short course on stanford gprs (general purpose research

Short Course on Stanford GPRS(General Purpose Research Simulator)

D. Echeverría Ciaurri and H. Pan

NTNU Workshop P2October 15, 2008

October 15, 2008 Trondheim, Norway 2

Outline

� Simple Examples

� Tutorial Presentation

� Black Oil� Compositional� Adjoint-based Optimization

� Hands-on Examples� Simulation� Adjoint-based Production Optimization� Derivative-Free History Matching


Outline

� Simple Examples





I. Tutorial Presentation


Outline

� Input Files

� Brief Sotfware Description

� Reservoir

� Wells

� Output Files

� Control

� Adjoint-based Optimization


Outline

� Input Files


� Reservoir

� Wells

� Output Files

� Control



A General Purpose Research Simulator

� New Generation of research simulator

� Developed by SUPRI-B/HW at Stanford

� GPRS is not a commercial simulator

� GPRS is research tool via source code

� limited support

� limited pre/post processing

� limited functionalities

� Object-oriented C++ code


Advanced Features

� Structured/unestructured grid

� Black-oil/compositional fluid

� Arbitrary choice of primary variables

� Two/multi-point flux

� Variable implicit levels (FIM, IMPES, AIM, …)

� Many direct/iterative solvers/preconditioners

� Gradients for adjoint-based optimization

� Multiple-segmented well-model


Fractured Porous Media

MultiscaleFormulation

Generalized Multiple Phase Compositional/Thermal Model

GPRS

Unstructured Grids/Advanced Solvers/Advanced Wells

CO2 Sequestration

GeomechanicsCoupling

Chemical Reaction

Opt

imiz

atio

n

Flexible Variable Set & Implicitness

Research Platform


GPRS Releases

� GPRS 1.0 (initial version, 2002)

� GPRS 1.1 (08/03)

� GPRS 1.3 (11/04)

� GPRS 1.2 (06/04)

� GPRS 1.4 (11/05)

� GPRS 2.0 (06/06)

� GPRS 2.2 (xx/xx)

� GPRS 2.1 (02/07)


Software Features

� Multiple platforms

� Visual Studio 6.0

� Visual Studio 2005

� Linux

� Unix (Solaris)

� Portable source code

� Single C++ source code for all platforms


Documentation

� Building instructions

� User manual

� Under release packages (Enhancements)

� GPRS software overview

� Aplication Programming Interfaces (API)

� generated by Doxygen

� GPRS.html


Packages

� Software package

� source code

� executable and support libraries

� building instruction files

� samples

� Document package

� basic simulator

� enhancements


Executing GPRS

� Support libraries

� File gprs.in required

� Executable is same directory as input files

� or GPRS directory in PATH variable

� Executables

� gprs.exe and gprs_adj.exe

� mkl_support.dll and samg_dyn.dll


Outline

� Input Files


� Reservoir

� Wells

� Output Files

� Control



# --- Field Data ---------------------FieldName Field1

# --- Reservoirs Data ---------------NumOfReservoirs 1INCLUDE res_spe1.inEND_RESERVOIRS

# --- Wells Data ----------------------NumOfWells 2INCLUDE wells_spe1.inEND_WELLS

# --- Control Data --------------------INCLUDE control.in

Main Input File: gprs.in


GPRS Input Files

� Keyword values

� Keywords

� beginning: GRID_DATA, FLUID_DATA

� single value: NumOfWells 2

� end: END, END_RESERVOIRS, END_WELLS

� multiple values: GRIDSIZE 3 3 1

� array: DX 100 50 50

� table (two-dimensional array)


GPRS Input Files

� INCLUDE for inserting files

� Comments by #

� n*X = X X … X (n times)

� Spaces at beginning of line are ignored

� one space between two inputs; rest ignored

� Keyword is case sensitive

� a blank line is treated as a comment

� 6*34 = 34 34 34 34 34 34


# --- Field Data ---------------------FieldName Field1

# --- Reservoirs Data ---------------NumOfReservoirs 1INCLUDE res_spe1.inEND_RESERVOIRS

# --- Wells Data ----------------------NumOfWells 2INCLUDE wells_spe1.inEND_WELLS

# --- Control Data --------------------INCLUDE control.in

Basic GPRS Input


Reservoir Input

� Grid data

� grid geometry and properties

� Fluid data

� phase and component properties

� Phase component relation data

� component existence in each phase


Reservoir Input

� Rock fluid data

� relative permeability and capillary pressure

� Rock data

� rock compressibility

� Initial equilibrium data

� initial pressure/saturation, WOC/GOC depth


GRID_DATA ###################GRIDSIZE 10 10 3DX

1000DY

1000DZ

100*20 100*30 100*50PERMX

100*500 100*50 100*200PERMY

100*500 100*50 100*200PERMZ

100*500 100*50 100*200PORO

0.3TOPS

8325TEMP

500END

Grid Data


FLUID_DATA ##################FLUID_TYPE BLACK_OILNPHASES 2NCOMPONENTS 2

PHASE_NAME OIL STANDARD_DENS 49.1NUM_OF_TABLE_ENTRIES 2# P BO VISC RGO # PSI RB/STB CP SCF/STB

14.7 1.03 1.2 01014.7 1.0106 1.2 0

PHASE_NAME WATER STANDARD_DENS 64.79NUM_OF_TABLE_ENTRIES 2# P BW VISC RGW# PSI RB/BBL CP SCF/STB

14.7 1.0410 0.31 0264.7 1.0403 0.31 0

END

Fluid Data


PHASE_COMP_RELATION_DATA ################### --- (nPhases by nComps) ---

#comp: oil water

1 0 #oil

0 1 #water

END

Phase Component Relation Data


ROCKFLUID_DATA ###################OILWATERPERMOWNUM_OF_TABLE_ENTRIES 12#TABLE Sw KRw KROw PCow

0.0 0.0 1.0 00.1 0.0 0.960 00.2 0.0 0.875 00.25 0.0 0.800 00.30 0.010 0.700 00.40 0.040 0.430 00.50 0.075 0.230 00.60 0.125 0.100 00.70 0.2 0.025 00.80 0.3 0.000 00.90 0.575 0.000 01.0 1.0 0.000 0

END

Rock Fluid Data


ROCK_DATA ##################### COMP. REF. PRES

3.E-6 14.7

Rock Data


EQUILIBRIUM_DATA #################### Swi Sor Sgr

0.15 0.00 0.00

# pres @depth WOC GOC

4800 8400 8500 8200

END

Initial Equilibrium Data


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


j

i

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

Grid Indexing


# PRODUCTION WELLS

# WELSPECS

# WELL_NAME GROUP RES_NAME TYPE STATUS

PROD01 GRP1 RES1 P OPENEND

# INJECTION WELLS

# WELSPECS# WELL_NAME GROUP RES_NAME TYPE STATUS

INJ01 GRP1 RES1 I OPEN

END

Well Specification Data


# COMPDAT

number_of_perforations 1

# LOC(i,j,k) WI

399 9410

END

Well Completion Data


# WELSEGS# PresDrop FlowModelHFA DF

END

number_of_segments 5# No.of Branch Outlet Length Depth Diam Rough # Seg Num Seg Change Change# 0 default homogeneous segment

1 0 0 0.1 0 0.15 0.0012 0 1 400 0 0.15 0.013 0 2 1 0 0.03 0.014 0 3 400 0 0.15 0.01

Multi-Segment Wells


# CHOKE DEFINITION

CHOKESnumber_of_chokes 1# Seg num Choke model Cv

4 0 0.66

# --- well completions (trajectory) -------# COMPDAT

number_of_connections 2#LOC(i,j,k) WI Seg No.

18 9705 1523 9705 20

Multi-Segment Wells


Well Control Data

� Control type

� ORATE

� WRATE

� GRATE

� LRATE

� BHP

� TBHP, TORATE, TWRATE, …


# PRODUCTION WELLS

# CTRL Q BHP std_den

ORATE 6000 1000.0 49.10

BHP 1000.0

END

# INJECTION WELLS

# CTRL Q BHP std_den NComp OCon WCon

WRATE 6000 10000.0 64.79 2 0 1

BHP 10000.0 2 0 1

END

Well Control Data


# PRODUCTION WELLS# CTRL tINI tEND BHP

TBHP 0 100 4277.99TBHP 100 200 4300.55TBHP 200 400 4283.54TBHP 400 500 4296.56

END

# INJECTION WELLS# CTRL tINI tEND BHP NComp OCon WCon

TBHP 0 100 5677.99 2 0 1TBHP 100 200 5645.23 2 0 1TBHP 200 400 5667.78 2 0 1TBHP 400 500 5679.29 2 0 1

END

Well Control Data


Control Input

� Timestep control

� Newton iteration

� minimum/maximum and fixed number

� Timestep

� initial, minimum/maximum and total

� desired variable change and tuning factor

� Newton iteration control

� convergence criteria for variables/residuals


Control Input

� Linear Solver

� Debug

� enable/disable, frequency of debug output

� Formulation

� type of variables to use, implicit levels

� solver/preconditioner and stopping criteria

� Restart

� enable/disable


# TSINIT TSMAXZ TSMIN1 60 1

# TSTEP

3650

# --- iteration control --------

# minNewtonIter maxNewtonIter fixedNewtonIter1 12 30

# --- time step size control ---

# dp ds dx w200 0.2 0.02 0.5

# --- Newton iteration convergence control ----

# MBE PEE Pchange Schange MFChange relWellEqE0.1 0.02 0.0001 0.005 0.001 0.001

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 reStartNo4 3 1E-6 1500 10

# --- debug information ---

#Flag NumOfTimeSteps1 10

# --- Re-start file setting information ---

#Flag NumOfTimeSteps output-control0 1 1

Control Input


Outline

� Input Files


� Reservoir

� Wells

� Output Files

� Control



Output Files

� Debug output (optional)

� Restat output (optional)

� reStartFile.dat

� One output file for each well

� name: reservoir_well.out

� name: reservoir_debug.out

� example: RES1_PROD.out, RES1_INJ.out

� example: RES1_debug.out


Results for well: PROD in the reservoir: RES1

t BHP g(Oil) q(Water)(days) (psia) (STB/day) (STB/day)0 4303.69 0 0 1 3856.11 6000 0 2 3779.25 6000 0 3.59794 3723.07 6000 0 6.36781 3673.08 6000 0 11.0357 3630.13 6000 0 18.256 3599.82 6000 0 29.8017 3583.64 6000 0 46.1893 3580.45 6000 0 69.5331 3585.56 6000 0

Production Well Output


Results for well: INJ in the reservoir: RES1

t BHP g(Oil) q(Water)(days) (psia) (STB/day) (STB/day)0 5260.07 0 0 1 5766.46 0 -6000 2 5881.56 0 -6000 3.59794 6021.55 0 -6000.01 6.36781 6221.39 0 -6000.77 11.0357 6512.4 0 -5999.78 18.256 6657.32 0 -6000.65 29.8017 6584.5 0 -6000.07 46.1893 6437.49 0 -6000.01 69.5331 6332.23 0 -6000

Injection Well Output


Results of block pressure and saturations for reservoir: RES1

BlockNo P T So Sw xi yi

t=0 (days)0 4781.88 40 0.85 0.15 1.0 0.0 0.0 1.01 4781.88 40 0.85 0.15 1.0 0.0 0.0 1.02 4781.88 40 0.85 0.15 1.0 0.0 0.0 1.0

...398 4781.88 40 0.85 0.15 1.0 0.0 0.0 1.0 399 4781.88 40 0.85 0.15 1.0 0.0 0.0 1.0

t=69.5331 (days)0 5460.95 40 0.322 0.678 1.0 0.0 0.0 1.0 1 5286.71 40 0.449 0.551 1.0 0.0 0.0 1.0 2 5144.51 40 0.651 0.342 1.0 0.0 0.0 1.0

...

Debug File


6000

0 9313.02 500 0.193141 0.806859 1 0 0 1

1 9208.15 500 0.194062 0.805938 1 0 0 1

2 9144.2 500 0.195721 0.804279 1 0 0 1

3 9099.27 500 0.198067 0.801933 1 0 0 1

4 9064.57 500 0.200184 0.799816 1 0 0 1

5 9036.33 500 0.205041 0.794959 1 0 0 1...

Restart File


Outline

� Input Files


� Reservoir

� Wells

� Output Files

� Control



Adjoint-based Optimization

� Optimization parameters in \data\adjoint.in

� exact gradient: BHP control + rate constraints

� MATLAB code in seven folders

� main script ResOptDT.m in \main folder

� approximate gradient: rate control

� simulation data in \data folder

� Features available

� history matching: permeability and porosity


NGRIDS605NCOMPONENTS2NPHASES2OIL_DENSITY // lbm/scf49.10WATER_DENSITY // lbm/scf64.79NPROD4NINJ1

adjoint.in


OIL_PRICE // $/bbl80WATER_INJ_COST // $/bbl0WATER_PROD_COST // $/bbl5TSTEPS4RESERVOIR_NAME // resevoir name as in gprs.inRES1MAX_ITERS // of optim algorithm (orig 2)20TOT_CNSTRNT // rate constraint (bbl/day)4000

adjoint.in


NPERFS //inj prod5 5 5 5 5 0LOWER_BNDS //inj prod1000 1000 1000 1000 1000 UPPER_BNDS //inj prod10000 10000 10000 10000 10000CONTROL_TABLE //dt inj prod180 10000.00 1000.0 1000.0 1000.0 1000.0180 10000.00 1000.0 1000.0 1000.0 1000.0180 10000.00 1000.0 1000.0 1000.0 1000.0180 10000.00 1000.0 1000.0 1000.0 1000.0180 10000.00 1000.0 1000.0 1000.0 1000.0180 10000.00 1000.0 1000.0 1000.0 1000.0

adjoint.in


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


Sample Files

� Compositional model

� CO2-H2O: sample for CO2 sequestration in aquifer; oil-gas 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


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


Enhancements

� \MSWells: implementing multi-segment well modeling

� \relativePermeability: hysteresis of relative permeability, Stone I model for three phase relative permeability

� \SAMG preconditioner: SAMG pre-conditioner in the iterative linear solvers

� \Time Dependent Well Control: implementing time-dependent well controls

� \Tracer Flow: implementing tracer flow.


Summary

� GPRS: research tool via portable source code

� Special needs/questions contact:

� Now some representative simple examples

� Huanquan Pan ([email protected])

� me ([email protected])

� In the afternoon more realistic cases


Some more questions?


Outline

� Simple Examples





II. Simple Examples


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


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


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


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


Outline

� Simple Examples





III. Hands-on Examples


� 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

controlAdapted from Brouwer and Jansen, SPE 78278

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


Adapted from Brouwer and Jansen, SPE 78278


0 5 10 15 20 25 30 35 400

5

10

15

20

25

30

Log10(K)[mD]

y

x

P1

P3

P2

P4

INJ

0

10mD

100mD

1000mD

10000mD

A Section of SPE10(from Dewi Rahmawati et al.)


• History Matching and Optimization

• Generic Workflow

• Case Study: Stanford VI Sector

• History Matching Results

History Matching Optimization


m ( ) ( ) ||mOmO|| minargm̂ *

Mm−=

∈

m**

observe ( )** mO

( )mO

History Matching


• Model m: facies

• Observable O(m) = [Op(m) Os(m)]

– Op(m): production data

– Os(m): seismic data

• Scaling: Op(m) ~ Os(m)

Integrating Data


• 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

Observables


• Production Op(m) = [Owi(m) Oop(m)]

• Seismic Os(m) = [Os1(m) Os2(m)]

• Two types of seismics

– wave velocity (VP)

– diffraction tomography

Observables


• Flexible cost function

• Weights modified along optimization

• Regularized:

( ) ( ) ( ) ( ) ||mOmO||||mOmO|| *sss

*ppp −ω+−ω

( ) ( ) ||mOmO|| *−

||mm|| prior−λ+

Cost Function


• VP cannot be directly measured

• VP indirectly estimated

– multiple sources

– inversion process

• Diffraction tomography

source

receptor

Gr

Sr

Seismic Data: Tomography


model m

VP tomography

Tomography Results


true model m*

VP tomography

Tomography Results


facies

Op(m)

Os(m)

||.||KPCA

m**

tooptimizer

manyparameters

lessparameters

rock properties

mξξξξ

Workflow


• Principal Component Analysis (PCA)

• Data compression approach

• Based on a priori statistical information

Principal Component Analysis


• Cost function = production + seismic

• No strategy for exact gradients

• Derivative-free optimizer

• Fairly efficient optimization scheme

• Very easy to implement and robust

13

Cost Function Gradients


• 20x20x10 sector from zone 3

• m: facies

• k, φφφφ: regression from well location

• VP as seismics

• PCA: 30 coefficients retained

• Measured data only after 3 months

Some Results


5 spot

injector

producer

Production Data


5 spot

injector

producer

Seismic Data


x

z

y

z

true

after production

initial

alternating

Velocities (VP)


x

y

LAYER 1

true

after production

initial

alternating

Facies


x

y

LAYER 4

true

after production

initial

alternating

Facies


x

y

LAYER 6

true

after production

initial

alternating

Facies


x

y

LAYER 10

true

after production

initial

alternating

Facies


Thank you for

attending!


Short Course on Stanford GPRS(General Purpose Research Simulator)

D. Echeverría Ciaurri and H. Pan

NTNU Workshop P2October 15, 2008

short course on stanford gprs (general purpose research

Documents