Short Course on Stanford GPRS
(General Purpose Research Simulator)
D. Echeverría Ciaurri and H. Pan
NTNU Workshop P2
October 15, 2008
Outline
Tutorial Presentation
Simple Examples
Black Oil
Compositional
Adjoint-based Optimization
Hands-on Examples
Simulation
Adjoint-based Production Optimization
Derivative-Free History Matching
October 15, 2008
Trondheim, Norway
2
Outline
Tutorial Presentation
Simple Examples
Black Oil
Compositional
Adjoint-based Optimization
Hands-on Examples
Simulation
Adjoint-based Production Optimization
Derivative-Free History Matching
October 15, 2008
Trondheim, Norway
3
I. Tutorial Presentation
October 15, 2008
Trondheim, Norway
4
Outline
Brief Sotfware Description
Input Files
Reservoir
Wells
Control
Output Files
Adjoint-based Optimization
October 15, 2008
Trondheim, Norway
5
Outline
Brief Sotfware Description
Input Files
Reservoir
Wells
Control
Output Files
Adjoint-based Optimization
October 15, 2008
Trondheim, Norway
6
A General Purpose Research Simulator
New Generation of research simulator
Developed by SUPRI-B/HW at Stanford
GPRS is research tool via source code
Object-oriented C++ code
GPRS is not a commercial simulator
limited support
limited pre/post processing
limited functionalities
October 15, 2008
Trondheim, Norway
7
Advanced Features
Structured/unestructured grid
Black-oil/compositional fluid
Two/multi-point flux
Arbitrary choice of primary variables
Variable implicit levels (FIM, IMPES, AIM, …)
Many direct/iterative solvers/preconditioners
Multiple-segmented well-model
Gradients for adjoint-based optimization
October 15, 2008
Trondheim, Norway
8
Research Platform
Optimization
CO2 Sequestration
Generalized Multiple Phase
Compositional/Thermal Model
Flexible Variable Set &
Implicitness
Unstructured Grids/Advanced
Solvers/Advanced Wells
GPRS
Multiscale
Formulation
Geomechanics
Coupling
Chemical
Reaction
Fractured Porous Media
October 15, 2008
Trondheim, Norway
9
GPRS Releases
GPRS 1.0 (initial version, 2002)
GPRS 1.1 (08/03)
GPRS 1.2 (06/04)
GPRS 1.3 (11/04)
GPRS 1.4 (11/05)
GPRS 2.0 (06/06)
GPRS 2.1 (02/07)
GPRS 2.2 (xx/xx)
October 15, 2008
Trondheim, Norway
10
Software Features
Multiple platforms
Visual Studio 6.0
Visual Studio 2005
Linux
Unix (Solaris)
Portable source code
Single C++ source code for all platforms
October 15, 2008
Trondheim, Norway
11
Documentation
GPRS.html
Building instructions
User manual
GPRS software overview
Aplication Programming Interfaces (API)
generated by Doxygen
Under release packages (Enhancements)
October 15, 2008
Trondheim, Norway
12
Packages
Software package
source code
executable and support libraries
building instruction files
samples
Document package
basic simulator
enhancements
October 15, 2008
Trondheim, Norway
13
Executing GPRS
Executables
gprs.exe and gprs_adj.exe
Support libraries
mkl_support.dll and samg_dyn.dll
File gprs.in required
Executable is same directory as input files
or GPRS directory in PATH variable
October 15, 2008
Trondheim, Norway
14
Outline
Brief Sotfware Description
Input Files
Reservoir
Wells
Control
Output Files
Adjoint-based Optimization
October 15, 2008
Trondheim, Norway
15
Main Input File: gprs.in
# --- Field Data --------------------FieldName Field1
# --- Reservoirs Data --------------NumOfReservoirs
1
INCLUDE res_spe1.in
END_RESERVOIRS
# --- Wells Data ---------------------NumOfWells
2
INCLUDE wells_spe1.in
END_WELLS
# --- Control Data -------------------INCLUDE control.in
October 15, 2008
Trondheim, Norway
16
GPRS Input Files
Keywords
beginning: GRID_DATA, FLUID_DATA
end: END, END_RESERVOIRS, END_WELLS
Keyword values
single value: NumOfWells 2
multiple values: GRIDSIZE 3 3 1
array: DX 100 50 50
table (two-dimensional array)
October 15, 2008
Trondheim, Norway
17
GPRS Input Files
Keyword is case sensitive
INCLUDE for inserting files
Comments by #
a blank line is treated as a comment
Spaces at beginning of line are ignored
one space between two inputs; rest ignored
n*X = X X … X (n times)
6*34 = 34 34 34 34 34 34
October 15, 2008
Trondheim, Norway
18
Basic GPRS Input
# --- Field Data --------------------FieldName Field1
# --- Reservoirs Data --------------NumOfReservoirs
1
INCLUDE res_spe1.in
END_RESERVOIRS
# --- Wells Data ---------------------NumOfWells
2
INCLUDE wells_spe1.in
END_WELLS
# --- Control Data -------------------INCLUDE control.in
October 15, 2008
Trondheim, Norway
19
Reservoir Input
Grid data
grid geometry and properties
Fluid data
phase and component properties
Phase component relation data
component existence in each phase
October 15, 2008
Trondheim, Norway
20
Reservoir Input
Rock fluid data
relative permeability and capillary pressure
Rock data
rock compressibility
Initial equilibrium data
initial pressure/saturation, WOC/GOC depth
October 15, 2008
Trondheim, Norway
21
Grid Data
GRID_DATA ###################
GRIDSIZE
10 10 3
DX
1000
DY
1000
DZ
100*20
100*30
100*50
PERMX
100*500
100*50
100*200
PERMY
100*500
100*50
100*200
PERMZ
100*500
100*50
100*200
PORO
0.3
TOPS
8325
TEMP
500
END
October 15, 2008
Trondheim, Norway
22
Fluid Data
FLUID_DATA ##################
FLUID_TYPE BLACK_OIL
NPHASES
2
NCOMPONENTS 2
PHASE_NAME OIL
STANDARD_DENS 49.1
NUM_OF_TABLE_ENTRIES 2
#
P
BO
#
PSI
RB/STB
14.7
1.03
1014.7
1.0106
PHASE_NAME WATER
STANDARD_DENS 64.79
NUM_OF_TABLE_ENTRIES 2
#
P
BW
#
PSI
RB/BBL
14.7
1.0410
264.7
1.0403
END
October 15, 2008
VISC
CP
1.2
1.2
RGO
SCF/STB
0
0
VISC
CP
0.31
0.31
RGW
SCF/STB
0
0
Trondheim, Norway
23
Phase Component Relation Data
PHASE_COMP_RELATION_DATA ##################
# --- (nPhases by nComps) --#comp:
oil
water
1
0
#oil
0
1
#water
END
October 15, 2008
Trondheim, Norway
24
Rock Fluid Data
ROCKFLUID_DATA ##################
#OILWATERPERM
OW
NUM_OF_TABLE_ENTRIES 12
#TABLE
Sw
KRw
KROw
PCow
0.0
0.0
1.0
0
0.1
0.0
0.960
0
0.2
0.0
0.875
0
0.25
0.0
0.800
0
0.30
0.010
0.700
0
0.40
0.040
0.430
0
0.50
0.075
0.230
0
0.60
0.125
0.100
0
0.70
0.2
0.025
0
0.80
0.3
0.000
0
0.90
0.575
0.000
0
1.0
1.0
0.000
0
END
October 15, 2008
Trondheim, Norway
25
Rock Data
ROCK_DATA ####################
#
COMP.
REF. PRES
3.E-6
14.7
October 15, 2008
Trondheim, Norway
26
Initial Equilibrium Data
EQUILIBRIUM_DATA ###################
#
Swi
Sor
Sgr
0.15
0.00
0.00
#
pres
4800
@depth
8400
WOC
8500
GOC
8200
END
October 15, 2008
Trondheim, Norway
27
Standard Well Input
Well specifications
well name
group name
reservoir it belongs to
producer or injector
well status
Well completions
completion block index
well index
Well control strategy
October 15, 2008
Trondheim, Norway
28
Grid Indexing
i
j
k
Grid index: (i-1) + (j-1)*Nx + (k-1)*Nx*Ny
Nx: number of grid blocks in x direction
Ny: number of grid blocks in y direction
October 15, 2008
Trondheim, Norway
29
Well Specification Data
# PRODUCTION WELLS
# WELSPECS
# WELL_NAME
PROD01
END
GROUP
GRP1
RES_NAME
RES1
TYPE
P
STATUS
OPEN
RES_NAME
RES1
TYPE
I
STATUS
OPEN
# INJECTION WELLS
# WELSPECS
# WELL_NAME
INJ01
END
October 15, 2008
GROUP
GRP1
Trondheim, Norway
30
Well Completion Data
# COMPDAT
number_of_perforations 1
# LOC(i,j,k)
WI
399
9410
END
October 15, 2008
Trondheim, Norway
31
Multi-Segment Wells
# WELSEGS
# PresDrop
HFA
END
FlowModel
DF
number_of_segments 5
# No.of Branch Outlet Length Depth
# Seg
Num
Seg Change Change
#
0
default homogeneous segment
1
0
0
0.1
0
2
0
1
400
0
3
0
2
1
0
4
0
3
400
0
October 15, 2008
Trondheim, Norway
Diam
Rough
0.15
0.15
0.03
0.15
0.001
0.01
0.01
0.01
32
Multi-Segment Wells
# CHOKE DEFINITION
CHOKES
number_of_chokes
1
# Seg num
Choke model
4
0
Cv
0.66
# --- well completions (trajectory) ------# COMPDAT
number_of_connections 2
#LOC(i,j,k)
WI
Seg No.
18
9705
15
23
9705
20
October 15, 2008
Trondheim, Norway
33
Well Control Data
Control type
ORATE
WRATE
GRATE
LRATE
BHP
TBHP, TORATE, TWRATE, …
October 15, 2008
Trondheim, Norway
34
Well Control Data
# PRODUCTION WELLS
#
CTRL
Q
BHP
ORATE
6000
1000.0
BHP
1000.0
END
# INJECTION WELLS
#
CTRL
Q
BHP
WRATE 6000
10000.0
BHP
10000.0
END
October 15, 2008
std_den
49.10
std_den
64.79
Trondheim, Norway
NComp OCon WCon
2
0
1
2
0
1
35
Well Control Data
# PRODUCTION WELLS
#
CTRL
tINI
TBHP
0
TBHP
100
TBHP
200
TBHP
400
END
tEND
100
200
400
500
BHP
4277.99
4300.55
4283.54
4296.56
# INJECTION WELLS
#
CTRL
tINI
TBHP
0
TBHP
100
TBHP
200
TBHP
400
END
tEND
100
200
400
500
BHP
NComp OCon WCon
5677.99
2
0
1
5645.23
2
0
1
5667.78
2
0
1
5679.29
2
0
1
October 15, 2008
Trondheim, Norway
36
Control Input
Timestep
initial, minimum/maximum and total
Timestep control
desired variable change and tuning factor
Newton iteration
minimum/maximum and fixed number
Newton iteration control
convergence criteria for variables/residuals
October 15, 2008
Trondheim, Norway
37
Control Input
Formulation
type of variables to use, implicit levels
Linear Solver
solver/preconditioner and stopping criteria
Debug
enable/disable, frequency of debug output
Restart
enable/disable
October 15, 2008
Trondheim, Norway
38
Control Input
#
TSINIT TSMAXZ
1
60
#
TSTEP
3650
TSMIN
1
# --- iteration control -------# minNewtonIter
maxNewtonIter
1
12
fixedNewtonIter
30
# --- time step size control --#
dp
ds
dx
w
200 0.2 0.02 0.5
# --- Newton iteration convergence control ---# MBE PEE Pchange Schange MFChange relWellEqE
0.1 0.02
0.0001
0.005
0.001
0.001
October 15, 2008
Trondheim, Norway
39
Control Input
# --- solution method control --# variType nImpTypes Percentages(AIM)
1
1
# nImpVars transOption CFL_Limit
2
4
1.0
# --- linear solver control -----# Solver Precond.
tol
maxIter
4
3
1E-6
1500
reStartNo
10
# --- debug information --#Flag
NumOfTimeSteps
1
10
# --- Re-start file setting information --#Flag
NumOfTimeSteps output-control
0
1
1
October 15, 2008
Trondheim, Norway
40
Outline
Brief Sotfware Description
Input Files
Reservoir
Wells
Control
Output Files
Adjoint-based Optimization
October 15, 2008
Trondheim, Norway
41
Output Files
One output file for each well
name: reservoir_well.out
example: RES1_PROD.out, RES1_INJ.out
Debug output (optional)
name: reservoir_debug.out
example: RES1_debug.out
Restat output (optional)
reStartFile.dat
October 15, 2008
Trondheim, Norway
42
Production Well Output
Results for well: PROD in the reservoir: RES1
t
(days)
0
1
2
3.59794
6.36781
11.0357
18.256
29.8017
46.1893
69.5331
October 15, 2008
BHP
(psia)
4303.69
3856.11
3779.25
3723.07
3673.08
3630.13
3599.82
3583.64
3580.45
3585.56
g(Oil)
(STB/day)
0
6000
6000
6000
6000
6000
6000
6000
6000
6000
Trondheim, Norway
q(Water)
(STB/day)
0
0
0
0
0
0
0
0
0
0
43
Injection Well Output
Results for well: INJ in the reservoir: RES1
t
(days)
0
1
2
3.59794
6.36781
11.0357
18.256
29.8017
46.1893
69.5331
October 15, 2008
BHP
(psia)
5260.07
5766.46
5881.56
6021.55
6221.39
6512.4
6657.32
6584.5
6437.49
6332.23
g(Oil)
(STB/day)
0
0
0
0
0
0
0
0
0
0
Trondheim, Norway
q(Water)
(STB/day)
0
-6000
-6000
-6000.01
-6000.77
-5999.78
-6000.65
-6000.07
-6000.01
-6000
44
Debug File
Results of block pressure and saturations for
reservoir: RES1
BlockNo
t=0
0
1
2
398
399
P
(days)
4781.88
4781.88
4781.88
.
.
.
4781.88
4781.88
T
So
Sw
xi
yi
40
40
40
0.85
0.85
0.85
0.15
0.15
0.15
1.0
1.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0
1.0
1.0
1.0
40
40
0.85
0.85
0.15
0.15
1.0
1.0
0.0
0.0
0.0
0.0
1.0
1.0
0.322 0.678 1.0
0.449 0.551 1.0
0.651 0.342 1.0
0.0
0.0
0.0
0.0
0.0
0.0
1.0
1.0
1.0
t=69.5331 (days)
0
5460.95 40
1
5286.71 40
2
5144.51 40
.
.
.
October 15, 2008
Trondheim, Norway
45
Restart File
6000
0 9313.02
1 9208.15
2 9144.2
3 9099.27
4 9064.57
5 9036.33
500
500
500
500
500
500
0.193141
0.194062
0.195721
0.198067
0.200184
0.205041
0.806859
0.805938
0.804279
0.801933
0.799816
0.794959
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
..
.
October 15, 2008
Trondheim, Norway
46
Outline
Brief Sotfware Description
Input Files
Reservoir
Wells
Control
Output Files
Adjoint-based Optimization
October 15, 2008
Trondheim, Norway
47
Adjoint-based Optimization
MATLAB code in seven folders
main script ResOptDT.m in \main folder
simulation data in \data folder
Optimization parameters in \data\adjoint.in
Features available
exact gradient: BHP control + rate constraints
approximate gradient: rate control
history matching: permeability and porosity
October 15, 2008
Trondheim, Norway
48
adjoint.in
NGRIDS
605
NCOMPONENTS
2
NPHASES
2
OIL_DENSITY
49.10
WATER_DENSITY
64.79
NPROD
4
NINJ
1
October 15, 2008
// lbm/scf
// lbm/scf
Trondheim, Norway
49
adjoint.in
OIL_PRICE
80
WATER_INJ_COST
0
WATER_PROD_COST
5
TSTEPS
4
RESERVOIR_NAME
RES1
MAX_ITERS
20
TOT_CNSTRNT
4000
October 15, 2008
// $/bbl
// $/bbl
// $/bbl
// resevoir name as in gprs.in
// of optim algorithm (orig 2)
// rate constraint (bbl/day)
Trondheim, Norway
50
adjoint.in
NPERFS
//inj
prod
5
5
5
5
5
0
LOWER_BNDS
//inj
prod
1000
1000
1000
UPPER_BNDS
//inj
prod
10000
10000
10000
CONTROL_TABLE
//dt
inj
180 10000.00 1000.0 1000.0
180 10000.00 1000.0 1000.0
180 10000.00 1000.0 1000.0
180 10000.00 1000.0 1000.0
180 10000.00 1000.0 1000.0
180 10000.00 1000.0 1000.0
October 15, 2008
1000
1000
10000
prod
1000.0
1000.0
1000.0
1000.0
1000.0
1000.0
10000
Trondheim, Norway
1000.0
1000.0
1000.0
1000.0
1000.0
1000.0
51
Sample Files
Black-oil model
SPE1: the first SPE comparative project
SPE1_HW: non-conventional well and SPE1
BlackOW: water-oil two phases with water injection
MSWell3Laterals: gas-oil two phases, three lateral
multiple segment wells, drift-flux wellbore flow model
Black3PinjGas: gas-oil-water three phases with gas
injection
Black3PinjWater: gas-oil-water three phases with
water injection
unstruc_mp: unstructured grids and multi-point flux
with water-oil two phases
October 15, 2008
Trondheim, Norway
52
Sample Files
Compositional model
CO2-H2O: sample for CO2 sequestration in aquifer; oilgas two phases, one prod. well and one gas inj. well
CO2-H2O-fast: fast flash method for CO2-H2O
COMP: four comp., oil-gas two phases, one prod. well
CompSPE9: nine comp., oil-gas two phases, one prod.
well
CompSPE9-3000: as CompSPE9 sample but initial
reservoir pressure is 3000 psia and initial fluid is gas
Comp2PinjGas: four comp., oil-gas two phases, one
prod. well and one gas inj. well
Comp3PinjGas: four comp., oil-gas-water three phases,
one prod. well and one gas inj. well
Comp3PinjWater: four components, oil-gas-water three
phases, one prod. well and one water inj. well
October 15, 2008
Trondheim, Norway
53
Enhancements
\CO2H2OfastFlash: fast flash for CO2-H2O
system in CO2 sequestration in aquifers
(replaced by LookUp-K)
\LookUp-K: lookup-K approach for flash in
compositional simulation
\Diffusion: diffusion & dispersion in
compositional simulation
\inactiveCells: removing inactive cells
\Multi_rockfluid: implementing multiple rock
fluid model
October 15, 2008
Trondheim, Norway
54
Enhancements
\MSWells: implementing multi-segment well
modeling
\relativePermeability: hysteresis of relative
permeability, Stone I model for three phase
relative permeability
\SAMG preconditioner: SAMG preconditioner in the iterative linear solvers
\Time Dependent Well Control:
implementing time-dependent well controls
\Tracer Flow: implementing tracer flow.
October 15, 2008
Trondheim, Norway
55
Summary
GPRS: research tool via portable source code
Now some representative simple examples
In the afternoon more realistic cases
Special needs/questions contact:
Huanquan Pan (hqpan@stanford.edu)
me (echeverr@stanford.edu)
October 15, 2008
Trondheim, Norway
56
Some more
questions?
October 15, 2008
Trondheim, Norway
57
Outline
Tutorial Presentation
Simple Examples
Black Oil
Compositional
Adjoint-based Optimization
Hands-on Examples
Simulation
Adjoint-based Production Optimization
Derivative-Free History Matching
October 15, 2008
Trondheim, Norway
58
II. Simple Examples
October 15, 2008
Trondheim, Norway
59
Simple Black-Oil (SPE1)
10 x 10 x 3 grid
3 distinct layers
Black-oil oil-water-gas model
One gas injector
One producer controlled by oil rate
Ten year production
October 15, 2008
Trondheim, Norway
60
Unstructured Grid and Multi-Point Flux
301 x 1 x 1 grid
Volume and connection list
Black-oil oil-water model
One water injector
One producer controlled by oil rate
Long production
October 15, 2008
Trondheim, Norway
61
Compositional (SPE3)
5 x 5 x 5 grid
Homogeneous reservoir
permx = 10*permz
9 components and 2 phases (gas-oil)
One producer controlled by BHP
2000 day production
October 15, 2008
Trondheim, Norway
62
Adjoint-based Optimization
11 x 11 x 5 grid
5 distinct layers
Black-oil oil-water model
Five-spot pattern
One water injector
All wells controlled by BHP
750 day production
25 control intervals (125 control variables)
+ total producing liquid rate constraint
October 15, 2008
Trondheim, Norway
63
Outline
Tutorial Presentation
Simple Examples
Black Oil
Compositional
Adjoint-based Optimization
Hands-on Examples
Simulation
Adjoint-based Production Optimization
Derivative-Free History Matching
October 15, 2008
Trondheim, Norway
64
III. Hands-on Examples
October 15, 2008
Trondheim, Norway
65
Optimizing Smart Wells
(from Sarma et al.)
1 ‘smart’ horizontal
injector
1 ‘smart’ horizontal
producer
45 segments in each
Two-phase flow, no
gravity
1 PV injection in
reference
Segments under BHP
control
October 15, 2008
Adapted from Brouwer and Jansen, SPE 78278
Trondheim, Norway
66
Optimizing Smart Wells
(from Sarma et al.)
45X45X1 (2025) Cells
5 control changes in time
Unknowns:
(45+45)*5 =450
Objective: maximize NPV
Max inj. rate ≤ 2710
bbl/day
October 15, 2008
Adapted from Brouwer and Jansen, SPE 78278
Trondheim, Norway
67
Optimizing Smart Wells
(from Sarma et al.)
October 15, 2008
Trondheim, Norway
68
A Section of SPE10
(from Dewi Rahmawati et al.)
Log10(K)[mD]
P3
P4
10000mD
30
25
1000mD
20
INJ
x
100mD
15
10
10mD
5
0
October 15, 2008
P1
0
P2
5
10
15
20
y
25
30
Trondheim, Norway
35
40
0
69
History Matching Optimization
• History Matching and Optimization
• Generic Workflow
• Case Study: Stanford VI Sector
• History Matching Results
October 15, 2008
Trondheim, Norway
70
History Matching
observe
m*
O* (m* )
O (m
)
m̂ = argmin || O(m ) − O(m ) ||
*
m
October 15, 2008
m∈M
Trondheim, Norway
71
Integrating Data
• Model m: facies
• Observable O(m) = [Op(m) Os(m)]
– Op(m): production data
– Os(m): seismic data
• Scaling: Op(m) ~ Os(m)
October 15, 2008
Trondheim, Norway
72
Observables
• Production Op(m) = [Owi(m) Oop(m)]
– Owi(m) : total water injection
– Oop(m): cumulative oil production
• Seismic
Os(m) = [Os1(m) Os2(m)]
– Os1(m) : crosswell section 1
– Os2(m) : crosswell section 2
October 15, 2008
Trondheim, Norway
73
Observables
• Production Op(m) = [Owi(m) Oop(m)]
• Seismic
Os(m) = [Os1(m) Os2(m)]
• Two types of seismics
– wave velocity (VP)
– diffraction tomography
October 15, 2008
Trondheim, Norway
74
Cost Function
• Flexible cost function || O(m ) − O(m* ) ||
ωp || Op (m ) − Op (m* ) || +ωs || Os (m ) − Os (m* ) ||
• Weights modified along optimization
• Regularized:
October 15, 2008
+ λ || m − mprior ||
Trondheim, Norway
75
Seismic Data: Tomography
• VP cannot be directly measured
• VP indirectly estimated
– multiple sources
– inversion process
• Diffraction tomography
October 15, 2008
Trondheim, Norway
source
rG
rS
receptor
76
Tomography Results
model m
VP
October 15, 2008
tomography
Trondheim, Norway
77
Tomography Results
true model m*
VP
October 15, 2008
tomography
Trondheim, Norway
78
History Matching Optimization
• History Matching and Optimization
• Generic Workflow
• Case Study: Stanford VI Sector
• History Matching Results
October 15, 2008
Trondheim, Norway
79
Workflow
m*
less
parameters
many
parameters
Op(m)
ξ
KPCA
m
rock
properties
to
optimizer
||.||
Os(m)
facies
October 15, 2008
Trondheim, Norway
80
Principal Component Analysis
• Principal Component Analysis (PCA)
• Data compression approach
• Based on a priori statistical information
October 15, 2008
Trondheim, Norway
81
Cost Function Gradients
• Cost function = production + seismic
• No strategy for exact gradients
• Derivative-free optimizer
• Fairly efficient optimization scheme
• Very easy to implement and robust
October 15, 2008
Trondheim, Norway
13
82
History Matching Optimization
• History Matching and Optimization
• Generic Workflow
• Case Study: Stanford VI Sector
• History Matching Results
October 15, 2008
Trondheim, Norway
83
Some Results
• 20x20x10 sector from zone 3
• m: facies
• k, φ: regression from well location
• VP as seismics
• PCA: 30 coefficients retained
• Measured data only after 3 months
October 15, 2008
Trondheim, Norway
84
Production Data
injector
producer
5 spot
October 15, 2008
Trondheim, Norway
85
Seismic Data
injector
producer
5 spot
October 15, 2008
Trondheim, Norway
86
Velocities (VP)
z
z
x
y
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
87
Facies
y
x
LAYER 1
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
88
Facies
y
x
LAYER 1
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
89
Facies
y
x
LAYER 4
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
90
Facies
y
x
LAYER 4
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
91
Facies
y
x
LAYER 6
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
92
Facies
y
x
LAYER 6
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
93
Facies
y
x
LAYER 10
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
94
Facies
y
x
LAYER 10
October 15, 2008
true
initial
after production
alternating
Trondheim, Norway
95
Thank you
for
attending!
October 15, 2008
Trondheim, Norway
96
Short Course on Stanford GPRS
(General Purpose Research Simulator)
D. Echeverría Ciaurri and H. Pan
NTNU Workshop P2
October 15, 2008
October 15, 2008
Trondheim, Norway
97