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

ByFrancois Joseph Groff

June 1992

I certify that I have read this thesis and that in my opinionit is fully adequate, in scope and in quality, as partial fulfillmentfor the degree of Engineer.

HeqfcrflTRamey, Jr. / j/(Principal Advisor)

I certify that I have read this thesis and that in my opinionit is fully adequate, in scope and in quality, as partial fulfilmentfor the degree of Engineer.

Roland N. Home

Approved for the University Committee on GraduateStudies:

11

Dedicated to

My AliceMy father RobertMy 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 suggestionsand guidance during this study. His profound kindness has made this work possible. Ialso thank Dr. Roland Home for serving on the committee for this thesis. I finally extendmy gratitude to Jean Cook from the Stanford Geothermal Program, and to theDepartment of Petroleum Engineering at Stanford for and encouragement

This work was supported by the Stanford Geothermal Program (SGP) underDepartment of Energy contract No. DE - F607 - 90ED12934 and by the SchlumbergerCorporation through the Schlumberger Fellowship for Earth Sciences at Stanford. Thissupport is gratefully acknowledged.

IV

Abstract

An interactive program that lets users study the flow of real gas through porousmedia under a graphic environment has been presented. The program treats highvelocity flow accurately so that it is not mistaken for formation damage. A rigoroustreatment 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'sfingertips. This program can be used in activities to perform sensitivityanalysis. It can also be used as a working tool for well test design or well testinterpretation. Finally, it can be used as an educational tool for all the tasks justmentioned.

Table of Contents Page

Dedication iiiAcknowledgment ivAbstract vTable of Contents vilist of Tables viMlist of Figures ix

1. Introduction 11.1 Previous Work 31.2 Turbulent How 41.3 WeEbore Storage 4

2. Mathematical Model 52.1 Turbulence Effect 62.2 Formation Damage 72.3 Initial Condition 72.4 Inner Boundary Condition 72.5 Outer Boundary Condition 82.6 Dimensionless Quantities 82.7 Resulting Equations 102.8 Comments on the Finite-Difference Simulation 11

3. Programing Language and Development Features 13

4. User Manual for REAL GAS FLOW 144.1 Installation 14

4.1.1 Configuration 144.1.2 Setting Up 154.1.3 Starting Up 164.1.4 A Quick Guide to REAL GAS FLOW 16

4.2 Overview 174.2.1 Methodology 174.2.2 Main Menu Bar 194.2.3 File Types 19

4.2.3.1 Files Created by a User 204.2.3.2 Files Created by REAL GAS FLOW 20

4.3 Setting Up the Data 214.3.1 Main Data File 21

4.3.1.1 Opening an Old Main File 224.3.1.2 Creating a New Main File 254.3.1.3 Detailed Description of Each Field 27

4.3.2 Flow Rate File 314.4 Running the Simulation 32

VI

4.4.1 Running the Right Case4.4.2 During the Simulation

4.5 Plotting Results4.5.1 Plot Menu4.5.2 Overview

4.5.2.1 Opening an Output File4.5.2.2 Plotting the Data4.5.2.3 Using the Cursor Utility

4.6 Special Features4.6.1 Using Field Data

4.6.1.1 Setting Up the Field Data4.6.1.2 Plotting Field Data

4.6.2 Creating Type Curves4.6.2.1 Background4.6.2.2 Creating One Type Curve4.6.2.3 Building a Library of Type Curves

4.7 Printing4.7.1 Printing Directly4.7.2 Printing with CLIPBOARD

4.8 Leaving REAL GAS FLOW4.9 Computing Aids

5. Using RGF as a Weil Test Interpretation Tool

6. Conclusions

323233333333363840404041424343444747474748

49

56

NomenclatureReferences

Appendix A. Computation of Gas PropertiesAppendix B. Flow Chart of Fortran CodeAppendix C. Source Code of Fortran Program for Flow SimulationAppendix D. Source Code of C Program for User Interface

5760

64697288

Vll

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 TypeCurves 55

a[p/z(p)lFig. A.I Wellbore derivative —? £ Vs Bottom Hole Pressure for y = 0.9 68

d[p/z(p)J

IX

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. Theterm 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 ton

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 pseudo-

pressure, 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

L201 (2.3)

In the computer program, the velocity ur for the Forchheimer equation is

calculated through an iterative method:

u, =•

MRT k

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:

JgPscT

TCnfn\ =r-

1 fi(p) am(p)k 2 3t

(2.9)

and:

q fS

[5. 3m(p)lSir ^ F

L l 3r Jr=r

(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 > 0r=r

(2.12)

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:

Dimensionless diffusiviry:

(2.17)

(2.18)

2.7 Resulting Equations

After substitution and rearrangement, the various flow equations and conditions

are:

In the undamaged zone:

1 3 dm (%»trj)D r , ^ ..= --aD[mD(ib,tD)J

(rD,to) (2.19)

In the damaged zone:

1 31D dr

- /v r^ /-». * ^= -—aD[m1D(rD,tD)J (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)]_3[p/z(p)]_

dtD= 1 (2.23)

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 toperform. Section 4.1 describes how to initiate the program. Section 4.2 presents anoverview 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 theresults. Section 4.6 special features available with the program. Finally,Section 4.7 two for printing, Section 4.8 pinpoints a few detailsrelevant to leaving the application, and Section 4.9 introduces two computing aids withWindows.

4.1 Installation

The hardware configuration is presented and followed by a guide to set up andstart the program.

4.1.1 Configuration

REAL GAS FLOW was designed to run on any IBM PC or compatible with aprocessor 286 or higher (386/486), 16 Mhz or more. A math coprocessor (8087 orhigher, 287/387) is not required, but recommended because of the matrix manipulationduring the simulation. 2 MB of RAM is enough to use the application, even thoughWindows is commonly used with 4 MB.

Table 4.1 shows simulation time for a drawdown test ran on differentconfigurations of computers. Run-time is sensitive to both processor type andfrequency. [The well was flowed for 1000 hours or 40 days. All computers wereequipped with math coprocessors.]

Darcy FlowNonDarcy Flow

286-6 MhzSmins12mins

386-1 6Mhz4mins7mins

486~25Mhz2minsSmins

Table 4.1. Simulation Time on Various Computers

REAL GAS FLOW is a "Window application", and Windows 3.0 or later isrequired, and so is a mouse. All actions during the program execution are triggered byusing the left button on the mouse. Finally, a graphics adapter/monitor either color ormonochrome is required.

14

There is no specific memory requirements for REAL GAS FLOW as long asWindows is installed. REAL GAS FLOW can also be run from a floppy disk drive, butthis 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. Theexecutable files are RGF.EXE and FRANC.EXE. All other files on the disk are notrequired to run the program, but are provided to give the user a better understanding ofthe program by looking at old synthetic gas well tests.

RGF.EXE and FRANC.EXE must be copied into the working directory andremain there at all times. To avoid building huge directories, it is recommended thatsub-directories be created with old tests. Old synthetic data can be retrieved andprocessed by REAL GAS FLOW independently of their location on the hard disk or anyfloppy disk. To install the program and the examples in a directory called RGF:

1. Insert the RGF floppy disk in drive A2. Go into the disk or directory where RGF is to be created3. Type: mkdirRGF4. Type: cd RGF5: Type: copy A:*.*

Files for REAL GAS FLOW have been named in a way that makes it easy for auser to organize the working directory. When we design a new well test, a name for thetest must be defined, for example: EXAMPLE. All data files related to the testEXAMPLE will differ only by their three character extensions : EXAMPLE.FLR is theflow rate history file; EXAMPLE.ACT is the pressure history file at the active well, andso on. More on the different files used by REAL GAS FLOW is presented in Section4.2.3.

After having made a backup copy of the disk provided and copied all files andespecially RGF.EXE and FRANC.EXE in the working directory , REAL GAS FLOWmust be set up into "program manager ". Using the mouse, click on WINDOWS SETUP inside the MAIN folder of program manager, then click on OPTIONS and select SETUP APPLICATIONS. Select the hard disk on which the working directory is locatedand then run the search by clicking OK. This can take a few minutes depending on thenumber of applications on the disk. After the search, select RGF.EXE on the leftwindow in the dialog box, click on ADD and then OK. RGF will be added, with itsrecognizable icon as a window application. At this point of course, it can be moved intoany group.

15

4.1.3 Starting Up

REAL GAS FLOW can be started from the program manager window by double-clicking on its icon. At this point, the main menu will fill the entire screen. REAL GASFLOW can also be started under the DOS environment by going into the workingdirectory 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 withREAL GAS FLOW (RGF) by using a first example. The following example files havebeen provided on the disk: GUIDE.MAI and GUIDE.FLO. The following instructionsshould 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.

Calloldfiles

InputParameters

Run

Simulation ^

Prepare Field data filefor comparison

Create type curvefor AUTOMATE

Plot and Erase

Open "Results11 filesfor 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:

Rate data file:

Type of test*Outer boundary:

Boundaryradius (ft):

Damaged zoneradius (ft):

Well radius (ft):Weil depth (ft):Thickness (ft):

Porosity (fr):Prod/obs

distance (ft):

Gas gravity;

H2S (fr):

C02 ffr):

N2 (fr):California or

condensate gas:Reservoir

Temperature (F):Weil-head

Temperature (F):Weilborevolume:

Initialres. press, (psia):

Skin factor:Initial

permeability (rnD):Turbulence fy/n):

Perm = ffPJ (y/nj:

Own perm file:Field data file:

Automate curve (y/n)

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:

Type of test

Outer b

Er

Damar

WeHr

Welh

Thidci

ParF

dist;

oundary:

loundaryadius (ft):ged zoneadius p);adius (ft):

(ft):

ness (ft):

osity (fr):*rod/obsinee (ft):

Wi^^SBHS^^i^KfliiiWitoaBBtiliiliMHHSB

Open File Manie:

*.mal

Files in d:\we\francois\newtest

IranfakefaketestxyzinpuM

•~ iJld §.act ^1n,m»i S§tfii I

ps

Hri wri

Initi»s. [psiidn facto

InWiility (mCnee (y/n

OT W

perm fil

\ data fl

irvc (y/i

alil:r:il

i):

e:

e:

nj:

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

titlemain file

rate data filetype of test

outer boundaryboundary radius

damaged zone radiuswell radiuswell depththicknessporosity

gas gravityCO2, H2Stype of gas

reservoir temperaturewell head temperature

wellbore volumeinitial reservoir pressure

skin factorpermeabilityturbulence

field data fileAutomate type curve

Meaning

title of test to runmain input file namerate data file name

drawdown or injectiondefines external boundary

external radius..-

pay zone thickness-

relative gravity to airgas impurities

.--.-

skin damageaverage in reservoir

consider or notname of file if applicable

create or not

Unit expected

optional1 to 8 letters1 to 8 letters

letterslettersfeetfeetfeetfeetfeet

fractionfractionfractionsletters

FahrenheitFahrenheitcubic feet

psiadimensionless

mDyes / no

1 to 8 letterscode: 0, 1 or 2,

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 caseand 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 OKbutton. The file will be saved in the active directory (again, this is the directory shownwhen clicking on OPEN in the parameter input window or on OUTPUT in the mainmenu 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 filesin 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:limM-m(p) = m(pi) ; 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: CAL

Condensate: The program checks on: 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)](4.3)

29

(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 inAUTOMATE 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 5000.

500. 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. This

is always the case if the active directory and the working directory are identical.

(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 RotLog-Log Derivative PlotCartesian PlotHomer PlotDimensionless Semi-Log PlotPressure History PlotLine Source Solution PlotRate 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

hours(3) Log-log derivative: 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: Not accessible

(6) Dimensionless: Semi-log plot of dimensionless pseudopressure versus

dimensionless time trj/lO^. The dimensionless variables are described by Eqs. 2.13 and

2.14.

(7) Pressure history: Cartesian plot of pressure in psia versus time in hours

(8) Line source solution: Not accessible

(9) Rate history: Cartesian plot of rate in Me^Dversus time in hours

4.5.2 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

1000Delta mp vs. delta time [hours]

1E+02

1E+01

1E+00

.1

.001 1E-02 1E-01 1E+OD 1E+01 1E+02 1000

Figure 4.8. Typical Log-Log Plot with REAL GAS FLOW

36

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.

1000Delta mp vs. delta time (hours)

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

1000Delta mp vs. delta time (hours

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

1000

100

10

1

1

Delta mp vs. delta time (hours) Cur. Y .* 30.0331

//

/•/

s*~~^\v__

.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:

0.010.050.10.20.81.010100

45074505449044854480447344604450

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 usershould 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 thecomputation 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:

atap

aint

( ln(ti+jtH/tf)AFfc ln(ti+j/ti)APi_k

41

1000

.;$£at;ti

Delta mp vs. delta time [hours]

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.

10000Delta mp vs. delta time (hours]

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

§ 0 o o o ^ ^ ^ ^ * ^ e o o o o o p o o o o o p o » n ^ ^ ^ o i » m ^ « ^ » « » - i « w » ^ w o * « * » » « » » « » « ^ w < r ' » n - - - « 1 ^ - - < ' W ' r -© o © «r*g»*f*pt* l fct^**f* t* i ige»»p»*i f**

§ P S» © # « O « ^ t f t 9 W 0 C > O O Q O O O O O O O O f & Q O * W M ^ ^ i n « ^ i P * ^ WP p © ^ iK f * in«p iKfc r * i»&r - r ' ^w i r t r« i^ i t t * r *p r *«w«»«*win » ** f» j< i iB«s t t *» 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

« •* 5- «« « « M < r t f t w » i A i * > « i 4 i r»»inowf* i* int*pKM&isf*t»wwani in inf f» i f t i r t

«***•* »"t «»*(

§ O O O 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 ^* o In & » e w i t t « © K w » w ^ e s ( ^ r * w * w « » f ^ . * * © * K « * i & f * # t » i « m i r * « * w » ^ « « r i ^

5* § § fa S«£S©355l ! i f2§!^^

§ C»oo • n ^ « v w « n w o o o o p o p o o o o o o o o o w c ^ m r ^ « « ^ t i W ( 9 i n N i ^ v M ^ « s i f ^ « n f ^ r t o

5 O o w ^ w ^ ^ ^ ^ r s i » ^ » ^ ! K e r o K o » s c » o o ^ w r « » ^ i n r ^ r ^ o » » i s » ^ o » » i « > w ' m » ^ . * r » > » w S 1 r . ^ ^ ^ o ^ ^^fr-.*^ ^ i f t O W ^ I B i f t ^ W l S t ^ O ^ O W W ^ ^ ^ l ^ W ^ ^ ^ W f ^ W W W I ^ w W W I O l n ^ ^

§ g g §g § 8 8 o 5 8 5 8 P Z g 8 S 8 S § § § 8 g 8 8 § 8 8 8 § 8 S 8 8 8 § § 8 § 8 8 8 8 8 8 S 8 8 8 8 § 8 8 8 § 1 8 8 8 8 8 8 §

8 o o o * ~ * ^ t % * i n ' * * f t i f j * » F ^ « i » t * . w « ' f v o » w w « s * o » w o o c c ' e o o o o r ' O o o o o o o o o o o o oO O O * " t ( H f " * W W l « * * f f c < R i B * ^ « » P * © « W W f S O t B * * W O O O O O O O O 0 Q O Q

r* » * o *n t - t rswrnwi r i i ^c ic r -aB^o

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

gg|||||§|||||||||gggg

«^^«<r inp^ iB in i r ^v«^wmcs to in^^nNr iw i ^ ie f ^vw»»oo»^

ib

S O « ? - » O » » - O O O O O O O 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 Oi B 0 ^ 2 * « ^ ' - « £ * » ^ * 2 « l « 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 ^ ^ « ^ w p ^ v « ^ m t ^ i B r ^ w i n p « ^ w f t v f ^ ^ i n c t p p ^ ^ v M m « ^ © ^ * w v f « S r ^

*

JD•o

I<o

U

IQ

CO

X)

SeoooooooeooooooW O W r v W W O O O O O O O O O O OOOOOOO

QOOOOC»SooooSoooooeoeoooO O O O O O O O O O O

45

<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 datausing the PRINT button provided by RGF, or a hard copy of the entire screen can be

made at any using the CLIP BOARD 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 ofthe 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 Windowsdirectory. To produce a hard copy of any screen, press the PRMTSCREEN button onthe 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 cleaningthe 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

00.0010,00270.00440.0060.00770.0120.0250.040.0520.0660.080.10.240.370.50.640.771.913.585.246.918.2410.82437.550.86477.5224458691

Pressure

80007997799179867981797679627923788678517816778377167460726471106985688164406243617461396120609560305996597359565942586558135784

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.

10000

ftfltilijte

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 ^

8000

7000

6000

iOOO

4000

3000

.

Pseudo-pressure vs. time (hours)

— \\\\\•*

""•"NH*" ***

"— <K

<*»

"" - ****-r

\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

—TC—BO XX

COCO

O

10rt0

eoM

30)

orHX

of-lx

Of-lX

ooo

oo

OO

i-lO

U

IoIgrt~QT3

I•a<u

1

o

c•v-4

-3

enm*bb

oo o

f-l

Qdui

55

6. Conclusions

An interactive software prop"am that simulates the flow of real gas throughporous media has been prepared. It runs under a graphic environment and allows a userto compare sets of data, perform sensitivity analysis, and display field data. Hie easyaccess to data and quick display of on the screen should reduce time waste causedby having such a program on a computer with access via terminal. Both theinstallation and the use of the are easy. A main menu bar controls the majoractions. 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 factorand changing wellbore storage on gas well tests. The program also can be used in orderto design well tests. It has also been shown that this software can be an interpretationtool by plot fitting real data in a trial and error approach. The program will allow a userto work in combination with other software programs that perform non-linear regressionon type curves.

Finally, this program can be tailored to work on other specific applications suchas the problem of adsorption in geothermal engineering. Further improvements couldalso be provided to the software in order to consider a large variety of well tests such asbuildup, 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 c = 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

57

t = time, hrs

T = forniation temperature, °R

T « average wellbore flowing temperature, °R

Tsc = standard temperature, °R

Tpc = pseudocritical temperature, °R

Tr SB reduced temperature, dimensionless

T c « corrected critical temperature, °R

u = macroscopic gas velocity

Vw|, = wellbore volume, cu ft

z = real gas law deviation factor

a = diffusivity parameter

P = turbulence parameter, nwH

yg = specific gas gravity (to air)

8j = Darcy's law correction factor for damaged region

8r = radial Darcy's law correction factor

v = dimensionless logarithm ratio

}^(p) = pressure dependent gas viscosity, cp

$ = porosity, fraction

p(p) s= pressure dependent gas density, lbm/cu ft

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",

Trans. AIME (1954) 201.149.

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.: "Pressure-

Drawdown 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

:706-5L7yg-lLly| (A3)' o * 8

(A.4)F~ O ' O

If the gas contains impurities, corrections are made using, Wichert and Aziz (1972):

(A5)

p* = Pc(Tg~e) (A.6)

Tc* = Tc-e (A.7)

The reduced pressure and temperature are:

pr=-£- (A.8)Ppc

Tr=^- (A.9)TPc

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 (pr) = 6ap + 3 b p + 2 c p + d - » - e p ( 3 + fp[3-2fp])csxp[-fp] (A. 12)

where:

and:

a = 0.06423b = 0.5353Tr- 0.6123

c = 0.3151Tr- 1.0467- 0.5783 /Tr2

d = Tr

e = 0.6816 / Tr2

f = 0.6845g = 0.27pr

p° = 0.27pr/Tr

65

Gas compressibility is computed from:

PcPr z

(AM)

where:

3z 1, _ rr» I "—r r>r PfTr

L4-cpr + e p + p -p

The viscosity is computed using the Lee et al. (1966) procedure which isapproximate for sour gases since the density is corrected for impurities:

|ig = K. HT4. exp(Xpy) (A. 16)

where:

(9.4 + 0.02M)TL5V —

209 + 19M + T

= 3.5+— + 0.01MT

y = 2.4 - 0.2X

afp/z(p)lThe final table 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 p ' (A. 1 7 )

J '

66

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)lA.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

QsO

li60

IO

§JO»~I

<w>

68

Appendix B. Flow Chart of Fortran Code

Start1

Get name of main file;Read "input, fil"

Create and Open all files

Creation of gasproperties tables

Compute initial values inreservoir at each ooint

tD=0 ; NSTEP=0

tD = tD + dtD

Iter = Iter •«• 1

Calculate Gama coefficientat each point

Subroutines:gaspro,

viscosity,^ wellpro. ^

»)Calculate Turbulence coef,for each bloc

Set up matrix coeffiecients

Solve matrix equationby Thomas Algorylhm "*•• .juui uutmc mum

>S

)f ^

as^

69

NoConvergeneached

Storage of Data forplots and type curves

Yess time >total flowing time 2

Is outerboundary felt ?

Squaring Re/RwRearrangement of matrix

ew log cycle oimensioless time ?

Set up new time step

{ New time step }

ubroutine Setdt

f

{ New time step }

New Iteration }

No convergence )

70

SubroutineTicartes,Tilog,

B***«

1Prepare data for graphics

iSet up scales of graphics

SubroutineTrancar,Tranlog,

ISet up pressure and timevalues into "pixel" form

No

SubroutineConvert

SubroutineConvert

Set up field data for graphics

No

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 builtby using the NMK command under Windows SDK. The maintenance file called FRANcontains the following instructions:

all: fran.exe

fran.res: fran.re fran.h filemgr.h input.h scope.hre -r fran.re

fran.obj: fran.c fran.h filemgr.h input.h scope.hcl -c -AM -Gsw -Od -Zipe -W3 fran.c

filemgr.obj: filemgr.c fran.h filemgr.h input.h scope.hel -c -AM -Gsw -Od -Zipe -W3 filemgr.c

fran.exe; fran.obj filemgr.obj fran.deflink Sfran.lre -K fran.res

fran.exe; fran.resre 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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