John R. Fanchi - Principles of Applied Reservoir Simulation, Second Edition

192

Principles

of

Applied

Reservoir Simulation

These points underscore

the

need

to

recognize that

the

history match process

does

not

yield

a

unique solution. Forecasts

of

reservoir behavior depend

on the

validity

of the

history

match.

Despite

the

uncertainty associated with simulator-based forecasts,

reservoir simulation continues

to be the

most reliable method

for

making

performance predictions, particularly

for

reservoirs that

do not

have

an

extensive

history

or for fields

that

are

being considered

as

candidates

for a

change

in

reservoir

management strategy. Other methods, such

as

decline curve analysis

and

material balance analysis,

can

generate performance forecasts,

but not to

the

degree

of

detail

provided

by a

reservoir model study.

As

Saleri

[

1993]

noted,

4

"While

a 10% to 40%

forecast uncertainty

may

appear alarming

in an

absolute

sense,

the

majority

of

reservoir engineering decisions require

choices based solely

on

comparative analyses (for example, peripheral

vs.

pattern

flood).

Thus,

in

selecting optimum management

strategies,

finite-difference

models

still

offer

the

most

effective

tools."

Saleri's

view

is

similar

to

that

of

Oreskes,

et

al.

[1994],

Even though

models

are

non-unique representations

of

nature, they still have many uses.

In

summary,

models

can be

used

to

4

corroborate

or

refute

hypotheses about physical systems;

4

identify

discrepancies

in

other models;

and

4

perform

sensitivity

analyses.

Part

IV

integrates

the

ideas presented above

in the

context

of a

case study.

Exercises

Exercise 19.1 Data

set

EXAM4.DAT

is a 2D

areal model

of an

undersaturated

oil

reservoir undergoing primary depletion.

(A) Run

EXAM4.DAT

and

determine

oil

recovery

at the end of the

run.

(B) Set the

bottomhole

pressure

(BMP)

in

well

P-l

ofEXAM4.DAT

to

150

psia

and run the

model.

How

much

oil

is

recovered

in the

modified model?

Exercise 19.2 Beginning

at the end of

year one,

add a

water injection

well

in

each

of the

four

corner gridblocks

in

data

set

EXAM4.DAT with

the

BHP

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193

modification

described

in

Exercise

19.1.

The

maximum allowable

BHP for an

injection

well

is

5000

psia.

Assume

the

target rate

for the oil

production

well

is

600

STB/D. Maximize

oil

recovery

by

varying

the

amount

of

water

injected,

Data

set

EXAM6.DAT

is an

example

of a

data

set

with

the

injection

wells

added.

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Chapter

20

Study

Objectives

and

Data

Gathering

The first

step

in a

study

is to

identify

its

objectives. Study

objectives

provide

information

about resource requirements.

After

stating

the

objectives

of the

study,

the

data

for

characterizing

the

reservoir

is

then described.

20.1 Study Objectives

Two

objectives

of the

case study

are to

increase your understanding

of

the

reservoir simulation process,

and to

acquire experience working with

a

simulator.

The

experience

you

gained working

the

exercises

in

Parts

I and II is

a

transferable

skill.

Many

of the

tasks

performed with

WINB4D

may

differ

in

detail

from

other simulators,

but are

conceptually universal. Although

the

above

objectives

are

important

from

a

pedagogical point

of

view, they

are

secondary

within

the

context

of the

case

study.

The

reservoir management objective

of the

case

study

is to

optimize

production from

a

dipping,

undersaturated

oil

reservoir. There

will

be

constraints imposed

on the

case study objective.

Before

discussing

the

con-

straints,

however,

it is first

necessary

to

gather some background

information

about

the field.

20.2

Reservoir Structure

A

seismic

line

through

an

east-west cross-section

of the field is

shown

in

Figure

20-1.

The

single well

(P-l)

has

been

producing

from

what appears

to

197

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198

Principles

of

Applied

Reservoir Simulation

be a

fault

block bounded

upstructure

and to the

east

by an

unconformity;

downstructure

and to the

west

by a

fault

or

aquifer;

and to the

north

and

south

by

sealing

faults.

Depth

A

(ft)

A

""*^~

DoO

""•"•HP*

1

"'

W

*•

"

r

"

T

*

„

Well

_920o

P-

1

.-",:'•"

Seismic Reflectors

(Processed

with

time-

_9600

.•.'•"

.

•

"

depth conversion)

_

i

»

"i

i i

i

11

0 400 800

1200 1600

2000

Distance

from

Western

Fault

(ft)

Figure

20-1.

East-west

seismic line.

A

well

log

trace

is

shown

in

Figure

20-2.

An

analysis

of the

well

log

data

shows

that

two

major sands

are

present

and

are

separated

by a

shale section. Well

log

results

are

presented

in

Table

20-1.

The

table headings refer

to

porosity

<|>,

water saturation

S

w

,

gross thickness

h, and the

net-to-gross ratio

NTG.

Well

P-l

Log

Trace

Sand

'

Shale

&!

Sand

with

Shale

Figure 20-2. Well

log

trace.

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199

Table 20-1

Well

Log

Analysis Summary

Lithology

(From

Cuttings)

Sandstone

Shale

Sandstone with

Shale Stringer

Depth (ft)

to

Top of

Formation

9330

9410

9430

*

(fr.)

0.20

—

0.25

s

w

(fr.)

0.30

—

0.30

h

(ft)

80

20

120

NTG

(fr.)

0.9

—

0.8

A

conceptual sketch

of

the

reservoir cross-section

is

shown

in

Figure

20-3,

Notice

that

we

have adopted

an

unconformity

as our

geologic model.

Impermeable

Cap

Rock

Oil

Water

Figure

20-3.

Conceptual sketch

of

reservoir cross-section

(after

Clark,

1969;

reprinted

by

permission

of the

Society

of

Petroleum Engineers).

20.3 Production History

Well

P-1

has

produced

for a

year.

Its

production history

is

shown

in

Tables

20-2a

and

20-2b.

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Applied

Reservoir Simulation

Table 20-2a

Production History

TIME

DAYS

5

13

24

41

66

91

122

153

183

214

245

274

305

336

365

RATES

OIL

STB/D

500

GAS

MSCF/D

228

WATER

STB/D

0

1

2

3

4

5

GOR

SCF/STB

457

WOR

0

A

review

of

Tables 20-2a

and

20-2b shows that

oil

rate

has

remained

constant. Real data would show some variability,

of

course,

but we are

using

an

idealized data

set to

simplify

the

problem.

Gas

production

has

also remained

constant,

and

there

has

been

no

change

in the

gas-oil ratio. This

suggests

that

the

reservoir

is

undersaturated; that

is,

reservoir pressure

is

above bubble point

pressure.

Only

one

hydrocarbon phase

- the

liquid

phase

- is

produced

at

reservoir conditions

from

an

undersaturated

reservoir.

The

fact

that

GOR

does

not

change over

the

life

of the field is

interpreted

to

mean that

the

reservoir

was

undersaturated

at

initial conditions.

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201

Table 20-2b

Production

History

TIME

DAYS

5

13

24

41

66

91

122

153

183

214

245

274

305

336

365

AVGRES

PRESSURE

PSIA

3929

3915

3906

3901

3899

3898

3897

3896

3895

3894

3893

3892

CUM

PROD

OIL

MSTB

3

6

12

20

33

46

61

77

91

107

122

137

152

168

183

GAS

MMSCF

1

3

5

9

15

21

28

35

42

49

56

63

70

77

83

WATER

MSTB

0

1

20.4 Drill Stem Test

Well

P-l

logs

and

cores showed

the

presence

of two

major

sands.

A

drill

stem test (DST)

was

subsequently

run in

each

major

sand. Basic

facts

from the

DST are

summarized

in

Table 20-3.

Table 20-3

Summary

of

Well

P-l DST

Results

Wellbore Radius

Wellbore

Skin

Initial

Pressure

No-Flow

Boundary

0.25

ft

-0.5

3936 psia

at

9360

ft

Within

700 ft

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