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Development of a 2-D Black Oil Reservoir Simulator with Unique Grid-Block System. Emeline Chong. July 7, 2004. Harold Vance Department of Petroleum Engineering. Presentation Outline. Motivation Problem Definition Objectives Approach Program Validation/Evaluation Conclusions.

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Development of a 2-D Black Oil Reservoir Simulator with Unique Grid-Block System

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Development of a 2 d black oil reservoir simulator with unique grid block system

Development of a

2-D Black Oil

Reservoir Simulator with

Unique Grid-Block System

Emeline Chong

July 7, 2004

Harold Vance Department of Petroleum Engineering


Presentation outline

Presentation Outline

  • Motivation

  • Problem Definition

  • Objectives

  • Approach

  • Program Validation/Evaluation

  • Conclusions


Motivation

Motivation

Diagonal

Parallel

Not to scale


Development of a 2 d black oil reservoir simulator with unique grid block system

GRID ORIENTATED PARALLEL

TO INJECTOR-PRODUCER PAIRS (PARALLEL RUNS)

GRID ORIENTATED AT 45

TO INJECTOR-PRODUCER PAIRS (DIAGONAL RUNS)


Development of a 2 d black oil reservoir simulator with unique grid block system

20 acres

Mobility Ratios :

M = 0.5

M = 1.0

M = 10.0

10 acres


Saturation distribution at pv inj 1 0 for m 0 5

Saturation Distribution at PVinj =1.0 for M=0.5


Saturation distribution at pv inj 1 0 for m 10 0

Saturation Distribution at PVinj =1.0 for M=10.0


Motivation1

Motivation

Brand, Heinemann, and Aziz (1992) –

“In general, Grid Orientation Effect

cannot be overcome with

grid refinement.”

(SPE 21228)


Motivation2

Motivation

Sammon (1991)

Chen & Durlofsky (1991)

Mattax & Dalton (1990)

Wolcott et.al. (1996)

Shiralkar (1990)

Brand et.al. (1991)

Ostebo & Kazemi (1992)

Yanosik &

McCracken

(1979)

Shiralkar & Stephenson (1987)

Pruess & Bodvarsson (1983)

Todd et.al. (1972)


Problem definition

Problem Definition

Grid orientation effect significantly affects the results of immiscible displacements in reservoir simulation


Objectives

Objectives

  • Developing a 2-D, 3-Phase reservoir simulator using finite difference formulation

    • Reducing the grid orientation effects in a grid model


Approach

Approach

2-D, 3-Phase IMPES finite difference simulator with unique grid model  “Sim2D”


Development of a 2 d black oil reservoir simulator with unique grid block system

2D,3-Phase

Cartesian Grid

  • Initial Condition

  • Rock/Fluid Properties

Well Model

Well Constraints

HGB Grid

IMPES

Matrix

Form

Matrix

Solver

Pn+1, Son+1, Swn+1, Sgn+1

Cutback/Saturation Control

Program Validation


Sim2d demo

Sim2D Demo


Sim2d vb application

Sim2D VB Application


Pressure plots

Pressure Plots


Impes method finite difference equations

IMPES MethodFinite Difference Equations

  • Oil

  • Water

  • Gas


Development of a 2 d black oil reservoir simulator with unique grid block system

IMPES Steps…

  • Calculate coefficients of the pressure equation

  • Calculate solution of the pressure equation implicitly (matrix equation) for: pn+1

  • Calculate solution of the saturation equations explicitly for: Son+1, Swn+1, and Sgn+1


Development of a 2 d black oil reservoir simulator with unique grid block system

IMPES Method

  • 4 unknowns per block:

    pn+1, Son+1, Swn+1, and Sgn+1

  • To find the unknowns, we need one more equation per block: Son+1 + Swn+1 + Sgn+1 = 1

  • Assures fluid volumes fit the pore volume


Development of a 2 d black oil reservoir simulator with unique grid block system

IMPES Method

  • Oil

  • Water

  • Gas


Development of a 2 d black oil reservoir simulator with unique grid block system

IMPES Method

Summing up all saturation equations:


Development of a 2 d black oil reservoir simulator with unique grid block system

IMPES Method

Approximate Vpn+1 on the right hand side using the identity:

and a chord slope:


Development of a 2 d black oil reservoir simulator with unique grid block system

IMPES Method

Then,

where,

Likewise,


Development of a 2 d black oil reservoir simulator with unique grid block system

IMPES Method

Final equation can now be written as:


Hybrid grid block hgb system

Hybrid Grid Block (HGB) System


Hybrid grid block hgb system1

I

I

J

J

N

W

E

S

Hybrid Grid Block (HGB) System

NW

NE

SE

SW


Hybrid grid block hgb system2

Hybrid Grid Block (HGB) System


Grid numbering

Grid Numbering

Numbering #1

Example: 18 Grid Blocks


Grid numbering1

Grid Numbering

Numbering #2

Example: 18 Grid Blocks


Grid numbering2

Grid Numbering

Numbering #3

Example: 25 Grid Blocks


Well model

Well Model

Peaceman Well Model

(1983):

Δm

For square gridblock,

where,

α = mass species; oil/water

ro = effective wellbore radius


Well model1

Well Model for regular

polygon (Palagi, 1992):

j = neighbor of wellblock i

bij= side of polygon

dij = distance between gridpoints

N = number of equal sides

Well Model

i


Program validation

Cartesian Sim2D

Cartesian Eclipse 100

HGB Sim2D

Program Validation


Example case

Example Case:

Two-Dimensional Areal Model Showing Primary Depletion of an Undersaturated Reservoir (One Producer Well, One Injector Well, Isotropic, 2-Phase, Oil/Water)


Validation with eclipse

Validation with Eclipse


Validation with eclipse1

Validation with Eclipse


Development of a 2 d black oil reservoir simulator with unique grid block system

Application ofHGB grid system to Reduce Grid Orientation Error


Saturation distribution map for diagonal hgb

Saturation Distribution Map for diagonal HGB


Saturation distribution map for parallel hgb

Saturation Distribution Map for parallel HGB


Conclusions

Conclusions

  • Grid orientation effect was observed in rectangular Cartesian grid models even at isotropic and homogeneous reservoir with favorable mobility ratio.


Conclusions1

Conclusions

  • Grid refinement can minimize the grid orientation effect in rectangular Cartesian grid models at favorable mobility ratios.


Conclusions2

Conclusions

  • At an unfavorable mobility ratio, neither the parallel grid, diagonal grid nor grid refinement is effective in reducing the grid orientation effect.


Conclusions3

Conclusions

  • HGB is able to minimize the grid orientation effect even for unfavorable mobility ratio displacement problems, with relative difference of about 6%.


Development of a 2 d black oil reservoir simulator with unique grid block system

THANK YOU

Acknowledgement

  • Dr. David Schechter

  • Dr. Erwin Putra

  • U.S Department of Energy


Development of a 2 d black oil reservoir simulator with unique grid block system

Development of a

2-D Black Oil

Reservoir Simulator with

Unique Grid-Block System

Emeline Chong

July 7, 2004

Harold Vance Department of Petroleum Engineering


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