between the maximum and minimum depths. 8 Click Close 9 Right-click on the new experiment (COMPG1) in the sample tree and select Export keywords... from the drop-down menu. 10 Select the RSVD/RVVD (black oil) on the Equilibration Keyword radio button. 11 Click OK. PVTi Reference Manual Tutorials Exporting ECLIPSE Black Oil PVT tables 55 12 Enter the filename RSVD.PVO for the exported keyword. Note In this case, only RSVD is generated. This is because the reservoir is all initially in the liquid phase. If there were a gas-oil contact, both RSVD and RVVD would have been generated. If the reservoir were all in the gas phase, only RVVD would be generated. Note In the case of a single-phase fluid, the RSVD keyword can be wrongly named as RVVD and vice versa. The workaround is to correct the name manually in the exported file. 13 PVTi: File | Exit. Keywords have now been generated and can be incorporated into an ECLIPSE data-set using ECLIPSE Office. Importing the keywords into ECLIPSE Office This section is not intended as a tutorial on using ECLIPSE Office. Refer to the "ECLIPSE Office User Guide" for details on using the product. 1 Start ECLIPSE Office with a new case (call it PVTI_TUTORIAL.OFF) and import the standard data set ECLIPSE100.DATA 2 Click ECLIPSE to let ECLIPSE Office know what type of data-set is being imported. 3 Open the Data Manager. 4 Open the PVT Sections. 5 PVT Section: File | Import | Append..., and import the PVT table keyword file (ECLIPSE100.PVO). Click OK to remove the warning message. 6 PVT Section: File | Import | Append..., and import the water keyword file (PVTW.PVO). Click OK to remove the warning message Note At this stage you may want to view the keywords or plot them. For details on how to do this, refer the "ECLIPSE Office User Guide". 7 Close the PVT Section, saving the file with the new keywords. 8 Open the Initialisation Section 9 Initialisation Section: File | Import | Append..., and import the equilibration keyword file (RSVD.PVO). Click OK to remove the warning message. 10 In the Equilibration Data Specification keyword, set the Rs/Pb v Depth Table to 1, so that the imported RSVD keyword is used. 11 Close the Initialisation Section, saving the file with the new keywords. 12 Run the simulation. 56 Tutorials Exporting ECLIPSE Black Oil PVT tables PVTi Reference Manual Discussion In this tutorial an existing fluid definition was imported into PVTi and exported as PVT tables that were used in an ECLIPSE Black Oil reservoir simulation. The basic requirements are that PVTi must simulate a Constant Volume Depletion or Differential Liberation experiment and a Separator experiment to allow the generation of black oil tables from the fluid definition. PVTi Reference Manual Tutorials Exporting ECLIPSE Black Oil PVT tables 57 Converting a black oil run to compositional This tutorial provides an example conversion from ECLIPSE BlackOil to ECLIPSE Compositional. This tutorial requires the use of ECLIPSE Office in combination with PVTi. Note Many conversion projects require conversion of SCHEDULE section keywords, which is outside the scope of this tutorial. This tutorial covers conversion of fluid properties and equilibration. Specifically, the PROPS and SOLUTION sections. Note Some familiarity with ECLIPSE Office is assumed for this tutorial. The data for this project are provided with the standard installation of PVTi under the directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. Note You should choose a short name for your directory and the name must not contain spaces. You can use underscore characters. ECLIPSE does not recognize directory names that are long or that contain spaces. The tutorial is split into several sections: • "Introduction" on page 58. • "Exporting the fluid model" on page 59. • "Converting equilibration keywords" on page 59. • "Creating the ECLIPSE Compositional case" on page 60. • "Discussion" on page 60. Introduction In this tutorial, the black oil PVT tables (PVTO and PVDG) and the Equilibration table (RSVD) are converted into a full compositional model and composition versus depth table (ZMFVD). This allows the ECLIPSE data-set from the previous tutorials to be run as a full compositional case. Caution 58 The --PVTi comments written out with the keywords are used by PVTi to reconstruct the original fluid model. Without these there is not enough information to convert blackoil projects to compositional models. It is important that the lines prefixed by --PVTi in the ECLIPSE data-set are not edited or moved around in the file. 1 Start ECLIPSE Office with the project created in "Exporting ECLIPSE Black Oil PVT tables" on page 53 or create a new project and load in the data-set ECLIPSE100_FULL.DATA. 2 Select the case. Tutorials Converting a black oil run to compositional PVTi Reference Manual 3 Click on the PVTi launch button. 4 Click Run. Note The launch button has a default selection of launching PVTi with the PVT section of the current case. PVTi reads this PVT section, creating a PVI file from the --PVTi comments. Exporting the fluid model The imported PVT section contains the samples from the original PVI file plus any experiments that were needed to generate the keyword. In this case the experiments are a Differential Liberation experiment and a separator. 1 PVTi: File | Export Keywords | ECLIPSE Compositional Fluid Model... 2 Select the fluid {None}. This means that PVTi does not write out a ZI keyword for the ECLIPSE Compositional fluid model. This is the correct selection in this case as the equilibration (RSVD) is used to create a composition versus depth table (ZMFVD). 3 Enter the reservoir temperature as 220o F. Hint The reservoir temperature is the temperature in the Differential Liberation experiment definition. You can right-click on the DL1 experiment and select Edit... from the dropdown menu to view the definition of the Differential Liberation experiment. 4 Click OK. 5 Export the fluid model to FLUID.PVO 6 PVTi: File | Exit (There is no need to save the PVI file as it can be created from the ECLIPSE Office case). Converting equilibration keywords 1 In ECLIPSE Office, click on the PVTi launch button. 2 Select Initialisation as the section to launch PVTi with. 3 Click Run. Hint Again, PVTi searches for the --PVTi comments and uses them to construct a PVI project file. 4 In PVTi, right-click on the composition versus depth experiment COMPG1. 5 Select Export keywords... from the drop-down menu. 6 In the COMPG1 export panel, select ZMFVD (Compositional) on the radio button. 7 Click OK. 8 Export the keyword to the file ZMFVD.PVO. PVTi Reference Manual Tutorials Converting a black oil run to compositional 59 9 PVTi: File | Exit (there is no need to save the PVI file as it can be created from the ECLIPSE Office case). Creating the ECLIPSE Compositional case 1 ECLIPSE Office: Case | Add Case | Clone . This creates an identical copy of the original case. 2 Name the case COMPOSITIONAL, and click OK. 3 Select the newly created case. 4 ECLIPSE Office: Module | Data Manager... 5 Select the Case Definition. 6 In the Case Definition module, select Compositional on the Simulator radio button. 7 Click OK to the warning about changing between black oil and compositional cases. 8 In the PVT folder set the number of components to 11, and click OK. 9 In the Data Manager, select the PVT section. 10 PVT Section: File | Import | Append... and import the file FLUID.PVO. 11 PVT Section: File | Import | Append... and import the file ZMFVD.PVO. 12 PVT Section: Section | Keywords... 13 Delete the PVTO and PVDG keywords. 14 PVT Keywords: File | Close... 15 PVT Section: File | Close... and save the section with a new name. 16 In the Data Manager select the Initialisation section. a Delete the RSVD keyword. b In the EQUIL keyword set the Compositional init type to 1 (so that ZMFVD is used for equilibration). 17 Initialisation Section: File | Close and save the section with a new name. 18 Run the simulation from the ECLIPSE Office Run Manager. Discussion In this tutorial, an ECLIPSE BlackOil simulation data-set was converted to ECLIPSE Compositional using the integration of PVTi and ECLIPSE Office. The insertion of the --PVTi comments into the keyword export from PVTi is a powerful tool, not just for converting data-sets, but also for developing projects in either black oil or compositional models. 60 Tutorials Converting a black oil run to compositional PVTi Reference Manual Workflow Tutorial Introduction This tutorial illustrates a typical workflow for an oil or gas condensate. It involves splitting the C7+ fraction into 2 pseudocomponents, special regression, normal regressing, grouping components, and matching viscosity data. We have an oil PVT case, with two fluid samples ZI and W2 (Well 2). There is a C7+ characterization with CO2 present. Well 2 has C7+ has a different MW and Specific Gravity, but the C7+ has been characterized with the ZI fraction only at this point. They are going to inject CO2 into this field, so there is a Swelling Test with CO2. The files for this tutorial are provided in the default PVTi installation in the following directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. This tutorial contains the following sections: • "Comparing the Default EOS Calculations to the Observations" on page 61. • "Splitting the C7+ Component" on page 62. • "Special regression to adjust the tail in the splitting calculation" on page 63. • "Normal regression to fine tune 11 component match" on page 64. • "Grouping Like Components to Reduce Nc" on page 64. • "Regressing to match viscosities" on page 67. • "Discussion" on page 68. Comparing the Default EOS Calculations to the Observations 1 Start PVTi. 2 Open WORKFLOW.PVI. 3 Run the Simulations; to do this click GO. 4 Review the calculated and observed Bubble Point Pressures for fluid ZI and W2 in the Output Display, that is the first and last experiments. 5 Close Output Display panel. 6 Plot the results one experiment at a time. 7 PVTi Reference Manual a Right-click on CCE1 - Plot. b After reviewing the plots clear the plots by clicking the Remove Plots button. Review all the experiments by observing the plots noting how well PVTi has done in each case in matching the observations. Tutorials Workflow Tutorial 61 Splitting the C7+ Component Creating a phase plot Before we split we will create a Phase Plot (P versus T) 1 Select View: Samples| Phase plot | ZI; click OK. 2 Rescale the y-axis as follows: 3 a Double click on the y-axis. b Select range. c Click off Limit Range. d Enter 0.0 in upper Visible Range area. e Enter 3000 in lower Visible Range area. f Click OK. Click the "Superimpose" button or select Options | Graph | Superimpose. Splitting the C7+ 1 Edit | Fluid Model | Split | Multi Feed.... We will split the C7+ into 2 Pseudo components. 2 Note the Mole Weight of the heaviest pseudo component. 3 Enter the following Specific Gravity and Molecular Weight of Samples Plus Fraction for W2: Molecular Weight 199 Specific Gravity 0.8338 4 Click OK. The C7+ has been split. 5 Select Edit | Samples | Compositions. Check the mole fractions of the 2 pseudo heavy components. The split creates FRC2 with small mole fraction (0.0477). We would rather have a splitting that has more of the mole fraction in the heaviest component so we will perform another split. 6 Close this project and do not save the project. 7 Open WORKFLOW.PVI again. 8 Plot the Phase Diagram. 9 Select the Split panel and repeat steps 1 to 3. 10 This time change the Mole Weight of Heaviest Pseudo Component to 300. This gives us a larger mole fraction for FRC2. 11 Click OK. 12 Check the Samples. The FRC2 mole fractions are 8.2% and 13.9% 62 Tutorials Workflow Tutorial PVTi Reference Manual 13 Create a Phase Plot superimposed on the unsplit plot. The phase diagram has not changed much at the reservoir temperature, which indicates a good splitting. 14 Before we move on the regression save these results, using File | Save As, give the file the name SPLIT.PVI. Special regression to adjust the tail in the splitting calculation Before we regress we want to set the weights of the viscosity observations to 0, so they are not included in the RMS. We will regress on the viscosity last, after we finish the phase behavior match. Hint Regressing on the viscosity coefficients after the phase behavior of the fluid has been matched is always strongly recommended. We will also increase the weights of the Bubble Point Pressure (Sat. pressure) Observation as this is a very important criterion to match. 1 Right-click on Vapor Visc and enter 0 as the Set Weight. 2 Right-click on Liquid Visc and enter 0 as the Set Weight. Note Setting the weight of an observation to zero turns off that observation. 3 Right-click on Z1 | BUBBLE1 | Sat pressure and enter 40 as the Set Weight. 4 Right-click on W2 | BUBBLE2 | Sat pressure and enter 40 as the Set Weight. 5 Select Run| Regression. 6 Click Special and then Variables 7 Select all 3 SCT variables and press OK. 8 Select Regress | Run. a 9 Note the RMS in the Log area. In the Regression panel click Simulation and observe the match of the 2 Bubble Point pressure. a Or alternately select Report | Regression. 10 Under Details check the matches of the observations, especially the 2 bubble point pressures, both should match very well. Look at the Modifiers to see the amount of change in the parameters. Note You may also view the Sensitivities and the Hessian, Covariance and Correlation matrices in the Report panel. These matrices are explained in the "Reference section" on page 89. Plotting the match 1 PVTi Reference Manual Switch off Superimpose, click Remove Plots. Tutorials Workflow Tutorial 63 2 Right-click on each experiment CCE1, etc. click plot, view the match and then click Remove Plots before proceeding to the next experiment. Note the DL results are much improved. The general rule is if this special regression improves the match of the phase behavior you should accept the regression. If it does not improve it or makes it worse reject the regression. In this case the match is improved so we will accept this regression. 3 Click Accept and close the Regression panel. 4 Save the results, select File | Save As and save as ALPHA.PVI. Normal regression to fine tune 11 component match You can do some normal regression to fine tune this 11-component match. The Swelling and Separator Experiments still need to match. Or you can group now and then do the normal regression to finish matching the phase behavior. This tutorial will do the fine tuning using Normal Regression before grouping. 1 Set weights on bubble point pressures, etc. Right click on Observation | Set Weight and: a Make sure the 2 bubble point pressure observations weights are still 40. b Set the Swelling Test | Saturation Pressure Weights to 10. c Select CCE and set the Liquid Density Weights to 5. d Set the Separator Exp | Gas-Oil-Ratio weights to 5. 2 Select Run | Regression. 3 Select Normal under the Variables section. 4 Click Variables box. 5 Refer to the procedure described in section "Normal Regression to fine tune match" on page 65 for fine tuning this 11 component match. Note 6 Do not attempt to get a perfect match since the grouping process described below changes the match. The key here is to get the Swelling Test; Saturation Pressures to match better before grouping. Save this characterization with a new file name. Grouping Like Components to Reduce Nc We will group the 11 components into 6 components. Rules for grouping a fluid like this are as follows: 64 • Keep Methane C1 as a pure component. • Keep CO2 as a pure component - we will inject CO2. • Keep the two heavy pseudocomponents that you created by splitting (and did a special regression on) as separate components. Tutorials Workflow Tutorial PVTi Reference Manual 1 Before we group create a Phase diagram of component ZI and click the Superimpose button. 2 Select Edit | Fluid Model |Group. 3 Type the following integers into the New Index column: CO2 1 C1 2 C2 3 C3 3 IC4 3 NC4 3 IC5 4 NC5 4 C6 4 FRC1 5 FRC2 6 4 Click Update. 5 Check the component (Group) names. You change them if you do not like a particular name. 6 Click Update again, and then click OK. 7 Click the Edit sample composition’s button to view the mole fractions of the new group. The usual rule is if one of the group mole fractions is significantly smaller than the others group it into one of its neighbor groups. 8 Plot a Phase diagram on top of the un-grouped diagram. If they are close to each other then the grouping is good. Your phase match should still be close to the observed data. 9 Click GO and view the bubble point pressures 10 Plot the experiments to see how much the grouping has changed the calculated results. 11 If the match looks reasonable save this characterization with a new file name. 12 If the match has changed substantially, close this project without saving and read in the .PVI file from the save at the end of the previous section. 13 Re-group with a different selection of groups or number of pseudocomponents. Normal Regression to fine tune match The steps in the normal regression process are: • Choose high weights on experiments or observations to improve the of key data • Pick various combinations of parameters to regress on, try it, look at the results, reject the regression and try a different combination PVTi Reference Manual Tutorials Workflow Tutorial 65 • Volume shift parameters may be dependent on Tc and Pc - so you cannot regress on them separately. They may be independent in which case you can regress on them. If you are having trouble matching liquid densities try making the volume shifts independent. A review of the match of the observations shows that the Saturation Pressure for the Swelling Experiment with CO2 contains the largest difference between the calculated and observed. We will increase the weight for these results. There are two ways to change the weight for experiments and observations: 1 2 To change the global weight for the experiment: a Right -click on the experiment and click on set weight - b Type in the new weight. To change the weight on individual observations: a select Edit | Observations: b click on the experiment type, c click experiment list, d then observation type, e then click on the large G in the upper left corner of the panel. Individual weights appear on the right most columns. f Insert weight values and click Apply. Suggested weight values: • Swelling, saturation pressure = 10. • CCE, liquid densities = 5. • SEPS, Gas-Oil Ratio = 5. • Bubble point pressure = 40 (previously set). Regression variable trial and error process For the remainder of the phase behavior regression, it is a trial and error procedure. Below are several suggested combinations of parameters to regress on. Remember a vertical column of numbers in the Regression panel: 1 1 1 1 creates one regression variable for all four components. To create 4 regression variables one should enter the following in the column: 1 2 3 4 Below are 3 combinations of suggested variables (with volume shift parameters "Independent") after grouping the 11 components into 6. A variable should be defined for the contents of each bullet point in the 3 combinations: 66 Tutorials Workflow Tutorial PVTi Reference Manual • Omega A - C9+, C23+ • Omega B - C9+, C23+ • AcenFac - C9+, C23+ • Shift - all components • BIC CO2 and C1, C2+, C5+, C9+, C23+ • BIC C1 and C5+, C9+, C23+ or: • Omega A - C2+, C5+, C9+, C23+ • Omega B - C2+, C5+, C9+, C23+ • AcenFac - C2+, C5+, C9+, C23+ • Shift - all components • BIC CO2 and C1, C2+, C5+, C9+, C23+ • BIC C1 and C5+, C9+, C23+ or: • Tc - C9+, C23+ • Pc - C9+, C23+ • AcenFac - C9+, C23+ • Sshift - all components • BIC CO2 and C1, C2+, C5+, C9+, C23+ • BIC C1 and C5+, C9+, C23+ 1 Try as many combinations as required to match the data to within the degree of accuracy you think is needed. Remember the accuracy of most PVT observations is 5% to 10% or about 20 Psi. 2 Once you have finished matching the phase behavior data, accept the results of the regression and save the file. Regressing to match viscosities Now that we have a match of the phase behavior, we next need to match the viscosity observations. First we need to remove the experiments that do not have viscosity data from the regression process. Then in the CCE we need to set the viscosity observations weights to 1 and the other observations to 0. 1 To remove an experiment from regression right click on the experiment and select Don't use in regression. Do this for all experiments except CCE. 2 In the CCE experiment for all the observations (except for the Vapor visc. and Liquid visc.) right click on the observation and select set weight. a Change the weight to 0. 3 For the Vapor visc. and Liquid visc. change the weight (using the same sequence) from 0 to 1. 4 Select Run | Regression. 5 In the Variable section click Normal then the Variables box. PVTi Reference Manual Tutorials Workflow Tutorial 67 First iteration 1 In the Select EOS parameters for regression panel enter 1 in all the boxes under the heading VcritV. 2 Click OK. 3 In the Regression panel click Run. 4 Plot the Liquid and Vapor viscosity and compare the new match with the observations. Second iteration 1 In the Regression panel press Reject to return the characterization back to the preregression values. 2 In the Select EOS parameters for regression panel enter 1 in the first box, 2 in the second box, 3 through 6 in the remainder of boxes under the heading VcritV. 3 Click OK. 4 In the Regression panel click Run. 5 Plot the Liquid and Vapor viscosity and compare the new match with the observations. Note this new match is better than the first match. 6 Press Accept to accept these results. 7 Save this characterization with a new file name. The phase matching process is now complete. You are ready to export the PVT properties or characterization for ECLIPSE simulations. Discussion This tutorial illustrated a typical workflow for an oil or gas condensate. It involved splitting the C7+ fraction into 2 pseudocomponents, special regression, normal regressing, grouping components, and matching viscosity data. 68 Tutorials Workflow Tutorial PVTi Reference Manual Multiphase Flash Introduction The multiphase flash experiment tends to find more than two phases in systems with Asphaltene/Waxes and/or with CO2 rich fluids at low temperatures. This tutorial demonstrates multiphase flashes with both systems. The files for this tutorial are provided in the default PVTi installation in the following directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into the following sections: • "Asphaltene and wax system" on page 69. • "CO2 Rich Fluids" on page 70. • "Summary" on page 72. Asphaltene and wax system 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 Load MULTIPHASE-START1.PVI into PVTi. 3 View this oil composition by selecting Edit | Fundamentals and view the 10 component oil.When finished click OK. 4 To add an experiment, click Edit | Experiments and then Add | Single Point | Multiphase Flash. 5 a Click Next> and then enter 50 F as the Temperature, b Click Observations, fill in 1000 Psia. c Click Next> and then Close. To run the experiment (again) click GO. The Output Display shows the results of the flash.You will see two phases, Liquid and Vapor, and their properties and compositions. Now we are going to split the C7+ fraction into Paraffin, Naphthalene, and Aromatic components, then redo the multiphase flash. 6 Select Edit | Fluid Model |Split | PNA Distribution. The C7+ fraction is now split. 7 To view the new characterization, select Edit | Fluid Model | Components. You will see that there are three new user-defined components which have replaced the C7+ component. 8 Click on the Complete folder to view the critical properties of these components. 9 Click on OK to close the panel. We are going to run the MFLASH experiment again and view the phases present. 10 Click on GO . PVTi Reference Manual Tutorials Multiphase Flash 69 The Output Display shows the following 4 phases: Liquid, Wax, Asphaltene Liquid, and Vapor. 11 Note that the compositions of the Wax is 100% PC7+ and the Asphaltene Liquid is 90.23% AC7+. 12 Close the project, do not save the changes. CO2 Rich Fluids Certain fluids with a high CO2 content at low reservoir temperatures partition into two liquid phases or two liquid phases in equilibrium with a vapor phase. This tutorial demonstrates such a system. SPE 71485, (see [Ref. 1]) gives fluid characterizations that exhibit multiphase behavior. This paper describes reservoir oil with 12 components. It has heavy components of C7-9, C10-13, C14-19, C20-35, and C36+. It also describes an injection gas called MI (Miscible Injection) that is a combination of CO2 and NGL. In the paper they use the Peng-Robinson Equation-ofState to calculate the phase behavior. They combine the reservoir oil and the MI gas in various mixtures at 86 °F and present a diagram of the phases present, which is shown in Figure 5.5. Figure 5.5 Phase Diagram for Schrader Bluff Fluids We will attempt to verify the phases present with a 0.8 fraction of MI with PVTi multiphase flash. 70 1 Load MULTIPHASE-CO2.PVI into PVTi. This contains the fluids and characterization from the SPE paper,[Ref. 1]. 2 View the compositions of the fluid sample by selecting Edit | Samples | Compositions. 3 Click OK to close the panel. Tutorials Multiphase Flash PVTi Reference Manual 4 To create a mixture of 80% MI and 20% reservoir oil, select Edit | Samples | Mix. 5 In the Mix panel enter the following: a Mixing Type By: Mole Fraction of Sample 2 b Fluid Sample 1: Z1 c Fluid Sample 2: MI d New Sample Name: .8MI e Temperature: 86 F f Mole Fraction: 80 percent 6 Click OK. 7 To view the new sample, click Edit | Samples | Compositions. Note the new sample has 65.209% CO2. Now we will create multiphase flash experiments at a series of pressures (Temperature = 86 F) starting in the Liquid-Liquid region (1100 Psia) then through the Liquid-Liquid-Vapor region and ending up in the Liquid-Vapor region (600 Psia). 8 Select Edit | Experiments and then Add | Single Point | Multiphase Flash. 9 Enter the following: a Fluid Sample: .8 MI b Temperature: 86 F 10 Select Observations and enter 1100 (psia) as Pressure. 11 Click Next> and Close. We now have MFLASH1 defined. 12 To create additional MFLASH experiments at a series of lower pressure, right click on MFLASH1 and select Clone. 13 Repeat for MFLASH2 through to MFLASH5. We now have 5 MFLASH experiments defined. 14 To change the flash pressures right click on the MFLASH experiment and select Edit | Observations | Pressure. 15 Enter the following pressure values: a MFLASH2: 1050 (psia) b MFLASH3: 1000 (psia) c MFLASH4: 900 (psia) d MFLASH5: 600 (psia) 16 To switch between MFLASH experiments press Next> and then Close. 17 To run all experiments and view results, click GO. 18 Observe the results in the Output Display. Note as the pressure decreases the flashes proceeds from the L-L region to the L-L-V region to the L-V regions, just as Figure 5.5 illustrates. Note PVTi Reference Manual The MFLASH5 experiment can sometimes label both the phases as liquid. However, one of them is clearly a vapor as the density value is 4.93598 lb./ft.3. Tutorials Multiphase Flash 71 Note If a standard two-phase flash is performed at the same temperature and pressure as with the multiphase flash, then one obtains liquid and vapor phases with the same density values as produced with the MFLASH5 experiment. Summary This tutorial demonstrated the multiphase flash experiment. It tends to find more than two phases in systems with Asphaltene/Waxes and/or with CO2 rich fluids at low temperatures. This tutorial demonstrates multiphase flashes with both systems. References Guler B. et al, "Three- and Four-Phase Flow Compositional Simulations of CO2/NGL EOR" [Ref. 1] SPE 71485, 72 Tutorials Multiphase Flash PVTi Reference Manual Exporting an ECLIPSE Thermal model Introduction This tutorial demonstrates using the new ECLIPSE Thermal export facility where a file can be exported containing a fluid model suitable for use in ECLIPSE Thermal. For technical information on the ELCLIPSE Thermal export facility see "ECLIPSE Thermal Export Module" on page 401 and for more general workflow guidelines see "Compositional Data for ECLIPSE Thermal" on page 366. The files for this tutorial are provided in the default PVTi installation in the following directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into the following sections: • "Verifying the Validity of the Fluid Model" on page 73. • "Fitting the Component K-values" on page 74. • "Viewing the K-value Fits" on page 75. • "Exporting the Model" on page 76.] Verifying the Validity of the Fluid Model 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 Open THERMAL.PVI. 3 Open the Fundamentals panel by selecting Edit | Fundamentals.... From the tree view on the left side of PVTi you can see that there is a single sample in this project called ZI. The Fundamentals panel shows the composition of this 3-component fluid as being C1, C5 and C20+. 4 On the tree view there are two experiments defined, a Differential Liberation (DL1) and a bubble point experiment (BUBBLE1). Right-click on the DL1 experiment and select Plot. Three observations should have been plotted oil density, oil relative volume and oil viscosity. You can see that the Equation of State (EoS) fluid model shows good agreement with all 3 observations. 5 Right-click on the bubble point experiment and select Report. You can see that the EoS model also gives good agreement with the observed bubble point pressure of 1784.1749psia. Since we have a good match for our EoS based fluid model we can now export the model for use in an ECLIPSE simulation. We have relatively few components (<4) so this fluid would be suitable for use in an ECLIPSE Thermal simulation. Note PVTi Reference Manual Simulations using ECLIPSE Thermal tend to use fluids consisting of two or three components. Tutorials Exporting an ECLIPSE Thermal model 73 Fitting the Component K-values 1 Right-click on the sample ZI and select the Export ECLIPSE Thermal model... 2 On the panel that opens, enter the following: a 1500 psia as the Maximum Pressure, b 400 F for the Maximum Temperature, c 1000 psia for the Minimum Pressure, d and 200 F in the Minimum Temperature box. Note 3 The default values here are Pmax=1000psia, Pmin=50psia, Tmax=400F and Tmin=50F and are considered reasonable max/min parameters within a reservoir. However, every reservoir is different and any knowledge of these parameters for your particular reservoir should be entered. Enter 40 in the Enter Number of Flashes to be Performed box. To model component K-values we can either export the KVWI keyword, which models them using Wilson’s formula, or the KVCR keyword, which uses Crookston’s formula. Crookston’s formula is in general much more accurate and we will use this. See "K-Values" on page 401 for a more detailed description regarding the modeling of K-values. 4 Tick the box Export Crookston Coefficient? to tell PVTi that you wish to export the KVCR keyword. 5 Since we are exporting the KVCR keyword we need to determine the values of the coefficients of Crookston’s equation to export. Click Fit Crookston Coefficients on the panel to open the Fit Crookston Coefficients panel. This panel shows Crookston’s equation where p is the pressure, T is temperature and the coefficients A-E are what we wish to determine values for. Note The Fit Crookston Coefficients panel enables you to calculate the optimum values of the coefficients A-E in Crookston’s formula, so that the best fit is found to PVTi’s EoS predicted K-values for each component over the temperature and pressure range defined by the user. 6 A and D should already be active. Click on B to make coefficient B active also. 7 Select the Plot option in the Plot P, T Values Used in Fitting Crookston Coefficient? box. In order to find values for the chosen coefficients PVTi throws in 40 points at random coordinates in the region you just defined in pressure-temperature space. The Plot option plots these points on the screen for you after the fit has been performed. Ideally, we would like to them superimposed on a phase plot. 8 Select PVTi: View | Samples | Phase Plot... and press OK to perform the phase plot. 9 Select PVTi: Options | Graph | Superimpose. Hint You can also access the Superimpose option using the toolbar. 10 Now click Apply on the Fit Crookston Coefficients panel to start the run. 74 Tutorials Exporting an ECLIPSE Thermal model PVTi Reference Manual Once the run has finished a results panel appears. In the Coefficients folder the best fit values of A, B and D are reported for each component. 11 Click on the Statistics panel. The mean error and standard deviation (in %) are reported for each fit. The C1 and C5 components have been fitted very well (rms<1.5%) and the C20+ fraction has been fitted reasonably well with an rms of somewhere between 7-9% (depending on the random number generator on your machine). Can we do better though? Caution Make sure you turn off the Superimpose option before moving to the next section. Viewing the K-value Fits In the last section "Fitting the Component K-values" on page 74 we saw how to use the module to calculate the optimum values of a chosen set of coefficients in Crookston’s equation in terms of fitting to PVTi’s Equation of State based K-values. We saw, for the fluid ZI in the THERMAL.PVI file, that the C20+ fraction had a reasonable fit when using just A, B and D. In this section we will see how to interactively view the fits in order to better understand why PVTi’s EoS K-values for this C20+ fraction has not been represented as well as the other components. 1 Click the View Fit button on the Fit Crookston Coefficients panel. The Plot K-values vs Temperature or Pressure panel opens. Hint Plots can either be performed of K-values versus pressure (at constant temperature) or K-values versus temperature (at constant pressure). First we will look at the K-value versus temperature fits, which are dictated by the D and E coefficients (just D in our case). 2 Enter 1250psia in the Enter Constant Pressure box and 400F and 200F as the Maximum and Minimum Temperatures respectively. Now click Apply. The PVTi EoS-based K-values are shown by the points and the K-values calculated using Crookston’s equation are shown by the curves. 3 Experiment by changing the value of the constant pressure in the range 1000<P<1500 (our chosen pressure range) to see how well Crookston’s formula models the temperature dependence of the K-values at a given pressure. In general, for the C20+ component, the D coefficient, models the observations pretty well over the whole pressure-temperature range, although using the E coefficient as well may well help slightly 4 Click the Plot at Constant Temperature box and enter 300F. 5 Now enter the appropriate pressure range, which is 1500 psia and 1000 psia for the maximum and minimum values. Click Apply. 6 Again, experiment by changing the value of the constant temperature in the range 200<T<400 to see how well Crookston’s formula models the pressure dependence of Kvalues. PVTi Reference Manual Tutorials Exporting an ECLIPSE Thermal model 75 In particular it can be seen in the range 300<T<400 (for the C20+ component) that Crookston’s formula struggles to model the pressure dependence at pressures at P<1100psia when using just the A and B coefficients. Using the C coefficient may well improve things significantly. You can see in particular, the K-value versus pressure curve for the C20+ component struggles to fit the observations.The problem is that the term A+B/P starts to run into problems for pressure values <1100psia (due to the strongly negative value of B) and therefore we require the C coefficient to get a good fit. 7 Close the Crookston Report panel and the Plot K-values vs Temperature or Pressure? panel. 8 Switch on the C and E coefficients by ticking the appropriate boxes on the Fit Crookston Coefficients panel. Now click Apply. This run will take slightly longer, as the introduction of the C and E terms vastly increases the amount of parameter space that PVTi must search. 9 Once the run has finished repeat steps 1-3. This time, due to the introduction of the C coefficient in the fit, we have done a better job in fitting the pressure dependence of Crookston’s equation. The introduction of the E coefficient has also slightly improved the modeling of the C20+ K-value versus temperature. 10 Click on the Statistics folder. Overall, the introduction of the C and E coefficients has decreased the rms fit for the C20+ component from ~8% to ~5%. Exporting the Model Now we are satisfied with our K-value fits we can export our ECLIPSE Thermal PVT model. Note If we had decided to export the KVWI keyword (that is use Wilson’s formula to model K-values) then we would not have needed to fit the coefficients of Crookston’s equation and could have exported straight away from the Export for ECLIPSE Thermal panel. Although this may be quicker, Crookston’s formula models K-values much better and spending this extra time is worthwhile. 1 Click the OK button on the Export for ECLIPSE Thermal panel. 2 Choose a name for the file to be exported. By default PVTi names it rootname.PVO, so in this case THERMAL.PVO if you do not choose otherwise. 3 Click Save. The ECLIPSE Thermal fluid model is written to the specified file. This file can now be used to model PVT behavior as part of an ECLIPSE Thermal simulation. 76 Tutorials Exporting an ECLIPSE Thermal model PVTi Reference Manual Data analysis and quality control This tutorial provides a typical workflow for PVTi in its role as a data quality assessment tool. Experimental results from analysis of a hydrocarbon gas is used to analyze the data quality and to modify spurious data. The data for this project are provided with the standard installation of PVTi under the directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 77 • "Material balance checking" on page 78 • "The Hoffman-Crump-Hocott test for separator data" on page 82 • "Recovery calculations" on page 83. Introduction In addition to allowing an equation of state to be fitted to laboratory results and facilitating the generation of ECLIPSE BlackOil/ Compositional PVT data, PVTi also provides material balance checks to assess data quality. For information on the calculations involved in material balance checking see "Compositional material balance" on page 308. Note Problems with the observations in a PVT report equate to problems with the fitted fluid model. It is therefore recommended that material balance checks are carried out on all PVT data. In this tutorial an existing project file (GAS.PVI) is read into PVTi and the data are checked and modified for material balance errors. 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 PVTi: File | Open... 3 Open GAS.PVI Hint 4 The Data Tree should show that there are three experiments, CVD1, defined with 10 different types of observations, SEPS1 with observations of fluid mole fractions (liquid and vapor) and CCE1 with observation of Vapor Z-Factor. Click and drag the ZI node from the Data Tree and drop it into the Main Plot Window. The phase envelope should look like Figure 5.6. PVTi Reference Manual Tutorials Data analysis and quality control 77 Figure 5.6 The phase envelope plot. Note This fluid system has no well-defined critical point. Material balance checking 1 Right-click on CVD1 in the sample tree and select Material Balance... This opens the Material Balance panel for this experiment. 2 Click Report to create a material balance report. The experiment is performed and the Output Display window opens showing messages that indicate the quality of the data. (Figure 5.7) 78 Tutorials Data analysis and quality control PVTi Reference Manual Figure 5.7 The main display shows messages indicating the quality of the data Warning Warning Warning Warning - Sg of final stage liquid plus fraction is not defined - Mw of final stage liquid plus fraction is not defined - Viscosities of gas of at least one stage of CVD is not defined - Mw of vapor plus fraction of at least one stage is not defined - setting constant Mw(CN+) = of Mw(CN+) at Psat Warning - Sg of vapor plus fraction of at least one stage is not defined Warning - Composition of final stage liquid does not sum to 100% Calculated liquid mole% of N2 at P= 6300.00000 is negative Calculated liquid mole% of CO2 at P= 6300.00000 is negative Calculated liquid mole% of IC4 at P= 6300.00000 is negative Calculated liquid mole% of NC4 at P= 6300.00000 is negative Calculated liquid mole% of IC5 at P= 6300.00000 is negative Calculated liquid mole% of NC5 at P= 6300.00000 is negative Calculated liquid mole% of C6 at P= 6300.00000 is negative Calculated liquid mole% of N2 at P= 5700.00000 is negative Calculated liquid mole% of CO2 at P= 5700.00000 is negative Calculated liquid mole% of N2 at P= 5100.00000 is negative Calculated liquid mole% of CO2 at P= 5100.00000 is negative Calculated liquid mole% of N2 at P= 4500.00000 is negative Calculated liquid mole% of N2 at P= 3800.00000 is negative Calculated liquid mole% of N2 at P= 3100.00000 is negative Calculated liquid mole% of N2 at P= 2400.00000 is negative Calculated liquid mole% of N2 at P= 1700.00000 is negative Calculated liquid mole% of CO2 at P= 1700.00000 is negative Calculated liquid mole% of N2 at P= 1000.00000 is negative Calculated liquid mole% of CO2 at P= 1000.00000 is negative Calculated liquid mole% of N2 at P= 300.00000 is negative Calculated liquid mole% of CO2 at P= 300.00000 is negative The messages show that some mole fractions were calculated as negative, so there are clearly problems with the data. PVTi supplies various options for plotting the data to ascertain the source of the errors. The first type of data check to perform is to view the pressure variation of the gas compositions. 3 Output Display: File | Close 4 Click Plot in the Material Balance panel. a Select Vapor Compositions v Pressure in the Select Plot Type panel and click on Plot. b Click Close 5 PVTi: View | Rubberband Zoom In 6 Click and drag the mouse to define the zoom area to approximately cover the region 2800 to 6500 psia and 0.1 to 2 vapor composition. After zooming in, the plot window should look similar to Figure 5.8. PVTi Reference Manual Tutorials Data analysis and quality control 79 Figure 5.8 The main plot window after zooming in Many of the components have non-monotonically varying gas compositions. In general, there are several fluids or analyses available, and bad data can be discarded. However, if no other data is available PVTi offers tools to make modifications to the bad data. Modifying CVD data 1 Click Modify in the Material Balance panel. 2 Select fraction modifiers. 3 Enter the following values in for 6996 psia: Component N2 CO2 ... IC4 NC4 IC5 NC5 C6 Percentage 10 10 ... 2 10 5 5 20 Note 80 The other components are modified in proportion to their existing mole fractions. Placing a letter in the thin column to the left of each column of modifiers allows the proportion of that component to be fixed and thus not modified in proportion to its existing mole fraction. 4 Click on OK in the Set correction factors for CVD compositions panel. 5 Click Report in the Material Balance panel to create a new material balance report. 6 Click on Yes to modify the vapor and liquid compositions in CVD1. 7 Click on No if you want to save the modified compositions, but retain their original values until after the modified results have been examined. Tutorials Data analysis and quality control PVTi Reference Manual Now none of the liquid mole percentages are negative. So this change to the data can be accepted. 8 Click Report in the Material Balance Panel 9 Click on Yes to modify the compositions. 10 This time, click on Yes so that the compositions are modified. Plotting K values versus Pressure 1 Click Plot in the Material Balance panel. 2 Select K-values:(1) log (k) v Pressure plot in the Select Plot Type panel and click on Plot. The plot window should now look like Figure 5.9. Figure 5.9 The plot of k values versus pressure. The K-values should plot monotonically in that N2 should be the largest, followed by C1, etc. This is clearly not the case, so although there are now no calculated negative compositions, the modified fluid definition is not fully consistent. The Hoffman-Crump plot 1 Select the K-values:(2) Hoffman-Crump Plot in the Select Plot Type panel and click on Plot. 2 Click Close in the plot panel. 3 Click Close in the Material Balance Panel. The plot window should look like Figure 5.10. PVTi Reference Manual Tutorials Data analysis and quality control 81 Figure 5.10 The Hoffman-Crump plot In this plot, one line is generated for each pressure stage. The Hoffman F coefficients correspond to C1, C2 etc. and the lowest to C11, C12+. In general, these lines should be monotonic with pressure, with the highest pressure at the top. This plot shows most of the error to be in the first stage. The Hoffman-Crump-Hocott test for separator data Applying the Hoffman-Crump-Hocott test to separator gas and oil samples indicates whether or not the streams are genuine equilibrium fluids. 1 Right-click on SEPS1 in the project tree-view and select Recombination... on the pop-up menu. 2 Click Report to create a recombination report. 3 Output Display: File | Close 4 Click Plot. The two lines on the Hoffman-Crump-Hocott plot (Figure 5.11) show the actual data and the Standing estimates of K-values. They are used as a consistency check and, in this case, give further evidence that the initial feed stream composition is in error. 82 Tutorials Data analysis and quality control PVTi Reference Manual Figure 5.11 Hoffman-Crump-Hocott plot. Recovery calculations PVTi can allow recovery calculations to be performed if a valid Constant Composition Expansion, Constant Volume Depletion and Separator test exist. 1 Right-click on CCE1 in the project tree-view and select Recovery... on the pop-up menu. 2 Click on Report to perform the recovery calculation. Hint This assumes that there is no direct production of reservoir liquid. If you want to include direct production of reservoir liquid, you need a relative permeability table, which you can enter be clicking on Rel. Perm. Note PVTi runs the material balance check on the Constant Volume Depletion experiment selected, and performs recombination on the Separator selected, before performing the recovery calculation. Discussion This tutorial has illustrated how fluids may be examined for consistency and, if necessary, modified, within a PVTi project. PVTi Reference Manual Tutorials Data analysis and quality control 83 Removing contamination from samples Introduction Oil-based muds are in widespread use and often contaminate PVT samples taken at the wellsite. This tutorial involves the cleaning of a sample that is contaminated by an oil-based mud. The PVI file CLEAN.PVI is used for this tutorial and is provided in the default PVTi installation in the following directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 84 • "Removing oil-based mud contamination by skimming" on page 84 • "Removing oil-based mud contamination by subtraction" on page 85 • "Discussion" on page 86 Removing oil-based mud contamination by skimming 1 Start PVTi (if you are unsure about this see "Starting PVTi" on page 29). 2 Open CLEAN.PVI. 3 Right-click on the sample ZI and select Fingerprint plot from the drop-down menu. In naturally occurring hydrocarbons there is expected to be semi-log straight-line behaviour for components C8+ (around a mole weight of 100). From the fingerprint plot, there is clearly not straight-line behavior for this fluid. The contaminating mud, like many oil-based muds, has a composition containing components C10-C23. In the skimming method, it is assumed that the composition is not known. 4 Right-click on the sample ZI and select Clean... from the drop-down menu. a Enter CLEAN as the sample name for the cleaned sample. b Enter CONTAM as the sample name for the contaminant. c Click OK. The sample has now been cleaned. 5 PVTi: Options | Graph | Superimpose - and ensure that the Superimpose option is on. 6 Right-click on the sample CLEAN and select Fingerprint plot from the drop-down menu. 7 Right-click on the sample CONTAM and select Fingerprint plot from the drop-down menu. The plot should now look like Figure 5.12. 84 Tutorials Removing contamination from samples PVTi Reference Manual Figure 5.12 The original sample, the cleaned sample and the estimated contaminant. Removing oil-based mud contamination by subtraction When the composition of the contaminant is known, the subtraction method can give better results than the simple skimming method. 1 Right-click on the sample MUD and select Fingerprint plot from the drop-down menu. The true composition of the contaminant contains components lighter than C8 and also up to the plus-fraction (C25+). The skimming method could not remove this contaminant completely, but the subtraction method can. 2 3 PVTi Reference Manual Right-click on the sample ZI and select Clean.... a Enter CLEAN2 as the sample name for the cleaned sample. b Select Subtraction as the method. c Select MUD in the Contaminant drop-down. d Click OK. Right-click on the sample CLEAN2 and select Fingerprint plot from the drop-down menu. Tutorials Removing contamination from samples 85 Discussion This tutorial showed how a fluid can be cleaned of oil-based contaminants such as drilling muds. For information on how the skimming and subtraction methods work see "Removing contamination from samples" on page 84. In general different PVT samples contain different levels of contaminant. It is usually best to fit the PVT reports from a number of (contaminated) samples. Once a consistent fluid model has been developed, the samples can be cleaned using either of the methods outlined in this tutorial. The cleaned samples can then be used in reservoir simulations. 86 Tutorials Removing contamination from samples PVTi Reference Manual Converting old projects to the current version This tutorial demonstrates conversion of an old project to the current version of PVTi. This is especially important for projects (PVI files) created with versions before 99B, as the default Field units for Gas Formation Volume Factor were changed for that release. The files for this tutorial are provided in the default PVTi installation in the following directory: $ECL/2014.1/pvti/tutorials and should be copied to the local directory before starting the tutorial. The tutorial is split into several sections: • "Introduction" on page 87 • "Preparing the PVI file for conversion" on page 87 • "Converting the file" on page 88 • "Discussion" on page 88. Introduction The VERSION keyword, introduced in 2000A, allows a systematic method for updating old PVI files to be compatible with the latest version of PVTi. This tutorial describes how the keyword can be used to convert an old PVI file into the current version. Caution Files in FIELD units containing Differential Liberation (DL) experiments that have Gas formation volume factor (GFVF) observations must be updated to the current version. Preparing the PVI file for conversion 1 Start PVTi with a new project. 2 Click Cancel in the Fundamentals panel. 3 PVTi: Utilities | Text Editor 4 Select OLD.PVI as the file to be viewed 5 In OLD.PVI enter the VERSION keyword in the RUNSPEC section with a value of 98B. Hint If you are unsure of the form of the VERSION keyword see "VERSION" on page 280. 6 File | Save As... 7 Save the file with the name CONVERT.PVI 8 File | Close Note PVTi Reference Manual You could now use the file CONVERT.PVI in a normal session and PVTi interprets it according to the version specified by the VERSION keyword. Tutorials Converting old projects to the current version 87 In this tutorial we go one step further and convert the PVI file to the current version. Converting the file 1 PVTi: File | Open 2 Select CONVERT.PVI as the file to open. 3 PVTi: File | Save As... 4 Save the file with the name NEW.PVI Hint You can compare the file NEW.PVI to OLD.PVI to see the differences (the DL observation GFVF is converted from rb/stb to rb/Mscf and the heat capacity keywords are added in the SYSTEM section). Discussion In this tutorial an old PVI file was converted to the latest version. This is important for files using FIELD units, containing Differential Liberation (DL) experiments that have Gas formation volume factor (GFVF) measurements as the units, for this type of observation was changed in 99B from rb/stb to rb/Mscf to make PVTi’s units systems consistent with those of the ECLIPSE simulators. 88 Tutorials Converting old projects to the current version PVTi Reference Manual Reference section Chapter 6 General information • "Main PVTi window" on page 90 • "File" on page 92. • "View" on page 95 • "The fluid model" on page 98 • "COMB - Compositional Material Balance" on page 112 • "Simulation using PVTi" on page 117 • "Regression in PVTi" on page 126 • "Exporting keywords" on page 133. • "Utilities" on page 144. • "Batch system and keywords" on page 152. • "Error handling" on page 165. PVTi Reference Manual Reference section General information 89 Main PVTi window General information PVT analysis involves fitting an Equation of State to experimental data and then using the Equation of State to produce PVT tables for use in reservoir simulations. PVTi contains facilities to allow you to import experimental data, fit the data to an Equation of State, and finally produce the PVT tables for reservoir simulation studies. The menu bar of the main PVTi window has the following options: 90 • "File" on page 92. • "Edit" on page 94 • "View" on page 95 • "Run" on page 96 • "Utilities" on page 97 • "Options" on page 97 • "Window" on page 150. • "Help" on page 150. Reference section Main PVTi window PVTi Reference Manual The PVTi main module The main module is shown in Figure 6.1. Figure 6.1 The main PVTi window Data Tree Log Window Equation of State Main Plot Window and Sub-plots The main window contains all the tools necessary for Equation of State model fitting. Basic features The Data Tree provides a view of the current project’s contents. Each fluid sample is identified with its experiments as sub-nodes in the tree. Likewise, each experiment has its observations as sub-nodes. The Log Window is updated with pertinent information relating to actions taken in PVTi. The Equation of State, upon which the current fluid model is based, is indicated in the status bar. The Main Plot Window and the Sub-plots provide an area for viewing project information graphically. PVTi Reference Manual Reference section The PVTi main module 91 File The File menu allows you to open, close and save PVTi project files (PVI files) and import sections from PVI files, and provides access to keyword export modules. Graph printing and plotting facilities are also available from this menu. • To open this menu, select File from the main PVTi window. The File menu consists of the following options: • New... This creates a new PVTi project. • Open... Opens a PVTi project (PVI) file. The complete file is read in and the most recent fluid model, experiment descriptions, observations, etc., are restored. For more information on the files PVTi creates see "Files created by PVTi" on page 93. • Close... Closes the current project. If the project is not empty you are asked if you want to save before closing. • Save... Saves the current PVI file, overwriting the previously saved project. • Save As... Saves the current project to a new PVI file. • Save (concise)... Saves a concise version of the current project containing the latest version of the fluid model plus any experiments and observations used in simulation and regression. No other information is saved, therefore information regarding regression variables or split/group sections will not be recorded by the Save (concise) option. • Export Keywords This provides access to the Keyword Export modules. Currently PVTi supports export for the ECLIPSE simulators and VFPi. See "Exporting keywords" on page 133. • Import This option allows a section from a previous PVI project or ECLIPSE data-set to be imported or a “concise” PVI project to be merged with the current project. The sections that can be imported here are SYSTEM,GROUP, SPLIT,SIMULATE and REGRESS. See "Reading the SYSTEM section from a PVI or DATA File" on page 98. • View PVI Section This opens a particular section from a PVI file and displays the keywords in a text editor. The sections that can be viewed this way are SYSTEM, GROUP, SPLIT, SIMULATE, and REGRESS. See "Displaying the SYSTEM section from a PVI file" on page 98. • Exit This exits PVTi. If there is an active project, you are asked whether you would like to save the project before exiting. 92 Reference section The PVTi main module PVTi Reference Manual Files created by PVTi All files in PVTi use the project name as their base name. PVTi creates the following files: • PVI file, for example ALL.PVI Input data file, although can be written by PVTi to save system specification or session. • PVP file, for example ALL.PVP Main printed output file. In interactive mode a prompt to write results to this file follows most operations. • PVO file, for example ALL.PVO Output file. Used for the output of ECLIPSE Black Oil, GI option (pseudo-compositional) or ECLIPSE 300 (equation of state) properties. • VEC file, for example ALL.VEC Vectors file. Contains vectors of plots performed in a PVTi section in a form suitable for inclusion into the GRAF program. • DBG file, for example ALL.DBG Debug file. This is only present if debug has been written. • MES file, for example ALL.MES Message file. A temporary file used throughout the program run to display results. This file is deleted when you quit the program. • LOG files, for example ALL.LOG Program Log File. This file exists in the startup directory of the program and contains a summary of keywords read in, tasks performed, etc. • NEW files, for example ALL.NEW New data file. This is a temporary file that holds the details of the new .PVI file. It is left in the working directory if the program does not shut down cleanly. Hint • The .NEW file contains all the changes made during the last session. If you change the file extension to .PVI you can use it to recover the session. REG files, for example ALL.REG Regress Module file. This temporary file holds details of the quantities plotted in the Regress module. It is left in the working directory if the program does not shut down cleanly. Only one project at a time can be in use with a single run of PVTi. To open another project, close the current project, either by selecting the File | Open option (the program prompts you save the session to a new .PVI file) or by using File | Close. Note PVTi Reference Manual Although only one project may be in use by the program, different sections of different .PVI files may be read in. Reference section The PVTi main module 93 Edit The Edit menu allows entry and editing of the fluid model, samples, experiments, observations and regression variables. 1 To open this menu, select Edit from the main PVTi window. The Edit menu consists of the following options: • Fundamentals... This opens the Fundamentals panel, See "Fluid Properties Estimation" on page 33. • Fluid Model This opens the sub-menu of fluid model editing options. • Equation of State... This opens the Equation of State selection panel. See "Equation of State" on page 100. • Components... This opens the component properties panel. See "Components" on page 101. • Binary Interaction Coefficients... This opens the binaries panel. See "Binary Interaction Coefficients" on page 104. • Volume Shifts... See "Volume shifts" on page 104. • Thermal Properties... See "Thermal properties" on page 104. • LBC Viscosity Coefficients... See "LBC Viscosity Coefficients" on page 104 • Split This opens the sub-menu of options for splitting fluid components. See "Splitting components" on page 105. • • • Constant Mole Fraction... • Whitson... • Multi-feed... • PNA Distribution Group... Samples. This opens the sub-menu of sample entry and editing options. • • Names... See "Sample names" on page 107. • Compositions... See "Sample compositions" on page 107. • Salinities... See "Sample salinities" on page 107. • Mix... See "Mixing samples" on page 108. Properties Estimation (FPE)... See "Fluid Properties Estimation" on page 33. • Experiments... See "Defining Experiments" on page 117. • Observations... See "Defining Observations" on page 122. 94 Reference section The PVTi main module PVTi Reference Manual View The View menu provides facilities for plotting and reporting. 1 To open this menu select View from the main PVTi window. The View menu has the following options: Samples: This option opens a sub-menu containing sample plot types. • • Phase plot. See "Sample phase plot" on page 109. • Fingerprint plot. See "Sample fingerprint plot" on page 108. • Ternary plot. See "Sample ternary plot" on page 110. • Observations... This allows you to plot an observations against calculated values, or any calculated values where corresponding observations do not exist. • Library. This option allows you to view the internal PVTi library. See "Library" on page 95. Library The properties of library components are preset by the program. To display the current list of library components select View | Library... Table 6.1 PVTi Reference Manual List of library components Mnemonic Name Mnemonic Name H2 O Water N2 Nitrogen H2 Hydrogen H2 S Hydrogen Sulfide CO2 Carbon Dioxide CO Carbon Monoxide C1 Methane C2 Ethane C3 Propane C4 Butane iC 4 Iso-Butane nC 4 Normal Butane C5 Pentane iC 5 Iso-Pentane nC 5 Normal Pentane C6 Hexanes C6 H6 Benzene C7 H8 Toluene C7 Heptanes C8 Octanes C9 Nonanes C 10 Decanes C 11 Undecanes C 12 Dodecanes C 13 Tridecanes C 14 Tetradecanes C 15 Pentadecanes C 16 Hexadecanes C 17 Heptadecanes C 18 Octadecanes C 19 Nonadecanes C 20 Eicosanes C 21 C21’s C 22 C22’s Reference section The PVTi main module 95 Table 6.1 List of library components (Continued) Mnemonic Name Mnemonic Name C 23 C23’s C 24 C24’s C 25 C25’s C 26 C26’s C 27 C27’s C 28 C28’s C 29 C29’s C 30 C30’s C 31 C31’s C 32 C32’s C 33 C33’s C 34 C34’s C 35 C35’s C 36 C36’s C 37 C37’s C 38 C38’s C 39 C39’s C 40 C40’s C 41 C41’s C 42 C42’s C 43 C43’s C 44 C44’s C 45 C45’s Note For components C 6 to C 45 , the properties stored in the internal library correspond to the “grouped” properties of Single Carbon Number Groups (SCN), [Ref. 5]. Obvious candidates for the pseudoisation of components for use in large regressions or compositional simulation are iso-butane and normal butane, and iso-pentane and normal pentane, into single butane and pentane components. A study of many PVT reports [Ref. 19] has shown that the typical ratios of iC4 : nC 4 , iC5 : nC 5 are 0.67:0.33 and 0.60:0.40 respectively. The library also contains two other components, with the mnemonics C4 and C 5 , whose properties are mole-weighted averages of the respective iso and normal component properties. Run The Run menu provides simulation and regression facilities. The following options are available: • Check Fluid System. This provides a consistency check of the current fluid, the results of which are posted to the log window. If there are a lot of fluid errors, the results are also displayed in a text window. • Save As Samples . If this option is turned on, any samples created by an experiment can be saved as additional project samples. • 96 Simulate Reference section The PVTi main module PVTi Reference Manual This simulates all active experiments and then display the simulation results in a text editor. PVTi has intelligent simulation, which means that the results of the last simulation run are stored, and if no change has been made to the experimental data the simulation run is not repeated, the results from the previous run being used. This keeps the time spent running simulations to a minimum. • Regression... This opens the Regression panel. See "Regression in PVTi" on page 126. Utilities The Utilities menu option provides access to miscellaneous information relating to the project and program set-up. • Units... See "Units..." on page 144. • Standard Conditions... See "Standard conditions..." on page 145. • Program This opens the sub-menu of program configuration options. • • Options... This opens the Options panel which mimics the OPTIONS keyword in the PVI file. See "Program options" on page 145. • Debug... See "Debug..." on page 150. Text Editor This opens the text editor used for displaying simulation results, etc. It can be used to view any ASCII file. Options This menu provides options related to the plotting of graphs. • Add New Graph... Adds a new graph to the existing plot windows. • Superimpose When the superimpose option is switched on, indicated by a tick next to the menu option, subsequent graphs are superimposed on the current main graph. • Tabulate... This option creates a table showing the values plotted in the current main graph. • Remove All This option deletes all graphs from the window. PVTi Reference Manual Reference section The PVTi main module 97 The fluid model Displaying the SYSTEM section from a PVI file Displays a RUNSPEC/SYSTEM section present in the current PVI file. 1 To display PVI data, select PVTi: File | View PVI Section | SYSTEM. Reading the SYSTEM section from a PVI or DATA File Reads data from a PVI or DATA file. You can use this option to load the equation of state, viscosity options and hydrocarbon system description from a PVTi PVI file or an ECLIPSE Compositional (E300) DATA file. Hint You can load the first two sections of a PVI file as a system specification, rather than using menu options. Additionally, you can choose to echo the contents of the whole PVI file to the current print file, PVP. Reading the PVT section from an E300 DATA file 1 PVTi: File | Import | ECLIPSE Compositional (*.DATA) and select the appropriate DATA file. PVTi searches for the required file and, if found, reads it looking for the number of EoS and Equilibration regions in the ECLIPSE model. The number of reservoir EoS regions is defined by the ninth entry of the TABDIMS keyword and the number of Equilibration regions is defined by the first entry of the EQLDIMS keyword. If the ECLIPSE model has just one of each region type then the program simply reads in the data. However if multiple EoS or Equilibration regions are found then the program displays a prompt specifying the numbers of each region found. You are asked to specify which EoS and/or Equilibration region they wish to read in. 2 Select the number of the EoS and /or Equilibration region you wish to load. Note EoS regions each have an EoS model defined within them that is an EoS plus a list of critical properties defined for each component. An Equilibration region is a group of cells where the initial pressure and saturation is defined. PVTi needs to know which Equilibration region to read in if there are any composition versus depth (specified by the ZMFVD or COMPVD keywords) tables in the ECLIPSE file. There is one table for each of the Equilibration regions. By specifying which Equilibration region to use this tells PVTi which table to read in. Reading the SYSTEM section from a PVI file 1 PVTi: File | Import PVI Section | SYSTEM and select the appropriate PVI file. PVTi searches for the required file and, if found, reads it looking for all occurrences of the required section. If there are no RUNSPEC or SYSTEM sections in the file then no further action is required. However, if one of more sections of the required type are found in the file, you must select which, if any, are required. The program displays a prompt specifying the number of sections found. 2 98 Select the section you wish to load. Reference section The fluid model PVTi Reference Manual Note If more than one section is found, the program offers the last section as the default, although you can read any of the sections. Hint If you are uncertain as to the contents of the selected section, use File | View PVI Section to display the section to the screen. The syntax of the external file is similar to that of ECLIPSE. The data file is free format, except for keywords, which must start in column 1. For further information on the keywords see "PVTi keywords" on page 167. An example of such a file for a trivial two-component CO2 -isoButane system is as follows: -----RUNSPEC section: specific number of components and the EoS ---RUNSPEC NCOMPS 2 / EOS PR / ------SYSTEM section: define hydrocarbon properties and composition ---SYSTEM ---Unit conventions UNITS METRIC ABSOL FRACTION / DEGREES KELVIN / ---Component names (library defaults) LNAMES CO2 IC4 / ---Overwrite default omega values by component OMEGAA 0.4572 0.4572 / OMEGAB 0.0778 0.0778 / ---Initial sample composition ZI 0.6 0.4 / ---Binary Interaction Coefficients BIC 2 1 1 0.13 / / ---------------END This defines the fluid, EoS etc. COMB, SIMULATE, REGRESS, BLACKOIL sections may now follow See examples in Appendix C Note the following points: PVTi Reference Manual Reference section The fluid model 99 • Any characters following ---- are taken as comments. The data is free format, apart from keywords which should start in column 1. You can split data over lines as required. The forward slash (/) characters terminate data for a keyword. • You can specify repeat counts for any item. For example 3 * 1.0 implies three values of 1.0. You can enter defaults by specifying a repeat count alone, such as 1*, or by the early termination of a data list with a forward slash (/). • You may enclose character data such as component or experiment names in quotes. This is optional and is only strictly required when the name contains embedded spaces or nonalphanumeric characters. Equation of State Hint The default Equation of State is the Peng-Robinson three-Parameter equation. This is suitable for most requirements, so generally you do not need to set the equation of state. This panel allows you to choose one of five main equations of state, to specify the required viscosity correlation, and to decide whether or not to activate editing of specific heat capacities. The equations of state are described in "Equation of state" on page 317; the viscosity options are described in "Viscosity correlations" on page 330 and in [Ref. 5], [Ref. 7] & [Ref. 41]. The available equations of state are: • Peng-Robinson • Soave-Redlich-Kwong • Redlich-Kwong • Zudkevitch-Joffe • Schmidt-Wenzel Choosing the Equation of State 1 PVTi: Edit | Fluid Model | Equation of State... This opens the Equation of State and Viscosity panel, which gives you radio buttons for selecting one EoS from the following list: 100 • PR: 2-Parameter Peng-Robinson • SRK: 2-Parameter Soave-Redlich-Kwong • RK: Redlich-Kwong • ZJ: Zudkevitch-Joffe • PR3: 3-Parameter Peng-Robinson • SRK3: 3-Parameter Soave-Redlich-Kwong • SW: Schmidt-Wenzel. 2 Select the appropriate equation of state. If you select either of the Peng-Robinson equations or the Schmidt-Wenzel equation, you must also select whether you wish to use the correction to the dependence of the Ωa upon acentric factor. The default is the modified (third-order in ω ) Peng-Robinson form. 3 Check the box for Yes, or leave it unchecked for No, as appropriate (see "Equation of state" on page 317). Reference section The fluid model PVTi Reference Manual Three-parameter extension of the EoS The three-parameter extensions of the EOS are: • PR3 - Peneloux et al. three-parameter EoS • SW - Schmidt-Wenzel EoS (implemented as a modified PR3) • SRK3 - Peneloux et al. three-parameter EoS. The PR3 EoS is the default setting. Hint It has been our experience that the Peneloux et al. three-parameter equations of state, PR3 and SRK3, generally give much better predictions of liquid properties and saturations. They also allow you an additional set of regression parameters, namely the component volume shifts, making for an easier match to measured data. Viscosity correlations The Lohrenz-Bray-Clark, Pedersen and Aasberg-Petersen viscosity models are available. Select the appropriate viscosity model. Note You can re-select the equation of state or viscosity correlation at any stage. However, the default EoS parameters for each component are dependent upon the EoS, and the program re-initializes these if you change the EoS. Alternatively you can manually reset the parameters to the default values at any time. Components PVTi: Edit | Fluid Model | Components... Fluid model components This option allows you to enter component names and properties. Use this option to enter new fluid components. You enter a mnemonic and a type, which determines how the program interprets the component. 1 Select the Names folder. 2 To enter a component, click in an empty index field. 3 Enter the mnemonic for the component and select its type. See "Component types" on page 102. 4 Click on Apply. 5 The other folders now have information in them: PVTi Reference Manual • Complete shows all the properties of all components • Library shows the properties that were retrieved from the internal library • User shows user-defined properties • Characterization allows definition of fluid-model properties by characterization. Reference section The fluid model 101 Component types Library The PVTi program checks this against the internal library of names. If this exists in the internal library, it adopts the internal description. If it does not recognize the mnemonic from amongst the set described in the previous section, you must re-enter the mnemonic name or respecify the component as a Char or User type, see below. User This option allows you to define components. Enter the required properties into the panel: critical pressure and temperature, acentric factors, etc. You should enter the components in order of increasing molecular weight, and nonhydrocarbons before hydrocarbons: Non-Hydrocarbons • H2 • H2 O • CO • N2 • H2 S • CO 2 Hydrocarbons • C1 • C2 • CN+ Hint By selecting PVTi: Run | Check fluid system the fluid is re-ordered into increasing mole weights. PVTi allows you to input a user component even if you know only the critical temperature and pressure. It calculates the other properties as follows: 102 • from T c and P c - Riazi-Daubert. For further information see [Ref. 30] and [EQ 8.11], [EQ 8.12]. • from T c and T b - Riazi-Daubert. For further information see [Ref. 30] and [EQ 8.11], [EQ 8.12]. • from T b , T b and Sg - Riazi-Daubert. For further information see [Ref. 30] and [EQ 8.33], [EQ 8.34]. • ω from P c , T b and T c - Edmister. For further information see [Ref. 30] & [EQ 8.10]. • P from Macleod and Sugden. For further information see [Ref. 14]. Tb Sg Mw Reference section The fluid model PVTi Reference Manual • Vc & Z c - Riazi-Dubert. For further information see [Ref. 12]. Use the Apply button to calculate the other properties of the component. Characterization If you give a characterization, you must generally specify at least two out of the following (these are specified in the Characterization folder): • molecular weight M w , • specific gravity S g , • normal boiling point temperature T b , • Watson characterization factor K w , • reference temperature K Hint If you have more than two of the set M w , S g , T b and K w , we recommend that you enter the best two first, as the order of entry decides which pair the program selects. For example, if you enter M w , T b and K w then the program uses M w and T b . Note It is possible to perform a characterization by entering just the molecular weight, whereupon the program estimates the specific gravity from a look-up of Single Carbon Number (SCN) groups. You can choose from the following correlations for estimating the physical properties and acentric factors: Critical properties • Kesler-Lee. See [Ref. 10]. • Cavett. See [Ref. 11]. • Riazi-Daubert. See [Ref. 12]. • Winn. See [Ref. 43]. • Pedersen. See [Ref. 43], [Ref. 41] and [Ref. 45]. Acentric factors • Kesler-Lee. See [Ref. 10]. • Edmister. See [Ref. 14]. • Thomassen. See [Ref. 30]. • Pedersen. See [Ref. 43], [Ref. 41] and [Ref. 45]. Note PVTi Reference Manual When reading in a file the critical volumes (Vc) and critical Z factors (Zc) for each component must satisfy the relation PcVc=ZcRTc (where Tc, Pc, R are the critical temperatures, critical pressures and universal gas constant respectively). If this is not the case then PVTi will alter the values of the relevant critical Z-factors in order that this relation is satisfied. Reference section The fluid model 103 Binary Interaction Coefficients This option enables you to enter the Binary Interaction Coefficients (BICs) for each component. 1 PVTi: Edit | Fluid Model | Binary Interaction Coefficients... This displays the Binary Interaction Coefficients panel. 2 Enter the Binary Interaction Coefficients for each component. 3 Alter the Cheuh-Prausnitz-A coefficient as required. 4 Click on Reset to return the interaction coefficients to default values. Volume shifts Note Volume shifts are only available if you use a three-parameter Equation of State. Use this option to enter the dimensionless volume shifts. The actual volume shifts in the equation of state are displayed beside them. 1 PVTi: Edit | Fluid Model | Volume Shifts... . This displays the Volume Shifts and Thermal Expansion Coefficient panel. 2 Enter the volume shifts for the required components. 3 Click on OK. Note If the "Temperature dependence for volume shifts" on page 147 option is set then you can enter a value for THERMX, the thermal expansion coefficient. Thermal properties Note You can only use this option if the program option "Specify/Calculate density and molar volume units" on page 147 is switched on. It can be switched on in the Equation of State panel (see "Equation of State" on page 100). Specific heat capacity coefficients and calorific values for each component are the thermal properties used in PVTi. 1 PVTi: Edit | Fluid Model | Thermal properties.... This opens the Thermal Properties panel. 2 Amend the thermal properties for the components, as required. 3 Click on OK. LBC Viscosity Coefficients Note LBC Viscosity coefficients are only available if you are using the LBC Viscosity model. Use the option to view or edit the LBC viscosity coefficients. 104 Reference section The fluid model PVTi Reference Manual 1 PVTi: Edit | Fluid Model | LBC Viscosity Coefficients.... This opens the LBC Viscosity Coefficients panel. 2 View or amend the coefficients as required. 3 Click on OK. Splitting components This menu allows for the automatic splitting of the plus fraction into a required number of subfractions for subsequent use in a large regression or for output to a compositional simulator such as the one in ECLIPSE. Splitting is also used to accommodate different plus-fraction properties for different fluid samples. This process is often known as a multi-feed split. This option allows you to input data for splitting the plus fraction. There are three methods available from this option for splitting the plus fraction, which must be the last component: • Constant Mole Fraction splitting (CMF) • Whitson • Multi-feed split or Semi-Continuous Thermodynamic (SCT) splitting 1 To choose the splitting method, select PVTi: Edit | Fluid Model | Split and select the splitting option. Constant Mole Fraction (CMF) 1 Specify the number of pseudo-components you require. The default is N frac = 3 . 2 Give the specific gravity and required sub-fraction split. By default, the program estimates the specific gravity of the plus fraction from the reference density, if one was given, and uses a constant mole fraction split of 1 ⁄ N frac . 3 Specify the Whitson Alpha Factor and the Whitson ETA factor, as required. 4 Enter the Critical Props. Correlation and the Acentric Props. Correlation. 5 Give the compositions of the pseudo-components. 6 Click on OK. Whitson or modified Whitson (Whitson) 1 Specify the first single carbon number (SCN) group to be included in the plus fraction split. For example, enter 7 if plus fraction is C 7+ . 2 Give the molecular weight, specific gravity and the mole fraction of the plus fraction. 3 Enter the number of pseudo-components to be used after the regrouping of the Whitson split. For example, N MCN = 3 . 4 Specify the Critical Props Correlation and the Acentric Props. Correlation. 5 Select the grouping technique. 6 Choose whether you wish to plot a fingerprint of the Whitson split fractions. 7 Click on OK. PVTi Reference Manual Reference section The fluid model 105 Multi-feed Split (also called semi-continuous thermodynamic (SCT) split) 1 Specify the number of pseudo-components for the split. This value must be between two and five. The default is two. 2 Confirm the default minimum mole weight in the plus fraction (Whitson η -parameter) or edit the data as required. 3 Confirm the default mole weight of the heaviest pseudo-component or edit the data as required. The default setting is twice the plus fraction mole weight. 4 Set the Critical Props. and Acentric Props. correlations. 5 Specify the group and the molecular weight of the sample’s plus fraction. 6 Amend the default names for the new components, if required. The default names are FRC1, FRC2, etc. Note Note that splitting is not necessarily the opposite of grouping. Splitting the plus fraction into two or more pseudo-components, followed by a re-grouping of those pseudo-components back into a single plus fraction, generally results in a different set of critical properties, etc., from those originally possessed by the plus fraction. PNA Distribution This splits all components heavier than the library C6 component into paraffinic (P), naphthalenic (N), and aromatic (A) components. This is done according to the method outlined in "The PNA distribution of heavy components" on page 394. The critical properties assigned to the PNA components are those described in "Critical properties of PNA species" on page 395. Group This menu allows for the automatic grouping of sub-fractions for subsequent use in a large regression or for output to a compositional simulator such as the one in ECLIPSE. This option allows you to choose components to group and perform the grouping operation. The default scheme for grouping is to group to the default sample ZI using the mole fraction weighting to group components. Other schemes of grouping include grouping by molecular weight and by mixing rule, see [Ref. 44]. Also the sample to group to can be changed to any in the defined set, or to an average of all samples. To group components, select PVTi: Edit | Fluid Model | Group... This displays the current component system, each component having an associated index. The first time you enter this option, all these indices are set to 0, indicating that they do not belong to any group. 1 To create a new pseudo component, give a new index of greater than zero to two or more components. 2 Select the Grouping Technique. 3 Give the group or pseudo-component a new component mnemonic, if required. Hint 106 Reference section The fluid model You can perform several groupings from the same original component description by specifying the new components with ascending indices, 1, 2, etc. PVTi Reference Manual 4 Click on the Update button to automatically display any of these new component names. 5 Click on the OK button to create the groups. Note Note that splitting is not necessarily the opposite of grouping. That is, splitting the plus fraction into two or more pseudo-components, followed by a re-grouping of those pseudo-components back into a single plus fraction, generally results in a different set of critical properties, etc., from those originally possessed by the plus fraction. Defining Samples Sample names 1 PVTi: Edit | Samples | Names... Defines sample names. Use this option to enter mnemonics for each component. You can enter more than one sample for later use; to do this, reference each sample by its mnemonic, of up to 8 characters. Note Note that the mnemonic for the default sample is “ZI”, for “z initial”. For alternative samples, you may specify a line of text to give additional information. For example: from different depths in the hydrocarbon column, a “saved” calculated composition from a simulation, etc. Sample compositions 1 PVTi: Edit | Samples | Compositions.... Enter the compositions for each defined sample. PVTi ensures that they all add up to unity. If a sample does not add up to unity, a message appears asking whether or not the program should redistribute the difference across the components. Sample salinities 1 PVTi: Edit | Samples | Salinities... This option allows you to enter sample salinities. If you have entered H 2 O as a component then use this option to add the salinity of each sample. Note PVTi Reference Manual This information is used in the MFLASH experiment in the "Simulation using PVTi" on page 117. Reference section The fluid model 107 Mixing samples This option allows you to form a new sample by mixing any two existing samples. You can enter the amount of each sample to mix either as the mole fraction of the second sample in the resulting mixture, or as a volume of gas of the second sample as a ratio to the volume of the first sample at its P sat or other pressure at the specified mix temperature. The latter case is useful when considering lean gas injections into an oil. The program produces the required mix provided that: • The two samples are different. • The amount of the second sample to mix is greater than zero. • The number of samples does not exceed the maximum allowed (50). • The name of the new sample is unique in the set. 1 To mix samples, select PVTi: Edit | Samples | Mix... This activates the Mix Samples panel. 2 Select the Mixing Type. 3 Choose the fluid samples you wish to mix. 4 Enter the new sample name. 5 Enter the temperature with its units, and the mole fraction. 6 If you are mixing by GOR, give the GOR and the pressure for GOR oil volume calculation 7 Click on OK. If the sample is mixed by recombination, the GOR is taken as the stock tank GOR, the conditions are separator conditions and the mixture is created such that the stock tank GOR matches the required value. Viewing samples Sample fingerprint plot This option allows you to generate fingerprint plots. This consists of plotting the logarithm of the component mole fractions against the component molecular weights. Hint 1 Fingerprint plots give an idea of the nature, that is condensate or volatile oil, of a given fluid sample. Providing a reasonable split of the Heptanes plus is available, then a condensate typically has straight line or down-turning slope proceeding towards the heavier fractions, whilst a volatile oil has an up-turning slope as it usually contains more heavy fractions. To generate fingerprint plots, select PVTi: View | Samples | Fingerprint Plot. This activates the Fingerprint Plot panel, which enables you to select the sample you require to be used for the plot from a drop-down panel. 2 108 Select the sample you wish to plot and click on Apply. An example of a plot is shown in Figure 6.2. Reference section The fluid model PVTi Reference Manual Figure 6.2 Fingerprint Plot Sample phase plot This option allows you to generate phase plots. This uses the equation of state model with the current fluid description to obtain the bubble point and dew point lines. Where the two lines meet is the critical point, at T = T c , p = p c . As part of the calculation process, an explicit calculation is made of the position of the critical point. You can choose how many quality lines (lines of constant vapor mole fraction) are required on the plot; this can vary between 0 and 9 (that is, 10%, 20%,..., 90%). 1 To generate phase plots, select PVTi: View | Samples | Phase Plot. This activates the Phase Plot and Quality Lines panel. 2 Select the sample you wish to plot. 3 Enter the number of quality lines (from 1 to 9). 4 Decide whether or not to plot the Hydrate formation line. 5 Click on OK. Hint A default phase plot (with one quality line) can be generated by simply dragging a sample name from the Data Tree and dropping it into the Main Plot Window. Note If depletion experiments or separators exist, they are plotted onto the phase plot too. PVTi Reference Manual Reference section The fluid model 109 Figure 6.3 Phase plot Sample ternary plot This option allows you to create a ternary plot for a particular sample. The ternary plot panel allows you to set: the sample to be plotted; the temperature and pressure for the plot; and the grouping of the fluid components so as to create three components for the ternary plot. 1 To generate a ternary plot, select PVTi: View | Sample | Ternary Plot 2 Select the fluid sample for plotting 3 Enter a temperature and pressure. 4 Select the component groupings and the names of the grouped components. Hint 110 Reference section The fluid model The default component groupings are: C1 and the non-hydrocarbons, C2-C6 and C7 and heavier hydrocarbons. This is typically the best choice, so you should only need to change the groupings from the default in special cases. PVTi Reference Manual Figure 6.4 Ternary Plot PVTi Reference Manual Reference section The fluid model 111 COMB - Compositional Material Balance Introduction Material balance checks provide an important tool in analyzing the quality of the data found in a PVT report. In PVTi, material balance checking is provided for Constant Volume Depletion (CVD) experiments, Separators by recombination, and the calculation of liquid and vapor recovery. Caution It is important to always examine PVT laboratory data for material balance errors. If the reported observations contain serious errors, these will be reflected in the fitted equation of state model. It is generally the case that for gas condensate and volatile oil samples, a constant volume depletion experiment (CVD) is performed as part of a laboratory analysis. Using material balance considerations, it is possible to calculate liquid compositions and hence K -values, molar masses, densities, etc. This can be very useful for two reasons: 1 With appropriate separator data, estimates of oil and gas recovery can be performed without recourse to an equation of state model. 2 The consistency checks provide a measure of the quality of laboratory data and consequently its value or otherwise in any subsequent regression analysis. Accessing material balance checks The Material Balance panel can be found by selecting the experiment in the project tree-view, right-clicking on it and selecting Material Balance... from the pop-up menu that appears. A technical outline of the methodology used in the Material Balance panels can be found in "Consistency checks and correlations" on page 308. There are three different Material Balance panels: one for depletion (CVD), one for separators, and one for Constant Composition Expansion (CCE). Each is described below. Material balance for Constant Volume Depletion (CVD) Experiments Right-click on the experiment in the project-tree and select Material Balance... from the popup menu. There are three buttons on this panel • Report • Plot This gives access to the full range of material balance diagnostic plots. For more details on these plots see "Consistency checks and correlations" on page 308. • 112 Modify Reference section COMB - Compositional Material Balance PVTi Reference Manual Report This option performs the material balance calculation and produces a report on any current problems with the fluid. Figure 6.5 Main display after performing material balance Plot Use this option to perform plots. The set of plots available from this option are: • Vapor composition (input) • Liquid composition • K -values • Produced moles • Vapor moles left in cell • Liquid moles left in cell PVTi Reference Manual (1): log( K ) versus pressure Reference section COMB - Compositional Material Balance 113 • Produced mass • Vapor compositions versus pressure • Liquid compositions versus pressure • Liquid volume in cell • K -values • Initial and recovered compositions • Final stage liquid composition • Calculated and correlated liquid density • Input and correlated vapor Z -factor (2): Hoffmann plot Figure 6.6 COMB module - vapor versus pressure plot Modify Use this option to modify data. Errors in the input data may become evident after you performed the CVD material balance. You can use this option to rectify these errors. You may consider changing the saturation pressure liquid saturations, Z -factors, etc. Hint 114 You can avoid calculated liquid mole fractions remaining in the cell by changing the composition of the feed stream (well stream) or one or more of the removed gas streams. Reference section COMB - Compositional Material Balance PVTi Reference Manual Negative calculated liquid moles Negative calculated liquid moles for a given component across a wide range of the sampled pressure stages probably indicate errors in the wellstream composition (which is usually a calculated recombination sample). Errors at a lesser number of stages or at just one or two specific stages probably indicate a measurement error on a given removed gas stream. In either case, you can modify the well stream or removed gas stream compositions by increasing (positive % or absolute value) or decreasing (negative % or absolute value) one or more component compositions. The program automatically re-scales the remaining (unmodified) compositions in the stream, according to their initial mole fraction, so that the total mole fraction for the stream sums back to 100%. If you require any of the compositions to remain fixed prior to the material balance calculation, type any character in the field immediately preceding the Modifier field for that composition. Separator recombination Use this panel to directly test the quality of recombinations. To open this panel, right-click on the separator experiment in the project-tree and select Material Balance... from the pop-up menu. Report Use this option to test recombinations. It generates the calculated and Standing's K -values and provides a report on the results. Testing combinations If sufficient volumetrics data has been entered in the previous item the recombined sample is calculated and output to the report and PVP file. The output details the calculated feed to either separator using the given values of GOR, oil density and liquid and vapor compositions from each separator stage and is printed together with the given feed composition for comparison. Plot Use this option to plot the recombination results. It produces a Hoffmann-Crump-Hocott plot, which gives a measure of the quality of the separator data. Constant Composition Expansion (CCE) recovery calculations Use this option to make estimates of the recovery of vapor and liquid from an initial reservoir pressure in excess of the saturation pressure defined in the CVD experiment. To open this panel, right-click on the CCE experiment and select Material Balance... from the pop-up menu. Note PVTi Reference Manual This option is only available if there are valid depletion and separators experiments in the project, in addition to the CCE experiment. Reference section COMB - Compositional Material Balance 115 Rel. Perm. Use this option to define liquid production. If oil is to be ‘produced’ in the recovery calculations (using the method of Reudelhuber Hinds, [Ref. 37]), you must enter two points on the plot of relative permeability versus total liquid saturation. Report Use this option to perform recovery calculations. It allows you to estimate recoveries of vapor and liquid. Plot Use this option to produce a plot of the gas and oil recovered as a function of pressure. 116 Reference section COMB - Compositional Material Balance PVTi Reference Manual Simulation using PVTi Introduction PVTi allows you to perform experiments on your defined hydrocarbon system. The experiments available include: • Flash calculation • Bubble and dew point determination • Simulation of laboratory experiments such as constant composition expansion, constant volume depletion, and differential liberation • Swelling tests • Separators • Variation of composition and pressure with depth • Vaporization tests • multiphase flash. • Wax appearance temperature • Asphaltene appearance pressure Note You can enter any experimentally determined observations available to compare with the output produced by the Simulate module, apart from the multiphase flash experiment. Defining Experiments 1 PVTi | Edit | Experiments... This opens the Define Simulate Experiments panel. 2 To add a new experiment select it on the Add menu. To edit an existing experiment, select its name from the drop-down list, which appears in the panel, and click OK. 3 Once an experiment has been created for definition or selected for editing, you will see a customizable form that can be tailored to suit your data. The information is entered in a number of folders. 4 In the first folder, General, you can select various single-valued pieces of information for entry. The required information is automatically selected and cannot be deselected, so an information line informs that this data is required. 5 The second folder, Observations, shows a table where you can customize column headings to match your observation data. If you are editing an existing experiment, the observations in the currently defined set are already shown as column headings. In this way you can match the data entry panel to your own data-set. If you forget to enter a required quantity (for example Pressure in a Differential Liberation experiment - see "Differential liberation" on page 119) PVTi warns you and does not create the customized entry form. PVTi Reference Manual Reference section Simulation using PVTi 117 6 The third folder, Components, allows you to determine whether you enter componentbase data or not. Typical options here are for Liquid Mole Fractions, Vapor Mole Fractions or K-values. 7 The fourth folder, Other, is used for miscellaneous observations that do not fit any of the other categories. Currently this folder is only used by the Constant Volume Depletion experiment for the Final Liquid Mole Fraction. When other experiments are being entered, this folder does not appear. 8 Click Apply. 9 A customized form is now created, with the same folders as described above. Now the folders contain data-entry fields and tables for observations. Once the data have been entered, click on Apply to submit the data and create or edit the experiment. 10 Finally, Close becomes active and can be used to close the panel Data requirements for the experiments Flash calculation For this experiment you must define the pressure and temperature of the flash. The program performs a stability test and establishes the number of phases present prior to the flash calculation. Note The gas-oil ratio reported by the calculation is defined as gas volume at standard conditions divided by liquid volume at flash conditions. The gas volume is obtained using a Z -factor of unity. Bubble point pressure For this experiment you must enter the temperature at which the bubble point is required. Note If the temperature is such that no bubble point can be found (above the critical temperature) the program returns a warning message. Dew point pressure For this experiment you must supply the temperature and choose between normal or retrograde dew points. The default dew point is retrograde. Note If the temperature is such that no dew point can be found (above the critical temperature) the program returns a warning message. Constant composition expansion For this experiment you must specify a temperature and a series of pressures. Additionally you must specify whether the fluid is oil or gas. You do not need to give a value at saturation pressure. 118 Reference section Simulation using PVTi PVTi Reference Manual Hint You can apply this experiment to a liquid (bubble point) or vapor (dew point) system. The program tests for both possibilities. It is also possible to perform a constant composition expansion on a true one-phase system (SIN), such as an (dry) injection gas above its cricondentherm. Note When obtaining relative volumes the program uses saturation volume as a normalisation volume, if one exists, or the volume at the highest pressure, if not. Constant volume depletion For this experiment you must specify a temperature and a series of pressures. You do not need to give a value at saturation pressure. Hint You can apply this experiment to a liquid (bubble point) or vapor (dew point) system. The program tests for both possibilities. It is not, however, possible to apply this experiment to samples that are above the cricondentherm. Note The relative volume reported by the program is the fraction of the cell filled with liquid at the end of the constant volume step, that is after the original volume has been restored by removing vapor. Differential liberation For this experiment you must specify a temperature and a series of pressures. You do not need to give a value at the bubble point. PVTi provides this pressure point. The program also provides automatically the last step in the differential liberation process, the reduction to standard conditions. However, the program does not provide the pressure point at standard pressure (usually 14.7psia) and at reservoir temperature and the user must enter this for the final stage. Note You may only apply this experiment to a liquid (bubble point) system. Hint The relative volume reported by the program is the ratio of the oil volume at each step to the oil volume at the final (standard conditions) step. Note There are alternative definitions of the GOR and the relative oil volume available using the program options "Definition of GOR in Diff. Lib." on page 148 and "Definition of Oil relative volume in Diff. Lib." on page 149. Swelling test A swelling test consists of adding increasing amounts of a lean gas to a reservoir fluid and determining the swelling of the mixture relative to the original fluid composition. For this experiment you must specify: PVTi Reference Manual Reference section Simulation using PVTi 119 1 The nature of the original fluid type, OIL or GAS. 2 The composition of the lean gas to be added. 3 The reservoir temperature. 4 A set of either mole percentages of gas in the mixture or GORs (the volume of gas at STC, that is 14.7 psi and 60 °F , per volume of oil at original saturation pressure or other specified pressure). Separators Separators consist of a set of connected equilibrium flashes at user prescribed pressures and temperatures. For this experiment you must specify: 1 The composition of the feed stream from the defined sample mnemonics. 2 A number of stages (up to seven) for which you must give a pressure and temperature. Additionally, you must connect the vapor and liquid outputs of each stream to some subsequent stream. The default routing is to connect the liquid output of stage (j) to stage (j+1), and to take the vapor output to stock tank conditions (as defined by the STCOND keyword or by the Standard Conditions menu option under OPTIONS). Note A stage output can be fed back to any previous stage though not back to the current stage. No stock tank stage is defined automatically, and whereas it is customary to quote vapor properties at stock tank conditions, liquid properties will be quoted at the “final stage” conditions. Therefore, if liquid properties at stock tank conditions are required, this should be the final (additional) stage which must be defined by the user. For example if we have a separator with 3 stages with the last stage being stock tank conditions, then a liquid FVF at stage 1 of the separator will be the volume of liquid divided by the final liquid volume (stock tank conditions in this case) after flashing the liquid feed of stage 1 through the remaining 2 stages of the separator chain. Hint The "Definition of Oil relative volume in Diff. Lib." on page 149 program option allows you to quote GORs as volume of gas at standard conditions per volume of stock tank oil as opposed to the default calculation of volume of gas at standard conditions per volume of separator liquid at separator conditions. The program can calculate oil formation volume factors, that is the volume of reservoir fluid at initial or bubble point conditions per stock tank volume (SRELV) and, by separator stage, volume of separator liquid at separator conditions per stock tank oil volume (ORELV). To use this option tick the box in the panel or use the FVFREF keyword in batch mode. Variation of composition and pressure with depth It is well known that composition varies with depth in a reservoir. For this experiment you must specify: 120 1 A reference sample composition (from the currently defined sample mnemonics). 2 A reference depth, pressure and temperature for the sample. 3 A set of depths above and/or below the reference depth, at which you wish the program to calculate the composition and pressure. Reference section Simulation using PVTi PVTi Reference Manual If during the increment up and/or down, either a genuine gas-oil contact is found or a transition from gas to oil (or vice-versa) without passing through a contact (a “critical” transition), then the program reports this depth. Note The assumptions made in the performance of this experiment, that there are no asphaltenes and that the reservoir is in thermal, gravitational and diffusive equilibrium, are probably not achieved in any real reservoir. However, despite these reservations, this is a useful test of the depth-variation of a particular fluid. Vaporization test This is a somewhat specialised test performed for gas-injection on reservoir fluids, but in fact it is rather similar to a swelling test. For this experiment you must specify: 1 The composition of the reservoir fluid and injection fluid from the currently defined sample mnemonics. 2 The reservoir pressure and temperature 3 The number of moles of injection gas to be added to the reservoir fluid. Multiphase flash calculation The inputs required for the multiphase flash experiment are the same as for the usual two-phase flash experiment ([Ref. 36]). For this experiment you must define the pressure and temperature of the flash. The program performs a stability test and establishes the number of phases present prior to the flash calculation. Note The gas-oil ratio reported by the calculation is defined as gas volume at standard conditions divided by liquid volume at flash conditions. The gas volume is obtained using a Z -factor of unity. Note also no facility currently exists for comparing these against observed values. Note If the sample you select for the experiment contains water, you should enter the salinity in the PROPS section. Saturation pressure calculation This is essentially the same as the bubble and dew point calculations. For this experiment you must enter the temperature at which the saturation point is required. The calculation is particularly useful if you have no a priori information about whether the saturation point is bubble or dew. Note PVTi Reference Manual In the case of the dew point, program returns the retrograde (highest pressure) dew point. Reference section Simulation using PVTi 121 Saturation temperature calculation For this experiment you must specify the pressure. Since there are generally two saturation temperatures (one from each side of the phase envelope), you must also specify which solution is required - lower or higher. Critical point calculation This is a convenient way of obtaining the critical point of a sample, without generating a full phase envelope. Enter the sample name for this experiment. First contact miscibility pressure calculation This calculation returns the lowest pressure at which the samples are directly miscible, regardless of the proportions in which they are mixed. The method used to determine the minimum pressure is described in the paper by Jensen and Michelsen, [Ref. 39]. For this experiment specify the temperature and the names of the two samples. Multiple contact miscibility pressure calculation This calculation determines the lowest pressure at which two samples (one oil, one gas) are always miscible (regardless of their relative proportions) after repeated contacts between them, when only one of the samples is affected at each contact. When the sample affected is the gas, this simulates a one-cell vaporizing drive. If the oil is affected each time, this mimics a one-cell condensing driveways method used to determine the minimum pressure. This case is also described in the paper by Jensen and Michelsen, [Ref. 38]. For this experiment, specify the temperature and the names of the two samples. Give the drive to simulate. Multiple contact test This experiment simulates the multiple contact test where a series of flashes are performed on mixtures of reservoir oil and injected gas. For this experiment specify: 1 The oil and gas samples 2 The temperature and pressure of the test 3 The drive to simulate (either condensing where the remaining oil is kept after each flash and contacted with the initial gas sample, or vaporizing where the remaining gas is kept after each flash and contacted with the original oil sample) 4 The fractions of remaining oil/gas to be contacted with the original gas/oil at each stage. Hint You can use this experiment in the REGRESS section. For further information see "Regression in PVTi" on page 126. Defining Observations Observations can be defined at the same time as the experiment; see "Defining Experiments" on page 117. 1 PVTi: Edit | Observations... This opens the Define Simulate Observations panel. 122 2 Choose the index of the experiment 3 Select abbreviation for the observation to be entered Reference section Simulation using PVTi PVTi Reference Manual 4 Enter the data for this observation 5 If you are entering data for regression purposes, give weightings, either individual or global, for the observation types. The observations available vary with experiment type, but will be from the following set: Table 6.2 Observation data Abbreviation Observation Liquid Z-Factor Liquid Z -factor Vapor Z-Factor vapor Z -factor Liquid Density Liquid density Vapor Density Vapor density Liquid Mol. Wght. Liquid molecular weight Vapor Mol. Wght Vapor molecular weight Liquid Visc. Liquid viscosity Vapor Visc. vapor viscosity Liquid Sat. Liquid saturation Vapor Sat. Vapor saturation Vapor Mol. Frac. Vapor mole fraction Sat. Pressure Saturation pressure: gas - p dew , oil - pbub Sat. Temperature Saturation temperature: not currently available Gas-Oil Ratio GOR: SEPS - gas (STC)/oil (stage/STC); DL gas (STC)/oil (STC/ p sat ) Relative Vol. Relative volume (SWELL = swelling factor) Total Gas-oil ratio Cumulative separator GOR: (Gas at STC/final stage Oil) Ternary Plot Ternary Plot (Multi-Contact Test and plotting only) Mole. wght. plus Mole weight of plus fraction (COMB Mat. Bal.) Rel. oil sat. Relative oil saturated volume ( B o ( p bub ) in DL) K Values K -values Liquid mol. frac. Liquid mole fraction Vapor mol. frac. vapor mole fraction Total mol. frac. Total mole fraction Spec. grav. plus Specific gravity of plus fraction (COMB Mat. Bal.) Moles Recov. Moles recovered from depletion experiment (CVD,DL) Liquid mol. vol. Liquid molar volume (specific volume) Vapor mol. vol. vapor molar volume (specific volume) Final mol. wght. liq. plus Mole weight of liquid plus fraction (COMB Mat. Bal.) Final spec. grav. liq. plus Specific gravity of liquid plus fraction (COMB Mat. Bal.) Final liq. mol. frac. Liquid mole fraction of final stage of CVD (COMB Mat. Bal.) PVTi Reference Manual Total rel. vol. Total (oil and gas) relative volume (DL) Oil rel. vol. Oil relative volume (DL, SEPS, vapor) (also see RVSAT) Gas Gravity Gas gravity (Differential Liberation) Reference section Simulation using PVTi 123 Table 6.2 Observation data (Continued) Abbreviation Observation Gas FVF Gas formation volume factor (DL) Gas Vol. Ext. Gas volume extracted (at STC) (DL) 2-phase Z Two phase Z -factor (CVD) Oil rel. FVF Oil FVF from p init ⁄ p bub to p stock (SEPS) Note Note that not all the observed data types are available for all experiments. Running a simulation Note 1 Simulations are automatically run on creation, so the results are immediately available. PVTi: Run | Simulate When the simulation is complete the program displays a text module detailing the success or otherwise of the runs. The PVTi main display window showing the experiment results will resemble the following: CCE : Constant Composition Expansion Soave-Redlich-Kwong (3-Parm) on Z1 Lohrenz-Bray-Clark Viscosity Correlation Density units are KG/M3 Viscosity units are CPOISE Surface Tension units are DYNES/CM Specified temperature Deg K 377.5944 Liq Sat calc. is Vol oil/Vol Fluid at Sat. Vol ------------------- ----------------------- -----------Rel Volume Vap Mole Frn Pressure Inserted ----------------------- -----------BARSG Point Observed Calculated Calculated ------------------- ----------------------- -----------344.739 0.9189 0.9485 310.265 0.9278 0.9565 275.791 0.9379 0.9652 241.317 0.9492 0.9750 199.948 0.9623 0.9882 193.053 0.9651 0.9906 186.159 0.9681 0.9930 179.264 0.9711 0.9955 Hint 124 -----------Liq Density -----------Calculated -----------682.4368 676.7593 670.6133 663.9241 655.0453 653.4620 651.8460 650.1961 PVTi recognizes which experiment simulations are up to date and then only performs necessary calculations. This means that to view the simulation results you should always use PVTi: Run | Simulate. Reference section Simulation using PVTi PVTi Reference Manual Hint If you click on an experiment in the sample-tree using the right mouse button, and select Report... from the drop-down menu, you can see the report for that experiment on its own. Plotting simulation results In addition to the simulation results tables, the results of simulations can be plotted. There are two ways to do this. Firstly, to view the comparison between the simulated results and the observations, simply drag the appropriate observation from the Data Tree and drop it into the Main Plot Space. Secondly, you can use the observation editor to plot any simulated quantity, not just those for which there are observations. For information on the observation editor see "Defining Observations" on page 122. PVTi Reference Manual Reference section Simulation using PVTi 125 Regression in PVTi Introduction Performing a regression To perform a regression you must specify: • The experiments to be used in the regression. You can choose from the experiments mentioned in "Defining Experiments" on page 117. • The weighting for the observations associated with those experiments. You can use most of the observations given in a laboratory experiment as observations to match against predicted data. • The Equation of State parameters you wish to vary to match predicted to observed quantities. Most of the Equation of State parameters are available as regression variables. Note The time taken for the regression operation rises rapidly with the number of variables chosen, and the use of the minimum possible set is suggested. That said, any combination of critical point data, Ωa and Ωb values, acentric factors, binary interaction coefficients, δ ij and volume shift parameters (if the PR3 or SRK3 forms for the Equation of State are being used) may be chosen to be modified. There is a maximum total of 50 regression variables. Regression function The regression function to be minimized is the normalized root mean square (RMS) error of predicted experiment results to the given (weighted) observed experiment results. See "Details Folder" on page 131 for a description of the RMS value used. Note In order to run the regression, there must be at least as many observations as chosen regression variables. Regression Panel 1 To open the Regression panel select PVTi: Run | Regression... 2 Use this menu to set up and perform regression. To open this menu, select PVTi: Edit | Regression Variables The Variables section has the following options: • Normal (component properties and BICs) Normal variables are individual fluid component properties and binary interaction coefficients. For further information see "Defining regression variables..." on page 127. 126 Reference section Regression in PVTi PVTi Reference Manual • Special (MW of characterized components etc.) The special variables available depends on the project settings and the fluid model properties. Typical special variables are the mole weight of the plus fraction or the CheuhPrausnitz coefficient for binary interaction coefficients. See "Setting special variables" on page 128. • PVTi Selects This sets up the regression variables according to the rules given in "Physical selection of regression parameters" on page 386. The two buttons are: • Variables... Opens a panel specific to the selection of variable types (see above). • Limits... Sets limits on regression variables. For further information see "Setting regression limits" on page 129. Report The Report section has the following buttons: • Regression: Opens the Regression Report panel. See"Regression Report" on page 130. • Simulation: Opens the simulation report of all experiments. Regress The Regress section is for running regressions. The buttons in this section are: • Run: Perform regression. For further information see "Performing a regression" on page 130. • Accept / Reject: Accept or reject the last regression. For further information see "Accepting or reject regression results" on page 130. Additional Information Defining regression variables... Use this option to define/re-define the set of variables for use in the regression. There may be two sets of variables available for use in regression, depending on the state of the "Program options" on page 145 and whether modified Whitson splitting (SCT) has been used on the plus fraction. The two sets are denoted normal and special. • The normal variables are the component dependent ones, that is variables such as critical properties, acentric factors, etc. • The special variables are system-wide or multi-component variables such as the thermal expansion coefficient or the Cheuh-Prausnitz A -factor for binary interaction coefficients. Setting normal variables There are two panels for setting normal variables. Use the first panel to define the EoS parameters, the parameters for the LBC viscosity correlation and the volume shifts for the currently defined N c components. PVTi Reference Manual Reference section Regression in PVTi 127 1 Enter integers for the EoS parameters: a Pc b Tc c ω d Ωa Hint 2 Enter integers for the LBC viscosity parameters: a Ωb b Vc c Vc Hint 3 If you wish to vary a given EoS parameter, say T c , of two or more components as separate independent quantities, you should give them different values. For example 1,2,..., etc. If you wish to vary the parameters as one or more groups of variables, you should give the required group members the same integer. This may be particularly useful when trying to vary V c values to match to viscosity data using the LBC correlation, for example. Enter integers for the volume shifts: a PR3 b SRK3 Note All of these data fields can take an integer value, 0,1,2,..., and so on. The default of zero (or blank/null field) implies that the particular component’s EoS parameter is not to be used in any subsequent regression. Use the second panel to define the status of the lower half of the (symmetric, zero-diagonal) matrix of binary interaction coefficients. Note Note that the rules regarding choice of groups for binary interaction coefficients are slightly different in that groups may be specified down columns or along rows of the lower half matrix but not both. Setting special variables 1 128 Give the following information: a Plus fraction mole weight. b Plus fraction skewness. c Thermal expansion coefficient for volume shifts. d Pre-multiplying coefficient for Cheuh-Prausnitz BICs. e Characterization for SCT-splitting. Reference section Regression in PVTi PVTi Reference Manual Note Note that the mole weight and skewness variables apply on a sample-by-sample basis, therefore there must be the appropriate number of measurements defined to allow this option to be used. Setting regression limits Use this option to change the regression control parameters. 1 Select PVTi: Edit | Regression | Limits... This opens the Regression Controls panel where you can set the following options. Maximum number of iterations The maximum number of successive iterations that the regression uses. Enter the maximum number of iterations. The default value is 10. Maximum step limit The maximum amount if change allowed in the regression vector during successive iterations. Give the maximum step limit, if required.The default value is 0.100000. For further information see "Regression" on page 348. Minimum step limit The minimum amount of change allowed in the regression vector during successive iterations. Enter the minimum step limit, if required. The default is 0.000010. For further information see "Regression" on page 348. Regression target The regression target is the size of the objective function at which the regression terminates as having achieved a match of calculated to observed values. Enter the regression target. The default value is 0.000001. Hint Normally you do not need to change any of these limits, except for the maximum number of iterations (which might be reduced, especially for larger problems) and the limits on some variables (for example to prevent violation of monotonicity relationships). Note For all variables specified in the regression the program displays the lower and upper limits. Variable VAR1 VAR2 : : PVTi Reference Manual Lower limit VAR1lo VAR2lo : : Upper limit VAR1up VAR2up : : Reference section Regression in PVTi 129 Note For all the equation of state parameters, except the acentric factor and binaries, these lower and upper limits are scaled (to unity) variables, with default settings of 0.5 and 1.5. That is, the program allows the variable to decrease/increase by up to 50% before it terminates the regression. Running a regression Use this option to perform regression. Note This option is only available if you first define a set of experiments, observations and variables. Performing a regression 1 PVTi: Run | Regression The program performs the regression after first checking that there are at least as many regression points as variables. Hint The results of regression can be viewed in the Sensitivity Analysis panel. See "Regression Report" on page 130. Accepting or reject regression results Use this option to accept or reject the last regression The program holds the regressed system in memory. This allows you to examine the plots and experimental output and decide whether you wish to accept or reject the regression. Accepting/rejecting a regressed system 1 Examine the plots and experimental output 2 PVTi: Run | Regression | Accept/Reject 3 Accept or reject the regression as appropriate. Regression Report The regression report contains detail of the current fit between the model and the observations. Also use this option to display the sensitivity matrix, that is the sensitivity of the program’s predictions to each of the given regression variables. This panel also gives detailed descriptions of the current fit and the conditioning of the regression problem. All the information required to develop a mathematically sound regression problem is available through this panel. The hints provided in this section help you interpret the wealth of information contained within the folders of this panel. Hint 130 Reference section Regression in PVTi In any regression, having a few very sensitive parameters is preferable to having hundreds of insensitive ones. Always look for parameters that can be discarded. This is called conditioning the problem - an ill-conditioned problem is difficult to solve. PVTi Reference Manual Details Folder The first folder, Details, shows the current fit. The numbers at the top of the folder show the Total (normalized) RMS fit and the Weighted (normalized) RMS fit. Hint The RMS values in PVTi are normalized (the difference between the observed and calculated values is divided by the observed value) so that, for example, pressures (which could be thousands of psi) are treated similarly to saturations (which are between zero and one). To calculate the weighted RMS, each normalized difference is multiplied by the assigned weighting. The default weight is 1 and so, initially, the two RMS values are the same. The remainder of this first folder shows the observations, their weighting in the regression, and the percentage difference between the observed and calculated values. Modifiers folder The second folder, Modifiers, shows the selected regression parameters, the minimum and maximum allowed values for each modifier, and the percentage change made to the modifier during regression (initially this is zero as no regression has been run). Sensitivities folder The Sensitivities folder shows the sensitivity of each observation to changes in each regression variable. Hint A large sensitivity indicates that changing that regression variable has a large effect on the fit to that observation. Likewise, consider discarding regression variables to which the observations are insensitive, since a large modifier is needed to obtain a fit and, in general, large modifications lead to unrealistic fluid models. Hessian folder The Hessian matrix is a good indication of the conditioning of the inversion problem (regression). Hint In a well-conditioned problem the leading diagonal of the Hessian matrix is dominant. Specifically, look at an element on the leading diagonal. If it is larger than the other values in that row (or column) of the Hessian, then it indicates that the regression is likely to succeed. Covariance folder The Covariance matrix shows the likely scale of variation in the regression variables that will occur during regression. The larger a value, the less well-determined the value of the regression variable will be. PVTi Reference Manual Reference section Regression in PVTi 131 Correlation folder The Correlation matrix is very important as it can indicate links between regression variables that are not obvious on first inspection. If two variables are strongly correlated (correlation close to 1), they both move the fit in the same direction; and so changing one is similar, in effect, to changing the other. If two regression variables are strongly anti-correlated, changing one has the opposite effect to changing the other. This latter case can cause a difficulty in regression as the two variables could be changed an unlimited amount in opposite directions without having a noticeable effect on the fit. Hint 132 Reference section Regression in PVTi Look at off-diagonal elements in the correlation matrix. If any are close to 1 or -1, consider removing one of the two regression variables that are correlated. This improves the likelihood of a good final fluid model being created. (If the variables are of the same type, for example if they are both Tcrit, you could consider combining them into a single regression variable.) PVTi Reference Manual Exporting keywords General information PVTi can be used to generated output for ECLIPSE BlackOil, ECLIPSE Gi option, ECLIPSE Compositional, ECLIPSE Thermal, VFPi and the API Tracking option in ECLIPSE BlackOil. The Export modules are used to produce models for the ECLIPSE simulators (see "Output for ECLIPSE simulators" on page 354 for background information). You can generate data files for exporting to ECLIPSE BlackOil , ECLIPSE Compositional, ECLIPSE Thermal, API Tracking and VFPi from PVTi. To open this menu, select PVTi: File | Export. The Export menu has the following options: • ECLIPSE Compositional Fluid Model... See "Export for ECLIPSE Compositional" on page 133. • ECLIPSE Thermal Fluid Model... See "Export for ECLIPSE Thermal" on page 134. • API Tracking option in ECLIPSE BlackOil... See "Export for API Tracking option in ECLIPSE BlackOil" on page 134. • Oil reservoir... See "Export Oil Reservoir" on page 135. • Gas reservoir... See "Export Gas Reservoir" on page 135. • Equilibration... See "Export Equilibration" on page 136 • Water... See "Export Water" on page 136. • VFPi Use this option to generate VFPi tables. For further information see "VFP module" on page 138. Export for ECLIPSE Compositional Description This panel exports the fluid model as keywords suitable for the ECLIPSE Compositional PROPS section. Units Allows you to export in the ECLIPSE unit set of choice. Sample If a sample is selected, it will be exported in the ZI keyword. PVTi Reference Manual Reference section Exporting keywords 133 Reservoir temperature This is exported in the RTEMP keyword. Export for ECLIPSE Thermal This panel exports the fluid model as keywords suitable for the ECLIPSE Thermal PROPS section. Sample The sample for which the keywords will be exported for. Number of Flashes to be Performed This number is used when calculating the coefficients of Crookston’s equation. You an usually leave this set as the default value of 20. Max/Min Pressure/Temperature You are recommended to enter the maximum and minimum values of pressure and temperature for your reservoir. Export Crookston Coefficients If the box is ticked then the coefficients of Crookston’s equation will be exported. If not then Wilson’s formula is used to calculate K-values. Units Allows you to export in the ECLIPSE unit set of choice. A detailed explanation of the workflow required for this export option is described in the "Compositional Data for ECLIPSE Thermal" on page 366. For a technical review of PVTi’s export facility for ECLIPSE Thermal see "ECLIPSE Thermal Export Module" on page 401. Export for API Tracking option in ECLIPSE BlackOil This panel can be used to export a series of black oil tables suitable for use with the API Tracking option in ECLIPSE BlackOil. Set of Fluid Samples Select which set of fluid samples to export the black oil tables for. Properties Keyword This sets the keywords that are exported, for example Live Oil (PVTO) and Dry Gas (PVDG). Hint All the keywords are described in the "ECLIPSE Reference Manual". Write Gas Tables for each Sample? If exporting the PVDG (dry gas) or PVTG (wet gas) tables then you can specify whether to write out a gas table for each sample. Often a table for each sample is only required for the oil keywords in ECLIPSE. If No is selected then PVTi exports a gas table for the sample in the list with the median vapor density at surface conditions. 134 Reference section Exporting keywords PVTi Reference Manual Plot Results? You can tell PVTi not to plot the tables if you wish. PVTi only has room for 8 plots so if there are many samples in the list then it may be useful not to plot the tables. Write Values to Double Precision? You can ask for full double precision values if you wish, but the table columns may not be fully aligned if this option is used. Separator Experiment You can select a separator in your project if you wish instead of the default standard conditions separator (usually 14.7psia and 60F). Table Generation Method The algorithm used to generate the black oil tables. See "Output for ECLIPSE simulators" on page 354. Units Allows you to export in the ECLIPSE unit set of choice. Export Oil Reservoir This panel exports keywords from a Differential Liberation experiment (that is, for an oil reservoir). The keywords are suitable for the ECLIPSE BlackOil and ECLIPSE Compositional PROPS section. Units Allows you to export in the ECLIPSE unit set of choice. Properties Keyword This sets the keywords that are exported. Hint All the keywords are described in the "ECLIPSE Reference Manual". Write Values to Double Precision? You can ask for full double precision values if you wish. Separator experiment If creating tables for ECLIPSE BlackOil, the output from the Differential Liberation can be passed through any separator. The default is to use a single stage at standard conditions (that is, a stock-tank only - normally 14.7 psia, 60F). Table generation method See "Output for ECLIPSE simulators" on page 354. Export Gas Reservoir This panel exports keywords from a Constant Volume Depletion experiment (that is for a gas reservoir). PVTi Reference Manual Reference section Exporting keywords 135 The keywords are suitable for the ECLIPSE BlackOil and ECLIPSE Compositional PROPS section. Units Allows you to export in the ECLIPSE unit set of choice. Properties Keyword This sets the keyword that is exported. Hint All the keywords are described in the "ECLIPSE Reference Manual". Separator experiment If creating tables for ECLIPSE BlackOil, the output from the Constant Volume Depletion can be passed through any separator. The default is to use a single stage at standard conditions (that is, a stock-tank only). Table generation method See "Output for ECLIPSE simulators" on page 354. Injection fluid For the Gi option only, this provides the injection sample to be used in creating the pseudocompositional keywords. See "Pseudo-compositional tables for ECLIPSE GI option" on page 360. Export Equilibration This panel exports keywords from a Composition versus Depth experiment. The keywords are suitable for the ECLIPSE BlackOil INIT section and ECLIPSE Compositional PROPS section. Units Allows you to export in the ECLIPSE unit set of choice. Properties Keyword This sets the keyword that are exported. Hint All the keywords are described in the "ECLIPSE Reference Manual". Separator experiment If creating tables for ECLIPSE BlackOil, the output from the Composition versus Depth experiment can be passed through any separator. The default is to use a single stage at standard conditions (that is, a stock-tank only). Export Water Description This panel exports water properties. 136 Reference section Exporting keywords PVTi Reference Manual The keyword PVTW or PVTWSALT can be exported for the ECLIPSE simulators. The keyword Hint All the keywords are described in the "ECLIPSE Reference Manual". WATPVT is described in the "VFPi User Guide". Units Allows you to export in the ECLIPSE Unit set of choice. Reservoir temperature This sets the reservoir temperature to be used in generating the keywords. Reservoir pressure See above. Dissolved natural gas If this option is checked, the properties account for the presence of dissolved gas in the water. Brine If this option is checked, salt concentration(s) can be accounted for. VFPi If this option is checked, the exported keyword will be WATPVT. The low temperature and low pressure fields become active, these values correspond to the lower values to be used in the flow table (for example, the top of the pipe). For more information see "Water properties" on page 362. PVTi Reference Manual Reference section Exporting keywords 137 VFP module Introduction The VFP module generates blackoil tables for VFPi. To open this menu, select PVTi: File | Export | VFPi from the main PVTi window. Figure 6.7 The VFP module The VFP module has the following options: • File This option allows you to read and display data from the PVI file. For further information see "File" on page 139. • Edit This option allows you to add a new graph and copy items to the clipboard. • View This option allows you to control the appearance of the plot workspace. • 138 Define Reference section VFP module PVTi Reference Manual This option allows you to define experiments and the method of calculation. For further information see "Define" on page 141. • Generate This option allows you to generate tables. For further information see "Generate" on page 142. • Options Allows the modification of the plot workspace. • Help Gives you access to the on-line help for this module. VFP toolbar The module toolbar contains the following buttons: Display section from PVI file. Use this option to display VFP sections from the PVI file. For further information see "Display VFP section from PVI..." on page 140. Read section from PVI file. Use this option to load VFP sections from the PVI file. For further information see "Read VFP section from PVI..." on page 140. Experiments Use this option to define VFP experiments. For further information see "Experiments..." on page 141. Generate. Use this option to select the method of generation for the VFPi blackoil tables. For further information see "Method" on page 142. Simulate Use this option to generate the tables. For further information see "Perform" on page 142. View results Use this option to review the tables. View plots Use this option to view plots of the tables. For further information see "Plot" on page 143. File Use this menu to read and display VFP sections from a PVI file. The File menu has the following options: PVTi Reference Manual Reference section VFP module 139 Display VFP section from PVI... Use this option to display a VFP section from the current PVI file. Displaying VFP sections 1 Select VFP | File | Display VFP section from PVI... . 2 Select the VFP section. Read VFP section from PVI... Use this option to read data from a PVI file. You can use this option to load all or part of the data required for the VFP section. Additionally you can choose to echo (the contents of the whole PVI file to the current printfile, PVP. Loading PVI data 1 Choose VFP | File | Read VFP section from PVI... and select the appropriate PVI file. PVTi searches for the required file, and looks for all occurrences of the required section. If it finds more than one section of the required type in the file, you must select which section you wish to read. The program displays a prompt specifying the number of sections found. 2 Select the section you wish to load. Note If the program does not find a VFP section in the PVI file it produces an error message and stops processing. Print preview Previews the printed plot in the main module area. Print layout Allows you to set the text styles and sizes for printing. Print setup Sets up the printer specifications. This option is specific to Windows. Print Prints the whole module print area, the main window and allows you to set the print type, for example color, postscript. Close Use this option to close the VFP module. To close the VFP module, select VFP | File | Close. Note 140 Reference section VFP module The data is not lost. If you reselect the module all data that was previously set is available. PVTi Reference Manual Define This menu allows you to set up experiments and the method of calculation. To open this menu, select VFP | Define. The Define menu has the following options: • Experiments... Defines experiments. For further information see "Experiments..." on page 141. • Method... Defines the method of calculation. For further information see "Method" on page 142. Experiments... Use this option to define experiments. Defining experiments 1 Select VFP | Define | Experiments... . This opens the Constant Composition Experiment panel. 2 Define a Constant Composition Expansion (CCE) experiment. This is a depletion experiment where the moles entering the wellbore must leave the wellbore. For further information on defining experiments see "Data requirements for the experiments" on page 118. Hint The first temperature you give for the CCE should be the highest temperature in the production string, which can safely be taken to be the reservoir temperature. The second temperature you give should be the lowest temperature in the production string, for example a sub-sea temperature of 4 °C . Note You do not need to give a saturation pressure as the program gives this data. It also calculates undersaturated properties for all pressures. See "Output for ECLIPSE simulators" on page 354 for further details 3 Define the separator conditions that take the reservoir liquid and/or vapor to surface conditions to define the various ratios in the blackoil tables. Note Note that to comply with the blackoil definition strictly, the last stage in the separator train should be at standard conditions. 4 Specify the composition of the injection gas using one of the currently defined sample mnemonics. 5 Give the gas-oil ratios in which the lean gas is to be added to the reservoir fluid. 6 Press OK. PVTi Reference Manual Reference section VFP module 141 Method Use this option to select the method of calculation. You can choose from Coats, or Whitson and Torp method. The default is the Whitson and Torp method Choosing the method of calculation 1 Select VFP | Define | Method... . This opens the Switch Method of Generation panel. 2 Choose the appropriate method. For further information on the Coats method, [Ref. 3], or the Whitson and Torp method, [Ref. 6], see "Output for ECLIPSE simulators" on page 354. Generate This menu allows you to generate blackoil tables for VFPi. To open this menu, select VFP | Generate. The Generate menu has the following options: • Perform Generates the blackoil tables. Perform Use this option to generate blackoil tables. Note You must define a depletion experiment and the separator configuration (which only need be a one stage default system to standard conditions) to generate the blackoil tables. Generating blackoil tables 1 Select VFP | Generate | Perform. This generates the blackoil tables OILPVT and WGASPVT. The program also writes gas, oil and water densities, at standard conditions, to the VFPi SURFDENS keyword. Note If the process is successful the program also writes the data to the PVO file which you can add to an VFPi input file. Note Note each set of tables is repeated twice, for the set of pressure nodes defined on the CCE experiment, at the specified high (reservoir) and low temperatures. Water properties 1 142 Click Yes when asked if you wish to generate water properties, using the VFPi keyword WATPVT. Reference section VFP module PVTi Reference Manual This opens a a series of data entry panels where you can enter the data necessary for the inbuilt correlations to generate the appropriate data. Plot Use this option to produce plots. Producing plots 1 Select VFP | View | Plot. You can generate any of the following plots: • oil formation volume factor, B o • gas formation volume factor B g • oil viscosity μ o • gas viscosity μ g • oil R s Help menu Gives access to help with PVTi. Help Opens the context-sensitive on-line help panel. PVTi Reference Manual Reference section VFP module 143 Utilities Introduction This menu allows you to change or redefine various program settings. It has the following options: • Units... This allows you to set unit types. For further information see "Units..." on page 144. • Standard Conditions... This allows you to set the standard temperature and pressure. For further information see "Standard conditions..." on page 145. • Program Option This allows you to change the program options For further information see "Program options" on page 145. • Debug... This allows you to set the debug flags. For further information see "Debug..." on page 150. Units... This option allows you to select various unit types. You can: • Choose the unit type within PVTi. • Choose the temperature unit type; this can be different from the one selected by the above. • Set mole fractions or percentages. • Select absolute or gauge pressures. For further information on the units see "Units" on page 409. Setting unit types 1 To define the units, select Utilities | Units. This opens the Set PVTi Unit Definitions panel. Each unit type is selected by clicking on the corresponding radio button. Choosing the unit type for PVTi Select from Metric, Field, Lab and PVT-Metric. Setting the temperature unit type Select the temperature unit type from Kelvin, Celsius, Rankine and Fahrenheit. Setting mole fractions or percentages Select the required option. Selecting absolute or gauge pressures Select the required option. 144 Reference section Utilities PVTi Reference Manual Standard conditions... This option allows you to set the standard temperature and pressure. Defining standard conditions 1 To set the standard conditions select Utilities | Standard Conditions.... This opens the Standard Conditions panel. 2 Enter the standard temperature. 3 Enter the standard pressure. 4 Click on OK. Program options This option allows you to set various program options. Various options which cannot be set elsewhere in PVTi have been collected together under this option. 1 To set the program options, select Utilities | Program Option. This opens the Set PVTi Program Options panel. You can set the following: Table 6.3 Set PVTi Program Options panel Program Option Available choices "Definition of Liquid Saturation in CCE" on page 146. Sliq = Vliq/Vsat See “Treatment of Volume Shifts” on page 146. Independent variables Sliq = Vliq/Vtot Dependent "Separator GOR Calculation" on page 147. Separator Conditions Stock Tank Conditions "Temperature dependence for volume shifts" on page 147 None Linear expansion only Polynomial correlations "Specify/Calculate density and molar volume units" on page 147 user units "Binary interaction coefficients for EoS" on page 147 Katz-Firoozabadi "Specific heat capacity coefficients and calorific values" on page 147 No Output of Values "Calculated compositions" on page 148 No save to samples gm/cc and cc/gm-mole Cheuh-Prausnitz Output Values to Screen/PVP Allow Optional Save to Samples "Component Library" on page 148 Katz-Firoozabadi Old PVTi Library "Experiment compositions" on page 148 Output to Screen/PVP No Output to Screen/PVP PVTi Reference Manual Reference section Utilities 145 Table 6.3 Set PVTi Program Options panel (Continued) Program Option Available choices "Experiment results" on page 148 Always Output to PVP Optionally Output to PVP Never Output to PVP "Plot vectors" on page 148 No Output to file Output to Graf .VEC files "Print file output" on page 148 A4 format 132 characters wide "Definition of GOR in Diff. Lib." on page 148 Normal No Last Stage Incremental Volume of Oil at Pbub "Definition of Oil relative volume in Diff. Lib." on Oil FVF = Voil(p)/Voil(stc) page 149 Oil FVF = Voil(p)/Voil(pbub) "Black oil table output" on page 149 All Data Truncation at Saturation Pressure "LBC viscosity coefficients" on page 149 Keep Fixed Allow Change when Regressing "Flash calculations" on page 149 E300 Flash Old PVTi Flash "Sample mole fractions when regressing" on page 149 Keep Fixed "Phase Plot Algorithm" on page 149 New Phase Plots Allow Change Old Phase Plots "Write Keywords for Batch Mode" on page 149 No Yes Definition of Liquid Saturation in CCE The definition of liquid saturation in the Constant Composition Expansion experiment varies from laboratory to laboratory. The standard definition is to quote liquid saturation as volume of liquid at pressure p per volume of fluid at saturation volume (usually referred to as the cell volume). However, some laboratories refer to Sliq as the volume of liquid at pressure p per the total volume of fluid at pressure p . 1 Select the appropriate option from the available list. Treatment of Volume Shifts Available options are Dependent and Independent. Dependent means that you cannot regress on the volume shifts. They are defined as a function of the other critical properties for each component and so if critical properties change, for example during a regression, then the volume shifts are dynamically altered to stay consistent with the new component data. 146 Reference section Utilities PVTi Reference Manual If you use the Independent option then you are allowed to regress on the volume shifts of the components. PVTi also de-couples the dependence of the volume shifts on the critical parameters so that a change in Tc, Pc, etc. does not effect a volume shift value. 1 Select the appropriate option from the available list. The default setting is the Dependent option. Separator GOR Calculation Some laboratories choose to quote separator liquid volumes at stock tank conditions, rather than the actual pressure and temperature of the separator stage at which the liquid is produced. 1 Select the appropriate option from the available list. The default setting is the volume quoted at the separator conditions. Temperature dependence for volume shifts The volume shift corrections applied to the three-parameter PR3 and SRK3 equations of state assume that the mis-match in predicted and measured liquid density at some reference conditions on a component-by-component basis can be used to correct volumes at all other pressures and temperatures. In an attempt to account for the known temperature dependence, two methods are available for modifying the volume shifts. You can modify the shifts by applying linear thermal expansion to all components, with an attempt at correction for molecular weight, or calculated for light components as a polynomial involving temperature, with heavy components being modified by thermal expansion, but without a correction for molecular weight. The methods are described in "Three-parameter equation of state" on page 321. 1 Select the appropriate option from the available list. Specify/Calculate density and molar volume units Overriding the current units convention, you may specify that liquid and gas densities should be output in units of gm/cc and molar volumes in cc/gm-moles. 1 Select the appropriate option from the available list. Binary interaction coefficients for EoS As an alternative to the BICs of Katz and Firoozabadi, the correlation of Cheuh and Prausnitz (see "Binary interaction coefficients" on page 337) can be used to calculate hydrocarbonhydrocarbon BICs. If selected, the pre-multiplying A - coefficient can be used as a special regression variable, especially useful for matching saturation pressures. 1 Select the BIC coefficients you wish to use. Specific heat capacity coefficients and calorific values The calculation of ideal gas specific heat in ECLIPSE Compositional can be accomplished by switching on this flag, which then outputs the coefficients used in the temperature-dependent expansion on a component-by-component basis. Calorific values of the components of the system are also output to ECLIPSE Compositional using this option. 1 Switch on the output of the coefficients and calorific values, if required. PVTi does not produce the coefficients and calorific values, by default. PVTi Reference Manual Reference section Utilities 147 Calculated compositions Compositions calculated during an EoS simulation of an experiment can be saved to be used later as samples for further experiments, phase plots, etc. This might be useful in swelling tests, separator calculations or estimating the variation of composition with depth. 1 Select the save samples option, if required. PVTi does not save these samples, by default. Component Library This option allows you to specify the component library to use. The choice is between the KatzFiroozabadi and the Oil PVTi Library. The Katz-Firoozibadi is the default and recommended choice. (Benzene and toluene are taken from Perry [Ref. 67].) Experiment compositions This option allows you to turn off lengthy output to the print file of liquid and vapor compositions calculated in experiments. 1 Switch off the output of the liquid and vapor compositions if they are not required. PVTi prints the liquid and vapor compositions to the screen and PVP file, by default. Experiment results On definition of fluid properties, completion of experiments, etc., you can optionally choose to write all the data to the PVP print file. 1 Select the appropriate output option. By default, PVTi always writes all the data to the PVP print file; however, you can choose to make this write optional or never done. Plot vectors For more advanced graphical manipulation of PVTi plots, you may choose to output data vectors to a file in GRAF user vector format. The vectors are written when the plots are performed. 1 Choose whether you wish to produce the vectors. PVTi does not produce these vectors by default. Print file output Use this option to determine the format of the print (PVP) file. 1 Select the appropriate option from the available list. PVTi uses A4 as the default paper size format for this file. Definition of GOR in Diff. Lib. This option allows you to alter the definition of the GOR calculation in a differential liberation experiment. Three alternative definitions are available: 148 • Normal where the last stage to standard conditions is removed with the volume of gas being normalized to the volume of oil at reservoir conditions • The GOR is defined in increments, that is, at each stage of the depletion process. • The GOR is the default GOR but normalized to the volume of oil at its bubble point pressure rather than at STC. Reference section Utilities PVTi Reference Manual See "Differential liberation" on page 340 for the precise definitions of these quantities. 1 Select the appropriate option from the available list. PVTi uses option 1 by default. Definition of Oil relative volume in Diff. Lib. This option allows you to define an alternative definition for the relative oil volume in a differential liberation experiment. When turned on, the option normalizes the volume of oil at each stage to the volume of initial oil at its bubble point rather than standard pressure. Refer to "Differential liberation" on page 340 for a precise definition of the alternative. 1 Select the appropriate option from the available list. Black oil table output Switching to the Truncation at Saturation Pressure option outputs and plots only the black oil table data relating to pressure values at the saturation pressure and below. If the default of All Data is used then for pressure values above the saturation pressure, PVTi swells the fluid with vapor in order to raise PSAT to the required value. 1 Select the appropriate option from the available list. PVTi outputs all data to the blackoil tables by default. LBC viscosity coefficients This option allows the coefficients used in the LBC viscosity correlation to vary when regressing to any viscosity observations. 1 Choose whether you wish to vary the coefficients. PVTi fixes the coefficients by default. Flash calculations This option allows the Flash and Psat algorithms to be changed from the default ECLIPSE Compositional algorithms to the old PVTi (pre-99B) algorithms. 1 Choose to use the old PVTi algorithms for Flash and Psat. Sample mole fractions when regressing This option allows you to vary mole fractions of components in any sample when using the special regression variables CHARMF and/or MIXING. Note This option must be set in the ON state for you to use these regression variables. You must have characterized and/or user components, or be mixing samples, for the variables to become of use. Phase Plot Algorithm This option allows the phase plot algorithm to be changed from the default New Phase Plots to the pre-2000A Old Phase Plots algorithm. 1 Choose to use the old pre-2000A phase plot algorithm. Write Keywords for Batch Mode This option allows a .PVI file to be prepared for use in batch by writing extra keywords. PVTi Reference Manual Reference section Utilities 149 1 Choose to instruct PVTi to write out the extra keywords required for use in batch mode. By default this option is disabled. This option cannot be saved, which means every time you open a project it is disabled by default. The reason for this is that when this option is enabled it writes many more keywords than is necessary in interactive mode. You could easily forget that a project had this option enabled when opening an existing project meaning that many more keywords than necessary would continue to be written to the PVI file. Debug... This option sets the debug flags. Note This is a programmer test facility to request additional information from the program at a debug level. You do not need to set one or more of the debug flags unless help is required in tracing an apparent anomaly. Monitor option This is a programmer test facility to trace the root of a problem in the program at a subroutine level. Note You do not need to need to set this flag ON unless asked to do so. Window This menu allows you to control the size and appearance of the program windows. To select this menu, select Window from the main PVTi window. Tile This puts all the visible windows into a “tiled” formation. Cascade This puts all the visible windows into a “cascade” formation. Minimize children This option minimizes all windows except the main PVTi window. Restore children This opens all minimized windows so that they are visible. Help This menu gives you access to the help for PVTi. To select this menu, select Help from the main PVTi window. 150 Reference section Utilities PVTi Reference Manual Help This opens the on-line help panels. ToolTips enabled The ToolTips provide a single line of text about each toolbar button when the mouse pointer is stationary over the icon. This option turns the ToolTips feature on and off. About PVTi -... This provides brief information on the program code version. Right mouse button menu Clicking the right mouse button on one of the buttons in the project tree displays a popup menu that provides short-cuts to some of the common operations used in PVTi. PVTi Reference Manual Reference section Utilities 151 Batch system and keywords This section focuses on the batch mode functionality of PVTi. First of all a general overview is given of the batch mode. The next section explains the new functionality for PVTi 2004A, which enables you to set up a batch mode file in interactive mode. The third section list all of the different keywords supported within the batch mode. The 3 sections are: • "General information" on page 152. • "Preparing Batch Mode Files in Interactive Mode" on page 153. • "Overview of all supported keywords in Batch Mode" on page 155. General information For the 2004A version of PVTi the batch mode has undergone a significant revamp. Over the last few years the user interface of PVTi has evolved rapidly and many of the PVTi sections are now no longer written out to the PVI file as they are no longer required when PVTi reads in a file. For example a BLACKOIL section is no longer written out by PVTi when black oil tables are exported using the user interface. Although they can be inserted into the file manually it was felt that a more user friendly way of constructing the .PVI files containing all the appropriate sections required for the batch mode was needed. The next section outlines how it is now possible to perform a workflow interactively in order for PVTi to be able to reproduce this workflow in batch mode at a later time. The way in which you run a file in batch mode has also changed. Pre-2004A you had to enter the keyword TESTCASE anywhere in the RUNSPEC section of the PVI file. You then launched batch mode the command line, for example using $pvti filename (if using a PC). This has changed for the 2004A release. It was felt that opening files and adding keywords and then remembering to remove them at a later data was cumbersome. The new way to run in batch mode is to launch PVTi from the command line and specify the word ‘-batch’ before the filename in the line command instruction. Hint To launch the file TEST.PVI to run in PVTi’s batch mode on a PC use the command ‘$pvti -batch TEST.PVI’. On a UNIX machine ‘@pvti -batch TEST.PVI’ runs the file TEST.PVI in batch mode. Sometimes users have more than 1 version of PVTi installed. It is also possible to specify which version of PVTi to use on the command line using the -ver command. Hint 152 On a PC, to specify the 2004A version of PVTi to run the file TEST.PVI in batch mode, use the command ‘$pvti -ver 2004a -batch TEST.PVI’. Reference section Batch system and keywords PVTi Reference Manual Preparing Batch Mode Files in Interactive Mode Overview As explained in the previous section this new functionality introduced for PVTi 2004A enables you to generate files suitable for batch mode using PVTi’s interactive mode. The idea is that you would go through a pre-defined workflow in interactive mode and then subsequently be able to make PVTi automatically perform this workflow in the batch mode. Note The workflow must be pre-defined. The batch mode is not designed to be able to reproduce workflows where you have been experimenting with a particular project. 1 Start PVTi in interactive mode with the file that you eventually wish to run in batch mode. 2 Save the file concisely by doing File | Save (concise).... This erases the history of any workflows stored in the file. 3 Open the Options panel using the File | Utilities | Program | Options.... 4 In PVTi 2004A a new option has been added at the bottom called Write Keywords for Batch Mode. Select Yes and then close the panel. 5 Perform the required workflow and, when finished, save the file (but not concisely) using the File | Save... option. Note 6 The file must not be saved concisely as this would erase all the history in the .PVI file that PVTi uses to reproduce your workflow in batch mode. The final task is to actually run the file in batch mode. To do this on a PC launch PVTi from the command line using the statement ‘$pvti -batch filename’ where filename is the name of your PVTi project, for example TEST.PVI. Note The word ‘-batch’ can be put after or before the filename but it has to be somewhere on the command line in order to tell PVTi to run in batch mode. When you are running in batch mode the program automatically sends printed output such as experiment simulation results to a print file with the same root name as the input .PVI file. For example, if the input file is CRUDE.PVI, the print file is CRUDE.PVP. See "PVI file" on page 155 for further information. In batch mode all the experiments are automatically simulated in the project by default. If any regression is to be performed in the batch mode then the experiment simulation is performed after this has been done. If keywords are exported for ECLIPSE during the batch run then .PVO files are created as normal, but they are named using a convention that is outlined in the next section. A file is also created called BATCH_OUT.PVI. This is a saved version of your project after all the steps in the workflow have been performed. It can be useful to have this file after the batch run has finished if the fluid model has changed (for example during regression) in your project during the course of the workflow PVTi Reference Manual Reference section Batch system and keywords 153 Constraints on the workflow In this new interactive approach to creating batch mode files there are constraints on the workflows that you can perform. However, despite these constraints, all of the commonly used functionality within PVTi is supported. Regression You are allowed a maximum of two REGRESS sections in the batch mode file. This is so that regression on both special and normal variables is possible. Any further regression sections are ignored by the batch mode. Splitting/Grouping You are allowed two GROUP sections and two SPLIT sections in the file. If there are REGRESS sections then one SPLIT and one GROUP section is allowed before the first REGRESS section and one SPLIT and one GROUP section is allowed after this REGRESS section. Export It is assumed that all exports would be performed at the end of the workflow. An unlimited amount of export sections (such as BLACKOIL, OUTECL3 sections) are allowed as long as they are after the last REGRESS section. Because multiple exporting is allowed a naming convention has been invented to stop PVTi just writing each exported .PVO file over the top off the last one that was written out. The naming convention depends on what kind of export is being performed: BLACKOIL If a BLACKOIL section has been read in the .PVI file then the naming convention of the .PVO file is “filename_samplename_experimenttype_keyword1keyword2.PVO” where: filename is the rootname of the project, samplename is the sample name used for the export, experimenttype is the type of depletion experiment used in the export, keyword1 is the name of the first keyword exported and keyword2 is the name of the second keyword exported. For example if the file CRUDE.PVI was used to export sample ZI based on experiment DL1 using Live Oil and Dry Gas keywords then the name of the produced file would be CRUDE_ZI_DLLIVEDRY.PVO. OUTECL3 If an OUTECL3 section has been read in the .PVI file then the naming convention of the outputted .PVO file is filename_samplename_FLUIDMODEL.PVO. APITRACK If an APITRACK section has been read in the .PVI file then the naming convention of the outputted .PVO file is filename_experimenttype_APITRACK.PVO. 154 Reference section Batch system and keywords PVTi Reference Manual Overview of all supported keywords in Batch Mode Listed below is a summary of all the keywords supported in a .PVI file using the batch mode: Note The COMB, PSEUCOMP and VFP sections-type keywords cannot currently be prepared in a .PVI file for batch mode using interactive mode. • "PVI file" on page 155. • "Keywords introducing sections" on page 156. • "RUNSPEC section keywords" on page 156. • "SYSTEM section keywords" on page 157. • "SPLIT section keywords" on page 158. • "GROUP section keywords" on page 159. • "COMB section keywords" on page 159. • "SIMULATE section keywords" on page 160. • "REGRESS section keywords" on page 160. • "BLACKOIL section keywords" on page 161. • "PSEUCOMP section keywords" on page 162. • "OUTECL3 section keywords" on page 162. • "VFP section keywords" on page 163. PVI file The PVI file consists of a number of sections, each introduced by a section keyword. • The first section must be RUNSPEC, which specifies the number of components, the equation of state option and the run title. • The SYSTEM section must follow the RUNSPEC section. • Other sections may be in arbitrary order, and may occur more than once. Using the PVI file After each operation that redefines the system, which may be by splitting, grouping or regression, the program rewrites the audit trail. When you exit from a session you can choose to write the audit trail to a PVI file. This creates new sections with the names MODSPEC and MODSYS (corresponding to RUNSPEC and SYSTEM). The program treats these new sections in the same manner as the original definitions. When you load a PVI file created in a previous PVTi session the program automatically searches for the RUNSPEC and any subsequent MODSPEC sections. The PVTi keywords are described in detail in Chapter 7. PVTi Reference Manual Reference section Batch system and keywords 155 Keywords introducing sections Each of the sections in a PVI file has a specific keyword to introduce it into the file. Table 6.4 details these keywords. Table 6.4 Keyword Keywords for introducing sections Comments Details RUNSPEC This must be the first section. See "RUNSPEC" on page 252 SYSTEM This must follow the RUNSPEC section. See "SYSTEM" on page 266 SPLIT See "SPLIT" on page 263 GROUP See "GROUP" on page 206 COMB See "COMB" on page 179 SIMULATE See "SIMULATE" on page 261 REGRESS See "REGRESS" on page 249 BLACKOIL See "BLACKOIL" on page 174 VFP See "VFP" on page 281 PSEUCOMP See "PSEUCOMP" on page 247 OUTECL3 See "OUTECL3" on page 240 Keywords by section Each of the main sections, for example the RUNSPEC section, has its own specific keywords. Note the following: • The keywords UNITS, DEGREES and STCOND are normally be specified in the SYSTEM section, but can occur elsewhere, and can occur more than once. • The keywords DEBUG and OPTIONS can be specified in the RUNSPEC section or in the SYSTEM, COMB, SIMULATE or REGRESS sections. • The keyword MESSAGE can be specified anywhere, its function being merely to echo the argument to the print file at the time of a batch run. RUNSPEC section keywords Table 6.5 details the keywords specific to the RUNSPEC section. Table 6.5 156 RUNSPEC keywords Keyword Comments Details EOS Selects the equation of state. See "EOS" on page 193 LBC Selects Lohrenz-Bray-Clark viscosities. See "LBC" on page 214 NCOMPS Sets the number of components. See "NCOMPS" on page 230 NEWPVI Outputs a new PVI file at the end of the See "NEWPVI" on page 231 batch run. PEDERSEN Selects the Pedersen viscosity correlation. Reference section Batch system and keywords See "PEDERSEN" on page 245 PVTi Reference Manual Table 6.5 RUNSPEC keywords (Continued) Keyword Comments Details PRCORR Selects the modified Peng-Robinson equation. See "PRCORR" on page 246 TITLE Sets the run title. See "TITLE" on page 271 ECHO Includes the PVI file in the PVP file. See "ECHO" on page 192 NOECHO Does not include the PVI file in the PVP file. See "NOECHO" on page 233 DEBUG Sets the Debug flags. See "DEBUG" on page 186 DEBUE Sets Debug flags. See "DEBUE" on page 185 OPTIONS Sets Options flags. See "OPTIONS" on page 238 VERSION Indicates the version of PVTi See "VERSION" on page 280 SYSTEM section keywords "The fluid model" on page 98 explains how to set up the SYSTEM keywords using menu options. Table 6.6 details the keywords specific to the SYSTEM section. Table 6.6 SYSTEM keywords Keyword Comments Details DEGREES Specifies the temperature convention. See "DEGREES" on page 188 STCOND Specifies the standard conditions. See "STCOND" on page 265 UNITS Specifies the unit convention. See "UNITS" on page 274 CNAMES Sets the component names. See "CNAMES" on page 177 LNAMES Sets the library component names. See "LNAMES" on page 217 CHARACT Specifies the characterisation of the components. See "CHARACT" on page 176 SCT Defines the Semi-ContinuousThermodynamic split. See "SCT" on page 259 ACF Defines the acentric factors. See "ACF" on page 169 ACHEUH Defines the Cheuh-Prausnitz A coefficient. See "ACHEUH" on page 170 BIC Defines the binary interaction coefficients. See "BIC" on page 172 CALVAL Defines the calorific values. See "CALVAL" on page 175 DEFBIC Defines the default binary interaction See "DEFBIC" on page 187 coefficients. DREF Defines the reference densities. See "DREF" on page 190 LBCCOEF LBC Specify the viscosity coefficients. See "LBCCOEF" on page 215, "LBC" on page 214 MW Specifies the molecular weights. See "MW" on page 228 OMEGAA Specifies non-default Ω a values See "OMEGAA/B" on page 237 (optional). PVTi Reference Manual Reference section Batch system and keywords 157 Table 6.6 SYSTEM keywords (Continued) Keyword Comments Details OMEGAB Specifies non-default Ω b values See "OMEGAA/B" on page 237 (optional). PARACHOR Specifies parachors. See "PARACHOR" on page 242 PCRIT Defines the critical pressures. See "PCRIT" on page 243 SPECHA,B,C,D Defines the specific heat capacity coefficients. See "SPECHA-D" on page 262 SSHIFT Specifies dimensionless volume shifts for PR3 EoS. See "SSHIFT" on page 264 TBOIL Specifies boiling points (for ZJ equation). See "TBOIL" on page 268 TCRIT Defines the critical temperatures. See "TCRIT" on page 269 THERMX Specifies thermal expansion coefficient for volume shifts. See "THERMX" on page 270 TREF Defines the reference temperatures. See "TREF" on page 273 VCRIT Specifies the critical volumes. See "VCRIT" on page 278 VCRITVIS Defines critical volumes used in LBC viscosity correlation. See "VCRITVIS" on page 279 ZCRIT Specifies critical Z -factors. See "ZCRIT" on page 290 ZCRITVIS Defines critical Z -factors used in LBC viscosity correlation See "ZCRITVIS" on page 291 ZI Defines sample composition (primary sample). See "ZI" on page 292 SAMPLES Defines other samples, lean gas for swelling test. See "SAMPLES" on page 255 SAMTITLE Defines long titles for other samples. See "SAMTITLE" on page 257 HYDRO Specifies hydrocarbon/Nonhydrocarbon. See "HYDRO" on page 211 SALINITY Defines the salinity of specified samples. See "SALINITY" on page 253 MIX Allows mixing of two samples to form a new sample. See "MIX" on page 224 SPLIT section keywords Table 6.7 details the keywords specific to the SPLIT section. Table 6.7 Keyword 158 SPLIT keywords Comments Details CORRACF Selects the acentric factor correlation. See "CORRACF" on page 181 CORRCP Selects the critical property correlation. See "CORRCP" on page 182 FRAC Sets the number and distribution of new plus fractions. See "FRAC" on page 202 Reference section Batch system and keywords PVTi Reference Manual Table 6.7 SPLIT keywords (Continued) Keyword Comments Details MDP Sets the molar distribution parameters. See "MDP" on page 220 MWS Specifies the plus fraction molecular weight. See "MWS" on page 229 SG Specifies the plus fraction specific gravity. See "SG" on page 260 SCT Defines the Semi-ContinuousThermodynamic split. See "SCT" on page 259 WHIT Defines a Whitson splitting. See "WHIT" on page 287 GROUP section keywords Table 6.8 details the keywords for the GROUP section. Table 6.8 GROUP keywords Keyword Comments Details COMBINE Specifies fractions to be grouped together. See "COMBINE" on page 180 GRPBYSAM Specifies which sample to group to. See "GRBYSAM" on page 209 GRPBYWGT Specifies grouping by molecular weight. See "GRPBYWGT" on page 210 GRPBYMIX Specifies grouping by mixing rule. See "GRBYMIX" on page 208 GRPBYALL Specifies grouping to average of all samples. See "GRBYALL" on page 207 COMB section keywords The "COMB - Compositional Material Balance" on page 112 allows you to set up the COMB keywords using menu options. Table 6.9 details the keywords for the COMB section. Table 6.9 PVTi Reference Manual COMB keywords Keyword Comments Details EXP Defines experiments. See "EXP" on page 195 OBS Defines observations. See "OBS" on page 234 OBSIND Defines the weight for individual observations. See "OBSIND" on page 235 COATS Requests Coats’ method for blackoil tables. See "COATS" on page 178 PEARCE Requests Pearce’s method for blackoil tables. See "PEARCE" on page 244 WHITSON Requests Whitson’s method for blackoil tables. See "WHITSON" on page 288 RECOVERY Sets the liquid production relative permeability for recoveries. See "RECOVERY" on page 248 Reference section Batch system and keywords 159 SIMULATE section keywords "Simulation using PVTi" on page 117 describes how to set up the SIMULATE keywords using menu options. Table 6.10 details the keywords for the SIMULATE section. Table 6.10 SIMULATE keywords Keyword Comments Details EXP Defines experiments. See "EXP" on page 195 OBS Defines observations. See "OBS" on page 234 OBSIND Defines the weight for individual observations. See "OBSIND" on page 235 FVFREF Sets the reference values for FVF calculations. See "FVFREF" on page 204 SAVCOMP Saves the information for calculated compositions. See "SAVCOMP" on page 258 REGRESS section keywords "Regression in PVTi" on page 126 describes how to set up the REGRESS keywords using menu options. Table 6.11 details the keywords for the REGRESS section. Table 6.11 160 REGRESS keywords Keyword Comments Details EXP Defines experiments. See "EXP" on page 195 OBS Defines observations. See "OBS" on page 234 OBSIND Defines the weight for individual observations. See "OBSIND" on page 235 VAR Defines variables. FVFREF Sets the reference values for FVF calculations. See "FVFREF" on page 204 FIT Perform regression. See "FIT" on page 201 MAXIT Specifies the maximum number of iterations. See "MAXIT" on page 218 MAXSTEP Specifies the maximum regression step limit. See "MAXSTEP" on page 219 MINSTEP Specifies the minimum regression step limit. See "MINSTEP" on page 223 REGTARG Specifies the regression target. See "REGTARG" on page 250 Reference section Batch system and keywords See "VAR" on page 275 PVTi Reference Manual BLACKOIL section keywords This section allows you to generate output for ECLIPSE Black Oil. The "Exporting keywords" on page 133 describes how to set up the BLACKOIL keywords using menu options. Table 6.12 details the keywords for the BLACKOIL section. Table 6.12 BLACKOIL keywords Keyword Comments Details UNITS Defines the units to use in the export. See "UNITS" on page 274 EXP Defines experiments. See "EXP" on page 195 Note you can only define CVD, DL and SEPS. PVTi Reference Manual COATS Requests Coats’ method for blackoil tables. See "COATS" on page 178 WHITSON Requests Whitson and Torp’s method for blackoil tables. See "WHITSON" on page 288 DIFFERENTIAL Requests Differential method for blackoil tables. See "DIFFERENTIAL" on page 189 FRAGOR Requests Fragor method for blackoil tables. See "FRAGOR" on page 203 MOSES Requests Moses method for blackoil tables. See "MOSES" on page 227 LIVEOIL Generates tables with live oil. See "Live oil tables" on page 216 DEADOIL Generates tables with dead oil. See "DEADOIL" on page 184 WETGAS Generates tables with wet gas. See "WETGAS" on page 286 DEADGAS Generates tables with dead gas. See "DRYGAS" on page 183 WAT100 Outputs water properties. See "WAT100" on page 282 MINDELP Specifies minimum compressibility test pressure difference. See "MINDELP" on page 222 Reference section Batch system and keywords 161 PSEUCOMP section keywords The "Exporting keywords" on page 133 describes how to set up the PSEUCOMP keywords using menu options. This section allows you to generate output for ECLIPSE Black Oil options. Table 6.13 details the keywords for the PSEUCOMP section. Table 6.13 PSEUCOMP keywords Keyword Comments Details EXP Defines experiments. See "EXP" on page 195 Note you can only define CVD and SEPS. GI Defines GI nodes for the GI option tables. See "GI" on page 205 WAT200 Outputs water properties. See "WAT200" on page 283 MINELP Specifies minimum compressibility test pressure difference. See "MINDELP" on page 222 COATS Requests Coats’ method for blackoil tables. See "COATS" on page 178 WHITSON Requests Whitson and Torp’s method for blackoil tables. See "WHITSON" on page 288 OUTECL3 section keywords This section allows you to generate output for ECLIPSE Compositional. The "Exporting keywords" on page 133 describes how to set up the OUTECL3 keywords using menu options. Table 6.14 details the keywords for the OUTECL3 section. Table 6.14 OUTECL3 keywords Keyword Comments Details UNITS Specifies the units to use in the export. See "UNITS" on page 274 SAMPLE Specifies the fluid sample to use in the export. See "Specify fluid sample" on page 254 RTEMP Defines the reservoir temperature. See "RTEMP" on page 251 NEWPVO Defines a rootname for the export file. See "Request new output PVO file" on page 232 EOSOUT Requests equation of state data for ECLIPSE Compositional. See "EOSOUT" on page 194 WAT300 Outputs water properties. See "WAT300" on page 284 EXP Defines experiments. See "EXP" on page 195 Note you can only define COMPG or CVD. 162 KVTABLE Requests K -value table for ECLIPSE Compositional. See "KVTABLE" on page 212 XMFVP Requests XMFVP and YMFVP tables for ECLIPSE Compositional. See "X/YMFVP" on page 289 YMFVP Requests XMFVP and YMFVP tables for ECLIPSE Compositional. See "X/YMFVP" on page 289 ZMFVD Requests ZMFVD table for ECLIPSE Compositional. See "ZMFVD" on page 293 Reference section Batch system and keywords PVTi Reference Manual VFP section keywords This section allows you to generate output for VFPi. The "VFP module" on page 138 describes how to set up the VFP keywords using menu options. Table 6.15 details the keywords for the VFP section. Table 6.15 VFP keywords Keywords Comments Details EXP Defines experiments. See "EXP" on page 195 Note you can only define CCE and SEPS. COATS Requests Coats’ method for blackoil tables. See "COATS" on page 178 WHITSON Requests Whitson and Torp’s method for blackoil tables. See "WHITSON" on page 288 WATVFP Outputs water properties. See "WATVFP" on page 285 TLOW Defines lowest temperature in the production string. See "TLOW" on page 272 APITRACK section keywords This section allows you to generate a series of black oil tables suitable for use with the API Tracking option in ECLIPSE BlackOil. The "Export for API Tracking option in ECLIPSE BlackOil" on page 134 describes how to set up the APITRACK keywords in interactive mode using the appropriate panel. details the keywords for the APITRACK section... Table 6.16 APITRACK keywords Keyword Comments Details UNITS Defines the units to use in the export. See "UNITS" on page 274 EXP Defines experiments. See "EXP" on page 195 Note you can only define CVD, DL and SEPS. PVTi Reference Manual SAMPLES The list of samples to export tables for. See "SAMPLES" on page 256 COATS Requests Coats’ method for blackoil tables. See "COATS" on page 178 WHITSON Requests Whitson and Torp’s method for blackoil tables. See "WHITSON" on page 288 DIFFERENTIAL Requests Differential method for blackoil tables. See "DIFFERENTIAL" on page 189 FRAGOR Requests Fragor method for blackoil tables. See "FRAGOR" on page 203 MOSES Requests Moses method for blackoil tables. See "MOSES" on page 227 LIVEOIL Generates table with live oil. See "Live oil tables" on page 216 DEADOIL Generates tables with dead oil. See "DEADOIL" on page 184 Reference section Batch system and keywords 163 Table 6.16 164 APITRACK keywords (Continued) Keyword Comments Details WETGAS Generates tables with wet gas. See "WETGAS" on page 286 DRYGAS Generates tables with dry gas. See "DRYGAS" on page 183 ALLDRY Generates gas tables for each sample. See "ALLDRY" on page 171 Reference section Batch system and keywords PVTi Reference Manual Error handling Keyword errors If an error occurs during keyword input, the program displays the offending line with ? characters under the field that is causing difficulties. The error numbers given by the program may be of two types: • Up to and including 100. These are errors detected within the PVTi data parser. Descriptions of these errors are given in Table 6.17. • Above 100 System data errors, usually caused by internal read operations used to convert a character to its value. Table 6.17 PVTi Reference Manual Error codes Error code Description 1 Unable to read next line from data file. 2 Length of current line is zero. 3 Quote misplaces in stack or data field. 4 / character found in the wrong place. 5 Data field length greater than 24. 6 End of file reached. 7 Invalid character found. 8 Zero length stack found. 9 Stack length 1 with illegal character. 10 Incorrect stack pointers. 11 Failed to find * character in repeated data field. 12 Multiplier for repeated data field has more than 24 characters. 13 Error after internal read of multiple value. 14 Negative multiplier for repeated data field. 15 * character found as first token in stack. 16 Unrecognisable character for number in repeated data field. 17 Single field has the wrong data type. 18 Empty token next on stack. 19 Unknown data type. 20 Data read which is not of the type expected and which cannot be easily converted. 21 Error in internal read to convert character data to number. 22 Repeated data has field length of more than 24 characters. 23 Error in internal read of repeated data multiplier. 24 More than one exponential character found. Reference section Error handling 165 Table 6.17 166 Error codes (Continued) Error code Description 29 Previous data type of repeated field not compatible for current repeated data field. 30 Error in internal read of previous repeated data field. 31 Unable to convert current value due to error in previous repeated data field. 32 Values for margin setting not valid. 33 Zero length string found internally. Reference section Error handling PVTi Reference Manual Keywords Chapter 7 PVTi keywords This chapter contains details of all the keywords in PVTi. The keywords are listed in alphabetical order. • "Keywords A-D" on page 168 • "Keywords E-K" on page 191 • "Keywords L- O" on page 213 • "Keywords P- S" on page 241 • "Keywords T - Z" on page 267 PVTi Reference Manual Keywords PVTi keywords 167 Keywords A-D This section contains the A-D keywords. The other PVTi keywords are listed as follows: "Keywords E-K" on page 191 "Keywords L- O" on page 213 "Keywords P- S" on page 241 "Keywords T - Z" on page 267. 168 Keywords Keywords A-D PVTi Reference Manual ACF RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Acentric factors Specifies the acentric factors for the components in the system. The keyword is followed by N c values, and terminated with a slash character (/), where N c is the number of components specified in the RUNSPEC section. Example ACF .22500 .20100 .34540 .57400 .80160 / PVTi Reference Manual .40000E-01 .22230 .38610 .61270 .84160 .13000E-01 .25390 .42510 .64860 .88300 .98600E-01 .30070 .46220 .68550 .92410 .15240 .27420 .49840 .72460 1.0590 .18480 .30560 .53420 .76340 Keywords ACF 169 ACHEUH RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP A-coefficient for Cheuh-Prausnitz BICs Specifies the value of the A -coefficient (pre-multiplying) of the Cheuh-Prausnitz binary interaction coefficients for hydrocarbon-hydrocarbon interactions. Its value generally lies between 0.1 and 0.5. Note Only available if OPTIONS flag 6 is active. Example --Default value:ACHEUH 0.15 / 170 Keywords ACHEUH PVTi Reference Manual ALLDRY RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 Dry Gas Tables for Each Sample This keyword requests that ECLIPSE BlackOil dry gas tables be output for each sample. If this keyword is not present then a dry gas table is written out for the sample with the median vapor density at surface conditions. The keyword ALLDRY has no arguments. VFP X APITRACK PVTi Reference Manual Keywords ALLDRY 171 Binary interaction coefficients BIC RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies binary interaction coefficients. There are two possible formats for this keyword. First format • The keyword should be followed by up to ( N c -1) lines of data followed by a forward slash character (/). • Each line should consist of three integers followed by the set of binary interaction coefficients between two specified components, terminated with a forward slash character (/). The first integer specifies the index of the first component and the second and third integers the lower and upper indices of the other component. Second format The program uses this format when saving. This format in effect displays the lower triangle of the BIC matrix, and there is no need for the first three columns informing the program of the component and the lower and upper indices. PVTi assumes the coefficients are read in as second, third component, etc., by row with the columns as the first, etc., component. Note For both formats the interaction coefficient between any given component and itself must be zero. PVTi always ensures that this is the case. Examples First format Binary interaction coefficients for a six component system. BIC 2 1 3 1 4 1 5 1 6 1 / 1 -0.02000 2 0.10000 2 0.13000 2 0.13500 5 0.12700 / 0.03600 0.05000 0.08000 2* / / / 2*0.0600 / Here there are zero binary interaction coefficients between components 4 to 3, 5 to 3,4 and 6 to 2,3. 172 Keywords BIC PVTi Reference Manual Second format The same system of BICs appears as follows: BIC -0.02000 0.10000 0.13000 0.13500 0.12700 / PVTi Reference Manual 0.03600 0.05000 0.08000 2* 2*0.0600 Keywords BIC 173 BLACKOIL RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP 174 Keywords BLACKOIL Start of the BLACKOIL section This is a delimiter keyword, specifying the start of the BLACKOIL section. Note If present, this section must not appear before the SYSTEM section. This section is used to generate blackoil tables for any of the currently defined fluid samples by simulating reservoir depletion with a constant volume depletion or differential liberation. Tables are generated that can then be input into ECLIPSE BlackOil. PVTi Reference Manual CALVAL RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify calorific values Specifies the calorific values for the components in the system. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section. It is terminated with a / character. The current units convention is used. The default is kJ ⁄ kg -ml kJ/kg-ml. For alternatives a UNITS keyword should have been previously read. For further information see [Ref. 39]. Example For a two component C1/I-C4 system, using PVT-Metric units: -- Calorific Values kJ/kgmol CALVAL 8.130000000E+02 2.659000000E+03 PVTi Reference Manual / Keywords CALVAL 175 CHARACT RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Components to be characterized Specifies the components that are to be defined by characterization. This keyword is followed by up to N c lines (or as many non-blank components as in the CNAMES keyword, below), each terminated with a / character. The last line of data is followed by a / character. Each line begins with the mnemonic of the component to be characterized, followed by five items of data: • Molecular weight M w • Specific gravity Sg • Normal boiling point temperature T b • Watson characterisation factor K w • Reference temperature T ref • Two strings which specify the characterisation procedure required for: • Critical properties. Kesler-Lee (K), Cavett (C), Riazi-Daubert (R), Winn (W) or Pedersen (P) • Acentric factor. Kesler-Lee (K), Edmister (E), Thompson (T) or Pedersen (P). Generally, you must provide two out of the four data items M w , S g , T b and K w to characterize a component. If more than two items are available, give the “best” two items since the order of entry dictates which two are used. It is possible to perform a characterization with a minimum data entry of M w ; the program estimates the specific gravity from a Single Carbon Number (SCN) table look-up. See [Ref. 18]. Note If no reference temperature is specified it is given the value of the standard temperature. Example Characterizes two plus fractions, the first of which has known specific gravity and normal boiling point temperature, the second of which has only molecular weight. Riazi-Daubert critical properties and Edmister acentric factor correlations to be used: CHARACT C7+1 1* C7+2 200.0 / 0.7500 / 390.0 2* R E / If more than two of the four items, M w , Sg , T b and K w are available, then the program uses the first two, that is given data for M w , T b and K w , then PVTi uses M w and T b . 176 Keywords CHARACT PVTi Reference Manual CNAMES RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Component names Specifies the mnemonics associated with the components in the system that are either to be characterized or fully user defined. This keyword is followed by N c component names, where N c is the number of components specified in the RUNSPEC section. It is terminated with a / character. Define library components using the LNAMES keyword. Any system containing both library and characterisation/user defined components should contain both LNAMES and CNAMES with the default specification 1*, where appropriate. The program translates the component names into upper case on input. The length may be up to 72 characters, but a limit of four is suggested to fit into the program output formats. Example For a nine-component condensate system, the first five being from library, the last four to be user defined: CNAMES 5* LNAMES CO2 N2 PVTi Reference Manual C4-6 C7+1 C7+2 C7+3 C1 C2 C3 4* / / Keywords CNAMES 177 Blackoil tables COATS X X X X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 178 Keywords COATS Specifies that the Coats method for the generation of blackoil tables is used in preference to the Whitson and Torp method. By default, the program uses the Whitson and Torp method. The keyword COATS has no arguments. PVTi Reference Manual COMB RUNSPEC SYSTEM SPLIT GROUP X COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Start of the COMB section This is a delimiter keyword, specifying the start of the COMB section. Note If present, this section must not appear before the SYSTEM section. This section is used for data and consistency checking of laboratory data of gas condensates and volatile oils. Material balance is performed on any Constant Volume Depletion data, to calculate liquid compositions, K-values, densities, etc. Additionally, tests of separator recombination data are available, as well as estimates of recovery, and generation of blackoil tables without recourse to the equation of state. PVTi Reference Manual Keywords COMB 179 COMBINE RUNSPEC SYSTEM SPLIT X GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Group existing components Requests the grouping of a range of existing components into a new combined fraction. This is done by specifying a group index for each existing component. PVTi groups together components with the same group index. Components not to be grouped may be ignored, or given a group index of zero. Note The group index has no significance other than to identify sets of components. You may enter a name for the new fractions. By default the program uses GRP1, GRP2 and GRP3 as the group names. The form of the keyword is: COMBINE icl1 icu1 ifr1 zfr1 icl2 icu2 ifr2 zfr2 / / / where: • icl1 is a lower existing component index; • icu1 is an upper existing component index; • ifr1 is a group index; • zfr1 is the mnemonic for a fraction. Example In a 19-component system, group the components 10 to 14 inclusive, and the components 15, 17 and 18. Accept default names for the fractions: COMBINE 10 14 1 15 15 2 17 18 2 / 180 Keywords COMBINE / / / PVTi Reference Manual CORRACF RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Splitting correlation for ACFs Specifies the correlation to be used for calculating the acentric factors of characterized split fractions. It should be either Kesler-Lee (K), Edmister (E), Thomassen (T) or Pedersen (P) [Ref. 13], [Ref. 14], [Ref. 30] & [Ref. 41] respectively. It must be terminated with a forward slash (/ ) character. The default is Kesler-Lee (K). Example Edmister correlation required: CORRACF E / PVTi Reference Manual Keywords CORRACF 181 CORRCP RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Splitting correlation for critical properties Specifies the correlation to be used for calculating the critical properties of characterized split fractions. It should be one of Kesler-Lee (K), Cavett (C) Riazi-Daubert (R), Winn (W), or Pedersen (P) [Ref. 10], [Ref. 11], [Ref. 12], [Ref. 42] , [Ref. 43], and [Ref. 41] respectively. It should be terminated by a forward slash (/) character. The default is Kesler-Lee (K). Example Cavett correlation required: CORRCP C / 182 Keywords CORRCP PVTi Reference Manual DRYGAS RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Dry gas tables This keyword requests that ECLIPSE BlackOil dry gas tables be output. The keyword DRYGAS has no arguments. X APITRACK PVTi Reference Manual Keywords DRYGAS 183 DEADOIL RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Dead oil tables This keyword requests that ECLIPSE BlackOil dead oil tables be output. The keyword DEADOIL has no arguments. X APITRACK 184 Keywords DEADOIL PVTi Reference Manual DEBUE X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Select output to debug file Requests that additional output from the PVTLIB annex be directed to the DBG debug file. The keyword is followed by up to eight integers in the range one to eight, terminated with a forward slash (/) character. The indices request the following output: Table 7.1 Output indices Index Output from 0 No debug 1 Full debug (see below) 2 Flash stability routines 3 Flash split routines 4 Newton routines 5 Fugacity routines (enter as -1 to obtain fugacities of components, batch mode only) 6 Water EoS routines 7 p sat routines 8 Critical point routines 9 Phase plot generator Example Request debug from Newton and p sat routines: CORRCP C / PVTi Reference Manual Keywords DEBUE 185 Select output to debug file DEBUG X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Requests that additional output from PVTi be directed to the DBG debug file. The keyword is followed by up to 16 integers in the range one to 16, terminated with a forward slash (/) character. The indices request the following output: Table 7.2 Output indices Index Output from 1 Array allocation routines 2 Phase plots 3 Zudkevitch-Joffe equation of state 4 Regression 5 Parser 6 Characterization/Splitting 7 Experiments (not p sat ) 8 Observations 9 Saturation pressure/temperature 10 Flash routine 11 Newton routines 12 Fugacity evaluation (set as -1 to obtain Fugacities of components - batch mode only) 13 Stability Check/Michelsen 14 Opening/closing of files 15 Regression output 16 LBC coefficients with regression 17 COMB routines Example Request debug from Flash and Michelsen routines only: DEBUG 9* 10 2* 13 / 186 Keywords DEBUG PVTi Reference Manual DEFBIC RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Default binary interaction coefficients Specifies that default binary interaction coefficients are required. These are only available between library/library and library/characterization components. The keyword DEFBIC has no arguments. PVTi Reference Manual Keywords DEFBIC 187 DEGREES RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Temperature convention Specifies the temperature convention to use. The keyword is followed by a character string identifying the convention, which may be one of the following four: • KELVIN Degrees Kelvin • CELSIUS Degrees Celsius • RANKINE Degrees Rankine • FAHRENHEIT Degrees Fahrenheit. Only the first character is significant, and may be lower or upper case. The default temperature convention is degrees Kelvin. Note This keyword must follow the UNITS keyword. Example Set to degrees Fahrenheit: DEGREES F / 188 Keywords DEGREES PVTi Reference Manual DIFFERENTIAL RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Blackoil tables Specifies that differential black oil tables are generated. By default, the Whitson and Torp method of composite black oil table generation is used. The keyword DIFFERENTIAL has no arguments. PVTi Reference Manual Keywords DIFFERENTIAL 189 Reference densities DREF RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the reference densities for the components in the system. The keyword is followed by N c values, and terminated with a forward slash (/) character, where N c is the number of components specified in the RUNSPEC section. Note • These reference densities are only required if the Zudkevitch-Joffe or three-parameter Peng-Robinson equations have been selected (although it is good practice to always enter them), and are associated with the reference temperatures specified with the TREF keyword. UNITS: METRIC: kg/ m 3 FIELD: lb/cu ft LAB: gm/cc PVT-M: kg/ m 3 Note Example For a two-component CO2/I-C4 system: DREF 777.00 190 Keywords DREF 557.00 / PVTi Reference Manual Keywords E-K This section contains the E-K keywords. The other PVTi keywords are listed as follows: "Keywords A-D" on page 168 "Keywords L- O" on page 213 "Keywords P- S" on page 241 "Keywords T - Z" on page 267. PVTi Reference Manual Keywords Keywords E-K 191 Insert PVI file into PVP file ECHO X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 192 Keywords ECHO This keyword inserts the PVI input file into the PVP print file. The keyword ECHO has no arguments. PVTi Reference Manual EOS X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Defines the required Equation of State Defines the required equation of state from the list: • PR Two-parameter Peng-Robinson. • PR3 Three-parameter Peng-Robinson. • RK Redlich-Kwong. • SRK Soave-Redlich-Kwong. • SRK3 Three-parameter Soave-Redlich-Kwong. • SW Schmidt-Wenzel. • ZJ Zudkevitch-Joffe. The default is PR3. Example EOS PR3 PVTi Reference Manual / Keywords EOS 193 EOSOUT RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP 194 Keywords EOSOUT EoS data for ECLIPSE 300 Requests that equation of state data be output to the PVO file for inclusion in ECLIPSE Compositional. The EOSOUT keyword has no arguments. By default, if this keyword is omitted and no other keywords are in the OUTECL3 section, EoS data is automatically output to the PVO file. PVTi Reference Manual EXP X X X X X X X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Experiments Specifies the experiments to be performed. Up to 100 experiments plus one set of BLACKOIL calculations can be defined. The form of the keyword and associated data is: EXP <no>1 <no>2 : <samp>1 <samp>2 <type>1 <type>2 <data>1 <data>2 / / where: • <no> specifies the experiment number, usually increasing sequentially from 1; • <samp> specifies the mnemonic of the required sample composition for this experiment; • <type> specifies the experiment type. One of: FLASH, BUBBLE, DEW, CCE, CVD, DL, SWELL, SEPS, COMPG, TERN, vapor, MFLASH, CRIT, TSAT, FCMP, MCMP, PSAT, MCT. In the above, a forward slash (/) character terminates entry of experiments, and the form of the <data> depends on the particular experiment type: Table 7.3 Required data for experiments Experiment Data FLASH T BUBBLE T DEW IRT P T CCE FLUID T P P2... ...PN CVD FLUID T P1 P2... ...PN DL T P P2... ...PN SWELL FLUID YMF T [PRESS P] STYPE X1... ...XN SEPS T1 P1 L1 V1 (option 1) T2 P2 L2 V2 . . . . TN PN LN VN SEPS T1 P1 FL11 FV11 FV1N (option 2) T2 P2 FL21 FV21...FL2N FV2N . . . . . TN PN LN FVN1...FLNN FVNN COMPG FLUID T P D D1 TERN T P ZG1 ZG2 ZG3 IG2... ...IGN T P M1... ...MN VAPOR FLUID YMF MFLASH T P IG1 CRIT PVTi Reference Manual Keywords EXP 195 Table 7.3 Required data for experiments (Continued) Experiment Data TSAT P TSAT FCMP YMF T MCMP YMF ICORV PSAT T MCT YMF FCMP T MCMP PSAT ICORV T P FL2...FLN-1N (option 1) MCT MCT (option 1) YMF ICORV T P FV2...FVN-1N (option 2) MCT (option 2) TCLOUD T P PCLOUD T P where: Table 7.4 Keyword arguments Keyword arguments Data requirements T Single temperature entry P Single pressure entry IRT Retrograde (IRT=1) or normal (IRT=0) dew point FLUID GAS or OIL system PI I’th pressure YMF Mnemonic of gas sample composition defined in SAMPLES or ZI. STYPE Specifies subsequent data is MOLE fraction of gas in the mixture or GOR gas volume at STP in the oil at original pressure or other pressure. ICORV Condensing (ICORV=0) or vaporizing (ICORV=1) multiple contact miscibility pressure required XI Mole fraction or GOR (see STYPE) for step I. MI Number of moles added cumulatively at step I. TI Temperature of I’th separator stage. LI Destination of liquid output from stage. Default is next stage, I+1. VI Destination of vapor output from stage. Default is the cumulative vapor output, 0. Note, for separators, cumulative output stage is labelled 0, with vapor at STC, liquid at final stage conditions. 196 Keywords EXP FLIJ Fraction of liquid output from stage I to stage J. Default is 1.0 to the next stage. FVIJ Fraction of vapor output from stage I to stage J. Default is 1.0 to the cumulative vapor output, 0. D Reference depth. PVTi Reference Manual Table 7.4 Keyword arguments (Continued) Keyword arguments Data requirements DI Depth I. ZGI Names of the I’th ternary group. IGI Ternary group index (1-3) for component I. Example Consider the following experiments: 1 Dew point pressure at 200 °F , no pressure estimate given; 2 Swelling test at 200 °F , injection gas composition specified in SAMPLES with mnemonic ZINJ, four stage addition with given mole percentage of gas in reservoir fluid; 3 Constant composition expansion of condensate (GAS) at 200 °F , pressures in psi; 4 Constant volume depletion of condensate at 200 °F , pressures in psi; 5 2-stage separator at 500 psi, 125 °F and 50 psi, 90 °F with second stage fed from liquid output of stage one; 6 Composition with depth: a volatile oil (OIL) at reference conditions of 220 °F , 4000 psi and 7500 ft. Require compositions and pressures at 7000, 7100,..., 8000 ft; 7 Ternary diagram calculation for an eight component system, explicit grouping; 8 Ternary diagram calculation for an eight component system, default grouping; 9 First contact miscibility pressure at 160 °F on ZI, injecting ZINJ; 10 Multiple contact miscibility pressure at 160 °F on ZI, injecting ZINJ, vaporizing drive; 11 Multiple contact miscibility pressure at 160 °F on ZI, injecting ZINJ, condensing drive; 12 Multiple contact test at 121.1 °F and 2738 psi on ZI, injecting ZINJ, condensing drive. At each stage all of the remaining oil from the flash is contacted with one mole of ZINJ. PVTi Reference Manual Keywords EXP 197 EXP 1 ZI 2 ZI DEW SWELL 1 GAS 3 CCE GAS ZI 200.0 ZINJ MOLE 200.0 / 200.0 0.1271 6000.0 2000.0 3000.0 0.3046 5000.0 1000.0 2400.0 4 ZI CVD GAS 200.0 -- old format for SEPS 5 ZI SEPS 125.0 500.0 2 90.0 50.0 0 7 ZI TERN N2C1 C2C5 C6+ 1 1 2 8 ZI TERN / 9 ZI FCMP ZINJ 160.00 / 10 ZI MCMP ZINJ 1 160.00 / 11 ZI MCMP ZINJ 0 160.00 / 12 ZI MCT ZINJ 0 121.10 2738.0 / Note 0.5384 4000.0 0.6538 3000.0 1800.0 1200.0 0 0 / 2 2 2 3 3 / / / / 1.0 1.0 1.0 1.0 / At pressures above the saturation pressure where no compositional changes take place, the Constant Volume Depletion (CVD) and the Differential Liberation (DL) are effectively a Constant Composition Expansion (CCE) experiment. Restrictions The EXP keyword arguments are subject to restrictions in the BLACKOIL, COMB, OUTECL3, REGRESS and VFP sections: Table 7.5 Restrictions for EXP keyword arguments Section Experiment BLACKOIL CVD, DL & SEPS only. PSEUCOMP CVD & SEPS only. COMB CVD, SEPS & CCE only. OUTECL3 CVD & COMPG only. REGRESS Not COMPG, TERN, MFLASH, CRIT, TSAT, FCMP, MCMP. VFP CCE & SEPS only. BLACKOIL section In the BLACKOIL section, to generate blackoil tables you must define a depletion experiment and a separator network. Number these experiments; 1 (CVD or DL) and 2 (SEPS). 198 Keywords EXP PVTi Reference Manual COMB section In the COMB section, you are restricted to the above experiments for the material balance (CVD), recombination of separator data (SEPS) and recovery calculations (CCE). Number these experiments 1 to 3, in any order. OUTECL3 section In the OUTECL3 section, you are restricted to a CVD for the purposes of generating either KVTABLE or XMFVP and YMFVP tabular data. Note Only two pressures should be entered, the maximum and minimum pressures required in the table. The other pressures are calculated by interpolation (up to 50 pressures in all). You can also specify a COMPG experiment for the purpose of generating ZMFVD tables for ECLIPSE Compositional. Note Only two depths should be entered, the maximum and minimum depths required in the table. The other depths are calculated by interpolation (up to 50 depths in all). Number these experiments 1 (CVD) and 2 (COMPG). VFP section In the VFP section, to generate blackoil tables you must define a depletion experiment and a separator network. Number these experiments 1 (CCE) and 2 (SEPS). PVTi Reference Manual Keywords EXP 199 EXPIND X X X X X X X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Set Status of Experiments This keyword is used to set the status of a particular experiment, necessary when performing a regression operation. The keyword is a list of integers, one for each experiment, where a 0 means the experiment is not to be used in a regression (‘turned off’) and a 1 means the experiment is to be used in a regression (‘turned on’). Example We have 20 experiments in total in our project and wish that they all be ‘turned on’ during regression except the 5th, 10th, 14th, 16th and 18th, which will be ‘turned off’: OPTIONS 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1/ 200 Keywords EXPIND PVTi Reference Manual FIT RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Perform fit by regression This keyword requests that a regression operation, previously specified using the EXP, OBS and VAR keywords, be carried out. The keyword FIT has no arguments. PVTi Reference Manual Keywords FIT 201 Specify plus fraction data FRAC RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the number and relative compositions of the plus fraction splitting. You specify the number of fractions required, the relative composition of the fractions, and the mnemonics to be associated with the split fractions (optional), terminated with a / character. Example Split the plus fraction into three sub-fractions: FRAC 3 0.72 202 Keywords FRAC 0.23 0.05 C7+1 C7+2 C7+3 / PVTi Reference Manual FRAGOR RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Blackoil tables Specifies that the Fragor method for the generation of composite from differential blackoil tables is used. By default, the program uses the Whitson and Torp method of composite black oil table generation. The keyword FRAGOR has no arguments. PVTi Reference Manual Keywords FRAGOR 203 FVFREF RUNSPEC SYSTEM SPLIT GROUP COMB X SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP FVF reference conditions The reference conditions for the liquid formation volume factors from Pinit/Pbub to Pstock (mnemonic SRELV) calculation in separator experiments may be input here. For each SEP experiment, a reference temperature and pressure are required. If the reference pressure is zero, the saturation pressure at the reference temperature will be used. Each record must be terminated with a / character. The set of records must end with a blank record, containing only a slash (/). Note If reference conditions are not entered for a SEP experiment, no FVFs are calculated for that experiment. This includes the FVFs at each stage, and the ORELV mnemonic, as well as SRELV. Example FVFREF 2 220.0 4 200.0 7 210.0 / 204 Keywords FVFREF 4000.0 0.0 / / / PVTi Reference Manual GI RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL X PSEUCOMP OUTECL3 VFP Define GI nodes for E200 tables Specifies the lean gas injection sample and the GI nodes (gas-oil ratios) for the generation of ECLIPSE pseudo-compositional tables. This keyword is followed by a mnemonic specifying the fluid sample (defined on the SAMPLES keyword) and up to ten GI values, terminated with a / character. Example Inject sample ZINJ at GI’s of 0.1, 0.2, 0.3 mscf/rb: GI ZINJ PVTi Reference Manual 0.1 0.2 0.3 / Keywords GI 205 Start of the GROUP section GROUP RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 206 Keywords GROUP This is a delimiter keyword, specifying the start of the GROUP section. Note If present, this section must not appear before the SYSTEM section. This section is used to define data necessary for the grouping of components into pseudocomponents. PVTi Reference Manual GRBYALL RUNSPEC SYSTEM SPLIT X GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Start of the GROUP section This keyword specifies that the grouping of components specified by the COMBINE keyword be performed with respect to an average of all samples rather than to the default ZI sample. The keyword GRBYALL has no arguments. PVTi Reference Manual Keywords GRBYALL 207 GRBYMIX RUNSPEC SYSTEM SPLIT X GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 208 Keywords GRBYMIX Start of the GROUP section This keyword specifies that the grouping of components specified by the COMBINE keyword be performed using a molecular weighting, rather than the default mole fraction approach. The keyword GRBYMIX has no arguments. PVTi Reference Manual GRBYSAM RUNSPEC SYSTEM SPLIT X GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Start of the GROUP section This keyword specifies that the grouping of components specified by the COMBINE keyword be performed with respect to the named sample, rather than to the default ZI sample. Example Group to sample ZINJ PVTi Reference Manual GRPBYSAM ZINJ / Keywords GRBYSAM 209 GRPBYWGT RUNSPEC SYSTEM SPLIT X GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 210 Grouping by molecular weight This keyword specifies that the grouping of components specified by the COMBINE keyword be performed using a molecular weighting, rather than the default mole fraction approach. The keyword GRBYWGT has no arguments. Keywords GRPBYWGT PVTi Reference Manual HYDRO RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Define component as hydrocarbon or nonhydrocarbon Specifies whether a component is a hydrocarbon or a non-hydrocarbon. The keyword is followed by up to N c (the number of components in the fluid system) flags indicating the component types and terminated by a forward slash (/) character. The available flags are given in Table 7.6. Table 7.6 Component Types Type Flag in HYDRO Non-hydrocarbon N Hydrocarbon H Paraffin P Cyclic-hydrocarbon (naphthalene) C Aromatic A By default, all components are assumed to be hydrocarbons, except for specific nonhydrocarbons in the “LIB” set, that is, CO2 , H2 S , H 2 O , N 2 , H 2 and CO . Example An 11 component system consisting of CO2, N2, C1, C2, C3, IC4, NC4, IC5, NC5, C6, C7+: HYDRO N N 9*H PVTi Reference Manual / Keywords HYDRO 211 KVTABLE RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP 212 Keywords KVTABLE Request K-value table for ECLIPSE 300 output Requests that a K -value table, consisting of the K -value of each component at a set of pressures, be output to the PVO file. The keyword KVTABLE takes no arguments. Note Your must also define a Constant Volume Depletion (CVD) experiment with the EXP keyword and associated data in order that the KVTABLE can be generated. Note, also, that only two pressures need be defined in the CVD; these should be the maximum and minimum required. PVTi Reference Manual Keywords L- O This section contains the L-O keywords. The other PVTi keywords are listed as follows: "Keywords A-D" on page 168 "Keywords E-K" on page 191 "Keywords P- S" on page 241 "Keywords T - Z" on page 267. PVTi Reference Manual Keywords Keywords L- O 213 Lohrenz-Bray-Clark viscosities LBC X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 214 Keywords LBC Specifies that the Lohrenz-Bray-Clark viscosity correlation is to be used, rather than the Pedersen method. The LBC correlation is the default and is used if neither of the LBC or PEDERSEN keywords is used. The keyword LBC has no arguments. PVTi Reference Manual LBCCOEF RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Set non-default LBC coefficients Enables the default coefficients used by the Lohrenz-Bray-Clark viscosity correlation to be modified. This should only be done with great care: the viscosity is obtained from a fourth order polynomial in reduced density and must clearly not go negative. There are five coefficients with default values of 0.1023, 0.023364, 0.058533, -0.040758 and 0.0093324. Any coefficient not specified with LBCCOEF takes these default values. Example Reset two of the LBC coefficients LBCCOEF 1* 0.025 1* -0.04 0.01 PVTi Reference Manual / Keywords LBCCOEF 215 LIVEOIL RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Live oil tables This keyword requests that ECLIPSE BlackOil live oil tables be output. The keyword LIVEOIL has no arguments. X APITRACK 216 Keywords LIVEOIL PVTi Reference Manual LNAMES RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify library names Specifies the mnemonics associated with the components in the system that are to be taken from the internal library. A system containing both library and characterized/user defined components should contain both LNAMES and CNAMES with the default specification, 1*, where appropriate. The component names are translated into upper case on input. The length may be up to 72 characters, but a limit of four is suggested to fit into the program output formats. Each record is terminated with a slash (/). Example For a nine-component condensate system, with the first five from library and the last four userdefined: CNAMES 5* C4-6 C7+1 C7+2 C7+3 / LNAMES CO2 N2 C1 C2 C3 4* PVTi Reference Manual / Keywords LNAMES 217 Max. number of regression iterations MAXIT RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies maximum number of function evaluations in the non-linear regression step. This does not include the initial stage required in setting up the numerical Jacobian. The default is 50. The record is terminated with a slash (/). Example MAXIT 40 / 218 Keywords MAXIT PVTi Reference Manual MAXSTEP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Maximum step size allowed in regression At each step of the regression, a maximum step size, or trust region radius is maintained. This is allowed to vary during the regression, depending upon how successfully the behavior of the regression function is predicted. However, a maximum trust region radius is also imposed. MAXSTEP allows this to be reset. The variables upon which this limit acts are scaled to unity in the case of p c , T c , V c , Z c , Ω a , Ω b , and are the actual values for binary interaction coefficients and acentric factors. Thus a maximum step of 0.1 corresponds to a change of 10% in a critical temperature. The default is 0.1. The record is terminated with a slash (/). Example MAXSTEP 0.2 / PVTi Reference Manual Keywords MAXSTEP 219 Data for Whitson splitting MDP RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the α (shape factor) and η (lowest mole weight) parameters used in the Whitson probability density function used to characterize plus fractions. Default values are 1.0 and 97.0 respectively. The record is terminated with a slash (/). Example Change η to 92.0, leave α unchanged: MDP 1* 92.0 220 Keywords MDP / PVTi Reference Manual MESSAGE X X X X X X X X X X X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Echo message to file and screen Echoes a single line to the screen and print file when a PVI input file is read. The MESSAGE keyword can occur anywhere after the first keyword, RUNSPEC, and takes the form: Example PVTi Reference Manual MESSAGE Message to echo goes here Keywords MESSAGE 221 MINDELP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL X PSEUCOMP OUTECL3 VFP Minimum pressure difference Specifies the minimum pressure step to allow during the automatic insertion of pressure nodes into pressure depletion experiments following blackoil table total compressibility tests. Note This keyword must be placed after the keywords defining the depletion and separator experiments. The default is one atmosphere. The record is terminated with a slash (/). Example MINDELP 14.7 / 222 Keywords MINDELP PVTi Reference Manual MINSTEP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Minimum step limit allowed in regression At each step of the regression, a maximum step size, or trust region radius is maintained. This is allowed to vary during the regression, and may be reduced • if the function is poorly predicted • if error conditions occur in the regression functional • if the solution attempts to cross a lower or upper limit. If the step size limit falls below a minimum value, for any reason, the regression terminates, as further progress is unlikely to be made. This minimum value may be reset with the MINSTEP keyword. Note This is not the minimum step that may be taken; it is the minimum upper limit imposed on a step. The default is 0.00001. The record is terminated with a slash (/). Example MINSTEP 0.000001 PVTi Reference Manual / Keywords MINSTEP 223 Mix samples MIX RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP This keyword allows two samples to be mixed to form a new one. The inputs are the two sample names, the new sample name, the type of mixing and the amount of mixing. The types of mixes are as follows: • MOL specifies that the mixing amount given is the mole fraction of sample two in the mixture with sample 1. • If the mixing method is GOR, then the amount is given as the gas volume at standard conditions of sample two as a ratio of the volume of the initial sample. The latter is useful for consideration of mixing of lean gases in oil samples. Note • Mixing is only performed if: - the two samples are different - the amount to mix is greater than zero - the name of the new sample is different from any other sample - the mixing does not take the number of samples over the program limit. For the GOR option, the volume of the initial sample is usually the volume at its P sat at the specified temperature. However, an alternative pressure can be specified; this is shown in Example 2, below. Each record must be terminated with a slash (/). The set of records must end with a blank record, containing only a slash (/). Examples Example 1 Mix sample Z1 with Z2 to form Z3. The amount to mix is such that sample Z2 is 0.45 of the mole fraction in the new sample Z3. MIX Z1 / Z2 Z3 80.000 MOL 0.45 / Example 2 Mix sample T1 with T2 to form T3. The amount to mix is represented as a GOR of 5.0 MSCF/ stb, and the volume of the first sample T1 is measured at a pressure of 5000 PSI at the mix temperature of 670 °F . If the saturated volume of T1 was required then the PRES could be set as 0.0, or those two items removed from the keyword. MIX T1 / 224 Keywords MIX T2 T3 670.0 PRES 5000.0 GOR 5.0 / PVTi Reference Manual MODSPEC x RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Denotes start of the run specification section Any split, group, regress or user change of the fluid system causes a new RUNSPEC/SYSTEM section to be appended to the audit trail, which can be saved on exit from PVTi to a PVI file. These new sections are labelled with the keywords MODSPEC and MODSYS to indicate they are modified definitions. They are interchangeable with RUNSPEC and SYSTEM. This section defines the number of components, equation of state and viscosity option, run title and name of any new output file. The keyword MODSPEC has no arguments. PVTi Reference Manual Keywords MODSPEC 225 MODSYS RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 226 Keywords MODSYS Start of the MODSYS section MODSYS is a delimiter keyword, specifying the start of the MODSYS section, which defines the component properties and the fluid sample compositions. As for MODSPEC, the MODSYS keyword denotes a modified fluid system that was saved from a previous PVTi session following on from a split, group, regress or manual change of the fluid system originally defined with RUNSPEC and SYSTEM. The MODSYS section generally follows the MODSPEC section. The keyword is interchangeable with SYSTEM. PVTi Reference Manual MOSES RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Blackoil tables Specifies that the Moses method for the generation of composite from differential blackoil tables is used. By default, the program uses the Whitson and Torp method of composite black oil table generation. The keyword MOSES has no arguments. PVTi Reference Manual Keywords MOSES 227 Specify molecular weights MW RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the molecular weights for the components in the system. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section. The set of records must be terminated with a forward slash (/) character. Example Molecular weights for 15-component system: MW 44.010 58.124 209.26 228 Keywords MW 28.013 72.151 281.29 16.043 72.151 462.30 30.070 86.178 44.097 106.09 58.124 152.68 / PVTi Reference Manual MWS RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Define plus fraction mole weight for CMF splitting This keyword specifies the mole weight of the plus fraction in the Constant Mole Fraction splitting algorithm. The keyword is followed by a single real number for the mole weight and a forward slash (/) character. Example Plus fraction mole weight of 140.0: MWS 140.0 PVTi Reference Manual / Keywords MWS 229 NCOMPS X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 230 Keywords NCOMPS Specify number of components Specifies the number of components in the sample. This keyword must be entered in the RUNSPEC section. The maximum value available for NCOMPS is usually 100. This is set by a parameter in the source code, and can be increased at specific request. Example NCOMPS 20 / PVTi Reference Manual NEWPVI X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Request new output PVI file Allows you to output the current system description at the end of a batch run if it is thought that the system changes during the run (because of splitting/grouping and/or regression). The keyword is followed by the required filename root (that is the file name less any prefix or suffix) and is terminated with a forward slash (/) character. Example Write out new PVI file with name SAVE: NEWPVI SAVE / PVTi Reference Manual Keywords NEWPVI 231 NEWPVO RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP Request new output PVO file Allows you to name the export file produced in batch mode when there is an OUTECL3 section present. The keyword is followed by the required filename root (that is the file name less any prefix or suffix) and is terminated with a forward slash (/) character. Example Write a PVO file with name SAVE: NEWPVO SAVE / 232 Keywords NEWPVO PVTi Reference Manual NOECHO X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP No insertion of PVI file into PVP file This keyword requests that the PVI input file is not to be inserted into the PVP output file. This is the default condition. The keyword NOECHO has no arguments. PVTi Reference Manual Keywords NOECHO 233 Specify observations OBS RUNSPEC SYSTEM SPLIT GROUP X COMB X SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the observations associated with experiments performed individually or as part of a regression analysis. Note This keyword can only be specified if the EXP keyword and associated experiments have already been defined. • In the SIMULATE section, this keyword provides the means of supplying experimentally determined data for comparison purposes in output. • In the REGRESS section, this keyword provides the experimental data to be regressed against. The form of the keyword and its associated data is: OBS no mnem mnem no mnem mnem weight weight data data / / : / weight weight data / data / : / / where: no specifies the experiment number given in the EXP keyword mnem specifies the observation mnemonic (see below) weight global weight to be given to subsequent data. Several observations can be associated with a given experiment, each of which must be terminated with a forward slash (/) character. The entry of observations for a particular experiment is then terminated with a forward slash (/) character. A forward slash character (/) also terminates the entry of all observations. 234 Keywords OBS PVTi Reference Manual OBSIND RUNSPEC SYSTEM SPLIT GROUP X COMB X SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify observation weights Specifies the individual observation weights associated with observations defined with an OBS keyword. Note Note that the OBS keyword must exist in the section of the PVI file before the OBSIND keyword is inserted. If no OBSIND keyword is used the individual observation weights take the value of the global observation weight defined for each mnemonic in OBS. The form of the keyword and its associated data is: OBSIND no mnem mnem : data data / / data data / / / no mnem mnem : / / where: no specifies the experiment number given in the EXP keyword ("EXP" on page 195); mnem specifies the observation mnemonic (see OBS keyword, "OBS" on page 234); data individual weights to be given to each point described in the previous OBS keyword. Example Observation weights for the experiments defined for the EXP keyword (compare with example in OBS keyword description): 1 Saturation pressure and vapor Z -factor of dew point 2 Saturation pressure and swelling factor (relative volume) at each stage of swelling test 3 Relative volumes at each stage of CCE, vapor Z -factors at pressures above saturation pressure only 4 Liquid saturation, vapor Z -factor and gas mole fractions at each stage of CVD (nine component system) 5 GOR at each stage and stock tank GOR (in Mscf/stb) from two stage separators. PVTi Reference Manual Keywords OBSIND 235 OBSIND 1 PSAT 50.0 / ZV 1.0 / / 2 PSAT 10.0 10.0 10.0 10.0 / RELV 1.0 1.0 1.0 1.0 / / 3 RELV 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 2.0 2.0 3.0 4.0 ZV 1.0 1.0 1.0 1.0 1.0 1.0 10* / 4 SL 1.0 1.0 1.0 1.0 / ZV 1.0 1.0 1.0 1.0 / YMF 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 1.0 / / 5 GOR 100.0 10.0 / TGOR 10.0 / / / 236 Keywords OBSIND / / PVTi Reference Manual OMEGAA/B RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify EoS omega values These keywords specify non-default Ω a and Ωb values for the components in the system. Each keyword is followed by N c values, where N c is the number of components in the system, and is terminated with a forward slash (/) character. You need only specify these keywords if you wish to override the default equation of state values, which are as follows: Table 7.7 Equation of State omega values Equation OMEGAA OMEGAB RK 0.4274802 0.08664035 SRK 0.4274802 0.08664035 ZJ 0.4274802 0.08664035 PR 0.457235529 0.07776074 Example Ωa and Ωb values for two component system: OMEGAA 0.457 0.456 OMEGAB 0.0780 PVTi Reference Manual 0.0781 / / Keywords OMEGAA/B 237 OPTIONS X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Set various program options This keyword is used to set the various program options. Each option is described in "Program options" on page 145. As from the release of PVTi 2004A there are 21 options with each option specified by an integer (usually 0 or 1). Note Upon program start-up, most options are OFF, specified by an option value 0 (zero). Options 2 and 7 are the only ones that are on (=1) by default. To subsequently turn any option ON, specify an the integer 1 (but be careful of the special options below). The vector of integers is terminated with a / character. Special option settings Option 4 Temperature dependence of volume shifts (when using a three-parameter EoS) takes the following arguments: • 0 - No temperature dependence; • 1 - Apply linear thermal expansion to all components; • 2 - Use polynomial correlations and thermal expansion. Option 11 Optional printing of results to the PVP file also takes specific arguments: • 0 - ALways print; • 1 - OPTionally print (that is user prompted); • 2 - NEVer print. Option 14 Alternative definitions of GOR in differential liberation experiments also takes specific arguments: 238 Keywords OPTIONS • 0 - Default definition; • 1 - Last stage removed and oil volume at its bubble point pressure; • 2 - Incremental GOR; • 3 - As default but volume of oil at its bubble point pressure rather than stock tank conditions. PVTi Reference Manual Example Separator liquid volumes to be output at stock tank conditions. Cheuh-Prausnitz BICs required. Optional printing of results to PVP file: OPTIONS 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 / PVTi Reference Manual Keywords OPTIONS 239 OUTECL3 RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP 240 Keywords OUTECL3 Start of the OUTECL3 section This is a delimiter keyword, specifying the start of the OUTECL3 section. Note If present, this section must not appear before the SYSTEM section. The section is used in generating output data for inclusion into the ECLIPSE compositional model. Either equation of state or pressure-dependent tabular data can be generated. PVTi Reference Manual Keywords P- S This section contains the P-S keywords. The other PVTi keywords are listed as follows: "Keywords A-D" on page 168 "Keywords E-K" on page 191 "Keywords L- O" on page 213 "Keywords T - Z" on page 267. PVTi Reference Manual Keywords Keywords P- S 241 PARACHOR RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Define parachors Specifies the parachors for the components in the fluid system. The keyword is followed by up to N c values (the number of components specified in the RUNSPEC section) and terminated by a forward slash (/) character. Units Should be consistent to obtain surface tensions in dyne/cm. Example Parachors from [Ref. 18] for N2, C1, C2 and C3: PARACHOR 41.0 77.0 108.0 150.3 / 242 Keywords PARACHOR PVTi Reference Manual PCRIT RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Critical pressures Specifies the critical pressures for the components in the system. The keyword is followed by N c (the number of components in the system) values, and terminated with a forward slash (/) character. • UNITS: bars (METRIC), psi (FIELD), atm (LAB), atm (PVT-M). Example For a two-component system, using atm: PCRIT 72.90 PVTi Reference Manual 36.00 / Keywords PCRIT 243 PEARCE RUNSPEC SYSTEM SPLIT GROUP X COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 244 Keywords PEARCE Blackoil tables Specifies that the Pearce method for generating blackoil tables is used in preference to the Whitson and Torp or Coats method. By default, the program uses the Whitson and Torp method. The keyword PEARCE has no arguments. PVTi Reference Manual PEDERSEN X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify Pedersen viscosities Specifies that the Pedersen corresponding state viscosity correlation is to be used, rather than the default Lohrenz-Bray-Clark method. The keyword PEDERSEN has no arguments. PVTi Reference Manual Keywords PEDERSEN 245 PRCORR X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 246 Keywords PRCORR Peng-Robinson correction This keyword requests that a modified form of Peng-Robinson equation of state is to be used. This changes the usual form of the Ω a value as a function of the component acentric factor. The keyword PRCORR takes no arguments, and has no effect on equations of state other than the Peng-Robinson. PVTi Reference Manual PSEUCOMP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL X PSEUCOMP OUTECL3 VFP Start of the PSEUCOMP section This is the delimiter keyword specifying the start of the PSEUCOMP section used for the generation of ECLIPSE pseudo-compositional tables. This section performs a depletion experiment to define fluid properties in the reservoir and then passes the liquid and vapor through a separator network to surface conditions to define standard blackoil tables. Then a series of gas injections are performed and modified blackoil tables generated with the various mixtures. PVTi Reference Manual Keywords PSEUCOMP 247 RECOVERY RUNSPEC SYSTEM SPLIT GROUP X COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Liquid production for recovery estimates The presence of the RECOVERY keyword turns on the ability to calculate liquid production by the method of Reudelhuber and Hinds ([Ref. 37]) in the COMB section recovery calculations. It should be followed by the coordinates of two points on the curve of relative permeability versus total liquid saturation. The order of entry is the minimum and maximum relative permeabilities, and then the total liquid saturations for the minimum and maximum points. Example RECOVERY <RPMIN> <RPMAX> <SRPMIN> <SRPMAX> / 248 Keywords RECOVERY PVTi Reference Manual REGRESS RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Start of the REGRESS section This is a delimiter keyword, specifying the start of the REGRESS section. Note If present, this section must not appear before the SYSTEM section. This section is used to perform a regression of the equation of state parameters such as to minimize the difference between observed and calculated results of the following experiments: • equilibrium flash • bubble and dew point evaluation • saturated pressure • constant composition expansion • constant volume depletion • differential liberation • swelling test • vaporization test • multi-stage separator networks • the multi-contact test. PVTi Reference Manual Keywords REGRESS 249 REGTARG RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Regression target This quantity allows the default regression target to be changed. The regression target is applied to the sum of squares of the differences between the calculated and observed values. If a solution is found for which the residual approaches zero, the regression returns successfully when the sum of squares falls below this value. If there is a non-zero residual minimum this limit is applied to the derivatives of the residual at the minimum. • DEFAULT: 0.000001. The record is terminated by a forward slash (/) character. Example RETARG 0.1D-8 250 Keywords REGTARG / PVTi Reference Manual RTEMP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP Reservoir temperature for ECLIPSE Compositional This keyword defines the reservoir temperature to be used in an ECLIPSE Compositional simulation by including it along with the EoS data, which is output on the PVO file. It is followed by a single real number and terminated with a forward slash (/) character. It should be in the current PVTi unit set: it may be converted on output into an appropriate ECLIPSE Compositional unit set. Example Specify a reservoir temperature of 200 °F : RTEMP 200.0 PVTi Reference Manual / Keywords RTEMP 251 RUNSPEC X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 252 Keywords RUNSPEC Denotes start of the run specification This keyword opens the run specification section, and is normally the first keyword in the input data file. This section defines the number of components, equation of state and viscosity option, run title and name of any new output file. PVTi Reference Manual SALINITY RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify sample salinity For systems containing water, this specifies the salinity of any sample. The data are only used in the multiphase flash experiment. The record is terminated by a forward slash (/) character. • UNITS: ppm (parts per million). Example RTEMP 200.0 PVTi Reference Manual / Keywords SALINITY 253 SAMPLE RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP Specify fluid sample This keyword is specifies the fluid sample to use in the exportation of a fluid model for use in an ECLIPSE Compositional simulation. APITRACK 254 Keywords SAMPLE PVTi Reference Manual SAMPLES RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify fluid samples This keyword defines different composition fluids. Up to 50 different samples can be defined on all platform types. This maximum number can be changed on request, please contact us for advice if this situation arises. Each composition must be given a unique mnemonic to distinguish it from all others. Note Note that the default sample composition is given by the ZI keyword and is given the mnemonic of ZI. Thus, each line consists of the composition mnemonic followed by up to N c mole fractions, which should sum to unity, followed by a forward slash (/) character. The last composition should be followed by another forward slash (/) character. The composition of the lean gas injection fluid used in a swelling test should be defined under this keyword. Example Lean gas composition for swelling test: SAMPLES ZINJ 2* / PVTi Reference Manual 0.9468 0.0527 0.0005 4* / Keywords SAMPLES 255 SAMPLES RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify fluid samples If this keyword is in the APITRACK section and not the SYSTEM section then it specifies the fluid samples involved when exporting a series of black oil tables to be used with the API Tracking option in ECLIPSE BlackOil. X APITRACK 256 Keywords SAMPLES PVTi Reference Manual SAMTITLE RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify titles of fluid samples This keyword defines a long description to be associated with each alternative sample, so as to give more information about the origin of the samples, etc. The description must be enclosed in quotes. Each record is terminated by a forward slash (/) character. The set of records must be ended by a blank record, containing only a slash. Note This keyword should not precede the SAMPLES keyword. Example Second sample from deeper in the column. Lean gas composition for swelling test: SAMTITLE Z2 ‘Second sample from deeper in the column’ / ZINJ ‘Lean gas composition for swelling test’ / / PVTi Reference Manual Keywords SAMTITLE 257 SAVCOMP RUNSPEC SYSTEM SPLIT GROUP COMB X SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Save compositions If you have turned on the OPTIONS switch for saving compositions calculated during experiments, this keyword may be used in the SIMULATE section to save compositions to named samples. Each line in this section contains the experiment number, the fluid type required (from XMF, YMF, ZMF, for liquid, vapor and total compositions), the stage of the experiment if it is a multi-stage experiment, and the sample name required. The stage index should be omitted if the experiment is not a multi-stage experiment. In the particular case of the stock tank stage of a SEPS experiment, you should enter ST for the stage indicator. Each record is terminated by a forward slash (/) character. The set of records must be ended by a blank record, containing only a slash. Example Save the total composition for experiment 4, a COMPG experiment, at stage (here depth) 4, and label it Z80. Save the liquid output from stage 3 of experiment 2, a SEPS experiment, and label it S23, and the stock tank vapor output of the same experiment, labelling it ST2: SAVCOMP 4 ZMF 4 Z80 / 2 XMF 3 S23 / 2 YMF ST ST2 / / 258 Keywords SAVCOMP PVTi Reference Manual SCT RUNSPEC X SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Defines Semi-Continuous Thermodynamics split This keyword requests the modified Whitson method, here denoted the Semi-ContinuousThermodynamics (SCT) split. This method has the advantage that it can take multiple plus fraction definitions from multiple samples and split them into a consistent set of pseudocomponents with mole fractions adjusted between the different samples to honour moles and mole weights. Each record is terminated by a forward slash (/) character. The set of records must be ended by a blank record, containing only a slash. The keyword is followed by N samp + 1 lines of information, where N samp is the number of already defined samples, including the default sample ZI. • The first line of data specifies the mnemonic of the heavy end to split, the number of pseudo-components required (which must be between two and five), the minimum mole weight in the plus fraction (the Whitson η -parameter) and the mole weight of the heaviest pseudo-component required. As a default, the heaviest pseudo-component weight could be set to 1.5 and 2.0 times the heaviest plus fraction mole weight. • Next follows N samp lines of data, one for each sample currently defined. On each line should be the sample mnemonic, the skewness parameter (Whitson α -parameter), the sample plus fraction mole weight and specific gravity. Example The default and one alternative sample from different depths in the hydrocarbon column, and therefore different mole weights and specific gravities for the C7+ plus fraction. Different compositions are on the ZI and SAMPLES keyword, sample ZALT, which preceded this keyword and data. Three pseudo-component split requested with minimum and maximum mole weights of 90.0 and 300.0. Different skewness parameters reflects compositional grading in fluid from top (ZI - low Alpha) to bottom (ZALT - high Alpha). SCT C7+ 3 ZI ZALT / PVTi Reference Manual 90.0 1.10 2.30 300.0 130.0 150.0 / 0.75 0.80 / / Keywords SCT 259 Specify specific gravity SG RUNSPEC SYSTEM Z SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 260 Keywords SG Specifies the specific gravity (with respect to water at standard conditions) for the plus fraction to be split. The record is terminated by a forward slash (/) character. Example SG 0.86 / PVTi Reference Manual SIMULATE RUNSPEC SYSTEM SPLIT GROUP COMB X SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Start of the SIMULATE section This is a delimiter keyword, specifying the start of the SIMULATE section. Note If present, this section must not appear before the SYSTEM section. This section is used to define any of the following experiments: • equilibrium flash • bubble and dew point evaluation • constant composition expansion • constant volume depletion • differential liberation • swelling test • vaporization test • multi-stage separator networks • multiphase flashes • ternary diagrams • saturated pressure and temperature • critical point • compositional gradient • minimum miscibility pressures all using the equation of state model. PVTi Reference Manual Keywords SIMULATE 261 SPECHA-D RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify specific heat capacity coefficients Specifies the specific heat capacity coefficients for the components in the system. The keywords are followed by N c values, and terminated with a / character, where N c is the number of components specified in the RUNSPEC section. Note The values are output only in EoS data for ECLIPSE Compositional input files and only if OPTION number 7 is turned on. Example For a two component system, in PVT-Metric units: -- Specific Heat Coefficients A kJ/kgm/K SPECHA 5.409000000E+00 -4.224000000E+00 / -- Specific Heat Coefficients B kJ/kgm/K SPECHB 1.781000000E-01 3.063000000E-01 / -- Specific Heat Coefficients C kJ/kgm/K SPECHC -6.938000000E-05 -1.586000000E-04 / -- Specific Heat Coefficients D kJ/kgm/K SPECHD 8.713000000E-09 3.215000000E-08 / 262 Keywords SPECHA-D PVTi Reference Manual SPLIT RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Start of the SPLIT section This is a delimiter keyword, specifying the start of the SPLIT section. Note If present, this section must not appear before the SYSTEM section. This section is used to define data necessary for the splitting of the plus fraction, assumed to be the last component. PVTi Reference Manual Keywords SPLIT 263 SSHIFT RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 264 Keywords SSHIFT Dimensionless volume shifts for PR3 This keyword defines the dimensionless volume shift parameters used in the three-parameter Peng-Robinson equation of state. The keyword is followed by N c real numbers and terminated with a / character, where N c is the number of components. Example SSHIFT 0.15 0.05 -0.05 -0.03 -0.01 0.01 0.05 0.12 / PVTi Reference Manual STCOND RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Standard conditions Specifies the current standard conditions. This is followed by the standard temperature and pressure values. The record is terminated by a forward slash (/) character. Example Standard conditions in degrees Fahrenheit and psia: PVTi Reference Manual STCOND 60.0 14.7 / Keywords STCOND 265 SYSTEM RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 266 Keywords SYSTEM Start of the SYSTEM section This is a delimiter keyword, specifying the start of the SYSTEM section. This section generally follows the RUNSPEC section. This section is used to define the component properties and the fluid sample compositions. PVTi Reference Manual Keywords T - Z This section contains the T-Z keywords. The other PVTi keywords are listed as follows: "Keywords A-D" on page 168 "Keywords E-K" on page 191 "Keywords L- O" on page 213 "Keywords P- S" on page 241. PVTi Reference Manual Keywords Keywords T - Z 267 Specify boiling points TBOIL RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the boiling point temperatures for the components in the system. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section, and terminated with a / character. The current temperature convention is used. The default is degrees K , and for alternatives a DEGREES keyword should have been previously read. Note Boiling points are only required if the Zudkevitch-Joffe equation has been selected. Example For a two component CO2/I-C4 system, using degrees K : TBOIL 194.70 268 Keywords TBOIL 261.30 / PVTi Reference Manual TCRIT RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify critical temperatures Specifies the critical temperatures for the components in the system. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section, and terminated with a forward slash (/) character. The current temperature convention is used. • DEFAULT: degrees K . For alternatives a DEGREES keyword should have been previously read. Example For a two component CO2/I-C4 system, using degrees K : TCRIT 305.6 408.1 / PVTi Reference Manual Keywords TCRIT 269 THERMX RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Thermal expansion coefficient for volume shifts Specifies the value of the volume expansion coefficient which may be applied to the threeparameter equations of state (PR3, SRK3) volume shifts. It is terminated with a forward slash (/) character. Note The specified value is only used if the appropriate OPTIONS switch is in force. Example Default value with temperature in degrees Centigrade, that is THERMX in °C –1 : THERMX 0.0005 270 Keywords THERMX / PVTi Reference Manual TITLE X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify run title This keyword introduces the title of the run, which appears on the header of each section of the PVP output file. The line following the title keyword is taken as the title to be used. Note The syntax is slightly different from that of other keywords, in that no terminating forward slash (/) character is required. Example TITLE 18 component condensate test PVTi Reference Manual Keywords TITLE 271 Define lowest temperature for VFP tables TLOW RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 X VFP PVT properties for VFPi must be defined at least for two temperatures. The highest temperature, assumed to be reservoir temperature, is set on the constant composition expansion (CCE) experiment definition under the EXP keyword. The lowest temperature in the production string is defined using this keyword. It is terminated with a forward slash (/) character. Example Production string runs through deep sea-water at 40 °F TLOW 40.0 / 272 Keywords TLOW PVTi Reference Manual TREF RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify reference temperatures Specifies the reference temperatures for the components in the system. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section, and terminated with a forward slash (/) character. The current temperature convention is used. • DEFAULT: degrees K . For alternatives a DEGREES keyword should have been previously read. Note These reference temperatures are only required if the Zudkevitch-Joffe equation has been selected. Example For a two component CO2/I-C4 system, using degrees K : TLOW 40.0 PVTi Reference Manual / Keywords TREF 273 Specify unit conventions UNITS X X X X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP APITRACK This keyword specifies which unit convention is required, and sets flags to specify whether absolute or gauge pressures, and mole fractions or mole percentages, are to be used. The UNITS keyword is followed by a character string identifying the units convention, which may be one of the following four: • METRIC: Metric unit system • FIELD: Field units • LAB: Laboratory units • PVT: PVT-metric units (metric units with pressures in atm). Only the first character is significant, and case is not significant. • DEFAULT: PVT-metric. The pressure switch is one of the two following strings: • ABSOL: Absolute pressure • GAUGE: Gauge pressure. • DEFAULT: ABSOLute pressures. The mole composition switch is one of the following strings: • FRAC: Compositions as fractions of unity • PERC: Compositions as percentages of a hundred. • DEFAULT: FRACtions. Example Set to field units: UNITS F / 274 Keywords UNITS PVTi Reference Manual VAR RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE X REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify regression variables Specify variables for regression. The keyword is followed by a number of lines of data, each specifying variables to be added to the regression set. The data is terminated by a blank record (a single forward slash (/) character). The keyword thus takes the form: VAR S1 S2 S3 : / 1 I1 I2 I3 : J1 J2 J3 : K1 K2 K3 : L1 L2 L3 : IND1 IND2 IND3 : LL1 LL2 LL3 : UL1/ UL2 / UL3 / : The strings S1,S2... identify variables for regression, the indices I1, J1 (and K1, L1 for binaries) identify component ranges, lower and upper. Possible strings identifying variables (that is, S1, S2 etc.) are: • TCRIT: Critical temperatures • PCRIT : Critical pressures • VCRIT: Critical volumes in LBC viscosity correlation • ZCRIT: Critical Z -factors in LBC viscosity correlation • ACF: Acentric factors • OMEGAA: Ω a values • OMEGAB: Ω b values • SSHIFT: Volume shift parameter • BIC : Binary interaction coefficients In all cases except BIC, the lower and upper component indices should be specified. In the case of BIC, lower and upper index ranges should be given, that is, in four values. For example BIC 1 3 7 8 contains the BICS for (1, 7), (1, 8), (2, 7), (2, 8), (3, 7) and (3, 8). 2 PVTi Reference Manual The indices IND1, IND2, etc., specify the variable index as applied to the particular variable. “Special” regression variables are available and are: • SCTALF: SCT Splitting parameter • SCTMW: SCT plus fraction weight • SCTKW: SCT Watson K factor • THERMX: Thermal expansion coefficient • CHEUHA: Cheuh-Prausnitz BIC coefficient • CHARMW: Molecular weights of characterized components • CHARMF: Mole Fractions of characterized and/or user components for any sample • MIXING: The mixing factor between two samples when using the MIX keyword. Keywords VAR 275 Note In the case of SCTKW, THERMX, CHEUHA and MIXING the component and variable indices are redundant as the variable applies to all components. In the case of SCTALF and SCTMW, the I1 and K1 indices refer to the sample rather than component range. For the CHARMF two other sets of indices are needed to indicate the range of samples over which the particular variable applies. This follows the syntax of the BIC keyword. For example, CHARMF 1 2 4 5 contains the mole fractions for components 4 and 5 for samples 1 and 2. The quantities LL and UL specify limits imposed on the variables during the regression. All variable limits are applied as a percentage of the current value, scaled to unity. Thus a maximum value of 1.5 corresponds to allowing a 50% increase in any variable; a negative value implies that the variable is allowed to change sign (restricted set!). Defaults are as follows: Table 7.8 Default limits for variables Variable Lower limit Upper limit pc 0.5 1.5 Tc 0.5 1.5 Vc 0.5 1.5 Zc 0.5 1.5 Ωa 0.5 1.5 Ωb 0.5 1.5 ω 0.5 2.0 BIC -5.0 +5.0 si -5.0 5.0 SCTALF 0.5 5.0 SCTMW 0.9 1.1 SCTKW 0.75 1.25 CHEUHA 0.5 1.25 THERMX -5.0 5.0 CHARMW 0.9 1.1 CHARMF .75 1.25 MIXING .75 1.25 Grouped regression variables can be defined by giving them the same variable index. 276 Keywords VAR PVTi Reference Manual Examples Example 1 Regression variables are the critical temperature for component 1, the Ωa values for components 2 and 3, the binary interaction coefficient for components 1 and 10, and the volume shift parameters for components 4 and 6 to 10 as a first grouped variable, and components 1 to 3 and 5 as a second grouped variable. Default limits are taken for all components except the binary, which is restricted to a lower limit of 30% and an upper limit of 200% of the current value: VAR TCRIT OMEGAA BIC SSHIFT SSHIFT SSHIFT SSHIFT / 1 2 1 1 4 5 6 1 1 / 3 1 / 1 10 10 1 0.30 2.00 3 1 / 4 2 / 5 1 / 10 2 / / That is a total of five variables. Example 2 The default settings for the first five special regression variables with a system of three samples is as follows: VAR ’SCTALF’ ’SCTALF’ ’SCTALF’ ’SCTMW’ ’SCTMW’ ’SCTMW’ ’SCTKW’ ’CHEUHA’ ’THERMX’ / Note PVTi Reference Manual 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 0.750000 0.500000 -5.000000 0.500000 0.500000 0.500000 0.900000 0.900000 0.900000 1.250000 / 1.500000 / 5.000000 / 5.000000 5.000000 5.000000 1.100000 1.100000 1.100000 / / / / / / The special regression variables SCTALF and SCTMW cannot be grouped into one variable and must be entered in the manner shown above, that is one variable for each sample. Keywords VAR 277 Specify volumes VCRIT RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the critical volumes for the components in the system. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section, and terminated with a forward slash (/) character. The critical volumes are in volume per mole at critical pressure and temperature. • UNITS: 3 m /kg-mole (METRIC), cc/gm mole (LAB), cub ft/lb mole (FIELD), 3 m /kg-mole (PVT-M). VCRIT values may be entered as an alternative to ZCRIT values - that is one of VCRIT or ZCRIT should be entered. If VCRIT values are entered, critical Z -factors are obtained internally using the usual relationship: p crit V crit Z crit = ------------------- , RT crit [EQ 7.1] where R is the gas constant. Example For a 20-component system, in field units: VCRIT 1.5057 4.0847 7.8058 13.779 / 278 Keywords VCRIT 1.4417 4.9337 8.8374 4.759 1.5698 4.9817 9.8465 15.684 2.3707 5.8948 10.830 16.018 3.2037 6.0710 11.799 16.018 PVTi Reference Manual VCRITVIS RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify volumes for LBC viscosity calculations Specifies the critical volumes for the components in the system, to be used in the LBC viscosity calculation only. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section, and terminated with a forward slash (/) character. The critical volumes are in volume per mole at critical pressure and temperature. • UNITS: 3 m /kg-mole (METRIC), cc/gm mole (LAB), cub ft/lb mole (FIELD), 3 m /kg-mole (PVT-M). VCRITVIS values may be entered as an alternative to ZCRITVIS values; that is, one of VCRITVIS or ZCRITVIS should be entered. If VCRITVIS values are entered, critical Z factors are obtained internally using the usual relationship: p crit V critv Z critv = --------------------- , RT crit [EQ 7.2] where R is the gas constant. Note If VCRITVIS or ZCRITVIS is not entered then values entered with VCRIT or ZCRIT are used in the viscosity correlation. The form of VCRITVIS is the same as that of VCRIT. Example For a 20-component system, in Field units: VCRITVIS 1.5057 4.0847 7.8058 13.779 / PVTi Reference Manual 1.4417 4.9337 8.8374 14.759 1.5698 4.9817 9.8465 15.684 2.3707 5.8948 10.830 16.018 3.2037 6.0710 11.799 16.018 Keywords VCRITVIS 279 VERSION x RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 280 Keywords VERSION Version of PVTi This keyword indicates the version of PVTi that created the PVI file. Caution Files in FIELD units containing Differential Liberation (DL) experiments that have Gas Formation Volume Factor (GFVF) observations must be updated to the current version. See "Converting old projects to the current version" on page 87 for a tutorial on converting old-version PVI files. VERSION 2001A / PVTi Reference Manual VFP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 X VFP Start of the VFP section This is a delimiter keyword, specifying the start of the VFP section. Note This section must follow the SYSTEM section. This section is used to generate blackoil tables for VFPi, for any of the currently defined fluid samples, by simulating phase and volumetric changes in the wellbore with a constant composition expansion and separator flash at high (reservoir) and low temperatures. Tables are generated that can then be input into VFPi. PVTi Reference Manual Keywords VFP 281 WAT100 RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Output water properties Specifies the following for calculation of water properties within a black oil table generation for ECLIPSE Black Oil: It is terminated with a forward slash (/) character. 1 Temperature at which water properties are required 2 Pressure at which water properties are required 3 Flag for salt dissolved in water (Y for Yes, N for No) 4 Flag for keyword required (S for PVTW, M for PVTWSALT) 5 Flag for units of salinity (P for Parts per million (ppm), G for grammes per liter (gpl)) 6 Flag for gas dissolved (Y for gas, N for no gas) 7 Salinities. This can have just one value if the PVTW keyword is required, but up to ten values if PVTWSALT is required (zero salinities can be defaulted with *). Units are given by the above flag. Examples Example 1 For PVTW output, salt present of salinity 10000 ppm, with gas dissolved. Temperature 200 °F , pressure 5514.7 psi. --Water properties requested for E100 WAT100 200.00000 5514.70000 Y S P Y 10000.0000 / Example 2 For PVTWSALT output, salt present with salinities 10, 20 and 30 gpl, with no gas dissolved. Temperature 200 °F , pressure 5514.7 psi. -- Water properties requested for E100 WAT100 200.00000 5514.70000 Y M G N 10.0000 20.0000 30.0000 7* / 282 Keywords WAT100 PVTi Reference Manual WAT200 RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL X PSEUCOMP OUTECL3 VFP Output water properties Specifies the following for calculation of water properties within a black oil table generation for ECLIPSE. It is terminated with a forward slash (/) character. 1 Temperature at which water properties are required 2 Pressure at which water properties are required 3 Flag for salt dissolved in water (Y for Yes, N for No) 4 Flag for keyword required (S for PVTW, M for PVTWSALT) 5 Flag for units of salinity (P for Parts per million (ppm), G for grammes per liter (gpl)) 6 Flag for gas dissolved (Y for gas, N for no gas) 7 Salinities. This can have just one value if the PVTW keyword is required, but up to 10 values if PVTWSALT is required (zero salinities can be defaulted with *). Units are given by the above flag. Examples Example 1 For PVTW output, salt present of salinity 10000 ppm, with gas dissolved. Temperature 200 °F , pressure 5514.7 psi. --Water properties requested for E200 WAT100 200.00000 5514.70000 Y S P Y 10000.0000 / Example 2 For PVTWSALT output, salt present with salinities 10, 20 and 30 gpl, with no gas dissolved. Temperature 200 °F , pressure 5514.7 psi. -- Water properties requested for E200 WAT200 200.00000 5514.70000 Y M G N 10.0000 20.0000 30.0000 7* / PVTi Reference Manual Keywords WAT200 283 WAT300 RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP Output water properties Specifies the following for calculation of water properties within a run involving EoS output for ECLIPSE Compositional. It is terminated with a forward slash (/) character. 1 Temperature at which water properties are required 2 Pressure at which water properties are required 3 Flag for salt dissolved in water (Y for Yes, N for No) 4 Flag for units of salinity (P for Parts per million (ppm), G for grammes per liter (gpl)) 5 Flag for gas dissolved (Y for gas, N for no gas) 6 Salinity, units of which are given by the above flag. Example For PVTW output, salt present of salinity 10000 ppm, with gas dissolved. Temperature 200 °F , pressure 5514.7 psi. --Water properties requested for E300 WAT300 200.00000 5514.70000 Y P Y 10000.0000 / 284 Keywords WAT300 PVTi Reference Manual WATVFP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 X VFP Output water properties Specifies the following for calculation of water properties within a run involving black oil output for the VFPi program. It is terminated with a forward slash (/) character. 1 Highest temperature at which water properties are required 2 Highest pressure at which water properties are required 3 Lowest temperature at which water properties are required 4 Lowest pressure at which water properties are required 5 Flag for salt dissolved in water (Y for Yes, N for No) 6 Flag for units of salinity (P for Parts per million, G for grammes per liter) 7 Flag for gas dissolved (Y for gas, N for no gas) 8 Salinity, units of which are given by the above flag. Example For PVTW output, salt present of salinity 10000 poem, with gas dissolved. Calculated at temperatures 200 °F and 80 °F , pressure 6000.0 psi. --Water properties requested for VFP WATVFP 200.00000 6000.00000 80.00000 6000.00000 / PVTi Reference Manual Y P Y 10000.0000 Keywords WATVFP 285 WETGAS RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS X BLACKOIL PSEUCOMP OUTECL3 VFP Wet gas tables This keyword requests that ECLIPSE BlackOil wet gas tables be output. The keyword WETGAS has no arguments X APITRACK 286 Keywords WETGAS PVTi Reference Manual WHIT RUNSPEC SYSTEM X SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Defines Whitson splitting This keyword defines data specific to the Whitson splitting algorithm. The method consists of taking the single plus fraction consisting of SCN groups N+ with composition, mole weight and specific gravity z N+ , M N+ , γ N+ and splitting from SCN group N to some large carbon number, say 45, and then re-grouping to a user specified number of pseudo-components N grp . The keyword is followed by an integer to specify the first SCN group in the plus fraction, three real numbers for the composition, mole weight and specific gravity and an integer to specify the required number of pseudo-components on re-grouping, all terminated with a forward slash (/) character. Example Split C 7+ with z7+ = 0.1 , M 7+ = 140.0 , γ 7+ = 0.85 into three pseudo-components: WHIT 7 0.10 PVTi Reference Manual 140.0 0.85 3 / Keywords WHIT 287 WHITSON X X X X RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP 288 Keywords WHITSON Blackoil tables Specifies that the Whitson and Torp method for the generation of blackoil tables is used in preference to the Coats method. By default, the program uses the Whitson and Torp method. The keyword WHITSON has no arguments. PVTi Reference Manual X/YMFVP RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP XMFVP and YMFVP ECLIPSE tables Requests that XMFVP and YMFVP tables, consisting of the liquid and vapor mole fractions of each component at a set of pressures, be output to the PVO file. The XMFVP and YMFVP keywords have no arguments. Note PVTi Reference Manual You must also define a Constant Volume Depletion (CVD) experiment via the EXP keyword and associated data in order that the XMFVP and YMFVP tables can be generated. Only two pressures need be defined in the CVD, which should be the maximum and minimum required. Keywords X/YMFVP 289 Specify critical Z-factors ZCRIT RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the critical Z -factors for the components in the system. The keyword is followed by N c values, where N c is the number of components specified in the RUNSPEC section, and terminated with a / character. ZCRIT values may be entered as an alternative to VCRIT values, but one of VCRIT or ZCRIT should be entered. If ZCRIT values are entered, critical volumes are obtained internally using the usual relationship: RT crit Z crit V crit = ----------------------- , p crit [EQ 7.3] where R is the gas constant. Example For a CO2/Methane/Ethane/I-C4 system: ZCRIT 0.2709 290 Keywords ZCRIT 0.2809 0.2808 0.279 / PVTi Reference Manual ZCRITVIS RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specify critical Z-factors for LBC calculations Specifies the critical Z -factors for the components in the system to be used in the LBC viscosity correlation only. The keyword is followed by N c values, where Nc is the number of components specified in the RUNSPEC section, and terminated with a forward slash (/) character. ZCRITVIS values may be entered as an alternative to VCRITVIS values, but one of VCRITVIS or ZCRITVIS should be entered. If ZCRITVIS values are entered, critical volumes are obtained internally using the usual relationship: RT crit Z critv V critv = ------------------------- , p crit [EQ 7.4] where R is the gas constant. If VCRITVIS or ZCRITVIS is not entered then the values entered with VCRIT or ZCRIT are used. The form of ZCRITVIS is the same as that of ZCRIT. Example For a CO2/Methane/Ethane/I-C4 system: ZCRIT 0.2709 PVTi Reference Manual 0.2809 0.2808 0.279 / Keywords ZCRITVIS 291 Specify sample composition ZI RUNSPEC X SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP OUTECL3 VFP Specifies the mole fractions for the components in the system. The keyword is followed by N c values, and terminated with a forward slash (/) character, where Nc is the number of components specified in the RUNSPEC section. Example For a two-component CO2/I-C4 system, 60/40 mixture: ZI 0.6 292 Keywords ZI 0.4 / PVTi Reference Manual ZMFVD RUNSPEC SYSTEM SPLIT GROUP COMB SIMULATE REGRESS BLACKOIL PSEUCOMP X OUTECL3 VFP Composition versus depth table Requests that a ZMFVD table for ECLIPSE Compositional input, consisting of the composition of each component at a set of depths, be output to the PVO file. The ZMFVD keyword takes no arguments. Note PVTi Reference Manual You must also define a COMPG experiment using the EXP keyword and associated data in order that the ZMFVD table can be generated. Only two depths need be defined in the experiment, which should be the maximum and minimum required. Keywords ZMFVD 293 294 Keywords ZMFVD PVTi Reference Manual Technical Description Chapter 8 Overview This section of the manual contains information on the following: • "Theoretical background of PVT" on page 296. • "Analysis techniques" on page 371. • "Regression in PVT analysis" on page 386 • "Wax and asphaltene precipitation in PVTi" on page 394 • "Cleaning samples contaminated with oil-based mud" on page 398 • "Mixing and recombination of samples" on page 400 PVTi Reference Manual Technical Description Overview 295 Theoretical background of PVT Introduction This section of the manual contains information on the following: • "General background" on page 296. • "Properties of pure components and mixtures" on page 297. • "Characterization, splitting and grouping" on page 301. • "Material balance" on page 317. • "Flash calculations" on page 317. • "Equation of state formulation" on page 318. • "Multiphase flash" on page 324. • "Viscosity correlations" on page 330. • "Binary interaction coefficients" on page 337. • "Blackoil systems" on page 339. • "Gas condensate systems" on page 341. • "Process simulation" on page 343. • "Gas injection processes" on page 344. • "Variation of composition with depth" on page 346. • "Practical considerations" on page 348. • "Theoretical model" on page 351. • "Blackoil model" on page 354. • "Pseudo-compositional tables for ECLIPSE GI option" on page 360. • "Compositional data for ECLIPSE Compositional" on page 361. • "Water properties" on page 362. • "Model for API Tracking option in ECLIPSE BlackOil" on page 363. • "Compositional Data for ECLIPSE Thermal" on page 366. General background Both in the fully compositional and extended black oil formulations of reservoir simulation, an accurate description of the hydrocarbon system and its properties is important. In the compositional case the phase behavior of the hydrocarbon system is an integral part of the simulation. Equal phase fugacity conditions or flash calculations are used to determine the phase split and composition. In the black-oil and extended black-oil formulations averaged properties of the oil and gas phases such as Bo (oil volume factor), Rs (solution gas-oil ratio), B g (gas volume factor) and R v (condensate gas ratio) are obtained through laboratory experiments or by using an equation of state description of the hydrocarbon system. 296 Technical Description Theoretical background of PVT PVTi Reference Manual Laboratory tests Information on oil and gas properties is normally obtained through laboratory tests upon oil and gas samples. These yield: 1 The mole fraction distribution of lighter components 2 The mole fraction, molecular weight and specific gravity of the residual 3 Pressure-volume relationships obtained through depletion and expansion experiments. The mole distribution of the lighter components is usually obtained through gas chromatography, providing a quantitative separation of the lighter components into pure compounds with known properties. The heavier components are then lumped into pseudocomponents, for example a C7+ fraction containing hydrocarbons with carbon numbers from seven upwards. Beside this simple laboratory analysis more complex methods for analyzing oil and gas samples are coming into use. In these methods the residual (C7+ fraction) is split up into sub-fractions through a distillation of the residual. The boiling point of each of these sub-fractions is then used to assign pseudo component properties through empirical correlations. Expansion experiments are often carried out on oil and gas samples from the reservoir to evaluate volume factors in conditions that reflect the depletion process in the reservoir as closely as possible. On the basis of these experimental data, a model composition of the hydrocarbon mixture can be developed and used in combination with an equation of state model to calculate additional oil and gas properties at reservoir conditions and at surface conditions. The oil and gas volume factors used in black oil type models depend on the process facilities and configuration. The equation of state model allows black oil tables to be evaluated for various process facilities and configurations. An excellent summary of many of the features required to build up an understanding of fluid phase behavior from sampling considerations through laboratory techniques to the use of Equations of State can be found in the text of Pedersen et al.[Ref. 30], and McCain, [Ref. 33]. Properties of pure components and mixtures All petroleum accumulations have hydrocarbons as their predominant constituents. The chemistry of the carbon atom is the richest of all the known elements making it difficult to assign simple rules to the volumetric behavior of petroleum mixtures. In order to understand the behavior of mixtures, let us firstly consider the pure components making up a typical petroleum. This section contains information on: • "Pure components" on page 297. • "Pure component properties" on page 300. • "Multi-component mixtures" on page 300. Pure components The natural gas and crude oil found in underground natural deposits are mixtures of a large number of different hydrocarbon components and some additional non-hydrocarbons such as CO2 , H 2 S , N 2 , H 2 and CO . PVTi Reference Manual Technical Description Theoretical background of PVT 297 Hydrocarbon groups Hydrocarbons are usually divided into groups based on characteristics in molecular structure. The most important of these groups are: Alkanes or paraffins Alkanes or paraffins are very stable chemical compounds. The chemical formula for compounds in the group is C n H 2n + 2 . The group contains hydrocarbon components such as: Table 8.1 Alkanes Formula Name C1 H4 Methane C2 H6 Ethane C3 H8 Propane C 4 H 10 Butane C 5 H 12 Pentane C 6 H 14 Hexane C 7 H 16 Heptane C 10 H 22 Decane Each of these molecules can exist as a single straight chain of carbon atoms attached to three (end carbons), or two (non-end carbons) hydrogen atoms (except Methane, which has four attached hydrogens). Isomers For molecules containing four carbons or more, additional structures other than the straight chains are possible. The number of these branched molecules or isomers increases with increasing carbon number. • Butane has one isomer in addition to the straight-chained normal-Butane, the branched molecule iso-Butane. • Pentane has two isomers in addition to the normal-Pentane, known as iso- and neo-Pentane. The neo- isomer (cross-shaped) is rarely found in naturally-occurring petroleum. Most fluid analyses include the iso- and normal- components of Butane and Pentane. • Hexane (six carbon atoms) has four isomers in addition to the normal-Hexane. Note 298 The number of isomers increases rapidly with carbon number making the identification of the increasingly small concentration of these isomers impossible. Technical Description Theoretical background of PVT PVTi Reference Manual Napthenes or cycloparaffins Napthenes are characterized by the chemical formula C n H2n . Important members in this family are: Table 8.2 Napthenes Formula Name C3 H6 Cyclopropane C 5 H 10 Cyclopentane They share the same formula as the alkenes, which are the same as the alkanes except that one or more pairs of carbon atoms are linked by double bonds with the consequent loss of one or more hydrogen atoms. Note Alkenes and their triple bond equivalents, the alkynes, are rarely found in naturally occurring petroleum. Any one of the hydrogens can be replaced by a methyl-( CH3 ) or higher group, for example C 7 H 14 , Methylcyclohexane. Aromatics The third family of hydrocarbons are aromatics. These are ring-type structures. Some of the best known members of this family are: Table 8.3 Aromatics Formula Name C6 H6 Benzene C7 H8 Toluene SCN groups All of napthenes, aromatics, more complicated hydrocarbons (polynuclear molecules), hydrocarbons compounds containing other species, namely Nitrogen, Sulphur, Oxygen and certain trace metals, are all capable of existing as isomers. Identification of even a relatively small number of the possible isomers within a petroleum mixture is a complicated and therefore expensive task. It is standard practice within the petroleum industry to lump all isomers together on the basis of the boiling point of the molecule. Single Carbon Number (SCN) groups are defined for components, for example hexanes, heptanes, etc. Components are pure hydrocarbon components with normal boiling point temperatures, that is at one atmosphere pressure, between consecutive normal-paraffin boiling points. For example, the SCN hexanes group consists of those hydrocarbons that boil between the normal boiling points of n-pentane and n-hexane. PVTi Reference Manual Technical Description Theoretical background of PVT 299 Pure component properties Each of the pure components, which is now taken to include SCN groups for hexane and above, in a hydrocarbon mixture is characterized by specific physical properties such as: Table 8.4 Physical properties Term Nomenclature Tc Critical temperature pc Critical pressure Vc Critical volume Zc Critical Z -factor Mw Molecular weight ω Acentric factor Tb Normal boiling point ρ ref Reference density (usually specified at a reference temperature) T ref Reference temperature [P] Parachor (see surface tensions) The component library in PVTi contains properties for some of the more common pure components. Multi-component mixtures As mentioned previously, natural gas and crude oil contains literally thousands of different components. No attempt is usually made to identify all the hydrocarbons beyond C 5 : rather, SCN groups denoted hexanes, heptanes, etc., are used. Even so, you may be left with ten or more components in any given petroleum mixture. To describe a multi-component system thermodynamically using an equation of state model, the system must be defined in terms of the properties of the components and their mole fractions in the mixture. The terms and nomenclature used to characterize multi-component mixtures may be summarized as follows, where the subscript i denotes the i th component: Table 8.5 300 Multi-component (ii) mixtures Term Nomenclature n Number of components in the mixture T c, i Critical temperature p c, i Critical pressure M w, i Molecular weight ωi Acentric factor Technical Description Theoretical background of PVT PVTi Reference Manual Table 8.5 Multi-component (ii) mixtures (Continued) Term Nomenclature xi Mole fraction in the liquid phase yi Mole fraction in the vapor phase zi Mole fraction in the mixture as a whole p Pressure of the mixture T Temperature of the mixture V Mole fraction of the vapor phase L Mole fraction of the liquid phase Note Not all of the parameters listed above are independent. The thermodynamic behavior of a multi-component mixture depends strongly on composition, pressure and temperature. Phase diagrams In terms of a phase diagram plotted against pressure and temperature, the upper part of the phase envelope, up to the critical point, represents the bubble-point curve. From the critical point the phase envelope continues as dew point curve. The phase envelope encircles the two phase region in the phase diagram. A phase diagram is often characterized by the maximum pressure, the cricondenbar, and the maximum temperature, cricondentherm. The area within the phase envelope bounded by a vertical line through the critical point and the line represented by the cricondentherm is the retrograde area. A reduction of pressure into this area results in retrograde condensation. For the RK and ZJ equations of state the critical point calculation implements the theory developed in [Ref. 50]. For the PR and SRK equations of state the calculations use the theory developed in the followup paper in [Ref. 47]. Characterization, splitting and grouping This section of the manual contains information on: • "Components" on page 301. • "Characterization" on page 302. • "Splitting" on page 303. Components All components in PVTi are labeled as being one of three possible types: • PVTi Reference Manual LIB: Library Technical Description Theoretical background of PVT 301 • CHAR: Characterization • USER: User defined LIB components Lib components are the commonly occurring hydrocarbons C 1 , C 2 ,..., C 45 and the specific nonhydrocarbons H2 O , H2 S , CO2 , N 2 , H 2 and CO . CHAR components Components designated as CHAR are typically the last component in a PVT report and as such comprise the plus fraction, that is, contains all remaining hydrocarbons. For such fractions, a laboratory would typically measure only the mole weight and specific gravity, denoted here by M N+ , γ N+ , where N is the number of the first carbon group in the fraction. User components User components are those for which you must supply all the data necessary to define the equation of state parameters, that is T c , pc , Vc , M w and ω . Characterization Clearly, correlations are required that are capable of generating the critical properties and acentric factors from just the mole weight and specific gravity. In general, any p - V - T report gives at least the mole weight of the plus fraction. If this is the only information available, PVTi estimates a value of the specific gravity from known (SCN) distributions. Otherwise, any two out of the four of M w , γ , T b , K w is sufficient to characterize a component. PVTi employs five sets of correlations for generating critical properties by: • Kesler and Lee [Ref. 10] • Cavett [Ref. 11] • Riazi and Daubert [Ref. 12] • Winn [Ref. 42] and [Ref. 43] • Pedersen [Ref. 41]. It also uses four sets of correlations for acentric factors by: • Lee and Kesler [Ref. 13] • Edmister [Ref. 14] • Thomassen [Ref. 30] • Pedersen [Ref. 41]. Watson characterization factor In many of these correlations, a quantity often quoted is the Watson characterization factor, denoted K w which is defined as: T bi = ( K w γ i ) 3 [EQ 8.1] where: • 302 T bi is the normal boiling point temperature (in degrees Rankine) Technical Description Theoretical background of PVT PVTi Reference Manual • γi is the specific gravity of the i th component. Splitting The plus fraction often has an importance that appears to far outweigh its relatively small mole fraction of a fluid sample. In particular, saturation pressure calculations can be extremely sensitive to the mole fraction and properties of the plus fraction. More accurate predictions requiring less regression of equation of state parameters can be achieved if a thorough description of the plus fraction can be made. Ideally, a complete true-boiling-point distillation (TBP) should be made that yields not only the detailed composition of the plus fraction but also the boiling points, specific gravities and molecular weights of the constituent components. However, this analysis is rarely performed and so a general procedure to describe the distribution of components and properties within a plus fraction is required. Three techniques are available within PVTi for the splitting of the plus fraction into subfractions: • Constant Mole Fraction (CMF); • Whitson. • Semi-Continuous Thermodynamics (Modified Whitson) All of these techniques rely on a probability density function (PDF) to relate mole fraction to mole weight. This approach is due to Whitson [Ref. 4]. Probability density model The PDF used by Whitson to describe the relation between mole fraction and mole weight is a three-parameter gamma function: (M – η) (α – 1) (M – η) exp ------------------β ------------------------------------------------------------------p(M) = α β Γ(α) [EQ 8.2] where: • α, β, η are parameters defining the distribution • Γ is the gamma-function • α gives a measure of the shape of the distribution • η is the lowest mole weight in the plus fraction • β is a normalization condition that can be determined from the condition: [EQ 8.3] M N + – η = αβ where M N + is the average mole weight of the plus fraction. The cumulative probability function, P ( X ≤ x ) is the integral of p ( x ) from η to x : P(X ≤ x) = x η p ( x ) d x [EQ 8.4] that is evaluated numerically from: ∞ P(X ≤ x) = e –y α+j y -----------------------------Γ(α + j + 1) [EQ 8.5] j=0 PVTi Reference Manual Technical Description Theoretical background of PVT 303 where y = ( x – η ) ⁄ β The frequency, f i of a component i having mole weight boundaries M i – 1 , M i is given by the integral: fi = Mi M p ( M ) dM [EQ 8.6] i–1 = P ( M ≤ M i ) – P ( M ≤ Mi – 1 ) [EQ 8.7] and the mole fraction z i is related to its frequency by: zi = zN + fi [EQ 8.8] The average mole weight in the same interval is given by: P ( M ≤ M i ,α + 1 ) – P ( M ≤ M i – 1 ,α + 1 ) M i = η + αβ -----------------------------------------------------------------------------------------------P ( M ≤ M i ,α ) – P ( M ≤ M i – 1 ,α ) [EQ 8.9] where the P ( X ≤ x ) functions all use the same value of β regardless of the value of α , (that is α or α + 1 ) and where z N + is the total mole fraction of the plus fraction. In the absence of any other data, you should assume that α is unity. The parameter η is the minimum mole weight that occurs in the plus fraction, therefore if the plus fraction were C 7+ , then a good estimate to η is 92.0. Generally, Whitson recommends: η = 14n – 6 [EQ 8.10] where n is the first SCN group in the plus fraction, for example 7. Note Both splitting techniques available in PVTi use the Whitson PDF to define the mole fraction/mole weight distribution of the plus fraction, however, they differ slightly in the way they sub-divide into the required number of pseudo-components. Constant mole fraction, CMF In this technique, you select the number of pseudo-components required from the split. From this PVTi calculates the mole fraction to be assigned to each of the pseudo-components, scaled to unity. Note By default equal mole fractions are assigned. Generally, you may consider skewing the distribution thus: highest mole fraction for the lightest pseudo-component to smallest mole fraction for the heaviest pseudo-component. Hint If you have evidence on the shape of the plus fraction distribution, it may be prudent to manually change the skewness parameter α , that is less than unity for a condensate and greater than unity for a crude oil. The value of the minimum mole weight in the plus fraction η rarely needs changing from its (calculated) default value. 304 Technical Description Theoretical background of PVT PVTi Reference Manual Knowing the required mole fraction split, PVTi then integrates the PDF from η up to some mole weight M 1 such that integral gives the correct first mole fraction, and then similarly for the remaining pseudo-components. Knowing the mole weight boundaries, the program can calculate the average mole weights of the pseudo-components, estimate the specific gravities from the SCN distributions and calculate the critical properties, etc., from the various correlations currently in force. Whitson The Whitson technique consists of splitting the plus fraction into SCN groups N (the first in the plus fraction) to some high number, for example 45. The mole weight boundaries are estimated from the user specified plus fraction mole weight and specific gravity from which one can calculate a plus fraction Watson factor: 0.15178 – 0.84573 [EQ 8.11] K w, N+ = 4.5579M w, N+ γ N+ Assuming that an average Watson factor K w, N+ can be applied to each individual SCN groups, the SCN groups’ specific gravities can be estimated from equation (1), namely: 1⁄3 T b, i γ i = --------------K w, N+ [EQ 8.12] where the T b, i are the normal boiling point temperatures of the SCN groups, which in fact define the SCN groups. That is SCN C 6 is all hydrocarbons that have normal boiling point temperatures between those of normal- C 5 and normal- C 6 , etc. Then, with known boiling points and specific gravities, mole weights can be estimated using the Riazi-Daubert correlation, which is of the general form: b c [EQ 8.13] θ = aT b γ where θ is the property to be evaluated, say M w and ( a ,b ,c ) are tabulated coefficients, see [Ref. 4]. With average mole weights for the SCN groups, the boundary mole weights are estimated from: 1 M i = --- ( M i – 1 + M i ) 2 [EQ 8.14] These can then be used to integrate the PDF to give mole fractions for each of the SCN groups. Hint Generally, you will not want to work with 20-30 additional components. Therefore the SCN groups are pseudoised down into Multi-Carbon Number (MCN) groups. A method for estimating the required number of MCN groups is that due to Sturge’s, discussed in [Ref. 4]. However, this often predicts the use of four or five pseudocomponents. It has been our experience that two or three pseudo-components is sufficient for most purposes. Multi-carbon number (MCN) groups In evaluating the properties of the MCN groups from the basis SCN groups, simple mole weighted averages are taken, that is.: i = lN 1 M l = --zl PVTi Reference Manual zi Mi [EQ 8.15] i = l1 Technical Description Theoretical background of PVT 305 where the summation is performed over the SCN groups i in the MCN group l and z l is the mole fraction of the l th MCN group. Modified Whitson splitting (1988) The Constant Mole Fraction (CMF) and Whitson Splitting methods described above both consist of a continuous molar distribution model, which is subsequently discretized into a set of pseudo-components. Another method to effect the discretization is to use quadrature methods; in particular, integrals of the form: ∞ 0 N wi f ( xi ) , –x f ( x )e dx = [EQ 8.16] i=1 where the weighting factors w i and quadrature points x i are determined from a class of Laguerre polynomials for a given order N , see [Ref. 31]. For our mole weight/mole composition model, we can associate the quadrature points xi with pseudo-component mole weights M i = η + βx i and the mole fractions z i = w i f ( xi ) . To account for compositional variations with depth, Whitson extended the standard model to account for these variations, or plus fraction mole weight and skewness parameter. Since different plus fraction mole weights and skewness parameters lead to different β parameters, the following modification was introduced: β0 β = --------------------------[ 1 + ln ( δ ) ] [EQ 8.17] where β 0 and δ are parameters in the modified distribution function p0 ( M ) given by: (α – 1) α – ( M – η ) ( 1 + ln ( δ ) ) (M – η) - = p(M) p 0 ( M ) = -------------------------------exp ---------------------- ----------------------------α [ ( M – η ) ⁄ β0 ] β0 β0 Γ ( α ) δ [EQ 8.18] that is numerically identical to the original function p ( M ) , see[EQ 8.2]. To determine the mole fraction, we integrate the PDF by Gaussian quadrature by making the following transformation: M–η x 0 = -------------β0 [EQ 8.19] with dM = β0 dx to give: ∞ 0 ( α – 1 ) –x0 x0 e --------------------------------------------------dx = 1 x –α 0 Γ ( α )δ 0 ( 1 + ln ( δ ) ) [EQ 8.20] Comparing with [EQ 8.16], we have: (α – 1) α ( 1 + ln ( δ ) ) x0 f ( x0 ) = ---------------------------------------------x Γ ( α )δ 0 [EQ 8.21] and thus the mole fraction and mole weight are given by: 306 z i = w i f ( x 0i ) [EQ 8.22] M i = η + β 0 x 0i [EQ 8.23] Technical Description Theoretical background of PVT PVTi Reference Manual Procedure The procedure for using this method is particularly attractive. Firstly we choose the number of pseudo-components required, N , which is normally in the range 2 ≤ N ≤ 5 : this then fixes the values of weights and points, w i and xi . The minimum mole weight η is chosen as before. Next we specify β 0 which is done by selecting the maximum mole weight component to be used: Whitson recommends M N = 500.0 but we prefer 2 × M N+ . Either way we now have: MN – η β 0 = ----------------x 0N [EQ 8.24] Next we estimate a value for the skewness parameter, which as before is taken as unity in the absence of any other information. Then to satisfy the total number of moles and mass, we calculate: β0 δ = exp ----- – 1 β [EQ 8.25] and calculate the mole fractions and mole weights. Finally, the average plus fraction mole weight is checked: zi M i M N+ = [EQ 8.26] i------------------=1 N zi i=1 and the δ is adjusted if [EQ 8.26]does not equate to the measured value. The appeal of this model is it allows a variable plus fractions mole weight and skewness parameter by sample composition. That is different plus fraction mole weight and mole fraction, but allows us to use a common set of pseudo-components with fixed mole weights and hence critical properties. Hint Having used this procedure to characterize the plus fraction(s), you can then use the special regression facility, which allows the sample plus fraction mole weights and skewness parameters to be variables. In particular, where there is a known variation of composition with depth and you have at least two samples from different depths in the hydrocarbon column, this technique can be used with some success, see [Ref. 32]. Special regression facility An additional special regression facility has been added to this model to allow different characterizations of the split pseudo-components from this technique. Having obtained mole fractions and mole weights from the above method, a variant on the Watson K factor may be derived, denoted Fc . This is then used to estimate specific gravities and hence critical properties, acentric factors, etc., as per the original Whitson model. The additional feature is the new characterization factor, F c , which can be regressed, that is: tot cal reg [EQ 8.27] Fc = Fc × Fc PVTi Reference Manual Technical Description Theoretical background of PVT 307 reg where Fcal is c is the value calculated by the Whitson model, that is assuming SCN-cuts, and F c the potentially regressable function which defaults to unity. This allows you to make your fluid more or less aromatic with respect to the standard distribution (equivalent to a K w ∼ 12.0 ), which in turn yields different critical properties, etc., and hence different fluid behavior. Grouping Grouping of components is performed by one of three techniques: • Molar averaging • Weight averaging • Mixing rule. All of these are explained in the comprehensive text of Joergensen and Stenby [Ref. 44]. Consistency checks and correlations PVT analysis of reservoir fluids is usually performed so that a model fluid, be it blackoil, compositional or otherwise, can be constructed for use in a reservoir simulator. This analysis requires that an equation of state model is used to match measured data from laboratory experiments. Any uncertainties in the laboratory data, brought about by inconsistencies in the laboratory measurements but more likely due to problems encountered in the taking of the fluid samples, feed through into a poor fluid model. Consistency tests Most fluids that show some form of compositional behavior, namely gas condensates and volatile oils, are subject to a constant volume depletion experiment (CVD) as part of their analysis. For further information see "Compositional material balance" on page 308. A material balance calculation can be performed using the data that is generated from such an experiment from which quantities such as liquid compositions, K -values, molecular weights and densities of vapor and liquid, etc., can be evaluated. This data can then be examined to look for any inconsistencies, such as lack of monotonicity. Additional data often given in a laboratory PVT report are separator compositions for the liquid and vapor streams. If such data is available, then K -values can be constructed and plotted against theoretical fits, again as a test of consistency. Finally, estimates of recovery of gas and oil from the reservoir can be made as well as generation of blackoil tables, without recourse to the use of the equation of state model. Compositional material balance Several authors have published models for testing the consistency of laboratory CVD data, [Ref. 19] and [Ref. 6]. This section of the manual contains information on: 308 • "Consistency checks and correlations" on page 308. • "Liquid compositions and K-values" on page 310. • "Physical properties" on page 312. Technical Description Theoretical background of PVT PVTi Reference Manual • "Correlations" on page 312. • "Recombination of separator data" on page 315. • "Recovery calculations" on page 316. Note The model employed in PVTi was adapted from a program developed by Pearce [Ref. 20]. A typical laboratory CVD report might be as follows [Ref. 6]: Table 8.6 CVD Report Equilibrium vapor Pressures (psi) Equil Liquid Component 714.7 6764.7 5514.7 4314.7 3114.7 2114.7 1214.7 714.7 Carbon Dioxide 2.37 2.40 2.45 2.50 2.53 2.57 2.60 .59 Nitrogen 0.31 0.32 0.33 0.34 0.34 0.34 0.33 .01 Methane 73.19 75.56 77.89 79.33 79.62 78.9 77.8 12.42 Ethane 7.80 7.83 7.87 7.92 8.04 8.40 8.70 3.36 Propane 3.55 3.47 3.40 3.41 3.53 3.74 3.91 2.92 isoButane .71 .67 .65 .64 .66 .72 .78 .91 n-Butane 1.45 1.37 1.31 1.30 1.33 1.44 1.56 2.09 isoPentane .64 .59 .55 .53 .54 .59 .64 1.4 n-Pentane .68 .62 .58 .56 .57 .61 .66 1.6 Hexanes 1.09 .97 .88 .83 .82 .85 .9 3.68 Heptanes plus 8.21 6.2 4.09 2.64 2.02 1.84 2.12 71.01 Total 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Mw(C7+) 184.0 160.0 142.0 127.0 119.0 115.0 114.0 213.0 Sg(C7+) .816 .799 .783 .770 .762 .758 .757 .833 Zvap 1.238 1.089 .972 .913 .914 .937 .960 Nprod 0.000 9.024 21.744 38.674 55.686 72.146 81.301 Sliq 0.00 14.1 19.70 21.60 21.30 20.20 19.3 This gas condensate with an assumed reservoir composition equal to composition at the first pressure, which corresponds to the saturation pressure of the fluid, psat = 6764.7 psia is put through the stages of the CVD. The CVD consists of reducing the pressure to the required stage pressure, and then removing gas so that the volume remaining in the cell is equal to volume at the saturation pressure. At each stage, the composition, mole weight and specific gravity of the plus fraction (denoted Mw and Sg), the vapor Z -factor (denoted Zvap), the number of moles produced (denoted Nprod) and the liquid saturation (denoted Sliq), are measured. The subsequent analyses used to generate liquid compositions, K -values, volumes, masses and densities follow those of Whitson and Torp [Ref. 6]. PVTi Reference Manual Technical Description Theoretical background of PVT 309 Liquid compositions and K-values Cell compositions A material balance performed on the total moles and individual components is: n tj = n lj + n vj [EQ 8.28] n tj z ij = n lj x ij + n vj y ij [EQ 8.29] where: • n tj , n lj , n vj are the total, liquid and vapor moles at stage j • ( p = p j ) and z ij , x ij , yij are the total, liquid and vapor mole fractions of component i . Starting with one mole of fluid at the saturation pressure (first stage in the reported CVD), the number of moles remaining the cell after the j th stage is: j n tj = 1 – Δnpk [EQ 8.30] k=2 where n pk is the number of moles of gas produced at stage, denoted Nprod in the table above, so that Δn pk is the incremental gas recovered during the kth stage, that is, reducing the pressure from p k – 1 to p k . Similarly, the mole fraction of the i th component remaining in the cell after the j th stage is: j n tj z ij = z i1 – Δnpk yik [EQ 8.31] k=2 Cell volumes To convert moles and mole fractions to volumes, one must have some reference volume, such as the volume of the cell. For a gas condensate, the cell volume, for one mole, can be calculated from the real gas law: Z 1 RT V cell = ------------p1 [EQ 8.32] where: • Z1 and p1 are the vapor Z -factor and pressure at the first (saturation) pressure • R • T is the temperature at which the CVD is performed, assumed constant throughout the experiment. is the universal gas constant For a volatile oil, a CVD report gives the molecular weight and density of the bubble point liquid, M w1 and ρ 1 , and thus the cell volume, again for one mole, is calculated as: M w1 V cell = ---------ρ1 [EQ 8.33] Knowing the cell volume and the liquid saturation at the j th stage, S lj (denoted Sliq in the table above), the volume of the cell occupied by liquid is: V lj = S lj V cell 310 Technical Description Theoretical background of PVT [EQ 8.34] PVTi Reference Manual and thus the volume of the cell occupied by gas is: [EQ 8.35] V vj = ( 1 – S lj )V cell Moles and mole fractions The number of moles of vapor remaining in the cell at the j th stage can be determined from the real gas law: p j V vj n vj = -----------Z j RT [EQ 8.36] Thus, the composition of the liquid remaining in the cell at the j th stage can be determined from: n tj z ij – n vj y ij x ij = ------------------------------n tj – n vj [EQ 8.37] Equilibrium K-values The K -values can now be estimated from the ratio of the vapor and liquid mole fractions: y ij K ij = ----x ij [EQ 8.38] The best test of the consistency of the CVD data is to plot the logarithm of the p j K ij product against the characterization factor F , [Ref. 20], where: 1 1 F = b i ------- – --- T bi T [EQ 8.39] where T is the reservoir or CVD experiment temperature and bi is the Hoffmann-Crump-Hocott b -factor for the i th component, which is given by: ( log ( p ci ) – log ( p ref ) ) b i = ---------------------------------------------------1 1 ------ – ------- T bi T ci [EQ 8.40] Here: • T ci and T bi are the critical and normal boiling point temperatures • p ci is the critical pressure (in psia) • p ref is the reference pressure, usually 14.7 psia. Plots As pointed out by Bashbush, [Ref. 19], the curves should plot in a parallel-like trend, that is, there should be no humps in any individual curve or crossing of any pair or pairs of curves. The highest curve should belong to nitrogen, followed by methane and carbon dioxide. Then depending on the fluid composition, either ethane or hydrogen sulphide should be plotted followed by the curves for the remaining hydrocarbon components in order of increasing molecular weight. Finally, it should be noted that the iso- components of butane and pentane should plot above their corresponding normal components. This plot is available from PVTi. PVTi Reference Manual Technical Description Theoretical background of PVT 311 Other useful plots consists of fingerprint plots of the liquid composition remaining in the cell at the end of the CVD (the last column in the above table) and the equivalent calculated liquid composition, and the calculated liquid compositions as a function of pressure. Both of these plots are available from PVTi. Physical properties As well as performing material balances on moles and mole fractions, material balance can be done on the total, liquid and vapor masses: m tj = m lj + m vj [EQ 8.41] The total mass remaining the cell at the j th stage is given by: j m tj = M s – Δnpk Mvk [EQ 8.42] k=2 where M s and M vk are the initial or saturation pressure molecular weight and the vapor molecular weight at the kth stage, respectively, both of which can be evaluated from Kay’s rule: Nc M vj = yij Mi [EQ 8.43] i=1 where M i is the molecular weight of the i th component. Vapor molecular weight is calculated from: m vj = n vj M vj [EQ 8.44] And liquid molecular weight from the mass balance: m lj = m tj – m vj [EQ 8.45] Now, knowing the masses and volumes of liquid and vapor in the cell at each stage, one can calculate densities from ρ = m ⁄ V Plots of these quantities are available from PVTi. Correlations Alani-Kennedy liquid densities The liquid molar volume of a pure hydrocarbon component is given by the smallest real positive root of the Van der Waal’s equation: a RT = p + -----2- ( V – b ) V [EQ 8.46] that contains the two unknown parameters ( a ,b ) . Alani and Kennedy, [Ref. 20], inserted known values of T , p and V into [Ref. 16] for two pressures for a variety of hydrocarbons. Thus they were able to observe the variations of ( a ,b ) from which they derived: a = K exp ( n ⁄ T ) [EQ 8.47] b = mT + C [EQ 8.48] where: 312 Technical Description Theoretical background of PVT PVTi Reference Manual • ( n ,K ,m ,C ) are tabulated constants for the hydrocarbons • C 1 , C 2 ,..., C 6 : • C 7+ can be calculated from given correlations in molecular weight and specific gravity of the plus fraction and temperature (see [Ref. 22]). the coefficients for the plus fraction The ( a ,b ) coefficients for a hydrocarbon mixture are given by Kay’s rule: C N+ a mix = C N+ xi ai b mix = C1 xi bi [EQ 8.49] C1 where xi are the liquid mole fractions. Note The non-hydrocarbons N 2 , CO2 and H 2 S are added into the C 1 fraction. Vapor Z-factor The vapor Z -factor, Z vap , can be estimated from the correlation due to Dranchuk, Purvis and Robinson [Ref. 21]: 0.27p r Z vap = --------------ρr Tr [EQ 8.50] where T r and p r are the reduced temperature ( = T ⁄ T c ) and reduced pressure ( = p ⁄ pc ) , and ρ r is the pseudoreduced density, which is found by iteratively solving: [EQ 8.51] f ( ρr ) = 0 where: 6 3 2 3 2 2 f ( ρ r ) = Aρ r + Bρ r + Cρ r + Dρ r + Eρ r ( 1 + Fρ r ) exp ( – F ρ r ) – G [EQ 8.52] and: A = 0.06423 [EQ 8.53] B = 0.5353T r – 0.6123 [EQ 8.54] 0.5783C = 0.3151T r – 1.0467 – --------------2 Tr [EQ 8.55] D = Tr [EQ 8.56] 0.6816 E = --------------2 Tr [EQ 8.57] F = 0.6845 [EQ 8.58] G = 0.27T r [EQ 8.59] with the initial estimate for the pseudoreduced density of: 0.27p r ρ r0 = --------------Tr [EQ 8.60] Pseudo-critical temperatures and pressures Pseudo-critical temperatures and pressures for a fluid mixture can be calculated from one of two methods: PVTi Reference Manual Technical Description Theoretical background of PVT 313 • Kay’s rule • Wichert and Aziz Correlation. Kay’s rule has been stated already, being a mole fraction weighted sum of the appropriate quantity. The correlations due to Wichert and Aziz, [Ref. 22], correct for the presence of the so-called sour gases, CO2 , H2 S and N 2 . The pseudo-critical temperature and pressure of the hydrocarbon portion of a condensate is given by: HC HC 2 [EQ 8.61] HC HC 2 [EQ 8.62] HC = 187 + 330γ g – 71.5 ( γ g ) HC = 706 + 51.7γ g – 11.1 ( γ g ) Tc pc where γ HC is the hydrocarbon gas gravity that is related to the mixture gas gravity, γ mix by: g g mix HC γg γ g – 0.9672y N – 1.5195y CO – 1.1765y H S 2 2 2 = -----------------------------------------------------------------------------------------------------------1 – y N – y CO – y H S 2 2 [EQ 8.63] 2 with: mix γg yi Mi = ------------------M air [EQ 8.64] and M air is the molecular weight of air (= 28.97). The pseudo-critical temperature and pressure for the mixture, including non-hydrocarbons, is: HC T pc = ( 1 – y N – y CO – y H S )T c + 227.3y N + 547.6y CO + 672.4y H 2 2 2 2 2 [EQ 8.65] 2S and HC p pc = ( 1 – y N – y CO – y H S )p c + 493.0y N + 1071.0y CO + 1306.0y H 2 2 2 2 2 2S [EQ 8.66] The correction to T pc and ppc in the presence of sour gas ( CO2 and H2 S ), due to Wichert and Aziz, is: ε = 120 [ ( y CO + y H S ) 2 0.9 2 – ( y CO + y H S ) 2 2 1.6 0.5 ] + 15 ( y H 2S 4.0 – yH S ) 2 [EQ 8.67] to give: [EQ 8.68] T∗ pc = T pc – ε and p pc ( T pc – ε ) p∗ pc = ----------------------------------------------------T pc + y H S ( 1 – y H S )ε 2 [EQ 8.69] 2 Gas viscosity The dynamic gas viscosity of a hydrocarbon gas at a temperature T can be estimated from a correlation due to Lee, Gonzalez and Eakin, [Ref. 23]: C μ g = A exp ( Bρ ) [EQ 8.70] where: 314 Technical Description Theoretical background of PVT PVTi Reference Manual –4 1.5 10 ( 9.4 + 0.02M w )T A = ---------------------------------------------------------( 209.0 + 19.0M w + T ) [EQ 8.71] 986.0 B = 3.5 + ------------- + 0.01M w T [EQ 8.72] C = 2.4 – 0.2B [EQ 8.73] and: pM w ρ = ----------ZRT [EQ 8.74] where ρ is measured in g/ cm3 . Recombination of separator data In most laboratory PVT reports, the well stream fluid used as the basis for the experiments is generally a recombined sample of separator gas and oil. The rates of production of the two phases are also recorded and the ratio of gas rate to oil rate defines the separator gas-oil ratio (GOR). Generally, the separator is operating at some pressure and temperature above what would be considered as standard conditions, such as 60 °F , 14.7 psia, in which case the separator oil is almost certainly not be stable at standard conditions since it probably still contains dissolved gas. The best laboratory analyses contain a mole fraction analysis of the separator oil and gas and the stabilized, standard conditions, oil and gas. Any available gas and oil compositional analysis can be used to generate a set of K -values. These K -values can be plotted using the Hoffmann-Crump-Hocott construction, see [Ref. 19] and"Correlations" on page 312. An analysis of sets of K -values from many fluid samples by Standing, [Ref. 24], indicated that for pressures less than 1000 psia, compositional dependency in K -values, usually indicated by the apparent convergence pressure of the log ( K ) versus log ( p ) plot, is small and can often be neglected. Noting this, Standing fitted the following form: 1 ( a + cF ) K = --- 10 p [EQ 8.75] with: –4 –8 2 [EQ 8.76] a = 1.20 + 4.5 ×10 p + 15.0 ×10 p –4 –8 2 [EQ 8.77] c = 0.89 – 1.7 ×10 p – 3.5 ×10 p where F is the Hoffmann et al. characterization factor, refer to [EQ 8.39]. As most separators are operated at pressures less than 1000 psia, the so-called Standing K values provide a reasonable test of the quality of the calculated separator data and can be used as an alternative for blackoil table generation etc., when no such actual data is available. The feed to each stage of the separator can be calculated given the compositions of liquid and vapor resulting from the separator flash, the GOR and the liquid density. It can be shown that the phase split β is given by F ⁄ ( 1 + F ) where: ( GP std M ) F = -------------------------( RT std ρ oil ) • PVTi Reference Manual [EQ 8.78] where: Technical Description Theoretical background of PVT 315 • G is the GOR (gas at STC, oil at stage conditions) • M is the molar weight of oil, that is xi Wi i • d ρ oil is the density of the separator oil. Given β , the feed z i can be found from z i = βyi + ( 1 – β )xi . Recovery calculations For reservoirs whose initial pressure, p init , is greater than its saturation pressure, psat , estimates of fluid recovery can be made if the Z -factors in the range p init ≥ p ≥ psat are known. Note Above the saturation pressure, no compositional changes in the fluid take place so for a unit volume of the fluid at isothermal conditions: n1 Z1 n2 Z2 ----------- = ---------p1 p2 [EQ 8.79] Starting with 100 moles of fluid at the initial reservoir pressure, the number of moles at some pressure p j above the saturation pressure is: left nj rem = 100 – n j [EQ 8.80] where: rem nj pj Z1 = 100 ---- ----- Z j p 1 [EQ 8.81] At pressures below the saturation pressure, the produced moles are known from the CVD experiment. The fluid at each stage can then be flashed to surface conditions, using separator or Standing’s K -values to get the volumes of liquid and vapor that could be expected at the surface, assuming 100% efficiency in the separators. An option exists to produce liquid along with gas, in a ratio defined by input relative permeabilities, using the technique described in Reudelhuber and Hinds, refer to [Ref. 37]. 316 Technical Description Theoretical background of PVT PVTi Reference Manual Equation of state General information PVTi allows you to fit data to an Equation of State. See "The fluid model" on page 98 and "Batch system and keywords" on page 152 for further information on how to define Equations of State in PVTi. This section of the manual contains information on: • "Material balance" on page 317. • "Flash calculations" on page 317. • "Equation of state formulation" on page 318. • "Surface tensions" on page 321. • "Three-parameter equation of state" on page 321. • "Binary interaction coefficients" on page 337. Material balance We consider a hydrocarbon system consisting of one mole of mixture or feed of composition z i . In general, this consists of: • L moles of liquid of composition xi • V moles of vapor of composition y i • at some pressure and temperature, p and T . The conditions exist that: [EQ 8.82] L+V = 1 xi = yi = zi = 1 [EQ 8.83] Lxi + Vy i = z i [EQ 8.84] i i i Flash calculations For a thermodynamic system to be in equilibrium it is further required that the fugacities in the liquid and vapor phases must be equal for each component: [EQ 8.85] f iL = f iV The equations [EQ 8.82] to [EQ 8.85] in the unknowns L , V , x i and yi may be solved to find the equilibrium state of a system of known composition z i . The fugacities are functions of temperature, pressure and composition (see "Equation of state formulation" on page 318), f i = f i ( T , p, x i) PVTi Reference Manual Technical Description Equation of state 317 The fugacities can be calculated directly from an equation of state. Defining equilibrium constants K i for each component as: yi K i = ---xi the mole fractions of each component in the liquid and vapor phases are defined as: zi x i = ------------------------------------[ 1 + ( K i – 1 )V ] [EQ 8.86] and Ki zi y i = ------------------------------------[ 1 + ( K i – 1 )V ] [EQ 8.87] The flash calculation determining the equilibrium conditions in the two-phase region is performed in two stages: Use Michelsen’s stability criterion, [Ref. 16], to establish how many phases are present. The stationary condition used to determine the Gibb’s energy minimum is obtained using successive substitution accelerated with the general dominant eigenvalue method, [Ref. 8], switched to BFGS minimization near the minimum, [Ref. 9]. If two phases are present, solve the phase split calculation to obtain equal fugacity liquid and vapor states. The solution variables used are Ji = log ( K i ) and the vapor mole fraction. The stability check provides an initial set of values, which are refined using accelerated successive substitutions, and finally solved using a full Newton-Raphson method. In the case of finding a saturation pressure, that is a bubble point for an oil or a dew point for a condensate, the same N -fugacity equations are used, [EQ 8.85], and a constraint based upon the difference in the sum of vapor and liquid mole fractions, [EQ 8.83]. Rather than iterating to find the vapor fraction, V , or liquid fraction L = 1 – V , from [Ref. 1], V is set to 0 (zero - bubble point) or 1 (one - dew point) and we vary pressure until the set of conditions is satisfied. Equation of state formulation The fugacities and Z -factors used in the flash calculations are obtained from the equation of state. The four equations of state implemented in PVTi are: • (RK) Redlich-Kwong • (SRK) Soave-Redlich-Kwong • (ZJ) Zudkevitch-Joffe • (PR) Peng-Robinson The equations of state listed above are implemented using the formulation presented by Martin, [Ref. 2], and Coats, [Ref. 3]. The equation of state for a real fluid is: PV = nRTZ [EQ 8.88] where P is the pressure, V the volume, n the number of moles, R the universal gas constant, T the temperature and Z is obtained from the solution of the cubic equation: 3 2 Z + E2 Z + E1 Z + E0 = 0 [EQ 8.89] with 318 Technical Description Equation of state PVTi Reference Manual [EQ 8.90] E 2 = ( m 1 + m 2 – 1 )B – 1 2 [EQ 8.91] E 1 = A – ( 2 ( m 1 + m 2 ) – 1 )B – ( m 1 + m 2 )B and 2 [EQ 8.92] E 0 = – [ AB + m 1 m 2 B ( B + 1 ) ] The coefficients m1 and m2 depend upon the equation used: Table 8.7 Equation of State coefficients value Mnemonic Equation of state m1 RK Redlich-Kwong 0 1 SRK Soave-Redlich-Kwong 0 1 ZJ Zudkevitch-Joffe 0 1 PR Peng-Robinson 1+ 2 m2 1– value 2 The cubic equation for the Z -factors may be solved to obtain Z -factors for liquid and vapor phases. Generally three solutions are obtained. The distinction between the liquid and vapor phase is then made by choosing the smallest root as the Z -factor for the liquid phase and the largest root as the Z -factor for the vapor phase. Fugacity coefficients are calculated using: fi ( Z + m2 B ) Bi 2S i B i A ln ------- = – ln ( Z – B ) + ---------------------------- ------- – ----- ln ------------------------- + ----- ( Z – 1 ) px i ( m 1 – m 2 )B A ( Z + m1 B ) B B [EQ 8.93] where Si = Aij xj n A = [EQ 8.94] n ( xj xk Ajk ) [EQ 8.95] j = 1k = 1 n B = ( xj Bj ) [EQ 8.96] j=1 A jk = ( 1 – k jk ) ( A j A k ) 1--2 [EQ 8.97] and kjk are binary interaction coefficients, normally between hydrocarbons and nonhydrocarbons. These four equations, [EQ 8.94] to [EQ 8.97], express the mixing laws used in all the equations of state. The variables A j and B j are defined by the following equations: p rj A j = Ω A ( T, j ) -----2 T rj [EQ 8.98] and p rj B j = Ω B ( T, j ) -----T rj PVTi Reference Manual [EQ 8.99] Technical Description Equation of state 319 and ΩB ( T, j ) used in equations [EQ 8.98] and [EQ 8.99] are functions of the acentric factor ω and the reduced temperature T rj . Ω A ( T, j ) For Redlich-Kwong 1 – --2 Ω A ( T, j ) = Ω A T rj [EQ 8.100] Ω B ( T, j ) = Ω B [EQ 8.101] 0 0 For Soave-Redlich-Kwong Ω A ( T, j ) = Ω A 1 + ( 0.48 + 1.57ω j – 0 Ω B ( T, j ) = Ω B 0 2 0.17ω j ) 1 – 2 --1- 2 T rj [EQ 8.102] . [EQ 8.103] For Zudkevitch-Joffe 1 – --2 Ω A ( T, j ) = Ω A F aj ( T )T rj [EQ 8.104] Ω B ( T, j ) = Ω B F bj ( T ) [EQ 8.105] 0 0 For Peng-Robinson 1 --- 2 2 Ω A ( T, j ) = Ω A 1 + ( 0.37464 + 1.54226ω j – 0.2669ω j ) 1 – T rj 0 Ω B ( T, j ) = Ω B 2 [EQ 8.106] [EQ 8.107] 0 The normal PR form can be optionally modified for large acentric factor, using the factor 2 3 rather than ( 0.37464 + 1.54226ωj – 0.2699ω 2j ) for ω j > 0.49 . This correction is invoked by use of the PRCORR keyword or interactively from the Equation of State panel. For further information see "The fluid model" on page 98. ( 0.379642 + 1.48503ω j – 0.164423ω j + 0.016666ω j ) ΩA 0 and Ω B0 are constants depending upon the equation of state: Table 8.8 Equation ΩA RK, SRK, ZJ 0.4274802 0.086640350 PR 0.457235529 0.077796074 Note 320 Equation of State constants 0 ΩB 0 In the program, these default values may be over-written on a component basis either interactively, or by the use of the OMEGAA and OMEGAB keywords. Technical Description Equation of state PVTi Reference Manual Zudkevitch-Joffe equation The Zudkevitch-Joffe equation contains additional temperature factors, denoted F aj ( T ) and F bj ( T ) , multiplying the usual RK temperature dependence. These are adjusted to match the purecomponent fugacity values along the vapor pressure line, and to observe the correct component liquid density. In the program the required variation of component saturation pressure and liquid density with temperature are obtained using correlations of Reidel, and Gunn and Yamada. These correlations require the input of the normal boiling point and the reference liquid density at a specified reference temperature. Surface tensions The surface tension between the liquid and vapor phase of a multi-component mixture can be estimated by the Macleod-Sugden relationship, [Ref. 18]: 1--4 σ mix Nc = [ Pi ] ( ρm Liq Vap [EQ 8.108] xi – ρm yi ) i=1 where [ P i ] is the parachor of the i th component, see [Ref. 18], which has a liquid and vapor mole Vap fraction of xi and yi respectively, and the liquid and vapor molar densities are ρ Liq m and ρ m respectively. If the parachors are assigned values consistent with [Ref. 18] and the molar volumes are expressed in gmoles/ cm3 then the surface tension σ have units of dynes/cm. Three-parameter equation of state The traditional weakness of the so-called two-parameter equation of state, such as the PengRobinson, Redlich-Kwong, etc., above, is their poor prediction of liquid properties, especially liquid densities and saturations. Peneloux et al., [Ref. 25], proposed a molar volume correction for the SRK Equation of State, which is also applicable to any cubic Equation of State. This technique, referred to as volume translation, adds a third parameter to the Equation of State, which greatly improves liquid properties estimations. Note In PVTi, this correction is available for the Peng-Robinson and the Soave-RedlichKwong Equation of State. For a mixture of N components, the phase volume, Vmol,p , is given by: N EoS V mol,p = V mol,p – zi ci [EQ 8.109] i=1 where: PVTi Reference Manual EoS • V mol,p is the molar volume of the phase • p • z i = ( x i ,y i ) • c ri = (liquid, vapor) predicted by the traditional (two-parameter) Equation of State are the liquid and vapor mole compositions constitute a set of volume corrections. Technical Description Equation of state 321 The component corrections are usually related to the set of dimensionless shift parameters, s i , by: c ri s i = -----bi [EQ 8.110] where: RT ci b i = Ω b, i ----------- . p ci [EQ 8.111] See [Ref. 25]. Shift parameters No Temperature Dependence (“None”) In the simplest case, where the Volume Shift dependence is “None”, the Shift parameters for the inorganic and light hydrocarbon components are calculated using the temperature-dependent correlations given by Søreide, [Ref. 34]. The functional form of these polynomials depends on whether the PR or SRK EOS is being used and on whether the reduced temperature, Tr (= T ⁄ T crit ) is less than or greater than 1. For this simple case, where there is no temperature dependence on the Volume Shifts a value of Tr=0.7 is used in the equations. In the case of the PR EOS the equation take the form: s i = T r – 0.741 1.355 – 0.164 + 0.479ω i + 0.428 exp [ 25.33 ( T r – 1 ) ] [EQ 8.112] + 0.587ω i + 0.369 exp [ 10.369 ( T r – 1 ) ] [EQ 8.113] and for the SRK EOS: s i = T r – 0.904 3.713 where, for each component, s i is the dimensionless Volume Shift, ω i the acentric factor and, as mentioned above, T r =0.7. For heavier components ( M w > 90 ) the shifts are estimated on a component by component basis as the difference in the calculated single component molar volume using the two-parameter Equation of State at the components reference pressure and temperature (often 60 °F and 14.7 psia), and the reference molar volume (mole weight divided by reference density). The shift parameters of the heavier components are potential regression variables and are added to the allowed set if you request either the PR3 or the SRK3 Equation of State. Experience has shown that simultaneous matches to saturation pressure and density can be achieved more easily as a result, and therefore the use of these Equations of State in PVTi is recommended. One obvious deficiency of this model is that the shift coefficients, ci , are only valid at one temperature. If one attempts to model the change of molar volume of a pure component, such as Hexane, with temperature using, say, the PR3 Equation of State, and compares that against the known thermal expansion coefficient, see [Ref. 18], one will find a discrepancy. In an attempt to overcome this deficiency, two options have been added to PVTi whereby temperature-dependence is introduced using differing methods which are now outlined. Linear Expansion Only In this model, the volume shifts of all the components are modified with a linear thermal expansion coefficient, κ , using the equation: 322 Technical Description Equation of state PVTi Reference Manual [EQ 8.114] c i ( T ) = c ri ( T ri, P ri ) [ 1 + κ i κ ( T – T ri ) ] where cri ( T ri, P ri ) for a particular component is the dimensional volume shift specified in equation [EQ 8.109]. Physically these cri coefficients correspond to the difference in volume of 1 mole of a particular component at temperature T and pressure P (pressure at standard conditions - usually 60F), and 1 mole of that component at its reference temperature and pressure, T ri and P ri . The κ i coefficients are determined using a formula which is a fitted functional (of mole weights) of the first ten paraffins from [Ref. 17] and is given by: [EQ 8.115] κ i = 0.9 – 0.002MW i, MW i < 200 κ i = 200, MW i ≥ 200 is a special regression function in PVTi, and takes the default value of 0.0005 °C –1 , determined from a fit to a crude oil. Physically, it represents a thermal expansion factor, and has keyword THERMX within PVTi. κ Polynomial Correlations If the temperature dependence of the Volume Shifts is set to Polynomial Correlations then the equations of Soreide are used which were introduced in the case of Tr<1 in equations [EQ 8.112] and [EQ 8.113]. When the None option was set we always set Tr=0.7 and so these equations were fine. However, if a temperature above Tc is supplied to the algorithm with the Polynomial Correlations option set so that Tr>1, then PVTi chooses from a set of equations depending on the mole weight of the component. These equations can be found in [Ref. 34]. Note The Soreide correlations only cover light components up to C 6 . For heavier components ( M w > 90 ) the thermal expansion scheme outlined in the "Linear Expansion Only" on page 322 is applied. However, since the scheme is now applied to regions where the fitted functional κ i is no longer valid, κ i is set to unity, and the thermal expansion factor, κ , applies directly. For this reason it is often a good choice as a regression variable for heavy hydrocarbon components if one is finding difficulty matching liquid densities. The Linear Expansion Only model has some advantages in that since the modification to volume shifts is linear, the volume shifts may be regressed for all components. For the Polynomial Correlations model, since the correlations of Søreide are not linear, you cannot regress the shift parameters of lighter components to which the correlations have been applied. Hint PVTi Reference Manual However, an inspection of the behavior of volume shifts with temperature, as given in [Ref. 36], shows that volume shifts generally do not obey a linear relation with temperature, and for this reason, the second method often gives better results and is the recommended choice. Technical Description Equation of state 323 Note If the volume shifts are Dependent, then they are calculated so that the calculated reference density (the density at the reference temperature and standard conditions pressure) is guaranteed to match the observed value. This means that the volume shifts are dependent on the critical properties and acentric factor of the component. If the volume shifts are Independent this guarantee is broken and the volume shifts can be varied during regression. In this situation they are not affected by changes in the critical properties or acentric factors. Multiphase flash Standard algorithm The conventional two phase flash calculation starts with a stability test for the feed composition, based on Michelsen’s (1982) stability criterion, . If unstable, a flash phase split calculation is performed to determine the two phase compositions. The multiphase flash continues in a stepwise fashion: if any one of the current N phases exhibits instability, an N+1 phase flash split calculation is performed, the resulting tested for stability. The maximum allowed number of phases is five, after that is reach no more phases are split off. Options with the Multiphase flash The Multiphase flash has three modes: 1 Conventional two phase mode. 2 Three phase mode, one of which is restricted to water. 3 The full multiphase flash mode. This is the default. In this mode there are now two different ways of performing a multiphase flash calculation. a The standard method. This method is the one that was in use for the 2002A release and initially assumes a single phase equal to the feed. Stability checks are performed and subsequent phases are split off if the system is unstable. b Instead of the flash starting with the feed an initial guess/guesses can be used assuming there are 4 phases present, which are initially undetermined. Stability analysis The stability of each phase present in a multiphase regime can be tested with the Michelsen analysis, [Ref. 16], precisely as for the two phase case, using the Gibbs energy tangent plane distance criterion. However, the initial estimates for phases that will be split off are not limited to the vapor/liquid equilibrium phases characterised by the Wilson K-values: additional estimates are chosen from the following phases: 324 • Each inorganic component • Lightest hydrocarbon • Heaviest hydrocarbon • Ideal gas • Arithmetic mean of existing phases. • Wax - prediction of cloud point - SPE 27629 Technical Description Equation of state PVTi Reference Manual The solutions method used for Michelsen stability criterion is a Successive substitution with GDEM (general dominant eigenvalue method) follow by BFGS if that does not work. These trial phases are tested in turn until one indicates instability, in which case the whole system is unstable, and the algorithm proceeds to split of that phase, provided that phase does not already exist. If none of the trial phase indicates instability, the state is assumed to be stable. Phase Split Calculations The multiphase flash calculations are based on Gibbs energy minimisation of the system, and is fully defined by the multiphase flash equation and the Gibbs energy stationary point criterion. Systems of Equations Material Balance, Mass conservation equations or consistency equations Consider a hydrocarbon system consisting of one mole of mixture or feed of composition { z i }. In general, this will consist of { β m } moles from each of the M phases, with composition { z im }, at some pressure P and temperature T. Mass conservation gives: βm = 1 [EQ 8.116] zim = 1 [EQ 8.117] m i βm zim = zi [EQ 8.118] m These consistency rules can be checked at the end of the multiphase flash calculation. Defining the multiphase equilibrium ‘K’-values as: z ij K ij = ----------z ir ( i ) Where r ( i ) is the reference phase index chosen for component i, usually so that the largest amount of component i is in the reference phase. Gibbs Energy Stationary Conditions The solution of the multiphase flash satisfies the consistency equations and is the absolute minimum of the Gibbs free energy. The reduced Gibbs energy of an M phase system is written as: G g° = ------- = RT βm zim ln ( fim ) i [EQ 8.119] m th where f im is the fugacity coefficient in the i component and the m fugacties are calculated from the equation of state. th phase. Where the The first derivative with respect to the scaled mole numbers Θ jk = β k z jk ⁄ z j can be written in various forms: g· ° = z j ( ln f jk – ln f jr ( j ) ) PVTi Reference Manual [EQ 8.120] Technical Description Equation of state 325 = z j ( ln z jk – ln z jr ( j ) + ln Φ jk – ln Φ jr ( j ) ) [EQ 8.121] = z j ( ln K jk + ln Φ jk – ln Φ jr ( j ) ) [EQ 8.122] where Φ jk is the fugacity coefficient of component j in the k’th phase. In equilibrium, the Gibbs energy is at a minimum, and the first order stationary condition thus implies fugacity balance between like components in all phases. The second derivative of the Gibbs free energy is: δ mk – δ mK δ ij ∂ ln Φ im g··° = z i z j ------------------------- ------- – 1 + ------------------ – z im βm ∂z im ∂ ln Φ iM δ Mk – δ MK δ ij – -------------------------- -------- – 1 + ------------------- – z iM βM ∂z jM ∂ ln Φ im zpm -----------------∂z pm p ∂ ln Φ iM - zpM -----------------∂z pM p where K = r ( k ) , M = r ( m ) and δ ij is the Kronecker delta and the fugacity coefficient derivatives are calculated from the Equation of State being used. Finding Stationary solutions Starting from initial conditions provided by the stability analysis (or input directly), the general algorithm is repeating cycle of the following: • iterate forward to new J = ln ( K ) values • solve the multiphase flash equation for new beta-values • update the compositions. Checking to see solution is consistent, that is mole fractions have to add up to one. The algorithm has two attempts at converging to a local minimum. First method updates with direct or successive substitution with GDEM of the J-values. If it does not converge that is the fugacity balance equation residuals fails to meet a specified tolerance, it proceeding to a try continuing the convergence with Newton-Raphson/Murray method. Successive Substitution (SS) The SS part incorporates the General Dominant Eigenvalue Method (GDEM) acceleration algorithm. For details see Crowe and Nishio. The variable used are the J-values themselves, updated from the second form of the first derivative given in equations [EQ 8.120], [EQ 8.121] and [EQ 8.122]. The reference phase for each component is chosen as the phase with the highest mole fraction of that component, so as to scale each K value close to and below one. Newton-Raphson (NR) The NR part uses a Murray decomposition of the Gibbs Hessian to ensure positive definiteness of the Jacobian, and therefore progress towards a minimum. Occasionally, a cubic trace back augmented line search in the Newton direction indicated is required when the Gibbs free energy is found not to decrease. The variables used are the scaled mole numbers, and the reference phase is the same as in the SS, that is, the phase with the highest mole fraction. 326 Technical Description Equation of state PVTi Reference Manual Trace Elements If a phase possesses a near-zero component composition, then the variable for that component and phase can be dropped from the variable list (that is not changed in the SS or NR) and its value calculated after each iteration by invoking fugacity balance between it and the fugacity of a variable that was update in the usual way. In doing so, the trace element fugacity coefficient is calculate by setting its composition to zero. If the component transcends the numerical zero boundary, its variable is reintroduced into the variable set ready for the next iteration. 4-Phase Guess Method Instead of doing a phase split method we can used initial guesses to obtain a different initial starting points for the find stationary solutions using SS and NR, which might converge to a different stationary state. See Trebble ([Ref. 62]). There are various initial guesses that can be implemented. • Wilson initiation, proposed by Wilson ([Ref. 1]) • Wilson and Antonie • NISA (Non-Iterative Stability Analysis) • Wilson and Stability • NISA and Stability • Liquid-Liquid Initiation • Trebble’s Vapor-Liquid-Liquid Initiation • Liquid-Vapor and Wax • Wax and Liquid-Liquid-Vapor Initiation. • Five phase initial guess. It was found that for a flash with wax that the wax initial guess did give a lower Gibbs free energy some of the time. For the wax initial guess we assume the composition of the liquid phase is the same as the feed. We then workout based on the wax, heavier liquid and vapor K values by: o ln y i = ln x i + ln Φ i, V ( x i ) – ln Φ i, L [EQ 8.123] o ln x 2i = ln x i + ln Φ i, L ( x i ) – ln Φ i, L [EQ 8.124] o ln x 3i = ln x i + ln Φ i, W ( x i ) – ln Φ i, L [EQ 8.125] o where Φ denotes pure fugacity, L,V and W denote liquid, vapor and wax. y i component in the vapor phase. x i , x 2i and x 3i are the components in the lightest liquid, the heavier liquid and the wax phase. Both result using the initial guess and standard algorithm can pass the stability test, so in the multiphase where it is possible for wax to form, we do both the four phase wax initial guess and the standard multiphase flash and compare results, taking the one with the lowest Gibbs free energy. In the case of the debug option switching on all the initial guesses and in the case for the wax possible case fail to give an answer which pass the stability test, then all initial guesses are tried and compared and the result with the minimum Gibbs free energy taken as the answer. PVTi Reference Manual Technical Description Equation of state 327 Treatment of water systems Water systems need to be given special treatment because of the inapplicability of the Equations of State generally used for any phase, liquid or vapor, containing water. The current lines of attack at this problem are • Lattice-gas models • local composition models • different mixing rules • use of henry’s law rather than an Equation of State • modification of commonly used Equations of State Lattice-gas models and local composition models have attracted attention through their strong theoretical basis, incorporating hydrogen-bonding and electrolyte thermodynamics respectively. Relaxation of the commonly used symmetry condition for τ ij s yielding different mixing rules, is attractive for similar reasons. As yet though, these approaches have found little application, and are not easily incorporated into existing Equation of State packages. Henry’s Law, based essential on ‘look-up’ fugacites for given solutes and solvent, has had a longer history of application to engineering ‘rule-of-thumb’ problem, but is difficult to incorporate in a GEM multiphase algorithm, requires significant amounts of data, uses nonexact models for pressure and salinity corrections, and is restricted to specific solvents and solutes. The Valderrrama-Patel-Teja Equation of State is a 3 degree Equation of State that has extra terms involving the compressibility factor, and has had some success in dealing with water systems. Again, this has not had wide use, and again, has still to be corrected for salinity. The most common approach in the literature is to use the more popular Equations of State, but with some modification, particularly to the τ ij s used. The Peng-Robinson Equation of State has received this treatment, using T-dependent τ ij s between water and most SCN groups. The ‘PRW’ Equation of State is used here details are given in "Peng-Robinson and Water Equation of State" on page 329. The multiphase flash allow three separate treatments for systems containing water that produce a water phase, each based on the PRW Equation of State: • maintain the water phase as pure • allow CO 2 only to dissolve • allow all components to dissolve If the given system contains water the stability analysis attempts specifically to split off a water phase before any other. A full Michelsen stability analysis is not required:- each of the above options describe a water-dominated phase, so it is enough to compare the activity of water in a pure water phase with that in the feed mixture, and reintroduce the impurities required by the option at a later stage. In terms of fugacities, a pure water phase will split off if and only if fugacity of water in the feed is greater than fugacity of a pure water ( f w ( feed ) > f w ( pure ) ) or: ln ( Φ w ) feed + ln ( z w ) feed > ln ( Φ w ) pure where the w denotes the component index of the water. The difference between the options is then implemented in the ‘bring-back’ treatment for trace components used in the phase split calculations, either none, CO 2 only, or all. 328 Technical Description Equation of state PVTi Reference Manual Water- CO 2 bic-fitting A particular modification to the use of PWR Equation of State is made when only CO2 is dissolved in water, in allowing for salinity effect CO 2 solubility decrease with salinity, but the PRW Equation of State makes no allowance for this. It has been possible, however, to establish a polynomial form for the H 2 O – CO 2 τ ij by iterating adjusting (with a NR scheme) the H 2 O – CO 2 τ ij until the solubility predicted by the flash calculation matches experimentally determined solubilities. With a set of such τ ij s one can fit a 3 degree surface polynomial in p, T, S (salinity): τ H O – CO = f 1 P, T ) + Sf 2 P, T ) 2 2 f i = a 1i + a 2i T + a 3i P + a 4i TP + a 5i T 2 2 3 +a 6i P + a 7i T P + a 9i T + a 10i P 2 3 where a linear correction for salinity is assumed. Peng-Robinson and Water Equation of State The treatment of water systems is based on the PRW (Peng-Robinson and Water) equation of state. The original PR Equation of State has the form (for the usual symbols): RT a(T) P = ------------ – ------------------------------------------------V – b V(V + b) + b(V – b) a = xi xj ( 1 – δij ) ( ai aj ) j i b = 1⁄2 xi b i i a i = a ci α i 2 2 R T ci a ci = 0.45724 ---------------P ci α 1⁄2 1⁄2 = 1 + κ ( 1 – Tr ) 2 κ = 0.37464 + 1.54226ω i – 0.26992ω i RT ci b i = 0.07780 ----------P ci Two modification are made for water systems. Firstly, for the water component in any phase, a correction is made to improve predicted water vapor pressures: α 1⁄2 = 1.0085677 + 0.82514 ( 1 – T r 1⁄2 when T r 1⁄2 ) < 0.85 Secondly, in the aqueous liquid phase, a temperature-dependent interaction parameter is used, so that the mixing rules change slightly to: PVTi Reference Manual Technical Description Equation of state 329 a = xi xj ( 1 – τij ( T ) ) ( ai aj ) i 1⁄2 j when T r ≥ 0.85 , or the phase is not the aqueous liquid phase, the original PR Equation of State is used. The temperature τ ij s required may be found from the published curves given by Peng & Robinson. The following forms have been derived: τ C ↔ H O = 1.659T r P rw – 0.761 1 2 τ C ↔ H O = 2.109T r P rw – 0.607 2 2 2 2 τ C ↔ H O = – 18.032T r P rw + 0.9441T r P rw – 1.208 3 2 τ C ↔ H O = 2.800T r P rw – 0.488 4 2 Tc τ C ↔ H O = 0.4 ------ T r P rw – 0.8 , n > 4 n 2 P c τ N ↔ H O = 0.402T r – 1.586 2 2 τ H S ↔ H O = 0.22T r – 0.19 2 2 2 τ CO ↔ H O = – 0.074T r + 0.478T r – 0.503 2 2 The general C n form, was fitted here. Viscosity correlations Three correlations are available in PVTi for the estimation of viscosities, namely that due to "Lohrenz, Bray and Clark" on page 330, [Ref. 7], the method due to "Pedersen et al." on page 331 (PED), [Ref. 5] and [Ref. 36], and also that of "Aasberg-Petersen et al" on page 333, [Ref. 63]. Lohrenz, Bray and Clark The most widely used correlation for the prediction of liquid and vapor viscosities in reservoir simulators is that due to LBC. The viscosity being related to a fourth-degree polynomial in reduced density, ρ r = ρ ⁄ ρ c : –4 1 ⁄ 4 [ ( η – η∗ )ξ + 10 ] 2 3 4 = a1 + a2 ρr + a3 ρr + a4 ρr + a5 ρr [EQ 8.126] where a 1 = 0.1023000 a 2 = 0.0233640 a 3 = 0.0585330 a 4 = – 0.0407580 a 5 = 0.0093324 330 Technical Description Equation of state [EQ 8.127] PVTi Reference Manual and η∗ is the low-pressure gas mixture viscosity. ξ is the viscosity-reducing parameter, which for a fluid mixture is given by: 1⁄6 N ξ = –1 ⁄ 2 N z i T ci i=1 i=1 –2 ⁄ 3 N z i M wi [EQ 8.128] z i p ci i=1 The critical density ρ c is evaluated from: N ρc = –1 Vc = i = 1, i ≠ C ( z i V ci ) + z C 7+ V cC 7+ 7+ –1 [EQ 8.129] where the critical volume of the plus fraction is found from: V cC 7+ = 21.573 + 0.015122M wC – 27.656γ C + 0.070615M wC γ C 7+ 7+ 7+ 7+ [EQ 8.130] The dilute gas mixture viscosity is as given by Herning and Zippener, [Ref. 28]: N –1 N η∗ = 1⁄2 z i η i∗ M wi i=1 1⁄2 [EQ 8.131] z i M wi i=1 where the dilute gas viscosities of the individual components, ηi∗ are derived from expressions due to Stiel and Thodos, [Ref. 29]: – 5 1 0.94 η i∗ = 34 ×10 ---- T ri ξi [EQ 8.132] T ri < 1.5 –5 1 0.625 η i∗ = 17.78 ×10 ---- ( 4.58T ri – 1.67 ) ξi [EQ 8.133] T ri > 1.5 where 1⁄6 –1 ⁄ 2 – 2 ⁄ 3 [EQ 8.134] ξ i = T ci M wi p ci Hint By making the viscosity a function of the fourth power of density, results are very sensitive to small differences in estimation of density. It is not unusual for this technique to predict a viscosity only 50% of the measured viscosity. Small changes in critical volumes or critical Z -factors remedy the error but it is recommended that they are changed as a single group, from [EQ 8.130]. Pedersen et al. Viscosities can be calculated from a modified form of the corresponding states method. A group of substances obey the corresponding states principle if the functional dependence of the reduced viscosity, η r , say, on reduced density and temperature, ρ r and T r , say, is the same for all components within the group, namely: [EQ 8.135] η r ( ρ, T ) = f ( ρ r ,T r ) in which case comprehensive viscosity data is only needed for one component of the group, which is denoted as the reference substance, to be given the subscript ( o ) all other components are identified with the subscript ( x ). Generally, the critical viscosity, ηc , is not known but it can be estimated from the inverse of [EQ 8.135]), –1 ⁄ 2 2 ⁄ 3 –1 ⁄ 2 Vc Mw [EQ 8.136] η r ( ρ, T ) = η ( ρ, T )T c PVTi Reference Manual Technical Description Equation of state 331 Thus, the viscosity of component x at temperature T and a pressure with density ρ , is given by: 1⁄2 –2 ⁄ 3 1⁄2 T cx V cx M wx η r ( ρ ,T ) = ----------- ------------- ------------ η o ( ρ o ,T o ) T co V co M mo [EQ 8.137] where ρ o = ρρ co ⁄ ρ cx , T o = TT co ⁄ T cx and ηo is the viscosity of the reference substance at T o and ρo . Oil mixtures contain a range of components with molecular weights ranging from 16 (Methane) to about 1100 ( C 80 ). It cannot be expected for C 1 and C80 to belong to a group where a simple corresponding states principle applies. Generally, a third parameter must be added to account for the shape of the molecules, such as the acentric factor. Pedersen et al., [Ref. 5], presented a corresponding states principle depending on reduced temperature and reduced pressure, η r = f ( p r, T r ) where: η η r = ηξ = ------------------------------------–1 ⁄ 6 2 ⁄ 3 1 ⁄ 2 Tc pc Mw [EQ 8.138] The deviation from the simple corresponding states principle is expressed in terms of a rotational coupling coefficient, denoted α , to give: –1 ⁄ 6 2⁄3 1⁄2 p c, mix M w, mix α mix T c, mix η mix ( p, T ) = ------------------------ ---------------------- ------------------------- ----------- η o ( p o, T o ) T co p co M wo αo [EQ 8.139] where p co α o p o = p ------------------------p c, mix α mix [EQ 8.140] T co α o T o = T -------------------------T c, mix α mix [EQ 8.141] The critical temperature and volume for unlike pairs of molecules are given by: T c, ij = ( T c, i T c, j ) 1⁄2 1 1⁄3 1⁄3 3 V c, ij = --- ( V c, i + V c, j ) 8 [EQ 8.142] [EQ 8.143] where the critical volume of a component can be expressed in terms of the critical temperature and pressure using the real gas law and the critical Z -factor. Assuming a constant Z c for all components,[EQ 8.143] becomes: T c, i 1 ⁄ 3 T c, j 1 ⁄ 3 3 1 V c, ij = --- constant --------- + -------- p c, j p c, i 8 [EQ 8.144] The mixture critical temperature is found from: zi zj Tc, ij Vc, ij T c, mix = i------------------------------------------------= 1j = 1 N N [EQ 8.145] zi zj Vc, ij i = 1j = 1 Combining [EQ 8.143] and [EQ 8.145] gives: 332 Technical Description Equation of state PVTi Reference Manual zi zj c, i T ------- p c, i 1⁄3 c, j T ------- p c, j 1⁄3 3 [ T c, i T c, j ] 1⁄2 [EQ 8.146] = 1j = 1 T c, mix = i---------------------------------------------------------------------------------------------------------------N N T c, i 1 ⁄ 3 T c, j 1 ⁄ 3 3 z i z j --------- --------- p c, i p c, j i = 1j = 1 and the mixture critical pressure is evaluated from: 8 zi zj c, i T ------- p c, i 1⁄3 c, j T ------- p c, j 1⁄3 3 [ T c, i T c, j ] 1⁄2 [EQ 8.147] i = 1j = 1 p c, mix = ------------------------------------------------------------------------------------------------------------------2 N N 1⁄3 T 1 ⁄ 3 3 T c , i c , j z i z j --------- --------- p c, i p c, j i 1 j 1 The mixture mole weight is given by: –4 M w, mix = 1.304 ×10 ( M w 2.303 – Mn 2.303 [EQ 8.148] ) + Mn where M w and M n are the weight average and number average mole weights, respectively. This mixing rule is derived empirically on the basis of available viscosity data and assigns a larger influence to heavier components. The α -parameter for the mixture is found from: – 3 1.847 α mix = 1.0 + 7.378 ×10 ρ r 0.5173 [EQ 8.149] M w, mix where the α of Methane, the reference substance, is given by: 1.847 [EQ 8.150] α 0 = 1.0 + 0.031ρ r Note The constants and exponents in equations [EQ 8.149] and [EQ 8.150] have been found from fitting to experimentally determined viscosity data. It has been our experience that the method of Pedersen gives much better prediction of viscosities than does the method of Lohrenz, Bray and Clark. Neither method is particularly good but typical errors based on un-regressed Equation of State data are, LBC ∼ 50 % and PED ∼ 90 % of the reported values. However, you should treat experimentally measured viscosities with some caution, as viscosities are often calculated. Aasberg-Petersen et al The Aasberg-Petersen model is also based on the principle of corresponding states, but uses two references fluids, methane and decane, instead of just the one (methane) in the case of the Pedersen et al. model. The usual problem with the Pedersen model is that inaccurate predictions occur for fluids with components that are significantly different in molecular weight to the reference component (methane). The idea of this model is to use a heavier second reference component and effectively create an optimum reference component by using the molecular weight of the fluid as an interpolation parameter between the two reference components. Decane is chosen as the second reference component because it is the heaviest alkane for which a significant amount of experimental viscosity data is known. Methane is a natural choice as the first reference component because of its presence in large mole fractions in most reservoir fluid mixtures The interpolation law is used to calculate the reduced viscosity of the optimum reference component (denoted with the subscript x) using the reduced viscosities of methane and decane and is obtained using the following expression: PVTi Reference Manual Technical Description Equation of state 333 η r2 MW x – MW 1 ln η rx = ln η r1 + ------------------------------- ln -------- MW 2 – MW 1 η r1 [EQ 8.151] MW is the molecular weight and subscripts 1 and 2 refer to the reference components. The functional form of equation [EQ 8.151] was originally suggested by Teja and Rice (1981), [Ref. 64], using the acentric factor instead of MW. This is not possible in the present work, since the acentric factor decreases with increasing molecular weight for heavy oil fractions. The reduced properties are determined from: E E r = ------, E = T, P, η Ec [EQ 8.152] Subscripts r and c indicated reduced and critical properties respectively. The following expression is used to evaluate the critical viscosity (Pedersen et al. 1989): ηc = C ⋅ 1 --- 2 --- – 1 --2 3 6 MW P c T c [EQ 8.153] C is a constant. From equations [EQ 8.151], [EQ 8.142] and [EQ 8.143] the following equations may be derived for determination of the viscosity: η cx η 1 ( T 1, P 1 ) η 2 ( T 2, P 2 )η c1 K η x = ----------------------------------- ----------------------------------η 1 ( T 1, P 1 )η c2 η c1 [EQ 8.154] MW x – MW 1 K = ------------------------------MW 2 – MW 1 [EQ 8.155] η 1 and η 2 are evaluated at conditions corresponding to the reduced temperature and pressure of component x: T ci T T i = -----------, i = 1, 2 T cx [EQ 8.156] P ci P P i = -----------, i = 1, 2 P cx [EQ 8.157] The model outlined in the above is extended to mixtures using the same mixing rule as the Pedersen et al. model, that is equations [EQ 8.146] and [EQ 8.147]. The mixture molecular weight is calculated using the formula: MW mix = MW n + 0.00867358 ( MW w where 1.56079 – MW n 1.56079 ) [EQ 8.158] [EQ 8.159] N 2 zi MWi =1 MW w = i-------------------------N zi MWi i=1 and N MW n = zi MWi [EQ 8.160] i=1 334 Technical Description Equation of state PVTi Reference Manual The constants in equation [EQ 8.142] are determined by regression using experimental viscosity data for binary mixtures and oils. The following equations are used for determination of the viscosity of the reference components: η 0 = η k ( T ) + ρη 1 ( T ) + η 2 ( ρ, T ) 9 GVi T ηk ( T ) = [EQ 8.161] (i – 4) --------------3 [EQ 8.162] i=1 T 2 η 1 ( T ) = A + B C – ln --- F [EQ 8.163] j4 η 2 ( T, ρ ) = H 2 exp j 1 + ---- T [EQ 8.164] H 2 = – 1 + exp ρ 0.1 j7 j3 j 0.5 - + θρ j 5 + ---6- + ---- j 2 + ------- 1.5 T T 2 T [EQ 8.165] where [EQ 8.166] ( ρ – ρc ) θ = ------------------ρc These equations were originally developed by Hanley et al. (1975), [Ref. 65], to correlate the methane viscosity. For methane the values of the GVi parameters in equation [EQ 8.152] given by Hanley et al. were maintained. For decane GV4-GV9 are equal to zero and GV1-GV3 were taken from the DIPPR tables (1985). All the parameters in equations [EQ 8.59]-[EQ 8.165] were estimated. In Table 8.9, data of the parameter estimation are given and Table 8.10 lists all parameters for the pure component viscosity correlation. Of the parameters in Table 8.10 are used the viscosity is obtained in μP if the density is given in g/cm3. Table 8.9 PVTi Reference Manual Parameter estimation data. N is the number of experimental points Methane Decane N 881 252 T-range (K) 91-523 244-477 P-range (atm.) 0-680 0-1000 Dev. (%) 3.1 3.8 Technical Description Equation of state 335 Table 8.10 Parameter Values for Pure Component Viscosity Correlation Methane Decane GV1 -209097 0.2640 GV2 264276 0.9487 GV3 -147282 71.0 GV4 47164 0.0 GV5 -9491.9 0.0 GV6 1220.0 0.0 GV7 -96.28 0.0 GV8 4.274 0.0 GV9 -0.0814 0.0 A.100 23946 0.00248 B 343.79 81.35 C 0.4487 5.9583 F 168.0 490.0 j1 -22.768 -11.739 j2 30.574 16.092 j3 -14929 -18464 j4 1061.5 -811.3 j5 -1.4748 1.9745 j6 290.62 898.45 j7 30396 119620 The density of the reference components as a function of the pressure and temperature is also required in equations [EQ 8.48] and [EQ 8.165]. For methane, as with the Pedersen model, the 33-parameter MBWR-equation given by McCarthy (1974), [Ref. 66], was used to calculate the density. For decane we decided to used the flash available within PVTi to obtain the density at a given pressure and temperature. 336 Technical Description Equation of state PVTi Reference Manual Finally, the following physical properties for methane and decane were used in Table 8.11 below when required. Table 8.11 Physical Properties of Methane and Decane Methane Decane Tc 190.55 617.40 Pc 45.39 20.18 MW 16.043 142.284 ω 0.008 0.484 ρc 0.1649 0.2269 The predictions of the Aasberg-Petersen model have been shown to agree well with experimental data over large pressure and temperature ranges. In particular this model is able to handle mixtures with CO2, paraffinic and aromatic components with better accuracy than the Pedersen model. A better match is also obtained than the Pedersen model for heavier oils, where the size and shape of the molecules differ substantially from the single reference component (methane). Note It should be noted that the Aasberg-Petersen model is not recommended for fluids with large concentrations of napthalenic components. Binary interaction coefficients Strictly, binary interaction coefficients are interpreted as accounting for polar forces between pairs of molecules. Another interpretation is they account for tertiary and higher-order interactions in the cubically (in volume) truncated form of the Second Virial Equation: RT a p = ------- + -----2- + … V V [EQ 8.167] Eitherway, they might be thought of as the fiddle-factors for the equation of state. Strictly, they should be determined for all possible binary mixtures of hydrocarbons and non-hydrocarbons by tuning their value to get a match between experimental and theoretical (Equation of State) behavior. Thus, each new Equation of State requires that a completely new set of binaries be developed: a laborious task indeed. This is the main reason why the Soave-Redlich-Kwong and Peng-Robinson Equations of State tend to dominate in reservoir applications. Caution Many authors have suggested that binaries are the obvious Equation of State parameter to adjust to match Equation of State to laboratory results, especially the Methane to plus-fraction binary. However, Pedersen et al., [Ref. 30], have shown that this is problematic. Given that our preferred Equation of State is the Peng-Robinson, we derive binaries from one of two sources. PVTi Reference Manual Technical Description Equation of state 337 The current default is to assume they are zero for all hydrocarbon-hydrocarbon interactions except for Methane to heavier hydrocarbons that vary like: KC 1, j [EQ 8.168] = 0.14γ j – 0.06 where γ j is the (liquid) specific gravity of the heavier component. In addition, the hydrocarbon to non-hydrocarbon interactions take certain fixed values, see [Ref. 4]. The alternative set, activated by the appropriate option switch is a set due to Cheuh and Prausnitz, see [Ref. 32]. The hydrocarbon to non-hydrocarbon interactions are as above but the hydrocarbon to hydrocarbon binaries are given by: 1⁄6 6 2 ( V c, i V c, j ) - K i, j = A 1 – --------------------------------- V 1c, ⁄i3 + V 1c, ⁄j3 [EQ 8.169] where V c, i is the molar volume of the i th component and A is a special regression variable which is generally in the range 0.15 ≤ A ≤ 0.25 . There is some appeal in using the pre-multiplying coefficient to regress all binaries together. This preserves symmetry, which might be lost using the Methane to plus fraction binary approach of [EQ 8.169], which (see [EQ 8.169] and [Ref. 28]) can lead to strange results. These particular binaries are also given a temperature dependence by the use of an additional multiplying factor that has the form: 1.0 + TC ( T – T std ) [EQ 8.170] where TC has the fixed value of 0.0025. 338 Technical Description Equation of state PVTi Reference Manual Basic laboratory experiments Introduction This section describes the basic laboratory experiments and how PVTi attempts to simulate them. More detail on experimental methods can be found in the excellent text by Pedersen et al. [Ref. 30]. Schematic diagrams of the apparatus used for the standard laboratory techniques to be described here can be found in the above text. See "The fluid model" on page 98 and "Batch system and keywords" on page 152 for further information on defining experiments in PVTi. This section contains information on the following: • "Blackoil systems" on page 339. • "Gas condensate systems" on page 341. • "Gas injection processes" on page 344. • "Process simulation" on page 343. Blackoil systems Essentially two experiments are performed on black or crude oil systems: • "Bubble point evaluation" on page 339 • "Differential liberation" on page 340 (sometimes referred to differential expansion). Bubble point evaluation Laboratory experiment 1 Having charged the PVT cell with the reservoir fluid, the system is left to come into equilibrium at the required (reservoir) temperature and pressure or some higher pressure where the fluid is a single phase liquid, whereupon the fluid volume is noted. 2 The pressure is then dropped (at constant temperature) and the new fluid volume is recorded. The bubble point pressure is then readily found from the discontinuity in the pressure/volume relationship where the first bubble of gas is evolved from the liquid. Since gases are more compressible than liquids, reduction in pressure and liberation of gas results in an increase in rate of volume expansion of the (two phase) fluid. PVTi 1 PVTi finds the bubble point by taking one mole of the reservoir fluid and using estimates for the K -values, constructs vapor compositions at a set of pressures, testing for the stability of the second (vapor) phase using the method of Michelsen [Ref. 16]. 2 Once the highest-pressure, two-phase state has been found, the N equal fugacity conditions and the one mole fraction constraint (see "Material balance" on page 317 and "Flash calculations" on page 317) are used to solve for the N + 1 unknowns of N K -values and the bubble point pressure by iteration. PVTi Reference Manual Technical Description Basic laboratory experiments 339 Differential liberation Having found the bubble point pressure, the crude oil would normally then be subject to this experiment. Laboratory experiment 1 Starting from the bubble point pressure, the pressure is dropped by several hundred psia, whereupon a volume of gas is evolved that is removed from the cell at the (new) constant pressure. This process is repeated several times noting the volume of gas evolved (at reservoir and surface conditions) and the volume of liquid remaining. 2 The volume of liquid remaining at the last stage, which should be at standard or atmospheric pressure, is then reduced to standard or atmospheric temperature and remeasured. This liquid is discharged and its density is obtained. The density of the liquid at the other pressure (and temperature) stages can be calculated from mass balance knowing the volumes and molecular weight of the removed gas streams. The data usually quoted is: • Bo Oil formation volume factor • Bg Gas formation volume factor • Rs Gas-oil ratio • ρo Oil density • γg Gas gravity (density) • Zg Gas deviation factor • μo Oil viscosity • μg Gas viscosity where: Vo ( p ) B o ( p ) = ------------std Vo [EQ 8.171] Vg ( p ) B g ( p ) = ---------------std Vg ( p ) [EQ 8.172] i = std 1 R s ( p ) = -------std Vo Vg std (i) [EQ 8.173] i=p and Mg ( p ) γ g = --------------M air [EQ 8.174] Here, Vo , Vg are volumes of oil and gas, M g , M air are mole weights of hydrocarbon gas and air, the superscript std implies standard conditions, and the summation for the gas-oil ratio is taken over the volumes of evolved gas from the current pressure, p to the final pressure at std . 340 Technical Description Basic laboratory experiments PVTi Reference Manual PVTi 1 In PVTi, the experiment is simulated by firstly locating the bubble point pressure, as above. Then one mole of bubble point fluid is dropped in pressure and a flash calculation is performed to determine the phase split and the volumes of oil and gas. All the gas is removed and the liquid composition forms the feedstream for the next pressure depletion stage, etc. Note The "Definition of GOR in Diff. Lib." on page 148 program option allows three further definitions of the GOR. The first removes the stage to standard conditions and normalizes gas volumes to the volume of oil at reservoir conditions, that is: i = plast 1 R s ( p ) = --------------------------V o ( T, p bub ) std [EQ 8.175] Vg ( i ) i=p where T is the temperature of the depletion experiment, and p last is the last pressure stage specified. 2 The second definition specifies the GOR as an incremental one, that is: std Vg ( p ) R s ( p ) = ---------------std Vo 3 [EQ 8.176] The third definition is the same as the default but the volume of oil is at its bubble point pressure rather than at stock tank conditions, that is: i = std 1 R s ( p ) = --------------------------V o ( T, p bub ) Vg std [EQ 8.177] (i) i=p The program option "Definition of Oil relative volume in Diff. Lib." on page 149 allows an alternative definition of the oil relative volume where the volume of oil is normalized to the initial volume of oil at reservoir rather than standard conditions: Vo ( p ) B o ( p ) = --------------------------V o ( T, p bub ) [EQ 8.178] Gas condensate systems Essentially three experiments are performed on gas condensate systems: • "Dew point evaluation" on page 342. • "Constant composition expansion" on page 342. • "Constant volume depletion" on page 343. Hint PVTi Reference Manual It is not uncommon for CCEs to be performed on all fluids, and it is recommended to perform CVDs on more volatile oils. Technical Description Basic laboratory experiments 341 Dew point evaluation Laboratory experiment This experiment is generally more difficult than the bubble point evaluation and consequently subject to larger uncertainties. 1 Most condensate systems are relatively compressible above the dew point so that the appearance of a heavier, less-compressible second liquid phase cannot be identified on a pressure/volume relationship. This means the dew point must be found by eye, by visual determination of the pressure when the first drop of liquid is formed in the cell. Note This can be affected by imperfections or grease in the cell, poor experimental procedures, etc., and it is not uncommon for errors of 100 psia to be associated with this measurement. PVTi In PVTi, this experiment is simulated in much the same way as the bubble point evaluation except that the trial second (liquid) phase is heavier than the original fluid. 1 The same stability test is done to find the highest two phase state and the same set of equations and variables iterated to solution. 2 As an alternative to this high-pressure dew point, usually referred to as the retrograde dew point, the low-pressure or normal dew point can be found by starting low in pressure and iterating higher. Constant composition expansion Laboratory experiment This experiment is often done while trying to find the dew point of a gas (or bubble point of a volatile or even crude oil). 1 It consists of varying the pressure and measuring the resulting volume of the single phase fluid above saturation pressure, and volumes of vapor and liquid (and total) phases below it. 2 For the single phase state, the vapor Z -factor or liquid density can be calculated from the other fluid properties. These data items are reported along with the relative volume, being the volume of the fluid at any given pressure per the volume of the fluid at the saturation pressure. PVTi In PVTi, the CCE is simulated by: 342 1 Finding the saturation pressure which for one mole of feedstream defines the cell or control volume. 2 Then at pressures above the saturation pressure it is sufficient to find the single phase liquid or vapor Z -factor to calculate the volumetric behavior. 3 Below the saturation pressure, the feedstream is flashed at each required pressure stage to determine the phase split and other volumetric properties. Technical Description Basic laboratory experiments PVTi Reference Manual Constant volume depletion Laboratory experiment The CVD is the most useful, and probably the most difficult experiment to perform on a gas condensate (and increasingly on volatile oils). 1 It consists of starting with a volume of fluid at its saturation pressure, which again defines the cell or control volume for the experiment. 2 Then the pressure is dropped by several hundred psia, or so, whereupon the fluid becomes two phase and expands in volume. 3 Any excess volume over and above the cell volume is removed by taking off gas which is analysed compositionally and volumetrically as well as noting the number of moles. 4 In addition, the percentage of liquid in the remaining fluid, the cell volume, defines the liquid saturation. Generally reported is: S liq : Liquid saturation; N pro : Moles of vapor removed; Z gas : Z -factor of removed vapor; y i, j : Composition of each removed vapor stream; and occasionally: x i, N : vap M N+ : vap γ N+ : Composition of liquid stream left in cell at last pressure stage; Mole weight of removed vapor plus fraction; Specific gravity of removed vapor plus fraction. PVTi In PVTi this experiment is simulated by: 1 First finding the saturation pressure. The volume occupied by one mole of fluid at its saturation pressure then defines the cell or control volume. 2 At some pressure less than the saturation pressure, the fluid is flashed into two phases and any excess gas is removed to return the volume to the control volume. 3 The number of moles of vapor and its properties are noted. 4 The composition of the remaining fluid is calculated by volumetric balance and this forms the feedstream for the next pressure stage, and so on. Process simulation For the purposes of process-type simulation and/or for the definition of blackoil tables for reservoir modeling, separator tests are performed to see what phase splits are achieved when a fluid is flashed at a series of pressures and temperatures in some prescribed sequence. PVTi Reference Manual Technical Description Basic laboratory experiments 343 Laboratory experiment 1 Most laboratory analyses consist of the reservoir fluid being flashed in a cell at some specified pressure and temperature, and (generally) the liquid output being fed to a second (and possibly third) cell at some reduced pressure and temperature: the last stage cell usually being at standard conditions. Volumes of gas evolved from each stage are generally collected together and the properties of the resulting mixture are quoted/evaluated at standard conditions. PVTi 1 In PVTi this process is simulated by a set of flash calculations at the required set of pressures and temperatures, taking the reservoir fluid as the feedstream and routing the liquid and vapor outputs to other stages. 2 The default output streams are liquid to the next stage and vapor to the stock-tank accumulation, but PVTi is capable of solving feedback loops, where, for example, vapor output is routed back to an earlier stage. 3 In addition, a user option allows the output streams to be split and directed to more than one other stage. Optimized separators In the Fluid Properties (FPE) workflow, PVTi offers the automatic generation of the optimum separator configuration for a fluid. The optimum separator configuration is defined as the twostage separator for which the stock-tank formation volume factor (Bo) is minimized. Given the reservoir temperature and the maximum separator pressure, the following separator chain is constructed: 1 A separator stage at some temperature below the reservoir temperature and some pressure below the highest separator pressure. This stage is optimized. 2 A second stage at standard conditions, the liquid output from Stage 1 passes into this second stage. 3 The stock tank. The vapor output from Stages 1 and 2 both pass into the vapor stock tank and the liquid output from Stage 2 passes into the liquid stock tank. A special regression procedure is used to determine the optimum temperature and pressure for Stage 1, such that Bo is minimized in the stock tank. This point coincides with minimum Total Gas-Oil Ratio and minimum stock tank vapor Gravity. Note If no maximum pressure is supplied, it is assumed that the maximum separator pressure available is 1440 psia (source: Oil Phase). For more information on fluid properties estimation see "Fluid Properties Estimation" on page 384. Gas injection processes PVTi has several simulations available for investigating gas injection processes. The three that correspond closely to laboratory experiments are: • 344 "Swelling test" on page 345 Technical Description Basic laboratory experiments PVTi Reference Manual • "Vaporization test" on page 345 • "Multiple contact test" on page 346 In addition, PVTi has available: a ternary diagram, and first and multiple contact minimum miscibility pressure experiments by one-cell simulation. Note These have no equivalent in the laboratory. Swelling test Laboratory experiment 1 The swelling test consists of finding the saturation pressure and hence volume of a reservoir fluid. 2 Followed by adding, in a series of steps, prescribed volumes (or moles) of lean injection gas, re-pressuring the resulting mixture to return to a single phase system and measuring the new saturation pressure and volume. The data quoted is the set of saturation pressures for the original fluid and the mixtures and the ratio of the saturation volume of the mixtures to the saturation volume of the original fluid, usually referred to as the swelling factor. PVTi In PVTi this is simulated by: 1 Firstly finding the saturation pressure of one mole of the required reservoir fluid and hence the saturation volume. 2 Then prescribed volumes of a lean injection gas are added as a GOR (volume of injection gas at standard conditions per volume of original reservoir fluid at its Psat or other prescribed pressure) or a mole% (moles of lean gas per moles of mixture) to give a new fluid composition. 3 The saturation pressure and volume of the new mixture are found, and hence the swelling factor. Vaporization test This is similar to the swelling test, except that it is performed at constant volume and pressure. Laboratory experiment 1 A volume of reservoir fluid at some pressure and temperature, usually below the saturation pressure and hence two phase, is contacted by a series of lean gas injections. 2 After each contact, a volume of (enriched) gas and/or liquid is removed to return the system to the original volume. The composition of the removed gas is measured. The experiment seeks to measure the extent of vaporization of intermediate and heavy components from the reservoir liquid phase by stripping into the injected gas stream. In PVTi, the procedure is as follows. 1 PVTi Reference Manual One mole of reservoir fluid at a prescribed pressure and temperature is flashed to calculate the phase split and volumes of liquid and vapor. Technical Description Basic laboratory experiments 345 2 Lean gas is then added in a series of steps of moles, to give a new mixture composition which is flashed at the same pressure and temperature, and any excess fluid volume removed. 3 The composition of the removed stream is noted and the resulting mixture is then subject to further lean gas injections. Multiple contact test PVTi 1 In condensing drive mode the initial reservoir oil (the mole fraction can be specified) is contacted with one mole of injection gas at a specified temperature and pressure. 2 This mixture is then flashed and a specified fraction of the resulting oil is then contacted with one mole of the initial injection gas. This process is repeated at each stage of the test. The vaporizing drive follows the same procedure as that of the condensing drive except that it is a specified fraction of the resulting gas from each flash that is contacted with one mole of reservoir oil. A special ternary plot is available for this experiment that plots the compositions at each stage of the oil and gas resulting from each flash, and these points effectively mark the boundary of the two-phase region at the specified conditions. Variation of composition with depth PVTi Although not a laboratory experiment, the estimation of the variation of a fluid’s composition with depth is of great possible value. 1 On purely thermodynamic principles, fugacity in an isothermal system that can be expected to vary with depth according to: Mi g ( h – h0 ) ln f i = ln f i, 0 + ----------------------------RT 0 2 Assuming thermodynamic equilibrium in the fluid at some reference height h0 (namely the equal fugacity conditions and mole composition constraints of "Material balance" on page 317 and "Flash calculations" on page 317), the N -equations, defined in [EQ 8.179], and a further mole constraint equation can be used to determine the N -compositions and pressure, z i , p , from the reference composition and pressure, z i, 0 , p 0 . Note 346 [EQ 8.179] However, the compositional gradient experiment assumes many conditions: namely thermal, gravitational and diffusive equilibrium. Any or all of these conditions can be violated in a given reservoir, thus invalidating the use of [EQ 8.179]). Technical Description Basic laboratory experiments PVTi Reference Manual Note The existence in some reservoirs of a temperature gradient indicates a lack of global thermodynamic equilibrium, but may still allow a steady-state situation, in which the mass flux is zero (that is hydrostatic equilibrium), whilst the energy flux is not. As yet, there is no consensus on how to treat such temperature gradients. The temperature gradient element has been implemented in PVTi for the compositional gradient experiment since 2002a. It is suitable for gentle temperature gradients. The algorithm is essentially the same as that described in Pedersen's SPE paper 84364 "Simulation of Compositional Gradients in Hydrocarbon Reservoirs Under the Influence of a Temperature Gradient". With the above caveats, the experiment may still be of use in the prediction of the existence and possible location of either gas-oil contacts or so-called critical transitions. This latter transition consists of the grading of a fluid from an oil to a gas, or vice-versa, without passing through a gas-oil contact. This occurs when an over-pressured reservoir has a fluid composition at some depth whose critical temperature is equal to the reservoir temperature at that depth. There is evidence that such behavior exists in some North Sea fields. Critical point experiment This experiment calculates the critical point of the given sample. FCMP experiment Refer to Jensen and Michelsen [Ref. 38] and Pedersen et al. [Ref. 30] for detail. MCMP experiment Refer to Jensen and Michelsen [Ref. 38] and Pedersen et al. [Ref. 30] for detail. Tsat experiment Refer to Michelsen [Ref. 15] for further details. PVTi Reference Manual Technical Description Basic laboratory experiments 347 Regression Introduction This section of the manual contains information on: • "Practical considerations" on page 348. • "Theoretical model" on page 351. Practical considerations There are no set rules for how to do regression of an equation of state model to match to laboratory measurements. The paper by Coats and Smart, [Ref. 27], contains an appendix on the choice, selection and range limits of regression variables. However, the Coats and Smart model is limited in its choice of regression variables to the Ωa ’s, Ω b ’s and the binary interaction coefficients. Another limitation of their model is the use of the standard two-parameter equation of state. It is well known that the two-parameter Equation of State is in error in prediction of liquid properties by as much as 10%. Therefore, to get matches to saturation pressures and densities it becomes necessary to change the properties of “well-defined” components, say Ωa ( C 1 ) and Ωb ( C1 ) . Such a problem is avoided in PVTi by use of the PR3 or SRK3 Equation of State, which allows the volume shift parameter to be a possible regression variable. Additionally, rather than varying just the Ωa ’s and Ωb ’s, PVTi allows you to change the critical pressures and temperatures. This has the advantage in that monotonicity tests can readily be applied to the set of T c ’s, p c ’s,..., etc., for the hydrocarbon components to ensure that critical temperatures increase with increasing mole weight, critical pressures decrease (except C 1 , C 2 , C 3 ) etc. For further information on performing a regression in PVTi see "Regression in PVTi" on page 126 and "REGRESS section keywords" on page 160. The present section also contains information on: • "Consistency and quality of measured data" on page 348 • "Plus fraction" on page 349 • "Performing regressions in PVTi" on page 350. Consistency and quality of measured data As a first step, before any regression is considered, as many tests as possible should be performed to test the consistency and quality of the measured data. Clearly it is not possible to match to an inconsistent PVT report, yet our experience is that all reports are flawed to a greater or lesser degree. The cause of these errors may be numerous. For example: • 348 Poor sampling and/or collection Technical Description Regression PVTi Reference Manual • Bad laboratory procedures • Simple typing mistakes in reporting (for example a composition does not add up to 100). It is most likely to be a combination of all these effects. However, an equation of state model cannot be used in isolation from measured data as no two fluids are ever likely to be the same. PVTi provides you with the ability to check the consistency of CVD reports in the COMB section. For further information see "COMB - Compositional Material Balance" on page 112 and "COMB section keywords" on page 159. This test should always be done if the data is available; the results may be surprising. Simple tests like checking compositions sum to 100% often reveal errors. Another useful check is to plot pressure-dependent data, for example liquid dropout from a CVD, relative volumes from a CCE, etc., to see if they are smoothly varying. One way this can be done is to enter this and other data as OBS to compare with the Equation of State predicted values from the experiments in the SIMULATE section. For further information see "Simulation using PVTi" on page 117 and "SIMULATE section keywords" on page 160. Generally, the properties of the multi-stage experiments vary smoothly (apart from discontinuities in vapor/liquid properties across a saturation pressure boundary), so that vapor Z -factors, etc., that decrease, increase and decrease again as pressure drops in a CVD, probably indicates data error. Check the definitions of measured data. It has been our experience that what one laboratory may call liquid saturation in a CCE experiment, for example liquid volume divided by volume of the fluid at the saturation pressure, may be different to that from another laboratory, say liquid volume divided by the current cell volume. Check that a consistent set of units is being used. The saturation density of a crude oil is often quoted as a specific volume in units of ft 3 /lb , for example. Plus fraction Having determined that the data is reliable, or having rejected either poor data or adjusted it to be consistent, one will usually find that the Equation of State predictions differ from the measured data. Most of this error can probably be associated with the incomplete fluid description, namely the failure to fully characterize the plus fraction, for example C 7+ , although some error has to be associated with the inadequacies of a cubic Equation of State. Clearly, the plus fraction, consisting as it does of many hundreds or possibly thousands of components, cannot be represented by just one component without some modification. Even then, just to represent a C 7+ of a condensate or volatile oil, which may be 5-20 mole percent of the fluid, by a single component with regressed properties may be insufficient for describing a multi-pressure process. On some CVD analyses the mole weight and specific gravity of the produced gas plus fraction are measured and reported. In such a case you may note that the plus fraction gets lighter as one would expect. Then it is clearly not adequate to represent the plus fraction by a single component and one should consider splitting it into two or three pseudo-components, say using the techniques available in PVTi. The properties of the plus fraction, or its pseudo-components if splitting has been performed are the obvious candidates for regression. However, one should avoid regressing the property of a component with a small mole fraction, say 1%. PVTi Reference Manual Technical Description Regression 349 This can be avoided by using the group facility in regression in which an Equation of State property of two or more components can be treated as a single variable. This grouping of components for regression should be borne in mind if the aim of the PVTi analysis is to produce a pseudoised set of components for a compositional simulation. Finally, one should always use the minimum set of variables possible. It is not possible to say what this set is for any given fluid/measurement set, but the symptoms of redundant variables are easy to spot; for example, one or more of the variables is hitting one of its limits, or there is bouncing of the reported Rms error within a small range. If the regression facility from an interactive session is being used, you have the option (as default) of rejecting the latest regression and restoring the pre-regression Equation of State. This makes it possible to vary the set of variables and test the success, or otherwise, of a given set of variables in a limited number of iteration steps, for example, 10. The sensitivity of the observations to which one is attempting to match as a function of the regression variable set is output both to the screen and to the PVP printable. This gives a direct measure to the relative importance, or otherwise, of a given variable. Performing regressions in PVTi Whilst not being complete, the following may be of assistance: 350 1 Always use one of the three-parameter Equation of State. We suggest the Peng-Robinson Equation of State (PR3). The extra degree of freedom allows the possibility of matching saturation pressure using critical properties etc., and then independently matching to saturation density (liquid) or Z -factor (gas) using the volume shifts. 2 Consider splitting the plus fraction for volatile fluids, that is gas condensates and volatile oils. Genuinely, crude oils are often well described by a single plus fraction, such as the C 7+ reported. Dry gases do not have a significant quantity of plus fraction to affect results. Of all the splitting algorithms currently available, the best appears the modified Whitson method, otherwise referred to as Semi-Continuous-Thermodynamics (SCT). The use of this model allows the use of the special regression parameters: sample by sample plus fraction mole weight, probability density function skewness parameter and overall PNAdistribution. 3 There is strong evidence to suggest that the adjustment of one or two binary interaction coefficients to create an un-symmetric pattern is very dangerous, see [Ref. 30]. The alternative is to select the Cheuh-Prausnitz BICS (see "Binary interaction coefficients" on page 337) using the appropriate “options” switch, and then regress the pre-multiplying A coefficient to adjust the binaries. 4 As an alternative to 3., one might consider other properties. If the SCT-splitting has been activated, one might consider the mole weight and skewness parameter or the overall characterization of the plus fraction. These techniques have the advantage of preserving monotonicity of all the key Equation of State variables, critical temperatures and pressures, and acentric factors. If choosing the critical properties or acentric factors, one should start with just those of the plus fraction, or the pseudo-components split from it. If this is not sufficient, remember that any SCN-group in your sample analysis (for example C 6 , C 7 ,...) are subject to uncertainty because of their PNA-content. One should not have to consider changing properties associated with C 1 , C 2 ,..., and so on. However, if you have a significant mole percentage of inorganics in your fluid or they are being injected into your fluid, it may be appropriate to adjust the set of inorganic-hydrocarbon binaries, probably as a single group change. Technical Description Regression PVTi Reference Manual 5 Critical volumes or Z -factors (equivalent variables) are only needed for the Lohrenz-BrayClark (LBC) viscosity correlation. Note The LBC correlation can be as much as 150% in error and is regularly 50% in error. The Pedersen correlation appears to be much better (and is insensitive to Vc , Z c ). This having been said, the fact that Z c ’s or V c ’s affect only LBC viscosities means they can be regressed independently of all other variables/results. If doing this, it is suggested they be regressed simultaneously as a single group because of the LBC functional form, [EQ 8.126]. PVTi now has independent sets of critical volumes and Z -factors, one set are used in the LBC viscosity correlation and can be selected as regression variables, the other for use in the equation of state. The latter are not available for regression as they do not affect results. 6 For characterized components try using the molecular weight of these components. This is available as a special variable and must not be used in conjunction with Tcrits etc., as changing the molecular weight of each characterized component changes most of the properties by way of the characterization technique anyway. The use of this variable is a very powerful alternative one to the approach of Tcrits, Pcrits and acentric factors etc. as described above All observations entered into PVTi can be assigned a weighting factor that multiplies the measured minus calculated residuals, see [EQ 8.181]. Clearly, some observations are more important than others and should be given a higher weight to account for this. As a general rule, the saturation pressure should be given the highest weight followed by saturation density and then other quantities. Users who have performed several material balance calculations on CVD experiments will probably recognize that mole compositions should generally be given low weights, if they are to be used at all. The only way to perform regression is by trial and error. Define your experiments and associated (consistent and reliable) observations and save them to a PVI file prior to starting regression. Include different sets of variables, experiments and observations. Use engineering judgement to decide when the best match has been achieved to the maximum amount of data while remembering to maintain monotonicity and physical consistency in one’s Equation of State model. Theoretical model Generally the results of an equation of state model must be tuned by regression of one or more variables, x = ( x1, …, x N )T to a set of laboratory experiments, y = ( y1, …, y M )T ˜ ˜ [EQ 8.180] where M ≥ N and: yi = yi ( x ) ˜ or in residual form: [EQ 8.181] ri ( x ) = wi [ ( y i – yi ( x ) ) ⁄ yi ] ˜ ˜ PVTi Reference Manual Technical Description Regression 351 where w i is the weighting factor applied to the i th item of observed (or measured) data, yi . This section of the manual contains information on: • "Regression algorithm" on page 352. • "First and second order derivatives" on page 352 • "Trust region" on page 353 • "Termination conditions" on page 353 Regression algorithm The regression algorithm in PVTi seeks to minimize the least squares residual ( l 2 norm) given by the objective function: M 1 f ( x ) = --2 ˜ ri ( x˜ ) 2 1 T = --- R ( x ) R ( x ) 2 ˜ ˜ [EQ 8.182] i=1 where R ( x ) is the residual function. ˜ The minimum of f ( x ) occurs at some x∗ , where: ˜ ˜ [EQ 8.183] ∇f ( x∗ ) = 0 ˜ Since f ( x ) is generally non-linear in the set x , [EQ 8.183] must be solved iteratively. Applying ˜ ˜ Newton’s method gives: –1 [EQ 8.184] x j + 1 = x j – ( ∇2f ( x j ) ) ∇f ( x j ) ˜ ˜ ˜ ˜ First and second order derivatives The first and second derivatives of the objective function can be readily evaluated, see Dennis and Schnabel, [Ref. 9]. It is possible to construct a numerical approximation to the first derivative using two function evaluations. That is with the current values of the variables, x , and shifted values x + δx . ˜ ˜ ˜ A similar procedure to evaluate the second derivative becomes prohibitively expensive and so an approximation is generated, see [Ref. 9]. The advantage of this pseudo second-order method is that it ensures that the algorithm proceeds towards a genuine minimum. A function of a single variable, say g ( x ) , has a minimum at the point xm if g' ( xm ) = 0 and the second derivative g'' ( x m ) is positive. For a multi-variate function like the objective function, f , the equivalent requirement is that the matrix ∇2f ( x ) is positive definite. ˜ A matrix is positive definite if it is symmetric and all its eigenvalues are positive. The approximation used to construct the second derivative ensures the symmetry condition. The program can correct for the lack of positive eigenvalues by adding a multiple of the identity matrix. 352 Technical Description Regression PVTi Reference Manual Trust region The algorithm only approaches the true solution rapidly if the current estimate xj is close to the ˜ actual solution x∗ . Generally, the objective function at any iteration j is only an approximation ˜ to the true solution. Therefore, it helps to identify a region surrounding the current solution, in which we trust our second order approximation to model the actual second order problem. PVTi employs the trust region model by defining a step length, δ c , which is a measure of the region in which our model can be thought to be representative. Ideally, the step-size, which is determined automatically subject to certain maximum and minimum sizes, decreases as the iterations proceed to convergence. The program uses the value of the current step length to adjust the second order derivative matrix, so that a zero or small value of δ c causes PVTi to solve the full Newton problem, refer to [EQ 8.184]. If following the evaluation of a step, the program determines that the objective function would not decrease, then the algorithm has a procedure for cutting back the step so that it ensures a decrease in f . Termination conditions A variety of termination conditions from the regression algorithm are possible. Note The required condition is that the residual goes to some small value, such as 10 –6 , but this is rarely achieved for larger problems. An alternative is that the gradient of the objective function goes to zero, indicating that the regression is approaching a minimum and no further improvement can be expected. As a result of one or more steps made by the algorithm, one or more of the selected regression parameters can be pushed out of physical range. What constitutes a physical range is debatable, but it is suggested that an increase or decrease in excess of 50% of the original value causes termination. You can change these limits but care should be taken. You can request a premature termination by allowing only a small number of iterations, say five or ten. Hint This is a good practice to follow for any regressions which involve several variables, experiments and observations. Finally, if any errors are detected in any of the experiments during the regression, then depending on their nature, the program may terminate the regression. PVTi Reference Manual Technical Description Regression 353 Output for ECLIPSE simulators General information Our suite of reservoir simulation software supports five different models for fluid behavior. There is the ECLIPSE extended blackoil model, the pseudo-compositional model (GI option), the ECLIPSE compositional model., the ECLIPSE Thermal model and the API Tracking option used in ECLIPSE BlackOil. p -V -T data suitable for use in any of these models can be generated from the PVTi package. Each of the models and typical output is discussed in the appropriate section. This section of the manual contains information on: • "Blackoil model" on page 354. • "Differential and composite from differential tables" on page 359. • "Pseudo-compositional tables for ECLIPSE GI option" on page 360. • "Compositional data for ECLIPSE Compositional" on page 361. • "Water properties" on page 362. • "Model for API Tracking option in ECLIPSE BlackOil" on page 363. • "Compositional Data for ECLIPSE Thermal" on page 366. Blackoil model ECLIPSE has a so-called extended blackoil model. That is, in addition to the standard blackoil parameters, Rs , B o and B g , it contains the parameter R v for modeling oil vaporization in the gas stream. Methods of obtaining black oil tables from compositional data are described by Whitson and Torp, [Ref. 6] and Coats, [Ref. 3]. In both cases the basis of the method is a constant volume depletion experiment, used to supply reservoir liquid and vapor compositions at a series of pressures. (In the case of crude oil samples, a differential liberation process is used in the same way.) The blackoil model, used by ECLIPSE, can be viewed as a two-component compositional model. The “components” are stock tank oil and stock tank gas that are assumed to be invariant and are assigned constant densities. PVT model The actual form of the PVT model for the hydrocarbons depends on whether: 354 • There is or could be liquid and/or vapor in the reservoir during its production. • The reservoir phases produce stock tank oil and/or gas on flashing to surface conditions. Technical Description Output for ECLIPSE simulators PVTi Reference Manual Reservoir fluids Assuming the stock tank fluids are constant, the reservoir fluids, named liquid and vapor to distinguish them from the surface fluids which are designated as oil and gas, are generally a combination of the stock tank fluids. The amount of surface gas dissolved in the reservoir liquid is given by the Gas-Oil-Ratio (GOR), denoted Rs , which has units of sm3 /sm3 (metric), mscf/stb (field) or scm 3 /scm 3 (lab). The volume of surface oil vaporized in the reservoir vapor is given by the Condensate-GasRatio (CGR), denoted Rv , which has units of sm3 /sm 3 (metric), stb/mscf (field) or scm 3 /scm 3 (lab). The model uses formation factors to account for changes in volume when the fluids are transferred from the reservoir to the surface. The factors for the liquid and vapor are denoted, Bo and Bg , and given units of rm3 /sm 3 (metric), rb/stb (field) or rm3 /sm 3 (lab), and rm3 /sm3 (metric), rb/mscf (field) or rcm 3 /scm 3 (lab), respectively. The model assumes that the reservoir has been depleted to a pressure below the saturation pressure (liquid bubble point or vapor dew point) and consequently has become two phase. One mole of reservoir vapor and liquid occupies the volumes V gr and Vor , respectively. If each of these volumes are then flashed through some separator system (two stages are indicated above but this can be variable) to stock tank conditions, then most generally each reservoir phase partitions into the streams named stock tank gas and oil. Stock tank components If the one mole of reservoir vapor, volume V gr , gives N gg moles of stock tank gas of volume Vgg and N og moles of stock tank oil of volume Vog , whilst the one mole of reservoir liquid, volume V or , gives N go moles of stock tank gas of volume V go and N oo moles of stock tank oil of volume V oo , then conservation of mass requires that: M gr = M og + M gg [EQ 8.185] M or = M go + M oo [EQ 8.186] where ( M gr, M or ) are the reservoir molar masses and ( M og, M gg ) , ( M go, M oo ) are the corresponding actual surface masses after flashing. Since ρ = M ⁄ V , we can write equations [EQ 8.185] and [EQ 8.186] as: ρ gr V gr = ρ og V og + ρ gg V gg [EQ 8.187] ρ or V or = ρ go V go + ρ oo V oo [EQ 8.188] or: 1 ρ gr = ------ ( ρ gg + R v ρ og ) Bg [EQ 8.189] 1 ρ or = ------ ( ρ oo + R s ρ go ) Bo [EQ 8.190] where: V go R s = -------V oo PVTi Reference Manual V og R v = -------V gg [EQ 8.191] Technical Description Output for ECLIPSE simulators 355 V or B o = -------V oo Note V gr B g = -------V gg [EQ 8.192] Strictly, the blackoil model requires that the stock tank “components” are constant and invariant with time. CVD process In the Coats method, only the reservoir vapor is taken through the separator, the oil B o and R s values being obtained by solving the mass conservation equations: ρ sto V 2 ( b g S g + b o R s S o ) 2 = ρ sto V 1 ( b g S g + b o R s S o ) 1 [EQ 8.193] ρ stg V 2 ( b g R v S g + b o S o ) 2 = ρ stg V 1 ( B g R v S g + b o S o )1 [EQ 8.194] for each expansion step of the CVD process from V 1 to V2 , where ρ sto and ρ stg are fixed surface densities, and b o = 1 ⁄ Bo , b g = 1 ⁄ B g . The stock tank densities are obtained from the output of the separators at the saturation pressure. Solving these equations yields values at all pressures except the saturation pressure, at which the Whitson method can be used. Alternatively, a small initial pressure step from the saturation pressure may be specified. Note The constant volume expansion method is usually applied to condensates, but can also be used for volatile oils. Differential liberation The differential liberation approach is only suitable for oils. In this case, the analogue of the Whitson method runs both reservoir oil and vapor through the separators as before. The analogue of the Coats method uses the conservation equations, [EQ 8.193] & [EQ 8.194] (although in this case S g1 is zero for each step), ρ sto and ρ stg are obtained from the reservoir oil at the saturation pressure. ECLIPSE 100 tables For both processes, you can produce the ECLIPSE live oil, wet gas, dead oil and dry gas tables. The respective keywords are PVTO, PVTG, PVDO, and PVDG. In addition, the model calculates the density of the oil, water and gas phases at stock tank conditions (final stage separator) for the saturation point fluid, and output under the DENSITY keyword. These values are important as the reservoir properties are calculated using the R s , Rv , B o , B g from the stock tank volumes and densities. Hint 356 The "Choosing the unit type for PVTi" on page 144 program option gives you a choice of outputting and plotting all the data (saturated and undersaturated) or just the saturated data. Technical Description Output for ECLIPSE simulators PVTi Reference Manual An example of a typical set of blackoil data (for a volatile oil fluid) is shown below: -- Blackoil tables for sample ZI at T = 176.00000 deg F -- With Peng-Robinson (three-parameter) EoS -- And Lohrenz-Bray-Clark viscosity correlation -- ECLIPSE 100 DENSITY data -- Surface densities of oil, water and gas: -- Units of FIELD DENSITY 50.74699 62.42797 0.05842 / -- Two stage separator at -- Pressures 214.69590 14.69590 -- Temperatures 100.00010 60.00001 -- Pressures in PSIA Temperatures in deg F --ECLIPSE 100 PVTG data --(Constant volume depletion) --Units are FIELD --Method used: Whitson and Torp PVTG -PRES RV BG VISC -PSIA STB/MSCF RB/MSCF CPOISE 1114.69590 0.00099 2.43709 0.0139554 --Saturated 0.00000 2.43919 0.0139489 / --Dry gas 1814.69590 0.00276 1.43004 0.0166381 --Saturated 0.00099 1.43350 0.0165733 --Undersat gas 0.00000 1.43543 0.0165380 / --Dry gas 2514.69590 0.00736 1.02359 0.0206166 --Saturated 0.00276 1.02929 0.0202678 --Undersat gas 0.00099 1.03150 0.0201382 --Undersat gas 0.00000 1.03272 0.0200669 / --Dry gas 3214.69590 0.01695 0.82309 0.0257392 --Saturated 0.00736 0.82851 0.0246867 --Undersat gas 0.00276 0.83111 0.0242117 --Undersat gas 0.00099 0.83211 0.0240316 --Undersat gas 0.00000 0.83267 0.0239322 / --Dry gas 3914.69590 0.03492 0.71605 0.0321610 --Saturated 0.01695 0.71725 0.0297284 --Undersat gas 0.00736 0.71789 0.0285431 --Undersat gas 0.00276 0.71820 0.0279877 --Undersat gas 0.00099 0.71831 0.0277758 --Undersat gas 0.00000 0.71838 0.0276584 / --Dry gas 4077.56801 0.04108 0.69977 0.0339734 --Psat 0.03492 0.69960 0.0329685 --Undersat gas 0.01695 0.69910 0.0306120 --Undersat gas 0.00736 0.69884 0.0293996 --Undersat gas 0.00276 0.69871 0.0288303 --Undersat gas 0.00099 0.69867 0.0286129 --Undersat gas 0.00000 0.69864 0.0284924 / --Dry gas PVTi Reference Manual Technical Description Output for ECLIPSE simulators 357 4614.69590 0.04109 0.65591 0.0368566 --Generated 0.03492 0.65447 0.0357868 --Undersat gas 0.01695 0.65029 0.0332692 --Undersat gas 0.00736 0.64806 0.0319664 --Undersat gas 0.00276 0.64699 0.0313522 --Undersat gas 0.00099 0.64658 0.0311171 --Undersat gas 0.00000 0.64635 0.0309867 / --Dry gas --ECLIPSE 100 PVTO data --(Constant volume depletion) --Units are FIELD --Method used: Whitson and Torp PVTO -RS PRES BO VISC -MSCF/STB PSIA RB/STB CPOISE 0.49137 114.6959 0.34107 0.30770 --Saturated 1814.69590 1.32574 0.33605 2514.69590 1.31260 0.36369 3214.69590 1.30116 0.39067 3914.69590 1.29106 0.41705 4077.56801 1.28887 0.42310 4614.69590 1.28206 0.44285 / 0.79978 1814.69590 1.49404 0.23723 --Saturated 2514.69590 1.47369 0.26054 3214.69590 1.45641 0.28344 3914.69590 1.44147 0.30594 4077.56801 1.43827 0.31112 4614.69590 1.42836 0.32808 / 1.16269 2514.69590 1.67183 0.18640 --Saturated 3214.69590 1.64551 0.20520 3914.69590 1.62331 0.22377 4077.56801 1.61862 0.22806 4614.69590 1.60421 0.24214 / 1.63520 3214.69590 1.90440 0.14692 --Saturated 3914.69590 1.87000 0.16174 4077.56801 1.86286 0.16517 4614.69590 1.84116 0.17646 / 2.34029 3914.69590 2.25803 0.11383 --Saturated 4077.56801 2.24611 0.11645 4614.69590 2.21050 0.12507 / 2.56913 077.56801 2.37483 0.10661 --Psat 4614.69590 2.33394 0.11462 / 2.66303 4614.69590 2.37492 0.10622 --Generated 5151.82379 2.33402 0.11423 / / Both the PVTO and PVTG tables are extended to include properties of the undersaturated oil and gas, respectively. In the case of the PVTG table the model computes, at all values of Rv between the saturated value and the dry gas value ( Rv = 0.0 ), a value for Bg by adding sufficient stock tank oil to the stock tank gas (both from the flash of the saturated gas to stock tank) to give the required R v and then taking the ratio of this fluid's volume at reservoir and stock tank volumes. 358 Technical Description Output for ECLIPSE simulators PVTi Reference Manual In the case of the PVTO table, the model compresses the saturated fluid from a given Rs node at all pressures from the saturated pressure up to the highest pressure. The ratio of these volumes to the resulting stock tank oil volume (from flashing the saturated oil) gives the undersaturated B o values. Monotonicity and compressibility tests If you specify a highest pressure that is higher than the saturation pressure fluid, then PVTi increases the saturated pressure of the sample to a value above the maximum pressure used in the depletion experiment by mixing the sample with a lighter gas sample. The gas sample used is the vapor split-off obtained from performing a p sat calculation on the original sample. The model mixes this vapor with the sample and performs a new p sat calculation on the new sample. It then mixes the resulting vapor split off with the new sample and repeats the process until a p sat forms that is higher than the maximum pressure stage. If this process is successful you can save the final sample and use it in the calculation of the black oil tables. Alternatively if you do not want to swell the sample, PVTi allows you to select to truncate the blackoil tables at the saturation pressure. Note Oil and gas properties below the saturation point generated as described above are also subjected to the ECLIPSE total compressibility test. Note If negative compressibilities are detected, PVTi (with confirmation) solves for intermediate points, which provide the necessary resolution to pass the compressibility test. Differential and composite from differential tables As an alternative to the composite tables described above, you can produce a differential black oil table. This technique involves simulating a differential liberation experiment, and the values of Bo and R s are taken to be the normal definitions of oil formation volume factor and gas-oil ratio, respectively, as defined in this experiment. Note These definitions are detailed in the manual (refer to "Basic laboratory experiments" on page 339 and "Gas condensate systems" on page 341, and to equations [EQ 8.171] and [EQ 8.173]). The quantities are known here as B Do and RDs . From these differential quantities, it is possible to estimate composite values of Bo and R s using a number of formulae. Two of the more popular methods are due to Moses, and Fragor [Ref. 40] (both now termed CM and CF respectively). PVTi Reference Manual Technical Description Output for ECLIPSE simulators 359 Both methods start by estimating a value for Bo and R s at the saturated pressure ( p sat ) of the CM initial oil. This oil is passed through a separator chain and the values of B CF o ( p sat ) and B o ( p sat ) are given by the oil formation volume factor from the separator. Likewise the values of R CF s ( p sat ) and RCM s ( p sat ) are given the value of the gas-oil ratio from the separator. Once these two values are computed, the rest of the values from the lowest pressure up to psat are found from the following formulae. Firstly the Fragor definitions: CF D ( B o ( p sat ) – 1 ) ( B o ( p ) – 1 ) CF B o ( p ) = 1 + ----------------------------------------------------------------D ( B o ( p sat ) – 1 ) [EQ 8.195] and CF D R s ( p sat )R s ( p ) CF R s ( p ) = -------------------------------------D R s ( p sat ) [EQ 8.196] The Moses expressions are given by: CM D B o ( p sat )B o ( p ) CM B o ( p ) = --------------------------------------D B o ( p sat ) [EQ 8.197] and CM B o ( p sat ) CM CM D D - R s ( p ) = R s ( p sat ) – ( R s ( p sat ) – R s ( p ) ) ---------------------- BD o ( p sat ) [EQ 8.198] PVTi can provide all four types of black oil output, that is, the usual composite, the differential, and the two composite from differential tables. Note The output form for the differential and composite from differential tables is by way of the PVTO/PVDO and PVDG keywords only. Pseudo-compositional tables for ECLIPSE GI option At pressures less than the saturation pressure, psat , compositional effects become important. Limitations of the ECLIPSE blackoil model 360 1 The blackoil approximation, discussed in the previous section, models compositional changes by making the parameters, Rs , B o , R v , and B g all functions of pressure, which it determines from the reservoir and surface properties of the liquid and vapor phases. 2 The extended blackoil treatment, that is variable R v as available in ECLIPSE, cannot model gas injection into condensates at pressures less than psat , without careful consideration (see keyword VAPPARS in the "ECLIPSE Reference Manual"). Lean gas injected into a saturated reservoir fluid causes the stripping of the light and intermediate components from the reservoir fluid, resulting in an enriched gas phase and a depleted liquid phase. Technical Description Output for ECLIPSE simulators PVTi Reference Manual 3 To model this process accurately requires a detailed fluid description and the use of a fully compositional simulator using a many-component model of the fluid. However, such is generally impractical, especially using a fully implicit formulation since the number of equations, which need to be solved increases with the product of the number of components and the number of gridblocks. ECLIPSE GI option One possible solution to this problem is to extend the three-parameter blackoil model as used in ECLIPSE BlackOil, that is p , S w and So , by adding a fourth parameter/equation. In the ECLIPSE pseudo-compositional model, this fourth parameter, denoted GI, is the cumulative gas volume, which has passed over the volume of reservoir liquid in a gridblock. As such, GI is equivalent to a gas-oil ratio of volume of injection gas at standard conditions to volume of oil at reservoir conditions: gas V stc GI = --------oil V res [EQ 8.199] This model determines the oil volume at reservoir conditions, V oil res , for the first stage of gas addition, from the GI=0.0, that is the standard blackoil model. It then calculates the gas volume at standard conditions, Vgas stc , from the gas law: add n ZRT stc gas V stc = -------------------------p stc [EQ 8.200] where n add is the number of moles of gas added. By convention, at standard pressure and temperature, p stc = 14.7 psia, T stc = 60.0 °F , and the gas-compressibility factor, Z = 1 . Having defined a Constant Volume Depletion (CVD) experiment and a separator network with the last stage corresponding to stock tank conditions, the model then performs a calculation of the conventional extended blackoil tables. This defines the GI=0.0 data. It then adds lean gas to the reservoir fluid in a series of stages and generates the blackoil table with the mixture. The ratio of the non-zero GI blackoil properties and the GI=0.0 properties defines a set of GI-multipliers. This gives a two-dimensional set of tables in ( p , GI) to describe the fluid behavior. Detailed evaluations of the model’s performance have been undertaken and with favourable conditions and tuning against a full compositional treatment, this model can give reliable predictions. Compositional data for ECLIPSE Compositional You can run ECLIPSE Compositional in one of three modes: • Blackoil - As ECLIPSE 100 • K -value • Compositional - Equation of state. - Specify K -values at given pressures It is envisaged that generally you will want to run ECLIPSE Compositional in compositional (Equation of State) mode. PVTi Reference Manual Technical Description Output for ECLIPSE simulators 361 However, in blackoil mode, ECLIPSE 300 reads the same PVTO and PVTG tables as used in ECLIPSE BlackOil. In K -value mode, you must specify a set of K -values for each component at a set of pressures spanning the operating pressure region. You can generate these, as in PVTi, by performing a CVD experiment on the reservoir fluid. Compositional mode The Equation of State mode is essentially the same as that employed by PVTi for its flash, saturation pressure, etc., calculations. You must specify the number of components, the Equation of State required (the same set as available in PVTi), and the critical properties, acentric factors, binary interaction coefficients, compositions, etc. Clearly, the more components used, the more accurate the simulation (assuming the component set has been optimised to measured data); however, such simulations require more CPU time. Hint If running ECLIPSE Compositional in fully implicit mode, more than six or seven components may become prohibitive for all but the largest of supercomputers or workstations, in which case you should consider pseudoisation of this fluid system to fewer components. Water properties ECLIPSE and VFPi consider water to be non-volatile (only exists as liquid water) and immiscible with the hydrocarbon phases (water cannot dissolve in the hydrocarbons or viceversa). This simplifies the PVT treatment of water. If water is present, the variation of water volume in the reservoir with pressure, V w ( p ) , is defined with respect to the volume of water at surface conditions, Vstw , by the formation volume factor, B w , where: Vw ( p ) B w ( p ) = --------------V stw [EQ 8.201] which has units of rm3 /sm 3 (metric), rb/stb (field) or rcm3 /scm3 (lab). Note Note that VFP only supports metric and field units. Within the models, B w is defined in terms of the Bw at some reference pressure, p ref : B w ( p ref ) B w ( p ) = ----------------------------2 (1 + X + X ) [EQ 8.202] where X = C w ( p – p ref ) [EQ 8.203] and C w is the water compressibility which is defined as: 1 dB w C w = – ------ --------- B w dp p = pref 362 Technical Description Output for ECLIPSE simulators [EQ 8.204] PVTi Reference Manual that has units of barsa–1 (metric), psia –1 (field) or atmos–1 (lab). Water viscosity is modeled in the same way as the formation volume factor: μ w ( p ref ) μ w ( p ) = ---------------------------2 (1 + Y + Y ) [EQ 8.205] where [EQ 8.206] Y = C μw ( p – p ref ) and C μw is the water viscosibility which is defined as: 1 dμ w C μw = – ------ --------- μ w dp p = p ref [EQ 8.207] that also has units of barsa–1 (metric), psia –1 (field) or atmos–1 (lab). An additional complication can arise if the effect of salt (brine) concentration is to be modeled (ECLIPSE BlackOil and GI option only). See the keyword PVTWSALT in the "ECLIPSE Reference Manual" for further details in this case. Note Correlations for generating default values for all the above correlations can be found in [Ref. 33]. Model for API Tracking option in ECLIPSE BlackOil For further information on the ECLIPSE keywords referenced in this section see the "ECLIPSE Reference Manual". Introduction The API Tracking facility enables ECLIPSE BlackOil to model the mixing of different types of oil, having different surface densities and PVT properties. Without the API Tracking facility, the presence of different types of oil in the reservoir could be handled with the aid of PVT region numbers. Oil in PVT region 1 would have its properties determined from PVT table number 1, and so on. However, this method cannot model the mixing of oil types. Oil flowing from region 1 into region 2 would appear to take on the properties associated with region 2. The API Tracking facility essentially replaces the concept of PVT regions for oil. The PVT tables used for determining the oil properties are selected at each time step according to the average API of the oil in each grid block (or to be more precise, its average surface density). A mass conservation equation is solved at the end of each time step to update the oil surface density in each grid block, to model the mixing of the different oil types. When using ECLIPSE BlackOil, the API Tracking facility is turned on by the keyword API in the RUNSPEC section. In dead oil systems the keyword RSCONSTT cannot be used with API tracking, but RSCONST (defining a uniform Rs value over the whole field) can be used. PVTi Reference Manual Technical Description Output for ECLIPSE simulators 363 Using PVTi to Export the Tables PVTi can be used to export the black oil tables in the required form outlined in the next few sections. Simply open the Export Panel for API Tracking option panel by using File | Export | API Tracking option in ECLIPSE BlackOil.... The user needs to select the samples for which the export is required. This is done by selecting a set of samples and dropping them in the use box. Next, the required keywords to export need to be specified in the normal way. Hint Since the API Tracking functionality in ECLIPSE models the mixing of live oil properties the usual procedure in PVTi is to use the API Tracking export facility to write out a series of tables containing the PVTO (live oil) and PVDG (dead gas). You can then specify whether they want a gas table for each sample. Normally the API Tracking option in ECLIPSE only uses a different oil table for each sample and just a single gas table is used, as explained in the next section, and so this is the default. If this default option is used then PVTi exports a single gas table for the sample with the median gas density at surface conditions. The separator and units to use for the export can be specified in the normal way. You can also specify a few other straightforward options such as whether to write to full double precision and whether to plot the tables. When the export is performed PVTi orders the tables so that the oil surface densities increase monotonically with table number, which is a requirement of ECLIPSE. Each table also has comments associated with it specifying which sample the table is linked to and what the oil surface density is for this particular table. ECLIPSE requires that the Rs ranges of any live oil tables are the same. To ensure this is the case PVTi analyzes all the samples you selected and calculates the Rs at the maximum pressure in the DL experiment. PVTi then finds the sample with the maximum Rs and then uses linear extrapolation to extend the black oil tables of the other samples so that the Rs ranges for all the samples are the same. See the next few sections for technical details of ECLIPSE’s API Tracking option. The PVT properties Two or more sets of PVT tables should be supplied, each set being associated with a particular value of the API. The oil property tables are entered in the usual way (with keyword PVTO or PVCO for live oil problems, or keyword PVDO for dead oil problems), but with the requirement that all the PVTO or PVCO tables must have the same upper and lower Rs values. From these tables, ECLIPSE constructs a set of internal tables that have a common set of Rs nodes, which includes the Rs nodes of all the input tables. This allows ECLIPSE to use an efficient method of interpolating between tables, for intermediate values of the API. The restriction that the upper and lower Rs values must be the same for each table prevents extrapolation of the input data during this process, which may cause unphysical behavior. The API values associated with each PVT table are set using the keyword GRAVITY, which inputs the oil, water and gas gravities for each PVT table number. The API values are converted internally to oil surface densities, using the formula given in "Conversion factors" on page 1236. The oil API values must decrease monotonically with the table number. Alternatively the surface densities associated with each table number can be input directly using the keyword DENSITY. In this case the oil surface densities must increase monotonically with the table number. 364 Technical Description Output for ECLIPSE simulators PVTi Reference Manual The PVT properties of water and gas are not affected by the API Tracking option. The same number of tables must be entered in all the PVT data keywords and the ROCK keyword, but normally only the first table is actually used in all except the oil PVT data. The unused PVT and rock compressibility tables can be defaulted by typing a single slash (/) on a new line for each unused table in the keyword. Grouping tables into PVT regions The API Tracking facility over-rides the concept of PVT table regions for oil. The tables used to determine the oil PVT properties are selected according to the surface density of the oil in the grid block, instead of the block’s PVT region number. Thus the PVTNUM keyword in the REGIONS section is not normally required with the API tracking facility. If however the concept of PVT regions for different types of oil is still required in an API Tracking run, the oil PVT tables can be partitioned into groups for use in different regions of the reservoir. The keyword APIGROUP must be entered, to specify the maximum number of groups of oil PVT tables. The grouping of the oil PVT tables is then determined by the order in which they are entered. Within each group, the oil API gravities should decrease (or the oil surface densities should increase) monotonically with the table number. A break in the required monotonicity is taken to indicate that the subsequent tables belong to the next API group. An error is flagged if the total number of API groups exceeds the maximum specified in the APIGROUP keyword. The separate groups of oil PVT tables can then be used in different areas of the reservoir. The REGIONS section keyword PVTNUM is used to specify which API group is to be used for each grid block. For example, a cell in PVTNUM region 2 will use the second API group to obtain the oil properties. For water and gas PVT properties, the PVTNUM regions correspond to the actual table numbers, as in runs that do not use API tracking. So a cell in PVTNUM region 2 still uses table number 2 for its water and gas properties. Setting the initial conditions The initial API distribution throughout the reservoir is specified in the SOLUTION section. If the initial conditions are determined by equilibration, the API can vary with depth independently in each equilibration region. Keyword APIVD supplies a table of API values versus depth for each equilibration region. When setting the initial conditions by enumeration (keywords PRESSURE, SWAT etc.), the keyword OILAPI is used to supply the initial API values for each grid block. The API tracking calculation The initial API values in the grid blocks are immediately converted into oil surface density. The hydrostatic pressure gradient calculation takes account of the varying surface density of the oil. The variation of other PVT properties with surface density (bubble point pressure, formation volume factor and viscosity) is handled by interpolating between PVT tables. The two adjacent PVT tables whose oil surface densities straddle the oil surface density value in the grid block are located, and their properties ( 1 ⁄ B o , 1 ⁄ ( Bo μo ) ) are interpolated linearly in oil surface density. To calculate the bubble point, the two PVT tables corresponding to oil surface gravities either side of the current grid block API value are located. The bubble point is then obtained by linearly interpolating between the bubble points in these PVT tables at the given grid block dissolved gas-oil ratio. PVTi Reference Manual Technical Description Output for ECLIPSE simulators 365 The oil surface density in each grid block and well is held constant over the time step. When a converged solution for the time step has been found, and the inter-block flows determined, a mass conservation equation is solved to update the oil surface densities. The new densities are used in the next time step. The oil surface densities are converted back into API values for the output reports. The mnemonic OILAPI in the RPTSCHED keyword provides an output of the grid block API values, and the well reports include the API values in the wells. API tracking in wells The oil surface density in each well is calculated at the end of the time step to reflect a flowweighted average surface density of the inflowing oil. A crossflowing well will reinject oil of this average surface density back into the formation. However, the hydrostatic head calculation in the wellbore will be based on a (more accurate) flow-weighted average of upstream connection inflows if WELSPECS item 12 is ‘SEG’, allowing the oil density to vary with position in the wellbore. (The pre-98A treatment of wellbore hydrostatic head, which uses the well’s average oil surface density, can be restored if required by setting switch 35 in the OPTIONS keyword.) If the well uses a VFP table to calculate the tubing pressure losses, this should be calculated using a suitable value of the oil surface density. However, it is possible to take account of the variation of the well’s producing API over time by defining the fifth lookup variable, the ALQ, to represent the surface density of the produced oil (see keyword WALQCALC). The VFP table should be prepared using the same definition of the ALQ, with values spanning the expected range of oil surface densities. The VFPi program contains an option to prepare tables with variable oil surface density. Behavior in wet gas systems By default, in wet gas systems, the surface density property (API) of the oil is transported in both the oil and gas phases, that is the API is interpreted as a property of the oil component rather than the liquid oil phase. By using OPTIONS switch 58 this behavior can be modified. When the switch is set greater than zero the API property will only be transported in the liquid oil phase. In this case the API property can be thought of as a heavy component which does not vaporize. Care needs to be taken when using this option as it is possible to vaporize all the oil in a cell, leading to high surface densities and negative API values. Compositional Data for ECLIPSE Thermal Introduction This introduction contains a brief outline of the reason for the introduction of this module. 366 • "Outline of keywords for ECLIPSE Thermal" on page 367 contains a brief description of the keywords exported. • "Workflow" on page 368 section gives step-by-step instructions of how to perform a typical export for use in ECLIPSE Thermal. • "Some handy hints for fitting the Crookston coefficients" on page 369 gives some hints and tips on how to export Crookston coefficients that provide accurate approximations to PVTi’s EoS K-values. Technical Description Output for ECLIPSE simulators PVTi Reference Manual For the 2003A version of PVTi a new ECLIPSE Thermal support module was available where you were able to interactively develop a correlation which accurately predicted K-values for each component in a given fluid. For the 2004A version this module has been extended to a full export facility where you can write out files that are suitable for use as PVT input for ECLIPSE Thermal. The motivation behind this is so that, just as you can export files to use as PVT input for ECLIPSE BlackOil and ECLIPSE Compositional, they will now be able to do the same for ECLIPSE Thermal. When you use this new export facility, they now have a choice of keywords to export regarding K-values - namely the KVCR keyword (which was available in 2003A PVTi) or the KVWI keyword which is tells ECLIPSE Thermal to use a simplified version of Crookston’s equation called Wilson’s formula. In addition PVTi also exports a series of other keywords enabling ECLIPSE Thermal to calculate properties of the feed fluid such as oil density, gas density and oil/gas phase enthalpies. For a technical description of how these keywords exported by PVTi are used in ECLIPSE Thermal see "ECLIPSE Thermal Export Module" on page 401. For a summary and brief outline of the nature of these keywords see the next section. Outline of keywords for ECLIPSE Thermal 1 STCOND - the standard temperature and pressure used in PVTi 2 NCOMPS - the number of components in the fluid. 3 CNAMES - the names of each component. 4 MW - the molecular weight of each component. 5 TCRIT - the critical temperature of each component. 6 PCRIT - the critical pressure of each component. 7 TREFT - the ECLIPSE Thermal reference temperature at which the reference density, DREFT, is calculated. Note In general the quantities TREFT, PREFT, DREFT are not the same as the related quantities of reference temperature, TREF and references density, DREF used in PVTi. Please see 8 ACF - the acentric factors of the components. 9 SPECHA - oil phase specific heat first coefficients. 10 SPECHB - oil phase specific heat second coefficients. 11 SPECHG - gas phase specific heat first coefficients. 12 SPECHH - gas phase specific heat second coefficients. 13 HEATVAPS - heats of vaporization at the standard temperature. 14 CREF - component isothermal compressibilities in the oil phase. 15 THERMEX1 - component thermal expansion coefficients in the oil phase. 16 ZFACTOR - the gas Z factor for each component. 17 KVWI - tells ECLIPSE Thermal to use Wilson’s formula to estimate K-values. 18 KVCR - tells ECLIPSE Thermal to use Crookston’s equation to estimate K-values. This keyword contains the values of the coefficients (A-E) for each component. 19 ZI - the feed mole fractions of each component PVTi Reference Manual Technical Description Output for ECLIPSE simulators 367 The keywords STCOND, SPECHA, SPECHB, SPECHG, SPECHH, HEATVAPS, CREF, THERMEX1, ZFACTOR, KVWI and KVCR are only exported for ECLIPSE Thermal and not for ECLIPSE Compositional. See "ECLIPSE Thermal Export Module" on page 401 for a technical description of how the values contained in these keywords are used to calculate K-values, oil/ gas densities and oil/gas enthalpies for each component. Workflow 1 To access the Thermal Support module select Edit | Samples | ECLIPSE Thermal Support | Export for ECLIPSE Thermal.... Alternatively right- click on a fluid sample of interest and select Export ECLIPSE Thermal Model.... 2 In the panel type in the maximum and minimum values of the pressure in your reservoir and also the maximum and minimum temperature. 3 Select the sample you wish to export the model for by using the drop-down menu. 4 You need to decide if you want to estimate K-values in ECLIPSE Thermal using Crookston’s equation or using Wilson’s formula. Wilson’s formula gives much less accurate results than Crookston’s formula but if you have time constraints then much less work is involved in exporting this information from PVTi. If you want to use Wilson’s formula then your work is finished and you do not need to go though steps 5-12. Simply select which units you want to export and click OK. Hint If you have time and you know the rough limits on temperature and pressure within your reservoir then Crookston’s equation will, in general, give you much more accurate estimates of K-values than Wilson’s formula. 5 If you want to export coefficients for Crookston’s equation then tick the box entitled Export Crookston Coefficients? 6 Now enter how many flashes you want to perform. Unless you have very large ranges in temperature or pressure in your reservoir then the default of 20 is probably fine. These flashes generate K-values using PVTi’s EoS algorithm at random points in the region defined by your maximum pressure and temperature. The generated K-values are the “observations” used when trying to optimize the values of the coefficients in Crookston’s equation. 7 Click the Fit Crookston Coefficients button. Another panel opens. 8 Select the coefficients to optimize. As a rule always start with B and D or A,B and D. Now click Apply and PVTi attempts to use a minimization algorithm to calculate the best values of your chosen coefficients that gives the most accurate prediction of K-values for each component. 9 Once PVTi has finished a results window opens with two folders. The Coefficients folder enables you to see the coefficient values derived by PVTi for each component. The Statistics folder enables you to observe the mean rms of the fit (in %) and the standard deviation (in %) of the fits for each component over the specified temperature and pressure range. 10 To view your fit click View Fit on the Fit Crookston Coefficients panel. Another panel opens. You are able to view the results by plotting K-values as a function of temperature (at constant pressure) or pressure (at constant temperature). Type in the appropriate information and click Apply. 368 Technical Description Output for ECLIPSE simulators PVTi Reference Manual 11 PVTi now show you the observations it was fitting to for each component, that is the Kvalues found using the Equation of State based flash (the points) and the curves, which are the predictions of the K-values found using Crookston’s formula. 12 Once you are happy with your results close the Fit Crookston Coefficients panel and click OK on the Export for ECLIPSE Thermal panel. A File | Save panel opens. Choose the name of the file you want to save it as and click Enter. A text file is created and shown in the output display containing the exported keywords. This file can be used as the PVT input in an ECLIPSE Thermal simulation. Note The default file extension when exporting for ECLIPSE Thermal is .PVO. The save panel assumes you want to call your exported file filename.PVO where filename.PVI is the name of your PVTi project file. See the next section for some hints on performing the optimization of the Crookston coefficients. Some handy hints for fitting the Crookston coefficients The goal of this optimization is to allow you to interactively develop a correlation that accurately predicts K-values for each component in a given fluid over a specified range of temperature and pressures. The functional form of the correlation used by PVTi is given by Crookston’s equation which is: B –D K ( P, T ) = A + --- + CP exp ------------- T – E P [EQ 8.208] You are able to specify which coefficients to use in equation [EQ 8.208] (as already explained in the previous section) and PVTi calculates the values of these coefficients which give the best fit to the PVTi flash for each component over the pressure and temperature range. The following things may help you in your workflow: 1 Try doing a phase curve first of your fluid to get an idea of the pressure and temperature range where your sample is two-phase. PVTi does not use any regions of pressuretemperature space where the fluid is single phase. 2 When choosing the values of the max/min temperature and pressure consider the following: 3 PVTi Reference Manual a The default values of Pmax=1000psia, Pmin=50psia, Tmax=400F and Tmin=50F are considered to be reasonable variations of conditions within a reservoir. b Make sure you alter these values to suit your particular reservoir. Try to make the region that is defined by your values as small as possible. For example if you think that the maximum temperature in your reservoir is going to be 300F then do not leave the default value in the panel (400F). c If the region you define is too big then Crookston’s formula may have trouble getting good fits to the EoS based K-values. This is because K-values are really a function of the fluid composition as well as the pressure and temperature. See "K-Values" on page 401 for an explanation of why this is so. The number of flashes variable is set by default to 20. PVTi randomly throws this number of points into your defined region and flashes are performed at each (P,T) coordinate in order to obtain K-values. These are the observations. You are probably fine using 20 as this value. If your region is particularly big (which is not recommended) then you may want to increase this. By the same token, decreasing this value will speed up the calculations significantly, but the fits may be less accurate. Technical Description Output for ECLIPSE simulators 369 4 The A and D coefficients are turned on by default. You can turn them off if you want to but experience shows that you will almost always need them to get the best fits to the observations. In theory, turning all of the coefficients on should give the best fits. In practice, although you will do this most of the time, you will find: a this slows the application down as it increases the parameter space to search. If you want to get a feel for how the module works start with A, B and D turned on. b the algorithm finds the nearest local minimum of the objective function. This may not be the global minimum. PVTi uses an intelligent guess and the idea is that it starts in the parameter space reasonably close to the global minimum so that this is the nearest local minimum. When all 5 coefficients are switched on this initial guess technique is not always guaranteed to give as good a guess as when less coefficients are selected. 5 When you view the fits, check to see how good they are when you use a constant value of temperature that is halfway between the maximum and the minimum one. In theory the pressure part of Crookston’s equation should show the best fit here. If the functional form of the line plots looks wrong for even a single component then you probably need another pressure coefficient in order to match all the components for this particular fluid. Check in the same way for the temperature part of Crookston’s equation and turn E on as well if the D coefficient is having trouble fitting the observations 6 In terms of the rms values you should expect in the fits, this depends on how large a region you define and how many components are in your fluid. If the region is, say 1000 psia high and 200K wide, then you should expect fits on the observations of 2-3% on average. For more technical information on the ECLIPSE Thermal export facility see "ECLIPSE Thermal Export Module" on page 401. 370 Technical Description Output for ECLIPSE simulators PVTi Reference Manual Analysis techniques Introduction • "Recommended PVT analysis for oil reservoirs" on page 372. • "Recommended PVT analysis for gas condensate reservoirs" on page 377. • "Consistency tests and correlations" on page 381. PVTi Reference Manual Technical Description Analysis techniques 371 Recommended PVT analysis for oil reservoirs Oil reservoirs Oil reservoirs have been divided into three classes in the following discussion: Under-saturated reservoirs Refers to those reservoirs that are under-saturated not only at the time of their discovery but also throughout their development. Note This class does not include reservoirs whose pressures fall below the bubble point at some time during their development, or reservoirs that are subject to gas injection. Under-saturated reservoirs can be represented by two-phase (oil and water) simulation models, usually using the black oil formulation. For further information see "Under-saturated reservoirs" on page 374. Saturated black oil reservoirs Refers to those reservoirs whose pressures fall below the bubble point somewhere in the oil column during development, but that can be modeled sufficiently accurately using the black oil formulation. Note All reservoirs with initial gas-caps are regarded as saturated (but may not be adequately represented by the black oil formulation). For further information see "Saturated blackoil reservoirs" on page 375. Volatile oil reservoirs Refers to those reservoirs in which phase behavior effects are important. These generally require extensive use of a PVT program and compositional modeling for accurate representation. Note Volatile oil usually refers to a reservoir fluid whose critical temperature is only slightly above the reservoir temperature under initial conditions. For further information see "Volatile oil reservoirs" on page 376. 372 Technical Description Recommended PVT analysis for oil reservoirs PVTi Reference Manual Black oil or compositional simulation You can generate both black oil tables (for black oil simulation) and equation of state data (for compositional simulation) using the PVTi package. In some cases you can generate black oil tables from laboratory results alone, rather than using the full equation of state model. See "COMB - Compositional Material Balance" on page 112 and "COMB section keywords" on page 159. Oil reservoirs Almost all under-saturated reservoirs, and most saturated oil reservoirs where the reservoir fluid has a critical temperature far above the reservoir temperature, do not normally require the complexity of compositional simulation, and a black oil formulation is normally of sufficient accuracy. Note Such a formulation does not allow the stock tank oil density or gas density to vary with time. You may wish to consider using compositional simulation if miscible or semi-miscible processes are involved. Volatile oil reservoirs For volatile oil reservoirs it may be possible to obtain some sort of approximation to reservoir fluid behavior during depletion using a black oil formulation, providing that this has been modified to allow the gas phase to contain some vaporized oil (variable Rv ). In general, however, a compositional simulation is required for accurate treatment. This applies even for depletion of the reservoir. A compositional approach is essential for reservoirs where gas injection is planned. Compositional grading with depth Many oil reservoirs exhibit some kind of grading of fluid properties with depth. If you use the black oil formulation, then you can often represent the effects of this grading by a variation of solution gas-oil ratio with depth. However, if the stock tank oil API varies with depth, and it is necessary to model the variation of API with time, then you should use a variable oil API option in the black oil runs. Where part of the fluid column is near critical conditions you would use an initial compositional gradient with depth in a compositional simulation. Some reservoirs may grade from a gas condensate to a volatile oil without an initial phase transition or contact of any kind. Others may have gas-liquid or even liquid-liquid interfaces. You can simulate this process with the COMPG experiment in PVTi. One of the quantities output to the PVP file is the API, which you then use as the basis for constructing the API versus depth variation. For further information see "Defining Experiments" on page 117. PVTi Reference Manual Technical Description Recommended PVT analysis for oil reservoirs 373 Under-saturated reservoirs For under-saturated reservoirs, it is not often that an equation of state representation is of particular value, although you may find the PVTi program useful for separator calculations. Although it is possible to derive black oil tables from equation of state models, for this application it is better to derive them from laboratory data for the following reasons: Laboratory analyses generally have sufficient information to derive the PVT tables directly. It is often difficult to characterize reservoir oils accurately. This leads to difficulty in establishing an equation of state model that satisfactorily matches the measured data. To establish a black oil PVT model of a single sample from an undersaturated reservoir the following procedure is recommended: 1 From the laboratory report take the saturation pressure (bubble point) of the sample, the reservoir density at that pressure, and the compressibility (as a function of pressure) above the saturation pressure. 2 If the field is under production there is normally data available on the producing GOR for the field separator conditions, the gas gravity ( γ g , air = 1), and the stock tank oil gravity (API). 3 Ensure that the GOR and gas gravity include all the separator and stock tank gases. If they do not then you can often make reasonable estimates. You can then combine this data with the reported oil density to give the formation volume factor ( Bo ) at the saturation pressure p b as follows (in field units): γ g ⋅ GOR ⋅ 0.00122 141.5 1 B o ( p b ) = -------- ---------------------------------- + ---------------------------------------------ρ res ( 131.5 + API ) 5.6146 [EQ 8.209] where ρ res is the reservoir density in gm/cc, and the GOR in scf/rb. 4 You can find the oil formation volume factor at pressures higher than the saturation pressure using the compressibility factor in the PVT report. 5 If the field has only been tested and there is no data on producing GOR and gas gravity then often a separator test for appropriate separator conditions are reported. This supplies a formation volume factor for bubble point oil at these conditions of separation. You can use the reported compressibilities to derive formation volume factors at higher pressures. If a separation test is reported and the field is under production, then you should rationalize the formation volume factors derived from point 2 with the separator test. 6 If no separation test was performed by the laboratory and there is no production data, then you can either use a suitable set of correlations, or, if the sample is a re-combination, it may be possible to use the re-combination data to derive data at separation conditions using PVTi, providing it is possible to characterize the fluid. Note It is important to avoid using what is often referred to as the formation volume factor (it is actually a relative volume) during a differential liberation experiment. The oil remaining at the end of this experiment has a completely different composition from stock tank oil and this formation volume factor is usually higher (by as much as 10%) than the correct value. For the simulation of undersaturated reservoirs this differential liberation experiment is usually superfluous, although laboratories often perform it anyway. If there are a number of samples you should follow the above procedure for each one. 374 Technical Description Recommended PVT analysis for oil reservoirs PVTi Reference Manual 7 Then determine if there evidence of an API gradient by plotting stock tank oil density against depth. 8 If there is no such evidence take the most appropriate sample (or average of samples). This becomes the PVT representation of the reservoir oil. If the reservoir has an API gradient the following additional stages are recommended: 9 Draw a representative curve through the API versus depth plot. Use this to represent the model API versus depth relationship of the reservoir oil. 10 There are a number of ways of allocating PVT properties as functions of API gravity. By suitable plots, such as saturation pressure against depth, formation volume factor for a common pressure against depth, and formation volume factor against pressure, you can find a method appropriate to that particular reservoir. You may find it necessary to use correlations to extrapolate to depths above and below the range of sample data. Saturated blackoil reservoirs Most of the stages for "Under-saturated reservoirs" on page 374 are appropriate for these reservoirs. In addition you must generate a table of solution gas-oil ratio, oil and gas formation volume factor, and oil and gas viscosities below the bubble point. Normally, you can derive this data from the separation test and differential liberation experiments performed in the laboratory. Note Again it must be stressed that you should not use differential liberation data alone. What is often referred to as the formation volume factor during the liberation makes no reference to separator conditions. To be completely accurate the laboratory should perform a separation test on the fluid resulting from each pressure stage of the differential liberation experiment. In practice this is rarely done, and the volumetric data is determined from the single separation test (at the bubble point pressure), and the relative volumes and gas volumes of the differential liberation experiment. The correct oil formation volume factor is this relative volume, divided by the relative volume of the bubble point fluid (during the same differential liberation), multiplied by the correct oil formation volume factor of the bubble point fluid for the separator conditions operating. This derivation, of course, uses the black oil approximation that the stock tank oil density is unchanging. Solution gas-oil ratio is derived in a similar way, the value at the bubble point pressure being exactly that derived from the separator test ( R s ( p b ) ). Simple material balance of gas and oil shows that the correct gas-oil ratio ( Rs ) at a pressure below the bubble point is given by: R s = R s ( p b ) – ( R s' ( p b ) – R s' )B o' ( p b ) ⁄ B o ( p b ) [EQ 8.210] where Rs' and Bo' refer respectively to the reported solution gas-oil ratio and formation volume factor from the differential liberation experiment. PVTi Reference Manual Technical Description Recommended PVT analysis for oil reservoirs 375 As well as API plots against depth for different samples, plots of producing gas-oil ratio and formation volume factor against depth (for a consistent pressure) may indicate a solution gasoil ratio for a such a reservoir. Volatile oil reservoirs A differential liberation experiment, or a constant volume depletion experiment, or both, may have been performed on a volatile oil sample. In practice, during depletion, some intermediate process occurs in the reservoir because gas migrates away from the oil, although it might be argued that enough gas will be trapped near the oil for a constant volume depletion experiment to be most representative. A swelling test may also have been performed if gas re-injection is planned. You should subject the results of any constant volume depletion experiment to the same analysis as for a gas condensate fluid sample, as described in "Recommended PVT analysis for gas condensate reservoirs" on page 377. The objective of the PVT analysis is to generate an equation of state model of the reservoir, which you then use for compositional simulation. If it is felt that the depletion experiment is a good enough representation then you can generate a black oil table from the equation of state model. 376 Technical Description Recommended PVT analysis for oil reservoirs PVTi Reference Manual Recommended PVT analysis for gas condensate reservoirs Introduction • "Blackoil or compositional simulation" on page 377. • "Data analysis" on page 378. • "Compositional grading with depth" on page 378. • "Data analysis" on page 378. • "Equation of state model" on page 379. Blackoil or compositional simulation For most gas condensate reservoirs the liquid that condenses in the pore spaces during depletion does not reach a high enough saturation to become mobile. Gas and oil do not move with respect to each other, and they therefore stay in equilibrium. It is possible to model this type of reservoir behavior quite accurately by the constant volume depletion (CVD) experiment performed in the laboratory. For further information on defining experiments in PVTi see "Defining Experiments" on page 117. For a straightforward gas condensate, a black oil formulation, modified to include a variable Rv vapor oil-gas ratio, can therefore do a reasonable job of modeling simple depletion. Although the black oil formulation nominally constrains stock tank oil and gas to have unvarying compositions and densities, it is possible to reproduce the compositional data available for the original constant volume depletion experiment for surface facility calculations by post-processing black oil output. However, if the gas condensate becomes very rich, perhaps grading to a volatile oil, then it requires a fully compositional simulation to model it. This is also the case when you wish to consider almost any other development scenario than depletion, except, perhaps, pressure maintenance by water injection. Dry gas cycling, in particular requires fully compositional modeling for accurate predictions of the phase effects when dry gas contacts condensed reservoir oil. The extended black oil formulation allows dry gas to pick up oil until the gas becomes saturated, an optimistic approximation to the actual reservoir behavior. When you generate black oil tables from a CVD experiment by PVTi, the program includes dry gas properties in the table, allowing gas cycling to be modeled. Note PVTi Reference Manual The results of such modeling are to over-estimate the condensate recovery from the field by a few percent for full and partial pressure maintenance. Low pressure recycling will probably be very poorly modeled. Technical Description Recommended PVT analysis for gas condensate reservoirs 377 Compositional grading with depth Where part of the fluid column is near critical conditions an initial compositional gradient with depth would be used in a compositional simulation. Reservoirs may grade from a gas condensate to a volatile oil without a phase transition or contact of any kind. More often there is an oil-rim, which can exist even without critical conditions being approached. For further information on defining experiments in PVTi see "Defining Experiments" on page 117. Provided reservoir fluids are not close to critical conditions, a reasonable approximation to recovery can often be made using a black oil formulation, by modeling the dew point variation and ignoring the condensate-gas ratio. The black oil formulation cannot normally reproduce, simultaneously, the variation in dew point pressure and in condensate-gas ratio. Data analysis A common failing when analyzing gas condensate reservoirs is to attempt to establish an equation of state representation without thorough analysis of the data on which it is to be based. A thorough comparison of samples, analysis of inter- and intra- sample consistency, and clarification of the aims of establishing an equation of state model, allows you to determine which data is worth trying to match, what components to use, and how best to establish a matched model. You should closely scrutinize all the available samples. Some of the questions that should be answered are as follows: 1 Are the samples properly constituted (examine recombination data and compare with correlations)? 2 Have experiments been performed consistently and accurately (examine compositional material balances)? 3 Are other experimental data such as Z -factors, implied K -values and liquid densities reasonable (correlations and tests of consistency)? 4 What are the characteristics of the heavy fractions (fingerprint plots)? During this analysis it may seem reasonable to establish alternative (modified) data by adjusting sample data to achieve material balance consistency and a reasonable fluid description. This can be a useful exercise but a good appreciation of the main sources of inaccuracy is required for it to be successful. If the sample is a recombination, the report usually contains recombination data that can be used for calibrating correlations, to obtain an analysis of separation using the COMB section of PVTi. For further information see "COMB - Compositional Material Balance" on page 112 and "COMB section keywords" on page 159. It is possible to obtain gas and condensate recovery estimates for different abandonment pressures by combining this with constant composition data above the dew point, and CVD data below the dew point. After you have analyzed each sample individually you should examine all the samples together by, for example, plotting dew point pressures and condensate-gas ratios against sampling depth, comparing compositions, fingerprint plots etc. Before rejecting any particular sample that appears to be anomalous, you should investigate the source of anomalies. Such an investigation may be useful in making recommendations concerning sampling techniques or laboratory analysis. 378 Technical Description Recommended PVT analysis for gas condensate reservoirs PVTi Reference Manual Equation of state model When a good overall view of the reservoir field has been gained, it is then possible to establish PVT models. If depletion is planned it may not be necessary to establish an equation of state model. If the basic (or modified) laboratory data is of sufficient quality you can use to establish black oil tables. Normally, however, you establish equation of state models. For further information on fitting data to an EoS in PVTi see "Equation of State" on page 100. Different engineers have their own methods of establishing an equation of state model, but a suggested approach is as follows: 1 Establish a model based upon as many components as the data defines, using correlations where necessary. Split the last component (the plus fraction) into, say, three further fractions, using one of the splitting options. The modified Whitson (Semi-ContinuousThermodynamics (SCT)) is recommended. For further information see "Multi-feed Split (also called semi-continuous thermodynamic (SCT) split)" on page 106. 2 Previously, it was recommended that the binary interaction coefficient between Methane and the plus fraction be varied to match the dew point pressure. This practice is no-longer recommended. Adjusting binaries to match saturation pressure at just one temperature often massively distorts the phase envelope at other (generally lower) temperatures, see [Ref. 30]. Instead, it is now recommended to use one of the following approaches: a If using Cheuh-Prausnitz BIC’s, try the (pre-multiplying) A -coefficient. This adjusts ALL hydrocarbon-hydrocarbon binaries by the same amount, maintaining symmetry and monotonicity. For further information see "Viscosity correlations" on page 101. b Having performed an SCT-split, regress on the plus fraction mole weight, PVTi’s internal correlations then convert this modified mole weight into critical properties, etc., which are monotonic and consistent. c If the above are unavailable, critical temperature of plus fraction usually requires changing less than any other individual EoS parameter. 3 Compare this first model with the data to be matched. This usually comprises the volumetric data associated with constant volume and constant composition experiments, separator data and swelling test data. As well as the volumetric data, it is important to compare compositional data, although the possible inaccuracies in reported compositions should be considered here. 4 Attempt to establish a model that is a good match with only a minimal modification of the data. Such modifications may be made manually or semi-automatically but you should obtain a good understanding of the effects of each modification. The emphasis is on the modification (preferably consistently) of individual component descriptions, especially those of the heavy components which are poorly defined. The splitting of the plus fraction may be a suitable modification to make. Other properties to consider are the critical temperature and pressure of the plus fraction along with its acentric factor. Additionally, because of the generally uncertain ParaffinicNapthanic-Aromatic (PNA) of the Single Carbon Number (SCN) groups, that is hexanes, heptanes, etc., these are a better option for a more limited change. If such a minimal set of modifications does not give a satisfactory match then a full regression procedure may be necessary as described for pseudoization below. Ideally this full regression will not be necessary before pseudoization. PVTi Reference Manual Technical Description Recommended PVT analysis for gas condensate reservoirs 379 1 Generate a black oil table from this many-component model from a simulated CVD experiment. For further information on defining experiments in PVTi see "Defining Experiments" on page 117. 2 Decide upon an appropriate set of pseudo-components, bearing in mind the objectives of the study. Use the grouping option to generate the pseudo-component model from the many-component model. In many cases about six pseudo-components is appropriate. 3 Compare the predictions of the pseudo-component model with the laboratory data. 4 Use the automatic regression procedure to modify the representation. The emphasis now is on obtaining a good match to the data and the results of the many-component model. Fairly coarse matching parameters may be required. Modify parameters for which a small change has a large effect. (The matrix of sensitivities produced by the regression algorithm may be useful here.) You should try several sets of regression parameters and you should compare the predictions over the whole area of interest (including mixing of dry and wet gases) with the predictions of the manycomponent model and with the data (where available). When pseudoizing, the ideal grouping results in minimal predictive change from the original system. This is not always possible and some small changes in the group properties may be necessary. 5 If there are problems matching reservoir data and separator data simultaneously then it is possible to divorce the two in ECLIPSE for compositional simulation, using different Ω values and binary interaction coefficients for the separators, or using K -values for the separators. It is also possible to account for temperature variation using the temperature-dependent volume shift. By matching separator volumetric properties first, that is at or near surface temperature where the volume shifts are actually defined, you can then attempt to match to reservoir volumetric properties, at the elevated reservoir temperature, by using the thermal expansion coefficient that is available as a regression variable. One advantage of the above procedure is that it addresses directly one of the main problem areas in this type of work: the characterization of the heavy fractions. These components have an effect on fluid behavior that far outweighs their sometimes small mole fractions. You always rationalize any splitting performed with any true boiling point (TBP) distillation data available, fingerprint plots, correlations etc. A second advantage of the recommended procedure is that it allows (through the manycomponent model) a good understanding of the character of the fluid. A third advantage is that if it is possible to obtain a good match to the laboratory data with minimal modification of the pure many-component equation of state model then it is more likely that accurate predictions are obtained away from the measured data. Note 380 A cubic equation of state can only supply approximations to the behavior of fluids. This must be borne in mind when matching laboratory data, but especially when extrapolating outside the area of data control. By the same token, laboratory analyses of samples only normally supply an approximation to the sample behavior and the sample itself is only an approximation to the reservoir fluid. Technical Description Recommended PVT analysis for gas condensate reservoirs PVTi Reference Manual Consistency tests and correlations Introduction During initial data analysis a number of tests are available in the COMB (COmpositional Material Balance) section of the program for examining the consistency and quality of a particular laboratory sample. For further information see "COMB - Compositional Material Balance" on page 112 and "COMB section keywords" on page 159. This section contains information on the following: • "Compositional material balances during the CVD experiment" on page 381. • "Fluid density correlations" on page 381. • "Viscosity calculations" on page 382. • "Separator calculations" on page 382. • "K-value checks" on page 382. • "Recovery calculations" on page 383. Compositional material balances during the CVD experiment From the volumetric and gas compositions reported during the various pressure stages of the CVD experiment it is possible to make deductions about the composition and density of the remaining liquid at each stage. For further information on defining experiments in PVTi see "Defining Experiments" on page 117. If the moles of liquid remaining after the last stage is reported (which, unfortunately, is not always the case) it is possible to combine this with the fractions recovered at each stage to compare the initial and recovered compositions. This overall comparison can be revealing in terms of laboratory accuracy and the desirability of making modifications to the basic data before making a match. Fluid density correlations It is possible to compare the liquid density calculated from compositional material balance with calculated values using the Alani-Kennedy correlation, [Ref. 22]. Several correlations are available for the gas phase. It is possible to compare the pseudo-critical temperature and pressures (the internal correlation uses the Wichert-Aziz correction for sour gases). You can compare these pseudo-critical properties with those calculated using a correlation based on the hydrocarbon molecular weight. It is possible to compare a representation of the Standing-Katz Z -factor correlation by Dranchuk et al., [Ref. 21], using the Benedict-Webb-Rubin equation of state with laboratory measured Z -factors. PVTi Reference Manual Technical Description Consistency tests and correlations 381 K-value checks The Hoffmann-Crump-Hocott (HCH) technique consists of plotting the logarithm of the product of the K -value and the pressure against a characterization factor for each component. HCH found that at any given pressure this data plotted close to a straight line, at least for the pure components. It is possible to check K -values derived from the (calculated) liquid and (reported) gas compositions during the various stages of the CVD experiment. For further information on defining experiments in PVTi see "Report" on page 113. This technique is also useful for checking the recombination of samples. It forms the basis of Standing’s method for performing separator calculations, discussed later. Another good check of the K -values from a CVD experiment is to plot them against the logarithm of pressure for each component. This allows an estimation of the apparent convergence pressure, which then allows cross-checking against NGAA tables. Viscosity calculations Laboratories generally do not have the equipment for measuring gas viscosities and usually calculate viscosities based on the Carr, Kobaysahi and Burrows correlation. Other correlations exist, such as the "Lohrenz, Bray and Clark" on page 330 method and the "Pedersen et al." on page 331 corresponding states technique. These different correlations often yield markedly different predicted viscosities. Ideally, a consistent correlation should be used throughout the reservoir engineering analysis, from the well test analysis used to derive permeabilities to the reservoir simulation. ECLIPSE accepts a set of critical volumes (entered with VCRITVIS or ZCRITVIS), which are only used for viscosity calculations, in order that significant changes in Vc values used to match viscosity correlations do not effect the remainder of the simulation. Separator calculations Standing evolved a method for calculating K -values for separators, based on the HCH method. For each component, a b -factor is calculated at the separator temperature. HCH suggested that this b -factor is based on pure component normal boiling points and critical temperatures. Standing suggested a slightly different set but this probably only applied to the particular oil he was considering. b -factors obtained by the HCH method may be used in PVTi to generate separator K -values. An alternative is to use those derived from recombination data, though these should first be checked against those obtained using the HCH method. From the K -values derived in this way, PVTi can calculate the condensate and oil recoveries for a given separator system. Separator liquid densities are based on the Alani-Kennedy correlation (see "Alani-Kennedy liquid densities" on page 312)and stock tank densities are calculated using Amagat's law (addition of specific volumes). 382 Technical Description Consistency tests and correlations PVTi Reference Manual Another method of calculating recovery factors is to assume stabilized liquid consists of, say, the Pentanes plus fraction, whilst the stabilized gas consists of the other, lighter components. With these assumptions, recoveries down to the last pressure in the CVD experiment are commonly reported in laboratory analyses in units of gallons of condensate per mscf of wet gas. Laboratories calculate these using Amagat’s law. You can perform these calculations in PVTi using input specific gravities and molecular weights. Recovery calculations From input CCE, CVD data and the separation system, PVTi can calculate gas and condensate recovery factors from any supplied initial reservoir pressure to any supplied abandonment pressure, for a depletion scenario. PVTi Reference Manual Technical Description Consistency tests and correlations 383 Fluid Properties Estimation Introduction Fluid properties estimation is used in situations where a full equation of state matching across numerous samples is not available. Typically, there is only one sample and limited information about the fluid behavior. From this, fluid properties estimation simulates typical experiments and provide analysis of the fluid ahead of full laboratory experiments. Minimum information In fluid property estimation the following data provide sufficient information to construct a complete set of example experiments: • Weight percentage of each component (or mole fractions) • The mole weight of the plus fraction • A saturation pressure (bubble or dew point) • The maximum pressure to use when constructing a depletion experiment (the default is to use the saturation pressure. Fitting to saturation pressure The plus fraction mole weight is used to characterize the critical properties of the plus-fraction. In general, the weight fraction of the plus-fraction is well known, but the appropriate mole weight to use in characterizing the critical properties is not. By varying the weight of the plus-fraction, whilst maintaining the weight fraction constant, PVTi is able to determine the most appropriate mole weight to use in characterizing the critical properties. This gives a good fit to the entered saturation pressure and creates a fluid model that can be used for fluid properties estimation. Generation of pressure depletion experiments In generating pressure depletion experiments, PVTi begins by creating the Constant Composition Expansion (CCE). There are up to ten pressure steps from the maximum entered pressure down to the saturation pressure, and up to ten pressure steps from the saturation pressure down to standard pressure. If no maximum pressure was provided, the CCE starts at the saturation pressure. If the saturation pressure was a bubble point, a Differential Liberation (DL) experiment is created, otherwise a Constant Volume Depletion (CVD) experiment is created. The DL or CVD has the same pressure steps as the CCE previously created. 384 Technical Description Fluid Properties Estimation PVTi Reference Manual Optimized separator An optimized separator calculation can be performed. The method for this is discussed in "Optimized separators" on page 344. Technical Information The default settings for the PVTi fluid properties estimation are in Table 8.12. Table 8.12 PVTi defaults for Fluid Property Estimation Property Value Equation of state Peng-Robinson 3-parameter (corrected) Library for component properties Katz-Firoozabadi Correlations for plus-fraction properties Kesler-Lee Viscosities Lohrenz-Bray-Clark The equation-of-state and the viscosity model can be changed using PVTi: Edit | Fluid Model | Equation of State... The component library in use can be selected in PVTi: Utilities | Program | Options... The correlation used for the plus-fraction can be changed in PVTi: Edit | Fluid Model | Components... PVTi Reference Manual Technical Description Fluid Properties Estimation 385 Regression in PVT analysis Introduction The goal of PVT analysis is to provide a tuned Equation of State that can model the reservoir fluid in simulations. The selection of regression parameters is crucial in determining the quality of the tuned fluid model. This chapter discusses the selection of regression variables in PVT analysis and consolidates traditional variable selection, based on physical principles ("Physical selection of regression parameters" on page 386), with variable selection based on mathematical analysis of the problem ("Mathematical analysis of the regression problem" on page 388). "A consistent methodology that can be applied automatically" on page 389, describes how information in the preceding two sections are used by the PVTi Quick Fit option. Fundamentally, the fitting process twists the standard cubic-equation of state to fit the supplied data. Across the temperature and pressure ranges of the observations the fitted model may be useful, at very different temperatures and pressures the model may not be representative of the fluid behavior at all. Note Always use data at reservoir conditions, such as depletion experiments, and at surface conditions, such as separator tests, when fitting a fluid model that is to be used in reservoir simulation. In "Weighting observations for regression" on page 390, there is a discussion on weighting the observation data to get the desired fit. This chapter does not contain a mathematical description of the Levenberg-Marquardt algorithm, that can be found in "Weighting observations for regression" on page 390. Physical selection of regression parameters The traditional, chemistry-centered approach to equation-of-state fitting relies on first determining which parameters are least well defined. Parameters that are not known accurately are candidates for fitting. Critical properties For pure library components, particularly the non-hydrocarbons and lighter hydrocarbons, the acentric factor (ω) and critical temperature (Tc) and pressure (Pc) are well known. It is generally not justifiable to tune these properties. Hint 386 It is very unlikely that the Pc, Tc and ω of H2O, H2S, N2, CO2, CO, C1, C2, C3, IC4, NC4, IC5, NC5, and C6 differ from the library values. So do not use them in regression. Technical Description Regression in PVT analysis PVTi Reference Manual The critical properties of the heavier components are less well determined. The plus-fraction is a mixture of many different hydrocarbons and usually the properties are determined by correlations based on mole weight and specific gravity of the plus fraction as a whole. Consequently the critical properties are only as good as the characterization method that generated them. Hint The Pc, Tc, and ω of the plus fraction usually come from characterization. This means that they are not well determined, making them ideal candidates for tuning. Pedersen et al. have suggested that the molecular weights of the characterized components might be a good choice of regression variable as this varies Pc, Tc and ω consistently, in line with the chosen characterization method, see [Ref. 59]. Binary interaction coefficients The binary interaction coefficients are introduced into the cubic equation-of-state to account for the effect of polar forces in the interactions between components. This means that for non-polar interactions, such as those between hydrocarbons, the binary interactions are close to zero. There are lots of binary interaction coefficients, generally there is insufficient PVT data to justify tuning all of them. Over-fitting, fitting the data more closely than is justified, can lead to a fluid model that is not physically valid outside the range of the data being fitted. In the reservoir simulator you model many compositions outside the observed PVT data-set. Over tuning, particularly using the binary interactions, can cause serious convergence problems. Caution Careless tuning of binary interaction coefficients often leads to a fluid model that has convergence problems in compositional simulations. The basic cubic equation-of-state uses the acentric factor to consider slight deviations in molecule shape; the assumption is that all molecules are close to being spherical. The binary interaction coefficient between light components and the heaviest hydrocarbon can be used to compensate for the non-sphericity of the heavy hydrocarbon molecules. ΩA and ΩB coefficients The default values of ΩA and ΩB are based on the following assumptions: 1 The critical isotherm of a component has a slope of zero and an inflection point at the critical point. In layman’s terms this means that the component is pure. 2 That the determination carried out, for the limited number of pure components available, can be extrapolated to all heavier and lighter components. 3 The values were valid for pure-component density and vapor pressure below critical temperature. In developing his equation of state, Tareq Ahmed explained why these basic assumptions are violated in many fluid models, see [Ref. 61]: 1 Pseudo-components and the plus fraction are not pure components, so assumption 1 is violated by these. 2 The heavier hydrocarbons and light components may not have the same ΩA and ΩB as the pure components tested. Specifically, assumption 2 might not be true. PVTi Reference Manual Technical Description Regression in PVT analysis 387 3 Light components such as methane and nitrogen are well above their critical points at temperatures typically encountered in PVT studies. Assumption 3 does not apply to these components. Hint The assumptions upon which the default ΩA and ΩB constants are based do not hold for light components, pseudo-components, and the plus fraction. This makes them candidates for regression. Lohrenz-Bray-Clark viscosity coefficients The Lohrenz-Bray-Clark viscosity correlation is a fourth order polynomial in density. Consequently it is very sensitive to the density of the fluid. In PVTi there is the option to regress on the critical volume or Z-factor used in calculating each component’s contribution to the total viscosity. Hint Varying the critical volume and Z-factor are equivalent in this case, so it is futile to vary both at once. This critical volume or Z-factor is only used to calculate the viscosity, so remember that in a regression only the viscosity observations themselves are used to tune these parameters. Caution As only a few observations apply to the tuning of the critical volumes for viscosity, make sure that there are no more than one or two regression variables of this type in a regression run. It is much better to put all critical volumes for viscosity into one regression variable than to vary all of them at once. There is another option in PVTi that allows the constants used in the fourth order polynomial in density to vary. Caution This option is available so that the original Lohrenz-Bray-Clark analysis can be repeated with new data-sets. It should only be used if you have a large number of samples and lots of viscosity observations. Fitting too many parameters to too few observations leads to convergence problems for the fluid in a compositional simulator. Mathematical analysis of the regression problem In this section the analysis of the regression problem is based upon the need to create a solvable mathematical system of equations. The physical reasons for changing parameters were laid out in the previous sections, this defined a set of candidates for regression. The mathematical analysis indicates which candidates should be regressed together in a single regression run. 388 Technical Description Regression in PVT analysis PVTi Reference Manual Understanding the Levenberg-Marquardt algorithm The Levenberg-Marquardt algorithm, like many non-linear regression algorithms, starts from the assumption that the non-linear problem can be solved as a set of small linear steps. This, in effect, means that the problem must not be too non-linear. The regression can be helped by designing the problem, that is choosing regression variables, such that the problem is not too non-linear. What is meant by too non-linear? It is more straightforward to start from the linear problem and bend the rules a little. The characteristics of the linear problem are: 1 No regression parameters are numerically redundant 2 All regression parameters are independent High sensitivities The first rule means that interest should focus on the most sensitive parameters, those for which a small change has a large effect on the fit. The Hessian tab of the Sensitivity Analysis panel gives an indication of the sensitivity of the different parameters. The values along the leading diagonal of the Hessian matrix are most useful, a high value means high sensitivity. Hint By removing insensitive regression variables from the set, the problem becomes less non-linear and thus more solvable. Kai Liu has reported success with an automatic regression technique based solely on selecting the eight most sensitive regression parameters, see [Ref. 61]. Correlations between parameters The second rule means that there should be no very strong correlations between parameters. A strong correlation means that the effect of a change in one parameter is the same as, or opposite to, the effect of changing another. The Correlation Sensitivity Analysis panel shows the correlations between parameters. A value close to 1 indicates a strong correlation, which means changing one parameter has the same effect as changing the other. A value close to -1 indicates a strong anti-correlation, which means changing one parameter has the opposite effect to changing the other. Hint Amalgamating strongly correlated regression variables of the same type (for example Tc) in a single regression variable or removing one of the two strongly correlated variables makes the problem less non-linear and thus more solvable. A consistent methodology that can be applied automatically This section describes how the rules laid out in "Physical selection of regression parameters" on page 386 and "Mathematical analysis of the regression problem" on page 388 can be applied to a automated regression system. PVTi Reference Manual Technical Description Regression in PVT analysis 389 Note By their nature automatic regression schemes do not make judgement calls that an experienced engineer would make. The choice of regression variables From the rule-of-thumb guidelines given in "Physical selection of regression parameters" on page 386, the following set of properties was determined as begin available candidates for regression: 1 Tc, Pc and ω of any non-library component. 2 Tc, Pc and ω of any component with mole weight of C7 or heavier. (As these are effectively mixtures of different molecule types and so may differ from library values). 3 ΩA and ΩB of any component with mole weight of C7 or heavier. Again because these are mixtures. 4 No binary interaction coefficients because of the risk of over-fitting. 5 No viscosity-specific parameters, again because of the risk of over-fitting. This gives a large number of regression variables, many of which are very closely interrelated. The next step is to apply a mathematical analysis onto this set. Reducing the set of regression variables From "Mathematical analysis of the regression problem" on page 388 it is clear the problem can be made more solvable by selecting those parameters with high sensitivities and low intercorrelations. From the discussion, the following rule was created: • Regress using the set of variables with the highest total sensitivity, for which no correlation between parameters is greater than 0.9 or less than -0.9; and for which the lowest sensitivity is at least 1% of the highest sensitivity. The total sensitivity of the set of variables was taken to be the sum along the leading diagonal of the Hessian. The sensitivity of a regression variable was taken to be the value on the leading diagonal of the Hessian relating to that variable. Note This method takes no advantage of amalgamating regression variables of the same type into a single variable. Weighting observations for regression The least-squares fit to the observation data is not necessarily the goal of equation-of-state fitting. To be precise, the goal is to create a fluid model that behaves like the reservoir fluid. There are aspects of the reservoir fluid that the model must capture accurately. PVTi allows the weighting of regression variables so that additional importance can be attached to some measurements over others. 390 Technical Description Regression in PVT analysis PVTi Reference Manual Matching saturation pressure Usually, it is important to match the fluid’s saturation point within the depletion experiment. This value is closely related to the gas-oil contact in the reservoir and can strongly affect the initial fluids in place calculation. Hint Use the saturation pressure measurement from the depletion experiment to create a dew-point or bubble-point experiment. Weight the observation of saturation pressure very high (1000+). Matching surface densities or GOR The separator densities or GOR strongly determine the total oil and gas produced. Also it is worth remembering that the depletion experiment often has 20 or more stages, whereas the surface separator is unlikely to have more than 2 or 3 stages. This means there are usually lots more observations for the reservoir depletion process than for the produced oil and gas. Hint Weight the separator densities or GOR highly (500+) to guarantee that the right amount of oil and gas are produced. Guiding the regression Sometimes a fluid does not seem to fit the observations. In this situation, the regression weights can be used to guide the regression algorithm. For example, an excellent fit may have been achieved for the bubble point using the method described in "Matching saturation pressure" on page 391, but there may be difficulty in fitting the liquid saturation below the bubble point. PVTi allows the weighting of individual observations for this purpose. In this situation, by weighting the observations for which the fit is worst by the highest amount, the regression is forced to take more account of the data as a whole. Hint Weight the worst-fit observation the most and successive observations less and less through to the best fit observations that retain their original weighting of 1. This guides the regression to take more account of the worst parts of the fit. Caution PVTi Reference Manual Be aware of the errors in the observed data and do not be tempted to over-fit. Models that are over-fitted cause convergence problems in compositional simulations. Technical Description Regression in PVT analysis 391 SmartOpt - Systematic MAtrix Reduction Technique for Optimization This algorithm performs a rapid and exhaustive search of the sensitivity matrix described in "Reducing the set of regression variables" on page 390. As the non-linear regression is, effectively, a succession of linear steps, the problem must be designed such that it is only weakly non-linear. The number of combinations of regression variables that could be used for regression is 2N where N is the number of regression variables. For even 20 regression variables this would be 1,048,576 combinations, for 30 variables the number of combinations is more than a billion. To calculate the correlations between parameters, a matrix inversion is required, clearly several million matrix inversions is impractical. By re-designing the problem, however, a fast and efficient exhaustive search can be made to find the most sensitive regression matrix representing a weakly non-linear problem. A starting point - the most sensitive single variable If the run is made with just one regression variable, there are no other variables so correlation is not an issue. The starting point then is to find the single most sensitive variable. This gives us an initial estimate of the best sensitivity - no combinations with lower sensitivity than this need be tried. Ordering for speed The Hessian is reformed with the most sensitive variable in the first row, down to the least sensitive variable in the final row. As is explained in the next section, this gives an important speed increase. Searching all combinations The speed in this method relies reducing the time spent analyzing combinations that do not turn out to be the best one. The first test to be applied, then, is the sensitivity difference - no parameter should have less than 1% the sensitivity of the most sensitive parameter. As the combination is constructed, it is tested against this criterion. If it fails, the search knows that any combination with a less sensitive parameter will also fail. The re-ordering of the Hessian means that it is easy to skip the other combinations that are not allowed. The next test to be applied is that of highest sensitivity. If the sensitivity of the constructed combination is less than the current best candidate, the search moves on the next combination. Again, by having the Hessian ordered, it can be quickly determined whether the sum of all remaining parameters would be higher than the highest sensitivity. If not, the search can skip the set of parameters that cannot form a matrix with a high enough sensitivity to be considered. Finally the correlations are tested. This is because the calculation of correlations requires the Hessian to be inverted. Again as the correlations are calculated, as soon as a single correlation is discovered that exceeds 90%, the search moves on to the next combination. If the construction of the correlations completes without discovering a correlation greater than 90%, this combination must be the best one found yet and so it is stored and the search continues. This method is very fast and guaranteed to find the best matrix according to the criteria: 392 Technical Description Regression in PVT analysis PVTi Reference Manual 1 Highest total sensitivity (determined as the sum along the leading diagonal of the Hessian). 2 Lowest sensitivity is not less than 1% of the highest sensitivity (again sensitivity refers to the terms along the leading diagonal of the Hessian). 3 No correlations more than 90%. These criteria could be adjusted, though you must take care that the criteria you choose define a weakly non-linear problem, otherwise the effort of analysis will not show any benefit for the regression. PVTi Reference Manual Technical Description Regression in PVT analysis 393 Wax and asphaltene precipitation in PVTi Introduction The solid precipitation model in PVTi handles waxes as a solid solution and asphaltenes as an additional liquid phase. The wax model assumes that paraffins and naphthalenes can precipitate as a solid solution. In the asphaltene model it is assumed that the heaviest aromatic component will form an asphaltenic liquid phase. To use the solid precipitation model, the paraffin, naphthalene and aromatic fractions for each carbon number are needed. These can be entered by hand, if known, or generated from the correlations described in "The PNA distribution of heavy components" on page 394 and "Critical properties of PNA species" on page 395. The theory behind the wax model is explained in "Wax precipitation" on page 395. The PNA distribution of heavy components In PVTi, the components heavier than C6 may be split into their paraffinic (P), naphthalenic (N) and aromatic (A) constituents. This is an important part of solid precipitation as it is the P and N species, which generally form wax and the heaviest aromatic is the major constituent (by weight) of the asphaltenic liquid phase. The PNA distribution is then estimated as described by Nes and Westerns, see [Ref. 48]. v = 2.51 ( n – 1.4750 ) – ρ + 0.8510 w = ρ – 0.8510 – 1.11 ( n – 1.4750 ) 3660 A% = 430v + -----------MW ( for v < 0 ) 3660 A% = 670v + -----------MW ( for v > 0 ) 10000 R = 820w + --------------MW ( for w > 0 ) 10600 R = 1440w + --------------MW ( for w < 0 ) N% = R – A% P% = 100 – R [EQ 8.211] Where P%, N% and A% are the percentages of paraffinic, naphthalenic and aromatic constituents respectively; ρ is the liquid density in gcm-3 at 20oC and 1 atm, and n is the refractive index of the true boiling point (TBP) fraction. n is given by Riazi and Daubert’s correlation, see [Ref. 49]: n = + 2I 1 -------------- 1–I [EQ 8.212] where I is a characterization factor given by: 394 Technical Description Wax and asphaltene precipitation in PVTi PVTi Reference Manual – 0.02269 I = 0.3773T B Hint SG 0.9182 If a full PNA specification of the sample is available, the mole fractions can be used in the normal way, over-riding the default estimates from this splitting procedure. First enter the single carbon number (SCN) fluid; perform the PNA split, then type in the measured mole fractions. Critical properties of PNA species In PVTi the critical properties of the PNA species are set up using the correlations of Riazi and Al-Sahhaf, see [Ref. 50], which are all of the form: ln ( θ ∞ – θ ) = a – bMW c [EQ 8.213] where MW is the mole weight of the hydrocarbon and the constants a, b, c and θ∞ have been determined for various basic properties of PNA species (refer to the reference for tables of their values). Note The critical properties of the PNA species can be tuned just as for any other components. In addition to the usual set of critical properties, the melting points of the PNA species are also determined, for use in the wax precipitation. For paraffins, the melting point is given by the correlation of Won (1986), see [Ref. 51]: f 20172 T = 374.5 + 0.02617MW – --------------MW [EQ 8.214] For naphthalenic and aromatic species, the melting point is given by (Pan, Firoozabadi and Fotland, 1997 - see [Ref. 52]): f T = 333.45 – 419e – 0.00855MW [EQ 8.215] where, in each equation, MW is the mole weight of the hydrocarbon. Wax precipitation In PVTi it is considered that the paraffinic and naphthalenic species of components heavier than C15 can form waxes and that the heaviest aromatic component forms the asphaltenic liquid phase. Chemically, the waxes that drop out of hydrocarbon fluids at lower temperatures, are known to contain paraffins and, to a lesser extent, naphthalenes. In PVTi the method of Pedersen et al. (see [Ref. 55]) has been improved to use the paraffin and naphthalene components, rather than a “wax forming component”. This means that the critical properties correlations for the paraffins and naphthalenes, as given by the correlations in "Critical properties of PNA species" on page 395, are used in determining the solid precipitation. PVTi Reference Manual Technical Description Wax and asphaltene precipitation in PVTi 395 The wax is modeled as a solid-solution and so we can apply an adjusted liquid fugacity and solve for the wax phase using a full multiphase equation-of-state flash calculation. For nonPNA species the solid fugacity is e50 , which effectively means that they cannot form wax. The adjustment to the liquid fugacity is given by: f f f f Δh i T i Δc Pi T i Δc Pi T i S L f pure i ( P,T ) = f pure i ( P,T ) × exp ---------f 1 – ----- – ----------- 1 – ----- – ----------- ln ----- R R T T T RT i [EQ 8.216] where Δh fi is the enthalpy of fusion for component i; ΔcPi is its heat capacity of fusion; and Tfi is its melting point temperature. Enthalpy of fusion The enthalpy of fusion for paraffins comes from the correlation by Won [Ref. 51]: f f [EQ 8.217] Δh i = 0.1426MW i T i For napthalenes the correlation of Lira-Galeana et. al. (1996) [Ref. 56] was used: f f [EQ 8.218] Δh i = 0.0527MW i T i For aromatics the correlation of Pan et al. [Ref. 52] was used: f f [EQ 8.219] Δh i = 11.2T i Heat capacity of fusion The heat capacity of fusion for all P, N, A species is given by the correlation of Pedersen et al.[Ref. 57]: –4 Δc Pi = 0.3033MW i – 4.635 × 10 MW i T [EQ 8.220] The asphaltenic liquid phase The asphaltenic phase is known to form at temperatures higher than the melting point of the heavy aromatic molecule that is the solid asphaltene. Maximum precipitation occurs close to the bubble point of the liquid and the precipitated phase is a thick, black liquid, see [Ref. 58]. After filtering, an asphaltene deposit is recovered. In PVTi there are a special set of default binary interaction coefficients introduced for the interactions between the heaviest aromatic component and the light components. This is based on the critical volumes of the components and takes a similar form to that of the CheuhPrausnitz binary interactions : 1⁄6 1⁄6 θ 2V ci V cj - k ij = A 1.0 – ---------------------------- V 1ci⁄ 3 + V 1cj⁄ 3 396 Technical Description Wax and asphaltene precipitation in PVTi [EQ 8.221] PVTi Reference Manual where kij is the binary interaction coefficient between the ith and jth components; Vc is the critical volume of the ith or jth component; A is the Cheuh-Prausnitz parameter, which can be varied as a special regression variable, the value used for interactions with the heaviest hydrocarbon is 10A; θ has been fitted using a number of asphaltene data-sets and is 6.0 for interactions involving hydrocarbons with mole weights less than that of SCN C7. It is zero for interactions involving hydrocarbons C7 and heavier, except for the heaviest aromatic component for which it is 12.0. This scheme is identical to the Cheuh-Prausnitz scheme for hydrocarbons up to C6, when the PNA split is not made, the Cheuh-Prausnitz binaries are the same as in pre-2002A versions of PVTi. For P, N and all A species apart from the heaviest aromatic, the binary interactions are zero. The strong interactions between the heaviest aromatic component and the light components creates the conditions for a precipitating asphaltenic liquid phase, which maximizes near the bubble line. Thus mimicking the behavior witnessed in laboratory tests. Discussion PVTi uses a consistent, single fluid model for all calculations, so the critical properties used in matching, say, the differential liberation experiment, are used in calculating the wax appearance temperature. Consequently all the observations, including those of the solid phase, can be regressed at once, leading to a more consistent and complete single description for use in both reservoir and process simulations. PVTi Reference Manual Technical Description Wax and asphaltene precipitation in PVTi 397 Cleaning samples contaminated with oil-based mud Introduction Oil-based muds are in widespread use and often contaminate PVT samples taken at the wellsite. PVTi offers two methods for cleaning oil-based muds, "Removing oil-based mud contamination by skimming" on page 398 describes a method that can be used when the composition of the contaminant is not known. If the contaminant composition is known, "Removing oil-based mud contamination by subtraction" on page 399 provides an accurate method for removing the contaminant. The methods used in PVTi are based on the work of Gozalpour et al, see [Ref. 53]. Removing oil-based mud contamination by skimming In naturally occurring hydrocarbon fluids, a semi-log straight-line relationship is seen between increasing mole fraction and increasing mole weight for components C8 and heavier, see [Ref. 56]. Many oil-based muds contain components in the range, C10 - C23, any contamination of the reservoir fluid, therefore, appear as a positive deviation from the semi-log straight-line behavior. The assumptions made for the skimming method are: firstly, that the semi-log straight-line behavior is exhibited by the fluid; and that there are uncontaminated components, heavier than the heaviest contaminated component. The second assumption is required for the straight-line to be constructed. The method involves constructing the straight-line between the C8 component and the uncontaminated heavy components. This line then gives the reservoir fluid and the excess molefractions provide the composition of the contaminating oil-based mud. In PVTi the light-end point is the first component with a mole weight heavier than 100 (if library components are used this is C8). The heavy end point is the lowest mole-fraction before the plus-fraction. Caution It is important that the sample being cleaned has heavier components than the oilbased mud, so that there is an uncontaminated point to use in constructing the straight line. If the composition of the oil-based mud is known, it is better to use the subtraction method described in "Removing oil-based mud contamination by subtraction" on page 399. 398 Technical Description Cleaning samples contaminated with oil-based mud PVTi Reference Manual Removing oil-based mud contamination by subtraction As described in "Removing oil-based mud contamination by skimming" on page 398, there is a semi-log straight-line relationship amongst the heavier components in a naturally occurring hydrocarbon fluid that can be exploited to allow the removed of oil-based mud contamination. The subtraction method is applicable when the composition of the contaminant is known. In this case, a small amount of the contaminant is subtracted from the sample. The resultant sample is tested for RMS fit to a semi-log straight-line defined as the same line used in the skimming method. A numerical optimization is performed to find the amount of contaminant that must be removed to minimize this RMS fit. Note The restriction that the oil-based mud contain components C10 - C23 does not apply here. The mud can be of any composition. Note The assumption that there are uncontaminated components, heavier than the oil-based mud components, is not necessary for this method. Hint If the composition is known, the subtraction method is a better choice than the skimming method. PVTi Reference Manual Technical Description Cleaning samples contaminated with oil-based mud 399 Mixing and recombination of samples Introduction PVTi offers both sample mixing and sample recombination. There is a subtle difference between mixing and recombining. In mixing, you provide a mole fraction or gas-oil ratio for the mix; these are used and the mixed sample is created directly. In recombining, you enter a target gasoil ratio for the mixture. In that case the proportion of mixing is determined iteratively using the scheme outlined in "Recombination" on page 400. Mixing Mixing is an addition of the two samples. If the mole fraction of the second sample is specified, the mixture is a weighted sum. If gas-oil ratio (GOR) is specified, this value is first translated to a mole fraction at the temperature and pressure requested. The conversion from GOR to mole fraction (MF) is as follows: n Assuming n moles of Sample 2 are mixed with 1 mole of Sample 1, then F = ----------- 1+n RT F std - where R is the universal gas constant, Tstd and - -----------------The GOR is then given by GOR = ----------1 – F P std V oil Pstd are standard temperature and pressure respectively and Voil is the oil volume at the temperature and pressure you specified. If you do not specify the pressure, it is taken as the saturation pressure of the sample Recombination In recombination, the aim is to create a mixture with the stock tank gas-oil ratio specified. In this case, the temperature and pressure you enter are used as the first stage in a two-stage separator. The second stage is always at standard conditions. The GOR you enter is the target GOR for the mixture. This is used as an initial guess and the fluids are mixed in the usual way (see "Mixing" on page 400). When this mixture is passed through the separators, a stock-tank GOR is calculated. A regression is performed, adjusting the mixing combination until the stocktank GOR is equal to the target value you requested. The mix applied at each iteration is recorded in the log window. 400 Technical Description Mixing and recombination of samples PVTi Reference Manual ECLIPSE Thermal Export Module Introduction In PVTi and ECLIPSE Compositional we deal with an isothermal flash. This means that, for a particular cell in a simulation, we know the composition of the fluid summed over all the phases and the pressure and temperature. We try to minimize the Gibbs Free Energy in order to determine how each component splits across the different phases present. In effect we try to find the K-values, which are the unknown variables. ECLIPSE Compositional assumes that the temperature of each cell stays constant over time, even if there is a distribution of temperatures across the cells to start with. It is assumed that if a particular drop of fluid moves from one cell with temperature, T1 to another cell with temperature T2 that the fluid takes on the temperature T2. When the Thermal option is used in ECLIPSE Compositional this is not the case. Thermal diffusion is allowed to take place over time, which means that the temperature in each cell is a free parameter that needs to be determined using a different type of flash; one at constant energy. We therefore know the pressure, functional form of the K-Values (K=K(P,T)), and the total energy of the system but the temperature is unknown. The long-term goal of this ECLIPSE Thermal module is to use PVTi’s powerful Equation of State (EoS) functionality to provide extensive support for the Thermal option in the ECLIPSE Compositional simulator. The first step was to introduce functionality into PVTi 2003A to calculate an optimal K-value functional relation. This can then be used within ECLIPSE Thermal to perform these flashes at constant energy. For PVTi 2004A the module has been extended to write out a whole file containing a series of keywords that can be used as the PVT input for an ECLIPSE Thermal simulation. In addition to the standard keywords written out for an ECLIPSE Compositional run, for example acentric factors (ACF), critical temperatures (TCRIT) etc., PVTi writes out additional keywords that enables ECLIPSE Thermal to calculate accurate values for K-values oil/gas densities and oil/ gas phase enthalpies. • "K-Values" on page 401, "Oil Density" on page 403, • "Gas phase density" on page 404, • and "Enthalpy" on page 405 explain how the relevant keywords are used in ECLIPSE Thermal to calculate the appropriate quantities. For a brief non-technical summary of these keywords see "Outline of keywords for ECLIPSE Thermal" on page 367. K-Values For PVTi 2004A you have the option of either using Crookston’s equation (the KVCR keyword) or Wilson’s formula (the KVWI keyword). Hint PVTi Reference Manual In fact Wilson’s formula is a simplified version of Crookston’s equation, which is explained below. Technical Description ECLIPSE Thermal Export Module 401 The coefficients of Crookston’s equation are written out by PVTi using the KVCR keyword. The general functional form of the K-Value correlation we use is given by Crookston’s formula: –D B K ( P, T ) = A + --- + CP exp ------------- T – E P [EQ 8.222] If a simplified version of equation [EQ 8.222] is used, given by setting A, C, E=0 that is: B D K ( P, T ) = --- exp – ---- P T [EQ 8.223] then B and D can be calculated by using at least two experimentally determined observations. Alternatively, Wilson’s formula can be used to estimate K-Values, which is given by the formula: Pc Tc K ( P, T ) = ------ exp 5.372697 ( 1 + ω ) 1 – ----- P T [EQ 8.224] where P, T are the pressure and temperature and K , P c , T c and ω are the K-value, critical pressure, critical temperature and acentric factor respectively for a particular component. In fact Crookston’s equation is a generalized form of Wilson’s formula, which can be obtained by setting: A = 0 B = Pc C = 0 Tc D = 5.372697T ( 1 + ω ) ----- – 1 T E = 0 in equation [EQ 8.222]. There are also tabulated values for B and D for certain components. The central problem we face though is that K-values for a particular component are not functions of just temperature and pressure, as Wilson’s formula would suggest, but also of the types and quantities of other substances present. Consider the following. If we have a fluid of say 50% methane and 50% decane then each component has its own K-value at a particular temperature and pressure. If we now add, say toluene, to the mixture then the K-values of methane and decane changes and we also have the K-value for the new component. This illustrates that changing the composition of a fluid clearly effects the K-values of respective components. Also, for heavier hydrocarbon components (anything above about C7), the K-values are an increasing monotonic function of pressure. It is clear that Wilson's formula is completely inadequate here as K=Pc/P is clearly a decreasing monotonic function of pressure. The full Crookston expression can cope with such components by using the A and C terms. PVTi can provide valuable assistance here because it provides its own experimental data using the flash; as we know that the flash accurately reproduces experimental observations. The ECLIPSE Thermal export facility then calculates the values of a chosen set of Crookston coefficients so that the correlation best approximates a set of flashes performed by PVTi in the pressure and temperature range you specified. This correlation is unique to the fluid sample and specified pressure and temperature range and ensures that the Thermal option in ECLIPSE Compositional is using accurate approximations to component K-values. 402 Technical Description ECLIPSE Thermal Export Module PVTi Reference Manual Oil Density PVTi writes out the keywords PREFT, TREFT, DREFT, CREF and THERMEX1, which ECLIPSE Thermal uses internally to calculate the oil density of the fluid at a specified pressure and temperature. For further information on the ECLIPSE keywords referenced in this section see the "ECLIPSE Reference Manual". Algorithm ECLIPSE Thermal calculates the molar oil density b o of the fluid using the following set of equations: bo is given by: b o = 1 ⁄ V oil [EQ 8.225] where the molar specific volume Voil of the oil phase is calculated using Amagat’s law of partial volumes: Nc V oil = c x Voil c [EQ 8.226] c=1 c and x is the mole fraction of component c in the oil phase. The component oil phase volume V oil c is given by: c c MW V oil = -----------c ρ [EQ 8.227] where MW c is the molecular weight of component c given by the MW keyword, and the component oil phase density ρ c is given by: c ρ ref ρ = --------------------------------------------------------------------------------------------( 1 + C T1 ( T – T ref ) ) ( 1 – C p ( P – P ref ) ) c The reference density ρ c ref [EQ 8.228] is defined by ECLIPSE Thermal’s DREF keyword (or PVTi’s DREFT keyword); the standard temperature and pressure, T ref and Pref are defined by keywords TREF (TREFT in PVTi) and PREF (PREFT in PVTi); the thermal expansion coefficient C T1 is defined by the THERMEX1 keyword; and the component isothermal compressibility C P is defined by the CREF keyword. The quantities C T1 and C p are defined by the usual thermodynamic relations: 1 ∂V C T1 = --- -----V ∂T P = PREF [EQ 8.229] 1 ∂V C p = – --- -----V ∂P T = TREF [EQ 8.230] PVTi Reference Manual Technical Description ECLIPSE Thermal Export Module 403 Remarks It is important to note that PVTi’s DREF, TREF keywords are, in general, not the same as ECLIPSE Thermal’s DREF, TREF keywords. PVTi’s DREF, TREF In PVTi the reference density DREF is an observed/measured quantity of each component at the reference temperature, TREF and standard pressure (14.7 psia). DREF is then used in conjunction with PVTi’s predicted density at these conditions (using a 2-parameter equation of state) to calculate volume shifts for each component. Volume shifts were introduced as a “third parameter” into EoS models to improve calculations of liquid density. Therefore the standard values of TREF for each component in the literature are chosen such that this component is in the liquid phase at the temperature TREF and standard pressure. ECLIPSE Thermal’s DREF, TREF, PREF In ECLIPSE Thermal it can be seen from equation [EQ 8.227] that we require knowledge of a reference density measured at a reference pressure and temperature. The reference density is used along with the isothermal and isobaric expansion coefficients (CREF and THERMEX1) to extrapolate linearly in order to obtain the density of the oil given an arbitrary temperature and pressure. PVTi’s reference quantities are not used because they may be very different to the conditions in the reservoir; and so it would be unreasonable to expect accurate answers using a linear extrapolation. In order to obtain reference parameters that are typical of the conditions in the reservoir PVTi calculates the quantities TREFT, PREFT and DREFT. TREFT and PREFT are the average of the maximum and minimum reservoir temperatures/pressures respectively. You input these extreme reservoir values of temperature and pressure on PVTi’s Export for ECLIPSE Thermal panel. DREFT for each component is then the density calculated by PVTi’s EoS model at pressure PREFT and temperature TREFT. Assuming that the component is in the liquid phase at these conditions then DREFT is a good point to perform linear extrapolation using [EQ 8.227] to find the density of the component at an arbitrary temperature and pressure in the reservoir. However, if the component is not in the liquid phase (which is the case for lighter components) at the initial values of TREFT and PREFT then we set TREFT=TREF (PVTi’s TREF) and PREFT=14.7psia, which we know guarantees that the component is in the liquid phase. We then use [EQ 8.227] to extrapolate to reservoir conditions and calculate the properties of the component. These lighter components contribute a relatively small amount to the overall density of the fluid and we have found this approach to give accurate values of oil density. The isothermal compressibility and thermal expansion coefficient are calculated by PVTi using [EQ 8.228]and[EQ 8.229] with the appropriate values of TREFT and DREFT TREFT, PREFT, DREFT are the same as ECLIPSE Thermal’s TREF, PREF, DREF. PVTi uses alias names because, as explained, it has already has definitions for TREF and DREF. ECLIPSE Thermal automatically recognizes these aliases and knows that it is dealing with its own internal keywords. Gas phase density PVTi writes out the keywords TREFT, PREFT, DREFT and ZFACTOR, which ECLIPSE Thermal uses internally to calculate the molar gas phase density of the fluid at a specified pressure and temperature. 404 Technical Description ECLIPSE Thermal Export Module PVTi Reference Manual Algorithm The molar density of the gas phase bg is given by: b g = 1 ⁄ V gas [EQ 8.231] where the molar specific volume Vgas of the gas phase is Nc V gas = c y Vgas c [EQ 8.232] c=1 assuming no water is present. yc is the mole fraction of component c in the gas phase. Each hydrocarbon component gas phase molar volume V gas c is obtained from the gas law, c c [EQ 8.233] PV gas = Z RT where Z c is specified with the ZFACTOR keyword. See the "ECLIPSE Reference Manual". Remarks The algorithm outlined above assumes that Z c does not change as a function of temperature. Z c is calculated by PVTi for each component by performing an EoS flash on a fluid consisting purely of the relevant component. If a single gas phase is found then Z c is set to the value of the Z-factor returned by PVTi’s EoS code. If a liquid phase is returned then Z c is set to ECLIPSE Thermal’s default value of 0.96. Enthalpy • "Algorithm" on page 405 outlines the three different approaches ECLIPSE Thermal can take in calculating oil and gas phase enthalpies. • "Remarks" on page 405 then explains which of these approaches PVTi supports. For further information on the ECLIPSE keywords referenced in this section see the "ECLIPSE Reference Manual". Algorithm ECLIPSE Thermal calculates the enthalpy of the oil phase using a mole fraction weighted average of the component enthalpies: Nc H oil = x c=1 c c ⋅ MW ⋅ H c [EQ 8.234] oil where xc is the mole fraction of component c in the oil phase and MW c is the component molecular weight given by the MW keyword. The enthalpy of the hydrocarbon components in the gas phase is calculated using a mole fraction weighted average of the component enthalpies: PVTi Reference Manual Technical Description ECLIPSE Thermal Export Module 405 Nc y H gas = c c ⋅ MW ⋅ H gas c [EQ 8.235] c=1 c where y is the mole fraction of component c in the gas phase. The component enthalpies in the oil and gas phases are calculated from component specific heats and heats of vaporization. Specific heat values must be given for each hydrocarbon component in at least one fluid phase. If they are only specified in one phase, then the heat of vaporization should be given. The following options are therefore available for the fluid phase enthalpies: 1 Set the specific heat of components in the oil and gas phases and the heat of vaporization at the standard temperature. 2 Set the specific heat of components in the oil phase and the heat of vaporization as a function of temperature. 3 Set the specific heat of components in the gas phase and the heat of vaporization as a function of temperature. Solid phase enthalpies are only required in simulations where a solid phase is present. Specific heats The specific heats C coil , C cgas of a component c in the oil and gas phases are given by c c c C oil = C oil + C oil ⋅ ( T – T st ) 1 2 c c c C gas = C gas + C gas ⋅ ( T – T st ) 1 2 where the oil phase coefficients are defined by keywords SPECHA and SPECHB and the gas phase coefficients are defined by keywords SPECHG and SPECHH. T st is the standard temperature defined by STCOND. The specific heats must always be positive. If oil phase specific heats are defined, the molar enthalpy of component c in the oil phase is: c H oil = c 2 1 c = C oil ⋅ ( T – T st ) + --- ⋅ C ⋅ ( T – T st ) 1 2 oil 2 c Coil dT T st [EQ 8.236] For temperatures above the critical temperature, T > T ccrit , the oil phase molar enthalpy is set equal to the gas phase molar enthalpy. If gas phase specific heats are defined, the molar enthalpy of component c in the gas phase is c c c H gas = H vaps + Cgas dT [EQ 8.237] T st c c 2 1 c = H vaps + C gas ⋅ ( T – T st ) + --- ⋅ C ⋅ ( T – T st ) 1 2 gas 2 where Hcvaps is the heat of vaporization at the standard temperature, defined by HEATVAPS. If a solid phase is simulated, the molar enthalpy of component c in the solid phase is c H sol = c Csol dT T st 406 c 2 1 c = C sol 1 ⋅ ( T – T st ) + --- ⋅ C ⋅ ( T – T st ) 2 sol 2 Technical Description ECLIPSE Thermal Export Module [EQ 8.238] PVTi Reference Manual Heat of vaporization A temperature dependent heat of vaporization ΔHc ( T ) can be specified instead of either the oil or gas specific heat. If the specific heat of a component c in the oil phase is not specified, then the oil phase enthalpy is calculated from the gas component enthalpy by c c c H oil = H gas – ΔH ( T ) [EQ 8.239] Alternatively, if the specific heat of a component c in the gas phase is not specified, then the gas phase enthalpy is calculated from the oil component enthalpy c c c H gas = H oil + ΔH (T) [EQ 8.240] The heat of vaporization is given by [Ref. 56]: c B c ΔH ( T ) = A ⋅ ( 1 – T ⁄ T crit ) c ΔH ( T ) = 0 T < T crit c T ≥ T crit c [EQ 8.241] [EQ 8.242] where the constant A is defined by the HEATVAP keyword, the exponent B is defined by the HEATVAPE keyword, and T crit c is the component critical temperature defined by the TCRIT keyword. Heats of vaporization are usually obtained at the normal boiling point T nb . The constant A , defined by the HEATVAP keyword can be found by inverting : c ΔH ( T nb ) A = ---------------------------------------B( 1 – T nb ⁄ T crit ) [EQ 8.243] where ΔHc ( T nb ) is the heat of vaporization at the normal boiling point. The exponent B for each component, entered with keyword HEATVAPE, is usually set to a value in the range 0<B<=1. Remarks PVTi uses the oil and gas phase component specific heat coefficients (SPECHA, SPECHB, SPECHG and SPECHH) and the heats of vaporization at the standard temperature (HEATVAPS) for each component. As explained in the previous section, the oil and gas phase enthalpies are then calculated using [EQ 8.236] and [EQ 8.237]. In the future this functionality could be extended so that you could specify in PVTi which of the three options to calculate enthalpies you wish to take advantage of in ECLIPSE Thermal. PVTi would then export the relevant keywords depending on which option you had selected. PVTi Reference Manual Technical Description ECLIPSE Thermal Export Module 407 408 Technical Description ECLIPSE Thermal Export Module PVTi Reference Manual Units Appendix A Units General information This option allows the current unit and temperature conventions to be changed. The options available are: • Metric unit system • Field units • Laboratory units • PVT-metric units The temperature conventions are: • Degrees Kelvin • Degrees Celsius • Degrees Rankine • Degrees Fahrenheit Any of the unit conventions are compatible with any of the temperature options. The unit conventions may be changed at any point in a session, existing quantities being converted to the new units. PVT-metric units are the same as metric, except in that pressure is measured in atmospheres. In addition, it is possible to enter mole compositions as fractions (of unity) or percentages (up to 100%), and pressures can be specified in absolute or gauge units. PVTi Reference Manual Units Units 409 The units for each data quantity are given in the table below. Table A.1 Units Quantity Metric Field Lab PVT-M Length metres feet cms metres days days hours days gm ⁄ cc kg ⁄ m Depth Time Density Pressure kg ⁄ m 3 lb ⁄ ft 3 3 barsa psia atma atma Pressure difference bars psi atm atm Compressibility 1 ⁄ bars 1 ⁄ psi 1 ⁄ atm 1 ⁄ atm Viscosity cPoise cPoise cPoise cPoise Permeability mDarcy mDarcy mDarcy mDarcy Liquid surface volume sm 3 stb scc sm 3 Gas surface volume sm 3 mscf scc sm 3 Reservoir volume rm 3 rb rcc rm 3 stb ⁄ day scc ⁄ hour sm ⁄ day Gas surface volume rate sm 3 ⁄ day mscf ⁄ day scc ⁄ hour sm ⁄ day Reservoir volume (rate) rb ⁄ day rcc ⁄ hour rm ⁄ day (absolute) Liquid surface volume rates Formation volume factor (liquid) Gas-oil ratio Oil-gas ratio Volume Specific volume Energy Enthalpy Specific heat Units Units 3 rm ⁄ day 3 3 3 rb ⁄ mscf rcc ⁄ scc rm ⁄ sm 3 3 mscf ⁄ stb scc ⁄ scc sm ⁄ sm 3 3 stb ⁄ mscf scc ⁄ scc sm ⁄ sm cc m sm ⁄ sm sm ⁄ sm m 3 3 rm ⁄ sm 3 ft 3 m ⁄ kg -ml 3 3 ft ⁄ lb kJ -ml cc ⁄ gm btu kJ ⁄ kg -ml kJ ⁄ kg – ml ⁄K Thermal conductivity kJ ⁄ m ⁄ d ⁄ K Gas-oil ratio (oil at reservoir) sm ⁄ rm Gauge pressure Surface tension Transmissibility 410 3 m ⁄ day -ml J btu ⁄ lb -ml btu ⁄ lb – ml ⁄R 3 3 3 3 3 3 3 3 m ⁄ kg -ml kJ J ⁄ gm -ml J ⁄ gm – ml kJ ⁄ kg ⁄K J ⁄ kg -ml – ml ⁄K btu ⁄ ft ⁄ d ⁄ R J ⁄ cm ⁄ h ⁄ K kJ ⁄ m ⁄ d ⁄ K mscf ⁄ rb scc ⁄ rcc sm ⁄ rm barsg psig atmosg atmosg dyne ⁄ cm dyne ⁄ cm dyne ⁄ cm dyne ⁄ cm cPrb ⁄ d ⁄ psi cPcc ⁄ h ⁄ a cPm ⁄ d ⁄ a 3 3 3 cPm ⁄ d ⁄ bar 3 3 3 PVTi Reference Manual A number of constants that depend upon the unit convention are used. These are: Table A.2 Constants Quantity Metric Field Lab PVT-M Gravity constant 0.000098066 0.00694444 0.000967841 0.0000967841 Darcy constant 0.00852702 0.00112712 3.6 0.00864 Atmos. pressure 1.01325 14.6959 1.0 1.0 Density of air 1.2232 0.076362 0.0012232 1.2232 Gas constant R 0.083143 10.732 82.055776 0.08205576 Standard conditions are taken as one atmosphere and 60 °F . Some useful conversion factors The following table contains conversion factors. Table A.3 Conversion factors Quantity Conversion factor Length 1m = 3.28084 ft 1ft = 0.30480 m Volume 1ft Mass 3 3 = 35.3146600 ft = 6.2898110 bbl 3 3 = 0.02831685 m = 0.1781076 bbl 1m = 2.20462300 lb 1kg 1lb Density = 0.45359237 kg 3 = 0.06242797 lb ⁄ ft = 1.0E-3 gm ⁄ cc = 16.0184600 kg ⁄ m 3 = 0.01601846 gm ⁄ cc 1 bar = 14.5037700 psi = 0.986923 atm 1 psi = 0.06894757 bar = 0.068046 atm 1kg ⁄ m 1lb ⁄ ft Pressure Gas-oil 3 3 3 1m ⁄ m 3 1 mcf ⁄ bbl Gravities API Temperatures = 5.614583E-3 mcf ⁄ bbl = 178.1076000 m 3 ⁄ m 3 (141.5/liq.grav.)-131.5 T (deg K ) = T (deg R )/1.8 Conversion of gas moles to volumes at Z=1 The volume occupied by one mole of gas, with an ideal gas Z -factor of unity, at temperature T (deg R ) and pressure p (psia), is: Vmolar = RT ⁄ p = 379.39445 at p = 14.70 psi, T = 519.67 deg R Vmolar = RT ⁄ p = 23.650203 at p = 1.013 bar, T = 288.15 deg K PVTi Reference Manual Units Units 411 The number of moles in unit volume V of gas with an “ideal gas” Z -factor of unity, at temperature T and pressure p , is: lb-moles = p ⁄ RT = 0.002635779 at p = 14.70 psi, T = 519.67 deg R kg-moles = p ⁄ RT = 0.042282930 at p = 1.1013 bar, T = 288.15 deg K 412 Units Units PVTi Reference Manual Symbols Appendix B Symbols f iL Fugacity of component i in the liquid phase f iV Fugacity of component i in the vapor phase Ki Equilibrium constant of component i L Mole fraction of liquid phase m1 Constant in Martins equation of state. m2 Constant in Martins equation of state. p Pressure of mixture. p ci Critical pressure of component i . p ri Reduced pressure of component i : p ri = ------i . T Temperature of mixture. Tc Critical temperature of component i . T ri Reduced temperature of component i : T ri = ------i- . V Mole fraction of vapor phase. xi Mole fraction of component i in the liquid phase. yi Mole fraction of component i in the vapor phase. Z Z -factor in equation of state. δ ij Binary interaction coefficient. ΩA PVTi Reference Manual p p ci T T ci i Omega- A values for each component. Symbols Symbols 413 ΩB ωi 414 Symbols Symbols i Omega- B values for each component. Acentric factor for component i . PVTi Reference Manual Bibliography Appendix C Wilson, G. “A Modified Redlich-Kwong Equation of State, Application to General Physical Data Calculations”. [Ref. 1] Paper No. 15C Ohio, presented at the AIChE 65th National Meeting, Cleveland. May 4-7, (1969). Martin, J.J. “Cubic Equations of State - Which?” [Ref. 2] IEC Fundamentals, Vol. 18, Page 81 , May, (1979). Coats, H. “Simulation of Gas Condensate Reservoir Performance”, [Ref. 3] SPE paper no. 10512, presented at the Sixth SPE Symposium on Reservoir Simulation, New Orleans , January 31st - February 3rd, (1982). Whitson, C.H. “Topics on: Phase Behaviour and Flow of Petroleum Reservoir Fluids”, [Ref. 4] Ph.D. Thesis, The University of Trondheim, Norwegian Institute of Technology, Department of Petroleum and Chemical Engineering, August, (1983). Pedersen, S.K., Fredenslund, Aa., Christensen, P.L., and Thomassen, P. Whitson, C.H., and Torp, S.B. Lohrenz, J., Bray, B.G., and Clark, C.R. Crowe, C.M., and Nishio, M. “Viscosity of Crude Oils”, [Ref. 5] Chemical Engineering Science, Vol. 39, Page 1011-1016 , No. 6, (1984) “Evaluating Constant-Volume Depletion Data”, [Ref. 6] J. Pet. Tech. Page 610-620. March, (1983) “Calculating Viscosity of Reservoir Fluids from their Composition”, [Ref. 7] J. Pet. Tech. Page 1171 , (1964); Trans., AIME,. 231. “Convergence Promotion in the Simulation of Chemical Processes - The General Dominant Eigenvalue Method”, [Ref. 8] AIChEJ, Vol. 23, No. 3 , Page 528-529. May (1975) PVTi Reference Manual Bibliography 415 Dennis, J.E., and Schnabel, R.B. “Numerical Methods for Unconstrained Optimisation and Non-linear Equations”, [Ref. 9] Prentice-Hall Inc., New Jersey, (1983) Kesler, M.G., and Lee, B.I. “Improved Predictions of Enthalpy of Fractions”, Hydro. Proc. Page 153-158 , March (1976) Cavett, R.H. “Physical Data for Distillation Calculations - Vapor-Liquid Calculations”, [Ref. 10] [Ref. 11] Proc. 27th API Meeting, San Francisco, Page 351-366, (1962) Riazi, M.R., and Daubert, T.E. “Simplify Property Predictions”, [Ref. 12] Hydro. Proc. Page 115-116 , March (1980) Lee, B.I., and Kesler, M.G. “Improved Vapor Pressure Predictions”, Hydro. Proc. Page 163-167. July (1980) Edmister, W.C. “Applied Hydrocarbon Thermodynamics”, [Ref. 13] [Ref. 14] Part 4: Compressibility Factors and Equation of State, Pet. Refiner , Page 173-179 , April, (1958) Michelsen, M.L. “The Isothermal Flash Problem. Part I. Stability”, [Ref. 15] Fluid Phase Equilibria, Vol. 9 , Page 1-19, , (1982) Katz, D.L. et al. “Handbook of Natural Gas Engineering”, [Ref. 16] McGraw-Hill Company , Page 129, (1982) Reid, R.C, Prausnitz, J.M., and Sherwood, T.K. Bashbush, J.L. “The Properties of Gases and Liquids”, [Ref. 17] McGraw-Hill Company, Third Edition, (1977) “A Method to determine K-values from Laboratory Data and its Applications”, [Ref. 18] SPE 10127 , (1981) Hoffmann, A.E., Crump, J.S., and Hocott, C.R. Alani, G.H., and Kennedy, H.T. Dranchuk, P.M., Purvis, R.A., and Robinson, D.B. Wichert, E., and Aziz, K. Lee, A.L., Gonzalez, M.H., and Eakin, B.E. 416 Equilibrium Constants for a Gas-Condensate System”, [Ref. 19] Trans. AIME., 198 , Page 1-10. “Volumes of Liquid Hydrocarbons at High Temperatures and Pressures”, [Ref. 20] Page Trans. AIME, 219, Page 288-292 , (1960) “Computer Calculations of Natural Gas Compressibility Factors using the Standing and Katz Correlation”, [Ref. 21] Institute of Petroleum Technical Series, No. IP 74-008, (1974). “Calculate Zs for Sour Gases”, [Ref. 22] Hydrocarbon Processing, 51, Page 119 , May (1972) “The Viscosity of Natural Gases”, [Ref. 23] J. Pet. Tech. Page 997-1000 , August, (1966) Bibliography PVTi Reference Manual Standing, M.B. “A Set of Equations for Computing Equilibrium Ratios of a Crude Oil/Natural Gas System at pressures below 1000 psia”, [Ref. 24] J. Pet. Tech. Page 1193-1195 , September (1979) Peneloux, A., Rauzy, E., and Freze, F. Søreide, I., Reffstrup, J., and Whitson, C.H. “A Consistent Correction for Soave-Redlich-Kwong Volumes”, [Ref. 25] Fluid Phase Equilibria 8 , Page 7-23, (1982) “Procedures for Reservoir Fluid Characterisation using an Equation of State Model”, [Ref. 26] , Report RE 88-8, Laboratory for Energetics, Danish Tech. Univ., Lyngby. Coats, K.H., and Smart, G.T. “Application of a Regression-Based EOS PVT Program to Laboratory Data”, SPE Res. Eng. Page 277-299 , May (1986) Herning, F., and Zippener, L. “Calculation of the Viscosity of Technical Gas Mixtures from the Viscosity of the Individual Gases”, [Ref. 28] [Ref. 27] Gas u. Wasserfach 79, Page 69-73, (1936) Stiel, L.I., and Thodos, G. Pedersen, K.S., Fredenslund, Aa., and Thomassen, P. Abramowitz, M., and Stegun, I.A. “The Viscosity of Nonpolar Gases at Normal Pressures”, [Ref. 29] AIChEJ , Page 611-615 , (1961) “Properties of Oils and Natural Gases”, [Ref. 30] Gulf Publishing Company, Houston , (1989) Handbook of Mathematical Functions [Ref. 31] New York , Page 923, (1972) Whitson, C.H., Anderson, T.F., and Søreide, I. “ C 7+ Characterisation of Related Equilibrium Fluid using the Gamma Distribution”, [Ref. 32] Paper in C 7+ Characterisation, Edited by Mansoori G.A., and Chorn L.G., Taylor and Francis, New York, (1989). McCain, W.D. “The Properties of Petroleum Fluids”, [Ref. 33] PennWell Publishing Company, Second Edition, Tulsa , (1990) Søreide, I. “Improved Phase Behaviour Predictions of Petroleum Reservoir Fluids from a Cubic Equation of State”, [Ref. 34] Ph.D. Thesis, The University of Trondheim, Norwegian Institute of Technology, Department of Petroleum and Chemical Engineering , April (1989) Søreide, I., and Whitson, C.H. “Peng-Robinson Predictions for Hydrocarbons, CO2 , N 2 , and H2 S With Pure Water and NaCl Brines”, [Ref. 35] Fluid Phase Equilibria, Vol. 77 , Page 217-240, (1992) Pedersen, S.K., and Fredenslund, Aa. “Chemical Engineering Science”, [Ref. 36] Vol. 42, No. 1 , Page 182-186, (1987) PVTi Reference Manual Bibliography 417 Reudelhuber, F.O., and Hinds, R.F. “A Compositional Material Balance Method for Prediction of Recovery from Volatile Oil Depletion Drive Reservoirs”, [Ref. 37] Petroleum Transactions, AIME, Vol. 210 , Page 19, (1957) Jensen, F., and Michelsen, M.L. Gmehling, J., Onken, U., and Arlt, W. “Calculation of First Contact and Multiple Contact Minimum Miscibility Pressures”, [Ref. 38] In Situ, 14(1) , Page 1-17, (1990) “Vapor-Liquid Equilibrium Data Collection DECHEMA Chemistry Data Series”, [Ref. 39] DECHEMA, Frankfurt/Main, (1981) Fragor Reference Manual Vol. 2.4, Chapter 5 [Ref. 40] J. Pet. Tech. Page 720-723 , July 1986. Pedersen K.S., Thomassen P, and Fredenslund Aa Winn F.W. “Characterisation of Gas Condensate Mixtures”, [Ref. 41] Adv. Thermodynamics 1 , Page 137, (1989b) “Physical Properties by Monogram”, [Ref. 42] Pet. Refiner 36 , Page 157-159, (1957) Sim W.J. and Daubert T.E. “Prediction of vapor-Liquid Equilibrium of Undefined Mixtures”, Ind. Eng. Chem. Process. Des. Dev. 19 , Page 386-393, (1980) Joergensen, M. and Stenby, E.H “Optimisation of pseudo-component selection for compositional studies of reservoir fluids”, [Ref. 43] [Ref. 44] SPE 30789, 70th Annual SPE Technical conference & exhibition. Dallas TX , (1995) Pedersen, K. Unpublished [Ref. 45] 1997 Michelsen, M.L. and Heidemann, R.A. Heidemann, R.A. and Khalil, A.M. Nes, K. and Westerns, H. A. van “Calculation of critical points from cubic 2-constant equation of state”, [Ref. 46] AIChE Journal (Vol 27 No3) , Page 769, (1980) “The Calculation of Critical Points”, [Ref. 47] AIChe Journal 26 No 5 , Page 521, (1981) “Aspects of the Constitution of Mineral Oils”, [Ref. 48] Elsevier, New York, (1951) Riazi, M. R. and Daubert, T. E. “Prediction of the composition of petroleum fractions”, Ind. Eng. Chem. Process Des. Dev., Vol. 19, Page 289 -294, , (1980) Riazi, M. R. and AlSahhaf, T. A. “Physical properties of n-alkanes and n-alkylhydrocarbons: Application to petroleum mixtures”, [Ref. 50] [Ref. 49] Ind. Eng. Chem. Res., Vol. 34, Page 4145 -4148, (1995) Won [Ref. 51] Fluid Phase Equilibria, Vol. 30, Page 265, (1986) 418 Bibliography PVTi Reference Manual Pan, H., Firoozbadi, A. and Fotland, P., Gozalpour, F., Densh, A., Tehranio, D. H., Todd, A.C. and Tohidi, B., Katz, D. “Pressure and composition effect on was precipitation: Experiment data and model results”, [Ref. 52] SPE Prod. and Fac - SPE 36740, Page 250, (, 1997) “Predicting reservoir fluid phase and volumetric behaviour from samples contaminated with oil-based mud”, [Ref. 53] SPE 56747, (1999) “Overview of Phase Behavior in Oil and Gas Production”, [Ref. 54] JPT, Page 1205-1214, , (1983) Pedersen, K. S. “Prediction of cloud point temperatures and amount of wax precipitation”, [Ref. 55] SPE 27629, (1995) Lira-Galeana, C., Firoozbadi, A., and Prausnitz, J. M. Pedersen, K. S., Skovborg, P. and Ronningsen, H. P. Rydahl, A. K., Pedersen, K. S., and Hjermstad, H. P. “Thermodynamics of wax precipitation in petroleum mixtures”, [Ref. 56] AIChE J., Vol. 42, Page 239, (1995) “Wax precipitation from North Sea crude oils. 4. Thermodynamic Modeling”, [Ref. 57] Energy and Fuels, Vol. 5 (6), Page 924, (1991) “Modeling of live oil asphaltene precipitation”, [Ref. 58] “Properties of Oils and Natural Gases”, [Ref. 59] Chapter 10, ISBN 0-87201-588-2, Ahmed, T. SPE 18532 [Ref. 60] Liu, K. SPE 66363 [Ref. 61] Trebble, M.A. “A preliminary evaluation of two and three phase flash initiation procedures”, [Ref. 62] Fluid Phase Equilibria. 53, Page 113-122, , (1989) Aasberg-Petersen, K. “The Viscosity of Hydrocarbon Fluids”, [Ref. 63] Fluid Phase Equilibria. 70, Page 293-308, (1991) Teja, A.S. & Rice, P. “Generalised Corresponding States Method for the Viscosities of Liquid Mixtures”, [Ref. 64] “Ind. Eng. Chem. Fundam., 20, Page 77, (1981) Hanley, H.J.M., McCarty, R.D. & Haynes, W.M. McCarthy, R.D., “Equation of the Viscosity and Thermal Conductivity Coefficients of Methane”, [Ref. 65] Cryogenics, 15, Page 413,(1975), “A Modified Benedict-Webb-Rubin Equation of State for Methane Using Recent Experimental Data” [Ref. 66] Cryogenics, 14, Page 276 , (1974) PVTi Reference Manual Bibliography 419 Green, Don W.; Perry, Robert H. 420 Perry’s Chemical Engineers’ Handbook (8th Edition) [Ref. 67] McGraw-Hill, (2008) Bibliography PVTi Reference Manual AIndex Index A Acentric factors. . . . 103, 169 Alani-Kennedy liquid densities312 Alkanes . . . . . . . . . . . . . 298 Aromatics. . . . . . . . . . . . 299 Asphaltene and Wax System 69 CCE . . . . . . . . . . . . . . . . 342 CVD . . . . . . . . . . . . . . . 343 Cell compositions . . . . . . 310 Cycloparaffins . . . . . . . . 299 Cell volumes . . . . . . . . . . 310 Celsius . . . . . . . . . . . . . . 409 CHAR components . . . . . 302 Characterization. . . . . . . . 176 Cheuh-Prausnitz . . . 147, 170 CMF. . . . . . . . . . . . . . . . 304 CO2 Rich Fluids . . . . . . . . 70 B Binary Interaction Coefficients104, 172, 319, 337 Coefficients default . 187 Black oil tables differential. . . . . . . . 189 Blackoil Compositional simulation373 Appendix D Coats . . . . . . . . . . . . 27, 178 COMB section keywords . . . . . . . . . 159 Command line . . . . . . . . . . 29 Components . . . . . . . . . . 230 Compositional Blackoil . . . . . . . . . . 373 grading with depth . . 373 D Data analysis . . . . . . . . . . 77 DBG file . . . . . . . . . .93, 186 Dead oil tables .171, 184, 216 Debug . . . . . . . . . . . . . . 150 Default Binary Interaction Coefficients 187 Dew point . . . . . . . . . . . 342 Differential black oil tables189 Dry gas tables. . . . . . . . . 183 Condensate systems . . . . . 342 BLACKOIL section keywords . . . . . . . . 161 E Consistency tests . . . . . . . 308 correlations . . . . . . . 381 ECLIPSE 300. . . . . . . . . 194 Boiling point temperatures 268 Constant Mole Fraction105, 303 to 304 Edmister . . . . .103, 176, 302 Bubble point pressure . . . 340 Conversion factors . . . . . . 411 EoS Correlation . . . . . . . . . . . 182 C Calorific values. . . . 147, 175 Cascade . . . . . . . . . . . . . 150 Cavett . . . . . . 103, 176, 302 PVTi Reference Manual Critical pressures . . . . . . . 243 omega values . . . . . 237 regression to measured data27 Critical temperatures . . . . 269 Equation of state. . . .193, 317 fitting to experimental results49 Critical viscosity . . . . . . . 331 Equilibrium K-values . . . .311 Critical volumes. . . . . . . . 278 Experiments . . . . . . . . . . 195 Critical Z-factors . .290 to 291 Export . . . . . . . . . . . . . . 136 Index 421 Equilibration. . . . . . .136 Gas Reservoir . . . . . .135 Oil Reservoir . . . . . .135 VFP . . . . . . . . . . . . .138 Export modules . . . . . . . .133 K Katz-Firoozabadi . . . . . . 147 Kelvin . . . . . . . . . . . . . . 409 Kesler-Lee . . . 103, 176, 302 Keyword errors . . . . . . . . 165 F Keywords PVTi. . . . . . . . . . . . 167 Fahrenheit . . . . . . . . . . . .409 K-value checks . . . . . . . . 382 Mole weight of the plus fraction229 Molecular weights . . . . . . 228 Monitor option. . . . . . . . . 150 MOSES keyword . . . . . . . 227 Moses method . . . . . . . . . 227 Multi-feed Split . . . . . . . . 105 MW keyword . . . . . . . . . 228 MWS keyword . . . . . . . . 229 Field units . . . . . . . . . . . .409 Fluid definition . . . . . . . . .25 Fourth-degree polynomial .330 Fragor method . . . . . . . . .203 L N Napthenes . . . . . . . . . . . . 299 Laboratory experiments . . 339 NCOMPS keyword . . . . . 230 Laboratory units . . . . . . . 409 NEW . . . . . . . . . . . . . . . . 93 LBC viscosity correlation 149 NEW files . . . . . . . . . . . . . 93 G Lee-Kesler . . . . . . . . . . . 302 NEWPVI keyword .231 to 232 LIB components . . . . . . . 302 Newton-Raphson . . . . . . . 318 Gas formation volume factor340 Library components. . . . . . 95 NOECHO keyword . . . . . 233 Gas gravity (density). . . . .340 Linear thermal expansion coefficient322 Non-hydrocarbon. . . 102, 211 Gas viscosity . . . . . . 314, 340 Liquid formation volume factors204 Gas-oil ratio. . . . . . . . . . .340 definition . . . . . . . . .148 Liquid saturation . . . . . . . 146 Fugacities . . . . . . . . . . . .317 GI nodes . . . . . . . . . . . .205 GOR definition . . . . . . . . .148 GRAF . . . . . . . . . . . . . . .148 GROUP section . . . . . . . .159 keywords . . . . . . . . .159 LNAMES keyword . . . . . 177 LOG files . . . . . . . . . . . . . 93 Lohrenz-Bray-Clark214 to 215, 245 O OBS keyword . . . . . . . . . 234 Observations . . . . . . . . . . 234 OBSIND keyword . . . . . . 235 M Oil density. . . . . . . . . . . . 340 Oil formation volume factor340 Martin . . . . . . . . . . . . . . 318 Oil viscosity . . . . . . . . . . 340 Material balance checks . . . 26 OMEGAA, OMEGAB keywords237 Maximum step size . . . . . 219 On-line help . . . . . . . . . . 151 MES file. . . . . . . . . . . . . . 93 Opening a project. . . . . . . . 95 H Metric units . . . . . . . . . . 409 OPTIONS keyword . . . . . 238 Michelsen’s stability criterion318 OUTECL3 keyword . . . . . 240 Hoffman-Crump plot . . . . .81 Mixing . . . . . . . . . . . . . . 224 Hydrocarbon . . 102, 211, 298 Mnemonics. . . . . . . . . . . 177 OUTECL3 section . . . . . . 162 keywords . . . . . . . . . 162 Grouping . . . . . . . . . 106, 180 components . . . . . . .206 Modified form of Peng-Robinson246 Modified Whitson . . . . . . 303 I Individual observation weights235 Internal library . . . . . . . . .217 Isomers . . . . . . . . . . . . . .298 422 Index Modified Whitson Splitting306 P MODSPEC keyword . . . . 225 PARACHOR keyword . . . 242 MODSYS keyword . . . . . 226 Paraffins . . . . . . . . . . . . . 298 Molar volume correction . 321 PCRIT keyword. . . . . . . . 243 Mole fractions. . . . . . . . . 292 PEARCE keyword . . . . . . 244 PVTi Reference Manual Pedersen. . . . . 103, 176, 302 Reference temperatures . . 273 Single Carbon Number . . 103 PEDERSON keyword . . . 245 REGRESS section . . . . . . 160 keywords . . . . . . . . . 160 Soave-Redlich-Kwong 25, 318 Regression operation . . . . . . . . . 201 target . . . . . . . . . . . . 250 variables . . . . . . . . . 275 SPECHA,B,C,D keyword 262 REGTARG keyword. . . . . 250 SPLIT keyword . . . . . . . 263 Reservoir temperature . . . 251 SPLIT section keywords . . . . . . . . 158 Peneloux . . . . . . . . . . . . 321 Peneloux et al. volume shift 25 Peng-Robinson . . . . . 25, 318 modified form of . . . 246 Phase diagrams . . . . . . . . 301 Plus fraction splitting. . . . 202 PRCORR keyword . . . . . 246 Pressure nodes automatic insertion. . 222 Probability density model. 303 Program options . . . 145, 238 PSEUCOMP keyword . . . 247 PSEUCOMP section . . . . 162 keywords . . . . . . . . 162 Reudelhuber and Hinds . . 248 Riazi-Daubert . 103, 176, 302 RTEMP keyword . . . . . . . 251 RUNSPEC . . . . . . . . . . . 155 RUNSPEC keyword. . . . . 252 RUNSPEC section keywords . . . . . . . . . 156 Søreide . . . . . . . . . . . . . 322 Specific heat. . . . . . . . . . 147 Specific heat capacity coefficients262 Splitting. . . . . . . . . . . . . 105 SSHIFT keyword . . . . . . 264 Standard conditions. . . . . 265 Standard pressure . . . . . . 145 Standard temperature . . . 145 STCOND keyword . . . . . 265 Surface tension . . . . . . . . 321 Pseudo-compositional tables247 Swelling test. . . . . . . . . . 345 Pseudo-critical temperatures, pressures313 S SYSTEM . . . . . . . . . . . . 155 Pseudoise definition . . . . . . . . . 26 SALINITY keyword . . . . 253 Pseudoised EoS data . . . . . . . . . . 27 SYSTEM section keywords . . . . . . . . 157 SAMPLES keyword254 to 256 Sample composition . . . . . 255 Pure . . . . . . . . . . . . . . . . 297 SAMTITLE keyword . . . . 257 Pure components. . . . . . . 300 Saturated black oil reservoirs372, 375 PVI file . . . . . . . . . . . . . . 93 Saturation liquid. . . . . . . . . . . . 146 PVO file. . . . . . . . . . . . . . 93 SYSTEM keyword . . . . . 266 T TBOIL keyword . . . . . . . 268 SAVCOMP keyword . . . . 258 TCRIT keyword . . . . . . . 269 Saving compositions . . . . 258 Temperature convention . 188 Schmidt-Wenzel. . . . . . . . . 25 Thermal expansion . . . . . 147 SCN . . . . . . . . . . . . . . . . 103 THERMX keyword. . . . . 270 SCN groups. . . . . . . . . . . 299 Thomassen. . . .103, 176, 302 SCT keyword . . . . . . . . . 259 Tiled . . . . . . . . . . . . . . . 150 SCT split. . . . . . . . . . . . . 259 TITLE keyword . . . . . . . 271 Semi-Continuous Thermodynamics105, 303 split . . . . . . . . . . . . . 259 TLOW keyword . . . . . . . 272 Separator liquid volumes . 147 True-boiling-point distillation303 R SG keyword . . . . . . . . . . 260 Trust region radius . .219, 223 Shift parameters. . . . . . . . 322 Two-parameter equation of state321 Rankine . . . . . . . . . . . . . 409 SIMULATE. . . . . . . . . . . 261 Recovery calculations . . . 383 SIMULATE keyword . . . . 261 RECOVERY keyword . . . 248 Redlich-Kwong. . . . . 25, 318 SIMULATE section keywords . . . . . . . . . 160 U Reference densities . . . . . 190 Simulation of experiments . 26 Undersaturated reservoirs 372 PVP file . . . . . . . . . . . . . . 93 PVT data for ECLIPSE simulators27 PVTLIB annexe . . . . . . . 185 PVT-metric units . . . . . . . 409 Q Quality control . . . . . . . . . 77 PVTi Reference Manual ToolTips . . . . . . . . . . . . 151 TREF keyword . . . . . . . . 273 Index 423 Unit convention . . . . . . . .274 View menu . . . . . . . . . . . . 95 Watson characterization factor302 Unit types . . . . . . . . . . . .144 Viewing the K-value Fits . . 75 WATVFP keyword . . . . . . 285 UNITS keyword. . . . . . . .274 Viscosities . . . . . . . . . . . 331 Wet gas tables . . . . . . . . . 286 UNIX . . . . . . . . . . . . . . . .29 Viscosity calculations . . . 382 WHIT keyword . . . . . . . . 287 UNIX platforms . . . . . . . . .29 Volatile oil reservoirs 372, 376 User components . . . . . . .302 Volume expansion coefficient270 Whitson . . . . . 105, 303, 305 probability density function220 splitting . . . . . . . . . . 287 Volume shift corrections . . . . . . . 147 Whitson and Torp . . . . . . 288 V Volume shift parameters dimensionless . . . . . 264 WHITSON keyword . . . . 288 Vapor Z-factor . . . . . . . . .313 Volume translation . . . . . 321 Window . . . . . . . . . . . . . 150 Whitson-Torp . . . . . . 27, 178 VAR keyword . . . . . . . . .275 Windows platforms . . . . . . 29 VCRIT keyword. . . . . . . .278 Winn. . . . . . . . 103, 176, 302 VCRITVIS keyword. . . . .279 VEC file . . . . . . . . . . . . . .93 VERSION keyword . . . . .280 VFP . . . . . . . . . . . . . . . .138 section . . . . . . . . . . .163 VFP keyword. . . . . . . . . .281 VFP section keywords . . . . . . . . .163 VFP Tables . . . . . . . . . . .366 VFPi . . . . . . . . . . . . 133, 272 424 Index W WAT100 keyword . . . . . . 282 WAT200 keyword . . . . . . 283 Z WAT300 keyword . . . . . . 284 ZCRIT keyword. . . . . . . . 290 Water properties ECLIPSE 100 . . . . . ECLIPSE 300 . . . . . ECLIPSE GI option . VFPi. . . . . . . . . . . . ZCRITVIS keyword. . . . . 291 282 284 283 285 Z-factors, critical . .290 to 291 ZI keyword . . . . . . . . . . . 292 ZMFVD keyword . . . . . . 293 Zudkevitch-Joffe 25, 318, 321 PVTi Reference Manual