MS Presentation

1
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
2
Presentation Outline

• Motivation
• Problem Definition
• Objectives
• Approach
• Program Validation/Evaluation
• Conclusions

3
Motivation
Diagonal
Parallel
Not to scale
4
(No Transcript)
5
20 acres
Mobility Ratios M 0.5 M 1.0 M 10.0
10 acres
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
Saturation Distribution at PVinj 1.0 for M0.5
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
Saturation Distribution at PVinj 1.0 for M10.0
16
Motivation

• Brand, Heinemann, and Aziz (1992)
• In general, Grid Orientation Effect
• cannot be overcome with
• grid refinement.

(SPE 21228)
17
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)
18
Problem Definition

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

19
Objectives

• Developing a 2-D, 3-Phase reservoir simulator
  using finite difference formulation
• Reducing the grid orientation effects in a grid
  model

20
Approach

• 2-D, 3-Phase IMPES finite difference simulator
  with unique grid model ? Sim2D

21
2D,3-Phase
Cartesian Grid

• Initial Condition
• Rock/Fluid Properties

Well Model
Well Constraints
HGB Grid
IMPES
Matrix Form
Matrix Solver
Pn1, Son1, Swn1, Sgn1
Cutback/Saturation Control
Program Validation
22
Sim2D Demo
23
Sim2D VB Application
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
Pressure Plots
30
IMPES MethodFinite Difference Equations

• Oil
• Water
• Gas

31
IMPES Steps

• Calculate coefficients of the pressure equation
• Calculate solution of the pressure equation
  implicitly (matrix equation) for pn1
• Calculate solution of the saturation equations
  explicitly for Son1, Swn1, and Sgn1

32
IMPES Method

• 4 unknowns per block
• pn1, Son1, Swn1, and Sgn1
• To find the unknowns, we need one more equation
  per block Son1 Swn1 Sgn1 1
• Assures fluid volumes fit the pore volume

33
IMPES Method

• Oil
• Water
• Gas

34
IMPES Method

• Summing up all saturation equations

35
IMPES Method
Approximate Vpn1 on the right hand side using
the identity and a chord slope
36
IMPES Method
Then, where, Likewise,
37
IMPES Method
Final equation can now be written as
38
Hybrid Grid Block (HGB) System
39
Hybrid Grid Block (HGB) System
NW
NE
SE
SW
40
Hybrid Grid Block (HGB) System
41
Grid Numbering
Numbering 1
Example 18 Grid Blocks
42
Grid Numbering
Numbering 2
Example 18 Grid Blocks
43
Grid Numbering
Numbering 3
Example 25 Grid Blocks
44
Well Model

• Peaceman Well Model
• (1983)

?m
For square gridblock,
where, a mass species oil/water ro effective
wellbore radius
45
Well Model

• Well Model for regular
• polygon (Palagi, 1992)

i

• j neighbor of wellblock i
• bij side of polygon
• dij distance between gridpoints
• N number of equal sides

46
Program Validation
47
Example Case

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

48
Validation with Eclipse
49
Validation with Eclipse
50
Application ofHGB grid system to Reduce Grid
Orientation Error
51
(No Transcript)
52
(No Transcript)
53
Saturation Distribution Map for diagonal HGB
54
Saturation Distribution Map for parallel HGB
55
Conclusions

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

56
Conclusions

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

57
Conclusions

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

58
Conclusions

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

59
Acknowledgement

• Dr. David Schechter
• Dr. Erwin Putra
• U.S Department of Energy

60
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