Res Sim Covers
description
Transcript of Res Sim Covers
Ref. No. RS/1, Version 1.1Ref. No. PT/2, Version 1.1 Date of issue 1 / 6 / 00
Introduction and Case Studies11
100.0
50.0
10.0
5.0
1.0
0.5
0.1
0.05
0.01
6 8 10 12 14 16 18 20 22
Core Porosity (%)
Cor
e P
erm
eabi
lty (
md)
10,000
1,000
100
10
10 10 20 30
Core Porosity (%)
Cor
e P
erm
eabi
lty (
md)
Ref. No. RS/1, Version 1.1
Basic Concepts in Reservoir Engineering22
ROCK
GASSg
OIL + GASSo
WATER + GASSw
Gas: C11, C21, C31....j = 1 = Gas
Oil: C12, C22, C32....
Water: C13, C23, C33....
j = 2 = Oil
j = 3 = Water
Component concentrationsin each phase:
Phase Labels:
Swc
Pc
Sw
krel
Sor
Capillary Pressure
Swc
kro
krw
Sw
Sor
Relative Permeability
Ref. No. RS/1, Version 1.1
Production well
Injection well
Two well quarterfive-spot grid
Reservoir Simulation Model Set-Up 33
123
505050
1
1
2
2
3
3
4
4
5
5
500
500
500
500
500
500
500
500
500
500No i j k1 1 1 12 2 1 13 3 1 14 4 1 15 5 1 16 1 2 17 2 2 18 3 2 1. . . .. . . .24 4 5 125 5 5 126 1 1 227 2 1 2. . . .. . . .75 5 5 3
Y
Z
X
Ref. No. RS/1, Version 1.1
0 0.2 0.4 0.6 0.8 1PVI
Rec
over
y fa
ctor
0.50.450.40.350.30.250.20.150.10.050
fine grid : 5 layersfine grid : 25 layersfine grid : 50 layersfine grid : 200 layerscoarse grid
VE Limit
Oil
Gas
x
x
Gravity Dominated
x
x
x
x
xxx
xx
xx
x
xx
xx
x
x
x
xx
x
x
xx x
Gridding And Well Modelling 44
Hybrid Grid
injector
producer Coarse gridin aquifer
Schematic of Local Grid Refinement (LGR)
Ref. No. RS/1, Version 1.1
The Flow Equations 55
Well
x (i)
y (j)
∆x ∆y
Area, Ay = ∆x.h Area, A
x = ∆y.h
h
i,j+1
i,ji,j-1 i+1,j
i-1,j
Thickness = h
Note for the control volume, block (i,j), the flow areas in the x and y directions,Ax and Ay are given by:
NOTATIONi - 1/2 = (i-1) � ii + 1/2 = i� (i+1)j - 1/2 = (j-1) � jj + 1/2 = j� (j+1)
Mij
Ref. No. RS/1, Version 1.1
Numerical Methods in Reservoir Simulation66
∆x = constant
P(x)
xi-1
Pi-1
Pi+1
Pi
xi-1xix
∆x ∆x
Notation:∆x = the x- grid spacing or distance between grid points(i - 1), i, (i + 1) = the x - label (subscript) for the grid point or block numbers
Pi-1, Pi, Pi+1 = the corresponding function values at grid point i-1, i, i+1 etc.
1
0x
Sw
Governing equation:
Vw = constant
∂Sw
∂t
∂Sw
∂x
∂2Sw
∂x2= - Vw +D
Ref. No. RS/1, Version 1.1
Permeability Upscaling77
Correlation Length
keff calculated for
this block
boundary conditions applied
to outer edges of model
Ref. No. RS/1, Version 1.1
Model Solutions to Examination
Q14Q14Q14Q14Q14
Upstream grid block Downstream grid block
With No Maths
Grid Block Interface
Treat This "Interface Block"
Coarse Block
Finegrid
i i+1
Consider only ACTUAL flows of Qw and Q
o across the coase block
interface only. Thus, if the fine grid water (say) flows have not
reached the coarse grid interface
then Qw = 0. => set k
rw= 0
When there is oil or water flow e.g. water flow.
Examination and Model Solutions
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INSTRUCTIONS TO CANDIDATES
8 Pages
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NAM
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Reservoir Simulation