Capillary Pressure Estimation and Reservoir Simulation
Rawan Haddad
Imperial College Supervisor - Tara La Force
Industry Supervisor - Marie Ann Giddins, Schlumberger
Capillary pressure is a key to accurately estimating the fluids in place by defining the distribution of reservoir fluids and the
fluids contacts. The initial state of equilibrium is ensured by correct capillary pressure determination.
Once lab capillary pressure data is provided, the data is imported into a reservoir simulator such as ECLIPSE.
The user can then apply a number of available keywords to scale the capillary pressure in order to honour other parameters
such as water saturation, porosity or permeability which are closely related to the capillary pressure.
The problem arises when the capillary pressure is scaled to a high value that the distribution of fluids no longer describes the
reservoir, initial equilibrium is unattained and the model becomes unstable with high CPU time and convergence problems.
The fluids in place are also wrongly estimated, which may be detrimental to a project’s economic target.
Furthermore; many reservoir engineering practices experience problems with estimating the water production in the transition
zone; sometimes being over estimated with early water breakthrough. Available quick fixes in the simulator set the water
saturation in the transition zone to equal the critical water saturation slowing down the water breakthrough; this however
assigns no dynamic range to the model making it unphysical with poor performance.
This project uses the Brugge model to investigate the scaling of capillary pressure performed by ECLIPSE, paying attention to
the estimation of fluids production in the transition zone.
Ten cases have been initialized and run by applying a hydrostatic equilibrium keyword; inputting a water saturation
distribution and scaling capillary pressure accordingly using an initial water saturation keyword; scaling capillary pressure as a
function of porosity and permeability using a J function keyword and end point scaling of capillary pressure curves using the
critical and connate water saturations keywords.
Applying a representative saturation height method to initialize the model using a water distribution keyword seemed to give
an efficient model with physical scaling of capillary pressure. It accurately estimated the oil in place, and matched the history
production well.
Using connate and critical water saturation to scale the capillary pressure and relative permeability curves gave an unphysical
model that overestimated the production both in and out of the transition zone, and using a function keyword underestimated
the production history.
The approach taken in this report confirms the importance of taking capillary pressure into account when performing
sensitivity analysis to match history data or initialize a model.
Acknowledgment
I would like to thank Marie Ann Giddins for giving me the opportunity to undertake this project and for her dedicated support,
expertise and guidance through many encountered technical problems and through all the long weekly meetings (despite her
rigorous schedules).
I wish to thank Dr. Charles Kossack for helpful meetings that lightened the project with brighter ideas.
I would like to thank my college supervisor, Dr Tara La Force for her supervision. I am overwhelmed to have been taught by a
truly professional group of lecturers and I appreciate the efforts of all Imperial College staff members who provided the
essentials for completing a final year project.
I would also like to thank all the staff of Schlumberger Abingdon Technology Center who have been very friendly and
supportive throughout my time of the project, especially Youcef, Rong and Chioma who have continuously taken time to share
their valuable knowledge.
Finally I would like to thank Daniel Robertson for the great support he has shown throughout the course of this project.
Contents
Acknowledgment .......................................................................................................................................................................... 2
1.
Introduction ........................................................................................................................................................................... 1
2.
Research Methods ................................................................................................................................................................. 2
2.1.
2.1.1.
J Function ................................................................................................................................................................ 2
2.1.2.
Lambda function ..................................................................................................................................................... 2
2.1.3.
Skelt and Harrison Method ..................................................................................................................................... 2
2.1.4.
Johnson Method ...................................................................................................................................................... 2
2.2.
3.
Saturation height equations ......................................................................................................................................... 2
Simulation Model ........................................................................................................................................................ 3
2.2.1.
Brugge Brief Description ........................................................................................................................................ 3
2.2.2.
Keyword definitions ................................................................................................................................................ 3
Results ................................................................................................................................................................................... 3
3.1.
Equilibration ................................................................................................................................................................ 4
3.2.
SWATINIT .................................................................................................................................................................. 4
3.2.1.
3.3.
3.3.1.
3.4.
Saturation height methods Simulation..................................................................................................................... 5
JFUNC Keyword simulation ....................................................................................................................................... 6
Simple model results ............................................................................................................................................... 8
Initial water distribution using SWCR and SWL .......................................................................................................10
4.
Discussion ............................................................................................................................................................................14
5.
Conclusion ...........................................................................................................................................................................14
6.
Recommendation .................................................................................................................................................................14
7.
References ............................................................................................................................................................................16
Appendix ......................................................................................................................................................................................17
Figures
Figure 1: Relation of a single accumulation to capillary type curve (Holmes 2002) .................................................................... 1
Figure 2: left: Brugge PORO- PERM according to facies and right: Capillary Pressure curves according to regions ................. 3
Figure 3: initialized model using EQUIL ...................................................................................................................................... 4
Figure 4: Scaled capillary pressure using SWATINIT.................................................................................................................. 4
Figure 5: oil and water production rate for all SWATINIT cases ................................................................................................. 5
Figure 6: Oil recovery factor for all SWATINIT cases ................................................................................................................. 5
Figure 7: Water Saturation in the transition zone .......................................................................................................................... 6
Figure 8: Impact of using JFUNC keyword on the oil production rate and the recovery ............................................................. 7
Figure 9: Impact of using JFUNC keyword on the water production ........................................................................................... 7
Figure 10: water production in transition zone using JFUNC keyword ........................................................................................ 8
Figure 11: Scaling capillary pressure using JFUNC ..................................................................................................................... 8
Figure 12: scaled capillary pressure for cell (10, 1, 5) .................................................................................................................. 9
Figure 13: Relative permeability curve scaling using SWCR/SWL ............................................................................................11
Figure 14: comparison of water and oil production profile using SWATINIT and SWL/SWCR ...............................................11
Figure 15: water production in the transition zone using SWL/SWCR .......................................................................................12
Figure 16: Effect of ignoring capillary pressure ..........................................................................................................................12
Figure 17: random water distribution using SWATINIT and SWCR/SWL .................................................................................13
Figure 18: 10 best cases showing the field oil production rate using EQUIL with case 9 giving the closest match ....................18
Figure 19:10 best cases showing the field water production rate using EQUIL with case 9 giving the closest match ................18
Figure 20: 10 best cases showing the field oil cumulative production using EQUIL with case 9 giving the closest match ........19
Figure 21: 10 best cases showing the field water cumulative production using EQUIL with case 9 giving the closest match ...19
Figure 22:10 best cases showing oil production rate using SWATINIT, J function water distribution .......................................20
Figure 23:10 best cases showing field water production rate using STAWTINIT, J function water distribution ........................20
Figure 24:10 best cases showing oil cumulative production using SWATINIT, J function water distribution ...........................21
Figure 25:10 best cases showing water cumulative production using SWATINIT, J function water distribution.......................21
Figure 26: 10 best cases of oil production rate using SWATINIT, Skelt and Harrison saturation distribution ...........................22
Figure 27: 10 best cases for water production rate using SWATINIT, Skelt and Harrison water saturation distribution ...........22
Figure 28: 10 best cases showing oil production cumulative using SWATINIT, Skelt and Harrison water saturation distribution
.....................................................................................................................................................................................................23
Figure 29: 10 best cases showing water production cumulative using SWATINIT, Skelt and Harrison water saturation
distribution ...................................................................................................................................................................................23
Figure 30: 10 best cases showing water production rate using SWATINIT, Lambda water saturation distribution ...................24
Figure 31: 10 best cases showing oil production rate using SWATINIT, Lambda water saturation distribution ........................24
Figure 32: 10 best cases showing oil production cumulative using SWATINIT, Lambda water saturation distribution ............25
Figure 33: 10 best cases showing water production cumulative using SWATINIT, Lambda water saturation distribution ........25
Figure 34: 10 best cases showing oil production rate using SWATINIT, Johnson water saturation distribution ........................26
Figure 35: 10 best cases showing water production rate using SWATINIT, Johnson water saturation distribution ...................26
Figure 36: 10 best cases showing oil production cumulative using SWATINIT, Johnson water saturation distribution ............27
Figure 37: 10 best cases showing oil production cumulative using SWATINIT, Johnson water saturation distribution ............27
Figure 38: 10 best cases showing oil production rate using JFUNC water saturation distribution ..............................................28
Figure 39: 10 best cases showing water production rate using JFUNC water saturation distribution .........................................28
Figure 40: 10 best cases showing oil production cumulative using JFUNC water saturation distribution ..................................29
Figure 41: 10 best cases showing water production rate using JFUNC water saturation distribution .........................................29
Figure 42: best cases showing oil production rate using SWATINIT=SWL=SWCR ..................................................................30
Figure 43: best cases showing water production rate using SWATINIT=SWL=SWCR .............................................................30
Figure 44: best cases showing oil production cumulative using SWATINIT=SWL=SWCR ......................................................31
Figure 45: best cases showing water production cumulative using SWATINIT=SWL=SWCR .................................................31
Figure 46: best cases showing oil production rate using SWATINIT=SWL=SWCR, 0 capillary pressures ...............................32
Figure 47: best cases showing water production rate using SWATINIT=SWL=SWCR, 0 capillary pressure ............................32
Figure 48: best cases showing oil production cumulative using SWATINIT=SWL=SWCR, 0 capillary pressure .....................33
Figure 49: best cases showing water production cumulative using SWATINIT=SWL=SWCR, 0 capillary pressure ................33
Figure 50: best cases showing oil production rate using SWL=SWCR= a) random Sw, b) randomly distributed SWATINIT ..34
Figure 51: best cases showing water production rate using SWL=SWCR= a) random Sw, b) randomly distributed SWATINIT
.....................................................................................................................................................................................................34
Figure 52: best cases showing oil production cumulative using SWL=SWCR= a) random Sw, b) randomly distributed
SWATINIT ..................................................................................................................................................................................35
Figure 53: best cases showing water production cumulative using SWL=SWCR= a) random Sw, b) randomly distributed
SWATINIT ..................................................................................................................................................................................35
Figure 54: best cases showing oil production rate using all methods ..........................................................................................36
Figure 55: best cases showing water production rate using all methods ......................................................................................36
Figure 56: best cases showing water cumulative rate using all methods .....................................................................................37
Figure 57: best cases showing oil production cumulative using all methods ...............................................................................37
Figure 58: effect of capillary pressure scaling using PPCW ........................................................................................................38
Figure 59: oil production rate using JFUNC. PHI/K=0.0001 ......................................................................................................40
Figure 60: water production rate using JFUNC. PHI/K=0.0001 ..................................................................................................40
Figure 61: Oil production cumulative using JFUNC. PHI/K=0.0001 ..........................................................................................41
Figure 62: water production cumulative using JFUNC. PHI/K=0.0001 ......................................................................................41
Figure 63: Oil production rate using JFUNC. PHI/K=0.001.......................................................................................................42
Figure 64: water production rate using JFUNC. PHI/K=0.001 ....................................................................................................42
Figure 65: Oil production cumulative using JFUNC. PHI/K=0.001 ............................................................................................43
Figure 66: Water production cumulative using JFUNC. PHI/K=0.001 .......................................................................................43
Figure 67: Oil production rate using JFUNC. PHI/K=0.01..........................................................................................................44
Figure 68: Water production rate using JFUNC. PHI/K=0.01 .....................................................................................................44
Figure 69: Oil production cumulative using JFUNC. PHI/K=0.01 ..............................................................................................45
Figure 70: Water production cumulative using JFUNC. PHI/K=0.01 .........................................................................................45
Figure 71: Oil production rate using JFUNC. PHI/K=0.1 ...........................................................................................................46
Figure 72: Water production rate using JFUNC. PHI/K=0.1 .......................................................................................................46
Figure 73: Oil production cumulative using JFUNC. PHI/K=0.1 ................................................................................................47
Figure 74: water production cumulative using JFUNC. PHI/K=0.1 ............................................................................................47
Figure 75: Oil production rate using JFUNC. PHI/K=1 ..............................................................................................................48
Figure 76: water production rate using JFUNC. PHI/K=1 ...........................................................................................................48
Figure 77: Oil production cumulative using JFUNC. PHI/K=1 ...................................................................................................49
Figure 78: Water production cumulative using JFUNC. PHI/K=1 ..............................................................................................49
Figure 79: Oil production rate using JFUNC. Negative 0.001 slope of phi vs K .........................................................................50
Figure 80: Water production rate using JFUNC. Negative 0.001 slope of phi vs K ....................................................................50
Figure 81: Oil production cumulative using JFUNC. Negative 0.001 slope of phi vs K .............................................................51
Figure 82: water production cumulative using JFUNC. Negative 0.001 slope of phi vs K .........................................................51
Figure 83: Oil production rate using JFUNC. Brugge POROPERM relationship .......................................................................52
Figure 84: Water production rate using JFUNC. Brugge POROPERM relationship ...................................................................52
Figure 85: Oil production cumulative using JFUNC. Brugge POROPERM relationship ............................................................53
Figure 86: Water production cumulative using JFUNC. Brugge POROPERM relationship .......................................................53
Figure 87: Oil production rate using JFUNC. Average layered Brugge POROPERM relationship ............................................54
Figure 88: Water production rate using JFUNC. Average layered Brugge POROPERM relationship........................................54
Figure 89: Oil production cumulative using JFUNC. Average layered Brugge POROPERM relationship.................................55
Figure 90: water production cumulative using JFUNC. Average layered Brugge POROPERM relationship .............................55
Tables
Table 1: PCW for all Saturation height cases................................................................................................................................ 6
Table 2: Water saturation distribution using JFUNC .................................................................................................................... 9
Table 3: Effect of using JFUNC on the recovery factor ................................................................................................................ 9
Table 4: PCW values for JFUNC based on a PORO-PERM .......................................................................................................10
Table 5: Initial water saturation distribution using JFUNC keyword cases. ................................................................................39
Table 6: Capillary pressure at the first time step using JFUNC keyword cases ...........................................................................39
Table 7:SWATINIT cases performance .......................................................................................................................................56
Table 8:SWL/SWCR cases performance .....................................................................................................................................56
1
1. Introduction
The difference in pressures within two fluid phases that are in mechanical equilibrium is defined as the capillary pressure.
When capillary pressure is described using a tube model the pore diameter d, surface tension and the contact angle between
the two fluids impact the pressure difference greatly (equation 1).
Equation 1
The capillary pressure curve allows the fluid
contacts to be determined correctly as shown in
figure 1. Capillary pressure scaling will have a
great impact on the reservoir volumes in place as
it will determine the critical water saturation,
which is the saturation at which the water in the
reservoir becomes mobile. The curve shape
depends on the pore diameter; tight reservoirs will
have higher, steeper capillary pressure curves,
resulting in an increased transition zone and less
oil in place.
The critical saturations will match those in the
relative permeability curves.
Figure 1: Relation of a single accumulation to capillary type curve (Holmes 2002)
Representative capillary pressure curves are a key to accurately predicting the process of oil recovery and describing the fluid
distribution. Capillary pressure is directly related to the Water saturation, Porosity and Permeability and whenever any of those
properties are to be honoured, the capillary pressure curves need to be scaled accordingly. Incorrect scaling of the capillary
pressure will invalidate the history match and the oil in place and may result in an un-equilibrated static model that has no
physical meaning.
This thesis concentrates on:
 Investigating the water saturation height methods and their impact on the scaling of capillary pressure,
 The scaling of capillary pressure using end points by defining the critical and connate water saturations and thirdly
 The scaling of capillary pressure based on the porosity and permeability which adjusts the water saturation values
during the scaling process.
With many water saturation height functions to choose from, each one giving different capillary pressure scaling, the question
that raises itself is which method should one use? Does it matter?
It becomes apparent from raised discussions about mobile water and transition zones that there are many opinions on how a
model should be initialized correctly in order to match water production rate as well as oil production rate.
Whilst some reservoir engineers prefer to initialize simulation models using an initial water saturation distribution, some use
critical water saturation values to define the initial saturation; and others prefer to use a J-function keyword which scales the
capillary pressure according to the porosity and permeability. It is not immediately obvious, how the choice of method will
impact results for a given model.
In this project, the different methods were investigated by initializing several model runs using:
 An initial water saturation keyword SWATINIT. The water saturation heights were calculated using four commonly
used methods and the results were compared.
 J function relationship to predict the initial water distribution. Different cases were run using different porositypermeability cross plots
 Critical water saturation SWCR set to Sw from initial SWATINIT, scaling the water relative permeability curves
2
accordingly.
The SPE Brugge benchmark model will be used to demonstrate the impact of scaling capillary pressure on the model’s
performance and output. Details of the Brugge field simulation can be found in SPE 119094. (E. Peters 2009)
Based on the results, a further attempt at recommending best industry practices is discussed.
2. Research Methods
2.1. Saturation height equations
2.1.1. J Function
In 1941, M.C. Leverett described a concept of a characteristic distribution of interfacial two-fluid curvatures with water
saturation. He described an “experimental determination of the curvature saturation relation for clean unconsolidated sand”.
(M.C.Leverette 1941).The relationship was based on the permeability and porosity of the rock sample.
Equation 2
Equation 2 is in a dimensionless form which attempts to convert all capillary pressure data, as a function of water saturation to
a universal curve. This however fails when more than one rock type is present and therefore a separate J function would have
to be used for each region.
The J function for each region can be plotted against the normal water saturation and the correlation can be described as a
power law (Adel Ibrahim 1992) in the form of:
Equation 3
Where
Equation 4
2.1.2.
Lambda function
Lambda function was introduced to represent water saturation heights in thick transition zone. The Lambda function has the
following form (Nick A. Wiltgen 2003):
Equation 5
To ensure that each region’s water saturation is distributed correctly a Lambda function can be used for each region
.
2.1.3.
Skelt and Harrison Method
This is a log based method that correlates water saturation and the free water level using four constants. This method is useful
for characterizing an extensive transition zone by applying a weighting factor based on the amount of gross rock area each data
point controls. This method works on both SCAL based capillary pressure and log based water saturation domain. (Harrison
1995)
The equation has the form below:
Equation 6
2.1.4. Johnson Method
This is a mathematical relationship between water saturation derived from standard laboratory capillary pressure
measurements and the permeability. The relationship is described bi-logarithmically as shown below. (Johnson 1992):
3
Equation 7
2.2. Simulation Model
The SPE Brugge benchmark model will be used to demonstrate the impact of scaling capillary pressure on the model’s
performance and output. It has seven regions sorted using the porosity. It has 30 producers and injectors and all producers are
drilled above the Oil Water Contact. The stock tank oil in place for the truth case is given as 775MBbl. Details of the Brugge
field simulation can be found in SPE 119094. (E.Peters 2009)
This simulation has been performed using ECLIPSE and Petrel RE
2.2.1.
Brugge Brief Description
The Brugge field is a two phase synthetic oil field, consisting of oil and water. The model consists of 64000up-scaled grid
cells. The facies are subdivided into 5 classes and the PORO-PERM characteristics are shown in (figure 2 left). The reservoir
is also split into seven regions corresponding to their porosity average. (fig 2 right)
Figure 2: left: Brugge PORO- PERM according to facies and right: Capillary Pressure curves according to regions
2.2.2.
Keyword definitions
The following simulator keywords and their definitions are of significance on this report and will be referred to throughout the
report:





EQUIL: sets the contacts and pressures for conventional hydrostatic equilibrium.
SWATINIT: Allows the input of water saturation distribution and the scaling of the water oil capillary pressure
curves such that the water distribution is honoured in the equilibrated initial solution.
SWOF: input tables of water relative permeability, oil in water relative permeability and water oil capillary pressure
as a function of water saturation
SWL: Specifies the connate water saturation. That is the smallest water saturation in a water saturation function table
(SWOF).
SWCR: Specifies the critical water saturation. That is the largest water saturation for which the water relative
permeability is zero.
3. Results
104 realizations have been run changing the porosities and permeabilities each time. 10 best cases have been chosen based on
4
the history match and the fluid in place for the purpose of analyzing the results of this report. The case discussed in the main
body of this report is case 9, the results for the other 9 cases are provided in the Appendix, Figures 19-53, showing water and
oil production rate and cumulative volume.
3.1. Equilibration
Liquid Flowrate (STB/d)
5E+04
Field Oil production rate
Observed 1
4E+04
EQUIL_BCENTERED
4E+04
3E+04
3E+04
2E+04
2E+04
1E+04
5E+03
0E+00
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06/24/03
12/14/08
06/06/14
Figure 3: initialized model using EQUIL
The Brugge field was first initialized using EQUIL
keyword. The contacts, datum depth and pressure are
specified, hydrostatic equilibrium is assumed and the phase
densities are then calculated using the equation of state for
oil which allows the hydrostatic pressure of the oil phase to
be calculated using equation 1. This is an iterative method
solved for oil phase pressure everywhere. Sw is then set by
reverse lookup of the capillary pressure curves supplied in
the SWOF table.
In Figure 3, the blue dotted line shows the simulation
results of an initialized model using the keyword EQUIL.
The phase pressures are calculated at 100 depth points
evenly distributed throughout the reservoir and water
saturation is assigned to each cell center.
Fig 3 shows that the history match obtained is good in the
first 10 years and starts to diverge in the second part. A
recovery factor of 0.212 is given for this method at the end
of the prediction period which is compared against other
methods used later on in the report. This model has been
run without any wells to check equilibrium state initially
and showed zero fluid displacement suggesting equilibrium
state.
3.2. SWATINIT
When the initial water saturation obtained from a geological model needs to be honoured, the initial distribution can be input
into the simulator using the SWATINIT keyword and the tabular capillary pressure curves given in SWOF tables are scaled
accordingly.
The capillary pressure is given by:
Equation 8
Where Pct is the capillary pressure value from the SWOF table and Pcm is the maximum capillary pressure value from the
table.
Consider a cell which has original water saturation obtained by using EQUIL of 0.4121 and a PC of 4.07Psi as shown in figure
Suppose a new water saturation of 0.3472 is specified. Pc
equals 12.38Psi by using equation 1. The maximum Pc from
the table is 26.75. Therefore:
PCW= (12.38/4.07)*26.75=81.36 Psi
Figure 4: Scaled capillary pressure using SWATINIT
This is the maximum scaled capillary pressure in that cell. If
that value has a very high magnitude then the method of the
scaling should be revised as it may be unphysical. Although
there is a keyword named PPCW which limits the maximum
capillary pressure, it has no physical meaning. An example of
this is shown in Appendix fig 59; the SWATINIT is entered as
a constant value of 0.8. The maximum scaled capillary
pressure changes from 720Psi to 30Psi. The scaled capillary
pressure curve is shown in both cases for an individual cell
5
when it is limited to 30Psi cells above the oil water contact which originally had high water saturations are now forced to have
a water saturation corresponding to 30Psi pressure. In fact by applying the PPCWMAX key word the water saturation
distribution is no longer honoured. SWATINIT affects the relative permeability curves therefore it is important to make sure
that the lowest input water saturation is higher than or equal to the critical water saturation. This issue is revisited in part 2.4 of
the report.
The next section investigates the effect of using the common four methods described earlier on the Brugge reservoir
simulation and performance.
3.2.1. Saturation height methods Simulation
The 10 selected cases were run using each of the four saturation height methods described in section 1.1 and the results are
shown in Appendix fig (23-38) and the CPU times are recorded in table 7. The results of case 9 are shown in fig 5:
Field Water production rate
METHOD
4.E+04
LAMBDA
STOIIP
Mbbl
776
JFUNCTION
760
SKELT
763
JOHNSON
783
EQUIL
774
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
J function
EQUIL
1.E+04
Johnson
2.E+04
2.E+04
1.E+04
Lambda
observed
Development strategy 1
0.E+00
0.E+00
01/01/98
3.E+04
5.E+03
Skelt and Harrison
5.E+03
3.E+04
Liquid Flowrate (STB/d)
Liquid Flowrate (STB/d)
Field Oil production rate
5.E+04
06/24/03
12/14/08
06/06/14
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06/24/03
12/14/08
06/06/14
Figure 5: oil and water production rate for all SWATINIT cases
The oil rate is worst matched by the J
function and best by the Lambda
METHOD
Rf %
function. The oil in place for all cases is
LAMBDA
0.216118
within 10% of the truth STOIIP with the
0.2
exception of Johnson which gave 13%
JFUNCTION
0.213094
difference. The Lambda function gives
SKELT
0.210435
an oil in place value of 776MBbl which
JOHNSON
0.216335
0.15
is very close to the truth case, the J
EQUIL
0.212064
function gives the minimum oil in place
value of 760MBbl and the maximum is
0.1
given by Johnson at 783MBbl, see Fig 5.
LAMBDA
JFUNC
The water breakthrough for all cases
starts at the same point, with on average
SKELT
JOHNSON
the same water cut ratio of 0.6 at the end
0.05
of the prediction period. The Skelt and
EQUIL
Harrison method gives the highest
estimate for water production. To
-8.6E-15
investigate each method further, the
01/01/98 09/27/00 06/24/03 03/20/06 12/14/08 09/10/11 06/06/14 03/02/17
recovery efficiencies have been plotted
and are shown in fig 6. All cases have
Figure 6: Oil recovery factor for all SWATINIT cases
similar recovery factors. The lowest is
0.210435 for the Skelt and Harrison method and the highest is 0.216335 for Johnson. In terms of capillary pressure scaling, the
Oil recovery efficiency
0.25
Field Oil recovery efficiency
6
maximum scaled capillary pressure PCW is given in table 1 with Lambda having the minimum PCW and Skelt and Harrison
having the maximum.
It can be seen that different saturation heights can have a big impact on the fluids
METHOD
PCW Psi
in place. Based on the results obtained, the Lambda function gave better results in
terms of fluids in place and the maximum scaled capillary pressure. Water
LAMBDA
28
saturation distributions are compared against log water saturations and showed
JFUNCTION
40
good match, the logs are compared in fig 7.
The water saturation using Lambda function in the transition zone of the well
SKELT
96
Producer 20 is checked against logs and the results are demonstrated below.
JOHNSON
30
Producer 15 is completed 55 ft above the oil water contact at a depth of 5447ft.
the well produces both oil and water initially with a water saturation of 0.6. When
EQUIL
compared to the logs the water saturation is 0.57 which is consistent.
Table 1: PCW for all Saturation height cases
BR-P-15;Tubing 1
2500
Liquid Flowrate (STB/d)
2000
1500
Water production rate
(STB/d) lambda
1000
Water production rate
(STB/d) Development
strategy 1
Oil production rate (STB/d)
lambda
500
Oil production rate (STB/d)
Development strategy 1
0
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12/14/08
06/06/14
Sw Lambda=0.6
Sw logs=0.57
Figure 7: Water Saturation in the transition zone
All SWATINIT methods have been tested with no wells and the results showed that they are all in equilibrium. SWATINIT is
a reliable method for scaling capillary pressure provided the water saturation is appropriately calculated. Of course like any
other simulation keyword, SWATINIT has its limitations which include:
 Resetting the water saturation to the maximum value when it cannot be honoured due to being located below the oil
water contact.
 If SWATINIT is below the connate value, the capillary pressure is left unscaled
3.3. JFUNC Keyword simulation
The Brugge field was equilibrated using the JFUNC key word which scales the capillary pressure curves based on the porosity
and permeability of each cell. Given below is the equation that ECLIPSE uses to perform the scaling:
Equation 9
The scaling factor is taken as:
7
Equation 10
The scaling factor can be output and checked for any unphysical values. The results of using JFUNC in comparison to the
cases discussed above are shown in figure 8
4.E+04
Field Oil production rate
Field Oil recovery efficiency
0.25
Oil recovery efficiency
4.E+04
Liquid Flowrate (STB/d)
3.E+04
3.E+04
0.15
2.E+04
2.E+04
1.E+04
5.E+03
0.2
Equil
Jfunc
Johnson
Skelt Harrison
LAmbda
Jfunction
Development
strategy 1
observed
0.1
JFUNC
Johnson
Skelt and Harrison
0.05
0.E+00
Lambda
Jfunction
0
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01/01/98 06/24/03 12/14/08 06/06/14
Figure 8: Impact of using JFUNC keyword on the oil production rate and the recovery
The JFUNC key word was found to greatly underestimate the original oil in place giving a value of 557 MBbl and a recovery
factor of 0.17 as opposed to the average of 0.2 that was obtained by using different methods. Consequently the history is
mismatched. The water breaks through drastically earlier than any other method at a very high rate. The watercut is estimated
at an initial value of 0.7(fig9) and oil water contact is shifted up.
0.9
Field Water cut
4.E+04
Field Oil recovery efficiency
0.7
Oil recovery efficiency
Liquid To Liquid Ratio
(STB/STB)
0.8
3.E+04
0.6
0.5
2.E+04
0.4
0.3
0.2
0.1
Equil
JFUNC
Johnson
Skelt and Harrison
Lambda
J function
Observed 1
0
1.E+04
0.E+00
01/01/98 06/24/03 12/14/08 06/06/14
EQUIL
JFUNC
Johnson
Skelt and Harrison
Lambda
Jfunction
Observed 1
JFUNC
01/01/98 06/24/03 12/14/08 06/06/14
Figure 9: Impact of using JFUNC keyword on the water production
The shift in the oil water contact causes most cells near the bottom of the reservoir to become fully saturated with water,
therefore decreasing oil production. The result for Producer 15 with JFUNC is shown in fig 10. It can be seen that the well has
more water initially and so produces less oil than expected. For the completion cell at a depth of 5447ft the water saturation is
1.0 which no longer agrees with the logs.
8
Liquid Flowrate (STB/d)
3E+03
BR-P-15;Tubing 1
2E+03
2E+03
1E+03
Oil Production
rate_JFUNC
Oil production rate
(STB/d) Observed 1
Water Production
rate_JFUNC
5E+02
Water production rate
(STB/d) Observed 1
0E+00
01/01/98 06/24/03 12/14/08 06/06/14
Sw JFUNC=1
Sw logs=0.57
Figure 10: water production in transition zone using JFUNC keyword
Figure 11: Scaling capillary pressure using JFUNC
The maximum scaling factor reported by ECLIPSE is stated as
187.511 at cell 16,21,1. When this scaling factor is applied to
the original capillary pressure the new scaled capillary curve
now gives a maximum value of 5000Psi as shown in fig 11 and
the cell now becomes fully saturated with water to account for
the new capillary pressure curve.
In summary it has been found that the JFUNC keyword
underestimates the oil in place by over scaling the capillary
pressure. JFUNC keyword differs from the Leverett J function
discussed earlier; the porosity and permeability are the reservoir
cell values and are not averaged. With the presence of
heterogeneity, grid cells are assigned a wide range of porosity
and permeability which give different results to the J function
method described in Section 3.2.1. In the next section of the
report the JFUNC keyword will be investigated further using a
simple model.
A simple 20×14×10 model was used to investigate the capillary pressure scaling using JFUNC. From equation 9 and 10, the
scaling is done based on the porosity and permeability of each grid cell. Different cases were run using different porosity
permeability relationships:
 Homogeneous reservoir with a porosity of 0.5 and a permeability of a)5000mD, b)500mD, c)50mD, d)5mD
 Homogeneous reservoir with a porosity of 1 and a permeability of 1mD
 A constant 0.0001, 0.001, 0.01, and 1 unit slope PORO-PERM relationship.
 A constant negative slope PORO-PERM relationship.
 Layered reservoir based on the PORO-PERM relationship used in Brugge.
3.3.1. Simple model results
A homogeneous case with a porosity of 0.5, permeability of 5000mD and surface tension value of 26 dynes/cm gives a JFUNC
scaling factor:
9
This is the multiplier that is applied to the capillary pressure values in the SWOF table. The water saturations are slightly
higher in each cell and the top of the transition zone is shifted up by one layer. Table 2shows the initial water distribution with
the JFUNC switch on and off. The critical water saturation is 0.252. From the table it is clear that the water is mobile at a
higher level in the reservoir with JFUNC activated. When the ratio of porosity and permeability becomes larger the scaling
factor increases and therefore the scaled capillary pressure increases, increasing the initial water saturation distribution. When
the ratio is 0.01, the oil water contact shifts up by one layer, when the ratio is 0.1 it shifts up by 3 layers and when the ratio is 1
the reservoir becomes fully saturated with water, in comparison to the original distribution based on the relative permeability
curves as shown in table 2. Constant slopes of 0.0001, 0.001, 0.01, 0.1, and 1 give the same ratios of porosity/permeability at
each grid cell as those gained from the homogeneous reservoirs.
0.001
0.01
0.1
1
LAYERE
D
0.2521
0.2521
0.2524
0.2539
0.2555
0.2629
0.308
0.7508
0.7752
Sw
JFUNCON
0.2521
0.2521
0.2521
0.2528
0.2544
0.2596
0.2948
0.7274
0.7752
Sw
JFUNCON
0.2857
0.2935
0.3027
0.319
0.3457
0.3936
0.5008
0.8125
1
Sw
JFUNCON
0.4672
0.5167
0.5865
0.6914
0.8586
0.981
1
1
1
Sw
JFUNCON
1
1
1
1
1
1
1
1
1
Sw
JFUNCON
0.252
0.252
0.252
0.252
0.252
0.2568
0.2859
0.4941
1
AVG
LARYERE
D
Sw
JFUNCON
0.252
0.252
0.252
0.252
0.252
0.252
0.252
0.252
0.252
1
1
1
1
1
1
1
Sw OFF
Table 2: Water saturation distribution using JFUNC
NEGATIVE
PHI/PERM
Rf- JFUNC
ON
Rf- JFUNC
OFF
% diff
Sw
JFUNC-ON
0.00010
0.05100
0.05100
0.00000
0.00100
0.03900
0.04100
4.87805
0.01000
0.01100
0.01700
35.29412
0.10000
0.00025
0.00200
87.50000
1.00000
0.00000
0.00060
100.00000
NEGATIVE
0.00420
0.00480
12.50000
LAYERED
0.00700
0.00780
10.25641
AVERAGE
LAYERED
0.07800
0.08000
2.50000
0.9907
0.3240
0.3002
0.2935
0.2924
0.2955
0.3061
0.3434
0.6638
1
Table 3: Effect of using JFUNC on the recovery factor
The oil production rate when the JFUNC is switched on decreases for each case and the water production increases with the
same water breakthrough. The oil and water production rates for each case are shown in appendix (59-84). The oil recovery
efficiency consistently decreases as the ratio increases, the recovery factors are plotted for all cases in table 3
A negative PORO-PERM relationship of the form
implied that the square root of /K is different for
each grid cell. The scaled capillary pressure is therefore different for each grid cell depending on the scaling factor; maximum
is 73Psi and min is 0.771Psi. In this case use of the JFUNC keyword has less impact on the oil rate.
Figure 12 shows cell (10,1,5) which has a porosity of
0.5959 and a permeability of 404.0510mD, the scaling
factor is taken as:
The new scaled PC at the critical water saturation would be:
4.61*26.75=123.31Psi as seen in fig 12. This confirms that
the JFUNC key word is performing the scaling as expected.
Figure 12: scaled capillary pressure for cell (10, 1, 5)
10
So far a simple linear relationship has been used to describe the relationship between porosity and permeability. It is common
practice to use a PORO-PERM relationship that is described by a log relationship.
A layered reservoir has been tested with the JFUNC using a PORO-PERM
PERM
POR
maximum
relationship of the following form:
capillary pressure
1.8152
9.1427
46.0492
231.936
1168.19
5883.81
29634.9
14926
751787
3.78E+06
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
530.97
334.59
182.59
93.94
46.80
22.84
10.99
16.56
2.47
1.16
Table 4: PCW values for JFUNC based on a
PORO-PERM
The porosities and permeabilities used for each layer are outlined in table. As
discussed earlier each layer will have a corresponding ratio of
/K and
therefore a different scaling factor. Table 4 shows the maximum capillary
pressure values for each layer, which vary between 1.16 and 530.97. The
production rate is underestimated using JFUNC and the water production is
consistently overestimated in each case (see Appendix fig 60-91)
An average value of porosity and permeability was used which gave an
unreliable scaling with High CPU time and convergence problems see fig8889-Appendix.
From the results discussed above, using a JFUNC keyword causes the volume of hydrocarbon in place to decrease as the ratio
of porosity and permeability increases. The recovery factor is defined as the volume of oil produced/volume of oil initially in
place. So why does the recovery factor vary when the JFUNC is used? Capillary pressure is scaled up and the corresponding
water saturation value increases. This results in much higher mobility for water, reduced mobility for the oil and higher water
cut at the production wells.
3.4. Initial water distribution using SWCR and SWL
Initial water distribution can be defined using SWL specifying the connate water saturation for each cell and the SWCR
specifying the critical water saturation for each cell. The relative permeability/capillary pressures are then scaled accordingly.
A common problem that reservoir engineers face when initializing a model is the control of water breakthrough in transition
zones. In most cases where a well has been completed above the oil water contact water free production is expected for the
early production period. In many cases the SWCR/SWL keywords are used to scale Kr curves to achieve the expected
behavior.
In order to control water movement in the transition zone, SWCR is set to the initial water saturation distribution. Water
saturation is described using the equation:
Equation 11
Setting SWCR to the initial water implies that the reservoir has no dynamic range and the water is immobile.
Several cases have been run to investigate the impact on controlling the water breakthrough using such keywords and weather
the stability of the model is affected. The CPU time is recorded and compared for all cases and the equilibrium state is
investigated.
Cases Performed include:
1. SWL=SWCR=SWATINIT array
2. SWL=SWCR+0.01=SWATINIT array
3. SWL=SWCR=SWATINIT, PC=0
4. a)SWL=Sw randomly distributed=SWATINIT b)SWATINIT=Sw randomly distributed
When SWCR is set to the initial water distribution, there are conditions that should be satisfied for the simulation to run:
SWCR≥SWL for each grid cell, critical oil saturation (1-SW) ≤critical oil saturation from SWOF table, and no major
convergence problems present.
Setting SWL=SWCR=SWATINIT meant that some cells have a water saturation of 1, causing a consistency problem with the
oil phase end points in some grid cells, as the critical oil saturation is greater than zero.. This also causes simulation
convergence problems. When the model was checked by running with no wells for thirty days, fluids were displaced, showing
that it was not initially in equilibrium. Fig15 shows the oil production rate match which was far from the observed data.
In the following case, the highest critical water saturation is 0.252, therefore the SWL=SWCR has been clipped to a value of
0.74 so that the maximum oil phase end point of 1-0.252 is taken into account. This gives a STOIIP of 775MBbl. Although
this has prevented inconsistencies, there were still some convergence problems.
11
Fig 14 shows the scaling for cell (61,1,9). The initial
SWCR on the Krw curve is 0.3, but is now scaled to 0.74.,
As this value also corresponds to the connate water
saturation, the water is never mobile. Fig 15 shows the oil
and water production profiles in comparison to the
observed data. Although the water breakthrough was
delayed, it matched the oil production profile for the first
year giving water free oil production and producing water
one year later than expected. The water production is then
greatly underestimated as shown in fig 15. , the oil
production rate is overestimated and the production history
is mismatched in comparison to Lambda function.
Figure 13: Relative permeability curve scaling using SWCR/SWL
45000
Field Oil production rate
30000
Field Water production rate
25000
35000
30000
20000
25000
15000
20000
15000
10000
10000
SWL=SWCR=SWATINIT capped at 0.74
Lambda
5000
Observed 1
0
01/01/98
Liquid Flowrate (STB/d)
Liquid Flowrate (STB/d)
40000
SWL=SWCR=SWATINIT
capped ot 0.74
Lambda
5000
Observed 1
0
06/24/03
12/14/08
06/06/14
01/01/98 06/24/03 12/14/08 06/06/14
Figure 14: comparison of water and oil production profile using SWATINIT and SWL/SWCR
Producer 13 is completed 66.78ft above the oil water contact, fig 16 shows the water production flow rate for that well using
both Lambda function and SWCR=SWL=SWATINIT cases. Both cases gain initial water free oil production, but Lambda
matches the oil production better after 2 years. The water cut is also better matched using Lambda function as shown in fig 16.
In this case, using capillary pressure scaling to obtain a representative input saturation distribution gives a better water
production rate match than when the SWCR and SWL are specified as the initialized water saturation array. Cases that
overestimate the water production rate in the transition zone are likely to be due to unrepresentative parameters applied in the
initial water saturation distribution such as porosity and permeability values.
12
0.7
3000
Field Water cut
0.6
BR-P-13;Tubing 1 Water
production rate
SWL=SWCR=SWATIN
IT capped at 0.74
Lambda
Liquid Flowrate (STB/d)
Liquid To Liquid Ratio
(STB/STB)
2500
0.5
Observed 1
2000
0.4
1500
0.3
1000
0.2
SWL=SWCR=SWATINIT
capped at 0.74
Lambda
0.1
500
Observed 1
0
0
01/01/98
06/24/03
12/14/08
06/06/14
01/01/98 06/24/03 12/14/08 06/06/14
Figure 15: water production in the transition zone using SWL/SWCR
Case SWATINIT=SWCR=SWL took longer than the Lambda function but was still in equilibrium. The recovery efficiency of
case 1 and Lambda case are 23% and 21% respectively.
When SWL=SWCR+0.1=SWATINIT clipped to a maximum value of 0.74 was run, the results were exactly the same as the
previous case but the run took less time to converge. The CPU time is recorded for each case in table 8 in the appendix
Finally, Case 3 was run to demonstrate the effect of ignoring the capillary pressure completely.
45000
30000
Field Oil production rate
Field Water production rate
40000
25000
30000
20000
25000
Liquid Flowrate (STB/d)
Liquid Flowrate (STB/d)
35000
15000
20000
15000
10000
5000
10000
SWL=SWCR=SWATINIT
capped at 0.74
Lambda
Observed 1
0
SWL=SWCR=SWATINIT
capped at 0.74
Lambda
5000
Observed 1
SWL=SWCR=SWATINI_0
Pc
0
01/01/98 06/24/03 12/14/08 06/06/14
1/1/98
6/24/03 12/14/08
6/6/14
Figure 16: Effect of ignoring capillary pressure
The oil production rate with no PC values shown in pink (fig 17) is overestimated and the water production consequently is
underestimated. The oil in place is estimated as 890MBbl compared to the 775MBbl found when the Pc is accounted for.
When comparing this to the truth STOIIP there is an error of 13%, with the same recovery factor.
13
45000
Field Oil production rate
50000
Field Water production rate
Observed 1
45000
ransom SWATINIT
distribution
35000
random
SWCR=SWL=SWATINI
T distribution
30000
40000
Liquid Flowrate (STB/d)
Liquid Flowrate (STB/d)
40000
35000
30000
25000
25000
20000
20000
15000
15000
10000
5000
5000
0
1/1/98
Observed 1
10000
SWATINIT random
distribution
SWL=SWCR=SWATINIT
random distribution
0
6/24/03
12/14/08
6/6/14
01/01/98 06/24/03 12/14/08 06/06/14
Figure 17: random water distribution using SWATINIT and SWCR/SWL
Case 4 was run using randomly distributed water saturation. Running a simulation model using case 4 a) with
SWL=SWCR=SWATINIT gives an oil volume of place of 553MBbl and case 4b) with SWATINIT only, gives oil in place of
547MBbl. From fig 18 the green line shows the match using case 4a and the red line using case 4b. Both had convergence
problems and while using SWCR and SWL can better match the oil rate history and delay the water breakthrough, it matches it
by using unphysical water saturation distribution that is not related to the original reservoir data.
14
4. Discussion
The problem of initializing a simulation model using a representative water saturation distribution is becoming widely
recognized. The Middle East has two thirds of all recoverable oil in the world. With most Middle Eastern reservoirs being
largely extensive carbonates and low permeable sandstone, the capillary pressure plays an important role in water saturation
modeling. Shehadeh (Shehadeh K. Masalmeh 2000) attempts to describe the mobility of oil in the transition zone and relates it
to the initial oil saturation distribution. It is found that as the initial oil saturation gets close to the residual, the mobility
increases. This implies that the mobility of oil in the transition zone is possibly higher than anywhere else in the reservoir. This
paper however did not explain how the saturations can be estimated accurately and utilized in the computer model. Many
papers have been published on the water saturation heights and their impact on the hydrocarbon in place such as Harrison
(B.Harrison 2001) and Wiltgen (Nick A. Wiltgen 2003) which compares the saturation heights predicted water saturations
against the log water saturations. Harrison (B.Harrison 2001)predicts that Cuddy’s log based method is the simplest most
effective method to use; Wiltgen (Nick A. Wiltgen 2003) concludes that the Skelt and Harrison method gave the best result
and using this project as an example, Lambda function gave the best estimates. Whilst all these findings may be contradictory,
it shows that each oil field is different, with many different reservoir features and behavior. This project therefore highlights
the differences in using those methods and does not necessarily recommend a specific method to be used. Those papers
mentioned investigate the best method to be used in terms of matching the logs water saturation, none of them however look at
the effects of scaling capillary pressure using the methods described and implementing them in the simulator which this
project does using the SWATINIT keyword.
Al Junaibi (Faisal Al Jenaibi 2008) addresses the importance of using dynamic rock typing where the reservoir is split into
regions according to the irreducible water saturation taken from logs and an equation relating the FWL to the irreducible water
saturation using two constants. The log water saturation vs. height above free water level sometimes gives a very weak
correlation and so correlation using porosity and permeability may be a better option as some of the water saturation height
methods provide.
Rojas (Rojas 2010) describes the application of J-Function to prepare a consistent tight gas reservoir simulation model. This
paper proposes inputting a J function keyword which calculates Sw according to the porosity and permeability. The conclusion
of this paper is that the “J function technique has proven to be a very powerful tool to accurately to distribute fluids in a tight
gas reservoir” it is claimed that the technique honours the capillary forces, permeability and porosity and shows that the
volume in place is representative providing a good history match. This is an interesting finding which is different from the
outcome of using JFUNC keyword in this report. This again could be due to a difference in the reservoir but could also be an
interesting area of further investigation. It could be that the JFUNC works better for gas than oil reservoirs.
Eigstead (Geir Terje Eigestd 2000) Investigates the capillary pressure in the transition zones using a hysteresis model but did
not apply it to a case where a match could be compared in a layered reservoir. Hysteresis is an important aspect of the fluid
distribution in the transition zone. In this project like many others only drainage is taken into account and the simulation is
performed accordingly. The discussion raised recently in the SPE TIG (SPE 2011) clearly reflects the many different opinions
about initializing models, to correctly describe an initial water distribution that best predicts later fluid production. The type of
problem that many engineers face is when water breakthrough occurs after a few months, with no evidence from relative
permeability curves or logs to explain what is happening. In the discussion it was suggested that, by setting the critical water
saturation and the connate water saturation equal to the initial water saturation distribution given by the geologist, the
simulation would be initialized correctly. However this approach does not generally give representative dynamic behavior and
the match is not accurate as seen in the previous section 3.4.
5. Conclusion
The case study using the SPE Brugge model demonstrates how the choice of capillary pressure model can significantly affect
the simulation results. The use of a simplified test example can help to explain how the different simulation options work.
The main findings of this project include:
 Representative capillary pressure curves are a key to accurately predicting the process of oil recovery and describing
the fluid distribution
 Based on the results obtained, the Lambda function gave a better match to the Brugge case in terms of fluids in place
and the maximum scaled capillary pressure
 The JFUNC keyword results in different scaling for every grid cell and causes the volume of fluids in place to
decrease as the ratio of porosity and permeability increases
 Setting SWCR=SWL=SWATINIT causes consistency errors, and even when limited to a maximum critical
saturation, convergence problems persist, dynamic behavior is restricted and the oil rate is overestimated
6. Recommendation
It is recommended that the approach taken in this report is followed and sensitivity analysis is performed on the capillary
pressure as well as other parameters when a good history match is required. This work could be further developed when a
three phase model is present; investigating the effectiveness of the keywords when a gas cap is present. This report
concentrated on drainage only and so further work on the effect of hysteresis could be done.
15
Nomenclature
Symbol
Description
Units
A,B,C and D
Regression Constants
None
J
J function
Dimensionless
K
Permeability
mD
Pc
Capillary Pressure
Psi
Pcm
Maximum Capillary pressure from SWOF table
Psi
Pct
Capillary Pressure from SWOF table
Psi
PCW
Maximum Scaled Capillary Pressure
Psi
PCOW
Simulator Oil Water Capillary Pressure
Psi
Sw
Water Saturation
None
Swirr
Irreducible Water Saturation
None
Swn
Normalized Water Saturation
None
a, b and c
Constants
None
d
Pore Diameter
Ft
g
Gravity acceleration
Ft2/sec
h
Height above free water level
Ft
λ
Regression constant
None
φ
Porosity
None
Density of oil
Lb/ft3
Density of water
Lb/ft3
Contact angle
degrees
θ
16
7. References
Cuddy, Steve. "A SImple Convincing Model For Calculating Water Saturations In Southern North Sea Gas Fields." SPWLA
34th Annual Logging Sypnosium, 1993.
A Rojas, ConcoPhillips. "Application of J-Function to Prepare a Consistent Tight Gas Reservoir Simulation Model: Bossier
Field." SPE138412, 2010.
Adel Ibrahim, Zaki Bassiouni, and Robert Desbrandes. "Determination of Relative Permeability Curves in Tight Gas Sands
using Log Data." SPWLA 33rd Annual Logging Symposium, 1992.
B.Harrison, X.D.Jing. "Saturation Height Methods and Their Impact on Volumetric Hydrocarbon in Place Estimates."
SPE71326, 2001.
E. Peters, R.J. Arts, and G.K.Brouwer and C.R.Geel. "Results of the Brugge Benchmark Study for Flooding Optimization and
History matching." SPE 119094, 2009.
E.Peters, TNO. "Results of the Brugge Benchmark Study for Flooding Optimization and History Matching." SPE119094,
2009.
Faisal Al Jenaibi, Khalid Hammadi, Lutfi Salameh, Abu Dhabi National Oil Company. "New Methodology for Optimized
Field Development Plan, Why Do We Need TO Introduce Dynamic Rock Typing." SPE 117894, 2008.
Geir Terje Eigestd, University of Bergen, Norway and Johne Alex Larsen, Norsk Hydro Research Center, Norway.
"Numerical Modelling of Capillary Tranzition Zone." SPE64374, 2000.
Harrison, Christopher Skelt and Bob. "An Integrated Approach to Saturation Height Analysis." SPWLA 36th annual Logging
Sypnosium, 1995.
Holmes, Michael. "Capillary Pressure & Relative Permeability Petrophysical Reservoir Models." Digital Formation. May
2002. http://www.digitalformation.com/Documents/CPRP.pdf (accessed 07 2011).
Johnson, A. "Permeability Averaged Capillary Data." SPWLA 28th Annual Logging Symposium, 1992.
M.C.Leverette. "Capillary Behaviour in Porous Solids." Transaction of the AIME(142), 1941.
Nick A. Wiltgen, Joel Le Calvez, and Keith Owen, Schlumberger. "Methods Of Saturation Modelling Using Capillary
Pressure Averaging and Pseudos." SPWLA 44th Annual Logging Symposium, 2003.
Shehadeh K. Masalmeh, Shell Technology Exploration and Production Rijswik, The Netherlands. "High Oil Recoveriesfrom
tranzition zones." SPE 87291, 2000.
SPE. Reservoir Simulation Discussion Forum/ Mobile Water and tranzition
http://communities.spe.org/TIGS/SIM/Lists/Team%20Discussion (accessed 06 28, 2011).
zones.
06
28,
2011.
Y.Wang, SPE,Schlumberger, and Petronas and M.Z.Sakdilah M.Bandal. "Asystematc Approch to incorporate Capillary
Pressure Saturation Data into Reservoir Simulation." SPE101013, 2006.
17
Appendix
SPE/SPWLA
No
Year
Title
Authors
Conclusions
SPE 941152
1941
Capillary behavior in
Porous Solids
M.C.Leverett
Multiple curves can be converted into
a single universal curve using the J
function.
SPE 5126
1975
The Effect of Capillary
Pressure in a Multilayer
Model of Porous Media
R.G.Hawthorne
Equations developed to describe
immiscible fluid displacement in a
multichannel model when capillary
pressure affects the crossflow between
channels.
SPE 8234
1981
A Simple Correlation
Between Permeabilities and
Mercury Capillary
Pressures
B.F Swanson
Direct
measurement
of
brine
permeability of clean sands from
capillary pressure plot data. New
correlation is developed to improve
measurements on drill cuttings and
sidewall core samples
SPWLA 28th
1987
Permeability averaged
Capillary Data
A Johnson
Log Sw=AlogK+B. permeability
averaged capillary analysis. Does not
rely on any profound theoretical basis.
SPWLA 36th
1995
An integrated approach to
saturation height analysis
Christopher Skelt and
Bob Harrison
Added a weighting function to give a
better fit to capillary pressure data
SPWLA 44th
2003
Methods Of Saturation
Modelling using capillary
pressure Averaging and
Pseudos
Nick.AWiltgen, Joel le
Calvez and Keith Owen
Lambda function similar to Skelt and
Harrison and Leverett is used to fit
capillary pressure data by applying a
constant called λ.
18
EQUIL
Field Oil production rate
5.E+04
4.E+04
Liquid Flowrate (STB/d)
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
Observed 1
Case9-EQUIL
Case49-EQUIL
Case91-EQUIL
case 2-EQUIL
Case40-EQUIL
Case80-EQUIL
Case1-EQUIL
Case11-EQUIL
Case84-EUIL
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 18: 10 best cases showing the field oil production rate using EQUIL with case 9 giving the closest match
Field Water production rate
3.E+04
Liquid Flowrate (STB/d)
3.E+04
2.E+04
2.E+04
1.E+04
Case2-EQUIL
Case40-EQUIL
Case80-EQUIL
Observed 1
5.E+03
Case1-EQUIL
Case11-EQUIL
Case84-EQUIL
Case9-EQUIL
Case49-EQUIL
Case91-EQUIL
0.E+00
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 19:10 best cases showing the field water production rate using EQUIL with case 9 giving the closest match
19
Field Oil production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
2.E+08
1.E+08
1.E+08
1.E+08
8.E+07
6.E+07
Case2-EQUIL
Case9-EQUIL
Case11-EQUIL
Case80-EQUIL
Case91-EQUIL
4.E+07
2.E+07
Case1-EQUIL
Case40-EQUIL
Case49-EQUIL
Case84-EQUIL
Observed 1
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 20: 10 best cases showing the field oil cumulative production using EQUIL with case 9 giving the closest match
Field Water production cumulative
1.E+08
Liquid Production Volume (STB)
1.E+08
8.E+07
Case2-EQUIL
Case1-EQUIL
Case9-EQUIL
Case40-EQUIL
Case11-EQUIL
Case49-EQUIL
Case80-EQUIL
Case84-EQUIL
Case91-EQUIL
Observed 1
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 21: 10 best cases showing the field water cumulative production using EQUIL with case 9 giving the closest match
20
SWATINIT
1. J-Function
Field Oil production rate
5.E+04
4.E+04
Liquid Flowrate (STB/d)
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
Observed 1
91-JFunction
80-JFunction
40-JFunction
11-JFunction
9-JFunction
49-JFunction
0.E+00
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 22:10 best cases showing oil production rate using SWATINIT, J function water distribution
Field Water production rate
3.E+04
Liquid Flowrate (STB/d)
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
Observed 1
49-JFUnction
9-JFunction
91-JFunction
40-JFunction
80-JFunction
11-JFUnction
0.E+00
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 23:10 best cases showing field water production rate using STAWTINIT, J function water distribution
21
Field Oil production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
2.E+08
1.E+08
1.E+08
1.E+08
8.E+07
6.E+07
Observed 1
Case80-JFunction
Case40-JFunction
Case9-JFunction
4.E+07
2.E+07
Case91-JFunction
Case49-Jfunction
Case11-JFunction
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 24:10 best cases showing oil cumulative production using SWATINIT, J function water distribution
Field Water production cumulative
Liquid Production Volume (STB)
1.E+08
1.E+08
8.E+07
Observed 1
Case91-JFunction
Case80-Jfunction
Case49-JFunction
Case40-JFunction
Case11-Jfunction
Case9-Jfunction
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 25:10 best cases showing water cumulative production using SWATINIT, J function water distribution
22
2.
Skelt and Harrison
Field Oil production rate
Observed 1
Case9-Skelt and Harrison
Case2-Skelt and Harrison
Case11-Skelt and Harrison
Case40-Skelt and Harrison
Case49-Skelt and Harrison
Case80-Skelt and Harrison
Case84-Skelt and Harrison
Case91-Skelt and Harrison
Case1-Skelt and Harrison
5.E+04
Liquid Flowrate (STB/d)
4.E+04
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
0.E+00
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 26: 10 best cases of oil production rate using SWATINIT, Skelt and Harrison saturation distribution
Field Water production rate
30000
Liquid Flowrate (STB/d)
25000
20000
15000
Observed 1
Case9-Skelt and Harrison
Case2-Skelt and Harrison
Case11-Skelt and Harrison
Case40-Skelt and Harrison
Case49-Skelt and Harrison
Case80-Skelt and Harrison
Case84-Skelt and Harrison
Case91-Skelt and Harrison
Case1-Skelt and Harrison
10000
5000
0
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 27: 10 best cases for water production rate using SWATINIT, Skelt and Harrison water saturation distribution
23
Field Oil production cumulative
Liquid Production Volume (STB)
2.E+08
2.E+08
2.E+08
1.E+08
1.E+08
1.E+08
Observed 1
Case9-Skelt and Harrison
Case2-Skelt and Harrison
Case11-Skelt and Harrison
Case40-Skelt and Harrison
Case49-Skelt and Harrison
Case80-Skelt and Harrison
Case84-Skelt and Harrison
Case91-Skelt and Harrison
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 28: 10 best cases showing oil production cumulative using SWATINIT, Skelt and Harrison water saturation
distribution
Field Water production cumulative
1.E+08
Liquid Production Volume (STB)
1.E+08
1.E+08
8.E+07
6.E+07
Observed 1
Case9-Skelt and Harrison
Case2-Skelt and Harrison
Case11-Skelt and Harrison
Case40-Skelt and Harrison
Case49-Skelt and Harrison
Case80-Skelt and Harrison
Case84-Skelt and Harrison
Case91-Skelt and Harrison
Case1-Skelt and Harrison
4.E+07
2.E+07
0.E+00
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 29: 10 best cases showing water production cumulative using SWATINIT, Skelt and Harrison water saturation
distribution
24
3.
Lambda
Field Oil production rate
5.E+04
4.E+04
Liquid Flowrate (STB/d)
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
Observed 1
Case9-Lambda
Case2-Lambda
Case11-Lambda
Case40-Lambda
Case49-Lambda
Case80-Lambda
Case84-Lambda
Case91-lambda
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 31: 10 best cases showing oil production rate using SWATINIT, Lambda water saturation distribution
Field Water production rate
3.E+04
3.E+04
Liquid Flowrate (STB/d)
2.E+04
2.E+04
1.E+04
Observed 1
Case9-Lambda
Case40-Lambda
Case80-Lambda
Case91-Lambda
5.E+03
0.E+00
01/01/98
27/09/00
24/06/03
20/03/06
14/12/08
Case2-Lambda
Case11-Lambda
Case49-Lambda
Case84-Lambda
10/09/11
06/06/14
02/03/17
Figure 30: 10 best cases showing water production rate using SWATINIT, Lambda water saturation distribution
25
Field Oil production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
2.E+08
1.E+08
Observed 1
Case2-Lambda
Case9-Lambda
Case11-Lambda
Case40-Lambda
Case49-Lambda
Case80-Lambda
Case84-Lambda
Case91-Lambda
1.E+08
1.E+08
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 32: 10 best cases showing oil production cumulative using SWATINIT, Lambda water saturation distribution
Field Water production cumulative
1.E+08
Liquid Production Volume (STB)
1.E+08
8.E+07
Observed 1
Case1-Lambda
Case9-Lambda
Case11-Lambda
Case40-Lambda
Case49-Lambda
Case80-Lambda
Case84-Lambda
Case91-Lambda
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 33: 10 best cases showing water production cumulative using SWATINIT, Lambda water saturation distribution
26
4.
Johnson Method
Field Oil production rate
5.E+04
Liquid Flowrate (STB/d)
4.E+04
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
Observed 1
Case9-Johnson
Case49-Johnson
Case91-Johnson
Case2-johnson
Case11-Johnson
Case80-Johnson
Case1-Johnson
Case40-Johnson
Case84-Johnson
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 34: 10 best cases showing oil production rate using SWATINIT, Johnson water saturation distribution
Field Water production rate
3.0E+04
Liquid Flowrate (STB/d)
2.5E+04
2.0E+04
1.5E+04
1.0E+04
Observed 1
Case1-Johnson
Case11-Johnson
Case49-Johnson
Case84-Johnson
5.0E+03
Case2-Johnson
Case9-Johnson
Case40-Johnson
Case80-Johnson
Case91-Johnson
0.0E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 35: 10 best cases showing water production rate using SWATINIT, Johnson water saturation distribution
27
Field Oil production cumulative
2.E+08
2.E+08
Liquid Production Volume (STB)
2.E+08
1.E+08
1.E+08
1.E+08
8.E+07
6.E+07
Observed 1
Case1-Johnson
Case11-Johnson
Case49-Johnson
Case84-Johnson
4.E+07
2.E+07
Case2-Johnson
Case9-Johnson
Case40-Johnson
Case80-Johnson
Case91-Johnson
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 36: 10 best cases showing oil production cumulative using SWATINIT, Johnson water saturation distribution
Liquid Production Volume (STB)
1.E+08
1.E+08
Field Water production cumulative
Observed 1
Case1-Johnson
Case11-Johnson
Case49-Johnson
Case84-Johnson
Case2-Johnson
Case9-Johnson
Case40-Johnson
Case80-Johnson
Case91-Johnson
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 37: 10 best cases showing oil production cumulative using SWATINIT, Johnson water saturation distribution
28
5.
JFUNCTION case
Field Oil production rate
5.E+04
4.E+04
Liquid Flowrate (STB/d)
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
Observed 1
JFUNC case9
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 38: 10 best cases showing oil production rate using JFUNC water saturation distribution
Field Water production rate
4.E+04
Liquid Flowrate (STB/d)
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
Observed 1
5.E+03
JFUNC-Case9
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
Figure 39: 10 best cases showing water production rate using JFUNC water saturation distribution
3/2/17
29
Field Oil production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
2.E+08
1.E+08
1.E+08
1.E+08
8.E+07
6.E+07
4.E+07
Observed 1
2.E+07
JFUNC-Case9
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 40: 10 best cases showing oil production cumulative using JFUNC water saturation distribution
Field Water production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
1.E+08
Observed 1
JFUNC-Case9
1.E+08
1.E+08
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
Figure 41: 10 best cases showing water production rate using JFUNC water saturation distribution
3/2/17
30
6.
SWL=SWCR=Capped at 0.74
Field Oil production rate
5.E+04
4.E+04
Liquid Flowrate (STB/d)
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
Observed 1
1.E+04
SWL=SWCR=0.74Capp
5.E+03
0.E+00
01/01/98
27/09/00
24/06/03
20/03/06
14/12/08
10/09/11
06/06/14
02/03/17
Figure 42: best cases showing oil production rate using SWATINIT=SWL=SWCR
Field Water production rate
3.E+04
Liquid Flowrate (STB/d)
2.E+04
2.E+04
1.E+04
Observed 1
SWL=SWCR=0.74capp
5.E+03
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
Figure 43: best cases showing water production rate using SWATINIT=SWL=SWCR
6/6/14
3/2/17
31
Field Oil production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
2.E+08
1.E+08
1.E+08
1.E+08
8.E+07
6.E+07
Observed 1
4.E+07
SWL=SWCR=0.74capp
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
6/6/14
3/2/17
Figure 44: best cases showing oil production cumulative using SWATINIT=SWL=SWCR
Field Water production cumulative
Liquid Production Volume (STB)
1.E+08
1.E+08
Observed 1
SWL=SWCR=0.74capp
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
Figure 45: best cases showing water production cumulative using SWATINIT=SWL=SWCR
32
7.
SWL=SWCR=SWATINIT 0PC
8.
Field Oil production rate
5.E+04
4.E+04
Liquid Flowrate (STB/d)
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
Observed 1
1.E+04
SWL=SWCR=SWATINIT-0Pc
5.E+03
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 46: best cases showing oil production rate using SWATINIT=SWL=SWCR, 0 capillary pressures
Field Water production rate
3.E+04
Liquid Flowrate (STB/d)
2.E+04
2.E+04
1.E+04
Observed 1
5.E+03
SWL=SWCR=SWATIN
IT- Pc=0
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
Figure 47: best cases showing water production rate using SWATINIT=SWL=SWCR, 0 capillary pressure
3/2/17
33
Field Oil production cumulative
Liquid Production Volume (STB)
3.E+08
2.E+08
2.E+08
1.E+08
Observed 1
SWL=SWCR=SWATINIT0Pc
5.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 48: best cases showing oil production cumulative using SWATINIT=SWL=SWCR, 0 capillary pressure
Field Water production cumulative
1E+08
Liquid Production Volume (STB)
1E+08
Observed 1
8E+07
SWL=SWCR=SWATINIT0Pc
6E+07
4E+07
2E+07
0E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 49: best cases showing water production cumulative using SWATINIT=SWL=SWCR, 0 capillary pressure
34
9.
Random water distribution using SWATINIT and SWL?SWCR
Field Oil production rate
5.E+04
Observed 1
Liquid Flowrate (STB/d)
4.E+04
swrandomswatinit
4.E+04
SWL=SWCR=swrandom
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 50: best cases showing oil production rate using SWL=SWCR= a) random Sw, b) randomly distributed
SWATINIT
Field Water production rate
5.E+04
Liquid Flowrate (STB/d)
5.E+04
4.E+04
4.E+04
3.E+04
3.E+04
2.E+04
2.E+04
1.E+04
Observed 1
swrandomswatinit
5.E+03
SWL=SWCR=swrandom
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 51: best cases showing water production rate using SWL=SWCR= a) random Sw, b) randomly distributed
SWATINIT
35
Field Oil production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
Observed 1
swrandomswatinit
SWL=SWCR=swrandom
2.E+08
1.E+08
1.E+08
1.E+08
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 52: best cases showing oil production cumulative using SWL=SWCR= a) random Sw, b) randomly distributed
SWATINIT
Field Water production cumulative
Liquid Production Volume (STB)
3.00E+08
2.50E+08
2.00E+08
Observed 1
swrandomswatinit
SWL=SWCR=SWrandom
1.50E+08
1.00E+08
5.00E+07
0.00E+00
01/01/98
09/27/00
06/24/03
03/20/06
12/14/08
09/10/11
06/06/14
03/02/17
Figure 53: best cases showing water production cumulative using SWL=SWCR= a) random Sw, b) randomly distributed
SWATINIT
36
Best case comparison using all methods
Field Oil production rate
5.E+04
Observed 1
lambda-Case9
4.E+04
Liquid Flowrate (STB/d)
JFunction-Case9
4.E+04
EQUIL-Case9
SWL=SWCR=0.75Cap
3.E+04
SkeltandHarrison-case9
Johnson-Case9
3.E+04
JFUNC-Case9
2.E+04
2.E+04
1.E+04
5.E+03
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
Figure 54: best cases showing oil production rate using all methods
Field Water production rate
4.E+04
3.E+04
Liquid Flowrate (STB/d)
3.E+04
2.E+04
2.E+04
1.E+04
5.E+03
Observed 1
JFunction-Case9
EQUIL-Case9
SkeltandHarrison-case9
lambda-Case9
Johnson-Case9
JFUNC-Case9
swlswcr085capp_2_2
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
Figure 55: best cases showing water production rate using all methods
9/10/11
6/6/14
3/2/17
37
Field Oil production cumulative
2.E+08
Liquid Production Volume (STB)
2.E+08
2.E+08
1.E+08
1.E+08
Observed 1
lambda-Case9
SkeltandHarrison-case9
JFunction-Case9
EQUIL-Case9
Johnson-Case9
JFUNC-Case9
SWL=SWCR=0.74cap
1.E+08
8.E+07
6.E+07
4.E+07
2.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
9/10/11
6/6/14
3/2/17
6/6/14
3/2/17
Figure 57: best cases showing oil production cumulative using all methods
Field Water production cumulative
Liquid Production Volume (STB)
2.E+08
2.E+08
Observed 1
JFunction-Case9
EQUIL-Case9
SkeltandHarrison-case9
lambda-Case9
Johnson-Case9
JFUNC-Case9
SWL=SWCR=SWATINIT capp at 0.74
1.E+08
5.E+07
0.E+00
1/1/98
9/27/00
6/24/03
3/20/06
12/14/08
Figure 56: best cases showing water cumulative rate using all methods
9/10/11
38
PPCW-Capped at 30Psi
Figure 58: effect of capillary pressure scaling using PPCW
39
Simple model results
Initial Water Distribution
SW
0.001
0.01
0.1
1 LAYERED
NEGATIVE
AVG LARYERED
ON
OFF
ON
ON
ON
ON
ON
ON
0.2521
0.2521
0.2857
0.4672
1
0.252
0.252
0.2521
0.2521
0.2935
0.5167
1
0.252
0.252
0.2524
0.2521
0.3027
0.5865
1
0.252
0.252
0.2539
0.2528
0.319
0.6914
1
0.252
0.252
0.2555
0.2544
0.3457
0.8586
1
0.252
0.252
0.2629
0.2596
0.3936
0.981
1
0.2568
0.252
0.308
0.2948
0.5008
1
1
0.2859
0.252
0.7508
0.7274
0.8125
1
1
0.4941
0.252
0.7752
0.7752
1
1
1
1
0.252
1
1
1
1
1
1
1
0.9907
0.3240
0.3002
0.2935
0.2924
0.2955
0.3061
0.3434
0.6638
1
Table 5: Initial water saturation distribution using JFUNC keyword cases.
Capillary Pressure at first time step
NEGATIVE
PC
0.0001
OFF
ON
0.001
ON
0.01
ON
0.1 LAYERED
ON
ON
AVG LARYERED
ON
ON
26.75
32.1097
38.1267
58.3931
58.1757
1.1668
2.4871
26.75
32.1097
33.6444
51.54253
51.3936
2.4842
2.4871
26.75
32.1097
28.4927
44.5047
44.6019
5.2564
2.4871
24.6772
32.1097
24.6772
37.7649
37.7736
11.0349
2.4871
20.4047
29.9112
19.9631
30.7127
31.0049
22.9281
2.4871
14.7304
24.4112
15.6181
23.7949
24.5377
23.9297
2.4871
10.6557
16.4099
11.0107
16.8788
23.2095
17.0795
2.4871
6.4098
9.6692
6.3828
10.3026
23.2095
9.8043
2.4871
1.4047
0.6114
1.9292
0.7339
2.9703
2.3209
7.3395
7.3395
23.2095
23.2095
7.6759
12.1812
1.1555
0.0658
Table 6: Capillary pressure at the first time step using JFUNC keyword cases
73.3583
33.5648
26.807
24.6772
20.1942
15.6216
10.9697
6.3939
1.9509
0.7711
40
Simple model simulation results
1.
Slope 0.0001/ Homogeneous reservoir (Phi/K)=0.0001
Field Oil production rate
60000
Liquid Flowrate (STB/d)
50000
40000
30000
20000
ro1homogeneous00001_ON
ro1homogeneous00001
10000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 59: oil production rate using JFUNC. PHI/K=0.0001
Field Water production rate
14000
Liquid Flowrate (STB/d)
12000
10000
8000
6000
4000
2000
ro1homogeneous00001
ro1homogeneous00001_ON
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 60: water production rate using JFUNC. PHI/K=0.0001
41
Field Oil production cumulative
70000000
Liquid Production Volume (STB)
60000000
50000000
40000000
30000000
20000000
10000000
ro1homogeneous00001_ON
ro1homogeneous00001
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 61: Oil production cumulative using JFUNC. PHI/K=0.0001
Field Water production cumulative
Liquid Production Volume (STB)
7000000
6000000
5000000
4000000
3000000
2000000
1000000
ro1homogeneous00001
ro1homogeneous00001_ON
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 62: water production cumulative using JFUNC. PHI/K=0.0001
42
2.
Slope=0.001/Homogeneous (Phi/K)=0.001
Field Oil production rate
14000
Liquid Flowrate (STB/d)
12000
10000
8000
pos0001slope_JFUNC:ON
6000
pos0001slope_JFUNC:OFF
4000
2000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 63: Oil production rate using JFUNC. PHI/K=0.001
Field Water production rate
10000
9000
8000
Liquid Flowrate (STB/d)
7000
6000
5000
4000
3000
pos0.001slopeJFUNC:ON
pos0.001slope_OFF
2000
1000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 64: water production rate using JFUNC. PHI/K=0.001
43
35000000
Field Water production cumulative
Liquid Production Volume (STB)
30000000
25000000
20000000
15000000
10000000
pos0001slope_ON
pos0001slope_OFF
5000000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 65: Oil production cumulative using JFUNC. PHI/K=0.001
Field Oil production cumulative
10000000
Liquid Production Volume (STB)
9000000
8000000
7000000
6000000
5000000
4000000
3000000
2000000
pos0001slope_ON
pos0001slope_OFF
1000000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 66: Water production cumulative using JFUNC. PHI/K=0.001
44
3.
Slope 0.01/ homogeneous (Phi/K)=0.01
Field Oil production rate
20000
Liquid Flowrate (STB/d)
18000
16000
14000
12000
10000
HOM_001_ON
HOM_001_Off
8000
6000
4000
2000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 67: Oil production rate using JFUNC. PHI/K=0.01
Field Water production rate
12000
Liquid Flowrate (STB/d)
10000
8000
6000
4000
2000
HOM_001_ON
HOM_001_Off
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 68: Water production rate using JFUNC. PHI/K=0.01
45
Field Oil production cumulative
Liquid Production Volume (STB)
25000000
20000000
15000000
10000000
5000000
HOM_001_ON
HOM_001_Off
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 69: Oil production cumulative using JFUNC. PHI/K=0.01
Liquid Production Volume (STB)
30000000
Field Water production cumulative
25000000
20000000
15000000
10000000
5000000
0
HOM_001_ON
HOM_001_Off
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 70: Water production cumulative using JFUNC. PHI/K=0.01
46
4.
0.1slope/ homogeneous(Phi/K)=0.1
Field Oil production rate
25000
Liquid Flowrate (STB/d)
20000
15000
HOM_01ON
HOM_01OFF
10000
5000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 71: Oil production rate using JFUNC. PHI/K=0.1
Field Water production rate
50000
45000
Liquid Flowrate (STB/d)
40000
35000
30000
25000
20000
15000
10000
5000
HOM_01ON
HOM_01OFF
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 72: Water production rate using JFUNC. PHI/K=0.1
47
Field Oil production cumulative
35000000
Liquid Production Volume (STB)
30000000
HOM_01ON
HOM_01OFF
25000000
20000000
15000000
10000000
5000000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 73: Oil production cumulative using JFUNC. PHI/K=0.1
80000000
Field Water production cumulative
Liquid Production Volume (STB)
70000000
60000000
50000000
40000000
30000000
20000000
10000000
HOM_01ON
HOM_01OFF
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 74: water production cumulative using JFUNC. PHI/K=0.1
48
5.
Unit slope/ homogeneous (Phi/K)=1
Field Oil production rate
700
Liquid Flowrate (STB/d)
600
500
400
300
200
100
HOM_1OFF
HOM_1ON
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 75: Oil production rate using JFUNC. PHI/K=1
4500
Field Water production rate
Liquid Flowrate (STB/d)
4000
3500
HOM_1OFF
HOM_1ON
3000
2500
2000
1500
1000
500
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 76: water production rate using JFUNC. PHI/K=1
49
Field Oil production cumulative
Liquid Production Volume (STB)
1600000
1400000
1200000
HOM_1OFF
HOM_1ON
1000000
800000
600000
400000
200000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 77: Oil production cumulative using JFUNC. PHI/K=1
Field Water production cumulative
8000000
Liquid Production Volume (STB)
7000000
6000000
HOM_1OFF
5000000
HOM_1ON
4000000
3000000
2000000
1000000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 78: Water production cumulative using JFUNC. PHI/K=1
50
6.
Negative 0.001 slope
Field Oil production rate
12000
Liquid Flowrate (STB/d)
10000
minus0001slope_ON_1
8000
minus0001slope_OFF
6000
4000
2000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 79: Oil production rate using JFUNC. Negative 0.001 slope of phi vs K
Field Water production rate
10000
9000
Liquid Flowrate (STB/d)
8000
7000
6000
5000
4000
3000
2000
1000
minus0001slope_ON_1
minus0001slope_OFF
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 80: Water production rate using JFUNC. Negative 0.001 slope of phi vs K
51
Liquid Production Volume (STB)
Field Oil production cumulative
9000000
8000000
7000000
6000000
5000000
4000000
3000000
2000000
1000000
minus0001slope_ON_1
minus0001slope_OFF
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 81: Oil production cumulative using JFUNC. Negative 0.001 slope of phi vs K
Liquid Production Volume (STB)
30000000
Field Water production cumulative
25000000
20000000
15000000
10000000
5000000
minus0001slope_ON_1
minus0001slope_OFF
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 82: water production cumulative using JFUNC. Negative 0.001 slope of phi vs K
52
7.
Brugge POROPERM relationship
Layered
Field Oil production rate
7000
Liquid Flowrate (STB/d)
6000
5000
4000
3000
2000
1000
BRUGGE_POROPERM_ON
BRUGGE_POROPERM_OFF
0
10/19/82 7/15/85 4/10/88 1/5/91 10/1/93 6/27/96 3/24/99 12/18/01 9/13/04 6/10/07
Figure 83: Oil production rate using JFUNC. Brugge POROPERM relationship
Field Water production rate
1600
1400
Liquid Flowrate (STB/d)
1200
1000
800
600
400
BRUGGE_POROPERM_ON
BRUGGE_POROPERM_OFF
200
0
10/19/82 7/15/85 4/10/88 1/5/91 10/1/93 6/27/96 3/24/99 12/18/01 9/13/04 6/10/07
Figure 84: Water production rate using JFUNC. Brugge POROPERM relationship
53
Field Oil production cumulative
6000000
Liquid Production Volume (STB)
5000000
4000000
3000000
2000000
1000000
BRUGGE_POROPERM_ON
BRUGGE_POROPERM_OFF
0
10/19/82 7/15/85 4/10/88 1/5/91 10/1/93 6/27/96 3/24/99 12/18/01 9/13/04 6/10/07
Figure 85: Oil production cumulative using JFUNC. Brugge POROPERM relationship
Field Water production cumulative
350000
Liquid Production Volume (STB)
300000
250000
200000
150000
BRUGGE_POROPERM_ON
100000
BRUGGE_POROPERM_OFF
50000
0
10/19/82 7/15/85 4/10/88 1/5/91 10/1/93 6/27/96 3/24/99 12/18/01 9/13/04 6/10/07
Figure 86: Water production cumulative using JFUNC. Brugge POROPERM relationship
54
Average across all layers
Field Oil production rate
60000
50000
BRUGGE_POROPERM_AVG_ON
Liquid Flowrate (STB/d)
40000
BRUGGE_POROPERM_AVG_OFF
30000
Convergence Problems
20000
10000
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 87: Oil production rate using JFUNC. Average layered Brugge POROPERM relationship
Field Water production rate
7
6
Liquid Flowrate (STB/d)
5
4
BRUGGE_POROPERM_AVG_ON
BRUGGE_POROPERM_AVG_OFF
3
2
1
0
10/19/1982
03/02/1984
07/15/1985
11/27/1986
04/10/1988
08/23/1989
01/05/1991
Figure 88: Water production rate using JFUNC. Average layered Brugge POROPERM relationship
55
Field Oil production cumulative
60000000
Liquid Production Volume (STB)
50000000
40000000
30000000
20000000
10000000
BRUGGE_POROPERM_AVG_ON
BRUGGE_POROPERM_AVG_OFF
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 89: Oil production cumulative using JFUNC. Average layered Brugge POROPERM relationship
7000
Field Water production cumulative
Liquid Production Volume (STB)
6000
5000
4000
3000
2000
1000
BRUGGE_POROPERM_AVG_ON
BRUGGE_POROPERM_AVG_OFF
0
10/19/1982 03/02/1984 07/15/1985 11/27/1986 04/10/1988 08/23/1989 01/05/1991
Figure 90: water production cumulative using JFUNC. Average layered Brugge POROPERM relationship
56
Case
JfuncCPU(mins)
probs
warnings
LambdaCPU(mins)
probs
warnings
skeltCPU(mins)
probs
warning
Johnson
probs
warning
91
1.520
0
2
1.2655
0
5
1.091
0
5
1.24
0
5
84
1.264
0
4
1.243
0
4
1.167
0
4
1.41
0
4
80
1.274
0
10
1.121
1
10
1.151
0
10
1.10
0
10
49
1.274
0
3
1.241
0
3
1.194
0
3
1.36
0
3
11
1.217
0
1
1.369
1
1
1.193
0
1
1.41
0
1
40
1.376
0
3
1.693
2
3
1.364
0
3
1.69
0
3
9
1.178
0
1
1.271
0
1
1.265
2
1
1.30
1
1
1
1.083
0
2
1.241
0
2
1.241
0
2
1.17
0
2
2
1.343
0
1
1.768
2
1
1.425
2
1
1.72
0
1
Table 7:SWATINIT cases performance
SWL=SWCR=SWATINIT
Case
9
probs
43.48
SWL=SWATINIT=Swrandom probs
40.23
Table 8:SWL/SWCR cases performance
SWL=SWATINIT=SWCR+0.01 probs
warnings
149
SWL=SWCR=SWATINIT
NO PC
warnings
probs
8
warnings
601
10528
61.56
SWATINIT=Swrandom
4.33
209
probs
8
warnings
0
8
2.67
warnings
0
453