Simulation
What is Simulation?
Governing Physics
Darcy’s Law (without gravity term)
q  
k

P
Material Balance Equation

 M  (   )  Q
t
Mass Flux
(In – Out)
=
Accumulation +/- Inj/Prod
1
Combine the Equations
– Simulator Flow Equation (with gravity term)
 
Q
[ (P    z)]  ( ) 
t 

where 

k

2
Methods to solve
– Finite Difference
• Governing equations discretized on a fixed grid
– Boundary Element / Finite Element
• Governing equations solved using basis functions
– Streamline Simulation
• Governing equations discretized but solved on separate grids
Types of Simulators
• Black Oil Simulators (ECLIPSE Blackoil)
– Oil & Gas phases are represented by one ‘component’
– Assumes composition of gas & oil components are constant with
pressure & time
• Compositional Simulators (ECLIPSE
Compositional)
– Oil & Gas phases are represented by multicomponent mixtures
– Assumes the reservoir fluids at all temperatures, pressures,
compositions & time can be represented by EOS
Reservoir Simulation Basics
The reservoir is divided into a number of cells
Basic data is provided for each cell
Wells are positioned within the cells
The required well production rates are specified as a
function of time
The equations are solved to give the pressure and
saturations for each block as well as the production
of each phase from each well
We are Interested in Simulating Flow
Flow from one grid block to the next
Flow from a grid block to the well completion
Flow within the wells (and surface networks)
• Flow= Transmissibility * Mobility * Potential Difference
Geometry
&
Properties
Fluid
Well
Properties Production
ECLIPSE Model: *.DATA
RUNSPEC
General model characteristics
GRID
Grid geometry and basic rock properties
• k
EDIT
Modification of the processed GRID data (optional section)
PROPS
PVT & SCAL properties
REGIONS
SOLUTION
SUMMARY
SCHEDULE
Subdivision of the reservoir (optional section)
Initialization
Request output for line plots (optional section)
Wells, completions, rate data, flow correlations, surface facilities
Simulator advance, control and termination
7
How ECLIPSE Works
– Each section of the data file is read, processed,
consistency checks are performed & required
information is written to various output files (ie
*.PRT)
– Exceptions:
• RUNSPEC: Used for allocation of dynamic memory
• SCHEDULE: Time dependent data is read & processed
at every time step
How ECLIPSE Sections Relate to the Equation
Flow =Transmissibility * Mobility*Potential Difference
Geometry&
Properties
Fluid
Properties
Well
Production
GRID
PROPS
SCHEDULE
EDIT
REGIONS
SOLUTION
9
RUNSPEC Section
This slide does not appear in the manual
Purpose of the RUNSPEC Section
– Set the start date of the simulation
– Define the basic character of the model
– Allocation of memory (RAM)
•
•
•
•
11
Simulation grid
Wells
Tabular data
Solver stack
Sample RUNSPEC Section
Units may also be
METRIC or LAB
Number of PVT, SCAL
Aquifer Tables, Wells,
Connections,Segments
Note: Required
12
{
•
•
•
•
•
•
•
•
•
•
RUNSPEC
TITLE
ECLIPSE Course Example
DIMENS
20 5 10 /
FIELD
•
•
•
•
•
•
•
•
WELLDIMS
4 20 1 4 /
AQUDIMS
4* 1 250 /
TABDIMS
2 2 50 50 /
START
1 JAN 1994 /
OIL
WATER
Phases present may be
oil, water, gas, disgas
(dissolved gas), vapoil
(vaporized oil)
RUNSPEC Keywords
– The ECLIPSE Reference
manual contains
information about all
keywords
Reference Manual
• Data File Overview
chapter shows keywords
by section
• Keywords chapter
contains details about
each keyword
13
Purpose of the GRID section
– The Grid section contains the properties used to
calculate pore volume & transmissibility
PV  Vcell    NTG
T(x, y,z) 
K ( x , y , z )  A ( x , y , z )  NTG
L ( x, y,z )
– ECLIPSE uses cell pore volume and transmissibility
to calculate flows from cell to cell
14
Minimum GRID Section
• Required Properties for each cell in the model:
• Geometry
– Cell dimensions & depths
• Properties
– Porosity
– Permeability
– (Net-to-gross or net thickness—if not included,
ECLIPSE assumes equal to 1)
15
Types of Grids Supported
“Cartesian”
Block Centered
Radial
16
Corner Point
Unstructured (PEBI)
1
Block-Centered vs Corner Point: Geometry
Block-Centered
DX keyword specifies the
thickness of the cells in
the I direction
(10,1,1)
DZ keyword specifies the
thickness of the cells in
the K direction
Corner Point
TOPS keyword specifies
the upper face depth
(10,1,1)
DY keyword specifies the
thickness of the cells in
the J direction
(11,1,1)
Note: DXV, DYV, DZV are alternate forms
17
ZCORN keyword
specifies the
height of all
corners of all cells
COORD keyword
specifies the X,Y,Z of
the lines that define
the corner of all
cells
(11,1,1)
3
Block-Centered vs Corner Point: Transmissibility
• Flow from
cell can flow to
cell(s)
Corner Point
Block-Centered
(10,1,1)
(10,1,1)
(11,1,1)
(11,1,1)
Cell connections are by
logical order:
Cell connections are by
geometric position:
(11,1,1)  (11,1,2) & (10,1,1)
(11,1,1)  (11,1,2), (10,1,2)partial & (10,1,3)
18
2
Block-centered vs Corner point:
Summary
• Block-centered
• Cell description is simple
– Pre-processor is not
required
– Geometry data is small
• Geologic structures are
modelled simplistically
– Pinchouts & unconformities
are difficult to model
– Incorrect cell connections
across faults (user must
modify transmissibility)
19
• Corner Point
• Cell description can be complex
– Pre-processor is required
– Geometry data is
voluminous
• Geologic structures can be
modelled accurately
– Pinchouts & unconformities
can be modelled accurately
– Layer contiguity across fault
planes is accurately
modelled
Grid Cell Property Definition
Cell properties
such as PORO,
PERMX,
PERMY,
PERMZ, NTG
are averages
defined at the
centre
20
Cartesian Data Reading Convention
• Cell data is read with i cycling fastest,
followed by j then k
k increasing
(1,1,1)
i increasing
j
increasing
(12,4,1)
21
1
Inactive Cells
• Avoid simulating fluid flow in “unimportant” cells
• ACTNUM — explicitly set each cell’s behaviour
– 0 indicates the cell is inactive
– 1 indicates the cell is active
• MINPV — indicate a minimum pore volume for a cell to be active
• PINCH — indicate a minimum thickness for a cell to be active
• ECLIPSE will automatically inactivate any cell with zero pore volume
•
•
22
Note: FloViz & FloGrid are normally defaulted to show active cells only
(Scene | Grid | Show | Inactive cells)
Cell Property Definition Rules
• One property per cell (NX*NY*NZ)
– Values must be defined for inactive cells too
• Explicit values only
– ECLIPSE has no facilities for entering data as a
function
– FloGrid, Office, FloViz have property calculators
• Define the property with the pre-processor
• Export the property as a text file (*.grdecl)
• Use the INCLUDE keyword
23
Input Examples
2
--NX = 5, NY = 3, NZ = 4
Specify each value
Specify similar values
with the *
EQUALS example
NTG
1.00 1.00
1.00 1.00
1.00 1.00
15*0.40
15*0.95
15*0.85 /
1
3
1
24
Applies to whole grid
Applies to cells specified
This would overwrite
PORO & PERMX
specified previously
1 /
85
83
ENDBOX
MULTIPLY example
1.00
1.00
1.00
PORO
9*0.28 /
PERMX
100 80
COPY example
1.00
1.00
1.00
EQUALS
'PORO ' 0.250 /
'PERMX' 45 /
'PERMX' 10
1 5 1 3 2 2 /
'PERMX' 588
1 5 1 3 3 3 /
/
BOX
1 3
BOX example
1.00
1.00
1.00
COPY
'PERMX' 'PERMY' /
'PERMX' 'PERMZ' /
/
MULTIPLY
'PERMZ' 0.05 /
/
99
110
92
91
84 /
Cell Property Definition using Petrel
– The properties are assigned to each cell during
upscaling & exported to a file
– The INCLUDE keyword is used to load the
properties from Petrel:
INCLUDE
grainne_props.grdecl /
25
GRID Section Output Controls
– For a report in the PRT file, use:
• RPTGRID (request report of many GRID Section
keywords, including ALLNNC)
• BOUNDARY limits the PRT output to specified I,J,K
range
– For 3D viewable output, use:
• Geometric data (*.egrid),
GRIDFILE
0 1/
• Static properties (*.init),
INIT
26
For an unstructured grid,
the *.egrid must be
exported from FloGrid
EDIT Section
Purpose of the EDIT Section
– Cell geometry, pore volume and transmissibily are
calculated in the GRID Section
– These properties are modified in the EDIT Section
– EDIT is optional
28
EDIT Section keywords
– GRID Section output that may be modified in the
EDIT Section:
• DEPTH, PORV, TRAN (X, Y, R, THT, Z)
• Diffusivity Option keywords
– Operators
• MULTIPLY, BOX, EQUALS, COPY, ADD, MINVALUE,
MAXVALUE
– Others
• EDITNNC, MULTPV, MULTFLT
• MULT (X, Y, R, THT, Z, etc) are allowed but not
recommended
29
PROPS Section - Fluid Properties
This slide does not appear in the manual
Purpose of the PROPS Section
– The PROPS section contains pressure and saturation
dependent properties of the reservoir fluids & rocks
– Fluid information required (for each fluid in
RUNSPEC):
• Fluid PVT as a function of Pressure
• Density or Gravity
– Rock information required:
• Relative permeabilities as a function of saturation
• Capillary pressures as a function of saturation
• Rock compressibility as a function of pressure
31
PVT: Pressure Volume Temperature
• Why is PVT needed?
– Mass balance is a key equation in simulation
• Produced volumes must be translated to reservoir
conditions
• Reservoir volumes must be converted to mass
• Where does PVT come from?
– Laboratory experiments Equation of State
Model
– Correlations
– Processed in PVTi
32
Black Oil vs. Compositional Simulation
Compositional
Black Oil
Flow equation solution for each
cell subject to material balance
Flow equation for each
cell subject to material balance
PVT data lookup from
supplied tables
Iterative solution of cubic
equation of state for each
component in each cell
Iterative flash of component
mixture to equilibrium conditions
for each cell
33
For every time step
Black Oil Model Phase Options
#
Phases
Dead Oil
Dry Gas
Water
1
2
3
RUNSPEC Keywords
Phase Combination
Dead Oil
Water
Dry Gas
Water
Dead Oil
Dry Gas
Live oil with dissolved
Water
Wet gas with vaporized
Water
Live oil with
Wet gas with
Water
dissolved gas vaporized oil
OIL
GAS
WATER
OIL, WATER
GAS, WATER
OIL, GAS
OIL GAS, DISGAS, WATER
OIL, GAS, VAPOIL, WATER
OIL, GAS, DISGAS, VAPOIL, WATER
A: Dead Oil
C: Live Oil,
Saturated
B: Live Oil,
Initially
Undersaturate
d
34
D: Dry Gas
E: Wet Gas
Dead Oil Entry Data Using PVDO &
PVCDO
•
•
•
•
•
•
•
PVDO
--P
2500
3000
3500
4000
4500
•
•
•
RSCONST
--GOR
0.656
Bo
1.260
1.257
1.254
1.251
1.248
Mu
0.50
0.55
0.60
0.65
0.70 /
Pb
2500 /
PVCDO
--Pref
2500
RSCONST
--Rs
0.656
Bo(Pref) Co
1.260 6E-6
Mu(Pref) Cv
0.5
E-6 /
Pbub
2500 /
ECLIPSE calculates the PVT table
using:
Bo P   Bo Pref e

C P  Pref
Bo o ( P)  Bo  o ( Pref )e
35


( C Cv ) P  Pref

Live Oil Data Entry Using PVTO & PVCO
•
PVTO
•
--Rs
Pbub
FVF
Mu
•
0.137
1214.7
1.1720
1.970
•
•
•
•
•
•
•
•
•
•
0.195
0.241
0.288
0.375
0.465
0.558
0.661
0.770
1414.7
1614.7
1814.7
2214.7
2614.7
3014.7
3414.7
3814.7
4214.7
4614.7
1.2000
1.2210
1.2420
1.2780
1.3200
1.3600
1.4020
1.4470
1.4405
1.4340
1.556
1.397
1.280
1.095
0.967
0.848
0.762 PVCO – a simple method for live oil data. When
0.691 calculating the undersaturated region, ECLIPSE
0.694 assumes:
dBo
C


B0
0.697 /
o
Saturated
Undersaturated
36
dP
d o
Cv 
0
dP
Gas EOS in the Black Oil Model

gr


gg
 R v  og
Bg
Where Bg (formation volume factor):
Bg
Subscripts:
gr = reservoir vapor
og = surface oil
from reservoir
vapor
gg = surface gas
from reservoir
vapor
37
V gr

V gg
And Rv (amount of surface oil vaporized in reservoir vapor):
Rv
V og

V gg
Dry Gas Data Entry Using PVDG & PVZG
•
•
•
•
•
•
•
•
•
•
•
•
38
PVDG
--P
1214
1414
1614
1814
2214
2614
3014
/
Bg
13.947
7.028
4.657
3.453
2.240
1.638
1.282
RVCONST
--Rv
Pd
0.0047 1214 /
Mu
0.0124
0.0125
0.0128
0.0130
0.0139
0.0148
0.0161
PVZG – Alternative of PVDG. The Z factor is related
to the formation volume factor Bg, reference
temperature Tref and pressure P by:
 Tref  Tbase  Ps

Bg  Z  
 T T
 P
base 
 s
Wet Gas Data Entry Using PVTG
•
•
•
•
•
•
•
•
•
•
39
PVTG
-- Pg
60
120
180
240
300
360
560
/
Rv
0.00014
0.00012
0.00015
0.00019
0.00029
0.00049
0.00060
Bg
0.05230
0.01320
0.00877
0.00554
0.00417
0.00357
0.00356
Mu
0.0234
0.0252
0.0281
0.0318
0.0355
0.0392
0.0393
/
/
/
/
/
/
/
Water EOS in the Black Oil Model

wr

 ws
Bw
Where
Bw
40
V wr

V ws
Reference Densities
• Surface densities are
specified using either
keyword:
– DENSITY
– GRAVITY
 or


gr
wr



x
Compressor
x
x
1st Stage
Separato
r
 oo  R s  go
2nd Stage
Separator
Stock Tank
Bo

gg
Water
Treatme
nt
 R v  og
Bg
 ws
Oil & Water at reservoir
conditions
Bw
41
Using Multiple PVT Regions
• Keywords necessary:
– In RUNSPEC, check TABDIMS & EQLDIMS
– In PROPS, include multiple tables (some may be
defaulted)
– In REGIONS, include PVTNUM & EQLNUM
42
Using API Tracking
• Keywords necessary:
– In RUNSPEC, use API
– In PROPS, at least full PVT for highest & lowest
API oil
– In SOLUTION, use OILAPI or APIVD
43
PROPS Section – Saturation
Functions
This slide does not appear in the manual
Purpose of the PROPS Section
• The PROPS section contains pressure and saturation
dependent properties of the reservoir fluids & rocks
• Fluid information required (for each fluid in
RUNSPEC):
– Fluid PVT as a function of Pressure
– Density or Gravity
• Rock information required:
– Relative permeability as a function of saturation
– Capillary pressures as a function of saturation
– Rock compressibility as a function of pressure
This slide does not appear in the manual
45
Rock Compressibility
• Required since the pore volume varies under pressure
– Simplest approach: ROCK keyword
• Rock compressibility is reversible and the same everywhere
– Additional options (see “Rock Compressibility” in the Technical
Description):
• A table of compaction as a function of pressure
– Reversible or Irreversible
• The ability to modify the transmissibility as a function of pressure
• A hysteretic model to allow partial reflation
• A water-induced compaction model
46
ROCK keyword
• Rock Compressibility
 V pore 
 V pore
C  
 P 
Cell Bulk Volume is constant and equal
to Pore Volume + Rock Volume
• ECLIPSE adjusts the pore volume using:


C ( P  P ) 


V P   V P  1  C ( P  P ) 


2
ref
pore
47
pore
ref

ref
2

Purpose of Saturation Functions
Used to calculate
the initial
saturation for each
phase in each cell
Used to calculate the
initial transition zone
saturation of each
phase
48
Used to calculate
fluid mobility to
solve the flow
equations between
cells and from cell
to well
3
Significant Saturation Endpoints
• SWL: connate water
saturation
• SWCR: critical water
saturation
• SWU: maximum water
saturation
• SOWCR: critical oil-water
saturation
• SGL: connate gas saturation
• SGCR: critical gas saturation
• SGU: maximum gas
saturation
• SOGCR: critical oil-gas
saturation
Oil Water Relative
Permeability
Krow
Krw
SWU
SWCR
SWL
+
Gas Oil Relative Permeability
Krog
SOGCR
(1 - Sg)
SGL
+
49
Krg
SGCR
SGU
SOWCR
(1 - Sw)
Saturation Function Keyword Families
• Family 1
– Kro entered in the same tables as Krw and Krg
– SWOF, SGOF, SLGOF
– Cannot be used in miscible flood
• Family 2
– Kro entered in separate tables versus oil saturation
– SWFN, SGFN, SGWFN, SOF3, SOF2, SOF32D
Different keyword families cannot be mixed in the
same run
50
Family 1 Example – SWOF, SGOF
These must be the same
SWL
•
•
•
•
•
•
•
•
•
•
•
•
•
•
SWOF
--Sw
0.1510
0.2033
0.3500
0.4000
0.4613
0.5172
0.5731
0.6010
0.6569
0.7128
0.8111
0.8815
Must be zero
Krw
0.0000
0.0001
0.0002
0.0695
0.1049
0.1430
0.1865
0.2103
0.2619
0.3186
0.4309
0.4900
= 1 - SOWCR
51
Krow
1.0000
0.9788
0.8302
0.1714
0.0949
0.0511
0.0246
0.0161
0.0059
0.0015
0.0000
0.0000
Must be SGOF
zero
Pcwo
400.00
20.40
11.65
3.60
2.78
1.93
1.07
0.83
0.66
0.38
0.16
0.00
Must be zero
/
--Sg
Krg
Krog
Pcgo
0.0000
0.0000
1.0000
0.00
0.0400
0.0000
0.6000
0.20
0.1000
0.0220
0.3300
0.50
0.2000
0.1000
0.1000
1.00
0.3000
0.2400
0.0200
1.50
0.4000
0.3400
0.0000
2.00
0.5000
0.4200
0.0000
2.50
0.6000
0.5000
0.0000
3.00
0.7000
0.8125
0.0000
3.50
0.8490
1.0000
0.0000
3.90 /
SGU = 1 - SWL
Must be zero
Family 2 Example – SWFN, SGFN, SOF3
SWFN
--Sw
Must be zero
SGFN
Must be zero
SOF3
Krw
Pcow
0.10
0.000
20.0
0.00
0.000
0.00
0.30
0.000
0.000
0.20
0.004
5.00
0.05
0.000
0.03
0.40
0.089
0.008
0.30
0.032
3.30
0.15
0.089
0.30
0.50
0.253
0.064
0.40
0.062
2.60
0.125
1.50
0.60
0.354
0.172
0.164
0.60
0.50
0.25
0.343
0.80
1.00
0.586
0.365
0.253
0.70
0.60
0.35
0.729
0.60
1.50
0.854
0.500
0.354
0.80
0.70
0.45
0.90
1.000
1.000
0.80
0.667
0.30
0.55
0.465
2.10
0.65
0.586
2.80
0.75
0.716
3.60
0.85
0.854
4.50
0.90
1.000
5.50
0.90
1.00
0.833
1.000
--Sg
0.10
0.00
/
/
52
Krg
Pcog
--So
/
Krow
Krog
Must be the same
SOILmax = 1 - SWL
3 Phase Oil Relative Permeability
SWL
• ECLIPSE default model is a
weighted sum:
kro 
S g krog   S w  SW Lkrow
1-So-SWL
So
Sg
GAS
S g  S w  SW L
1
S g  S w  SW L
OIL
• Other options in ECLIPSE
– Modified STONE 1
– Modified STONE 2
WATER
S w  SW L
S g  S w  SW L
1-So
Uses Krog table
Uses Krow table
53
S g  S w  SWL  1  S o  SWL
Saturation Table Scaling
• Given a few generic saturation
functions:
– Saturation functions are
transformed and applied to the
existing rock types
– Three main types:
• Horizontal Scaling – scales
relative permeability along the
saturation axis
• Vertical Scaling – scales relative
permeability values
• Capillary pressure scaling
54
Before Scaling
After Scaling
Horizontal Scaling End-Points
Increasing Oil Saturation
Increasing Oil Saturation
SOWCR
Relative Permeability
SWCR
Increasing Water Saturation
55
Krg
Krog
SOGCR
Relative Permeability
1-SWL-SGL
Krw
Krow
SWU
1-SWL-SGL
SGCR
Increasing Gas Saturation
SGU
Implementing Horizontal Scaling
• 1) Decide on what needs to be scaled
• Which end-points?
• Which relative permeability curves?
• 2) Input un-scaled saturation functions
• Family 1 or Family 2 keywords
• 3) Insert ENDSCALE in RUNSPEC
• 4) Input scaled end-points in PROPS
• Entered on per cell basis or with ENPTVD
56
Example – Scaling SWCR
SWOF
-- Sw
0.150
0.240
0.295
0.350
0.405
0.460
0.515
0.570
0.625
0.680
0.735
0.790
0.845
0.900
1.000
/
•
•
BOX
1 1 1 1 1 2 /
•
•
SWCR
0.16 0.45 /
Krw
0.000
0.000
0.005
0.017
0.036
0.062
0.095
0.134
0.180
0.231
0.290
0.354
0.424
0.500
0.700
Krow
1.000
0.784
0.665
0.555
0.454
0.363
0.282
0.210
0.149
0.097
0.056
0.026
0.007
0.000
0.000
Pcow
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Krw (1,1,1)
Krw (1,1,2)
Krw (1,1,3)
Krow
Relative
Permeability
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
SWCR=0.24
(1,1,3)
SWCR=0.45
SWCR =
(1,1,2)
0.16
(1,1,1)
Water Saturation
57
Example – Scaling SWL and SOWCR
SWOF
0.150 0.000
0.240 0.000
0.295 0.005
0.350 0.017
0.405 0.036
0.460 0.062
0.515 0.095
0.570 0.134
0.625 0.180
0.680 0.231
0.735 0.290
0.790 0.354
0.845 0.424
0.900 0.500
1.000 0.700
/
BOX
1 1 1 1 3 3 /
SWL
0.22 /
SOWCR
0.25 /
1.000
0.784
0.665
0.555
0.454
0.363
0.282
0.210
0.149
0.097
0.056
0.026
0.007
0.000
0.000
32.43
15.01
10.48
7.66
5.76
4.41
3.41
2.65
2.05
1.57
1.17
0.85
0.57
0.34
0.00
Oil – Water Relative Permeability
Relative Permeability
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Krw
Krow – Original
Krow – Scaled
1-SWL-SGL
(SWL=0.22
)
SOWCR=0.25
Water Saturation
58
Example – Scaling SWL and SOWCR
(continued)
SGOF
0.000
0.100
0.154
0.208
0.263
0.317
0.371
0.425
0.479
0.533
0.588
0.642
0.696
0.750
0.850
/
•
•
SGU
0.78 /
0.000
0.000
0.005
0.019
0.044
0.078
0.122
0.175
0.238
0.311
0.394
0.486
0.588
0.700
1.000
1.000
0.699
0.563
0.443
0.341
0.254
0.182
0.124
0.078
0.045
0.022
0.008
0.001
0.000
0.000
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Note – SGU is scaled for consistency
(otherwise SGU+SWL > 1)
59
Oil – Gas Relative Permeability
Relative Permeability
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Krg – Original
Krg – Scaled
Krog – Original
Krog – Scaled
SGU=0.78
1-SWL-SGL
(SWL=0.22)
Gas Saturation
Vertical Scaling End-Points
Oil – Water Relative Permeability
KRORW
KRW
KRWR
Water Saturation
60
KRO
Krw
Krow
Relative Permeability
Relative Permeability
KRO
Oil – Gas Relative Permeability
Krg
Krog
KRORG
KRG
KRGR
Gas Saturation
Example – Scaling SWCR and KRWR
SCALECRS
YES /
SWOF
0.150 0.000
0.240 0.000
0.295 0.005
0.350 0.017
0.405 0.036
0.460 0.062
0.515 0.095
0.570 0.134
0.625 0.180
0.680 0.231
0.735 0.290
0.790 0.354
0.845 0.424
0.900 0.500
1.000 0.700
BOX
1 1 1 1 1 2 /
SWCR
0.16 0.45 /
KRWR
0.60 0.35 /
Oil - Water Relative Permeability
1.000
0.784
0.665
0.555
0.454
0.363
0.282
0.210
0.149
0.097
0.056
0.026
0.007
0.000
0.000
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00 /
Krw (1,1,1)
Krw (1,1,2)
Krw (1,1,3)
Krow
Relative
Permeability
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
KRWR=0.6
0
(1,1,1)
KRWR=0.5
0
(1,1,3)
KRWR=0.3
5
(1,1,2)
Water Saturation
61
Capillary Pressure Scaling End-Points
Oil – Gas Capillary Pressure
Oil – Water Capillary Pressure
PCW
Capillary Pressure
Capillary Pressure
PCG
SW
U
SWL
Water Saturation
62
SGU
SGL
Gas Saturation
Example – Scaling SWL and PCW
SWOF
0.150 0.000
0.240 0.000
0.295 0.005
0.350 0.017
0.405 0.036
0.460 0.062
0.515 0.095
0.570 0.134
0.625 0.180
0.680 0.231
0.735 0.290
0.790 0.354
0.845 0.424
0.900 0.500
1.000 0.700
BOX
1 1 1 1 3 3 /
SWL
0.22 /
SOWCR
0.25 /
PCW
50.0 /
1.000
0.784
0.665
0.555
0.454
0.363
0.282
0.210
0.149
0.097
0.056
0.026
0.007
0.000
0.000
32.43
15.01
10.48
7.66
5.76
4.41
3.41
2.65
2.05
1.57
1.17
0.85
0.57
0.34
0.00 /
Oil – Water Capillary Pressure
PCW=50.
0
Pcow - Original
Pcow - Scaled
Capillary Pressure
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
SWL=0.22
Water Saturation
63
PROPS Section Output Control
• RPTPROPS
– Controls output from PROPS section to the PRT file
• INIT
– Saturation functions & PVT data written to the INIT file
– Can be displayed in 2D & 3D (Petrel, Office, FloViz, FloGrid)
• FILLEPS
– All saturation endpoints to the INIT file
• EPSDBGS / EPSDEBUG
– Writes scaled saturation tables to DEBUG file for specified
cells
64
REGIONS Section
This slide does not appear in the manual
Purpose of the REGIONS Section
– The REGIONS section divides the reservoir
according to
• Variations in reservoir characteristics
• For reporting purposes
– Examples:
• Different PVT properties and equilibration characteristics
could be assigned to areas of the grid separated by a
sealing fault
• Fluid in place could be reported by fault block or
leasehold position
– The REGIONS section is optional
66
Use: Variations of Reservoir Properties
– 3D view of EQLNUM
property
– EQUIL keyword tables
now associated with
EQLNUM regions
– Resulting initial oil
saturation
EQLNum
SOLUTION
EQUIL
2 TABLES
7100 3814.70 7500 0 7100 0
1
0
5 /
8000 4145.39 7550 0 7000 0
1
0
5 /
67
Use: Reporting Purposes
1. FIPNUM (fluid in place
regions) are defined in the
REGIONS section
2. In the Solution section:
•
RPTSOL
•
FIP=2 /
3. The PRT file now shows the
fluids in place both
originally & at each report
step
68
REGIONS Section Keywords
– Commonly Used
– Special Use
– Operators
– Exceptions
• (these are in GRID
Section)
FIPNUM
SATNUM
PVTNUM
EQLNUM
FIPXXXXX (ex: FIPLAYER,
FIPEXPL)
EQUALS, ADD, COPY, etc
FLUXNUM, RESVNUM,
NINENUM, PINCHNUM
69
Output Controls
– For a report in the PRT file:
• RPTREGS in REGIONS Section
– BOUNDARY can be used to limit this output
}
• RTPSOL (FIP=1,2 or 3) in SOLUTION Section
• RPTSCHED (FIP=1,2 or 3) in SCHEDULE Section
– For 3D viewable output:
• INIT in GRID Section = regions keywords
• RPTRST (FIP) = fluids in place
70
same result
How to specify Regions keyword arrays
REGIONS
Use the Operator keywords
(EQUALS, COPY, ADD, etc)
EQUALS
'FIPNUM'
1 /
'FIPNUM'
2
11
20 /
/
FIPLAYER
100*1
100*2
100*3
100*4
100*5
100*6
100*7
100*8
100*9
100*10 /
71
Specify the number for each cell
How to specify Regions keyword arrays
• Interactively
– FloViz
– Office
– Petrel
– FloGrid
72
SOLUTION Section
This slide does not appear in the manual
Purpose of the SOLUTION Section
– The SOLUTION is used to
define the initial state of
every cell in the model
• Initial pressure and phase
saturation
• Initial solution ratios
• Depth dependence of
reservoir fluid properties
• Oil and gas re-solution
rates
• Initial analytical aquifer
conditions
74
ECLIPSE Initialization Options
– Equilibration - initial pressures and saturations are
computed by ECLIPSE using data entered with the
EQUIL keyword
– Restart - initial solution may be read from a
Restart file created by an earlier run of ECLIPSE
– Enumeration- initial solution is specified by the
user explicitly for every grid block
75
EQUIL
– Sets the contacts and pressures for conventional
hydrostatic equilibrium
– EQUIL items are interpreted differently depending
on the phases present
– May have more than one equilibration region (see
EQLDIMS)
EQUIL
--
D
P
7000 4000
OWC
Pcow
7150
0
GOC
1*
Pcog
RSVD/PBVD
1*
1*
EQUIL
76
RVVD/PDVD
1*
N
0 /
Block Center Equilibration, Part 1
Pressure
EQUIL
--D
3500
GOC
TZ
Datum
1.
2.
P
4000
OWC
7150
Pcow
0
GOC
3500
Depth
77
0
/
Given: Contacts, Datum and
Pressure
Using BO EOS, calculate phase
pressures throughout the model,
for example:
TZ
OWC = FWL
(Pcow = 0)
Pcog
h2
Po(h 2)  Po(h1)    o gdh
h1
2
Block Centered Equilibrium, Part 2
Pressure
1
G-O Rel Perm
Sg = 0.77
Sw = 0.23
GOC
GAS ZONE:
Sg = SGU
Sw = SWL
So = 1 – SWL - SGU
TZ
Krg
Krog
SGL
Datum
So = 0.77
Sw = 0.23
OIL ZONE:
Sg = SGL, usually zero
Sw = SWL
So = 1 – SWL – SGL
SGU
O-W Rel Perm
Kro
SWU
TZ
Krw
OWC = FWL
(Pcow = 0)
SWL
Sw = 1.00
Depth
78
WATER ZONE:
Sg = SGL, usually zero
Sw = SWU
So = 1 – SWU – SGL
Block Centered Equilibrium, Part 3
Pressure
1. Calculate Pcog and Pcow in
the transition zones of the
model
Sg = 0.77
Sw = 0.23
GOC
Pcow  Po  Pw
Pcog  Pg  Po
TZ
Datum
So = 0.77
2. Reverse-lookup Sw from Pc
tables in PROPS section &
assign to cell centers
Sw = 0.23
TZ
Pco
w
OWC = FWL
(Pcow = 0)
Swi = 0.25
Sw = 1.00
So = 0.75
Sw
Depth
79
2
Not Steady-State
(use EQLOPTS ‘QUIESC’)
EQUIL Item 9
1
Better FIP estimate
i=1
i=2
i=3
TZ
OWC
TZ
OWC
Effective
OWC
Tilted or level block
integration OWC
i = 2Ni = 12N
Level Block Equilibrium
Block Center Equilibrium
N = 0: fluid saturations at the
center of each cell
Steady State
Potential errors in FIP errors
80
N < 0: average of the conditions at (2 *-N)
horizontal levels within each grid cell
Tilted Block Equilibrium
N > 0: average of the conditions at N levels
within each cell half, weighted according to
the cell’s horizontal cross-section at each level
Initial Solution Ratios
– Used for fluid density calculation
– Required as part of the equation of state for the
oil and gas phases
• Dissolved gas concentration, Rs or RSVD
• Vaporized oil concentration, Rv or RVVD
• Bubble point and / or dew point depth variation, PBVD
and/or PDVD
This information may
be supplied in your
PROPS keywords
81
Restart Runs
– The solution at the end of
the initialization is set as
start conditions for the
history match
Field Production Rate
(Initialization Run)
– Why bother to
recalculate initial
saturations & pressures?
Cell
Saturations &
Pressures
recorded
History Period
(Restart Run)
– Restarts save simulation
time!
Time
82
Enumeration
– Initial conditions may be set explicitly
– This may be appropriate in reservoirs with initially
tilted contacts or non-equilibrium situations
– ECLIPSE will check supplied information against
phases in the Runspec section
83
Output Controls
RPTSOL
‘SOIL’ ‘EQUIL’ ‘RESTART=2’ /
– Tabular and printed data to the PRT file
• Lots of other properties can be written
– Initial conditions to the restart file
• Can write out interblock flows & FIP
• Can be viewed in 3D ( Petrel, FloViz, FloGrid)
RPTSOL
84
SUMMARY Section
This slide does not appear in the manual
Purpose of the SUMMARY Section
– The SUMMARY section is used to specify variables
that are to be written to the Summary file(s) after
each time step of the simulation
– These variables can be plotted with Petrel, Office
or GRAF
– Optional section (if there is no SUMMARY section,
ECLIPSE does not create any Summary files)
• Examples: FOPT (field oil production total), WWCT
(well water cut), CGFR (connection gas flow rate)
86
Purpose of the SUMMARY Section
87
SCHEDULE Section: History Match
This slide does not appear in the manual
Purpose of the SCHEDULE Section
– The SCHEDULE section is used to specify
• Well operations to be simulated
• Times (TSTEP, DATES) to be simulated
• Simulator tuning parameters
– The SCHEDULE Section is often used in two
modes:
• History matching – specify actual wells, facilities and
Focus of this session
production/injection
• Prediction – specify control mechanisms, new wells,
economic limits
89
History Matching vs. Prediction
Interpreted geology,
geophysics, petrophysics
Reservoir
Description
ECLIPSE
Model
Tuning Runs
Modify properties until
model & actual rates
match
Actual
Production &
Pressure
OK?
Model
Production &
Pressure
Sensitivity Runs
Produce results for
risk evaluation
economics
Sensitivity Runs
Identify uncertain
properties
Prediction Runs
 Existing wells
continue to produce &
are worked-over
logically
 New well drilling may
be implemented
 EOR options may be
tested
History
Match
Prediction
90
Predictions depend on quality of reservoir description!
3
Typical History Match Schedule Section
–
–
–
Specify output
Specify wells, VFP tables, completions & rates
Advance the simulation
•
•
•
–
–
91
Specify old well rates
Specify any workovers
Specify any new wells
Repeat
End of history match
VFP Curve Specification
– The VFP table is a table of BHP versus FLO, THP,
WFR, GFR and ALQ
•
•
•
•
FLO is the oil, liquid or gas production rate
WFR is the water-oil ratio, water cut or water-gas ratio
GFR is the gas-oil ratio, gas-liquid ratio or oil-gas ratio
ALQ is a variable that can be used to incorporate an
additional parameter, such as the level of artificial lift
– VFPi is the ECLIPSE family pre-processor that can
be used to generate this keyword
92
VFP Table Usage
93
Well Specification: WELSPECS
– Introduces new well and specifies some of its
general data
– This keyword is compulsory
• A well must be introduced with this keyword before it
can be referenced in any other keyword
WELSPECS
--nm
P1
G
2 2 1*
OIL
-1 /
P21 G
8 1 1*
OIL
-1 /
I20 G 20 1 1*
WAT
-1 /
/
94
grp I J refD phase drad
WELSPECS
WELSPECS Item 7, Drainage Radius
rd
– Productivity index (PI)
and well drawdown
depend upon:
Physical
Model
P* average
reservoir
pressure
• Grid block size in
ECLIPSE
ECLIPSE Model
– A significant part of
history matching is
adjusting well parameters
to achieve the correct
inflow performance
WELSPECS
95
Pw
Pw, well BHP
rd, re drainage radii
re
Pc, cell
pressure
Pw
Measure of Pressure
– Appropriate drawdown behavior is achieved by adjusting
the productivity index:
• Request WBP & WBP9 in the Summary Section
• Use the approximation:
WBP 9  WBHP  H
WPIMULT 
WBP  WBHP  H
WBP9
WBP9
WBP
Where:
WBHP - bottomhole pressure from well test
H - hydrostatic correction (midperfs to ECLIPSE datum)
96
WBP9
WBP9
WELSPECS Item 8, Flow in Gas Wells
P/z
Q  P2
P  m(P )
Non- Darcy flow
Non-linear behaviour
- use pseudo pressure
QP
Low compressibility
Darcy flow
2000
3500
WELSPECS
97
P (psia)
Completion Specification: COMPDAT
– Used to specify the position and properties of
one or more well completion
COMPDAT
--nm
I J Ku Kl status sat CF Dwell Kh S
P1
2* 1 10
OPEN
1* 1* 0.583 /
P21
2* 1 10
SHUT
1* 1* 0.583 /
I20
2* 1
AUTO
1* 1* 0.583 /
5
/
COMPDAT
98
2
COMPDAT Item 8: Connection Factor
– ECLIPSE default:
• Assumes full penetration along only one axis
– Petrel & Schedule program:
• Three-part Peaceman formula with full vector
representation, accounts for:
–
–
–
–
Well orientation
Grid permeabilities
Well
Portion of the cell perforated
Trajectory
Effective wellbore diameter
Cell Permeability in
I, J, & K
Kj
Kk Ki
h1
Perforations
h2
COMPDAT
99
Historical Flow Rate: WCONHIST
– Used to set a history-matching well’s observed
flow rate
– Control modes: ORAT, WRAT, GRAT, LRAT, RESV
– WCONINJH is injection counterpart
DATES
1 'FEB' 1970 /
/
WCONHIST
--nm stat ctl-by
P1
OPEN
ORAT
oil
wat
gas
VFPtbl
822.3
0.58
6122.5
/
Repeated for each date….
WCONHIST
100
5* /
1
History Strategy in Petrel
• Import
– Well paths (deviation surveys)
– Well completion data
• Completion intervals
• Work-over events
– Production/injection data
• Export
– ECLIPSE Schedule section keywords
10
1
Simulation Advance & Termination
•
•
•
DATES
1 JAN 1998
1 JUN 1998
•
•
TSTEP
1 /
Advance to 12.00 am on 2/6/98
•
•
TSTEP
0.2 /
Advance by 0.2 days
•
END
Conclude simulation
102
/
/
Advance to 12.00 am on 1/1/98
Advance to 12.00 am on 1/6/98
Common Workover Keywords
• WELOPEN
– Open and shut wells at known time
• COMPDAT
– Alter completion properties to simulate plugs, squeezes, frac
jobs
• WELPI, WPIMULT
– Modify well PI
• MULTX, MULTX-, MULTY, MULTY-, MULTZ, MULTZ– Change cell transmissibility to simulate damage
103
Output Control
– To send output to the PRT file:
• RPTSCHED
– Can request many properties to be output
– To send output to Restart file(s )
• RPTRST
– Can request many properties to be output
– Can specify the frequency of output
– Can be used for Restart runs & 3D post-processors
RPTSCHED
104
RPTRST
SCHEDULE Section: Prediction
This slide does not appear in the manual
Purpose of the SCHEDULE Section
• The SCHEDULE section is used to specify
– Well operations to be simulated
– Times (TSTEP, DATES) to be simulated
– Simulator tuning parameters
• The SCHEDULE Section is often used in two
modes:
– History matching – specify actual wells, facilities and
production/injection
– Prediction – specify control mechanisms, new wells,
economic limits
This slide does not appear in the manual
106
Typical Prediction Schedule Section
1.
2.
3.
4.
•
•
5.
6.
107
Specify/Change output frequency
Specify wells, VFP tables, completions
Choose keywords that
Specify Groups
will cause ECLIPSE to
treat wells in a manner
Specify Group & Well:
similar to the company
Economic limits, Well tests
Automatic Workovers, Drilling, etc
Advance the simulation
End of Prediction
operating the field.
Well Production Control: WCONPROD
3
WCONPROD
--nm status ctl-by Oil
ORAT 4000 2000 3* 3000 2* /
P1 is
P1
isunder
underoiloilrate
rate
control…
control…
2.
2.
P1
P1 isismoved
movedtotoBHP
BHP
control…
control…
3.
Water
cut is
rising
and BHP
dropping
P1 is switched to
control by water
rate…
WMCTL = 7 BHP Control
The waterflood has
reached P1 but is not
providing enough
pressure support
BHP rises due
to pressure
support from
the aquifer &
injector
WMCTL = 2
WRAT Control
WMCTL = 1
ORAT
Control
Days
108
WCONPROD
PSIA
1.
WBHP
P1 OPEN
W-G-Limit BHP THP VFP#
Group Production Control
– Group control is used to mimic field operation
– Some Examples:
• Platform A has a certain water-handling capacity
(GCONPROD)
• Facility B uses 25% of it’s gas production to run a treater, the
remaining is sold (GCONSUMP)
• A voidage replacement scheme is implemented in Block C
(GCONINJE)
• To maintain pipeline capacity, Company D will drill wells
whenever the field production falls below a rate (PRIORITY)
109
Economic Limit Definition
– Field/group economic limit (GECON)
– Well economic limit (WECON)
– Individual connection economic limit (CECON)
– Economic limits can be triggered when:
•
•
•
•
•
110
Oil production rate falls below limit
Gas production rate falls below limit
Water cut exceeds limit
Gas-oil ratio exceeds limit
Water-gas ratio exceeds limit
Automatic Workovers
– Triggered by
• Economic limit keywords (WECON, WECONINJ,
CECON)
• Maximum limit set in GCONPROD
– Some examples:
•
•
•
•
•
111
Plug back a well (WPLUG)
Test shut-in wells and reopen (WTEST)
Retube or add pump/gas lift, ie change VFP table (WLIFT)
Cut back producers and injectors (WCUTBACK)
Set up drilling queue (QDRILL, WDRILTIM)
Restart Runs
Field Production Rate
– The solution at the end of
the history period is set
as start conditions for the
prediction runs
– Why bother to
recalculate past
saturations & pressures?
– Restarts save simulation
time!
Cell
Saturations &
Pressures
recorded
History Period
(Base Run)
Prediction Period
(Restart Run)
Time
11
2
Restarts in ECLIPSE Blackoil
• Flexible restart
– Data must be processed (ie the transmissibilities are
recalculated)
– User can change some of the data items from their values
in the original run (ie increase the number of wells)
– Can restart on files written by earlier versions of ECLIPSE
• Fast restart
– Data is stored in a processed form
– Must have been produced by the current version of
ECLIPSE
113
Convergence
Purpose of this session
– Convergence of the simulation equation affects:
• validity of the results
• speed of the simulation run
– Recognizing and correcting convergence problems
is an important part of simulation
– ECLIPSE can be made to produce reports showing
how both the linear and non-linear iterations are
proceeding and the methods by which time steps
are selected
115
What is “Convergence”
–

Advance
Timestep
ECLIPSE uses an iterative
process based on
Newton's method to
solve the non-linear
equations
Linearize the
Equations
Iterate to solve
the linear
equations
The number of non-linear
iterations is a guide to
model convergence
Non-linears
per Timestep
Guide
1
Very easy to converge
2 to 3
Easy to converge
Increasingly difficult flow
situation
4 to 9
> 10
4
Plug the linear
solution into
the non-linear
equation
“Non-linear
iteration”
Problem with model?
11
6
No
Is the
solutio
n
good?
Yes
Requesting Convergence Information
• RPTSCHED
•
“NEWTON=2” /
Days since SOS
Length of
current
timestep
# Satn changes # times P, Rs, Rv
# of linears suppressed changes reduced
Values of worst
residuals
117
Cell w/ that
residual
Material
balance for
that cell
Reason for
# of
Date of current
timestep non-linears
timestep
# cells with
different phases
Press & SWAT change for
that cell (since last
iteration)
# state
transitions
3
Simulation Run Time Improvements
Linear
Iteration
Linear
Iteration
Linear
Iteration
Non-linear
Iteration
Non-linear
Iteration
Non-linear
Iteration
Timestep
Timestep
Reduce when difficult
modeling situations arise
Request reports only
when you need them
The greatest improvements in performance
are obtained by identifying & correcting the
cause of any non-linear problem
118
4
Check all Warning Messages
for data problems
Timestep
Report Step Report Step Report Step
ECLIPSE
Simulation
TUNING keyword
– Controls available from the Schedule section:
• TUNING sets timestepping, iteration and convergence
criteria
– TUNINGL is used for the LGRs in the model
– Guidelines:
• Timestepping controls need alteration fairly frequently
• Iteration controls seldom need adjustment
• Convergence controls need adjustment only in highly
TUNING
unusual circumstance
119
EXTRAPMS
– This keyword instructs ECLIPSE to warn the user
whenever extrapolations are made to PVT (or VFP)
tables
– ECLIPSE stores PVT tables internally as the
reciprocals of FVF and Viscosity* FVF
– If insufficient PVT data is supplied, ECLIPSE may
extrapolate the PVT table data to inaccurate or
non-physical values!
EXTRAPMS
120
Common Causes of Problems
– Data Error
• Typographic errors
• Special Characters & missing
values
Plot & Fix!
– Grid geometry
• Small PV cells next to large PV
cells
– LGRs
• LGR smaller than drainage radius
• Initial contacts outside LGR
– Dual porosity
• High value of sigma
Inactivate with PINCH
or MINPV!
12
1
Treatment of LGRs
– Local time stepping (E100
Only)
• Global time step not limited
by local time step
• Semi-explicit (potentially
unstable)
Local Time Stepping Algorithm
Global Dt Defined
Global Model Solved
– In-place solution
• Fully implicit (unconditionally
stable)
• Global time step = local time
step
• LGRLOCK / LGRFREE turn inplace solution on / off (E100
only)
Local Dt Defined
Local Grid Solved
N
Tglobal =
Tlocal ?
Y
122
Pressures at boundary
Fluxes across boundaries
Group targets solved
Local block pressure
Local saturations
Material balance check
between global and local
Convergence Checklist
– Check all problem and warning messages
– Try removing TUNING keywords
– Identify problem cells and try to work out what is
happening in the cells at the time of the
convergence problems
• For example, PINCH & MINPV can eliminate some
throughput related problems
– Check rel-perm tables for sharp derivative changes
– Avoid PVT extrapolations (EXTRAPMS)
– Avoid VFP extrapolations (EXTRAPMS)
123
Thank You
• Extra Slides
Radial vs Cartesian Keywords
Block-centered
126
Corner Point
Cartesian
Radial
Cartesian
Radial
NX, NY, NZ
NR, NTHETA, NZ
NX, NY, NZ
NR, NTHETA, NZ
DX, DY, DZ
(or
D*V form)
DR (INRAD &
OUTRAD),
DTHETA, DZ (or
D*V form)
COORD, ZCORN
COORD, ZCORN
PERMX, -Y, -Z
PERMR, -THT, -Z
PERMX, -Y, -Z
PERMR, -THT, -Z
MULTX, etc…
MULTR, etc…
MULTX, etc…
MULTR, etc…
Aquifer Modelling
This slide does not appear in the manual
Aquifer Modeling
– ECLIPSE Blackoil provides these aquifer options:
• Numerical Aquifer
• Analytical Aquifer
– Carter-Tracy aquifer
– Fetkovich aquifer
• Flux Aquifer
• Grid Cell Aquifer
128
Numerical Aquifer
GRID
– Nominate grid cells below the OW contact
(AQUNUM)
– Attach the aquifer to the reservoir using AQUCON
– Leave a row of water cells between the aquifer & oil
zone
AQUNUM
--Aq#
I
J
K
Area
Length
Φ
1
3
7
1
1E2
1E2
0.3
/
1
4
7
1
1E4
1E3
0.3
/
1
5
7
1
1E6
1E4
0.3
/
Oil Zone
No Flow
AQUCON
--Aq#
1
129
I1
I2
J1
J2
K1
K2
Face
1
1
2
6
1
1
‘I-’
/
Aquifer Cells
Fetkovich Aquifers
– Fetkovich aquifers are based on a pseudo-steady
state productivity index and material balance
between aquifer pressure and cumulative influx
– They are best suited for smaller aquifers which
may approach psuedo steady state quickly
– In the Solution Section:
• Set up lists of aquifers AQUALIST
• Define the aquifer with AQUFETP
• Connect the aquifer with AQUANCON
130
Carter-Tracy Aquifers
– Carter-Tracy aquifers use tables of dimensionless
time td versus dimensionless pressure Pd(td)to
determine the influx
– Carter-Tracy approximates a fully transient model
– In the Solution Section:
•
•
•
•
131
Set up lists of aquifers AQUALIST
Define the aquifer with AQUCT
Define pressure response with AQUTAB
Connect the aquifer with AQUANCON
Flux Aquifers
– The flux rate is specified directly by the user:
Qai  Fa Ai mi
Fa is the flux
Ai the area of the connecting cell
block
mi is an aquifer influx multiplier
– It may be negative, representing
flux out of the
reservoir
– The flux rate may be modified in the Schedule Section
– In the Solution section
• Set up lists of aquifers AQUALIST
• Specify the aquifer using AQUFLUX
• Attach the aquifer using AQUANCON
132
Grid Cell Aquifer
– Simulation model extends over the water zone
– No extra keywords necessary
133
Output Controls
– Summary Quantities
• Analytic aquifers
– AAQR, AAQT, AAQP
• Numerical aquifers
– ANQR, ANQT, ANQP
– Print file data
• RPTGRID, RPTSCHED, RPTSOL
134