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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yyyyyyyyyyyyyyyy

Date:

1. Complete the sections above but do not seal until the examination is finished.

2. Insert in box on right the numbers of the questions attempted.

3. Start each question on a new page.

4. Rough working should be confined to left hand pages.

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6. Additional books must bear the name of the candidate, be sealed and be affixed to the first book by means of a tag provided

Subject:

INSTRUCTIONS TO CANDIDATES

8 Pages

PLEASE READ EXAMINATION REGULATIONS ON BACK COVER

No. Mk.

NAM

E:REGISTRATION N

O.:

COURSE:

YEAR:

SIGNATURE:Complete this section but do not

seal until the examination

is finished

Reservoir Simulation