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
Emeline Chong
July 7, 2004
Harold Vance Department of Petroleum Engineering
Diagonal
Parallel
Not to scale
GRID ORIENTATED PARALLEL
TO INJECTOR-PRODUCER PAIRS (PARALLEL RUNS)
GRID ORIENTATED AT 45
TO INJECTOR-PRODUCER PAIRS (DIAGONAL RUNS)
20 acres
Mobility Ratios :
M = 0.5
M = 1.0
M = 10.0
10 acres
Brand, Heinemann, and Aziz (1992) –
“In general, Grid Orientation Effect
cannot be overcome with
grid refinement.”
(SPE 21228)
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)
Grid orientation effect significantly affects the results of immiscible displacements in reservoir simulation
2-D, 3-Phase IMPES finite difference simulator with unique grid model “Sim2D”
2D,3-Phase
Cartesian Grid
Well Model
Well Constraints
HGB Grid
IMPES
Matrix
Form
Matrix
Solver
Pn+1, Son+1, Swn+1, Sgn+1
Cutback/Saturation Control
Program Validation
IMPES Steps…
IMPES Method
pn+1, Son+1, Swn+1, and Sgn+1
IMPES Method
IMPES Method
Summing up all saturation equations:
IMPES Method
Approximate Vpn+1 on the right hand side using the identity:
and a chord slope:
IMPES Method
Then,
where,
Likewise,
IMPES Method
Final equation can now be written as:
I
I
J
J
N
W
E
S
NW
NE
SE
SW
Numbering #1
Example: 18 Grid Blocks
Numbering #2
Example: 18 Grid Blocks
Numbering #3
Example: 25 Grid Blocks
Peaceman Well Model
(1983):
Δm
For square gridblock,
where,
α = mass species; oil/water
ro = effective wellbore radius
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
i
Cartesian Sim2D
Cartesian Eclipse 100
HGB Sim2D
Two-Dimensional Areal Model Showing Primary Depletion of an Undersaturated Reservoir (One Producer Well, One Injector Well, Isotropic, 2-Phase, Oil/Water)
Application ofHGB grid system to Reduce Grid Orientation Error
THANK YOU
Acknowledgement
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