class="bi x0 y0 w0 h1"
Principles
of
Applied
Reservoir Simulation
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Second
Edition
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Principles
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Applied
Reservoir
Simulation
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paper.
Library
of
Congress
Cataloging-in-Publication
Date
Fanchi,
John
R.
Principles
of
applied
reservoir
simulation/John Fanchi.
- 2
nd
edition
p. cm.
Includes bibliographical references
and
index.
ISBN
0-88415-372-X(alk.
paper)
1.
Oil fields-Computer
simulation.
2.
Petroleum-Geology-Mathematical models.
I.

contact:
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of
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Printed
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United
States
of

.,1
Consensus Modeling
2
1.2
Management
of
Simulation Studies
4
1.3
Outline
of the
Text
6
Exercises
7
Part
I -
Reservoir
Engineering
Primer
2
Basic Reservoir Analysis
11
2.1
Volumetrics
11
2.2
Material Balance
12
2.3

Conservation
of
Mass
31
4.2
Flow Equations
for
Three-Phase Flow
33
4.3
Flow Equations
in
Vector Notation
36
Exercises
37
5
Fluid Displacement
39
5.1
Buckley-Leverett
Theory
39
5.2
Welge's
Method
42
5.3
Miscible Displacement
44

Pattern Recovery
61
Exercises
63
8
Recovery
of
Subsurface Resources
64
8.1
Production
Stages
64
8.2
Enhanced
Oil
Recovery
69
8.3
Nonconventional Fossil Fuels
71
Exercises
73
9
Economics
and the
Environment
75
9.1
SPE/WPC

10.4
Major
Elements
of a
Reservoir Simulation
Study
92
Exercises
94
11
Conceptual Reservoir
Scales
95
11.1
Reservoir Sampling
and
Scales
95
11.2
Integrating Scales
- the
Flow Unit
97
1
i .3
Geostatistical
Case Study
101
Exercises
104

131
14.1
Porosity, Permeability, Saturation
and
Darcy'sLaw
131
14.2 Relative Permeability
and
Capillary
Pressure
135
14.3 Viscous Fingering
139
Exercises
141
15
Fundamentals
of
Reservoir Simulation
142
15.1
Conservation Laws
142
15.2
Flow Equations
143
15.3
Well
and
Facilities Modeling

Data Preparation
for a
Typical Study
168
17.1
Data Preparation
168
17.2
Pressure Correction
170
17.3
Simulator Selection
and
Ockham's
Razor
172
Exercises
175
18
History Matching
176
18.1
Illustrative History Matching Strategies
177
18.2
Key
History
Matching
Parameters
180

Validity
of
Model Predictions
191
Exercises
192
Part
III -
Case Study
20
Study
Objectives
and
Data Gathering
20.1
20.2
20.3
20.4
20.5
20.6
Study
Objectives
Reservoir Structure
Production
History
Drill
Stem Test
Fluid
Properties
Reservoir

197
197
197
199
201
203
207
207
208
208
209
212
214
215
216
,
218
218
222
223
224
Part
IV -
WINB4D
User's
Manual
23
Introduction
to
WINB4D

Distributions
249
XI
24.4 Rock
and PVT
Regions
255
24.5 Relative Permeability
and
Capillary
Pressure Tables
257
24.6 Fluid
PVT
Tables
258
24.7 Pressure
and
Saturation Initialization
262
24.8
Run
Control Parameters
264
24.9 Solution Method Specification
265
24.10 Analytic
Aquifer
Models
267

27.3
Petrophysical
Model
288
27.4
Material Balance
291
28
Rock
and
Fluid
Models
292
28.1 Three-Phase Relative Permeability
292
28.2
Transmissibility
294
28.3 Terminology
and
General Comments
295
28.4 Extrapolating Saturated Curves
300
28.5
Gas PVT
Correlation Option
301
29
Initialization

Well
Flow
Index
(PID)
318
31.1 Productivity Index
318
31.2
Vertical Wells
319
31.3
Horizontal Wells
320
32
The
IMPES Formulation
322
32.1
Flow Equations
and
Phase Potentials
322
32.2
Introduction
of the
Capillary Pressure
Concept
323
32.3
The

oil
companies
(Marathon, Cities Service,
and
Getty),
and
served
as
an
international
consultant.
His oil and gas
industry responsibilities have revolved around
reservoir modeling, both
in the
areas
of
simulator development
and
practical
reservoir management applications.
Dr.
Fanchi's
publications
include
software
systems
for
the
United States Department

xiv
Preface
to the
Second Edition
The
second edition
of
Principles
of
Applied
Reservoir
Simulation
has
been
expanded
to
include background material
on
reservoir engineering.
The
chapters
in
Part
I
-
Reservoir
Engineering
Primer
are
intended

been added
or
modified
to
improve their
usefulness.
Much
of the
material
in the
program
technical
supplement
has
been integrated
into
the
main body
of the
text because
it is
relevant
for
flow
simulators
in
general,
and not
just
for the

range
of
applicability
of
the
program.
A
visualization program
(3DVIEW)
is
included
on the
accompanying
CD. It
lets
the
reader obtain
a 3D
perspective
of the
reservoir
using
WINB4D
output.
I
would like
to
thank
my
students

version
of
3DVIEW.
Any
written comments
or
suggestions
for
improving
the
material
are
welcome.
John
R.
Fanchi,
Ph.D.
Golden,
Colorado
June
2000
xv
Preface
Principles
of
Applied
Reservoir Simulation
is a
vehicle
for

process
of
reservoir
modeling
and
includes
a
fully
functioning
reservoir simulator
for the
reader's
personal use.
Part
I
explains
the
concepts
and
terminology
of
reservoir simulation.
The
selection
of
topics
and
references
is
based

and
condensate
fields.
Participation
is one of the
best ways
to
learn
a
subject.
The
exercises
in
Part
I
give
you an
opportunity
to
apply
the
principles that
are
discussed
in
each
chapter.
As a
means
of

Parts
III and IV are the
User's
Manual
and
Technical Supplement,
respectively,
for the
three-dimensional, three-phase black
oil
simulator
BO
AST4D
that accompanies
the
text.
BOAST4D
is a
streamlined
and
upgraded
version
of
BOAST
II, a
public domain black
oil
simulator developed
for
the

are
applicable
to an
emerging
technology:
4D
seismic monitoring
of fluid flow. The
inclusion
of
reservoir
xvi
geophysical calculations
is the
motivation
for
appending
"4D"
to the
program
name.
In
addition, BOAST4D includes code changes
to
improve computational
performance,
to
allow
the
solution

reservoir simulator,
for
developing
an
understand-
ing
of
reservoir management concepts,
and for
solving many
types
of
reservoir
engineering problems.
It is an
inexpensive tool
for
performing studies that
require more sophistication than
is
provided
by
analytical solutions,
yet do not
require
the use of
full-featured
commercial simulators. Several example data
sets
are

geologists
and
geophysicists,
or
hydrologists;
in a
graduate course
for
modelers;
and
in
continuing education courses.
An
Instructor's Guide
is
available
from
the
publisher.
I
developed much
of the
material
in
this book
as
course notes
for a
continuing education course
I

industrial
and
academic employers, both past
and
present,
for the
opportunity
to
work
on a
wide variety
of
problems.
I
would also
like
to
acknowledge
the
contributions
of Ken
Harpole,
Stan Bujnowski, Jane
Kennedy,
Dwight Dauben
and
Herb Carroll
for
their work
on

of
this material.
Any
written comments
or
suggestions
for
improving
the
material
are
welcome.
John
R.
Fanchi,
Ph.D.
Houston,
Texas
August
1997
XVll
This page intentionally left blank
Chapter
1
Introduction
to
Reservoir Management
Reservoir modeling exists within
the
context

Humphreys,
1996;
Thakur,
1996].
These
two
outcomes
-
optimizing recovery
and
minimizing cost
-
often
conflict
with each other. Hydrocarbon recovery
could
be
maximized
if
cost
was not an
issue, while costs could
be
minimized
if
the field
operator
had no
interest
in or

field.
Reservoir modeling
is the
most
sophisti-
cated
methodology available
for
achieving
the
primary reservoir management
objective.
There
are
many reasons
to
perform
a
model study. Perhaps
the
most
important,
from
a
commercial perspective,
is the
ability
to
generate cash
flow

Table
1
-1.
Several
of the
items
are
discussed
in
greater
detail
in
later
chapters.
2
Principles
of
Applied
Reservoir Simulation
Table
1-1
Why
Simulate?
Corporate
Impact
+
Cash Flow Prediction
0
Need Economic Forecast
of

Plan Development
or
Operational Changes
4
Select
and
Optimize Project
Design
0
Maximize Economic Recovery
1.1
Consensus
Modeling
Reservoir modeling
is the
application
of a
computer simulation system
to the
description
of fluid flow in a
reservoir [for example,
see
Peaeeman,
1977;
Aziz
and
Settari, 1979; Mattax
and
Dalton,

disciplines contribute
to the
preparation
of the
input data
set.
The
information
is
integrated during
the
reservoir modeling
process,
and
the
concept
of the
reservoir
is
quantified
in the
reservoir simulator. Figure
1-1
illustrates
the
contributions
different
disciplines make
to
reservoir modeling.

as a
filter
that selects
from
among
all of the
proposed descriptions
of the
reservoir.
The
simulator
is not
influenced
by
hand-waving
arguments
or
presentation style.
It
provides
an
objective appraisal
of
each hypothesis,
and
constrains
the
power
of
personal

of a
reservoir
representation.
This task
is
made more complex when
available
field
performance data
can be
matched
by
more than
one
reservoir
model.
The
non-uniqueness
of
the
model
is
discussed
in
greater detail throughout
the
text.
It
means that there
is

is a
factor
in the
process,
particularly when
the
data
do not
clearly
support
the
selection
of a
single reservoir representation
from
a set of
competing
representations.
The
dual criteria
of
reasonableness
and
Ockham's
Razor
4
Principles
of
Applied
Reservoir Simulation

team
to
develop
a
meaningful
reservoir model. Team development proceeds
in
well
known stages
[Sears,
1994]:
+
Introductions: Getting
to
know each other
4
"Storming":
Team members disagree over
how to
proceed
0
Members
can
lose sight
of
goals
4
"Norming":
Members
set

as
project teams
in a
matrix management
organization.
Matrix
management
is
synonymous here with Project Management
and
has two
distinct
characteristics:
4
"Cross-functional organization with members
from
different
work areas
who
take
on a
project."
[Staff-JPT,
1994]
+
"One employee
is
accountable
to two or
more superiors, which

members should have unique roles
to
avoid redundant functions.
If the
responsibilities
of two or
more members
of the
team overlap considerably,
confusion
may
ensue with regard
to
areas
of
responsibility and,
by
implication,
of
accountability. Each team member must
be the key
decision
maker
in a
particular discipline, otherwise disputes
may not get
resolved
in the
time avail-
Introduction

deadlines will require
one
team member
to
serve
as
team leader. Deadlines
cannot
be met if a
team cannot agree,
and
there
are
many areas where decisions
may
have
to
be
made that
will
not
be
by
consensus.
For
this reason, teams should
have
a
team leader with
the

they
will
weaken
the
team
and
wind
up
with
a
group.
According
to
Maddox [1988], teams
and
groups
differ
in the way
they
behave. Group behavior exhibits
the
following characteristics:
+
"Members
think they
are
grouped together
for
administrative purposes
only.

of
team behavior
are the
following:
4
"Members recognize their interdependence
and
understand both
personal
and
team goals
are
best accomplished with mutual support. Time
is
not
wasted straggling over territory
or
seeking personal gain
at the
expense
of
others."
^
"Members
feel
a
sense
of
ownership
for

Haldorsen
and
Damsleth
[1993]
argue that each team member should have
the
following
focus:
4
Innovation
and
creation
of
value through
the
team approach
6
Principles
of
Applied
Reservoir Simulation
4
Customer orientation with focus
on "my
output
is
your input"
Mclntosh,
etal.
[

likelihood that
a
team
will
function
as it
should,
A
sense
of
ownership
or
"buy-in"
can be
fostered
if
team
members
participate
in
planning
and
decision making. Team member views should
in-
fluence
the
work scope
and
schedule
of

borne
in
mind when performing
studies using
teams:
"Fewer
ideas
are
generated
by
groups than
by
individuals
working alone
-
a
conclusion supported
by
empirical evidence
from
psychology
[Norton,
1994]."
In
describing
changes
in the
work
flow of
exploration

both asset
teams
and
individual
work
environments."
His
solution
is a
work
flow
that allows
the
"simultaneous
coexistence
of
decoupled individual
efforts
and
recoupled asset team coordina-
tion."
1.3
Outline
of
the
Text
The
remainder
of the
text

and
terminology
of
reservoir
simulation.
A
typical
exercise
in
Part
II
asks
you to find and
change data records
in
a
specified
example
data
file.
These records
of
data must
be
modified
based