Download Microcomputer Simulation of the Transient Flow of Real Gas through

A THESIS
SUBMITTED TO THE DEPARTMENT OF PETROLEUM ENGINEERING
AND COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE
FOR THE
OF
ENGINEER
By
Francois Joseph Groff
June 1992
I certify that I have read this thesis and that in my opinion
it is fully adequate, in scope and in quality, as partial fulfillment
for the degree of Engineer.
HeqfcrflTRamey, Jr. / j/
(Principal Advisor)
I certify that I have read this thesis and that in my opinion
it is fully adequate, in scope and in quality, as partial fulfilment
for the degree of Engineer.
Roland N. Home
Approved for the University Committee on Graduate
Studies:
11
Dedicated to
My
Alice
My father Robert
My
Genevieve, Norman and Adegboyega.
In some way, you all made this work possible.
111
Acknowledgments
I would like to express my gratitude to Dr. Henry Ramey, Jr. for Ms suggestions
and guidance during this study. His profound kindness has made this work possible. I
also thank Dr. Roland Home for serving on the committee for this thesis. I finally extend
my gratitude to Jean Cook from the Stanford Geothermal Program, and to the
Department of Petroleum Engineering at Stanford for
and encouragement
This work was supported by the Stanford Geothermal Program (SGP) under
Department of Energy contract No. DE - F607 - 90ED12934 and by the Schlumberger
Corporation through the Schlumberger Fellowship for Earth Sciences at Stanford. This
support is gratefully acknowledged.
IV
Abstract
An interactive program that lets users study the flow of real gas through porous
media under a graphic environment has been presented.
The program treats high
velocity flow accurately so that it is not mistaken for formation damage. A rigorous
treatment of welbore storage is also a major departure from traditional well test models.
A mathematical model written by Fligelnian in 1981 is the foundation of this project.
The program presented here, with its graphic capabilities places results at the user's
fingertips.
This program can be used in
activities to perform sensitivity
analysis. It can also be used as a working tool for well test design or well test
interpretation.
Finally, it can be used as an educational tool for all the tasks just
mentioned.
Table of Contents
Page
Dedication
Acknowledgment
Abstract
Table of Contents
list of Tables
list of Figures
iii
iv
v
vi
viM
ix
1. Introduction
1
1.1 Previous Work
1.2 Turbulent How
1.3 WeEbore Storage
3
4
4
2. Mathematical Model
5
2.1 Turbulence Effect
2.2 Formation Damage
2.3 Initial Condition
2.4 Inner Boundary Condition
2.5 Outer Boundary Condition
2.6 Dimensionless Quantities
2.7 Resulting Equations
2.8 Comments on the Finite-Difference Simulation
6
7
7
7
8
8
10
11
3. Programing Language and Development Features
13
4. User Manual for REAL GAS FLOW
4.1 Installation
4.1.1 Configuration
4.1.2 Setting Up
4.1.3 Starting Up
4.1.4 A Quick Guide to REAL GAS FLOW
4.2 Overview
4.2.1 Methodology
4.2.2 Main Menu Bar
4.2.3 File Types
4.2.3.1 Files Created by a User
4.2.3.2 Files Created by REAL GAS FLOW
4.3 Setting Up the Data
4.3.1 Main Data File
4.3.1.1 Opening an Old Main File
4.3.1.2 Creating a New Main File
4.3.1.3 Detailed Description of Each Field
4.3.2 Flow Rate File
4.4 Running the Simulation
14
14
14
15
16
16
17
17
19
19
20
20
21
21
22
25
27
31
32
VI
4.4.1 Running the Right Case
4.4.2 During the Simulation
4.5 Plotting Results
4.5.1 Plot Menu
4.5.2 Overview
4.5.2.1 Opening an Output File
4.5.2.2 Plotting the Data
4.5.2.3 Using the Cursor Utility
4.6 Special Features
4.6.1 Using Field Data
4.6.1.1 Setting Up the Field Data
4.6.1.2 Plotting Field Data
4.6.2 Creating Type Curves
4.6.2.1 Background
4.6.2.2 Creating One Type Curve
4.6.2.3 Building a Library of Type Curves
4.7 Printing
4.7.1 Printing Directly
4.7.2 Printing with CLIPBOARD
4.8 Leaving REAL GAS FLOW
4.9 Computing Aids
32
32
33
33
33
33
36
38
40
40
40
41
42
43
43
44
47
47
47
47
48
5. Using RGF as a Weil Test Interpretation Tool
49
6. Conclusions
56
Nomenclature
References
57
60
Appendix A.
Appendix B.
Appendix C.
Appendix D.
Computation of Gas Properties
Flow Chart of Fortran Code
Source Code of Fortran Program for Flow Simulation
Source Code of C Program for User Interface
Vll
64
69
72
88
List of Tables
page
Table 4.1 Simulation Time on Various Computers
14
Table 4.2 Summary of Main Input Data File
26
Table 4.3 Data File for Library of Type Curves Generated by RGF
45
Table 5.1 Pressure History for Synthetic Field Data
51
Vlll
List of Figures
page
Fig. 2.1 Radial How Model
5
Fig. 4.1 Main Structure of REAL GAS FLOW
17
Fig. 4.2 Input Parameter Window to Oeate and Display Main Input Files
21
Fig. 4.3 OPEN Window to Access Files on Disks
23
Fig. 4.4 Example of File for Sensitivity Analysis, with k=10mD
24
Fig. 4.5 Example of File for Sensitivity Analysis, with k=100mD
25
Fig. 4.6 Choice of Available Plots for Viewing Results
33
Fig. 4.7 OPEN Window to Access Output Files Stored on Disks
35
Fig. 4.8 Typical Log-Log Plot with REAL GAS FLOW
36
Fig. 4.9 Typical Graph of Both Log-Log and Derivative Plots
37
Fig. 4.10 Superposition of Log-Log Plots from Two Different Output Files
38
Fig. 4.11 Using the Cursor Utility to Pick Points on a Graph
39
Fig. 4.12 Superposition of Field and Synthetic Data
42
Fig. 4.13 Example of Combination of Five Type Curves to Build a Library
44
Fig. 5.1 Plot Fitting Field Data and Simulated Data by Trial and Error,
Log-Log Plot
52
Fig. 5.2 Plot Fitting Field Data and Simulated Data by Trial and Error,
Semi-Log Plot
53
Fig. 5.3 Non-Linear Regression Fit of Synthetic Field Data on Generated Type
Curves
55
a[p/z(p)l
Fig. A.I Wellbore derivative —?
£ Vs Bottom Hole Pressure for y = 0.9
d[p/z(p)J
IX
68
1. Introduction
This section presents the purpose of tMs study and previous studies. The initial
objective of early studies was to investigate pressure-dependent wellbore storage for Mgh
drawdown gas wells. The project described in this report is primarily concerned with
improving gas well test analysis by providing an interactive graphic-driven software
usable by all engineers. The main goals are to investigate the effects of wellbore
storage, sMn, and high-velocity flow on real gas transient pressure
during
drawdown or injection tests. Drawdown tests are performed on gas wells to determine
the flow capacity, kh, of the formation, the condition of the wellbore and high-velocity
flow parameters.
Eilerts (1964) and Eilerts et al. (1965) solved real gas flow for
linear and
radial reservoirs with inclusion of real gas
and turbulence.
(1961)
observed that the sMn effect for gas wells often appeared to depend upon flowrate. Tek
et al. (1962) and Swift and Kiel (1962) presented a fundamental
for this
observation: Mgh-velocity flow could cause a pseudo-skin effect in the
region
near a gas well. The language used when describing the mechanism that consumes
energy at more than a linear rate with velocity is not consistent in the literature. The
term used in flow equations (generally known as P) also has been given various names.
Ramey (1965) and Agarwal et al. (1970) defined Mgh-velocity flow as non-Darey flow
which can be treated as a flow-rate dependent skin effect. Firoozabadi and Katz (1979)
argued that the term "non-Darcy flow" was not specifically descriptive. The same was
said for defining Darcy flow for low velocities and an inertia regime for higher
velocities, since the inertia effects are always present. Firoozabadi and Katz proposed to
n
adopt the term "high-velocity flow" to describe the condition where neglecting ppv
calculates less pressure drop than would occur, and "velocity coefficient" to describe p
instead of "turbulent factor" or "inertial coefficient". Fligelman et al. (1989) adopted the
term "non-Darcy flow effect" defined as a pseudo-skin DqgC that is not simply an
additional term as are the other skin factor components. Although high-velocity flow
was studied in this paper, we will refer to this effect as "turbulence" for convenience.
Wellbore storage, skin effects and high-velocity flow were considered in a
numerical solution for transient gas well test analysis for one-dimensional flow by
Fligelman (1981). This solution is the starting point for this project.
The effect of high-velocity flow near a wellbore can be detrimental to the
producing capacity of a gas well. The calculation of
conductivity for cases of
high flow rates using conventional semilog graphing yields values which are lower than
the true formation conductivity. Turbulence
if not properly identified, can be
mistaken for formation damage and can lead to serious
in the interpretation.
Using a constant weEbore storage model to analyze
test
data exhibiting
changing storage may lead to large errors in the estimation of the
damage. In the
case of a drawdown with storage, when plotted on a log-log
of the real gas pseudopressure,
time,
a shifting of the conventional graph
one
wellbore
constant to a greater value might occur. As these
would involve a
high pressure drop of several thousands psi, it was beMeved
changing wellbore
was responsible for this behavior. This led to Fligelman's (1981)
model wherein wellbore storage is treated rigorously. In a similar model developed by
Wattenbarger (1967), wellbore storage was not treated accurately.
A modern, interactive tool for investigating these important effects was needed.
The objective of this project was to provide a numerical simulation for the isothermal
and horizontal flow of real gas from a well through a homogeneous and isotropic
formation on a personal computer, under a graphic environment. It is assumed that the
gas flow in the formation is properly represented by a Forchheimer (1901) type
equation. The weEbore boundary condition is a specified surface flow rate. The exterior
boundary condition is either constant pressure, no-flow across the boundary, or infinite
acting.
A major concern was to provide others involved in research activities and
students with a software package as easy to use as possible, in order to produce future
results, and/or design weE tests. The software can also be used in future studies of other
systems, as in geothermal engineering, for instance. Specific goals for the program were
to aEow a user to compare synthetic weE tests with each other, compare field data and
synthetic data, create libraries of type curves from synthetic well tests, obtain graphic
representation of synthetic data as soon as the simulation is over, and finaEy, have easy
access to past data.
1.1 Previous Work
Van Everdingen and Hurst (1949) published analytical solutions to the diffusivity
equation for radial systems. Many solutions were available as Laplace transform
inversion integrals and could not be expressed in term of elementary functions. The first
ideal gas flow solutions were published by Aronofsky and Jenkins (1952) and Jenkins
and Aronofsky (1953). They introduced computer techniques to solve non-linear gas
flow equations, followed by Brace et al. (1953). Cornell and Katz (1953) graphically
integrated the differential equation for ideal gases and included the effects of turbulence.
Van Everdingen (1953) and Hurst (1953) introduced the skin effect, later generalized by
Wattenbarger (1967) by including a damaged annular region adjacent to the well. Smith
(1961) studied the effect of flow rate on drawdown testing and Swift and Kiel (1962) and
Tek et al. (1962) explained Smith's
as due to
flow.
Ramey
(1965) considered the combined effects of turbulence, wellbore storage and skin damage.
Matthews (1961) presented an early comprehensive paper on pressure buildup
analysis, and later Matthews and Russell (1967) published an SPE monograph on well
testing, concentrating mainly on liquid flow. Until 1960, most gas flow studies
concerned ideal gas. Carter et al. (1962, 1963a, 1963b) and later Russell et al. (1966)
solved real gas flow problems and presented approximate methods for correcting ideal
gas solutions to include real gas properties.
An important step was taken by Al-Hussainy et al. (1966a, 1966b) who
introduced the real gas pseudo-pressure concept. Following Wattenbarger (1967),
Fligelman (1981) used this concept to investigate short term drawdown tests where the
exterior boundary does not influence the flow behavior at the well. Fligelman's program
solves a non-linear partial differential equation that resulted from the consideration of
various parameters, simultaneously or not. This work considered a constant rate inner
boundary for the infinite reservoir case. Couri (1987) used Fligelman's approach to
verify classical correlations in the gas engineering literature that did not consider the
effects of wellbore storage, skin, and turbulent flow simultaneously. Couri also
considered only drawdown cases.
1.2 Turbulent Flow
Turbulent flow causes an extra pressure drop at the well which can be mistaken
for well damage. Forchheimer (1901) added an additional term to Darcy's law to include
the increased pressure drop. According to Hubbert (1956) and Houpert (1959), what is
referred to as a "non-Darcy" component does not correspond to the classical
of
turbulent flow, but is caused by convective accelerations of fluid particles in passing
through the pore space. Most experiments indicate that true turbulence occurs at
Reynolds number values at least one order of magnitude higher than the Reynolds
number values at which deviation from Darcy's law for laminar flow is observed. All
experiments have confirmed the general applicability of the Forchheimer type of flow
equation. Turbulence factors for the Forchheimer
were
by
Cornell and Katz (1953). Katz and Coats (1968)
a
of the
turbulence coefficient as a function of permeability for the consolidated sandstones,
dolomites and limestones. Additional experiments by Fkoozabadi and Katz (1979)
showed differences in slopes between correlations for consolidated media and
unconsolidated media.
13 Wellbore Storage
The effect of wellbore storage was considered by Van Everdingen and Hurst
(1949) and termed the "annulus unloading" effect. It was further investigated by Ramey
(1965, 1970). Agarwal et al. (1970) presented a storage and skin type curve. Others
presented several other type curves thereafter. See Earlougher and Kersch (1974).
Ramey and Agarwal (1972) presented an analytical solution for a step change in wellbore
storage. Hegeman et al. (1991) presented an analytical model in Laplace space
representing increasing or decreasing wellbore storage during well testing for a variety
of well / reservoir models. They investigated exponential and error function time
dependence to represent changing wellbore storage, and considered buildup tests to
demonstrate utility of their results.
We consider details of Fligelman's (1981) model in the next section.
2. Mathematical Model
A schematic of a radial flow model is shown in Fig. 2.1:
Figure 2.1. Radial Flow Model
The assumptions made by Fligelman (1981) were:
1. Horizontal radial flow, no gravity effects.
2. Isotropic rock properties.
3. Gas saturation at 100% of pore volume.
4. Isothermal flow.
5. Constant porosity value.
6. Newtonian fluid behavior.
7. No Klinkenberg effect.
2.1 Turbulence Effect
High-velocity, non-Darcy effects were represented by the Forchheimer equation
transformed into a modified Darcy's law form by Swift and Kiel (1962).
u
-.-
(2.1)
Sr is a radial Darcy's law correction factor that is equal to unity for laminar flow, and
less than unity for turbulent flow.
(2.2)
1+
is the Katz, et al., (1959,1968) turbulence parameter:
23.83
(2.3)
L201
In the computer program, the velocity
ur for the Forchheimer equation is
calculated through an iterative method:
M
RT k
u, =•
2pp(p)
(2.4)
2.2 Formation Damage
We assume an annular damaged region around the well with an altered
permeability Iq and radius rj:
S=s
(2.5)
of course many combinations of rj and Iq can provide the same sMn effect, s.
2.3 Initial Condition
The initial condition is that the pressure throughout the circular system at time
zero is equal to a constant:
p =P i ; t = O s r w < r < r e
(2.6)
Or, in term of pseudopressure:
m(p) = m(pi); t = 0, rw <r<r e
(2.7)
2.4 Inner Boundary Condition
We assume a constant surface production rate. In this case, a material balance on
the wellbore leads to:
in which:
T
Cnfn\ =r-
Jg
PscT
1 fi(p) am(p)
k 2
3t
(2.9)
and:
[5. 3m(p)l
Sir
^F
l
L
3r Jr=r
qf
S
(2.10)
2.5 Outer Boundary Condition
The outer boundary is circular.
The condition for the infinite outer boundary is:
(2.11)
If a no-flow condition is imposed at the outer boundary:
thn(p)
=0 ; t >0
(2.12)
r=r
2.6 Dimensionless Quantities
The partial differential equation describing flow was transformed into a
dimensionless form using:
Dimensionless time:
(2.13)
Dimensionless pseudo-pressure for constant mass rate:
sc
(2.14)
Dimensionless rate:
(2.15)
Dimensionless wellbore storage:
T3[p/z(p)]'
T 3[p/z(p)]
(2.16)
Dimensionless distance:
(2.17)
Dimensionless diffusiviry:
(2.18)
2.7 Resulting Equations
After substitution and rearrangement, the various flow equations and conditions
are:
In the undamaged zone:
1 3
dm
D (%»trj)
, ^ ..
r
= --aD[mD(ib,tD)J
(r D ,to)
(2.19)
In the damaged zone:
1 3
1D
dr
r^1D(r
/-».D,t*D)J^
=- -—a/v D[m
(2.20)
Initial condition:
(2.21)
At the interface between damaged and undamaged zones:
(2.22)
10
The inner boundary condition is:
d p/z(p)]
=1
dtD
(2.23)
_3[p/z(p)]_
The outer boundary conditions are:
For the infinite acting case:
(2.24)
For the no-flow condition:
(2.25)
2.S Comments on the Finite-Difference Simulation
The equations described were transformed into a finite difference form by
Fligelman (1981). Although a time-weighting factor can be used with simulation, all
runs are made with a fully-implicit scheme.
The simulation runs with a dynamic time step. In order to study early time flow
accurately without wasting computing time after the transient period, the incremental
time step is always taken as 10% of the lowest time value inside a log cycle.
11
Another important point is the selection of the radial space coordinates. In order
to cover the entire reservoir while focusing on the near-well effects, a logarithmic scale
was used with the following transformation:
(2.26)
At early time, the outer reservoir radius is very small. When the pseudopressure at the
outer limit is affected by production, v is doubled, which means that the external radius
is squared. This provides a large number of points near the wellbore where pressure
gradients are large, and fewer mesh points further from the well. We consider
programming in the next section.
12
3. Programming Language and Development Features
The code was developed on a personal computer. The numerical model written in
FORTRAN reads the input parameters, computes the gas properties, solves the gas flow
equations and computes the results in a "pixel" format ready to be ^aphed. The interface
program that manages the screen and the windows with the use of the mouse and graphic
tools such as push-on buttons and pull-down menus is written in C language and
compiled with the Windows software development kit. This program performs the
acquisition of the main input parameters, calls the FORTRAN simulator through a "shell"
command, opens and reads ASCII files containing the results of the simulation, plots
graphs on the
and sends plots to the printer.
The choice of FORTRAN was straightforward because Fligelman's (1981)
program used by Couri (1987)
written in FORTRAN for a mainframe computer.
The C programming language has had a large impact on the computing world in the last
seven years. It allows
to write code for both very simple
and very
sophisticated applications. It
modular program design, with an extensive set of
instructions and capabilities. Finally, many of the programming features of Windows
were designed with the C language in mind.
The choice of Windows was also straightforward since this program has become a
standard
tool for most corporations. Windows is a graphic-based, multitasking
windowing environment that runs under MS-DOS. Applications written for Windows
have a consistent appearance and command structure that makes new Windows programs
easy to use. In order to write programs for Windows, the software development kit
provides an abundance of built-in subroutines that allow easy implementation of pop-up
menus, scroll bars, dialog boxes, icons, and many other features of a user-friendly
graphical interface. The next section presents a user manual for the program.
13
4. User Manual for REAL GAS FLOW
This user manual is arranged in the order of the operations a user is most likely to
perform. Section 4.1 describes how to initiate the program. Section 4.2 presents an
overview of REAL GAS FLOW. Section 4.3 describes how to arrange the input data.
Section 4.4 explains how to run the simulation. Section 4.5 describes how to plot the
results. Section 4.6
special features available with the program. Finally,
Section 4.7
two
for printing, Section 4.8 pinpoints a few details
relevant to leaving the application, and Section 4.9 introduces two computing aids with
Windows.
4.1 Installation
The hardware configuration is presented and followed by a guide to set up and
start the program.
4.1.1 Configuration
REAL GAS FLOW was designed to run on any IBM PC or compatible with a
processor 286 or higher (386/486), 16 Mhz or more. A math coprocessor (8087 or
higher, 287/387) is not required, but recommended because of the matrix manipulation
during the simulation. 2 MB of RAM is enough to use the application, even though
Windows is commonly used with 4 MB.
Table 4.1 shows simulation time for a drawdown test ran on different
configurations of computers. Run-time is sensitive to both processor type and
frequency. [The well was flowed for 1000 hours or 40 days. All computers were
equipped with math coprocessors.]
Darcy Flow
NonDarcy Flow
286-6 Mhz
Smins
12mins
386-1 6Mhz 486~25Mhz
2mins
4mins
Smins
7mins
Table 4.1. Simulation Time on Various Computers
REAL GAS FLOW is a "Window application", and Windows 3.0 or later is
required, and so is a mouse. All actions during the program execution are triggered by
using the left button on the mouse. Finally, a graphics adapter/monitor either color or
monochrome is required.
14
There is no specific memory requirements for REAL GAS FLOW as long as
Windows is installed. REAL GAS FLOW can also be run from a floppy disk drive, but
this practice is not recommended because of disk-access time.
4.1.2 Setting Up
REAL GAS FLOW is provided on a disk with a group of example files. The
executable files are RGF.EXE and FRANC.EXE. All other files on the disk are not
required to run the program, but are provided to give the user a better understanding of
the program by looking at old synthetic gas well tests.
RGF.EXE and FRANC.EXE must be copied into the working directory and
remain there at all times. To avoid building huge directories, it is recommended that
sub-directories be created with old tests. Old synthetic data can be retrieved and
processed by REAL GAS FLOW independently of their location on the hard disk or any
floppy disk. To install the program and the examples in a directory called RGF:
1. Insert the RGF floppy disk in drive A
2. Go into the disk or directory where RGF is to be created
3. Type: mkdirRGF
4. Type: cd RGF
5: Type: copy A:*.*
Files for REAL GAS FLOW have been named in a way that makes it easy for a
user to organize the working directory. When we design a new well test, a name for the
test must be defined, for example: EXAMPLE. All data files related to the test
EXAMPLE will differ only by their three character extensions : EXAMPLE.FLR is the
flow rate history file; EXAMPLE.ACT is the pressure history file at the active well, and
so on. More on the different files used by REAL GAS FLOW is presented in Section
4.2.3.
After having made a backup copy of the disk provided and copied all files and
especially RGF.EXE and FRANC.EXE in the working directory , REAL GAS FLOW
must be set up into "program manager ". Using the mouse, click on WINDOWS SET
UP inside the MAIN folder of program manager, then click on OPTIONS and select SET
UP APPLICATIONS. Select the hard disk on which the working directory is located
and then run the search by clicking OK. This can take a few minutes depending on the
number of applications on the disk. After the search, select RGF.EXE on the left
window in the dialog box, click on ADD and then OK. RGF will be added, with its
recognizable icon as a window application. At this point of course, it can be moved into
any group.
15
4.1.3 Starting Up
REAL GAS FLOW can be started from the program manager window by doubleclicking on its icon. At this point, the main menu will fill the entire screen. REAL GAS
FLOW can also be started under the DOS environment by going into the working
directory and typing the command: WIN RGF.
4.1.4
A Quick Guide to REAL GAS FLOW
Before learning more about the program, users will familiarize themselves with
REAL GAS FLOW (RGF) by using a first example. The following example files have
been provided on the disk: GUIDE.MAI and GUIDE.FLO. The following instructions
should be followed:
Start the program.
Click on INPUT in the main menu bar.
Click on OPEN inside of the new window.
Select GUIDE.MAI in the working directory and press OK.
The main parameter input file is now displayed.
Click on OK at the bottom of the window.
Click on RUN in the main menu bar.
The simulator is now running in a DOS window for a few minutes.
Click on OUTPUT in the main menu bar.
Select GUIDE. ACT in the working directory.
Click on OK in both messages on the screen.
Click on PLOT MENU in the main menu bar.
Select Log-Log plot.
Click on GRAPH in the main menu bar.
The results of the simulation are now displayed.
Click on ERASE in the main menu bar.
The user should now have a basic understanding of the software capabilities.
16
4.2 Overview
This section provides an overview of REAL GAS FLOW. The methodology
followed by the program is presented, the main menu bar is introduced, and a description
of the files used during a simulation is provided.
4.2.1 Methodology
After starting RGF, the main menu bar appears on the screen. The process is self
explanatory. Figure 4.1 shows the arrangement of the major components of REAL GAS
FLOW.
Callold
files
Input
Parameters
Run
Simulation
^
Prepare Field data file
for comparison
Create type curve
for AUTOMATE
Plot and Erase
Open "Results11 files
for plotting
Figure 4.1. Main Structure of REAL GAS FLOW
The first task is to input all the parameters which are relevant to the test we intend
designing. Clicking on the INPUT button provides a window (or dialog box) where the
17
characteristics of the well and the reservoir, the gas properties and the flow considered
must be defined. At this point, we can decide if we wish to compare field data with the
computed data produced by the program, and also whether computed results should be
stored as a future custom type curve for the AUTOMATE well test interpretation
software.
Instead of inputting a new set of parameters from scratch, an old test can be called
and opened. This can be done to verify parameters from old tests, or to modify a
parameter from a previously-run test design in order to perform a sensitivity analysis.
Once the list of input parameters is filled, it can be automatically saved by simply
clicking on an OK button. Furthermore, a control
one that we cannot
move on and save the input file if a critical parameter has been accidentally omitted.
The second task is to run the
by clicMng on the RUN button in the
main menu bar. Windows 3.0 will open a DOS window, and perform the calculations.
Run-time will vary from computer to computer, depending on the processor. During
computation, a message is displayed in the DOS window giving information on the
of the simulation. The simulator also prepares field data files (if any) so they can be
displayed on the screen and compared with computed data. Finally, the simulator will
save the results in a custom type curve for AUTOMATE (if required), and
messages will appear on the screen for this purpose.
The next logical step is to view the result of the simulation. Clicking OUTPUT
in the main menu Bar gives access through a dialog box to the content of any directory
on the hard disk or any floppy disk. An output file from the last simulation, or any old
simulation can be loaded by selecting the desired file in the appropriate directory and
clicking OPEN in the dialog box. A set of messages informs us that the computer is
loading the file and when this task is completed. By clicking PLOT MENU on the main
menu bar, we have a choice of different plots ranging from a simple rate history plot to
straight line analysis or log-log plots. Graphs can be plotted on the screen, superposed,
or erased by using the two remaining buttons in the main menu bar.
18
4.2.2 Main Menu Bar
The use of the six main buttons on top of the screen when the program is started
was explained briefly in the previous chapter. A quick summary follows:
INPUT:
Calls a dialog box that allows one to design a new well test or call an old
one.
RUN:
Run the FORTRAN simulator in a DOS window.
OUTPUT:
Allows user to select output files in any direction in order to create
graphs on the screen.
PLOT MENU: Present a Mst of nine different graphs.
GRAPH:
Execute the plotting of data on the screen.
ERASE:
Clears the screen, leaving only the main menu Bar.
The ERASE button can be used at any moment if the user wishes to
clear the screen.
The top title inside the screen heading reads REAL GAS FLOW when the
program is first started. This heading will change throughout the use of the program to
include the title of a graph when a plot is made, and the name of the output file that is
being graphed.
4.23
File Types
All files used by REAL GAS FLOW are ASCH files. All the files related to the
same simulation will have the same name and will differ only by the three-digit
extension. Some files are created by the program while others must be created by a user.
19
4.23.1 Files Created by a User
Let's suppose we are working on a well test design named TESTL We must
create a file TEST1JFLO containing the rate history using an editor. The details for all
input files will be found in Section 4.3; Setting Up the Data. If we wish to compare the
computed data from the simulation with field data, we must provide the program with a
pressure history file named TESTLPRS.
4.23.2 Files Created by EEAL GAS FLOW
The first file that RGF will create is the
parameter input file called by
clicking the INPUT button in the main menu bar. This parameter file is saved by RGF
under TEST1.MAL Hie most important file containing graphic information from the
simulation data produced by the program is TESTL ACT for all data related to the active
well. This file is the largest one used by the program, and will require on the average 10
to 20 Kbytes of memory, depending on the duration of the test.
Finally, if a file TESTLPRS was provided by a user in order to compare
computed and field data, a new file TESTLFLD will be created by RGF containing
graphic information related to the field data. Also, if RGF is asked to generate a custom
type curve to be used with AUTOMATE, a file TESTLMSG will be created containing
the type curve, as well as other relevant information.
At all times when RGF is used, an internal file MPUT.FEL requiring 10 bytes of
memory will appear on the working directory. This file is very small, and can be ignored
or deleted by a user because it will be recreated as needed by the program.
For each test design there will be between four and eight files on the working
directory depending on the different options selected.
20
43 Setting Up the Data
In order to create the rate history file, a user will require an editor under DOS that
saves data in ascii format. The same goes for the field pressure history file if needed.
The main data file (TESTLMAI) presented in detail in the next chapter does not require
the use of an editor since it is created by RGF.
4.3.1 Main Data File
After starting REAL GAS FLOW, a user should press the INPUT button in the
main menu bar. This action produces a dialog box on the screen with the heading:
"Parameter Input" as in Fig. 4.2.
Real Gas Flow
Title:
Main file:
Gas gravity;
Initial
res. press, (psia):
Rate data file:
H2S (fr):
Type of test*
Outer boundary:
Boundary
radius (ft):
Damaged zone
radius (ft):
Well radius (ft):
Weil depth (ft):
Thickness (ft):
C02 ffr):
Skin factor:
Initial
N2 (fr):
California or
condensate gas:
Reservoir
Temperature (F):
Weil-head
Temperature (F):
Weilbore
volume:
permeability (rnD):
Turbulence fy/n):
Perm = ffPJ (y/nj:
Own perm file:
Field data file:
Automate curve (y/n)
Porosity (fr):
Prod/obs
distance (ft):
Figure 4.2. Input Parameter Window to Create and Display Main Input Files
There are 24 parameters that should be considered, plus a title that is optional.
There are three action buttons in the dialog box: OK, CANCEL, and OPEN.
21
OPEN: Opens a second dialog box displaying the content of a
directory.
This directory will be refered to as the active directory. Selecting a file (with the
extension .MAI) in this second window will display it in the parameter input window.
OK: Accepts the parameter presently displayed in the dialog box as input data for
the next run of the simulator. These
could be freshly entered or could come
from an old file with the use of the OPEN button. OK will validate the display and make
the dialog box disappear. The parameter file will be saved automatically in memory
inside the active directory. OK will save all files in the active directory. Therefore the
active directory and the working directory should be the same in
to run a
simulation. If some parameters have been omitted intentionally or accidentally, pressing
OK will produce an error message.
CANCEL: Closes the parameter input window without saving any file, and goes
back to the main menu bar.
4.3.1.1 Opening an Old Main File
A main file can be opened in order to be displayed for changes or to run a
simulation. A user can display any main file on the template on the
by clicking
OPEN in the parameter input window. The new OPEN window will display all
in
the active directory. To limit the list to the main files only, the user can type *.mai in the
text box instead of *.* and then click on OPEN or by Mtting the ENTER or RETURN
key on the keyboard. Only *.mai files will be displayed in the list box. If there are more
choices than can fit the list box, scroll bars are provided so that the mouse can be used to
move up and down the list.
Changing the active directory will show a weakness of the Windows
environment: the user must possess a slight knowledge of the DOS environment.
One alternative to Change Directory is to type the entire path for the new
directory inside the text box. For example, if the present active directory is, as in Fig.4.3
D:\we\francois\newtest\* .mai a user can type in the text box: D:\we\johnNdoe\* .mai to
have access to this set of files.
22
Parameter Input
Title:
Main file:
Rate data file:
Wi^^SBHS^^i^KfliiiWitoaBBtiliiliMHHSB
Ope n File Manie:
InWiil
ility (mC
nee (y/ni):
Type of test
Outer b oundary:
*.mal
Eloundary
radius (ft):
Dama ged zone
radius p);
WeHr adius (ft):
(ft):
Welh
Files in
Thidciness (ft):
Par osity (fr):
F*rod/obs
dist;inee (ft):
Initial
»s. [psiiil:
dn facto r:
d:\we\francois\newtest
•~
Iran
fake
fake Jld
test.act
n
xyz 1 ,m»i
inpu
M
tfii
OT W
i
perm fil e:
§
^
S§
\ data fl e:
irvc (y/inj:
I
ps
Hri
wri
Figure 4.3. OPEN Window to Access Files on Disks
An alternative is to type in the text box: D:\*.mai and use the mouse to select the
successive subdirectories by double-clicking on them. Once a user is in the desired
directory, the quickest way to select a file is to double-click on its name.
Old main files can be used to run the simulator if old result files have been lost or
erased. However the most useful aspect of displaying old main files is to be able to
perform sensitivity analysis. This can be done by displaying an old main file, changing
one input parameter (permeability for instance) and saving the new input file under a
name that is slightly different from the previous one. Figures 4.4 and 4.5 show two
main files using the same rate data file. The two files differ only by the value of
permeability (10 and 100) and by their name.
23
Figure 4.4. Example of File for Sensitivity Analysis, with k=10mD
24
Perm = f|PJ (y/nj:
Own perm file:
Field data file:
Figure 4.5. Example of File for Sensitivity Analysis, with k=100mD
Once an old file is displayed inside the parameter input window, clicking on OK
will save the displayed file in the active directory and, if and only if, the active directory
is also the working directory (that contains RGF) will the simulator be able to run. This
is an area where caution is required because distraction can lead to running the simulator
with an unwanted input file.
4.3.1.2 Creating a New Main File
In order to run a new simulation, a main file must be created. The well test can
be designed by trial and error, and RGF permits one to perform sensitivity analysis in an
easy fashion.
Table 4.2 is a practical summary of the 24 fields required to complete the file.
25
Name of Field
Meaning
Unit expected
title
main file
rate data file
type of test
outer boundary
boundary radius
damaged zone radius
well radius
well depth
thickness
porosity
gas gravity
CO2, H2S
type of gas
reservoir temperature
well head temperature
wellbore volume
initial reservoir pressure
skin factor
permeability
turbulence
field data file
Automate type curve
title of test to run
main input file name
rate data file name
drawdown or injection
defines external boundary
external radius
optional
1 to 8 letters
1 to 8 letters
letters
letters
feet
feet
feet
feet
feet
fraction
fraction
fractions
letters
Fahrenheit
Fahrenheit
cubic feet
psia
dimensionless
mD
yes / no
1 to 8 letters
code: 0, 1 or 2,
.
.
pay zone thickness
relative gravity to air
gas impurities
.
.
-
skin damage
average in reservoir
consider or not
name of file if applicable
create or not
Table 4.2. Summary of Main Input Data File
To fill up a file, the mouse must be used to move from one field to another,
clicking into the box of the field to enter next. The order in which the fields are entered
is irrelevant. Only the title is optional. All other fields are required Both lower case
and upper case can be used when creating a file, as long as the
is consistent! For
instance, both "drawdown" and "DRAWDOWN" would be
as type of test, but
"Drawdown" would be rejected. The program uses only oil field units.
To save a main file that has just been created, the user should press the OK
button. The file will be saved in the active directory (again, this is the directory shown
when clicking on OPEN in the parameter input window or on OUTPUT in the main
menu bar.)
26
We cannot overemphasize the point that in order to run the simulation, the main
file must be in the working directory. The working directory is the directory that
contains RGF.EXE.
Saving a main file will add the extension .MAI to whatever was entered in the
main file field. If the user wishes to call a test TEST123, RGF will automatically save
the main file as TEST123.MAL If a file TEST123.MAJ already exists in the directory,
RGF will write over it!
If the user presses CANCEL instead of OK, the parameter input window will
disappear, and all parameters currently entered will be erased from the screen without
being saved. Also RGF cannot be minimized (upper right arrow on window
applications) while the parameter input window is on the screen.
Finally, we should be aware that under the Windows configuration, all characters
do not require the same space on the screen. For instance an "m" will require more than
three times the space of an "i". On the average, eight characters should fit in each field
box, but a box that can accept fourteen "i" characters will accept only four "rn" or seven
"a" characters. When choosing names for the different data files, remember that DOS
requires that spaces or periods are excluded as characters.
4.3.1.3 Detailed Description of Each Field
(1)
TITLE—This field is optional, and can contain any type of character. It is
useful to a user, in order to remember specific runs, dates, or well locations.
(2)
MAIN FILE—This is the filename under which the input parameters will
be saved, with the addition of the extension .MAI. Any character can be used except
periods or spaces, with a maximum of eight characters.
(3)
RATE DATA FEJE-Requirements are the same as for the main file
name. The user should give the name of the file they previously created under a DOS
editor, and saved with an extension .FLO. Example: NAME .FLO. The rate data file
must be saved or copied in the working directory as well as all other relevant input files
in order for the simulator to run.
27
(4)
TYPE OF TEST-In the future, Buildup test or multirate test could be
added to REAL GAS FLOW. In the present version, only drawdown and injection tests
can be run. The user should therefore write INJECTION or DRAWDOWN getting as
many letters in the box as possible. A drawdown is defined as a flowing period where at
time zero the pressure is constant and identical at all points throughout the reservoir.
(5)
OUTER BOUND ARY-lTiree options exist. The program checks only
the first two letters of the input, but as many letters can be used as wiU fit in the box.
Infinite Acting:
Hie program checks on:
IN.
No Flow:
The program checks on:
NO.
with:
The condition for the infinite outer boundary is:
lim M- m(p) = m(p i ) ; t > 0
(4.1)
If a no-flow condition is imposed at the outer boundary:
dm(p)
=0 ; t > 0
(4.2)
(6)
BOUNDARY RADIUS-If the outer boundary condition is no flow or
constant pressure, a radius must be provided in feet In the case of infinite acting, an
entry such as zero ("0") should be made.
(7)
DAMAGED ZONE RADIUS-This field concerns a cylindrical zone
around the wellbore altered by the drilling process which has a permeability different
from the reservoir. A damaged zone radius in feet is required. If there is no damage, a
radius of zero ("0") is required.
(8)
WELL RADEJS-A value in feet is required.
(9)
WELL DEPTH-This value is required to compute the gas properties table
in order to compute wellbore storage. A value in feet is required.
28
(10) THICKNESS—The reservoir is modeled as a constant thickness circular
layer. A value in feet is required.
(11)
POROSITY-Enter fractional porosity between 0.01 and 0.8.
(12) GAS GRAVTTY-The specific gravity of the gas compared to air at
standard conditions is required.
(13-14) The concentration of the gas impurities N2, CO2, and H2S should be
entered as fractions. Values should therefore be between zero and 1.0.
(15) TYPE OF GAS~This information is required in order to select the proper
Standing (1977) correlation. RGF performs a test on the first letters of the information
provided. The user is encouraged to write as many letters as possible in the field box.
California:
The program checks on:
Condensate: The program checks on:
CAL
CON
(16) RESERVOIR TEMPERATURE-A temperature value in degrees
Fahrenheit is required. The simulated flow by RGF is isothermal. The temperature
value is used both in the flow equations and to generate the gas properties table.
(17) WELLHEAD TEMPERATURE-As for the reservoir temperature, a
degree Fahrenheit value is required. This parameter is used to compute the temperature
gradient in the well. The temperature is required to compute weUbore storage.
(18) WELLBORE VOLUME-The wellbore volume between the pay zone and
the surface is required in cubic feet. This value is used to compute wellbore storage, and
therefore the inner boundary condition. As presented in Eq. 2.16, the dimensionless
wellbore storage is:
CD =
T 3[p/z(p)]
T 3[p/z(p)]
29
(4.3)
(19) INITIAL RESERVOIR PRESSURE -This is the pressure in psia at any
point in the reservoir before the flowing period.
(20) SKIN FACTOR—This value is dimensionless and reflects the formation
damage around the weU. If k is the permeability in the reservoir and Jq the permeability
in the damaged region, the skin factor s is defined in Eq. 2.5:
s=
_i
(4.4)
(21) PERMEABILITY-This is the constant permeability in mD of the
homogeneous reservoir.
(22) TURBULENCE—A yes or no answer is required here. RGF checks only
the first letter and looks for a y or an n in either upper or lower case. YES means that
turbulence effects will be included by RGF in the Forchheimer equation. NO means that
the flow wiH follow Darcy's law.
(23) FIELD DATA FDLE-TMs field asks for the name of a time/pressure file
allowing the user to compare field test data with the computed results from a simulation.
More is presented on this feature in Section 4.4.1. If field data is to be used, the data file
must be created by the user with an editor under DOS before starting the program. As
with other data files, the field data file should be saved in the working directory with the
extension JPRS. Example: NAME.PRS. In the parameter input window, the file name
should be provided without the extension. If field data will not be used, a space (blank)
should be entered in the field box in order to
and leave the input parameter screen.
(24) AUTOMATE TYPE CURVE-Creates user-made type curves to be used
with the AUTOMATE-II Computer-Aided Well Test Analysis package. It is possible to
build a library of type curves in order to match field data, or to run a non-linear
regression. The requirements for this field are:
Enter "0" if the user doesn't want a type curve to be saved from the simulated results.
Enter "1" for a standard ppjj versus trj type curve, where the estimated parameters in
AUTOMATE will be k, the permeability, and $ the porosity.
Enter "2" for a storage type curve ppD versus tjyCrj where the estimated parameter in
AUTOMATE will be k, the permeability, and C, the storage factor.
30
More on this utility will be found in Section 4.6: Special Features.
4.3.2 Flow Rate File
Some conventions must be adopted.
(1) Time zero is the time at which the well starts flowing.
(2) All time data are in hours.
The flow rates will be in Mcf/D. It is mandatory to have a flow
data point at
time zero since we need to specify at what time the well started to flow. A typical flow
rate data file for a constant rate drawdown test is:
0.0
500.
5000.
end
This means that the well flows at 5000 Mcf/D from time zero for 500 hours. If the user
is familiar with AUTOMATE, the same drawdown on AUTOMATE would have a rate
data file like:
0.0 5000.
RGF requires one more line in order to tell the simulator when to stop. This
means that any rate data file already created for AUTOMATE can be used by adding a
second line containing a time and "end" or "stop" instead of a rate. Notice the free
format for the data file. The data can appear in any column in any format, provided that
there are only two numbers (a time and a flow rate) on each line. It is important to
provide RGF with a final Mne that specifies when to stop computing. To find an easier
way to modify data files under Windows without having to go back to the DOS
environment, please refer to Section 4.9: Computing Aides.
31
4.4
Running the Simulation
Clicking on RUN in the main menu bar wiU ran the simulator. The main issue
is: what case is being run? A second point concerns the various messages on the screen
during the simulation.
4.4.1 Running the Right Case
There should be no uncertainty as long as the user gives special attention to the
next few steps:
(1) Make sure that the main data file is created and saved in the working directory.
is always the case if the active directory and the working directory are identical.
This
(2) Be aware that the main file that will feed the simulator is the last one that was OK'ed
before pressing RUN.
(3) Make certain that all files required for a specific simulation to ran are available in
the working directory.
(4) Double check values and units in the main data file before saving it by pressing OK.
4.4.2 During the Simulation
MS Windows 3.0 runs the simulator in a DOS window.
The window will
display periodically what fraction of the computation has been completed. A simulation
ends by informing the user that "Everything went fine" and that "Data are now being
stored for graphics". If all data files have been set accordingly, the only error message
that might appear on the screen is to inform the user that with the parameters provided,
convergence toward a solution is not possible.
Mistakes made while editing the input
data files can end the simulation prematurely. In this case the final message will not
appear on the screen. This is a sign for the user to double check input files, beginning
with their location in the proper directory.
Once a simulation is completed, the screen
returns to the main menu which appears when RGF is first started.
32
4.5
Plotting Results
Nine different graphs can be obtained from the results by the push of a button.
To get a Hst of the graphs, press on PLOT MENU to get the screen shown in Fig. 4.6.
The Homer plot and the Hne source solution are not accessible but have been placed in
the menu for future development.
Log-Log Rot
Log-Log Derivative Plot
Cartesian Plot
Homer Plot
Dimensionless Semi-Log Plot
Pressure History Plot
Line Source Solution Plot
Rate History Plot
Figure 4.6. Choice of Available Plots for Viewing Results
4.5.1
Plot Menu
(1) Miller Dyes Hutchinson: Semi-log plot of pseudopressure in psia versus time in
hours
(2) Log-log :
Log-log plot of log(Amp) in psia versus log(At) in
(3) Log-log derivative:
hours
Log-log plot of At log(9mp/3At) in psia versus log(At)
in hours
33
For the computed data from the simulator, the derivative is a simple forward first degree
finite-difference calculation with no attention to noise reduction.
(4) Cartesian:
Cartesian graph of normalized pseudopressure in psia
versus time in hours
The normalized pseudopressure for this plot is:
This is an excellent way to express the pseudopressure
because a unit of pressure is obtained. This expression was introduced by Meunier et al.
(1987) and is also presented in Home (1990).
(5) Homer:
(6) Dimensionless:
dimensionless time trj/lO^.
2.14.
(7) Pressure history:
(8) Line source solution:
(9) Rate history:
4.5.2
Not accessible
Semi-log plot of dimensionless pseudopressure versus
The dimensionless variables are described by Eqs. 2.13 and
Cartesian plot of pressure in psia versus time in hours
Not accessible
Cartesian plot of rate in Me^Dversus time in hours
Overview
Any output file containing results from simulation can be opened to create graphs
on the screen. The following two
describe how to open an output file and plot
the data on the screen. A third section introduces the use of a cursor to pick points on a
graph.
4.5.2.1 Opening an Output File
RGF treats files from the current simulation and those run in the past in the same
manner. To select a file for plotting, go to the main menu bar and press the OUTPUT
button.
34
An OPEN window similar to that for input files appears on the screen as in Fig.
4.7. The pressure response data at the active well for a simulation where the main file
was EXAMPLE.MAI will be found in the file EXAMPLE. ACT. RGF created this file in
the working directory at the end of a simulation. Using the file manager utility of
Windows 3.0, a user can move the output files (with an extension .ACT) to different
directories or sub-directories for storage.
Loo Derivative Plot. Output tile : xyzl O.mai
Files in
d:\we\francois\nevrtest
Figure 4.7. OPEN Window to Access Output Files Stored on Disks
To open a file, the procedure is the same as for opening a main file. It can be
easier to view the available files by typing *.ACT in the text box instead of *.*. The
user can move up or down in the tree of directories and change disk drive to search for
old files, and can cancel the search by pressing CANCEL with the mouse.
35
Pressing OPEN after having selected an output file with the mouse will load the
data into the graphics subroutine and will trigger two messages that require the approval
of the user by clicking on OK with the mouse. Hie two messages are: "About to read &
convert data points. This may require a few seconds to process." and "Completed reading
of output file." The screen will then go back to the initial main menu bar. RGF is now
ready to graph results. IMPORTANT: INPUT and OUTPUT show the same active
directory. If output files are selected in a directory different from the working directory,
the user should make certain that the next time a main file is created, it is saved in the
working directory.
4.5.2.2 Plotting the Data
Once an output file has been selected, select a specific plot by clicking on the plot
menu, and clicking on the GRAPH button as in Fig. 4.8. The ERASE key
everything on the screen except the main menu bar. It can be used to view different
graphs in sequence. It is also possible to superpose two or more graphs on the same
screen.
88-Sxl
Delta mp vs. delta time [hours]
1000
1E+02
1E+01
1E+00
.1
.001
1E-02
1E-01
1E+OD
1E+01
Figure 4.8. Typical Log-Log Plot with REAL GAS FLOW
36
1E+02
1000
Since different plots have different scales, only the log-log plot and the log-log
derivative plot are meaningful to display together. To do this, select the output file, then
select one plot in the PLOT MENU, press GRAPH, select the second plot in the plot
menu and press GRAPH again. The screen should display a graph similar to Fig. 4.9.
Delta mp vs. delta time (hours)
1000
1E+02
1E+01
1E+00
.1
.001
1E-02
1E-01
1E*00
1E+01
1E+02
1000
Figure 4.9. Typical Graph of Both Log-Log and Derivative Plots
RGFs ability to superpose plots from different output files is useful in order to
compare results in the case of a sensitivity analysis. An unlimited number of plots can
be superposed so as to see the influence of one parameter on well test results. If two runs
were made with two different skin factors, s=+2 and s=+10, the output files would be
SKM2.ACT and SKIN10.ACT. Let's assume we wish to see a log-log plot for both
files. First select skm2.act with the OUTPUT button, then select log-log plot in the
37
PLOT MENU and click on GRAPH. The first plot is now on the screen. Using the
OUTPUT button again, select skinlO.aet, click on GRAPH again, and the second plot
appears. See Fig. 4.10. There is no need to go to PLOT MENU since RGF kept in
memory that the last selection was LOG-LOG. This can be done repeatedly if more than
two plots are desired. Superposing plots for comparison is meaningful only if the scales
are the same. This is almost always the case when a sensitivity analysis is performed.
On the other hand, two very different well tests would not be comparable, because the
plot scales could be different
Delta mp vs. delta time (hours
1000
10002
10+01
1E+00
.001
.01112
.1E-01
1E+00
10002
1000
Figure 4.10. Superposition of Log-Log Plots From Two Different Output Files
4.523 Using the Cursor Utility
Once a plot is on the screen, clicking once with the mouse anywhere inside of the
plot area will draw a cursor. Whenever the mouse is clicked, the cursor will reposition
itself at the very tip of the arrow. Holding the left button of the mouse down, the cursor
can be dragged on the screen.
38
As soon as the cursor appears on the screen, the x and y coordinates of the
intersection between the cursor and the plotted curve are printed on the upper right side
of the screen. For example, on Fig. 4.11, the cursor shows the maximum of the
derivative curve at delta(mp)=30.03 psia^/cp and time=0.23 hours.
l||i:<lRiW
X : 0.238iBI
Cur. Y .* 30.0331
Delta mp vs. delta time (hours)
1000
100
/• ~^\ v__
/
/
s*~
10
1
/
1
.001
.01
.1
10
100
1000
Figure 4.11. Using the Cursor Utility to Pick Points on a Graph
This cursor allows a user to compute the slopes of straight lines in a rapid fashion.
When more than one curve is plotted at the same time, the cursor will show coordinates
relevant to the last curve plotted on the screen. It is therefore important to remember
which one that was!
39
4.6 Special Features
This section describes two features available with RGF. First, the procedure to
compare field data and computed data is presented. The remaining sections introduce the
generation of type curves for use with other well test analysis programs such as
AUTOMATE.
4.6.1 Using Field Data
An overview of the process of comparing field and computed data from a
simulation follows. A user creates a data file of
and pressure data from field
measurements in the working directory. This
file
will have a name, and an
extension .PRS. The name will be listed in the main file. RGF will read NAME.PRS
and convert it into a graphic file: NAME.FLD ready to be graphed("FLD" for "field").
It is important to declare the name of the field data file in the main file each time a run is
made in order for RGF to check that all data will be plotted with the same scale.
4.6.1.1 Setting Up the Field Data
A pressure file must be
in pairs of numbers, one pair per line, with time
in hours and a pressure in psia. Again, free format is used. We require that the file
contains no more than 500 lines in order to Emit computing and plotting time. A typical
part of a file for a drawdown would look like:
0.01
0.05
0.1
0.2
0.8
1.0
10
100
4507
4505
4490
4485
4480
4473
4460
4450
40
For users familiar with AUTOMATE, the same pressure files can be used for
both programs. However RGF does not require a pressure point at time zero. A user
should be certain to input an accurate initial pressure value in the main file before the
simulation. Writing the pressure file, it is very important not to leave blank lines at the
end of the file as RGF will read them as pairs of zeros.
When a pressure file has been provided to compare field and computed data, a
message appears in the DOS window at the end of the simulation telling the user that the
field data is being converted in order to be plotted.
4.6.1.2 Plotting Field Data
All field data files to be plotted will have an extension .FLD. These files can be
handled the same way as the output files from a simulation. To select a file, go to
OUTPUT and make the selection in the working directory. Then use PLOT MENU,
GRAPH, and ERASE, the same way as for all other files. For instance, field data and
simulated data can be superposed as on Fig. 4.12.
Unlike simulated data that is graphed in blue as a continuous function, field data
will be shown in green or red in large points as a discrete function.
A second difference with the way field data is handled by RGF lies in the
computation of the derivative. As presented in Home (1990), in order to reduce the
noise in the shape of this derivative, only data points that are separated by at least 0.2 of
a log cycle are used, rather than points that are immediately adjacent.
The derivative can be written as:
ap
aint
at
(
ln(t i+j t H /tf)AFfc
41
ln(ti+j/ti)APi_k
.;$£at;ti^
Delta mp vs. delta time [hours]
1000
1E+02
1E+01
1E+00
.001
1E-02
1E-01
1E*00
1E+01
1E+02
1000
Figure 4.12. Superposition of Field and Synthetic Data
4.6.2 Creating Type Curves
The following procedure is based on the use of the AUTOMATE Well Test
Analysis package, but similar software that uses user-installable type curves could have
been used. A useful complement to this section is the AUTOMATE-n user manual (any
version), and especially Appendix D: User installed type curves.
42
4.6.2.1 Background
AUTOMATE allows a user to enter their own type curves for plotting and/or
matching. To do so, the type curve must be digitized in a standard format file. This is
the task that Real Gas Flow wiU perform. The name of this file must be included in the
message file: DIGITIZE.MSG mat is inside the AUTOMATE working directory.
Modifying DIGITIZE.MSG can be achieved under DOS with any editor.
The format for the type curve input data file must be rigorously observed. This
requires no action by the user since RGF will write the entire file. The correct format is
nevertheless presented in detail in the AUTOMATE manual, in case the user decides to
make custom changes. In addition to the digitized type curve, AUTOMATE requires a
minimum of 12 parameters related to the scales and legends of the plots.
To use the installed type curves, CUSTOM CURVES must be selected inside the
AUTOMATE menu, followed by DIGITIZED TYPE CURVES. An automated match
can also be performed by
DIGITIZED TYPE CURVES from the Mst of
available models.
4.6.2.2 Creating One Type Curve
As presented in section 4.3.1.3, three entries related to a type curve can be made
in the main file before a simulation is ran:
0" if no type curve is desired
1" for a standard pwp versus t£j plot
2" for a storage p j j versus tryCfj plot
In all cases, both the pseudopressure and the derivative curves will be provided.
If a simulation is run from TEST1.MAI, the type curve file will be: TEST1.MSG.
Additionally, the curves will be marked by their respective value of CD.eA2s at their end,
CD being defined in Eq. 2.16.
Again, for one type curve only, a user does not need to know the content of the
type curve file NAME.MSG. But plotting field data against a unique type curve is
43
definitely not enough to analyze a test fully. It nevertheless gives a user a good idea of
how the field and the simulated data compare.
4.6.2.3 Building a Library of Type Curves
This task is more difficult since it requires a user to "paste" type curve files
together. Therefore, a good knowledge and understanding of the content of files is
required. See the AUTOMATE manual. The physical task of putting files together is
simple and not time consuming. It must be done in DOS. Figure 4.13 shows a simple
Mbrary of five type curves. The type curve data file for this particular pair of curves is
presented in Table 4.3 and should be studied.
Delta mp vs. delta time (hours]
10000
1000
100
10
.001
.01
.1
10
100
1000
1000
Figure 4.13. Example of Combination of Five Type Curves to Build a Library
A type curve file with derivative values has the following structure:
44
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§ 0© oo ©o
P S» ©
#«O«^tft9W0C>OOQOOOOOOOOf&QO*WM^^in«^iP*^W
P p©
§ in
» **
^iKf*in«piKfcr*i»&r-r'^wirtr«i^itt*r*pr*«w«»«*w
f»j<iiB«stt*»lK*w'WWW*or*. N » i P v i f t W © ! ^ w « w v « » « i f t < * p * f & f * l * ^ W * * f t < w w
««M<rtftw»iAi*>«i4i r»»inowf*i*int*pKM&isf*t»wwaniininff»iftirt
« •* 5- ««
«***•* »"t «»*(
§ O* Oo OIn
ir>«wM!>*rw»c>**i^(«or*' © w ^ » r v S p f * * > ^ * n * P t ^ v w » w p » w t * i ^ # « * » * 0 ^ f * w * ^ o t ^
&»ewitt«©Kw»w^es(^r*w*w«»f^.**©*K«*i&f*#t»i«mir*«*w»^««ri^
5* § § fa
S«£S©355l!if2§!^^
§ C»oo
•n^«vw«nwoooopopooooooooowc^mr^««^tiW(9inNi^vM^«sif^«nf^rto
5 Oo
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g § 8 8o
^ t % * i n ' * * f t i f j * » F ^ « i » t * . w « ' f v o » fw
w«s*o»woocc'eoooor'Ooooooooooooo
c
8 oOoOo O* ~ *
r* » * o
JD
w^w^^^^rsi»^»^!KeroKo»sc»oo^wr«»^inr^r^o»»is»^o»»i«>w'm»^.*r»>»wS
^iftOW^IBift^WlSt^O^OWW^^^l^W^^^Wf^WWWI^wWWIOln^^
*"t(Hf"*WWl«**f
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t-trswrnwirii^cicr-aB^o
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I S i O ^ r s i n v D n O O O O O O O O O O O O O O O O O O C O O O O O O O O O O O O O O O D O O O O O O O O O O O
r - » « » - « 5 « - r - . r - » ^ » ^ r - i m ' » m O O O O O O O O O O O O C O C 3 O C - O O D O O O D O D O D O O O O O O O
g
g
|
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§
|
|
|
|
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|
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g
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g
g
I
Q
CO
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X)
ib
S
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O«?-»O»»-OOOOOOO
l O O O O O O O G O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
i B 0 ^ 2 * « ^ ' - « £ * » ^ * 2 « « w j r p P O £ O O o o 0 e e « » o © g © o o o o o o © o o © o o o o o o © o o o o ©
f^^«^wp^v«^mt^iBr^winp«^wftvf^^inctpp^^vMm«^©^*wvf«Sr^
*
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Seoooooooeoooooo
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45
SooooS o o o o o e o e o o o
OOOOOOOOOOO
<line 1 to 12> :
<Hne 13ton+13>:
<next Hnes> :
<next n Mnes>:
<last Mnes>
:
12 parameters
Data points for the curves: tj> Ppj)l, PpD^» etc..
All curves must have the same number of points and share the
same time values.
Parameters related to the curve labels.
Data point for the derivative curves.
They must have the same number of points as the
curves.
Parameters related to derivative curve labels.
Under DOS, a short program is required to read the data points from each
individual type curve file and to rewrite them as in the AUTOMATE manual.. All other
parameters were edited manually when needed.
Going into AUTOMATE, field data can be plotted with the library of type curves
by performing a manual match with the "type curve" command, after selecting "digitized
type curves". A nonlinear regression can also be run with any library of type curves
using the "automatch" function of AUTOMATE. The result can be displayed with the
function "plot match".
46
4.7
Printing
There are two ways to print from RGF. It is possible to print a graph of the data
using the PRINT button provided by RGF, or a hard copy of the entire screen can be
made at any
using the CLIPBOARD utility of Windows.
4.7.1
Printing Directly
Printing directly from RGF to either a postscript file or to a printer is possible and
easy. Clicking on the PRINT button in the main menu bar will print the content of the
plotting box on the screen. PRINT doesn't send a hard copy of the screen to the printing
device. Therefore, it does not print the input parameter window that displays main files
for instance. PRINT
a
to the printer the
way the
was to the
screen. Therefore, only the last plotted curve will be printed. To print a superposition of
curves (when comparing field and synthetic data for instance), or to print a hard copy of
the screen, a Windows accessory called CLIPBOARD must be used.
4.7J Printing with CLIPBOARD
The CLIPBOARD utility is embedded into Windows. CLIPBOARD does not
need to be opened or activated in order to be used, as long as it is present in the Windows
directory. To produce a hard copy of any screen, press the PRMTSCREEN button on
the keyboard (sometime PTSCR). The screen is stored into the CLIPBOARD. It can be
pasted into any of the following programs: MS Word, Excel, or PowerPoint using the
EDIT menu. At this point it can be sent to a printer.
4.8
Leaving REAL GAS FLOW
RGF can be exited at any time by double-clicking on the upper left square button.
Two relevant issues when leaving the program are: Saving important files, and cleaning
the working directory.
47
All files created by RGF are automatically saved in the working directory. After
using RGF, it is recommended to save batches of test results under related names in
specific directories or subdirectories. Remember that when reusung old tests, the main
input files (as for the flow rate files and field data files) must be put back into the
working directory.
Before leaving the working directory, one should remove unnecessary old input
and output files. All files *.AAA and INPUT.FIL which are temporary files for RGF can
be removed also.
4.9
Computing Aids
It is recommended to open a FILE MANAGER window in RGFs background in
order to copy files between directories and sub-directories. This is an easy way to insure
that all
needed are in the working directory before running a simulation.
NOTEPAD, one of the Windows accessories, can be used as an editor. All
NOTEPAD files are also text files. The objective is to have easy access under Windows
to files with the following extension:
*.FLO Flow rate files
*.PRS Pressure files for field data
*.MSG Type curve dam files
in order to edit them.
To do so, a user must start the FILE MANAGER, go into the Windows directory
and double-click on the file "win.ini11. A file called NOTEPAD-WW.INI will appear.
In the [extensions] section, the following lines should be inserted:
flo=notepad.exe A.flo
msg=notepad.exe A.msg
prs=notepad.prs A.prs
If win.ini is saved, and the computer rebooted, any files with the extensions
specified will be accessible for editing as text files under FILE MANAGER. The next
section shows an example of the use of RGF as a tool for well test analysis.
48
5. Using RGF as a Well Test Interpretation Tool
A major application of the software is to design well tests. Another application is
to have an interactive tool with which sensitivity analysis can be performed. But RGF
can also be used as a tool for interpreting field test data, especially when software based
on traditional models shows poor confidence limits. For a high velocity and high
pressure drop well test, changing weUbore storage, changing turbulence coefficient, or a
combination, can cause a poor interpretation. Another cause of poor interpretation may
result from a poor estimation of the initial pressure in the reservoir before the start of
flow.
In this example, an associate created a set of synthetic field data with RGF, and
submitted a pressure history file, a
data file, and
additional
concerning the
reservoir and the well completion to an associate (the analyst). This should simulate the
analysis of a field test, where permeability and skin would be the unknowns.
The objective was to determine whether an analyst could find the permeability
and skin by plot-fitting the synthetic field data and a succession of data simulated by trial
and error with the help of RGF to find a satisfactory match.
REAL GAS FLOW offers a variety of graphs to choose from. Experience
showed that a satisfactory way to perform the match, which was a time consuming task,
was to follow these directions:
Plot fit with the log-log graph first.
Plot fit next with the combination log-log and derivative graph.
Check the coherence of the solution with a semi-log plot Hke MDH.
AUTOMATE (or a similar well test program) was helpful in finding estimated
values of permeability and skin effect before starting with RGF.
49
The case studied was the following:
Flowrate of 10,000 Mcf/D for 1,000 hours or 42 days
Infinite acting case, no external boundary
Damaged region of three feet around the wellbore
Wellbore radius of 0.333 feet
Pay zone of 15 feet
Wellbore Depth of 20,000 feet. We considered a wellbore volume of 10,000 cubic feet.
The porosity was 15%, the gas gravity 0.9, and the reservoir temperature 375 °F.
The initial reservoir pressure before the start of the flow was 8,000 psia.
Part of the synthetic field data produced by RGF is presented in table 5.1.
AUTOMATE gives the following solution for this test:
Permeability k=12 mD +/- 3%.
Total sMn = 4.4 +/- 5.5%.
A manual plot fit is a time consuming task, but experience will allow a user to
anticipate how to change permeability and skin effect to affect the position of the plots
on the screen of REAL GAS FLOW. The fastest way to perform a manual fit is to
perform a sensitivity analysis with one parameter at a time; permeability first, then skin
effect, then permeability again, and so on.
50
Time
Pressure
0
0.001
8000
7997
7991
0,0027
0.0044
0.006
0.0077
0.012
0.025
0.04
0.052
0.066
0.08
0.1
0.24
0.37
0.5
0.64
0.77
1.91
3.58
5.24
6.91
8.24
10.8
24
37.5
50.8
64
77.5
224
458
691
7986
7981
7976
7962
7923
7886
7851
7816
7783
7716
7460
7264
7110
6985
6881
6440
6243
6174
6139
6120
6095
6030
5996
5973
5956
5942
5865
5813
5784
Table 5.1. Pressure History for Synthetic Field Data
51
After a significant trial and error period, we were able to obtain the following
match in Fig. 5.1. The data in discrete points is the field data. The simulated data, a
continuous line, was obtained by entering into RGFs input parameter window all the
information given before, in addition to an estimated permeability of 17 mD and a skin
of factor of 3.
ftfltilijte
10000
Delta mp vs. delta time [hours]
1000
100
10
.001
.01
.1
10
100
1000
1000
Figure 5.1. Plot-Fitting Field Data and Simulated Data by Trial and Error, Log-Log Plot
52
Even though the log-log graph shows the best match after a trial and error period
of an hour and a half, the semilog plot shows some divergence at late times:
3^:w^^
Pseudo-pressure vs. time (hours)
8000
\\
—^
7000
\\
\
6000
iOOO
•*
""•"NH*" ***
4000
<*»
"— <K
""^-^ ****
-r
^\
3000
.001
.01
.1
1
10
100
1000
1000
Figure 5.2. Plot-Fitting Field Data and Simulated Data by Trial and Error, Semi-Log
Plot
The values that were used in order to create the set of data with RGF in the first
place were:
Permeability = 17.5 mD.
Skin damage = 2.8
53
Our trial and error plot-fit was within 3% of the correct solution for the
permeability and 7% for the skin. In this particular case, we were persistent enough to
get very close to the solution by the method of trial and error. A process to accelerate
the fit or confirm it is to bracket the values of s and k» buM a library of type curves
covering this range as presented in Section 4.6.2, and use AUTOMATE to perform a
nonlinear regression of the field data onto the type curves.
For instance, for values of skin between 0 and 5 and values of
between 10 and 20, AUTOMATE will perform an automatic match as on Fig. 5.3.
Keeping track of each type curve displayed and knowing its corresponding parameters,
the best interpolation can be read directly on the screen.
54
o
—TC—BO XX
rH
X
COCO
o
f-l
x
U
O
f-l
X
O
I
o
10
rt
0
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g
o
o
o
rt
~
o
o
e
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Q
T3
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-3
en
m*
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55
6. Conclusions
An interactive software prop"am that simulates the flow of real gas through
porous media has been prepared. It runs under a graphic environment and allows a user
to compare sets of data, perform sensitivity analysis, and display field data. Hie easy
access to data and quick display of
on the screen should reduce time waste caused
by having such a program on a
computer with access via terminal. Both the
installation and the use of the
are easy. A main menu bar controls the major
actions. Creating input files or plotting data from old well tests is a matter of seconds.
This program will allow investigation of the effects of changing turbulence factor
and changing wellbore storage on gas well tests. The program also can be used in order
to design well tests. It has also been shown that this software can be an interpretation
tool by plot fitting real data in a trial and error approach. The program will allow a user
to work in combination with other software programs that perform non-linear regression
on type curves.
Finally, this program can be tailored to work on other specific applications such
as the problem of adsorption in geothermal engineering. Further improvements could
also be provided to the software in order to consider a large variety of well tests such as
buildup, multirate and interference tests.
56
Nomenclature
Crj
=
dimensionless weUbore storage
Cg
SB
gas compressibility, psi'l
h
=
formation thickness, ft
k
=
foimation permeability, md
ki
=
damaged annular region permeability, md
M
=
molecular weight, lbm/mole
m(p) =
real gas potential, psi^/ cp
p
=
pressure, psia
p
=
average wellbore flowing pressure, psia
Pi
=
initial formation pressure, psia
psc
=
standard pressure, psia
Ppn
=
normalized pseudopressure, psia
p«c
=
pseudocritical pressure, psia
p
=
corrected critical pressure, psia
Pj-
=
reduced pressure, dimensionless
qsc
=
gas production rate, Mcf/D
qsf
=
sandface gas flow rate, Mcf/D
qwb
=
wellbore rate, Mcf/D
r
=
radial distance from wellbore center, ft
TI
=
damaged annular region radius, ft
re
=
external radius, ft
%
=
wellbore radius, ft
R
=
universal gas constant
s
=
real skin effect
c
57
time,
t
=
T
=
forniation temperature, °R
T
«
average wellbore flowing temperature, °R
Tsc
=
standard temperature, °R
Tpc
=
pseudocritical temperature, °R
Tr
SB
Tc
«
corrected critical temperature, °R
u
=
macroscopic gas velocity
Vw|, =
hrs
reduced
temperature, dimensionless
wellbore volume, cu ft
z
=
real
a
=
diffusivity parameter
P
=
turbulence parameter, nwH
yg
=
specific gas gravity (to air)
8j
=
Darcy's law correction factor for damaged region
8r
=
v
=
dimensionless logarithm ratio
}^(p)
=
pressure dependent gas viscosity, cp
$
=
porosity, fraction
p(p)
s=
pressure dependent gas density, lbm/cu ft
radial
gas law deviation factor
Darcy's law correction factor
Subscripts:
1
=
damaged around the well
D
=
dimensionless
e
=
external
58
g
=
gas
i
SB
initial
r
=
distance r from the wellbore center
sc
=
standard condition
sf
=
sandface
w, wb =
wellbore
59
References
Agarwal, R.G., Al-Hussainy, R., and Ramey, HJ., Jr.: "An Investigation of Wellbore
Storage and SMn Effect in Unsteady Liquid How: I. Analytical Treatment.", Soc. Pet.
Eng. J. (Sept 1970), 279.
Al-Hussainy, R., Ramey, HJ,, Jr. and Crawford, P.B.: "The Flow of Real Gases
Through Porous Media", J. Pet. Tech.. (May 1966a), 624.
Al-Hussainy, R. and Ramey, H.J., Jr.: "Application of Real Gas Flow Theory to Well
Testing and Deliverability Forecasting", J. Pet. Tech.. (May 1966b), 637.
Aronofsky, J.S., and JenMns, R.: "Unsteady Flow of Gas Through Porous Media-One
Dimensional Case", Proceedings. 1st U.S. Nat. Cong. Appl. Meek (1952), 763.
Aronofsky, J. S., JenMns, R.: "A Simplified Analysis of Unsteady Real Gas Flow",
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Brace, G.H., Peaceman, D.W., and Rachford, H.H., Jr.: "Calculations of Unsteady-State
Gas Flow Through Porous Media", Trans.. AIME (1953), 198.79.
Carter, R.D.: "Solutions of Unsteady-State Radial Gas Flow", Trans.. AIME (1962) 225.
549.
Carter, R J).: Supplemental Appendix to "Determination of Stabilized Gas Well
Performance from Short Flow Tests", ADI Doc. No. 7471, Library of Congress,
Washington, D.C. (1963a).
Carter, R.D. Miller, S.C., and Mey, H.G.: "Determination of Stabilized Gas Well
Performance from a Short Flow Test", Trans.. AIME (1963b) 228.651.
Cornell, D. and Katz, D.L.: "Flow of Gases Through Consolidated Porous Media", Ind.
andEng. Chem. (1953) 41, No. 2,145.
60
Couri, F.R.: "Effect of Stress Sensitive Permeability, Skin and WeUbore Storage on
High Velocity Flow in Gas Well Test", Master's Thesis, Stanford University, Califomia,
1987.
Cullender, M.H. and Smith, R.V.: "Practical Solution of Gas Flow Equations for Wells
and Pipelines with Large Temperature Gradient," Trans. AME (1956), 2Q7.281.
Dranchuek, P.M., Purvis, R.A., and Robinson, D.B.: Computer Calculations of Natural
Qas Compressibility Factors Using The Standing and Katz Correlation, Institute of
Petroleum Technical Series, No. IP-74-008, (1974).
Earlougher, R.C., Jr., and Kersch, K.M.: "Analysis of Short-Time Transient Test Data by
Type-Curve Matching." J. Pet. Tech. (1974), 793.
Eilerts, C.K.: "Integration of Partial Differential Equation for Transient Linear Flow of
Gas-Condensate Fluids in Porous Structures", Trans.. AIME (1964) 2jl. 291.
Eilerts, C.K., Sumner, E.F., and Potts, N.L.: "Integration of Partial Differential Equation
for Transient Linear Flow of Gas-Condensate Fluids in Porous Structures", Trans.. AIME
(1965)224,141.
Firoozabadi, A., and Katz, D.L.: "An Analysis of High Velocity Gas Flow Through
Porous Media," J. Pet. Tech. (Feb. 1979), 211.
Fligelman, H.: "Drawdown and Interference Test Analysis for Gas WeEs with Wellbore
Storage, Damage, and Non-Laminar Flow Effects", Ph.D. Dissertation, Stanford
University, California, 1981.
Fligelman, H., Cinco-Ley, H., Ramey, H.J., Jr., Braester, C., and Couri, F.: "PressureDrawdown Test Analysis of a Gas Well - Application of New Correlations," SPE
Formation Evaluation, (Sept. 1989), 406.
Forchheimer, PH.: "Wasserbewegung durch Boden," z. Ver Deutsch. Ing. (1901), 45.
1781.
61
Hegeman, S., Hallford, D.L. and Joseph, J.A.: "Well Test Analysis with Changing
Wellbore Storage", paper 21829, presented at the SPE Rocky Mountain Regional
Meeting, Denver, CO, Apr. 15-17, 1991.
Home, R.N.: Modern Well Test Analysis: A Computer- Aided Approach. Petroway Inc.,
Palo Alto, (1990).
Houpeurt, A.: "On the Flow of Gases in Porous Media," Revue de 1'Ins.titut Francais du
Petiole. (1959), ME, No. 11, 1468.
Hubbert, M.: "Darcy's Law and the Field Equations of Flow of Underground Fluids,"
Trans.. AIME (1956), 207. 222.
Hurst, W.: "Establishment of the Skin Effects and its Impediment to Fluid Flow into a
Wellbores" Pet Eng.. (Oct. 1953), 21 , B-6.
Jenkins, R. and Aronofsky, J.S.: "Unsteady Radial Flow of Gas Through Porous Media",
J.Appl. Mech.. ASME (June 1953), 20. No.2. 210.
Katz, D.L., and Coats, K.H.: Underground Storage of Fluids. Ann Harbor: UMch's
Books, Inc. (1968).
Katz, D.L., Cornell, D., Kobayashi, R., Poettman, F.H., Vary, J.A., Elenbaas, J.R., and
Weinaug, C.F.: Handbook of Natural Gas Engineering. New York: McGraw-Hill Book
Co., Inc. (1959).
Lee, A.L., Gonzales, M.H., and EaMn, B.E.: "Hie Viscosity of Natural Gases", i.
PetTech. , (August 1966), 997.
Matthews, C.S.: "Analysis of Pressure Buildup and Flow Test Data," J. Pet. Tech. , (Sept
1961), 862.
Matthews, C.S., and Russell, D.G.: "Pressure Buildup and Flow Tests in Wells," Soc.
Pet. Eng. Monograph Series (1967),JL
62
Meunier, D., Kabir, C.S. and Wittmann, M.J.: "Gas Well Test Analysis: Use of
Normalized Pressure and Time Functions", SPE Formation Evaluation. (Dec. 1987), 629.
Ramey, H.J., Jr.: "Non-Darcy Flow and Wellbore Storage Effects in Pressure Buildup
and Drawdown of Gas Wells", 1 Pet. Tech.. (Feb. 1965), 223.
Ramey, H.J., Jr.: "Short -time Well-Test Data Interpretation in Presence of SMn Effect
and Wellbore Storage," J. Pet. Tech.. (Jan. 1970), 97.
Russell, D.C., Goodrich, J.H., Perry, G.E. and Braskotter, J.F.: "Methods for Predicting
Gas Well Performance", Trans.. AME (1966) 237.99.
Smith, R.V.: "Unsteady-State Gas Flow into Gas Wells", Trans.. AME (1961), 222.
1151.
Standing, M.B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems ,
SPE reprint, 8th edition, (1977).
Swift, G.W., and Kiel, O.G.: "The Prediction of Performance Including the Effect of
Non-Darcy How", Trans.. AIME (1962) 225.791.
Tek, M.R., Coats, K.H., and Katz, D.L.: "The Effect of Turbulence on the Flow of
Natural Gases Through Porous Reservoirs", Trans.. AME (1962), 225.799.
Van Everdingen, A.F.: "The Skin Effect and its Influence on the Productive Capacity of
a Well", Trans.. AME (1953), 198.171.
Van Everdingen, A.F., and Hurst, W.: "The Application of the Laplace Transformation
to Flow Problems in Reservoir Problems," Trans.. AME (1949), 186. 305.
Wattenbarger, R.A.: "Effects of Turbulence, Wellbore Damage, Wellbore Storage and
Vertical Fractures on Gas WeE Testing," PhJD. Dissertation, Stanford University,
Stanford, California, 1967.
Wichert, E., and Aziz, K.: "Calculating Z's for Sour Gases", Hydrocarbon Processing.
(May 1972), 51.
63
Appendix A.
Computation of Gas Properties
"The pseudocritical pressure p«c in psia and temperature Tpc in degrees RanMne
are determined from the gas gravity, using the Standing correlations.
For California gases:
Tpc = 168 + 325yg - 12.5yg
(A.2)
For Condensate
:706-5L7y
-lLly|
' og
*8
F~
O
(A3)
(A.4)
' O
If the gas contains impurities, corrections are made using, Wichert and Aziz (1972):
(A5)
p* =
Pc(Tg
~ e)
(A.6)
Tc* = T c -e
(A.7)
The reduced pressure and temperature are:
p r =- £ Ppc
(A.8)
T r =^-
(A.9)
T
Pc
64
The reduced density is computed iteratively using Newton's method. Then the z
factor is estimated using the Dranchuek, et al. (1974) procedure:
where:
p]™g
(A.H)
f (p r ) = 6ap + 3 b p + 2 c p + d - » - e p ( 3 + fp[3-2fp])csxp[-fp]
(A. 12)
where:
a = 0.06423
b = 0.5353Tr- 0.6123
c = 0.3151Tr- 1.0467- 0.5783 /T r 2
d = Tr
e = 0.6816 / Tr2
f = 0.6845
g = 0.27pr
p° = 0.27pr/Tr
and:
65
Gas compressibility is computed from:
(AM)
PcPr
z
where:
3z
,
>r
1
4-cpr + e p
_ rr» LI "—r r
+ p
-p
PfTr
The viscosity is computed using the Lee et al. (1966) procedure which is
approximate for sour gases since the density is corrected for impurities:
|ig = K. HT4. exp(Xpy)
(A. 16)
where:
V —
(9.4 + 0.02M)TL5
209 + 19M + T
= 3.5+— + 0.01M
T
y = 2.4 - 0.2X
afp/z(p)l
Thefinaltable concerns the term —5-f used to calculate changing weUbore
storage as defined in Eqs. 2.9 and 2.16. This task is performed by the subroutine
WELLPRO based on the Cullender and Smith (1956) method to compute the static
bottom hole pressure using:
0.01875yeH= f
J
p
'
66
'
(A. 1 7 )
where H is the length of the section along which the integration is performed, and Pt and
P are the wellhead and bottomhole pressure values, respectively. The total length of the
well was divided into three equal sections. The right hand side of Eq. A. 17 was
integrated using a third-order numerical method. Using the top pressure of the lowest
section as the bottom pressure of the next section, the procedure was repeated until the
wellhead was reached. An average value of P/z was obtained by calculating P/z at
various depths. A range of sandface pressure values at the well from 500 to 9000 psia
was chosen, and the appropriate values of P/z were calculated. • A spline function was
used to cover the entire range of bottom hole pressures from 500 to 9000 psia. Figure
dfp/z(p)l
A.1 shows the behavior of the term --*-- as a function of the bottom hole pressure
for a wellhead temperature of 75° F, a temperature gradient of 20° F per 1000 Ft, a gas
gravity of 0.9, and three different values of well depth: 3000, 9000 and 15000 Ft.
67
Qs
O
li
60
I
O
§
JO
»~I
<
w>
68
Appendix B. Flow Chart of Fortran Code
Start
1
Get name of main file;
Read "input, fil"
Create and Open all files
Subroutines:
gaspro,
Creation of gas
properties tables
viscosity,
^ wellpro.
^
Compute initial values in
reservoir at each ooint
tD=0 ; NSTEP=0
tD = tD + dtD
Iter = Iter •«• 1
»)
Calculate Gama coefficient
at each point
>
S
Calculate Turbulence coef,
for each bloc
Set up matrix coeffiecients
Solve matrix equation
by Thomas Algorylhm
)f ^
^.juui uutmc mum as^
"*••
69
No
Convergen
eached
New Iteration }
No convergence )
Storage of Data for
plots and type curves
s time >
total flowing time 2
Yes
Is outer
boundary felt ?
Squaring Re/Rw
Rearrangement of matrix
ew log cycle o
imensioless time ?
{ New time step }
Set up new time step
ubroutine Setdt
f
{ New time step }
70
B
***«
1
Prepare data for graphics
i
Subroutine
Ticartes,
Tilog,
Set up scales of graphics
I
Subroutine
Trancar,
Tranlog,
Set up pressure and time
values into "pixel" form
No
Subroutine
Convert
Set up field data for graphics
No
Subroutine
Convert
Create type curve file
71
Appendix C.
Source Code of Fortran Program for Flow Simulation
72
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Appendix D.
Source Code of C Program for User Interface
RGF.EXE is a copy of FRANJEXE which is described here. FRANJEXE is built
by using the NMK command under Windows SDK. The maintenance file called FRAN
contains the following instructions:
all: fran.exe
fran.res: fran.re fran.h filemgr.h input.h scope.h
re -r fran.re
fran.obj: fran.c fran.h filemgr.h input.h scope.h
cl -c -AM -Gsw -Od -Zipe -W3 fran.c
filemgr.obj: filemgr.c fran.h filemgr.h input.h scope.h
el -c -AM -Gsw -Od -Zipe -W3 filemgr.c
fran.exe; fran.obj filemgr.obj fran.def
link Sfran.l
re -K fran.res
fran.exe; fran.res
re fran.res
This appendix presents the source code of the following C programs: FRAN.C,
FRAN.H, FRAN.MAP, FRAN.L, FRAN.DLG, FRAN.RC, FRAN.DEF, FILEMGR.C,
FILEMGR.H, INPUT.H, SCOPE.H, SCOPEX>LG in this order.
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