United States
Environmental Protection
Agency
Robert S. Kerr Environmental Research
Laboratory
Ada OK 74820
EPA-600/2-79-170
August 1979
Research and Development
&EPA
Radius of Pressure
Influence of
Injection Wells
.'
,.
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1 Environmental Health Effects Research
2. Environmental Protection Technology
3 Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution. This work
provides the new or improved technology required for the control and treatment
of pollution sources to meet environmental quality standards.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-79-170
August 1979
RADIUS OF PRESSURE INFLUENCE
OF INJECTION WELLS
by
Don L. Warner
Leonard F. Koederitz
Andrew D. Simon
M. Gene Yow
University of Missouri - Roll a
Roll a, Missouri 65401
Grant No. R-805039
Project Officer
Jack W. Keeley
Groundwater Research Branch
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
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DISCLAIMER
This report has been reviewed by the Robert S. Kerr Environmental
Research Laboratory, U.S. Environmental Protection Agency, and approved for
publication. Approval does not signify that the contents necessarily
reflect the views and policies of the U.S. Environmental Protection Agency,
nor does mention of trade names or commercial products constitute endorse-
ment or recommendation for use.
ii
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FOREWORD
The Environmental Protection Agency was established to coordinate
administration of the major Federal programs designed to protect the
quality of our environment.
An important part of .the Agency's effort involves the search for
information about environmental problems, management techniques, and new
technologies through which optimum use of the Nation's land and water
resources can be assured and the threat pollution poses to the welfare
of the American people can be minimized.
EPA's Office of Research and Development conducts this search through
a nationwide network of research facilities.
As one of these facilities, the Robert S. Kerr Environmental Research
Laboratory is responsible for the management of programs to: (a) investi-
gate the nature, transport, fate, and management of pollutants in ground
water; (b) develop and demonstrate methods for treating wastewaters with
soil and other natural systems; (c) develop and demonstrate pollution con-
trol technologies for irrigation return flows; (d) develop and demonstrate
pollution control technologies for animal production wastes; (e) develop
and demonstrate technologies to prevent, control or abate pollution from
the petroleum refining and petrochemical industries; and (f) develop and
demonstrate technologies to manage pollution resulting from combinations
of industrial wastewaters or industrial/municipal wastewaters.
This report contributes to that knowledge which is essential in order
for EPA to establish and enforce pollution control standards which are
reasonable, cost effective, and provide adequate environmental protection
for the American public.
William C. Galegar
Director
iii
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ABSTRACT
It is often necessary, in injection well design, to predict the
probable rate of pressure increase in the injection reservoir that would
be expected to result from a proposed injection program. Areas of appli-
cation include oilfield brine injection, waterflcoding for secondary
oil recovery, industrial wastewater injection, uranium leaching, etc.
This report presents a number of available analytical solutions that
can be used for pressure buildup calculation and three methods of per-
forming such calculations. The methods are, manual calculation, calculation
by programmable desk calculator, and calculation by digital computer.
Programs for the desk calculator and for the digital computer are presented
and examples of their use are given.
This report was submitted in fulfillment of Grant No. R-805039 by
The University of Missouri at Rolla under the sponsorship of the U.S.
Environmental Protection Agency. This report covers a period from
March 8, 1977, to January 7, 1979, and work was completed as of January 1979.
iv
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CONTENTS
Foreword 111
Abstract 1 v
Figures and Tables vii
Symbols and Abbreviations viii
1. Introduction 1
Objectives and Scope 1
Organization of Report 2
2. Theory of Pressure Buildup 3
3. Pressure Buildup Equations and Sample Calculations 5
Infinite Confined Reservoirs 5
Constant Injection Rate 6
Single Well 6
Multiple Wells 8
Variable Injection Rate 11
Single Well 11
Multiple Wells 13
Wells with Skin Effects 14
Partially Penetrating or Partially Completed Wells 16
Fractured Reservoirs 18
Single Vertical Fracture—Well bore Case 18
Single Vertical Fracture—General Case 20
Single Horizontal Fracture 20
Infinite Semiconfined Reservoirs 22
Leakage in One Di rection 23
Leakage in Two Directions 24
Bounded Reservol rs 26
Linear Boundaries 26
-------
Completely Bounded Reservoirs 26
Reservoirs'with Variable Permeability 29
Layered Reservoi rs 32
Layered Reservoirs with Crossflow 32
Layered Reservoirs without Crossflow 35
Radially Varying Permeability 35
Fluids of Variable Viscosity 37
Dipping Reservoirs 38
4. Calculation of Pressure Buildup with the Programmable Desk
Cal cul ator 40
Program Entry for the Keyborad 40
Recordi ng a Program 40
Program Entry• from Magnetic Cards 41
Program Editing 41
Example Calculation 42
5. Calculation of Pressure Buildup with the Digital Computer 43
Card Format 43
Exampl es 59
6. Selected Examples of Fluid Injection and Pressure Buildup 117
Texas Gulf Coast 117
Celanese Corporation
Harris County, Texas 117
E. I. DuPont
Vi ctori a, Texas 119
Fl ori da 121
Ohio 122
References 124
Appendices
A. Tables for Use in Manual Pressure Buildup Calculations 126
B. Programmable Desk Calculator Programs 151
C. Digital Computer Program 190
vi
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FIGURES
Figure 1 Profile and plan views of a completely penetrating
well injecting into a confined reservoir 7
Figure 2 Profile and plan views of two completely penetrating
wells injecting into a confined reservoir 9
Figure 3 Diagrammatic representation of the injection history
of an injection well operating at a variable rate 12
Figure 4 Wells with varying degrees of penetration and
completion. 17
Figure 5 Plan view of an injection well adjacent to an
impermeable boundary, with an image well used to
simul ate the boundary 25
Figure 6 Plan view of a real injection well adjacent to two
intersecting impermeable boundaries, with the image
well system used to simulate the boundaries 27
Figure 7 A layered reservoir, with vertical communication
between 1 ayers 33
Figure 8 A layered reservoir without vertical communication
between 1 ayers 34
Figure 9 A reservoir with radially varying permeability 36
Figure 10 Location map for Celanese Corporation wastewater in-
jection and monitor wells, Harris County, Texas 118
Figure 11 Location map for E. I. DuPont Company injection and
monitor wells, Victoria County, Texas 120
Table 1
TABLES
Shape Factors for Various Closed Single-well Areas 30
VII
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SYMBOLS AND ABBREVIATIONS
a = an integer in a summation
2
A = area of a completely bounded reservoir, ft
b = an integer in a summation
B = leakage factor for semiconfined reservoirs =
$ = formation volume factor, RB/STB for liquid, RB/Mcf for gas
c = compressibility, psi"
C^ = shape factor for fully confined reservoirs
d = distance from top of reservoir to top of screen or per-
forations in a partially penetrating well, ft
AP$ _ pressure drop across skin, psi
e = natural log base, 2.718
erf = error function
E, = exponential integral
f = mathematical symbol meaning "a function of"
3
Y * = specific weight of reservoir fluid, Ib/ft
h = reservoir thickness, ft
h = thickness of semiconfining layer, ft
C
h' = thickness of second semiconfining layer, ft
hD = dimensionless thickness = h/r-
h. = thickness of ith layer in a layered reservoir, ft
viii
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i = an integer in a summation
I (x) = zero order modified Bessel function of the first kind
k = permeability, md
ic = equivalent permeability of a layered reservoir, md
k = vertical permeability of semiconfining layer, md
\f
k1 = vertical permeability of second semiconfining layer, md
w
ki = permeability of ith layer in a layered reservoir, md
KO(X) = zero order modified Bessel function of the second kind
k = radial permeability, md
k = permeability in the skin zone, md
kz = vertical permeability, md
1 = length of penetration of a partially penetrating well, ft
log = logarithm, base 10
In = logarithm, base e
m = an integer in a summation
u = viscosity, cp
y.-: = viscosity of injected fluid, cp
y - = viscosity of reservoir fluid, cp
n = an integer in a summation
PQ = dimension!ess pressure
PDF = dimensionless pressure for a well intersected by a single
vertical fracture - general case
PDHF = dimensionless pressure for a well intersected by a single
horizontal fracture
PDL = dimensionless pressure for semiconfined reservoirs
= dimensionless pressure for a partially penetrating well
PDWF = dimensionless pressure for a well intersected by a single
vertical fracture - well bore case
= porosity, fraction
ix
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P. = initial reservoir pressure, psi
P = reservoir pressure at radius r, psi
Vi = ln''t1a^ reservoir pressure at radius r, ft
PWO = reservoir pressure at the well bore, psi
P = reservoir pressure at coordinates x and y, psi
xy
q = flow rate, STB/D for liquid, Mscf/D for gas
r = radial distance from well to point of investigation, ft
r~ = dimensionless radius = r/r.
r = external radius, ft
r.p = radial extent of horizontal fracture, ft
r.,. = radius of cylinder of injected fluid, ft
r = radius of skin zone, ft
r = radius of well bore, ft
w
s = skin factor, a positive or negative number
a = pseudo skin function for a well intersected by a single
vertical fracture, dimensionless
t = time, days
tD = dimensionless time
tp.. = dimensionless time based on drainage area
(tn.) „ = dimensionless time at the beginning of pseudo steady-
DA pss state flow
9 = angle of dip of reservoir in the radial direction of
investigation
t = time at the beginning of pseudo steady-state flow, days
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x = space coordinate, ft
Q = dimension!ess fracture coordinate =
y = space coordinate, ft
p = dimension!ess fracture coordinate =
z = distance from top of reservoir to point of investigation
in a reservoir with a partially penetrating well, ft
ZQ = dimensionless fracture coordinate = z^/x^ /kr/kz
zf = distance from bottom of reservoir to center of horizontal
fracture
ABBREVIATIONS
cp = centipoise
D = day(s)
ft = feet
md = millidarcys, 1/1000 darcy
Mscf = thousands of cubic feet of gas at standard temperature
and pressure (460° R, 14.7 psi)
psi = pounds per square inch
RB = reservoir barrels, or barrels of liquid at reservoir
temperature and pressure
STB = stock tank barrels, or barrels of liquid at standard
temperature and pressure (520° R, 14.7 psi)
XI
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CHAPTER 1
INTRODUCTION
OBJECTIVES AND SCOPE
An engineering task that is often required of injection well oper-
ators and those regulating injection well operation is the prediction of
the probable rate of pressure increase in the injection reservoir, result-
ing from a proposed injection operation. The pressure increase associated
with any injection operation, whether it is oilfield brine injection,
waterflcoding for secondary oil recovery, industrial wastewater injection,
uranium leaching, etc., is of concern because it is a major factor in
determining the economics and the potential environmental impact of the
operation on the hydro!ogic system.
The objective of this report is to present a number of available
analytical equations that can be used for pressure buildup calculations
under various hydrologic and operational conditions. Three methods of
performing such calculations are presented; they are, manual calcula-
tion, calculation by use of programmable desk calculator, and calcu-
lation by digital computer. Manual calculations can be performed by
anyone and are quite adequate for many simple cases, but the calcula-
tions can be tedious, if many are needed. The programmable desk calr-
culator allows some calculations to be made that are not possible to
make manually, but more importantly, it allows many calculations to
be made rapidly and at little cost. The digital computer allows
combinations of solutions to be made easily that can only be made with
difficulty by the other methods and is the most rapid method of all,
when large numbers of wells, numerous injection rates, or large numbers
of calculations are involved.
In recent years, numerical models have become widely used for
predicting reservoir performance. Such models are needed when reser~
voir properties vary considerably or where conditions exist for which
analytical solutions are not available. However, for cases where
analytical solutions are available, such as those given in this report,
use of the analytical solution is more rapid and more accurate! Further*-
more, it is good practice to check the results of a problem solved by a
numerical model against the results of the analytical solution that most
closely represents the problem. This helps to insure that no major
error has been made in the numerical modeling process.
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While none of the analytical solutions incorporated in this report
are original, many of them have never been presented in a manner that
would allow their use for pressure buildup (or decline) calculations
without an impractical amount of effort. The writers do not know of
any other existing sets of tables, programmable desk calculator programs,
or FORTRAN programs that have been published that will allow the range
of calculations made possible by the material in this report.
Projection of the probable pressure buildup during system design allows
estimates of well numbers, well spacings, and operating rates to be made.
Such projections can show whether a proposed operation is economically
realistic or unrealistic. From an environmental viewpoint, the projected
pressure increase is examined to determine if there is potential for
hydraulic fracturing or escape of fluid through nearby abandoned wells.
In many cases, the projected pressure buildup pattern is used to project
the rate and direction of flow of the injected fluids in the receiving
reservoir.
ORGANIZATION OF REPORT
As discussed above, three methods for pressure buildup calculation
are presented, each of which is appropriate under different circumstances.
Chapter 3, is devoted to the presentation of the equations that are used
and to the development of examples of problem solving. The examples
given in Chapter 3 are relatively simple, but are realistic problems. The
examples are simple, because their solution, by the manual method is
demonstrated in Chapter 3. The examples are, at the same time, examples
that can be used to develop competency in the operation of the programmable
desk calculator and in use of the FORTRAN program.
Tables that must often be used in conjunction with the manual
solution method are given in Appendix A. Programmable desk calculator
programs are included in Appendix B, and a discussion of the use of the
program is given in Chapter 4. The FORTRAN program is included in
Appendix C and a discussion of its use is given in Chapter 5.
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CHAPTER 2
THEORY OF PRESSURE BUILDUP
As discussed in the introduction, the purpose of the equations
that are presented is to allow the calculation of the increase in
pressure, with time, at any selected point in the vicinity of a well
into which fluids are being injected. The basic equation governing
steady fluid flow through an aquifer is the Darcy equation. Combination
of the Darcy equation with the continuity equation and an equation of
state allows development of solutions for cases in which pressure increases
with time (unsteady or transient conditions).
The basic differential equation for the unsteady radial flow of
a slightly compressible fluid from an injection well (or to a pumping
well) is (Matthews and Russell, 1967):
aff_ . 1 3P _ 4>yc 8P
,2 r 9r " k at
O I
In the development of Equation 1, the following assumptions were
made:
1. horizontal flow
2. negligible gravity effects
3. a homogeneous and isotropic reservoir
4. a single fluid of small and constant compressibility
The equations that will be presented and analyzed in the rest of the
manual are solutions of Equation 1, or a similar equation, for various
selected conditions.
When a particular solution to Equation 1 or a similar equation is
obtained, it is initially in a nonunitized form. That is, any set of
consistent units can be used. However, an engineer or scientist will
usually be working with practical units such as gallons or barrels for
volume, darcys for permeability, feet for length, etc. Therefore, it is
necessary to adjust the equations for these heterogeneous units by using
constants. All of the equations given in this manual will be adjusted
for use with the following units:
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Parameter or Symbol Practical
Variable ' Units
compressibility c psi
porosity decimal fraction
reservoir thickness h ft
permeability k md
viscosity y cp
pressure P psi
flow rate q STB/D
radial distance • r ft
time t D
The equations can easily be converted to other practical units, if
so desired.
Throughout the text, pressure buildup equations are written using
dimensionless pressure (PD) and dimensionless time (to). These dimen-
sionless quantities are groups of variables that commonly occur in buildup
equations and which can conveniently be replaced by a single term.
Dimensionless time, for the units listed above is:
. 6. 33x1 O"3 kt (?)
= ~
In unsteady state or transient flow equations, dimensionless pressure
is a function of dimensionless time and, perhaps, other quantities,
depending on the particular buildup solution. It is defined for each
equation in which it is used, throughout the report.
The equations presented all contain the variable 3, the formation
volume factor, which is the ratio of the volume of the fluid being in-
jected at reservoir pressure compared with the volume at standard conditions
(520°R, 14.7 psi). For liquids, 3 can, for practical purposed, be con-
sidered to be 1.0, as in all examples in this report. However, 3 is quite
variable when the injected fluid is gas. When a highly compressible fluid
is being injected, 3 should be evaluated at an average reservoir pressure.
In cases where the pressure is not known, enter a value of 3 = 1.0, obtain
the approximate pressure, then evaluate 3(Amyx, et al , 1960) and recalculate
the pressure.
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CHAPTER 3
PRESSURE BUILDUP EQUATIONS AND SAMPLE CALCULATIONS
This chapter is devoted to the documentation of the equations that
have been selected for incorporation in the manual. Each equation is
listed, the assumptions that apply are given, and an example calculation is
presented. Where possible, hand solution methods are used in presenting
the examples. Any example that is given can also be solved with the
programmable desk calculator programs that are given and/or with a digital
computer, using the FORTRAN program that is given. The desk calculator
programs allow a wider range of solutions than are practical by hand and
the FORTRAN program includes capabilities greater than those of the desk
calculator programs.
INFINITE CONFINED RESERVOIRS
For many practical situations, an adequate approximation of the pressure
buildup resulting from well injection can be obtained by assuming that:
1. The receiving reservoir is infinite in areal extent
and is completely confined above and below by impermeable
beds.
2. Prior to injection the piezometric surface in the vicinity
of the well is horizontal, or nearly so.
3. The volume of fluid in the well is small enough so that
the effect of the we11 bore can be neglected.
4. The injected fluid is taken into storage instantaneously.
That is, pressure effects are transmitted instantaneously
through the aquifer.
To these assumptions must be added those previously listed, which are:
5. Flow is horizontal.
6. Gravity effects are negligible.
7. The reservoir is homogeneous and isotropic.
•8. The injected and reservoir fluids have a small and con-
stant compressibility.
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These eight assumptions are basic to all equations in this chapter,
with modifications noted where appropriate.
Constant Injection Rate
Single Well —
The equation for pressure buildup resulting from a constant rate of
injection through a single well that fully penetrates the receiving aquifer
{Figure 1) is (Matthews and Russell, 1967):
0)
For cases where the quantity in parentheses (1/td) is less than 0.01,
an adequate approximation of Equation 3 is (Matthews and Russell, 1967):
P = P + 162.6 9j£ log f - *t ] (4)
r 1 W U.4
As an example of the use of Equations 3 and 4 assume the following
conditions:
Pi = 0 psi
q =1714 STB/D
3 = 1
c = 7.5xlO"6 psi "]
k = 50 md
h = 45 ft
= 0.15
y = 1 cp
r = .292 ft (7 inch well bore)
t = 3650 days
Entering these values into Equation 3, the results are:
Pr = 0 + 53.78 CE1(2.08xlO"11)D
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INJECTION
WELL
R
CONFINING STRATA
INJECTION RESERVOIR
Figure 1 Profile and plan views of a
completely penetrating well
injecting into a confined
reservoir. Pressure is to
be calculated at a point r
distance from the well.
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Obtaining the E-j value from Table A-l ,
Pr = 0 + 53.78 (24.02) = 1292 psi
Applying Equation 4,
Pr = 0 + 123.9 (10.43) = 1292 psi
The two methods give the same result in this case and will give the
same or nearly the same result in all cases where l/tj < 0.01. Where
1/td > 0.01, Equation 3 should be used to assure accurate results,
As a second example, assume all of the same conditions, but let
r = 1000 ft. Using Equation 4, the pressure buildup is 416 psi.
Equation 4 is sufficiently accurate, since l/td = 2.43x10-4 < o.Ol.
An initial pressure of zero has been used to facilitate comparison
among the various cases that are examined. In fact, the initial pressure
in any subsurface reservoir cannot be zero, but rather will generally be
close to the hydrostatic pressure resulting from the saturated thickness of
overlying rock.
Multiple Wells—
A fortunate characteristic of the equations used in this manual is
that the effects of individual wells can be superimposed to obtain the
combined effect of multiple wells. That is, the pressure at any selected
point in a reservoir can be evaluated by summing the pressures caused by
each of the individual injection wells (Figure 4).
The equation for pressure buildup resulting from constant rate in-
jection through multiple fully-penetrating wells is:
Where n is the well number.
For cases where 1/t^ < 0.01, an adequate approximation is:
p - P, + 162.6 c I Yir1 Io9 1 — — — z-b (6)
' ' "=in^ l?0-4 WnV
Equations 5 and 6 are the same, respectively, as Equations 3 and
4, with the additional instruction to compute the pressure for m wells and
sum the pressures to obtain the total pressure at a point, which is rn distance
from well n.
8
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WEI
1
1-
h
^•—
^^
i
1
1
LL
f
L
WELL
2
t CONFINING STRATA
INJECTION RESERVOIR ^_
r, ^«« r2
-»•- -^t-
nf^m
1
-^
-^fc.
Profile and plan views of two completely
penetrating wells injecting into a confined
reservoir. Pressure is to be calculated at
a point at radii r, and r« from wells 1 and 2,
respectively.
-------
pi •
q
3
c =
k
h
y
r
t
Well 1
0
100 STB/D
1
7.5xlO~6psi~1
50 md
45 ft
0.10
1 cp
30 ft
100 days
As an. example of the use of Equations 5 and 6, assume the follow-
ing conditions:
Well 2
0
200 STB/D
1
7.5xlO"6psi"]
50 md
45 ft
0.10
1 cp
70 ft
150 days (begins 50
days before Wei1 1)
Entering these values into Equation 5, the results are
Pr = 0 + [3.138 £-,(5.332 10"6)] + [6.275 E^l .936x10"5)]
Obtaining the values for E-, from Table A-l,
Pp = 0 + [3.138 (11.56)] + [6.275 (10.27)] = 0 + 36.27 +
+ 64.48 = 100.8 psi
Applying Equation 6,
Pr = 0 + [7.227 log (1.052xl05)] + [14.45 log (2.899xl04)]
Pr = 0 + [7.227 (5.022)] + [14.45 (4.462)] = 0 + 36.29 +
+ 64.48 = 100.8 psi
As for the single-well example, the two equations give the same result,
since 1/tn is < 0.01 for both wells.
10
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Variable Injection Rate
Single Well--
The assumptions for this case are the same as those previously
applied in this chapter, except that injection is at a variable rate. The
applicable equation is:
=P ,
kh ul I k(t-ta_.,)
For cases where 1/t^ < 0.01,
39.5 4>yicr ]-[ (7)
a=
Where a is the time interval under consideration and qa is the rate
during that time interval.
The equations are based on the principle of superposition. That is,
the pressure effects begin with the initial injection period t] and rate q-j
When a new rate q? is adopted, it is as if a new well begins to operate at
that rate, with the effects superimposed on the original well, while
the original well continues to operate at rate q-j . For example, assume that
a well begins to operate at an injection rate of 200 B/D and continues at
that rate for 30 days; the injection rate is then reduced to 150 B/D and
continues at that rate for an additional 30 days, at which time the rate
is increased to 400 B/D and continued at that rate for 10 days. This
performance is shown diagrammatical ly in Figure 5. The problem is
calculation of the pressure buildup at the well at the end of the 70 day
period.
Equation 7 expanded to show the example described above and for the
following values is:
Pi = °
q1 = 200 B/D, q2 = 150 B/D, q3 = 400 B/D
3 = 1
c = 7.5xlO"6
k = 50 md
h = 50 ft
= .15
11
-------
UJ
or
r\>
TIME
Figure 3 Diagrammatic representation of the injection
history of an injection well operating at a
variable rate.
-------
y = 1 cp
r = .292 ft (well radius)
t-j = 30 days, t2 = 30 days, t3 = 10 days, t = 70 days
P - n + ?n K r 200x1x1 P [39.5x0.15x1x7.5x10"6x(0.292)2].
> " u /U>D L 50x50 Ll (50(70-0)j
. (150-200)xlx1 p f39.5x0.15x1x7.5x10"6x(0.292)2l .
50x50 Ll[50(70-30)J
. (400-150)x1xl p f39.5x0.15x1x7.5x10"6x(0.292)21
50x50 Ll[50(70-60)j
Pr = 0 + 70.6 CO.08 E] (1.49xlO"7)-0.02 E] (2.61xlO"7) +
+ 0.10 E](1.043x10~6)]
Obtaining the E] values from Table A-l
Pr = 0 + 70.6 CO.08(20.07) - 0.02(19.50) + 0.1(18.11)]
Pr * 214 psi
Applying Equation 8,
Pr = 0 + 162.6 CO.08 log (6.714xl06) - 0.02 log (3.836x106) +
+ 0.1 log (9.591xl05):
Pr = 0 + 162.6 CO.08(6.826) - 0.02(6.584) + 0.1(5.982)3
Pr = 214 psi
Multiple Wells—
In computing the pressure buildup caused by multiple injection wells
operating at variable rates, the principle of superposition is applied
twice, once for computation of the pressure effects of each well and a
second time in summing the effects of the individual wells. Figure 4
depicts two wells whose effects must be summed and Figure 5 shows a
possible pattern of variable rate injection that might exist.
13
-------
The applicable equation is:
2
p _ n _L r v v "o u\o-ij- r- I * b b b b
r i ^ ^ kbhb ^
Where b is the well number, a is the time interval under consideration
for well b, and q^ is the rate for well b during time interval a. For
cases where 1/td < 0.01, an adequate approximation is:
m n 162.6(q. -qk/a ,x) fkuUK-tKfa i 0 1
P = P + C I I k h 1o9 b b b(a-1) h (10)
r b=l a=l b b 7^'^h^bcbrb
In summary, these two equations state, perform the calculation for each
well, as done for the single-well variable-rate case, then sum the effects
of the wells as shown for the constant rate, multiple-well example. Be-
cause examples of both of these procedures have been given, no new example
will be developed for this case.
Wells With Skin Effects
Injection wells may suffer permeability loss in the vicinity of the
well bore during construction or operation or they may experience per-
meability gain. Permeability loss can result from drilling mud invasion,
clay-mineral reactions, chemical reactions between injected and aquifer
water, bacterial growth, etc. Permeability gain can result from chemical
treatment such as acidization or from hydraulic fracturing and other
mechanical stimulation methods. These permeability changes, which occur
in the immediate vicinity of the wellbore are called "skin effects" by
the petroleum industry and are described by a "skin factor" (van Everdingen,
1953; Hurst, 1953). The skin factor (s) is positive for permeability loss
and negative for permeability gain.
The skin factor can vary from about -5 for a hydraulically fractured
well to +«> for a well that is completely plugged (Earlougher, 1977).
The incremental pressure difference caused by the skin effect is described
by:
= s
01)
Equation 11 is applied by combining it with equations that are J
derived for pressure buildup without skin effects. For example, Equation
3 is rewritten below to include skin effects:
-------
When 1/td < 0.01, an adequate approximation of Equation 12 1s:
Pr = Pi + 70'6
r 1
Equations 12 and 13 are only valid at the wellbore. No equations
are presented here for calculation of pressure buildup near the well bore,
in the zone of damage or improvement, because this zone is relatively thin
and because the calculations are of relatively limited application. Out-
side of the skin zone, the standard equations can be applied with no
correction (Earlougher, 1977). The thickness of the skin is determined
by (Hawkins, 1956):
s ks/k-k . .
rs = rw e s s 04)
Seldom, if ever, will k§ be known. Reasonable estimates of ks can,
however, be made to allow calculation of the range of possible skin
thicknesses. Consideration of the sources of permeability reduction
around a wellbore indicates that, in the case of wellbore damage, rs would
seldom be greater than a few feet. The radius of permeability improve-
ment can be greater, in the tens of feet for an ordinary hydraulic
fracturing program, but probably less than 100 feet unless massive
fracturing is done. It would, therefore, be safe to use 100 feet as the
maximum rs, except in cases of massive hydraulic fracturing.
As an example of the significance of the skin factor, the example
that accompanies Equation 4 has been recomputed below for s=2 (well bore
damage) and s=-2 (wellbore improvement), using Equation 13.
For the wellbore damage case, where s=2,
Pr = 0 + 53.78 [24.02 + 2(2)]
Pf = 1507 psi
For the wellbore improvement case, where s=-2,
Pf = 0 + 53.78 [24.02 + 2(-2)D
Pr = 1077 psi
These values compare with Pr = 1292 psi for the wellbore with no skin
effect.
It should be noted that these examples are computed for pressure
buildup at the well. As discussed above, s is assumed to be zero and the
ordinary 'buildup equations applied for points outside of the skin zone,
15
-------
which Is estimated by Equation 14 or assumed to be less than 100 feet,
if Equation 14 can not be used.
Partially Penetrating or Partially Completed Wells
It is generally assumed, in estimating the pressure effects of
injection wells, that the wells will be drilled completely through the
injection reservoir. This will usually be true, since it maximizes
the injection efficiency of the well. However, for mechanical or geo-
logical reasons, drilling is sometimes stopped before complete penetration
of the reservoir has been achieved. Such wells are described as partially
penetrating. In other cases, a well may be drilled completely through a
reservoir, but only a part of the reservoir is completed for injection.
Figure 6 depicts partially penetrating and partially completed wells.
The equation for pressure buildup as a result of injection into (pumping
from) such a well (Hantush, 1964; Witherspoon, et al, 1967) is:
p = p + p l41.2qu&
r PI DPP
where:
P = — FF
*DPP 2 Ltl
+ f(r, h, 1, d, z): (16)
Partial penetration results in greater pressure buildup (decline) at
and near the wellbore than would be experienced in a fully penetrating well
for the same injection (pumping) rate. The magnitude of difference
depends on the degree of penetration, 1; the ratio of the radius of
investigation to aquifer thickness, r/h; the length of the completed
interval, 1-d; and the vertical point of investigation, z. The expanded
form of Equation 15 is too complex for practical use by hand and the
number of variables so large that it is impractical to provide tables
for evaluation of Pgpp. Therefore, solutions of Equation 15 are provided.
through programs for the programmable desk calculator and for digital
computers using FORTRAN.
As an example of the effect of partial penetration on pressure buildup,
consider the example given for a single fully penetrating well injecting
at a constant rate, except that the well will now penetrate only 10 feet
into the injection reservoir. The example data are:
Pi = 0 psi
q =1714 STB/D
3 = 1
c = 7.5xlO~6psi~1
16
-------
o
L,
INJECTION
RESERVOIOR
'LOWEXR CONFINING UNJT
Figure 4 Wells with varying degrees of penetration and completion
1. Fully penetrating fully completed well.
2. Fully penetrating partially completed well.
3. Partially penetrating partially completed well.
4. Partially penetrating fully completed well.
5. Non-penetrating well.
-------
k
h
*
y
r
1
d
z
t
= 50 md
= 45 ft
= 0.15
= 1 cp
= .292 ft
= 10 ft
= 0 f t
= 0 f t
= 3650 days
The pressure buildup is 2704 psi, which compares with the value of 1292
psi for the fully penetrating well. The vertical point (z=0) selected
for evaluation yields the maximum pressure buildup.
Fractured Reservoirs
Single Vertical Fracture—Wei 1 bore Case —
It is a common practice to artificially fracture injection wells,
by hydraulic means, to increase their capacity to accept injected fluid.
Such fracturing will affect pressure buildup, particularly near the well.
Although the geometry of induced hydraulic fractures is never exactly
known, estimates of fracture length can be obtained by well testing. Under
the conditions that most commonly exist, induced hydraulic fractures are
vertical (Hubbert and Willis, 1957). For a well that completely penetrates
an infinite confined aquifer that is intersected by a single vertical
fracture, the equation for pressure buildup at the well is (Gringarten
et al, 1974):
Where:
PWB " Pi
DWF
DWF
erf
141.2que
k~Fi
(17)
08)
and,
6.33xlO"3kt
ycxf
09)
18
-------
Equation 17 is for a fracture across which flow is uniform.
Alternative solutions are available that consider the fracture to be
of infinite conductivity, but the uniform flow solution is considered
to be more realistic (Earlougher, 1977).
As an example of the use of Equation 17, assume:
P1 = 0 psi
q =1714 bbl/day
3 = 1
c = 7.5xlO"6psi"1
k = 50 md
h = 45 ft
4> = 0.15
U = 1 cp
xf = 10 ft
t = 3650 days
From Equation 19,
t = (6.33xlO"3)(50)(3650) . ] 027xlo7
D (0.15)(l)(7.5xlO 6)(10)2
From Equation 18,
PDWF = 568° erfO-56*10~4) + \ £^2.435x10~8)
Using Tables A-l and A-2,
PDWF = 568° O-8*10"4) + 7 (16.95) = 9.5
Then from Equation 17,
p =0 + 95 [1*1-2x1714x1x11 _ 1Q21 _.,
PWB ° + 9'5 50x45 10Z1 PS1
19
-------
Single Vertical Fracture—General Case—
The previous equations apply only at the well bore. A general solution
that can be used for points other than the wellbore is (Gringarten, et al,
1974):
P = P + P |141.^MP[ r?f]\
rxv Ki * Knp th v^u;
xy ri rDF I kh
Where:
PDF = l(ln tD + 2.809) + a(xD, yQ) (21)
and
t _ 6.33xlO"3kt v _ x „ _ y
**n ~ 9 > xn~ v > J^n ~ v
LJ i t \ c. u A.C *J ™£
(j)yc(x^) f f
As an example, use all of the data for the previous fracture case,
except let the fracture be 100 feet in radial length and consider a
point at 50 feet from the well bore and 50 feet outside of the fracture
plane. From Equation 21,
p _l[1n (6.33x10"3)(50)(3650) , 2 opg] ,
DF 2l (0.15)(l)(7.5xlO"6)(100)2 " J
+ a(xD = 0.5, yD = 0.5)
From Table A-3, a = -0.257
and
PDF = |<11.54 + 2.809) - 0.257 = 6.92
Therefore, from Equation 20
»/171/I x/1 vll
= 744
Single Horizontal Fracture—
In areas where the sedimentary rock sequence is under active tectonic
compression, hydraulic fractures would be expected to be horizontal
(Hubbert and Willis, 1957). Although this situation is relatively uncommon,
equations have been developed to simulate it. For a well penetrated by a
single horizontal symmetrical fracture of radius rf centered at the well
and with all other assumptions the same as given at the beginning of the
section (Gringarten and Ramey, 1974 ):
20
-------
= p +
K
l41.2que
kh
(22)
For points of investigation (r) that are greater than
r > rf + 3h
and for
tD >_ 12.5(2^+1), and tQ >_ ^ ho
IT
DHF
Where :
.
D=
0.81]
(23)
6.33x10"3kt
hD = h/rf
rD = r/rf
As defined, the solution given above is limited to points which are
farther from the well than rf + 3h. For example, if the fracture has a
radius of 100 feet and the formation is 50 feet thick, then the solution
can be applied at a radial distance greater than 100 + 3(50) = 250 feet.
The tp limitations must also be met. In order to obtain solutions for
points of investigation closer to the well, the programmable desk calculator
or FORTRAN programs must be used. As an example of the application of
Equations 22 and 23, assume the following conditions.
P.J = 0 psi
q = 5000 STB/D
y = 1
3 = 1
k = 100 md
h = 50 ft
4> =0.25
c =
21
-------
rf = TOO ft
r = 300 ft
t =1000 days
First, checking t^ against the limitations that are given,
t = (6.33xlO"3)(100)(1000) = 3 38xlQ4
D (0.25)(l)(7.5xlO'6)(100)2
Therefore :
tD > 12.5(2r2+l) > 238,
tD > ^2 ho > * ' and
IT
r > rf + 3h > 250
Since the necessary conditions are met, Equations 22 and 23
can be used. From Equation 23,
PDHF
and from Equation 22
INFINITE SEMICONFINED RESERVOIRS
The beds considered to provide confinement of the receiving aquifer
may be sufficiently permeable so that significant pressure bleed-off may
occur by virtue of vertical transfer of fluid through them. The assumptions
applied in the infinite confined aquifer case apply except that:
1. The confining bed(s) is (are) sufficiently permeable so that
the transfer of fluid across it (them) must be considered.
2. The adjacent aquifer(s) is (are) permeable enough so that
no significant pressure buildup occurs in it (them).
3. Compressibility of the caprock(s) is neglected.
22
-------
Leakage in One Direction
The equation for pressure buildup as a result of a fully penetrating
well injecting into a reservoir fully confined on one side and semicon-
fined on the other is (Hantush and Jacob, 1955):
p = p + p fl41.2qy3l (24)
pr pi PDI4 kh j l '
Where:
PDL = f(tD, r/B)
. 6.33x10"3kt
D "
B = /khh r/k
c* c
As an example of the use of Equation 24, apply all of the same
values used in the example of the fully penetrating well with a constant
injection rate; that is:
q = 1714 bb/day
3 = 1
c = J.SxlO'
k = 50 md
h = 45 ft
$ = .15
y = 1 cp
r = 0.292 ft
t = 3650 days
Additionally:
hc = 100 ft
kc = 1 md
23
-------
Therefore:
td = 1.2 x TO10
and
B = 474
£= 6.16 x 10"4
From Table A-5, PQ = 7.50
and
Pr = 7.50(107.6) = 807 psi
This value compares with the value of 1292 psi for the completely
confined case. Now, to test the validity of this calculation assume
kc=0.001 md and hc=1000. For these values, the answer should approach
the completely confined case. For these two new values,
and
tD = 1.2 x 1010
B = 4.74 x 104, £= 6.16 x 10"6
From Table A-5, PD = 11.78 and
Pf = 1268 psi
This answer compares well with the 1292 psi calculated for the com-
pletely confined case.
• 'f •'-•
Leakage in Two Directions
The equations for determination of pressure buildup in an aquifer
that is semiconfined both above and below are as given for leakage in one
direction, except that:
khh h'
B_ / c c
—
No example is given, since the procedure is exactly as that developed for
leakage in one direction.
24
-------
•Image Injection ^
Well
Real Injection
Well
Impermeable
Boundary
Figure 5 Plan view of an injection well adjacent
to an impermeable boundary, with an image
injection well used to simulate the boundary.
25
-------
BOUNDED RESERVOIRS
Linear Boundaries
In the proceeding two sections, the aquifers being injected into
(pumped from) were considered to be infinite in areal extent. In many
cases the injection reservoir will be bounded on one or more sides by
geological features, principally faults or facies changes, that act as
flow barriers or recharge sources. Such features cause the aquifers to
have limited extent. The presence of flow barriers or recharge sources
is handled by use of image well theory in which imaginary wells are used
to hydraulically simulate the effect of the boundary (Todd, 1959; Davis
and DeWiest, 1966; Walton, 1970; Earlougher, 1977).
Figure 5 shows the placement of an image well to simulate an
impermeable fault adjacent to a single injection well. The image
well is considered to be receiving the same flow as the real well
and the aquifer to have the same properties as at the real well. The
pressure buildup at any point of investigation is computed by summing the
effects of the real well and the image well. If the boundary were leaky,
one through which flow could occur with no perceptible pressure buildup,
then the image well would be a pumping well that would deplete reservoir
pressure rather than add to it. Where several injection wells are present,
each one will have its own image well and all real and image wells will
contribute to the total reservoir pressure at any selected point of
investigation. In other words, the problem is simply that of a multiple
well system.
The image well concept is relatively easy to employ for a single
hydro!ogic boundary, but becomes more complex for multiple boundaries,
since multiple image wells are required for each real well. Figure 6
shows the placement of image wells in the case of a single injection well
and two impermeable barriers intersecting at right angles. For a more
complete discussion of image wells, including development of image well
systems for boundaries intersecting at angles of less than 90° (wedge-
shaped reservoirs) the reader is referred to Ferris, et al (1962).
No example is given because, as mentioned above, once the image wells
have been located, the problem is handled as any multiple well problem by
superimposing the effects of all real and image wells at the point of
investigation.
Completely Bounded Reservoirs
During injection into (pumping from) completely bounded or closed
reservoirs, a relatively short initial time period occurs during which
pressure changes are nonuniform throughout the reservoir. After this
initial period, as the pressure changes with time, it changes uniformly
throughout the reservoir (Earlougher, 1977). During the second period of
so-called pseudosteady-state pressure change, the pressure buildup
(drawdown) at the well is given by (Earlougher, 1977):
26
-------
^-Impermeable
Jk Boundary
Real Injection
Well
Impermeable
Boundary
I-l, 1-2, 1-3 Are Image Injection Wells
Figure 6 Plan view of a real injection well adjacent to two
intersecting impermeable boundaries with the image-
well system used to simulate the boundaries.
27
-------
p - p + p fl41.2qy3
PWB Pi + PD kh
P - s>,pt + in A1 + 1 in f 2. 2458
PD - 27rtDA + 2 ln + 2 ln
Where
and
. 6.331x10"3kt (27]
rDA v ;
The time necessary for flow to become pseudosteady-state can be
estimated from:
(28)
Where :
(tQA) is given in the "Exact for tQA >" column in Table 1.
As an example of the calculation of pressure buildup in completely
bounded reservoirs, assume a square reservoir created by impermeable
boundaries on four sides, with the sides each 5,000 feet in length, and
the well centered in the reservoir. Calculate the pressure buildup for
the same data used in the single fully-penetrating well injecting into an
infinite confined aquifer.
The data are:
q = 1714 STB/D
3 = 1
c = 7.5xlO"6
k = 50 md
h = 45 ft
<)> = 0.15
y = 1 cp
28
-------
r = .292 ft
A = 25,000 ft2
t = 3650 days
First, verify that the pseudosteady-state solution applies by use of
Equation 28.
t > (0.15)(1)(7.5x10"6)(25,000) ,
PSS~ (6.331xlO-3)(50) D
From Table 1, (t = -05» therefore:
t = 0.004 days and Equation 26 can be used, since the
}Jd d
time of interest is 3,650 days.
From Equations 26 and 27 and Table 1:
PD = 27r(41,081) +^-ln (2.932xl05) - 1.3106
PD = 2.581xl05 + 6.29 - 1.31
PD = 2.581xl05
From Equation 25:
5(141-2174
P =0+2 5Slx10r-H
KWB U ^baixlu L (50)(
PWB = 27. 8x1 O6 psi
The resulting answer of 27.8x10 psi is clearly unrealistic, but it
emphasizes the fact that such a completely bounded reservoir is not
suitable for injection use under the conditions specified.
RESERVOIRS WITH VARIABLE PERMEABILITY
Thus far, in the presentation, reservoirs have been assumed to be
homogeneous and isotropic and to be characterized by a single average
value of permeability. This is probably seldom close to the actual
circumstances, but for reasons that will be explained this assumption
29
-------
TABLE I—SHAPE FACTORS FOR VARIOUS CLOSED SINGLE-WELL AREAS
(Earlougher, 1977)
CA
IN BOUNDED RESERVOIRS
• I 31.62
31.6
27.6
EXACT
FOR toA>
LESS THAN
1% ERROR
FOR tDA>
USE INFINITE SYSTEM
SOLUTION WITH LESS
THAN 1% ERROR
3.4538 -1.3224
3.4532 -1.3220
3.3178 -1,2544
27.1 3.2995 -1.2452
21.9 3.0865 -1.1387
0.098 -2.3227 4-1.5659
30.8828 3.4302 -1.3106
12.9851 2.5638 -0.8774
4.5132 1.5070 -0.3490
3.3351 1.2045 -0.1977
21.8369 3.0836 -1.1373
10.8374 2.3830 -0.7870
4.5141 1.5072 -03491
2.0769 0.7309 +0.0391
3.1973 1.1497 -0,1705
0.1
O.I
0.2
0.2
0.4
0.9
0.1
0.7
0.6
0.7
0.3
0.4
1.7
0.4
0.06
0.06
0.07
0.07
0.12
0.60
0.05
0.25
0.30
0.25
0.15
0.15
1.5 0.50
0.50
0.19
0.10
0.10
0.09
0.09
0.08
0.015
0.09
0.03
0.025
0.01
0.025
0.025
0.06
0.02
OXJ05
(continued)
30
-------
TABLE 1—(continued)
/ \ LESS
•> i n 1*0 ix -o *\d9*t +n ft7*\n 5" ft n
2
._._
' 1
2
nu, USE INFINITE SYSTEM
'"TB SOLUTION WITH LESS
.KROT THAN 1% ERROR
**>*> FOR to* <
50 0.02
60 OJ005
• 1 5.3790 1.6825 -0.4367 0.8 0.30 0.01
4
4
4
4
50 0.01
M 0.03
)0 0.01
• i 2.3606 0.8589 -0.0249 1.0 0.40 0.025
INVEffTH
1
1
1
1
1
1
1
5
•ALLY-FRACTURED RESERVOIRS USE (xe/xf)* IN PLACE OF A/r£ FOR FRACTURED SYSTEMS
0.1
1
02
1
03
1
¥-
1
0.7
1
1.0
:xf/xe 2.6541 0.9761 -0.0835 0.175 0.08 CANNOT USE
2.0348 0.7104 +0.0493 0.175 0.09 CANNOT USE
1.9986 0.6924 +0X3583 0.175 0.09 CANNOT USE
1.6620 0.5080 +0.1505 0.175 0.09 CANNOT USE
1.3127 02721 +02685 0.175 0.09 CANNOT USE
0.7887 -02374 +0.5232 a 175 0.09 CANNOT USE
• J 19.1 2.95 -1.07 — — -_
• J 25JO 322 -1.20 — — —
31
-------
will often yield adequate results. In those cases where variable per-
meability must be considered, special techniques can be applied.
Layered Reservoirs
Most reservoirs are layered, because of stratification developed
during their deposition or as a result of selective development of secondary
permeability. Permeable layers may be vertically interconnected or they
may be separated by thin shales, dense carbonate layers, evaporite layers
or other relatively impermeable beds. Where there is hydraulic inter-
connection, the system is often referred to as a layered reservoir with
crossflow. Where the permeable layers are hydraulically interconnected
only through the well bore, the system is layered without crossflow.
Layered Reservoirs With Crdssf low--
Figure 7 shows an aquifer with three layers that are hydraulically
connected. Russell and Prats (1962) concluded that such reservoirs can be
treated as a single equivalent homogeneous system. The equivalent system
is determined by using the relationship:
n
.1 kihi
k = & - (29)
For example, given the following data:
k1 = 50 md h1 = 30 ft
k2 = 200 md h2 = 40 ft
k3 = 75 md h3 = 200 ft
The equivalent reservoir permeability is:
F - (50x30)+(200x40) (75x200) = g, .
30+40+200
And the equivalent reservoir thickness is 270 ft.
The equivalent ¥ and total h are used in equations such as 3, 4,
etc., just as if the aquifer were a single homogeneous unit.
32
-------
CONFINING STRATA
'•..*.'.*••»' '.'.'.•••*".
'"•.*'•*"/ ° ••'.*•" '',- "
•• »*.<• '«"«*••••*.»
.••...•.'.•.•. • » • .
* I/ * •• •
•.' • • •. *•'.."• • .'•
km .
*. '
— LOWER
ZCONFINING
— STRATA
Figure 7 A layered reservoir, with vertical
communication between layers.
33
-------
Impermeable /
Layer T =
Impermeable^
Layer _£.
UPPER
—CONFINING —
STRATA
lONFINING^d
STRATA
Figure 8 A layered reservoir without vertical
communication between layers.
34
-------
Layered Reservoirs Without Crossflow—
In aquifers where the permeable layers are separated by impermeable
ones, as shown in Figure 8, the same procedure is applied as is given
above, except that the permeabilities and thicknesses of the impermeable
layers are ignored.
In such reservoirs, only the pressure buildup at the well bore can
be calculated using the uniform aquifer equations that have been presented.
Radially Varying Permeability
It is possible to have radially varying rock or fluid properties
as shown in Figure 9. Such radial variations are most likely to be
man-induced. Radial permeability and porosity variations can be caused
by formation damage or improvement during well construction or during in-
jection well operation. Such permeability and porosity variations may be
deliberately created as in the case of the fracture zones in a nuclear
stimulation project or the burned zone of an in-situ oil or oil shale
combustion project.
The general equation for determination of an average permeability
value, where there are two or more zones of radial permeability is:
F- n*" _ (30)
I
k1
The difficulty in using this solution for pressure buildup calcula-
tions is that it requires the knowledge of re,the radius to the point at
which pressure is that of the undisturbed reservoir. This concept is
normally only applied in the so-called steady state flow equations, but
can be used in the unsteady state equations presented herein by treating
re as a varying quantity using the following equation:
r . ' kt
/7D7
e 70.33yc
By inspection, Equation 31 states that re is proportional to the
square root of time.
As an example, assume that there are two radial zones around an
injection well with the following properties and conditions:
35
-------
C
o
0)
cT
,.
Figure 9 A reservoir with radially varying
permeability.
36
-------
rw = 0.292 ft
= 100 ft
re =
k] = 10 md
k2 = 50 md
c = 7.5xlO~6psi~1
t = 30 days
= 0.15
y = 1 cp
Applying Equation 31,
x 30
.15x1x7.5x11
re = 4,354 ft
Applying Equation 30
k = log 4,3547.292 m 4.173 = H 5g d
K log 100/.292 + log 4,354/100 .2535 + .0327 l^°° ma
10 50
The average value of permeability to be used for calculations of
pressure buildup at the well is then 14.58 md.
FLUIDS OF VARIABLE VISCOSITY
It is common for the fluids being injected to have a viscosity
different from the native reservoir fluids. This problem can be handled
by considering the effect on hydraulic conductivity caused by the viscosity
differences. If flow is considered to be radial, then the average radius
37
-------
to which the injected fluid has traveled after a period of injection is:
_ /5.615qte (32)
if Trh
The ratio of the hydraulic conductivity in the radial zone containing
the injected fluids to the remainder of the reservoir is:
(33)
This.ratio can be rearranged to give a new apparent permeability for
the zone containing injected fluid
(34)
k
a Prf
The problem can then be treated as if there were zones of varying
radial permeability, as is discussed earlier.
DIPPING RESERVOIRS
All of the equations developed previously have incorporated the
assumption that the reservoir is horizontal. In cases where the reservoir
has a significant dip, the initial pressure (Prj) at a point r, when
referenced to the origin is:
p = p + r tan ft (35)
pri pi r tan e 144
Equation 4 would, for example, then become:
P = P + r tan 6 + kt
Pr Pi+rtane^H-
Assume the following conditions:
38
-------
P. =0
q = 1714 STB/D
e = i
c = 7.5xlO"6psi
k = 50 md
h = 45 ft
= 0.15
y = 1 cp
r = 1000 ft
6 = 10°
Yrf =65.5 16/ft3
t = 3650 days
From Equation 36,
P.. = 0 + 80.2 + 416.5 = 497 psi
r
39
-------
CHAPTER 4
CALCULATION OF PRESSURE BUILDUP WITH
THE PROGRAMMABLE DESK CALCULATOR
The programs listed in Appendix B are written for a Texas Instruments
Programmable 59 calculator which allows the storage of programs on magnetic
cards.
It is probably safe to assume that most people who will use this
publication are familiar with some type of electronic desk calculator. If
readers are not, it may prove helpful to read the parts of the Texas
Instruments owners manual "Personal Programming" which deal with charging
and maintenance of the Texas Instruments Programmable 59 calculator. The
section covering keyboard operations will also be profitable, but is not
needed for the operation of the programs in this publication. The use of
these programs is quite simple. All necessary instructions are contained
in this chapter and with the programs in Appendix B. If a reader should
wish to modify any of the programs in Appendix B or if a reader should wish
to write similar programs of their own, it will then be necessary to become
familiar with the programming procedures described in the Texas Instruments
publication "Personal Programming" that accompanies the calculator.
PROGRAM ENTRY FROM THE KEYBOARD
To enter one of the programs in Appendix B, turn the calculator on
and press the sequence of five keys listed after Partitioning in the
program heading. If the program heading says Partitioning normal, skip
this step. Next press the LRN key to enter the "learn mode." The display
should show 000 00. Now press, in order, each key shown in the Key column
of the program listing. As this is done the first three digits of the
display should keep pace with the number in the Location column of the
program display. The location number shown is that of the step about to
be entered.
When all the keys shown in the program listing have been pressed,
press LRN again to leave the learn mode. The program is now ready to use
according to the User Instructions given with each program. To avoid
losing the program when the calculator is turned off (necessitating entering
it through the keyboard again) it may be recorded on a magnetic card.
RECORDING A PROGRAM
To record a program on one of the cards accompanying a calculator,
40
-------
hold it with the printed side up and the printing upright. Press the keys
1, 2nd, Write, and insert the card into the lower slot on the right side
of the calculator. Keep pushing until the motor starts pulling the card—then
let go. When the card stops, pull it out the left side. This records
the program steps through location 239. If the program goes beyond this
location, turn the card so the printed side is up, but the printing is
upside down. Press 2, 2nd, and Write, and insert the card as before. This
records steps 240 through 479. If the program continues beyond step 479
a second card will be needed. Hold it with the printed side up and the
print upright, press 3, 2nd, and Write, and insert the card as above. This
records steps 480 through 719.
The program is now recorded and may be easily re-entered from the card
whenever it is needed. For convenience, the key sequence, if any, following
Partitioning should be written on the card along with the program title.
PROGRAM ENTRY FROM MAGNETIC CARDS
To enter a program from a magnetic card, turn the calculator on and
press the series of five keys (if there is one) following Partitioning in
the program listing. Press CLR and insert the card in the same position
and into the same slot used for recording. Remove the card when it stops.
The display should show 1 for the side which was recorded first (steps 000
through 239). If the display is flashing press CLR, check to be certain
the card is clean, and insert it again. If the display still flashes after
several trys, see page VII-5 in the owner's manual. It contains some
suggestions as to what may be wrong.
To enter the second edge or the next card, hold it in the same
position it was in when recorded, press CLR, and insert it as above. The
second edge should result in a display of 2, the third (on the second card)
should yield 3, and the fourth should cause a display of 4.
PROGRAM EDITING
In the event a mistake is made when a program is being entered from
the keyboard, it is important to know how to check and correct the program.
While in the learn mode, the SST key may be used to move forward through
the program one step at a time without changing the program. Similarly
BST may be used to back up one step at a time. If the vsrromj- key was
pressed at location 115 for example, use the SST or BST keys, while in the
learn mode, to reach location 115 and then simply press the correct key.
This replaces the incorrect step in the program with the correct one. If
a key has been skipped which should have been entered in location 076, go
to that location and press 2nd Ins. This moves the remainder of the program
one step leaving location 076 empty. The empty location may now be filled
with the omitted key. If an extra key has been pressed somewhere in a
program it may be removed by going to that location and pressing 2nd Del.
This deletes the unwanted step and moves all subsequent steps in the
program to close the gap.
41
-------
For the purpose of checking a program it should be noted that for any
location the two numbers to the right of the location number should match
the code shown with that location number in the program listing.
All the editing techniques mentioned thus far are used while in the
learn mode. To reach different locations in a program it is sometimes
easier to use the GTO (go to) key. This is used while not in the learn
mode. Simply press GTO followed by the location number desired. Then
press LRN to enter the learn mode for corrections. To illustrate this
press GTO 053. If LRN is pressed now, the display will show location 053.
EXAMPLE CALCULATION
As an example of the use of one of the programs, turn to the program
titled "Single or multiple wells, constant injection or pumping rate" in
Appendix B. The partitioning is normal and so may be ignored. Turning to
the listing of the program steps we see that E](x) subroutine must be
entered first. Turn to the listing of the subroutine titled "Exponential
Integral", press the LRN to enter the learn mode, and begin pressing the keys
shown in the KEY column. When all steps 000 through 109 have been entered,
return to the main program and enter the steps from 110 through 201. Press
the LRN key to leave the learn mode. The program should now be ready to use.
To try out the program, enter the following data according to the
User Instructions given with the program.
m 1 well h 45 ft.
P. 0 psi .15 fraction
qn 1714 STB/D y 1 cp.
rn .292 ft. c 7.5xlO"6 1/psi
t 3650 days Bn 1 RB/STB
k 50 md. Sn 0
If all the instructions have been followed correctly, the answer displayed
will be 1292 psi.
If your efforts produce a different result, re-enter the data and try
again. If that doesn't work press GTO 000, enter the learn mode, and start
comparing the two digit code for each step with the code shown beside the
same location number in the program listing. The section on Program
Editing should be helpful at this point. When the mistake has been corrected
and the right results are obtained, the program is ready to be recorded on a
magnetic card for future use.
42
-------
CHAPTER 5
CALCULATION OF PRESSURE BUILDUP WITH THE DIGITAL COMPUTER
A computer program has been written for the determination of
aquifer pressure behavior under fluid injection and/or production systems,
The program is written in ANS FORTRAN and the required data forms are
shown on the following pages.
CARD FORMAT
There are four types of formats used to input data in the program.
A Format - for alphanumeric data (data which may be alphabetic
letters or numbers; also, sometimes referred to simply as
alphameric). Used for titles, etc. Values read with this
type of format are not used in calculations and are for
print-out clarity.
I Format - used for input of integers. No decimal point is allowed.
A group of five columns in the card is used for integers.
A group of columns is called a field. Blanks in numerical
fields are interpreted as zeros, therefore all integer
quantities must be punched in the right-most portion of
their allotted fields (i.e., right-justified).
A large number of integer variables are used to indicate to
the program a selection between several options. These
logical switches require that the number entered be one of
the possible values listed (most are restricted to zero
and one). Most of the switches are set so that the default
(no entry = zero) action is to NOT use a certain feature.
F Format - used for input of real numbers. The decimal point must be
punched. Blanks in numerical fields are interpreted as
zeroes. A group of ten columns in the card is used for real
numbers.
X Format - for skipping spaces. All X formats indicate a card label for
user convenience, and may be omitted by the experienced user.
It is strongly recommended that the card labels be employed.
43
-------
TITLE CARD
(There will be one TITLE Card).
TITLE
f*. rail
I/COMMENT
51ATEM IT
NUMBER
10 00
12345
11111
I
1
i
*
0
E
1
0000
I 1 9 10
1111
EHTER TITLE IN THIS SPACE
FORTRAN! STATEMENT
100000 000 0 00000 (i DC 0 3 0 fl 0 0 0 0 Q C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C 0 0 0 0 0 0 G 0 0 0 C
II 12 DM 15 18 17 !B 19 2021 2223?;:32S 2) 2C2S."0 3'323;j) :". 3S;i:'3!HO
-------
SELECT CARD
(There will be one SELECT card)
fSELEQ
FG.I
COMMENT
S1AT1 ttNT
NUMBER
10000
1 2 3 4 5
11111
TO
MufflUM:
s
1
0000
7 8 9 10
1111
NT
0000
11 12 13 14 IS
11111
NW
ooos
C B B 19 30
11111
NRAD
JOflOO
n r :? ?« 2:
111 1
IVIS
FC
03 0
!627;i«-3
11111
IMAGE
FTR/
o'ii'cco
111
:LEAK
r s-
00000
637313340
i r i
IDIP
"ATE'
00000
41 42 4C445
inn
1PENT
/! -:r T
0000
6-7484950
1111
tFRAC
.
9000C
SI 52 E3 54 50
1 1 r i
IREF
!CE)00
S 57 53 £3 60
mil
PI
00000009GO
Cl GZS'JEi t-UC;SS£970
1111111111
00
71 72
1 1
DU
IDENTIFICATK5N
03 090U 0
(3 74 Tj 76 77 78 79 10
11111111
FORMAT (10X, 1015, 2F10.2)
NT - Number of time entries at which pressures will be calculated.
NW - Number of wells to be included when determining pressures.
NRAD - Number of distances at which pressures will be calculated.
IVIS - Switch for variable fluid viscosity
= 0, constant viscosity
= 1, viscosity varies with distance
IMAGE - Switch for boundary effects
= 0, no image welIs
= 1, image wells will be included
I LEAK - Aquifer leakage indicator
= 0, no leakage
= 1, leakage exists
IDIP - Switch to account for dipping beds
= 0, horizontal bed
= 1, dipping bed
IPENT - Indicator for partially penetrating wells
= 0, wells completed throughout bed
= 1, partial penetration exists
IFRAC - Fracture analysis switch
= 0, no fractures
= 1, vertical fracture solution
= 2, horizontal fracture solution
IREF - Well to be used in printing distances to pressure calculations
(default value is 1)
•*
PI - Initial pressure, psi
DW = Water density, lb./ft.3
45
-------
LEAK CARD
If 1LEAK « 0 (on the
SELECT card), omit this card.
(There will be one LEAK card, when needed).
LEAK
f* ,'OB
U> COM*€KT
rATEM V Si 56 57 5! K CO 51 G2 El 64 60 $6 C7 C3 63 70 71 l<
1111111111111111111111
IDENTlFICAriON
03 000 DUO
C! 74 75 76 77 71 "5 30
11111111
FORMAT (10X, 4F10.3)
CAPKT - Permeability of overlying leaky bed, md. (if no leakage occurs,
leave blank)
CAPHT - Thickness of overlying leaky bed, ft.
CAPKB - Permeability of underlying leaky bed, md. (if no leakage
occurs, leave blank).
CAPHB - Thickness of underlying leaky bed, ft.
46
-------
IMAGE CARD
If IMAGE » 0 (on the SELECT card),
omit this card.
(There will be one IMAGE card, when needed)
IMAGE]
r *«—:><
LX COMMENT
ST; -EMEMT
NUMBER
DID 0 0 0
12345
It'll
1
I
1
0
6
1
0000
7 8 9 10
1111
ANGLE
OOOC8COCOO
11 12 13 H 15 K !7 » 19 29
1 1~1 1 11 111
IB1
00090
si 22 :• :t 25
1111
IBS
FC
OOOOG
?t 2) 28 29 :0
11111
RTRAN STATEMENT
0 0 C 0 0 0 0 0 0 0 0 0 0 C 0 0 0 G 0 0 Q 0 0 0 2 C 0 0 0 0 0 0 0 0 0 0 0 G 0 0 0 0
3' 32 31 .1 35 36 37 3* 39 40 41 42 43 41 <5 48 -7 48 49 90 SI 57 S3 S-l 15 K 'jl ii iS K El 62 E) E4 CS CC G) C: i9 7-0 71 72
111111111111111111111111111111111111111111
IDENTIFICATION
030000UO
13 74 75 K 77 73 70 SO
11111111
FORMAT (10X, F10.2, 215)
ANGLE - Angle of intersection between boundaries, degrees (for a
single boundary, enter 180; and for parallel boundaries, enter
360)
IB1 - Indicator for lower boundary
= 0, sealing boundary
= 1, leaky boundary
IB2 - Indicator for upper boundary
= 0, sealing boundary
= 1, leaky boundary
162
^Angle ()
IB1
NOTE: For the single boundary case (Angle = 180), only IB1 is required;
for the case of parallel boundaries (ANGLE = 360), IB1 is
the left boundary and IB2 is the right boundary (top and bottom
may be substituted for left and right, respectively).
47
-------
TIME CARD
(There will be as many TIME cards as
required for NT values, 7 values per card).
TIME a
TIME
L»'cOMMENT
STOT1 ENT
NUMBER
||0 0 0 0
12345
1'1 1 1 1
1
1
I
i
0
6
T^
0000
7 II 9 10
1111
TIME<8>
TIMEC1)
1 !
1 80000000
1 12 lj 14 13 1! 17 !! 19 20
1 1 1 1 1 1 ~ 1 1 1
TIMEC9)
TIMEC2)
l iFO
) OOQ090CQ
1 22 23 2< 25 28 27 23 29 30
11 1 1 1 1 1 1 ! 1
TIMEUO)
TIMEC3)
1 >i
=JTRAN T S-
) 00000000
! 32 33 J< 3r; 38 37 31 39 40
1111111111
1 TIMEC11)
TIME (4)
•ATflMETMT
0 00000000
II 42 43 44 45 46 - 7 4t 49 50
1111111111
TIMEU2)
TIMEC5)
i i
0 00000000
1 52 » 54 C5 X 57 53 '.'. CO
1111111111
ITIMEC13)
TIMEC6)
r
3 00000000
SI C2 GJ E4 C5 K n £3 G9 10
1111111111
p
T
0
71 72
1 1
"|IHEC14>
IME<7>
I ar
03000000
1) 74 75 75 77 73 79 60
11111111
FORMAT (10X, 7F10.3)
TIME(l) - Cumulative tjme at which pressure is calculated, days
TIME(2) - Cumulative time at which pressure is calculated, days
TIME(3) - etc.
48
-------
WELL CARDS
(There will be NW well cards, each
card followed by the options selected)
JJELL
^•^M^MMa*
•v ron
J COMMENT
mm « 9 70
1111
RU
FC
10000 0 C 0 0
i 22232«i-r:c 3?:'3:no
1111111111
TSTART
RTRAh S'
00 3000
132jJ343J3S3;33:«l
111111111
VISM
"ATEM :NT
000 0 0000
!l 42 43 <•! 4'j 45 <7 :i » SO
1111111111
TIMS
000 00 000
il 52 S3 14 55 i6 57 53 59 03
1111111111
RADSKIH
10000 0000
ii E2Slli-l05CeC.'C1!5ra
111 111111
o'u
/: /.
1 1
ICENTiFICATION
UDOOGOOO
:~, ,, ~j H :i .» /380
11111111
FORMAT (10X, 215, 5F10.0)
LWN - Well number (number wells sequentially from 1 to NW)
NRATE - Number of rates for this well
RW - Wei I bore radius, in. (default value is 3")
TSTART - Time to start of first rate for this well, days (relates all
wells to same start time)
VISN - Viscosity of injected fluid, cp. (used if IVIS = 1 on the
SELECT card)
TINS - Time to start of injection of VISN, cp.
RADSKIN - Radius of skin effect, ft. (default value is 100')
49
-------
PENT CARD
If I PENT = 0 (on the SELECT
card), omit this card.
(There will be one PENT card
per well, when required).
=>ENT
r+ FOB
Ij COMMENT
•ATI CUT
NUMBER
0100 0
12345
1J1 11 1
S
i
i
0
s
i
0000
7 8 tr tO
1111
PARTHK
90000 0000
i! 12 13 H is ;; 17 13 19 7;
1 1 1~1 1 11 1 1
DPEMT
FC
OOOOOC 000
:i J2232. :5:52;?82i.;]
1111111111
RTRAN STATEMENT
OUOOOOGOOOOOOOOOOOOOOOOOOOOOOQOOOOOOOOOOUQ
31 32 AW K 35 37 33 39 40 «: 4? 43 44 45 46 47 48 49 13 51 5253 H 5555 57 58 55 C3 61 U K 51 WE6G? C8 69 70 /I It
111111111111111111111111111111111111111111
IDENTIFICATION
30000000
(3 74 /5 16 77 71 li tit
11111111
FORMAT (10X, 2F10.0)
PARTHK - Length of partial penetration, ft.
DPENT - Distance from top of reservoir to top of partial
penetration, ft.
50
-------
LOCATION CARD
IF IMAGE = 0 (on the
SELECT card), omit this card.
(There will be one LOCATION card
per well, when required).
LDCftT
fV rfcrf
*/ COUCH-,
Tl •EMENT
NUMBER
01000
12345
1'1 1 1
I
s
1
6
1
DM
0000
7 t 9 10
1111
X
0000 OOOOQ
11 12 13 ii K K n a u :i
minim
Y
FC
5003 OOOGO
a 2: r. v 23 23 :i K 29 :3
1 1 1 11 1 1 1 ! 1
RTRAN STATEMENT
0 0 C 0 0 0 0 0 0 0 0 0 0 C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 G 0 0 0 0 0 0
1< K 3i In :c. A 37 3< 3! 40 41 42 <3 44 45 4C -7 48 43 !>0 51 'A U 54 ~.i K '*'. 58 '.t CO CI G2 « C4 GS ES C7 C3 C9 /O (1 12
111:11111111111111111111111111111111111111
lOENTFICATION
030000UO
j: 71 75 7! 77 76 J3 30
11111111
FORMAT (10X, 2F10.3)
X - Horizontal distance of well from boundary intersection, ft.
Y - Vertical distance of well from lower boundary, ft.
IB2
Well
IB1
I-
NOTE: For parallel boundaries, X(l) is the distance to IB1 and
Y(l) is the distance to IB2; thus well #1 becomes the
origin of the parallel boundaries system and all remaining
locations are measured with respect to well #1 (i.e.,
X(2) is the horizontal distance from wel1 #1 to well #2, etc.)
51
-------
WELLPROP CARD
(There will be one WELLPROP card for each well)
UELLPI
•V FOP
./COMMENT
STATI t *
NUMBER
10300
12345
l'l 1 1 1
R|
p
5
0
G
1
DP
0000
? » 9 n
1111
BU
DOOOO GOOu
11 i: 13 M 15 IS 17 IB 13 ~3
1111111111
VIS
FC
100 0 0000
!i 2: 23 i; K 26 :; 28 29 30
1111111111
PERM
FTRiM S1
DCCOOOOOOO
J' 32 33 .» 35 36373*33 40
1111111111
THK
HATEMENT
000 000000
4! 42 43 44 45 46 -J 48 49 50
1111111111
POR
0000000000
51 52 53 54 'A X SI 58 £9 CO
1111111111
CQMP
3000000800
il C2 6'J 64 65 66 67 68 69 70
1111111111
f
ou
ii ;2
1 1
SKIH
1 -NT 'ICAriON
3000000
n ;4 TJ •& n 'is 79 BO
11111111
BW -
VIS -
PERM -
THK -
POR -
COMP -
SKIN -
FORMAT (10X, 7F10.3)
Formation volume factor of injected (or produced) fluid,
RVB/STB.
Reservoir fluid viscosity, cp.
Areal effective permeability, md.
Reservoir thickness, ft.
Reservoir porosity, fraction
Total system compressibility, bbl/MMbbl/psi
Well bore skin factor
When observing a highly compressible s.ystejp (e.g,, a gas reservoir),
BW should be evaluated at an average reservoir pressure; if BW
cannot be estimated, enter a value of 1.0, run the program, check
the calculated pressures, re-evaluate BW and run the program a
second time. For a gas system, BW may have units of RVB/MCF
for well rates in MCF/day.
52
-------
RATE CARDS
(There will be NRATE RATE cards per well
as specified on the WELL card)
ftATE
RATE
5 =
f\ Foil
LscOMner:
IATEMENT
NUMBER
010 00
12345
lj" 1 1 1
1
3
6
fl
rr
0000
7 C 9 10
1111
GK2>
oa>
n n
OOOOOGOOOO
11 12 n v. i; is n i; is ;a
1 1 1 1 1~1 n i
QTIME*a>
QTIME<1>
ft n InC
0 0 1 0 9 0 C 0 G 0
il 22 :3 2< 23 33 :l :0 29 ;0
1111111"!!
RTRAN STATEMENT
IGCDOOOOGOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOG
i' 32 3: ii :; x 3i 31 39 49 41 42 43 44 45 4e -: 49 o so 51 52 53 S4 a :s s; se u GO EI 62 u E« ra EC c? ss ES 70 )i 72
111111111111111111111111111111111111111111
IDENTIFICATION
030000UO
O 74 n 75 77 73 79 80
11111111
FORMAT (10X, 2F10.3)
Rate of well until OJIME(l), STB/day, (positive for injection
and negative for production).
QTIME(l) -
Q(2) - etc.
Cumulative time to end of rate Q,(l), days (all times are
measured from TSTART on well #1 in multiple well situations).
53
-------
RADIUS CARDS
IF IFRAC > 0 or IMAGE = 0 (on the
SELECT card), omit this card.
(There wil] be NRAD values as
specified on the SELECT card)
KHDIIJ
C^>l
COMMENT
IATEMENT
NUMBER
0009
1 2 3 4 t
1' 1 1 1
Pi
s
i
I
6
1
1
0000
7 II 9 ID
I'll
RADIUSCl)
00000 000
II 12 U It K IS 17 13 IS 20
11 111111
RADIUS<£>
F 3
10000 000
'i a :; K 23 is :> 28 :•: 30
11 1 1 1 1 1 ! 1
RADIUS<3>
F TRAN S '
IOCOO OGO
! 32 X, Ji r. 36 37 2' 35 40
11 1111111
RADIUSC4)
>.TEMEN"
10000 000
II4243«O«S-7««950
11 1111111
RADIUSC5)
00000 000
il 5253545SSt57M5SGO
11 1111111
RADIUS<6)
00000 800
Gl G2 fl C4 EJ CE C7 68 69 70
11 1 i 1 1 1 1 1
R
0
1 72
1 1
*DIUS<7>
IDENTIFKUriON
030 000
n 74 75 76 77 7! 79 10
1111111
FORMAT (10X, 7F10.3)
RADIUS(l) - Distance from well to observation point of pressure cal-
culation, ft.
RADIUS(2) - etc.
-------
VFRAC1 CARD
If IFRAC f 1, skip this page.
(There will be one VFRAC1 card
per well when required).
tfFRAQ
FC.I
^CMCNT
sum CUT
NUMBER
10 0 0 0
12345
l'l 1 1
1
$
i
§
U
s
0000
7 6 9 13
1111
XF
OGGO 00000
ii 12 u 14 1: K 17 a a :o
1111111111
FORTRAN STATEMENT
lOQOOOOObjOCCOOdOOCUOOOOdOOOOOGOOGGaCOOOOOOOOOOOOOOO
!1 i: ?3 K 23 23 21 23 2S i3 3! 32 jl jl 3'. it 37 3" :» 4 j 41 41 43 44 « 45 -7 41 49 SO 31 52 3 ti !'j :c 57 53 ;9 E3 61 52 E) 84 Eli EG 07 C8 E9 70 /I 72
1 1 1 1 1 1 1 1 ! 1 1 1 1 : n 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
lOENTIFICAHON
ODOOOOUO
/3 14 75 7S 77 7B 79 10
11111111
FORMAT (10X, F10.3)
XF - Fracture length (or 1/2 length from well bore), ft.
VFRAC2 CARDS
(There will be NRAD cards as
specified on the SELECT card),
WFRAQ
fc'FRACj
rt_EA*
\JCOUVEN:
sacrdftn
NUMBER
IOOOO
11 1 1
3
|
o
1
as
1
i
0000
1~1 1
XV<£>
XVC1)
0
0001 1 00030
11 12 13 14 IS IS 17 C ;9 23
1 1 1 1 1 1 ~ 1 '. 1
YVC2>
VV<1)
OFC
3 0 0 1 1 0 B C t Q
1 22 :.-;< 21 25:120 29:3
1 1 1 1 1 1~1 i 1
'
RTRAN STATEMENT
)GC9UOOOOOOOOOGOOOOagOOOQOOOOOOOOOOOOOOOOO
r :; 33 >< ' '. 26 :; ;' r 40 41 42 43 44 <5 46 -7 49 49 so si 52 53 54 55 st 57 sa sa c; ei 62 ft a K> f.r. c; 60 69 73 n n
111:11111111111111111111111111111111111111
lOENTIFICAilON
03GOOOUO
/3 74 15 75 77 73 79 83
11111111
FORMAT (10X, 2F10.3)
XV(1) - Horizontal distance from well to observation point of pressure
calculation, ft.
YV(1) - Distance from fracture to observation point of pressure cal-
culation, ft.
XV(2) - etc.
XV
XF
+
-N
observation point
YV
55
-------
HFRAC CARD
IF IFRAC f 2, skip this page.
(There will be one card per well, when required)
riFRAC]
rVFUl
U' COMMENT
sun err
NUMBER
010 a o o
IJ2 J 4 1
ih i i
£
i
6
1
0000
7 » 9 1C
1111
XF
1000 OOGOO
11 a n M is is ij n x n
1 1 1 1 1 1 1 1 M
PERMZ
FC
100000 OCD
I2223?<2S262J25M!3
M 1 1 11 1 1 ! 1
ZF
RTRAN S'
1GCP 00000
n 31 x M 35 3$ 37 :< 39 ,2 3 4 5
1111
Si
s
i
i
E
1
i
0000
7 II 9 ID
1 1 1
RADIUSU)
30000 000
11 12 a K 15 IS 17 13 19 :3
11 11111 1
RADIUS<2>
F :
10000 OC3
3 n 3 2< 23 35 2) 28 39 53
11 1111111
RftDIUS<3>
F TRAN S
OOCDO 000
1! 32 31 J4 35 36 31 3' 39 40
11 1111111
RABIUSC4>
•/.TEMENT'
00900 000
II 42 434)45 46-74349 SO
11 1111111
RADIUS<5>
00000 000
il 22 S3 S4 K it S7 S3 M C3
11 1111111
R AD I USC 6 >
10000 000
il 62 61 M K K C7 61 C9 10
I 1 1111111
^
00
II 72
1 1
ADIUSC7)
IDENTIFICAflON
oao ouo
13 74 75 J6 77 78 13 M
1111111
FORMAT (10X, 7F10.3)
RADIUS(l) - Distance from well to observation point, ft.
RADIUS(2) - etc.
NOTE: This is the last possible card in the well sequence; return to the
well card until NW (on the SELECT card) well sets have been input.
56
-------
IMAGEP CARDS
If IMAGE = 0, omit these cards
(There will be NRAD cards).
JMAGEPI s XP<:E>
jlMAGE
.v^
ScumBT.
ST, -EMENT
NUMBER
010 0 0 0
12345
I'l 1 1
-J
S
1
s
u
6
1
"I 1
0000
7 t 9 10
1 1 1
XPCO
1 i
)DO 000000
1 13 13 14 'A IS 17 \» K :3
1 1 1 1 1 i~m
VP<2>
vpa>
r i FC
000 000060
n :i :: v r> K r< K x ;o
1 1 11 1 r 1 1 1
i
RTRAN STATEMENT
0 G C 0 0 ti 0 0 0 G 0 0 0 0 0 0 0 0 0 0 Q 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3! 32 3i H 3; 36 37 34 39 40 41 42 43 41 45 40 .7 48 49 90 SI 52 S3 54 K X SI 56 59 CO El C2 tl 64 CS 65 67 63 6' 73 7; 12
1 1 1 '. 11 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 11 1 1 1 1 1 1
|
'
IDENTIRCAnON
03000000
/; 74 75 7E 77 78 73 80
11111111
FORMAT (10X, 2F10.3)
XP(1) - Horizontal distance to observation point from boundary inter-
section, ft.
YP(1) - Vertical distance to observation point from lower boundary, ft,
. observation point
YP
IB2
Well
i o i
XP
XP(2) - etc.
NOTE: For the parallel boundaries case, XP and YP are distances from
well #1.
57
-------
DIP CARD
If IDIP = 0 (on the SELECT
card), omit this card.
.DIP ai
(DIP 1
(k^' FOR
\f COHHCMT
telTVTfCNT
NUMBER
010 0 0 0
12345
1J1 1 1~
I
u
E
1
0000
7 II 9 10
1111
1 DELH<8>
DELH<1>
r r
0000000000
11 12 13 M 15 IB 17 13 ii 20
1 1 1 11 1~H 1
(There w
1 DELrK9>
DELrK£>
r rFC
0000000009
!l 22 :2 2< 25 28 27 28 29 23
1111111111
ill be NRAD
IDELHC10)
DELJ-K3)
C •" "> A
RTftANr S-
ocoooooooo
3! 32 X> ii K 36 37 31 33 40
IIKIIIlll
values) .
IDELHU1)
DELHC4)
•j >• r K
"ATrlMETMT
100CQOOOOO
II 42 41 44 45 46^7 41 49 SO
1111111111
|DELH<1£)
DELH<5)
r r
0000000000
SI 52535455505758:960
1111111111
1 DELH<13>
DELH<6)
r r
0000000000
11 G2 n 64 £5 8S C7 68 69 70
1111111111
rDjELH<14)
DELH<7>
_Jl ,„
JO
n 73
1 1
iniDFionoN
oaooouuo
11 74 75 76 77 78 79 80
11111111
L
DELH(l) -
FORMAT (10X, 7F10.3)
Vertical distance from we11 bore to observation point for
pressure calculation (a positive value indicates a lower
position), ft.
DELH(2) - etc.
58
-------
EXAMPLES
Single Well - Constant Rate
Two Well - Constant Rate
Single Well - Variable Rate
Single Well - Skin Factor (damage)
Single Well - Skin Factor (improvement)
Single Well - Partial Penetration
Single Well - Vertical Fracture (wellbore pressure)
Single Well - Vertical Fracture (reservoir pressure)
Single Well - Horizontal Fracture
Single Well - Leaky Aquifer (Case 1)
Single Well - Leaky Aquifer (Case 2)
Single Well - Intersecting Sealing Faults
Single Well - Parallel Sealing Faults
Sfngle Well - Dipping Reservoir
59
-------
f?ADIL
8
j
->
a
in
O
M
U
RATE
I
WELLF
WELL
flME
SELEC
riTLE
J !!
f^_i f np v>
STUTEM^T
NUMBER
;io ; o o
lii 3 4 5
ih 1 11
I
2|2 2 2 2
,3,,3
Sl5 55 ,
6JS 6 6 6
7I7777
88888
9' ' 9 9 9
l|2 1 4 S
Sj .292 1000. . j
r
I
1
i
0
i
1
t
3
5
6
7
8
9
1714. J 1
DP 1. 1. 50. 45. 15 7.5
1 17. 0.0
3650.
1
1
112000000 0.0 j
SINGLE WELL EXAMPLE — CONSTANT INJECTION RATE
f L .. . P -1 ' 1 .1
•n -a m TmhfOrn'Ti'RAhin 3T/sTENiENT nij M
00000 , 0 0 0 0 0 0 , 0 0 0 0 0 J 0 0 G 0 C 0 0 0 0 0 0 0 0 M 0 Q , 0 0 0 0 0 0 i 0 0 0 0 0 0 i 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 8 9 10 II 12 U 14 ISIS 17 10 192021 22 23 24 25 28 27 28 20 30 3132 33 34 35 36 37 39 39 « 4- 42 13 44 45 46 47 48 49 50 51 52 S3 54 55 56 57 58 59 60 61 62 63 84 65 6S 87 63 69 70 71 72
1111111111111111111,1111111111111101111111111111111111111111111111
22222,22222222222222222222222222,222222222222222222222222222222222
3 3 3 3 3 3 3 3 3 , 3 3 3 3 x t 3 3 3 3 3 3 „ 3 3 3 3 3 3 * 3 3 3 ,, 3 3 1 3 3 3 3 3 tt 3 3 3 3 3 3 t 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
5 5 5 5 5 5 5 c 5 5 e 5 5 e 5 5 5 < 5 5 5 5 5 ( 5 5 5 5 5 5 5 c 5 ti 5 1 5 5 5 i 5 i 5 5 5 5 < 5 5 5 5 « 5 5 5 5 5 5 5 5 5 5 5 5 5 5
666666666666,66666666666666666:66666666666666166666666666666666666
77777777,777777777,77,77777777777777777777777777777777777777777777
888888888888888888888888888888888888888888888888888888888888888888
9 9 9 9 9 9 j 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — CONSTANT INJECTION RATE
INITIALIZATION DATA:
NT= 1 NUMBER OF
NW= 1 NUMBER OF
NPAD= 2 NUMBER OF
TIMES AT WHICH PRESSURE IS TO BE CALCULATED
WELLS TO BE CONSIDERED
POINTS AT WHICH PRESSURE IS TO BE CALCULATED
AQUIFER CHARACTERISTICS TO BE CONSIDERED
IVIS =
IMAGE=
ILEAK=
IDIP=
IPENT=
IFRAC=
IREF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
0 FRACTURE ANALYSIS? NO
I REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT
CAPHT
CAPKB
CAPHB
ANGLE
IB1 =
IB2 =
PI =
DW=
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY OF OVERLYING BED {MD)
THICKNESS C3F OVERLYING BED (FT)
PERMEABILITY OF UNDERLYING BED (MD)
THICKNESS OF UNDERLYING BED (FT)
ANGLE OF BOUNDARY INTERSECTION (DEG)
BOUNDARY 1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSI)
DENSITY OF RESERVOIR FLUID (LB./CU. FT.)
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
ro
TSTART
PARTHK
PERMZ=
RADSKN
PERM=
NRATE=
VIS*
SKIN=
POR=
TINS=
THK=
VISN=
BW =
COMP =
RW =
X=
XF =
Y=
ZF=
DPENT=
0.0
0.0
0.0
LOO.00
50.00
I
I.000
0.0
0.150
0.0
45.00
0.0
I.00
0.00000750
0.583
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATE
-------
PRESSURE AT TIME 3650.000 (DAYS)
POINT RADIUS FROM
NUMBER REFERENCE WELL
• 1 0.292
2 1000.000
PRESSURE
(PSIA)
1291.857
416.441
CO
-------
1
•,_
5
m
5 5 5 5 5 5 5 5 5 5 . 5 5 5 , 5 5 5 5 5 . 5 5 5 5 5 5 5 . 5 5 5 . 5 5 5 5 5 . 5 5 5 5 , 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 b
S666666 . .6 .66 6 6 6 6666666666 6 6 j 6 6 66 66 6 66 66 6 6 66666666666 G6 666666 66666 6
r 777777777777 7 77 ;77 ] 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
888888888888888888888888888888888888888888888888888888888888888888
199999999999999999999999999999999999*999999999999999999999999999999
7 1 9 10 II IJ OH B IS 17 » "120 21 22 23 24252(2721 29 30 31 32 3134 35 36 37 31 39 40 4142 « « 45 4847 41 49 SO 51 52 53 54 55 51 57 SB 59 6061 tt 63 64 69 66(7 (B 69 70 71 J2
IDCNTIFICATION
00000000
73 74 75 76 77 78 73 80
11111111
22222222
33333333
4 A A K A A A It
4414444
55555555
66666666
77777777
88888988
99999999
73 74 75 76 J7 78 79 80
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
TWO WELL EXAMPLE ~ CONSTANT RATE CASE
INITIALIZATION DATA:
NT= 1 NUMBER OF
NW= 2 NUMBER OF
NRAO = I NUMBER OF
TIMES AT WHICH PRESSURE IS TO BE CALCULATED
WELLS TO BE CONSIDERED
POINTS AT WHICH PRESSURE IS TO BE CALCULATED
en
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IVIS =
IMAGE=
ILEAK=
IDIP=
IPENT=
IFRAC=
IREF=
0 INJECTED FLUID TO HAVE VARIABLE
0 AQUIFER CONFINED BY BOUNDARIES?
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED?
0 FRACTURE ANALYSIS? NO
2 REFERENCE WELL FOR PRINTING
VISCOSITY? NO
NO
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT-
CAPHT-
CAPKB*
CAPHB=
ANGLE'
IB1=
IB2 =
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY OF OVERLYING BED (MD)
THICKNESS OF OVERLYING BED (FT)
PERMEABILITY OF UNDERLYING BED (MOI
THICKNESS CF UNDERLYING BED (FT)
ANGLE OF BOUNDARY INTERSECTION (DEG)
BOUNDARY 1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESFRVOIR PRESSURE (PSD
DENSITY OF RESERVOIR FLUID (LB./CU. FT.
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL I
TSTART=
PARTHK=
PERMZ=
RAOSKN=
PERM*
NRATE*
VIS=
SKIN=
POR=
TINS=
THK=
VISN=
BW=
COMP =
RW =
X=
XFs
Y=
ZF=
DPENT=
0.0
0.0
0.0
100.00
50.00
1
1.000
0.0
0.100
0.0
45.00
0.0
1.00
0.00000750
0.250
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION CFT)
VERTICAL RESERVOIR PERMEABILITY (MD)
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MO)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS CFT)
NEW FLUIO VISCOSITY (CP)
FORMATION VOLUME FACTOR (R8/STB)
SYSTEM COMPRESSIBILITY (1/PSI)
WELLBORE RADIUS (FT)
PEAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL RATE
(STB/DAY)
CUMULATIVE TIME
TO END OF RATE
DAYS
200.00
150.00
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 2
CTl
TSTART=
PARTHK=
PERMZ=
RADSKN=
PERM=
NRATE=
VIS =
SKIN=
POR =
TINS =
THK =
VISN =
BW =
COMP=
RW =
X=
XF=
Y=
ZF=
DPENT=
50.00
0.0
0.0
100.00
50.00
1
1.000
0.0
0.100
0.0
45.00
0.0
1.00
0.00000750
0.250
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY (MO I
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY CMD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS!
RESERVOIR THICKNESS IFTI
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY Cl/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL RATE
(STB/DAY)
100.00
CUMULATIVE TIME
TO END OF RATE
DAYS
150.00
DISTANCE TO POINT X FOR WELL
CHANGE IN
POINT ELEVATION
NUMBER (FT)
1 0.0
RADIUS
(FT}
70.00
DISTANCE TO POINT X FOR WELL 2
CHANGE IN
POINT ELEVATION RADIUS
NUMBER (FT) (FTI
0.0
30.00
-------
PRESSURE AT TIME 150.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
1 30.000 100.768
00
-------
o-i
S
-f
-
<0
10
o
M
0
2
RADILJ|S| .292
RATE |3
0 0 0 0 0 0 0 0 0 0 « 0 0 0 0 si 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 1 9 10 II 12 '3 14 ISIS 17 13 192021 22:3:4252(272823:3 3i K 33 34 15 36 37 :l 39 40 4142 43 U «5
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — VARIABLE RATE CASE
INITIALIZATION DATA:
NT=
NW=
NRAD=
NUMBER OF TIMES AT WHICH PRESSURE IS TO BE CALCULATED
NUMBER OF WELLS TO BE CONSIDERED
NUMBER OF POINTS AT WHICH PRESSURE IS TO BE CALCULATED
AQUIFER CHARACTERISTICS TO BE CONSIDERED;
IVIS=
IMAGE=
LEAK=
DIP=
PENT=
FRAC =
REF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAK.AGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
0 FRACTURE ANALYSIS? NO
1 REFERENCE KELL FOP PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IBl =
IB2=
PI =
DW=
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS DF
OF OVERLYING BED (MOI
OVERLYING BED (FT)
OF UNDERLYING BFD IMD1
UNDERLYING BED (FT)
ANGLE QF BOUNDARY INTERSECTION (DEG)
BOUNDARY 1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE IPSI)
DENSITY OF RESERVOIR FLUID (LB./CU. FT,
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
TSTART
PARTHK
PERMZ=
RADSKN
PERM=
NRATE=
VIS =
SKIN=
POR =
TINS =
THK =
VISN =
BW =
COMP =
RW =
X=
XF =
V =
ZF =
DPENT=
0.0
0.0
0.0
100.00
50.00
3
1.000
0.0
0.150
0.0
50.00
0.0
1.00
0.00000750
0.583
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATF (DAYS)
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY (MD)
RADIUS EFFECTED BY SKIN (FT)
ARFAL RESERVOIR PERMEABILITY (MO)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (1/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
1
2
3
WELL RATE
(STB/DAY)
200.00
150.00
400.00
CUMULATIVE TIME
TO END OF RATE
DAYS
30.00
60.00
70.00
DISTANCE TO
POINT
NUMBER
POINT X FOR WELL 1
CHANGE IN
ELEVATION RADIUS
(FT) (FT)
0.0
0.29
-------
PRESSURE AT TIME 70.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
1 0.292 213.723
ro
-------
CO
5i
n
^
•t
>~-
OJ
m
it
n
o
M
O
i
?ADIU|S| .292 1000. ,
?ATE
JELLP
JELL
TIME
SELEC
TITLE
•j >n
(^— FOR "^
t/ccMMon
STATEM^IT
NUMBED
:io j. it »
ij: 3 4 s
1M f 1 1
212222
i
.3 . . 3
4j4 4 4 4
Sis 5 5
1
6|6 6 6 8
77777
88888
3'' 9 99
'2345
1714.
*PP 1- 1- 50. 45. .15 7.5 2.0
1 117. 0.0
3650.
112000000 0.0 \
SINGLE WELL EXAMPLE -- SKIN FACTOR (DAMAGE)
!
! „ , ,,i;OF,-,'RAr, STATEMENT,
) 0 0 0 0 0 '.' 0 0 0 0 0 0 '; 0 0 0 0 0 '^ 0 0 0 0 C 0 0 0 0 0 ^ 0 0 0 0 0 Q 0 '; 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I 1 3 "0 11 12 11 14 15 K 17 18 13 20 21 22 23 74 25 26 27 28 79 39 31 32 33 34 35 36 37 38 39 40 41 42 '3 14 45 46 47 48 49 58 3! 52 53 54 K 5S 57 58 59 60 61 62 63 64 65 66 67 66 69 70 71 72
1 1 11 1 1 1 1 1 1 1 1 11 1 11 1 1 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 1 . 1 . 1 1 1 1 1 1 1 1 1 1 f 1 1 1 1 1 1 1 1 1
222222. 22222222222222222222 222.. 22222 222222222222222222222222222222
J 3 3 3 3 3 3 3 3 3 . 3 3 3 3 . . 3 3 3 3 3 3 . 3 3 3 3 3 3 3 3 3 3 3 3 3 . . 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
14444444444 U4444 4444. 4444444 44444444444444. 4. 44444444444444 4444444
55555555.55.55.555.55555.55555555.55555555.55555 55555555555555555
5666G6666B 6G6. 6 66666B66666666666666. 666. 66666666666666666666666666 6
777777777.777777777.77.777777777777777777777777 7777777777777777777
(88888888888888888888888888888888888888888 888888 88888888888888888
9999999 " 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 " 9 9 9 9 9 9 94.' 999 9"9 993999999999999999999
6" 6 9 10 II 12 13 M 15 16 17 11 11 20 21 21 23 24 2S 26 27 2t 29 30 31 32 U 34 35 36 37 38 39 40 41 42 43 44 45 4J 47 48495051 52 53 54 55 56 57 SI 99 H 61 62 63 M 65 66 67 66 69 70 71 >2
IDENTIFICATION
00000000
73 74 75 76 77 78 79 80
11111111
22222222
33333333
44444444
55555555
6R666666
77777777
88888 988
99999999
73 74 75 76 77 78 79 60
MC-HtlllST
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLF WELL EXAMPLE — SKIN FACTOR (DAMAGE)
INITIALIZATION DATA:
NT= 1
NW= 1
NRAD= 2
NUMBER OF TIMES AT WHICH PRESSURE IS TO BE CALCULATED
NUMBER OF WELLS TO BE CONSIDERED
NUMBER OF POINTS AT WHICH PRESSURE IS TO BE CALCULATED
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IVIS=
IMAGE=
ILEAK=
IDIP=
IPENT=
IFRAC=
IREF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
0 FRACTURE ANALYSIS? NO
1 REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IB2=
PI =
DW=
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
OF OVERLYING BED (MD)
OVERLYING BED (FT)
OF UNDERLYING BED (MD)
UNDERLYING BED (FT)
ANGLE OF BOUNDARY INTERSECTION (DEG)
BOUNDARY 1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OP LEAKING? SEAL
INTIAL RESERVOIR PRESSURE
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL I
tn
TSTART=
PARTHK=
PERMZ=
PADSKN=
PERM =
NRATE=
VI S=
SKIN=
POR=
TINS*
THK=
VISN=
BW=
COMP=
PW =
X*
XF =
Y=
ZF=
DPENT=
0.0
0.0
0.0
100.00
50.00
1
1.000
2.00
0.150
0.0
45.00
0.0
1.00
0.00000750
0.583
0.0
0.0
0.0
0.0
0.0
TIME T3 START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY IMD)
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION
RESERVOIR THICKNESS i FT )
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STBI
SYSTEM COMPRESSIBILITY I1/PSI )
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
(DAYS)
RATF
NUMBER
WELL RATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATF
DAYS
0.0
DISTANCE TO
POINT
NUMBER
POINT X FOR
CHANGE IN
ELEVATION
(FT)
WELL
1
RADIUS
(FT)
1
2
0.0
0.0
0.29
1000.00
-------
PRESSURE AT TIME 3650.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
I 0.292 1506.983
2 1000.000
-------
3>
«
^
&
0
10
s
M
O
?ADll
?ATE
4ELLP
JELL
TIME
SELEC
TITLE
JsSeiT
IXTEM^T
NUMKR
;|o ; o o
12345
1 1 f 1 1
2J2 2 2 2
I, 0
r-3
44444
5l555
1 "
6J6666
7l?777
8|8888
gl'999
ih J 4 5
5| .292 1000. i
1714.
SPP 1. 1. 50. 45. .15 7.5 1-2.0
1 1 7. 0.0 j
3650. \
112000000 0.0 j
SINGLE WELL EXAMPLE — SKIN FACTOR (IMPROVEMENT)
!
TI TI it TiTihi"OF|"TiRAISi £TATEMENYini n •» n
i 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 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
7 8 9 10 11 12 13 M 1516 17 11 102021 22 23 !< K 21 21 28 29 30 31 32 J3 34 35 3£ 3? 33 39 40 f f. i; M <5 « 47 41 49 SO 51 52 53 S4 55 it 57 58 59 60 61 S2 S3 64 65 66 87 69 69 70 71 72
1111111111111111111,111111111111111,111111111111111111111111111111
!22222, 22222222222222222222222,, 222222 22222222222222222222222222222
1 3 3 3 3 3 3 3 3 3 , 3 3 3 3 ,, 3 3 3 3 3 3 , 3 3 3 3 3 3 3 3 3 3 3 3 .-,, 3 3 3 3 3 3 3 3 3 3 3 3 3 3 . 3 3 3 3 3 3 3 3 3 3 3 3 3
H444444444 H44 444444 ,4444444444444^44444444 ,44444 C4444 444444444444
j 5 5 5 5 5 5 5 „ 5 5 , 5 5 „ 5 5 5 , 5 5 5 5 5 , 5 5 5 5 5 5 5 5 , b 5 5 5 5 5 5 5 , 5 5 5 5 5 „ „ 5 „ , 5 „ 5 5 5 5 5 5 5 5 5 5 5 5
5666666666666 ,666666666666666666666,6 SB, 6666666 ,666666666666666666 6
1 7 7 7 7 7 7 7 7 . 7 7 7 7 7 7 7 7 7 „ 7 7 . 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 . 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
388888888888888 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 « 8 8 88 ,88888888888 ,888888888888
3 9 9 9 9 9 9 ' 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ' 9 9 9 9 9 9 9 i 9 9 ' 9 9 " 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
S" 8 9 10 II 12 13 M 15 18 17 18 '1 20 21 2223242526 27 282930 31 12 33 34 35 31 37 31 39 4041 ««1 44 4S4« 47 484J 5051 SJ5J 54 555*5758 SJ SO llWt) (4 8568 17 MM 70 71 M
IDENTIFlainON
00000000
n 74 75 76 77 78 i9 60
11111111
22222222
33333333
44444444
55555555
6R666666
77777777
88888888
99999999
73 74 75 16 77 78 79 80
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — SKIN FACTOR (IMPROVEMENT)
INITIALIZATION DATA:
NT= 1 NUMBER OF
NW= 1 NUMBER OF
NRAD= 2 NUMBER OF
TIMES AT WHICH PRESSURE IS TO BE CALCULATED
WELLS TO BE CONSIDERED
POINTS AT WHICH PRESSURE IS TO BE CALCULATED
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
- oo
IVIS =
IMAGE
ILEAK
IDIP=
IPENT
IFRAC
IREF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
0 FRACTURE ANALYSIS? NO
1 REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IB1 =
IB2 =
PI =
DW=
0.
0,
0.
0.
0,
0
0
0
0
0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
OF OVERLYING BED (MD)
OVERLYING BED IFT)
OF UNDERLYING BED (MD)
UNDERLYING BED (FT)
ANGLE OF BOUNDARY INTERSECTION (DEG)
BOUNDARY I SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSI)
DENSITY OF RESERVOIR FLUID tLB./CU. FT,
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
TSTART
PARTHK
PERMZ=
RADSKN
PERM =
NRATE=
VIS =
SKIN=
vo
TINS =
THK=
VISN =
BW =
COMP =
RW«
X=
XF =
Y =
ZF-
DPENT=
0.0
0.0
0.0
100.00
50.00
1
1.000
-2.00
0.150
0.0
45.00
0.0
I.00
0.00000750
0.583
0.0
0,0
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY IMD)
RADIUS EFFECTED BY SKIN (FT*
ARFAL RESERVOIR PERMEABILITY «MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID
-------
PRESSURE AT TIME 3650.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
I 0.292 1076.731
2 1000.000
-------
00
K>
J
^
£i
ID
<0
IO
O
eg
3
3
RADIU|S| .292 1000. 1
5!ATE
1 1714. i
4ELLPJ?
>ENT |
4ELL |
FIME
SELEC
riTLE
V FOR
JWTBI^T
NUMBER
]|0 I 0 0
ih 1 1 1
1
2|2 2 2 2
.3. .3
4|4 4 4 4
1
Sis 5 5
1 *
E|6 6 6 6
77777
88888
9!' 9 99
l|2 3 4 5
T
8
i
\
0
i
2
3
/
5
6
1
8
;
PP 1. 1. 50. 45. .t5 7.5 1
10. 0.0 1
1 1 7. 0.0 j
3650. 1
112000010 0.0 \
SINGLE WELL EXAMPLE — PARTIAL PENETRATION
,,i;OF,-,-RAN,ST^T*igENT
00000 "000000" 00000 ^' 0000000000000 "OOOCOOOO^OO'j 000000000000000000000
7 8 9 10 11 1? 13 14 15 16 17 13 13 20 2' 22 ^3 24 25 26 27 28 29 30 31 32 33 34 35 3S 37 33 39 40 41 '! -3 *4 45 46 47 43 43 50 51 52 53 54 55 56 57 56 59 60 61 62 63 64 65 66 67 €8 65 70 71 72
1111111111111111111.1111111111.111.11111111.1111111111111111111111
22222.222222222222222222222222222222222222222222222222222222222222
3 3 3 3 3 3 3 3 3 . 3 3 3 3 .. 3 3 3 3 3 3 . 3 3 3 3 3 3 3 3 3 . 3 3 . 3 3 3 3 3 . 3 3 . 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
4444444444 H44444444. 444444444444444444444444444444444444444444444
:, 5 5 5 5 5 5 . 5 5 . 5 5 . 5 5 5 . 5 5 5 5 5 . 5 5 5 5 5 5 5 5 5 b 5 5 5 5 . . . -5 5 5 5 5 5 . 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
66666 6666666 .6 66666666666666 66666 6666 E66666666 .6666666 66666666666 6
77777777.777777777.77.7777777.7777777.7777777777777777777777777777
888888888888888888888888888888888888888888888888888888888888888888
9 9 9 9 9 9 " 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 * 9 " 9 9 9 9 9 9 9 9 " 9 9 " 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
« 7 | 9 1011 12 DM 15 1617 II 11 20 21 22 23 24 25 26 27 21 29 30 31 32 33 34 35 M 37 M 39 40 «1 « « 44 4$ 41 47 4141 SO 51 5253 54 9$ M 57 58 59(0 (1 12 83 64 65 66 67 61 69 70 71 )2
HC-HCMIST
1
IDENTIFICATION
00000000
13 74 75 76 77 78 79 Bfl
11111111
22222222
33333333
44444444
55555555
66666666
77777777
88888988
99999999
73 74 75 76 77 71 79 ID
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — PARTIAL PENETRATION
INITIALIZATION DATA:
NT= 1
NW= 1
NP AD= 2
NUMBER OF TIMES AT WHICH PRESSURE IS TO BE CALCULATED
NUMBER OF WELLS TO BE CONSIDERED
NUMBER OF POINTS AT WHICH PRESSURE IS TO BE CALCULATED
00
ro
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IVIS=
IMAGE=
ILEAK=
IDIP=
IPENT=
IFRAC=
IREF =
0 INJECTED FLUID TO HAVE VARIABLE
0 AQUIFER CONFINED BY BOUNDARIES?
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
I WELLS PARTIALLY PENETRATING BED?
0 FRACTURE ANALYSIS? NO
1 REFERENCE WELL FOR PRINTING
VISCOSITY?
NO
YES
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IB1 =
IB2=
PI =
DW=
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
ANGLE OF
BOUNDARY
OF OVERLYING BED (MD)
OVERLYING BED
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
CO
CO
TSTART=
PARTHK=
PERMZ=
RADSKN=
PERM=
NRATE=
VIS=
SKIN=
POR =
TINS=
THK=
VISN =
BW =
COMP =
RW=
X=
XF =
Y=
ZF =
DPENT=
0.0
10.00
0.0
100.00
50.00
1
1.000
0.0
0.150
0.0
45.00
0.0
1.00
0.00000750
0.583
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION {FT)
VERTICAL RESERVOIR PERMEABILITY (MD)
RADIUS EFFECTED BY SKIN (FT)
AREAl. RESERVOIR PERMEABILITY (MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (1/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL PATE
(STB/OAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
DISTANCE TO
POINT
NUMBER
1
2
POINT X FOR WELL
CHANGF IN
ELEVATION
(FT)
0.0
0.0
1
RADIUS
(FT)
0.29
1000.00
-------
PRESSURE AT TIME 3650.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
I 0.292 2707.638
2 1000.000 416
CO
-------
CO
en
§
5
0)
1
I
fc'FRACf
/F£AC
/FRAC
/FRAC
/FRAC
VFRAC
RATE
4ELLP
JELL
FIME
SELEC
FITLE
L/*cowon
STOTEH^T
NUMBER
yio f o o
"l 2 3 4 5
1'1 1 1 1
1
2)2222
, 3
I3"3
41 A A A 1
4 4 4 *
5)555.
6)6666
1
7l?777
i
8J8 8 8 8
9h9S9
\\2 3 4 S
E| 5 50. 50.
2| 4 5. 5.
>| 3 I. 1.
JJ 2 .5 .5
31 o.o o.o
10.
1714.
>PP 1. 1. 50; 45.
1 17. 0.0
3650.
115000-00
SINGLE WELL EXAMPLE"— VERTICAL FRACTURE
i
1 „ „ ,, , j;OF,VRAN, STAVE WENT,
1
So o o o o '< o o o o o o •• o o o o 0'; o o o o o o o o o o? o o'.j o o Q o o o o o o'j? o o
1 7 9 9 1011 12 1314 1516 17 13 13:0 21 22 23 1425 26 27 21 29 30 31 32 H 3435 36 373833W41 42 43 4445 4S 47 49 49 5051 S2
11111111111111111111.111111111111111.1111.11111
222222.2222222222222222222222222222222222222222
3333333333 . 3333 .. 333333 . 333333333 . 3 . 3 . 3333 . .333
5 5 5 !> 5 5 5 5 . 5 5 . 5 5 . 5 5 5 . 5 5 5 5 5 . 5 5 5 5 5 .. 5 5 b 5 5 5 5 5 5 5 5 5 5 5 .
666666 6G6G 656.E 6 6666066666 6666666666666. 6666666
777777777 J777 7 7 777 7.77 j 7 777777 77777 77777 7777777
88888888888888888888888888888888888888888888888
9 9 9 9 9 9 9 '1 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 1 9 '' 9 9 9 9 9 2 9 9 9 9 "1 9
6'J 1 9 10 II n 13 H IS II 17 11 '' !0 21 22 23 !4 2526 27 21293011 3233 34 IS 3637 31 31 40 41 42 4J444S 4(474141 50 SI 52
.15
1
7
CWELLEDRE
•a
00^00
53 51 55 M 57
11111
22222
3333 .
5.5.5
66j66
77777
8 J888
99999
53 S4 55 51 57
00
5359
1 1
2.
.3
55
66
77
88
99
51 M
0
60
1
2
3
5
-
7
8
9
60
0
Cl
1
2
3
5
6
7
8
11
n
0
62
1
2
3
6
7
8
9
u
.5
0.0
\
1
1
i
PRESSURE)
•a i
uuu
63646S
1 1 1
222
333
555
666
7 ,7
888
99"!
«3MH
a
Q Bl D( H Q
66 67 61 69 7C
11111
2. .22
33333
.5555
66666
77777
88888
99991
66 67 61 69 70
JS
00
71 72
1 1
22
33
4»
4
66
77
8J
99
71 72
iDauuTomoN
00000000
73 74 75 76 )7 7« 79 10
11111111
22222222
33333333
«A A A A A A A
4444444
55555555
66666866
77777777
88888888
99999999
73 74 75 76 77 78 79 M
MC-M«(*IIT
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — VERTICAL FRACTURE (WELLBCRE PRESSURE)
INITIALIZATION DATA:
NT=
NW=
NRAD=
I NUMBER OF TIMES AT WHICH PRESSURE IS TO BE CALCULATED
1 NUMBER OF WELLS TO BE CONSIDERED
5 NUMBER OF POINTS AT WHICH PRESSURE IS TO BE CALCULATED
oo AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IVIS =
IMAGE*
ILEAK*
IDIP=
IPENT=
IFRAC=
IREF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
1 FRACTURE ANALYSIS? YES
i REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IB2=
PI =
DW=
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
ANGLE OF
BOUNDARY
OF OVERLYING BED
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
oo
TSTART
PARTHK
PERMZ=
RADSKN
PERM =
NRATE=
VIS =
SKIN =
POR =
TINS =
THK=
VISN=
BW=
COMP*
RW =
X=
ZF=
DPENT
0.0
0.0
0.0
100.00
50.00
1
1.000
0.0
0.150
0.0
45.00
0.0
1.00
0.00000750
0.583
0.0
10.000
0.0
0.0
0.0
TIME TO START OF FIRST RATE IDAYS)
LENGTH OF WELL PENFTRATION (FT)
VERTICAL RESERVOIR PERMEABILITY (MO)
RADIUS EFFECTED BY SKIN (FTI
AREAL RESERVOIR PERMEABILITY (MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (R8/STB)
SYSTEM COMPRESSIBILITY (l/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FTI (FTI
RATE
NUMBER
1
WELL RATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
POINT
NUMBER
1
2
3
4
5
DISTANCE TO
CHANGE IN
ELEVATION
(FT)
0.0
0.0
0.0
0.0
0.0
POINT X FOR WELL
X-LOCATION
(FT)
0.0
0.50
I.00
5.00
50.00
Y-LOCATION
(FT)
0.0
0.50
1.00
5.00
50.00
-------
PRESSURE AT TIME 3650.000 (DAYS)
RADIUS POINT
WELL NUMBER
1
RADIUS POINT
WELL NUMBER
1
RADIUS POINT
WELL NUMBER
1
RADIUS POINT
WELL NUMBER
I
RADIUS POINT
WELL NUMBER
I
NUMBER*
NUMBER*
NUMBER*
NUMBER*
PRESSURE (PSIA)
1019.39
PRESSURE (PSIA)
1019.12
PRESSURE (PSIA)
1018.31
NUMBER* 4
PRESSURE (PSIAI
991.75
PRESSURE (PSIA)
701.42
oo
oo
-------
00
vo
n
J
•»
S
m
n
o
i
fFRAC
JATE
JELLP
JELL
TIME
JELEC
TITLE
- a
^^OMCNT
smrm^n-
NUMBER
;|o;oo
IJ2 3 4 5
11 1 1 1
1
2)2 2 2 2
.J3..3
•'•14 444
sis s s ;
1 '
GJ6666
1
?b 7 7 7
i
8J8 8 8 8
9'' 9 9 9
50. 50. i
100.
1714. i
]P I. 1. 50. 45. .15 7.5
1 17. 0.0
3650.
111000001 0.0
SINGLE WELL EXAMPLE — VERTICAL FRACTURE CRESERVDIR PRESSURE
:. ' i 1 i ! 1 i ! I
* i -»•» ,APOF,-,-RAN,STAVEWENTJ , J - j Jj J
00000" 000000^00000^0000000000^00 ^OOQOOOOOO4!5! 000000s! 00^0000000 G|E<1* 00
7 B 9 10 11 12 13 M '5 16 t? IS W 20 21 22 23 24 25 28 77 28 2$ 30 31 32 33 34 35 36 37 31 39 40 41 42 43 44 45 46 47 46 49 50 51 52 53 54 55 56 57 51 59 60 61 02 63 S4 65 6B £7 68 69 70 71 Yi
1111111111111111111.111111111111111.1111.1111111111111111111111111
22222,22222222222222222222222222222222222222222222 2222222222 222
333333333 .3333 . .333333 .333333333 .3 .3 3333 33333333333333333333333
4444444444 1444444444. 4444444444444444444444 :4444444444444444444:44
5555555^55.55. 555. 55555. 55555. . 55555555555555 5555 555555 5555:
666666666666,6666666666666666666666666.666666666666666 66666666666
77777777.777777777.77.777777777777777777777777777777777777:7777777
88888888888888888888888888888888888888888888888 888888888888888888
999999l999999999999999999999999l9" 9999 9|H 999 95l999i^999^99l^sl99il9999?ll9
)
JiDormamoN
00000000
7] 74 75 76 77 18 79 80
11111111
22222222
33333333
44444444
,5555555
66666666
77777777
8888988
99999999
73 M 75 7» 77 78 79 80
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — VERTICAL FRACTURE (RESERVOIR PRESSURE)
INITIALIZATION DATA:
NT= 1
NH= 1
NRAD= 1
NUMBER OF TIMES AT WHICH PRESSURE IS TO BE CALCULATED
NUMBER OF WELLS TO BE CONSIDERED
NUMBER OF POINTS AT WHICH PRESSURE IS TO BE CALCULATED
10
o
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IVIS=
IMAGE=
ILEAK=
IOIP=
IPENT=
IFRAC*
IREF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
I FRACTURE ANALYSIS? YES
I REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE*
IB1 =
IB2=
PI =
DW=
0,
0,
0,
0,
0
0
0
0
0.0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
OF OVERLYING BED
-------
KESERVQIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL I
TSTART
PARTHK
PERMZ=
RADSKN
PERM*
NRATE=
VI S=
SKIN*=
POR =
TINS =
THK=
VISN=
BW=
COMP=
RW=
X=
XF=
Y=
ZF=
DPENT=
0.0
0.0
0.0
100.00
50.00
1
1.000
0.0
0.150
0.0
45.00
0.0
1.00
0.00000750
0.583
0.0
100.000
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYSI
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY IMD)
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MDI
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIMF TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (1/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
PEAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL RATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
POINT
NUMBER
DISTANCE TO POINT X FOR WELL
CHANGE IN
ELEVATION X-LOCATION
(FT) (FT)
Y-LOCATION
(FT)
1
0.0
50.00
50.00
-------
PRESSURE AT TIME 3650.000 CDAYS)
RADIUS POINT NUM8ER= 1
WELL NUMBER PRESSURE (PSIA)
1 744.07
ro
-------
10
CO
at
40
8
M
U
4
RADIUS
1FRAQ
?ATE j
CLLPR
JELL |
TIME 1
50. 300. 600. \
100. 100. 25. \
5000. i
]P 1. 1. 100. 50. .25 7.5 \
1 I 0.0 i
1000.
SELECfTJ 113000002 0.0 \
TITLE]
«- F T
ASaEHTJS
mra^r?
MtMER
MO 1 0 0
1 2 3 4 5
11111
2|2 2 2 2
J3 •
I M U
1 '•
4j j i «
4444
5l5 5 5 .
6(6 6 6 6
77777
88888
9 Z999
l|i 3 4 5
f
0
c
t
2
3
5
6
7
8
9
t
SINGLE WELL - HORIZONTAL FRACTURE
^ , „ ..FORTRAN, STAVEMENT
00000 * 000000 'JO 000000000*00*0000000 *•; 00000000000000 0000000000000000
7 1 9 10 II 12 1314 IS 16 17 10 132021 22 23 24 25 2627 J»W 30 31 32 33 3435 3S 37 3« 39 <0 .;; 42 4344 « 46 4J 43:95301 52 53 54 55 56 57 5! 59 60 6162 63 64 65 66 6761 G9 70 71 72
1 11 11 1 1 It 1 1 It 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . 1 1 1 1 .1 1 1 1 11 1 1 1 1 1 11 1 1 11 1 1 1 11 1 1 1 1 1 1 1 11 M
22222.222222222222222222222222222222222222222222222222222222222222
3 3 3 3 3 33 3 3 . 3 3 3 3 . ; 3 3 3 3 3 3 3 3 3 3 . 3 . 3 3 3 3 . . 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
5555555. 55. 55. 55555555555. 5555555S555. 5555555555555555555555555555
66666 6666666. 6 666666. 666. 66666. S66666EE66666666666666666B6666G666 6
77777777.777777777777777777777777777777777777777777777777777777777
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ,8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
999999^999999999999992H3l9999999'9999*99999999999999999999999999999
; 1 9 10 n 12 13 H IS l( 17 » :1 TO 21 K 23 24 25 24272829 30 31 32 33 34 35 3637 3t 35 4041 4J*3 44 45« 47 4449 50 51 52 53 54 55 56 57 54 5960 S1C 63 6465666)68 69 70 H »2
nc-H«»«isr
I
IOEHT1FICWK*
00000000
73 74 75 76 77 U 75 SO
11111111
22222222
33333333
55555555
6B666666
77777777
88888988
99999999
n747i7i777lttBO
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL - HORIZONTAL FRACTURE
INITIALIZATION DATA:
NT= I
NW= I
NRAD = 3
NUMBER OF TIMES AT WHICH PRESSURE IS TO BE CALCULATED
NUMBER OF WELLS TO BE CONSIDERED
NUMBER OF POINTS AT WHICH PRESSURE IS TO BE CALCULATED
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IMAGE=
ILEAK=
IDIP=
IPENT=
IFRAC=
IREF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
2 FRACTURE ANALYSIS? YES
1 REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IBU
IB2=
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
OF OVERLYING BED (MO)
OVERLYING BED (FT)
OF UNDERLYING BED (MD)
UNDERLYING BED tFTI
ANGLE OF BOUNDARY INTERSECTION (DEG)
BOUNDARY 1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSI)
DENSITY OF RESERVOIR FLUID (LB./CU.
FT.)
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR HELL I
iO
en
TSTART
PARTHK
PERMZ*
RADSKN
PERM*
NRATE*
VIS =
SKIN=
POR=
TINS=
THK=
VISN=
BW=
COMP=
RW =
X*
XF=
DPENT=
0.0
0.0
100.00
100.00
100.00
I
1.000
0.0
0.250
0.0
50.00
0.0
1.00
0.00000750
0.250
0.0
100.000
0.0
25.000
0.0
TIME T3 START OF FIRST RATE CDAYS)
LENGTH OF WELL PENETRATION (FTI
VERTICAL RESERVOIR PERMEABILITY (MO)
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MD)
NUMBER OF PATES
VISCOSITY OF RESERVOIR FLUID CCP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION!
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP )
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (I/PS!)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL RATE
(STB/DAY)
5000.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
DISTANCE TO
POINT
NUMBER
2
3
POINT X FOR
CHANGE IN
ELEVATION
(FT)
0.0
0.0
0.0
WELL
RADIUS
(FT)
50.00
300.00
600.00
-------
PRESSURE AT TIME 1000.000 (DAYS!
RADIUS POINT NUMBER= 1
WELL NUMBER PRESSURE IPSIA)
PROXIMATIONS FOR HORIZONTAL FRACTURE FAIL DUE TO RADIUS LIMITATIONS FOR WELL I RADIUS= 50-00
I 1541.36
RADIUS POINT NUMBER= 2
WELL NUMBER PRESSURE (PSIA)
1 638.17
RADIUS POINT NUMBER= 3
WELL NUMBER PRESSURE IPSIA)
1 540.30
en
-------
10
RADIUS .292 IOOO. 1 1
FATE |
1714.
UELLPR3P 1. 1. 50. 45. .15 7.5
WELL || 117. 0. 0
frlME |
LEAK i
SELECT
friTLQ
Ji ™d
5>
n
4
ft
at
V
n
8
0
I 4-—- _l
mrnfyr
NUMBER
1
1
0*00
1111
2|2 2 2 2
4
5
6
7
8
9
3 . .3
4444
555 .
8666
7777
8888
2;999
2345
i
i$
0
1
2
3
4
5
6
7
8
9
1
3650. i
I. 100.
112001000 0.0 j
SINGLE WELL EXflHPLE -- LEflKY flQUIFER CCASE^I?
i : : : ' i ' ' !
j i _ L'OF " "R/-.N J3TA" "EME.NT"
00000 '1 000000 1]OOOOOz]00000000000000 1 9 10 n U OH KH 17 11" » 2122 23 24 25 Hit 2IM 3811)23] 34 UN J7 MM 44 41 O 4444541 47 4141 SO 51525354 5} H 575! i960 61 M U 64 M M 67 MM 10 n n
«-*•«• rsr
iDBmnamoN
00000000
Q747376777879IC
1 1 1 1 1 1.1 1
22222222
33333333
44444444
55555555
6666666E
77777777
88888988
99999999
71 74 75 78 77 71 71 K)f
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLF — LEAKY AQUIFER (CASE 1)
INITIALIZATION DATA:
NT=
NW*
NRAD =
1 NUMBER OF
I NUMBER OF
2 NUMBER OF
TIMES AT WHICH PRESSURE IS TO BE CALCULATED
WELLS TO BE CONSIDERED
POINTS AT WHICH PRESSURE IS TO BE CALCULATED
10
00
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IVIS=
IMAGE=
ILEAK=
IDIP=
IPENT=
IFRAC»
IREF=
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
I VERTICAL AQUIFER LEAKAGE? YES
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
0 FRACTURE ANALYSIS? NO
1 REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IB1 =
IB2=
Pl =
DW=
1.
100.
0.
0.
0.
0.
0.
000
00
0
0
0
0
0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
OF OVERLYING BED (MDJ
OVERLYING BED (FT)
OF UNDERLYING BFO (MD»
UNDERLYING BED (FT)
ANGLE OF BOUNDARY INTERSECTION IDEG)
BOUNDARY 1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSI)
DENSITY OF RESERVOIR FLUID (LB./CU. FT.)
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL I
TSTART
PARTHK
PERMZ=
RADSKN
PERM*
NRATE=
VIS=
SKIN»
POR=
TINS =
THK =
VISN=
BW=
COMP =
RW=
X=
XF^=
Y=
ZF =
DPENT=
0.0
0.0
0.0
100.00
50.00
1.000
0.0
0.150
0.0
45.00
0.0
1.00
0.00000750
0.583
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY (MD)
RADIUS EFFECTED 8Y SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (l/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL RATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
DISTANCE TO
POINT
NUMBER
POINT X FOR
CHANGE IN
ELEVATION
(FT)
WELL
RADIUS
(FT)
1
2
0.0
0.0
0.29
1000.00
-------
o
o
PRESSURE AT TIME 3650.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
1 0.292 807.695
2 1000.000 2.600
-------
.
s
i
m
1
s
z
RADII
?ATE
JELLP
CLL
TIME
LEAK
BELEC
S
?
T
TITLE!
J3 FOBd
iUimCjmi
NUMBER
MO 3 0 0
1 2 3 4 S
11111
2|2 2 2 2
3 3
4I4 4 4 4
5)555 i
I
6(6 6 6 6
7)7 7 7 7
i
8J8 8 8 8
gl'lggg
l|2 ) 4 S
3
0
6
1
2
3
4
5
6
7
8
9
.292 1000.
1714.
P I. 1. 50. 45. .15 7.5
1 17. 0.0
3650. (
.001 1000.
I 12001000 0.0
SINGLE WELL EXAMPLE — LEAKY AQUIFER (CASE 2)
-.^L'OF^VR/5^ _3TAVEME_NT
00000 <| 000000') 00000 2{ 00000000000000 4| 000^00000000^0000000000000000000
7 8 9 10 11 12 13 14 15 IE T7 18 19 20 21 22 23 24 K 26 27 !t ti 30 31 21 33 34 35 35 37 39 39 <0 41 42 '! 44 45 4t 47 48 49 M 51 52 5} 54 55 58 57 M 99 60 61 62 63 64 6S (S (1 SI 69 70 71 72
1111111111111111111 11111111111 111 111111111 11111111111111111111
22222 22222222222222222222222222 2222222222222 22 2222222222222222
333333333 3333 :333333 333333 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
44444444441444444444 4444444444444444 4444444444444444444444444444
5555555 55 55 555 55555 555555 55b555555 55 555 55 555555555555555
666666666666 66666666666666666666666666 66666666666666666666666666
77777777 777777777 77 77777777777777777777777777777777777777777777
888888888888888888888888888888888 88 888888-888888 888888888888888
999999 '5 9999999999999999999999999999999!! 99 ,'j 999999999999999999999999
1 7 1 > IDII 12 1314 1515 17 » "120 21 22 2324 25 28 27 21 29 30 3112 B 34 35 M 37 3139 « 41 4] «344 4S4«47 41 49 SO SI 52 53 54 55 M 57 SI 99(0(1 1253(4 S9WC7U 69 70 71 »
MC-NCtflCT
lOENTFICXTMN
00000000
73 74 75 76 77 78 79 M
11111111
22222222
33333333
44444444
55555555
66666666
77777777
88888988
99999999
73 74 75 71 77 78 79 10
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE
EXAMPLE — LEAKY AQUIFER ICASE 2)
INITIALIZATION DATAs
NT* I
NW= 1
NRAO* 2
NUMBER OF
NUMBER OF
NUMBER OF
TIMES AT WHICH PRESSURE IS TO BE CALCULATED
WELLS TO BE CONSIDERED
POINTS AT WHICH PRESSURE IS TO BE CALCULATED
o
ro
AQUIFER CHARACTERISTICS TO BE CONSIDERED:
IVIS*
IMAGE*
ILEAK*
IDIP=
IPENT=
IFRAC=
IREF*
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
1 VERTICAL AQUIFER LEAKAGE? YES
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED? NO
0 FRACTURE ANALYSIS? NO
1 REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB=
ANGLE=
IBl*
IB2*
PI =
DW=
0.001
1000.00
0.0
0.0
0.0
0.0
0.0
0
0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
ANGLE OF
BOUNDARY
OF OVERLYING BED (MD)
OVERLYING BED (FT)
OF UNDERLYING BED (MD)
UNDERLYING BED (FT I
BOUNDARY INTERSECTION (OEG)
1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSI)
DENSITY OF RESERVOIR FLUID ILB./CU. FT,
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
o
CO
TSTART
PARTHK
PERMZ=
RADSKN
PERM*
NRATE=
VI S=
SKIN=
POR=
TINS'
THK=
VISN=
BW=
COMP*
X=
XF =
Y=
ZF=
DPENT=
0.0
0.0
0.0
100.00
50.00
I. 000
0.0
O.L50
0.0
45.00
0.0
I. 00
0.00000750
0.583
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY (MD)
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MO)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (L/PSI)
WELLBCRE RADIUS (FT)
PEAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
(DAYS)
RATE
NUMBER
WELL RATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
DISTANCE TO
POINT
NUMBER
POINT X FOP
CHANGE IN
ELEVATION
(FT)
WELL
RADIUS
(FT)
1
2
0.0
0.0
0.29
1000.00
-------
PRESSURE AT TIME 3650.000 (DAYS I
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
i 0.292 1269.900
2 1000.000 394.516
-------
flMAGEFI 3 500. 250. 1 1
(IMflGEJ
_,
o
en
at
a
j
~*
m
«
g
S
3
IMAGED
RATE |
•JELLPF
.acATti
JELL
FIME
IMAGE
JELEC
TITLE
^% , FOR™
l/OOHCOT
SftTVTHCjn
NUMBER
.10 3 o o
I'll 1 1
1
2|2 2 2 2
•i3 • • 3
414 4 4 4
5l555 ;
1 '
CJ6666
717777
8|8888
ahsss
IJ2 3 4 5
2 50. 15. i
1 100. 30.
1714.
IP I. 1. 50. 45. .15 7.5 I
]N 100. 30.
1 1 7: 0.0
3650.
38. 0 0 i i
113010000 0.0 i |
SINGLE WELL EXAMPLE — INTERSECTING SEALING FAULTS
: i ; • , i
.-,.. T_
* * i* ^OF^'RAN SjTATEWENT a j J
0 0 0 0 0 '1 0 0 0 0 0 0 '; 0 0 0 0 0 ^ 0 0 0 0 0 0 0 0 0 0 0 0 Jj 0 0 '.' Q 0 ^ 0 0 0 0 '.' 0 0 0 0 0 0 0 0 0 JJ 0 °j 'J 0 0 0 0 0 0 0 0 0 0
1 II 9. in 11 19 11 11 13 Tfi 11 18 19 9n 71 97 91 71 9*i 9fi 97 91 79 3D 11 19 11 11 iS 3fi 37 18 14 in 11 19 11 11 H 11! 11 It Id 1ft *1 « M U w W « {• CO Cfi ct £9 ci ej C1 CC fil fit Co m n n
/ 0 9 IU 11 I/ IJ 14 13 IB If IB 19 fit l\ It /J <4 i3 /O *( U <3 <1U 01 it •!•) J4 J3 JO Jf JO J3 4U 41 44 44 M 43 40 41 48 49 311 31 92 3J 94 93 3O Of M 39 Ml 61 6? W 64 w* few O/ Ofl 69 (U (1 7Z
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 „ 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 j 1 1 1 1 1 1 „ 11 1 1 1 1 1 1 1 1 1 1 1 1
22222J2222222222222222222222222222. 2222222 J 222222222222. 2222222222
3 3 3 3 3 3 3 3 3 . 3 3 3 3 . . 3 3 3 3 3 3 . 3 3 3 3 3 3 3 3 . 3 3 3 3 . . 3 3 3 3 3 3 3 „ 3 3 3 3 3 3 3 . . 3 3 3 3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4 4 4 H 4 4 4 4 4 4 4 4 .. 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 , 4 4 4 4 4 4 4 4 4 4 4 4 4
5555555.55.55.555.55555.555555.5.15.555 j 555 ,5 55^555 55 5 55 555 5 5 5555 5
,
666666666666.6666666666666666666666666666666666666,666666666666666
77777777.777777777.77.777777777777777777 j 77777 77.77 777 77777 777777 7
888888888888888888888888888888888888888888888888888888888888888888
9 9 9 9 9 9 'J 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 * 9 9 9 " 9 9 9 9*1 9 9 9 9 9 9 9 * 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9
i<7 1 9 10 11 12 11 H 15 It 17 II V2021 22 23 24 25 IS J7 21 29 30 31 32 33 34 35 M 37 M 3)40 41 « OM «4S 47
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE
INTERSECTING SEALING FAULTS
INITIALIZATION DATA:
NT= 1
NW = 1
NRAD= 3
NUMBER OF TIMES AT WHICH PRESSURE IS TO BE CALCULATED
NUMBER OF WELLS TO BE CONSIDERED
NUMBER OF POINTS AT WHICH PRESSURE IS TO BE CALCULATED
£ AQUIFER CHARACTERISTICS TO BE CONSIDERED:
o
IVIS*
IMAGE=
ILEAK=
IDIP=
IPENT=
IFRAC=
IREF =
0
0
0
0
0
1
INJECTED
AQUIFER
FLUID TO HAVE VARIABLE VISCOSITY?
_.. CONFINED BY BOUNDARIES? YES
VERTICAL AQUIFER LEAKAGE? NO
DIPPING BED? NO
WELLS PARTIALLY PENETRATING BED? NO
FRACTURE ANALYSIS? NO
REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB=
CAPHB*
ANGLE*
161=
IB2 =
PI =
DW=
0.
0.
0.
0.
.0
.0
.0
.0
38.00
0
0
0.0
0.0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
OF OVERLYING BED (MD)
OVERLYING BED CFT1
OF UNDERLYING BED (MDI
. . . UNDERLYING BED (FT)
ANGLE OF BOUNDARY INTERSECTION (DEG)
BOUNDARY I SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSII
DENSITY OF RESERVOIR FLUID (LB./CU. FT,
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
TSTART=
PARTHK=
PERMZ=
RADSKN=
PERM=
NRATE=
VIS =
SKIN=
POR=
TINS =
THK=
VISN=
BW =
COMP=
RW =
X=
XF =
Y=
ZF=
DPENT=
0.0
0.0
0.0
100.00
50.00
L
1.000
0.0
0.150
0.0
45.00
0.0
1.00
0.00000750
0.583
100.00
0.0
30.00
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION (FTI
VERTICAL RESERVOIR PERMEABILITY (MD)
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (i/PSIl
WELLBORE RADIUS (FT I
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL RATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
POINT
NUMBER
1
2
3
DISTANCE TO
CHANGE IN
ELEVATION
(FT)
0.0
0.0
0.0
POINT X FOR WELL
X-LOCATION
(FT)
100.00
50.00
500.00
Y-LOCATION
(FT)
30.00
15.00
250.00
-------
o
00
PRESSURE AT TIME 3650.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
1 0.583 8184.102
2 52.202 6272.133
3 456.509 4432.625
-------
flMAGEf
IMAGE
[MAGE
?ATE
JELLP
.DCAT
JELL
TIME
3>
in
j(
flD
•8
s
U
IMAGE)
SELECT
riTLq
^
C
n
$ jj
'
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — PARALLEL SEALING FAULTS
INITIALIZATION DATA:
NT= 1 NUMBER OF
NW= 1 NUMBER OF
NRAD= 3 NUMBER OF
TIMES AT WHICH PRESSURE IS TO BE CALCULATED
WELLS TO BE CONSIDERED
POINTS AT WHICH PRESSURE IS TO BE CALCULATED
AQUIFER CHARACTERISTICS TO B€ CONSIDERED:
IVIS=
IMAGE=
ILEAK=
IDIP-
IPENT=
IFRAC*
IREF =
0 INJECTED FLUID TO HAVE VARIABLE
1 AQUIFER CONFINED BY BOUNDARIES?
0 VERTICAL AQUIFER LEAKAGE? NO
0 DIPPING BED? NO
0 WELLS PARTIALLY PENETRATING BED?
0 FRACTURE ANALYSIS? NO
1 REFERENCE WELL FOR PRINTING
VISCOSITY?
YES
NO
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT*
CAPHT=
CAPKB-
CAPHB*
ANGLE-
IB1=
IB2=
PI*
DW=
360
0.0
0.0
0.0
0.0
00
0
0
0.0
0.0
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
ANGLE OF
BOUNDARY
OF OVERLYING BED (MD)
OVERLYING BED (FT)
OF UNDERLYING BED IMD)
UNDERLYING BED 1FT)
BOUNDARY INTERSECTION IDEG)
1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSI)
DENSITY OF RESERVOIR FLUID {LB./CU.
FT.)
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
TSTART
PARTHK
PERMZ=
RADSKN
PERM=
NRATE=
VIS=
SKIN=
POR=
TINS =
THK=
VISN=
BW =
COMP =
RW =
Y=
ZF=
DPENT=
0.0
0.0
0.0
100.00
50.00
1
1.000
0.0
0.150
0.0
45.00
0.0
1.00
0.00000750
0.583
50.00
0.0
100.00
0.0
0.0
TIME TO START OF FIRST RATE (DAYS)
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY (MD>
RADIUS EFFECTED BY SKIN (FT)
AREAL RESERVOIR PERMEABILITY (MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (l/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
I
WELL RATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
POINT
NUMBER
1
2
3
DISTANCE TO
CHANGE IN
ELEVATION
(FT)
0.0
0.0
0.0
POINT X FOR WELL
X-LOCATION
(FT)
0.0
-25.00
50.00
Y-LOCATION
(FT)
0.0
-50.00
-50.00
-------
PRESSURE AT TIME 3650.000 {DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
I 0.583 5196.781
2 55.902 4202.145
3 70.711 4174.375
-------
'
s»
n
i
-
s
8
01
u
DIP |
?ADIli
?ATE |
WELLPf
. i
JELL
TIME
SELEC
TITLE
!l! S
j*maast
SWTEM^T
MIMED
;|o ; o o
12345
11111
2|2 2 2 2
H3 3
1
41 A A t i
14 4 4 '
Sis 5 5 .
1
6|6 6 6 6
7b 7 7 7
1
8J8 8 8 8
gl ! 9 9 9
l|2 1 4 5
. 052 1 76."33 I
; .292 1000. „ j
1714.
3P I. 1. 50. 45. .15 7.5
I 1 7. 0:0
3650.
I 120001 00 0.0
SINGLE WELL EXAMPLE — DIPPING RESERVOIR
: ! ! ! ^ .i J 1
!
i •» •* -i-i -a-jla"OF,~,'RANTiT3~TATTtME-iN'.i" -d
JOOOOO'J 000000'; 00000^00000000000000009000^00 "j 00000000000000000000000
7 1 9 10 11 12 13 14 ISIS 17 II 19 20 21 11 23 24 25 K 27 21 29 30 31 32 33 S« M 36 37 31 39 40 414} I! U 45 46 47 41 49 SO SI 52 S3 54 S5 56 57 SS 59 CO 61 M 63 64 65 66 67 II 69 70 71 72
1111111111111111111.1111111111111111111111111111111111111111111111
222222. 222222222222222222222222222222222. 22222222222222222222222222
3333333333 .3333 , .333333 .3333233333333333333333333333333333333333333
55555555 .55 .55 .555 .55555 .555555555S .555 .5 j5 .55555555555555555555555
6666666666666.666666666666666666666666666666,6666666666666666666666
777777777 .777777777 .77 .777777777 . .77 .777777777777777777777777777777
B88888888888888 8888888888888888888888888888888888888888888888888888
9999999 "99999999999999999999999 J99*999c999sl99 ^199999999999999999999
1 7 | i (0 II 12 13 14 1516 17 Iin2021 22 23 24 25 2«Z7 21 21 30 31 123334 3536 37 3l3t 4041 W444 4546 47 4I49SO SI S253S4 95 56 57 SI S960 11 U 63(4 69MI7 MM 70 71 72
•C-NMIIB7
65.5 1
lOENTFiainON
00000000
71747576777879M
11111111
22222222
33333333
4 A A A A A A A
4444444
55555555
GBG6666B
77777777
88888988
99999999
1374K7S777I79N
-------
DETERMINATION OF
AQUIFER PRESSURE BEHAVIOR
UNDER FLUID INJECTION
AND/OR PRODUCTION SYSTEMS
SINGLE WELL EXAMPLE — DIPPING RESERVOIR
INITIALIZATION DATA:
NT= 1 NUMBER OF
NW» 1 NUMBER OF
NRAD= 2 NUMBER OF
TIMES AT WHICH PRESSURE IS TC BE CALCULATED
WELLS TO BE CONSIDERED
POINTS AT WHICH PRESSURE IS TO BE CALCULATED
AQUIFER CHARACTERISTICS TO BE
CONSIDERED:
IMAGE=
ILEAK=
IDIP=
IPENT=
IREF =
0 INJECTED FLUID TO HAVE VARIABLE VISCOSITY?
0 AQUIFER CONFINED BY BOUNDARIES? NO
0 VERTICAL AQUIFER LEAKAGE? NO
1 DIPPING BED? YES
0 WELLS PARTIALLY PENETRATING BED? NO
0 FPACTURE ANALYSIS? NO
1 REFERENCE WELL FOR PRINTING
NO
GENERAL DATA CORRESPONDING TO OPTIONS SELECTED:
CAPKT=
CAPHT=
CAPKB-
CAPHB*
ANGLE=
IBl =
IB2=
PI =
0.0
0.0
0.0
0.0
0.0
0
0
0.0
65. 50
PERMEABILITY
THICKNESS OF
PERMEABILITY
THICKNESS OF
OF OVERLYING BED (MD)
OVERLYING BED IFT)
OF UNDERLYING BED (MD)
UNDERLYING BED (FT)
ANGLE OF BOUNDARY INTERSECTION (DEG)
BOUNDARY 1 SEALING OR LEAKING? SEAL
BOUNDARY 2 SEALING OR LEAKING? SEAL
INTIAL RESERVOIR PRESSURE (PSII
DENSITY OF RESERVOIR FLUID (LB./CU.
FT.I
-------
RESERVOIR DESCRIPTIVE AND WELL COMPLETION
INPUT DATA FOR WELL 1
TSTART=
PARTHK=
PERMZ=
RADSKN=
PERM=
NRATE=
VIS =
SKIN=
POR=
TINS =
THK=
VISN=
BW=
COMP=
RW =
X=
XF=
Y=
ZF=
DPENT=
0.0
0.0
0.0
100.00
50.00
1
1.000
0.0
0.150
0.0
*5.00
0.0
1.00
0.00000750
0.583
0.0
0.0
0.0
0.0
0.0
TIME TO START OF FIRST RATE (DAYS!
LENGTH OF WELL PENETRATION (FT)
VERTICAL RESERVOIR PERMEABILITY IMD)
RADIUS EFFECTED BY SKIN (FTI
AREAL RESERVOIR PERMEABILITY (MD)
NUMBER OF RATES
VISCOSITY OF RESERVOIR FLUID (CP)
SKIN FACTOR AT WELLBORE
RESERVOIR POROSITY (FRACTION)
TIME TO START OF NEW FLUID INJECTION (DAYS)
RESERVOIR THICKNESS (FT)
NEW FLUID VISCOSITY (CP)
FORMATION VOLUME FACTOR (RB/STB)
SYSTEM COMPRESSIBILITY (i/PSI)
WELLBORE RADIUS (FT)
REAL WELL X-LOCATION (FT)
FRACTURE LENGTH (FT)
REAL WELL Y-LOCATION (FT)
DISTANCE FROM HORIZONTAL FRACTURE
DISTANCE FROM TOP OF ZONE TO TOP OF
PENETRATION (FT) (FT)
RATE
NUMBER
WELL PATE
(STB/DAY)
1714.00
CUMULATIVE TIME
TO END OF RATE
DAYS
0.0
DISTANCE TO
POINT
NUMBER
POINT X FOR
CHANGE IN
ELEVATION
(FT)
WELL
RADIUS
(FT)
1
2
0.05
176.33
0.29
1000.00
-------
PRESSURE AT TIME 3650.000 (DAYS)
POINT RADIUS FROM PRESSURE
NUMBER REFERENCE WELL (PSIA)
1 0.292 1291.880
2 1000.000 496.647
cr>
-------
CHAPTER 6
SELECTED EXAMPLES OF FLUID INJECTION AND PRESSURE BUILDUP
It is of practical interest to examine a few selected examples of
injection and pressure response and to compare such histories with the
theoretical response that would be predicted on the basis of the equations
presented earlier. Although injection through wells is widely practiced,
probably the most closely monitored systems have been for industrial
wastewater injection and the examples are based on such cases. The ex-
amples have been selected because they represent particularly significant
regional disposal reservoirs and because sufficient data were available to
allow the calculations and a comparison with actual performance.
TEXAS GULF COAST
Celanese Corporation, Harris County, Texas
As an example of the performance of injection wells in the Texas
Gulf Coast area, the pressure buildup resulting from injection into two
wells located in the Bayport Industrial Development, near Clear Lake City,
Texas, will be studied (Figure 10). The wells began operation in 1967
and 1969, respectively, and their injection history through 1974 will be
analyzed. The two wells were constructed for injection into a basal
Miocene sand unit with an average thickness of 220 feet. The injection
unit occurs at a depth of about 5300 feet. An observation well was in-
stalled to monitor the pressure buildup in the injection reservoir, as
shown in Figure 10. The data used for the calculations are given below.
The data were obtained from information in the files of the Texas Depart-
ment of Water Resources, except for the reservoir compressibility, which
is an assumed average value.
Parameter Well TX-33 Well TX-45
P. = 2394 psi 2394 psi
q = 7096 STB/D 4430 STB/D
3 = 1 1
c = 7.5xlO"6psi'1 7.5xlO'6psi'1
k =' 389 md 389 md
117
-------
GEO. B. Me KINS TRY
A-47
SE Cor. Gto UcKinttry
TRACT I
CELANESE CORPORATION OF AMERICA
MONITOR WELL
**
DAVID HARRIS
A-25
HARRIS COUNTY, TEXAS
SCALE : l"s MOO'
Location mop of wells TX-33, 45, 69
Figure 10 Location map for Celanese Corporation wastewater
Injection and monitor wells, Harris County, Texas,
118
-------
h = 220 ft 220 ft
* = 0.30 0.30
y = 0.55 cp 9.55 cp
r = 6224 ft 7652 ft
t = 2618 D 2040 D
S = 0 0
Using the programmable desk calculator, the reservoir pressure at
the observation well at the end of 1974 can be calculated to be 2423 psi,
an increase of 29 psi over the original reservoir pressure of 2394 psi.
The observed pressure was 2438 psi. This is considered an adequate com-
parison. One possible reason for the difference between the observed
and predicted values is that the wells were actually operated in an erratic
manner, with considerable variation in injection rates and with periods
in which the wells were not operated at all. The actual operating schedule
could be simulated by using the variable rate equations that are presented;
however, it would be extremely time consuming in this case and not
worthwhile in view of the quite reasonable result obtained by using the
constant rate equation. The result of assuming a constant average rate
is, in any such situation, to predict a lower than actual pressure buildup,
as has occurred in this case.
E.I. DuPont, Victoria, Texas
As a second Texas Gulf Coast example, the multiple well system at the
E.I. DuPont, Victoria, Texas, plant will be considered. Injection at that
site began in 1953, with one well and was expanded to a system of eight
injection wells and a monitor well by 1974 (Figure 11). The pressure
buildup at the monitor well resulting from injection during the period
1953 through December 1973 will be calculated. The data for use in the
calculation are:
Parameter Well No. 1
Pi = 1750 psi
q = 3572 STB/D
3 = 1
c = 7.5xlO"6psi"1
k = 828 md
h = 600 ft
119
-------
&TX-I05
A2
ATX-106
(-30
-28
-29
E. I. Dtt PONT OE NEMOURS a CO
VICTORIA PLANT
DESIDERIO GARCIA LEAGUE
A -38
NOTE: Diipotal wells 1,2 S3 originally permitted by
Texas Railroad Commission, a mentioned on Texas
Water Quality Board permit WDW-4, a here
identified with that well as TX-4.
GUADALUPE
RIVER
VICTORIA COUNTY, TEXAS
SCALE i .1" s 1500'
Location map of welts TX-4, 28, 29, 30, 105, 106
Figure 11 Location map for E. I. DuPont Company injection, and
monitor wells, Victoria County, Texas.
120
-------
= 0.31
y = 0.75 cp
r = 2395 ft
t = 7665 days
s = 0
The data remain the same for the other seven injection wells, except
for the injection rates, radii, and injection times, which are:
Parameter Well No. 2 No. 3 TX-4 TX-28 TX-29 TX-105 TX-106
q(STB/D) 3733 3240 4812 8748 8594 2794 102
r(ft) 1650 1275 2025 1725 2700 1950 1275
t(D) 7300 5840 4015 2190 2190 730 365
Entering these data into the constant-rate, multiple-well desk
calculator program, the reservoir pressure at the end of 1974 would be
predicted to be 1782 psi. The observed pressure at the observation well
ranged from about 1798 to 1814 psi during 1974, and was about 1813 psi
at the end of the year. As in the previous example, the results are
considered adequate in view of the simplified analysis used. In this case
as in the previous one, injection rates were averaged to give a single
constant rate. Data were obtained from files of the Texas Department of
Water Resources, except for the reservoir compressibility, which is an
assumed value. Distances from the injection wells to the observation
well (TX-30) were measured from Figure 11.
FLORIDA
Wastewater injection is extensively practiced in Florida, where the
injection reservoirs are carbonates of Tertiary age. One injection system
that has been intensively monitored is that operated by the Monsanto
Chemical Company near Pensacola, Florida. Two injection wells are used.
The first began injection in 1964 and the second well was constructed in
1965. Both wells inject into the lower limestone of the Floridan aquifer,
which occurs at a depth of about 1400 feet at the plant site. Although
there are two injection wells, they can be treated as a single well when
calculating pressure buildup at a location more than a few thousand feet
away. The point to be considered is a monitor well located 10,000 feet
north of the two injection wells. Other data needed for the calculation
are given below. The data are from Goolsby (1972) and Faulkner and
Pascale (1975). The pressure calculation is for late 1971, because
Goolsby (1972) provides a cumulative injection volume for the two wells and
121
-------
the measured head at the monitor well for late 1971. Although injection
rates varied between 1963 and 1971, an average rate is used.
Pi = 26 psi
q = 49,200 STB/D
3 = 1
c = 1.32 x 10"5
k = 878 md
h = 350 ft
= 0.10
y = 1
r = 10,000 ft
t = 3000 D
s = 0
Entering these data into the single-well, constant-rate desk cal-
culator program, the pressure buildup is calculated to be 64 psi and the
total pressure 90 psi. For fresh water, this is a total head of 208
feet, which is approximately the head observed at the monitor well near
the end of 1971, according to Goolsby (1972)
OHIO
An injection reservoir that is widely used in the north-central states,
including Ohio, is the Mt. Simon Sandstone. The Mt. Simon is the basal
sedimentary unit in that area, it is generally well separated from fresh-
water-bearing aquifers, and it often has adequate reservoir properties for
small to moderate amounts of injection. Data for an injection well in
northern Ohio are:
Pi = 2750 psi
q = 2503 STB/D
3 = 1
c = 7.5 x 10"6
k = 6.3 md
122
-------
h = 255 ft
= 0.08
y = 1.065 cp
r = 0.396 ft (wellbore radius)
t = 57 D
s = -2.8
Entering these data into the single-well, constant-rate desk cal-
culator program the total pressure at the end of 57 days is predicted to
be 5172 psi and the predicted pressure buildup is, therefore, 1422 psi.
The actual observed buildup was 1420 psi. Note that the skin factor in
this case is -2.8, as a result of the well having been hydraulically
fractured.
The data used in this example were derived from core analyses and
well tests provided by the well operator. The accurate agreement between
the predicted and observed results during the early phase of well operation
indicate that considerable confidence could be placed in longer-term
pressure buildup projections.
123
-------
REFERENCES
Amyx, J. W.s D. M. Bass, and R. L. Whiting. 1960. Petroleum Reservoir
Engineering. McGraw-Hill Book Co. New York, N.Y. 610 pp.
Davis, S. N. and R. J. M. DeWiest. 1966. Hydrogeology. John Wiley and
Sons, Inc. New York, N.Y. 463 pp.
Earlougher, R. C., Jr. 1977. Advances in Well Test Analysis. Soc. Petro-
leum Engineers. Monograph Volume 5. 264 pp.
Faulkner, G. L., and C. A. Pascale. 1975. Monitoring Regional Effects
of High Pressure Injection of Industrial Waste in a Limestone Aquifer.
Ground Water. Vol. 13. No. 2, pp. 197-208.
Goolsby, D. A. 1972. Geochemical Effects and Movement of Injected Indus-
trial Waste in a Limestone Aquifer. TJI Underground Waste Management and
Environmental Implications. T. D. Cook, ed. Am. Assoc. Petroleum Geolo-
gists Memoir 18, pp. 355-368.
Gringarten, A. C. and H. J. Ramey. 1974. Unsteady-State Pressure Dis-
tributions Created by a Well With a Single Horizontal Fracture, Partial
Penetration, or Restricted Entry. Jour. Soc. Petroleum Engrs. August.
pp. 413-426.
Gringarten, A. C., H. J. Ramey, and R. Raghaven. 1974. Unsteady-State
Pressure Distributions Created by a Well With a Single Infinite-
Conductivity Vertical Fracture. Jour. Soc. Petroleum Engrs. August.
pp. 347-360.
Hantush, M. S., and C. E. Jacob. 1955. Nonsteady Radial Flow in an
Infinite Leaky Aquifer. Trans. Am. Geophysical Union, V. 36, p. 95.
Hawkins, M. F., Jr. 1956. A Note on the Skin Effect. Trans. Am. Inst.
Mining and Metallurgical Engrs. pp. 356-357.
Hubbert, M. K. and D. G. Willis. 1957. Mechanics of Hydraulic Fracturing.
Trans. Am. Inst. Mining and Metallurgical Engrs. pp. 153-166.
Hurst, William. 1953. Establishment of the Skin Effect and Its Impediment
to Fluid Flow Into a Well Bore. Petroleum Engineering. October.
pp. B6-B16.
124
-------
Matthews, C. S. and D. 6. Russell. 1967. Pressure Buildup and Flow Tests
in Wells. Soc. Petroleum Engineers Monograph Vol. 1. 178 pp.
National Bureau of Standards, 1964, Handbook of Mathematical Functions With
Formulas, Graphs, and Mathematical Tables. Nat. Bureau of Stds.
Applied Mathematics Series 55. U.S. Govt. Printing Office, Washington,
D.C. 1046 pp.
Russell, D. G., and Prats, M. 1962. The Practical Aspects of Interlayer
Cross-flow. Jour. Petroleum Technology. June. pp. 589-594.
Todd, D. K. 1959. Ground Water Hydrology. John Wiley and Sons, Inc.
New York, N.Y. 335 pp.
Van Everdingen, A. F. 1953. The Skin Effect and Its Influence on the
Productive Capacity of a Well. Trans. Am. Inst. Mining and Metallur-
gical Engrs. pp. 171-176.
Walton, W. C. 1970. Groundwater Resource Evaluation. McGraw-Hill Book
Company, New York, N.Y. 664 pp.
Witherspoon, P.A., I. Javandel, S.P. Neuman, and R.A. Freeze. 1967.
Interpretation of Aquifer Gas storage Conditions from Water Pumping
Tests. American Gas Assoc. New York, N.Y. 273 pp.
125
-------
APPENDIX A
TABLES FOR USE IN MANUAL PRESSURE BUILDUP CALCULATIONS
A-l Values of the exponential integral - E, (x)
A-2 Values of the error function - erf (x)
A-3 Values of the pseudo skin factor (a) for the
general vertical fracture case
A-4 Values of dimensionless pressure (Pm) for
semiconfined reservoirs
126
-------
0.0
TABLE 1
VALUES OF EKX)
0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
PO
1
2
3
4
5
6
7
a
9
1
2
3
4
5
6
7
8
9
1
2
3
4^
5
6
7
3
9
1
2
3
4
5
6
7
R
9
POWER OF 10
36.2642
35.5710
35.1655
34.8779
34.6547
34.4724
34.3182
34.1847
34.0669
36.1688
35.5222
35.1328
34.8532
34.6349
34.4559
34.3041
34.1723
34.0559
36.0818
35.4757
35.1010
34.8291
34.6155
34.4396
34.2901
34.1600
34.0450
36.
35.
35.
34.
34.
34.
34.
34.
34.
0018
4312
0702
8055
5965
4236
2763
1479
0341
35.9277
35.3887
35.0404
34.7825
34.5778
34.4079
34.2627
34.1359
34.0234
POWER OF 10
33.9616
33.2684
32.8630
32.5753
32.3521
32.1698
32.0157
31.8821
31.7643
33.8663
33.2196
32.8302
32.550t>
32.3323
32.1533
32.0015
31.8697
31.7533
33.7793
33.1731
32.7984
32.5265
32.3129
32. 1370
31.9875
31.8574
31.7424
33.
33.
32.
32.
32.
32.
31.
31.
31.
6992
1287
7676
5030
2939
1210
9737
8453
7316
33.6251
33.0861
32.7378
32.4800
32.2752
32.1053
31.9601
31.8333
31.7209
POWER OF 10
31.6590
30.9658
30.5604
30.2727
30.0495
29.8672
29.7131
29.5795
29.4618
31.5637
30.9171
30.5276
30.2480
30.02P7
29.8507
29.6989
29.5671
29.4507
31.4767
30. 8705
30.4958
30.2239
30.0103
29.8344
29.6849
29.5549
29.4398
31.
30.
30.
30.
29.
29.
29.
29.
29.
3966
8261
4651
2004
9913
8184
6711
5427
4290
31.3225
30.7835
30.4352
30.1774
29.9726
29.8027
29.6575
29.5307
29.4183
POWER OF 10
29.3564
28.6633
28.2578
27.9701
27.7470
27.5646
27.4105
27.2770
27.1592
29.2611
28.6145
28.2250
27.9454
27.7272
27.5481
27.3963
27.2645
27.1481
29.1741
28.5679
28.1933
27.9213
27.7077
27.5318
27.3823
27.2523
27.1372
29.
28.
28.
27.
27.
27.
27.
27.
27.
0940
5235
1625
8978
6887
5159
3685
2401
1264
29.0199
28.4809
28.1326
27.8748
27.6700
27,5001
27.3549
27.2282
27.1157
= -16
35.8587
35.3479
35.0114
34.7601
34.5594
34.3923
34.2493
34.1241
34.0129
= -15
33.5561
33.0453
32.7088
32.4575
32.2568
32.0898
31.9467
31.8215
31.7103
= -14
31.2535
30.7427
30.4062
30.1549
29.9542
29.7872
29.6441
29.5189
29.4077
= -13
28.9509
28.4401
28. 1036
27.8523
27.6517
27.4846
27.3415
27.2163
27.1051
35.
35.
34.
34.
34.
34.
34.
34.
34.
33.
33.
32.
32.
32.
32.
31.
31.
31.
31.
30.
30.
30.
29.
29.
29.
29.
29.
28.
28.
28.
27.
27.
27.
27.
27.
27.
7941
3086
9832
7381
5414
3771
2360
1124
0024
4916
0061
6806
4355
2388
0745
9334
8098
6998
1890
7035
3781
1329
9362
7719
6308
5072
3972
8864
4009
0755
8303
6336
4693
3282
2046
0946
35.7335
35.2709
34.9558
34.7166
34.5237
34.3620
34.2229
34.1008
33.9920
33.4309
32.9683
32.6532
32.4140
32.2211
32.0595
31.9203
31.7982
31.6894
31.1284
30.6657
30.3506
30.1114
29.9185
29.7569
29.6178
29.4957
29.3869
28.8258
28.3631
28.0481
27.8088
27.6159
27.4543
27.3152
27.1931
27.0843
35.6764
35.2345
34.9292
34.6955
34.5063
34.3472
34.2100
34.0894
33.9818
33.3738
32.9319
32.6266
32.3930
32.2037
32.0446
31.9074
31.7868
31.6792
31.0712
30.6294
30.3240
30.0904
29.9011
29.7421
29.6049
29.4842
29.3766
28.7686
28.3268
23.0214
27.7878
27.5985
27.4395
27.3023
27.1816
27.0740
35.6223
35.1994
34.9032
34.6749
34.4892
34.3326
34. 1973
34.0781
33.9716
33.3197
32.8969
32 .6006
32.3723
32.1866
32.0300
31.8947
31.7755
31.6690
31.0171
30.5943
30.2980
30.0697
29.8840
29.7275
29.5921
29.4729
29.3665
28.7145
28.2917
27.9954
27.7672
27.5815
27.4249
27.2895
27.1703
27.0639
-------
TABLE 1
VALUES OF El(XI
0.0
0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
ro
oo
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
27.0538
26.3607
25.9552
25.6675
25.4444
25.2621
25.1079
24.9744
24.8566
24.7512
24.0581
23.6526
23.3649
23.1418
22.9595
22.8053
22.6718
22.5540
22.4486
21.7555
21.3500
21.0623
20.8392
20.6569
20.5027
20.3692
20.2514
20. 1461
19.4529
19.0474
18.7598
18.5366
18.3543
18.2001
18.0666
17.9488
26.9585
26.3119
25.9224
25.6428
25.4246
25.2455
25.0937
24.9619
24.8455
24.6559
24.0093
23.6198
23. 3402
23.1220
22.9429
22.7911
22.6594
22.5430
22.3533
21.7067
21.3172
21.0377
20.8194
20.6404
20.4886
20.3568
20.2404
20. 0508
19.4041
19.0147
18.7351
18.5168
18.3378
18.1860
18.0542
17.9378
26.8715
26.2654
25.8907
25.6187
25.4052
25.2293
25.0797
24.9497
24.8346
24.5689
23.9628
23.5881
23.3161
23.1026
22.9267
22.7771
22.6471
22.5320
22.2663
21.6602
21.2855
21.0136
20.8000
20.6241
20.4746
20.3445
20.2294
19.9637
19.3576
18.9829
18.7110
18.4974
18.3215
18.1720
18.0419
17.9268
26.
26.
25.
25.
25.
25.
25.
24.
24.
24.
23.
23.
23.
23.
22.
22.
22.
22.
22.
21.
21.
20.
20.
20.
20.
20.
20.
19.
19.
18.
18.
18.
18.
18.
18.
17.
POWER
7915 26
2209 26
8599 25
5952 25
3861 25
2133 25
0659 25
9376 24
8238 24
POWER
4889 24
9183 23
5573 23
2926 23
0835 23
9107 22
7634 22
6350 22
5212 22
POWER
1863 22
6157 21
2547 21
9900 20
7809 20
6081 20
4608 20
3324 20
2186 20
POWER
8837 19
3132 19
9521 18
6874 18
4783 18
3055 18
1582 18
0298 18
9160 17
OF 10
.7173
. 1783
.8300
.5722
.3674
.1975
.0523
.9256
.8131
OF 10
.4147
.8758
.5275
.2696
.0648
.8949
.7497
.6230
.5105
OF 10
.1122
.5732
.2249
.9670
.7622
.5923
.4472
.3204
.2079
OF 10
.8096
.2706
.9223
.6645
.4597
.2898
. 1446
.0178
.9053
= -12
26.6483
26.1375
25.8011
25.5497
25.3491
25.1820
25.0389
24.9137
24.8025
= -11
24.3458
23.8349
23.4985
23.2471
23.0465
22.8794
22.7363
22.6112
22.4999
= -10
22.0432
21.5323
21.1959
20.9446
20.7439
20.5768
20.4337
20.3086
20.1974
= -9
19.7406
19.2298
18.8933
18.6420
1.8.4413
18.2743
18.1311
18.0060
17.8948
26.
26.
25.
25.
25.
25.
25.
24.
24.
24.
23.
23.
23.
23.
22.
22.
22.
22.
21.
21.
21.
20.
20.
20.
20.
20.
20.
19.
19.
18.
18.
18.
18.
18.
17.
17.
5838
0983
7729
5278
3311
1667
0257
9021
7921
2812
7957
4703
2252
0285
8642
7231
5995
4895
9786
4931
1677
9226
7259
5616
4205
2969
1869
6761
1906
8651
6200
4233
2590
1179
9943
8843
26.5232
26.0606
25.7455
25.5063
25.3134
25.1517
25.0126
24.8905
24.7817
24.2206
23.7580
23.4429
23.2037
23.0108
22.8491
22.7100
22.5879
22.4791
21.9180
21.4554
21. 1403
20.9011
20.7082
20.5465
20.4074
20.2853
20.1765
19.6154
19.1528
18.8377
18.5985
18.4056
18.2440
18.1048
17.9827
17.8739
26.4660
26.0242
25.7188
25.4852
25.2960
25.1369
24.9997
24.8791
24.7714
24.1634
23.7216
23.4162
23.1826
22.9934
22.8343
22.6971
22.5765
22.4688
21.8609
21.4190
21. 1136
20.8800
20.6908
20.5317
20.3945
20.2739
20.1663
19.5583
19.1164
18.8111
18.5774
18.3882
18.2291
18.0919
17.9713
17.8637
26.4120
25.9891
25.6928
25.4646.
25.2789
25.1223
24.9870
24.8678
24.7613
24.1094
23.6865
23.3903
23.1620
22.9763
22.8197
22.6844
22.5652
22.4587
21.8068
21.3839
21.0877
20.8594
20.6737
20.5171
20.3818
20.2626
20.1561
19.5042
19.0813
18.7851
18.5568
18.3711
18.2145
18.0792
17.9600
17.8535
-------
TABLE 1
VALUES OF EKX)
0.0
O.LOOO 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
PO
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
&
7
8
9
L
2
3
4
5
6
7
8
9
17.8435
17.1503
16.7449
16.4572
16.2340
16.0517
15.8976
15.7640
15.6463
15.5409
14.8477
14.4423
14.1546
13.9315
13.7491
13.5950
13.4615
13.3437
13.2383
12.5452
12.1397
11.8520
11.6289
11.4466
11.2924
11.1589
1 1.0411
17.7482
17.1015
16.7121
16.4325
16.2142
16.0352
15.8834
15.7516
15.6352
15.4456
14.7990
14.4095
14.1299
13.9117
13.7326
13.5808
13.4490
13.3326
13.1430
12.4964
12.1069
11.8273
11.6091
11.4300
11.2782
11.1465
11.0300
17.6611
17.0550
16.6803
16.4084
16.1948
16.0189
15.8694
15.7393
15.6243
15.3586
14.7524
14.3777
14. 1058
13.8922
13.7163
13.5668
13.4368
13.3217
13.0560
12.4499
12.0752
11.8032
11.5897
11.4138
11.2642
11.1342
11.0191
POW
17.5811
17.0106
16.6496
16.3849
16.1758
16.0029
15.8556
15.7272
15.6135
POW
15.2785
14.7080
14.3470
14.0823
13.8732
13.7003
13.5530
13.4246
13.3109
POW
12.9759
12.4054
12.0444
11.7797
11.5706
11.3978
11.2504
11.1221
11.0083
ER OF 10
17
16
16
16
16
15
15
15
15
.5070
.9680
.6197
.3619
.1571
.9872
.8420
.7152
.6028
ER OF 10
15
14
14
14
13
13
13
13
.2044
.6654
.3171
.0593
.8545
.6846
.5394
.4127
13.3002
ER
12
12
12
11
11
11
11
11
10
POWER
10.9357
10.2426
9.8371
9.5495
9.3263
9.1440
8.9899
8.8564
8.7386
10.8404
10. 1938
9.8044
9.5248
9.3065
9.1275
8.9757
8.8439
8.7275
10.7534
10.1473
9.7726
9.5007
9.2871
9.1112
8.9617
8.8317
8.7166
10.6734
10.1028
9.7418
9.4772
9.2681
9.0952
8.9479
8.8196
8.7058
10
10
9
9
9
9
8
8
8
OF 10
.9018
.3628
.0145
.7567
.5519
.3820
.2368
.1101
.9976
OF 10
.5993
.0603
.7120
.4542
.2494
.0795
.9343
.8076
.6951
= -8
17.4380
16.9272
16.5907
16.3394
16.1387
15.9717
15.8286
15.7034
15^5922
= -7
15.1354
14.6246
14.2881
14.0368
13.8361
13.6691
13.5260
13.4008
13.2896
= -6
12.8328
12.3220
11.9856
11.7342
11.5336
11.3665
11.2234
11.0983
10.9870
= -5
10.5303
10.0195
9.6330
9.4317
9.2310
9.0640
8.9209
8.7957
8.6845
17.
16.
16.
16.
16.
15.
15.
15.
15.
15.
14.
14.
14.
13.
13.
13.
13.
13.
12.
12.
11.
11.
11.
11.
11.
11.
10.
10.
9.
9.
9.
9.
9.
8.
8.
8.
3735
8880
5625
3174
1207
9564
8153
6917
5817
0709
5854
2600
0148
8181
6538
5127
3891
2791
7683
2828
9574
7123
5155
3512
2102
0866
9766
4657
9802
6548
4097
2130
0487
9077
7840
6741
17.3129
16.8502
16.5351
16.2959
16. 1030
15.9414
15.8023
15.6802
15.5714
15.0103
14.5476
14.2326
13.9933
13.8004
13.6388
13.4997
13.3776
13.2688
12.7077
12.2451
11.9300
11.6908
11.4979
11.3362
11.1971
11.0750
10.9662
10.4051
9.9425
9.6274
9.3882
9.1953
9.0337
8.8946
8.7725
8.6637
17.2557
16.8139
16.5085
16.2749
16.0856
15.9266
15.7894
15.6687
15.5611
14.9531
14.5113
14.2059
13.9723
13.7830
13.6240
13.4868
13.3661
13.2585
12.6505
12.2087
11.9033
11.6697
11.4805
11.3214
11.1842
11.0636
10.9559
10.3480
9.9061
9.6008
9.3672
9.1779
9.0189
8.8817
8.7611
3.6534
17.2016
16.7788
16.4825
16.2542
16.0685
15.9120
15.7766
15.6574
15.5509
14.8990
14.4762
14.1799
13.9517
13. 7659
13.6094
13.4740
13.3548
13.2484
12.5965
12. 1736
11. 8773
11 .6491
11.4634
11.3068
11.1715
11.0523
10.9458
10.2939
9.8710
9.5748
9.3465
9.1608
9.0043
8.8689
8.7498
8.6433
-------
TABLE 1
VALUES OF EKX)
0.0
0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
CO
o
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
R
9
1
2
3
4
5
6
7
8
9
1
3
4
5
6
7
8
9
8.6332
7.9402
7.5348
7.2472
7.0242
6.8420
6.6879
6.5545
6.4368
6.3316
5.6394
5.2349
4.9483
4.7261
4.5448
4.3916
4.2591
4.1423
4.0379
3.3547
2.9591
2.6813
2.4679
2.2953
2.1509
2.0270
1.9188
1.8229
1.2227
0.9057
0.7024
0.5598
0.4544
0.3738
0.3106
0.2602
8.5379
7.8914
7.5020
7.2226
7.0044
6.8255
6.6738
6.5421
6.4258
6.2363
5.5907
5.2023
4.9237
4.7064
4.5284
4.3775
4.2468
4.1314
3.9436
3.3069
2.9273
2.6576
2.4491
2.2798
2.1376
2.0155
1.9087
1.7371
1.1829
0.8815
0.6859
0.5478
0.4454
0.3668
0.3051
0.2557
8.4509
7. 8449
7.4703
7.1985
6.9850
6.8092
6.6598
6.5298
6.4149
6.1494
5.5443
5.1706
4.8997
4.6871
4.5122
4.3637
4.2346
4.1205
3.8576
3.2614
2.8966
2.6344
2.4306
2.2645
2.1246
2.0042
1.8987
1.6596
1.1454
0.8584
0.6700
0.5362
0.4366
0.3599
0.2996
0.2513
8.
7.
7.
7.
6.
6.
6.
6.
6.
6.
5.
5.
4.
4.
4.
4.
4.
4.
3.
3.
2.
2.
2.
2.
2.
1.
1.
1.
1.
0.
0.
0.
0.
0.
0.
0.
POWER
3709
8005
4395
1750
9660
7932
6460
5177
4041
POWER
0695
4999
1399
8762
6681
4963
3500
2226
1098
POWER
7786
2179
8668
6119
4126
2494
1118
9930
8888
POWER
5889
1099
8361
6546
5250
4280
3533
2943
2470
OF 10
8.2968
7.7579
7.4097
7.1520
6.9473
6.7775
6.6324
6.5057
6.3934
OF 10
5.9955
5.4575
5.1102
4.8533
4.6495
4.4806
4.3365
4.2107
4.0992
OF 10
3 . 70 54
3. 1764
2.8379
2.5899
2.3949
2.2347
2.0991
1.9820
1.8791
OF 10
1.5242
1.0763
0.8148
0.6397
0.5140
0.4197
0. 3467
0.2891
0.2428
—
8
7
7
7
6
6
6
6
6
_
5
5
5
4
4
4
4
4
4
=
3
3
2
2
2
2
2
1
1
a
1
l
0
0
0
0
0
0
-4
.2278
.7171
.3807
.1295.
.9289
.7620
.6190
.4939
.3828
-3
.9266
.4168
.0813
.8310
.6313
.4652
.3231
.1990
.0887
-2
.6374
.1365
.8099
.5684
.3775
.2201
.0867
.9711
.8695
-1
.4645
.0443
.7942
.6253
.5034
.4115
.3404
.2840
0.2387
8.1633
7.6779
7.3526
7.1075
6.9109
6.7467
6.6058
6.4822
6.3723
5.8622
5.3776
5.0532
4.8091
4.6134
4.4501
4.3100
4.1874
4.0784
3.5739
3.0983
2.7827
2.5474
2.3604
2.2058
2.0744
1.9604
1.8600
1.4092
1.0139
0.7745
0.6114
0.4930
0.4036
0.3341
0.2791
0.2347
8.1027
7.6402
7.3252
7.0860
6.8932
6.7317
6.5927
6.4707
6.3620
5.8016
5.3400
5.0259
4.7877
4.5958
4.4351
4.2970
4.1759
4.0681
3.5143
3.0615
2.7563
2 . 5 269
2.3437
2.1918
2.0623
1.9498
1.8505
1.3578
0.9849
0.7555
0.5979
0.4830
0.3959
0.3280
0.2742
0.2308
8.0455
7.6038
7.2985
7.0650
6.8759
6.7169
6.5798
6.4593
6.3517
5.7446
5.3037
4.9994
4.7667
4.5785
4.4204
4.2842
4.1646
4.0579
3.4581
3.0262
2.7306
2.5068
2.3273
2.1779
2.0504
1.9393
1.8412
1.3098
0.9573
0.7371
0.5848
0.4732
0.3883
0.3221
0.2694
0.2269
7.9915
7.5687
7.2726
7 . 0444
6.8588
6.7023
6.5671
6.4480
6.3416
5.6906
5.2687
4.9735
4.7462
4.5615
4.4059
4.2716
4.1534
4.0479
3.4050
2.9921
2.7056
2.4871
2.3112
2.1643
2.0386
1.9290
1.8320
1.2649
0.9309
0.7195
0.5721
0.4637
0.3810
0.3163
0.2648
0.2231
-------
TABLE 1
VALUES OF EKX)
0.0
0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
1
2
3
4
5
6
7
8
9
0.2194
0.0489
0.0131
0.0038
0.0012
0.0004
0.0001
0.0001
0.0000
0.1860
0.0426
0.0115
0.0034
0.0010
0.0003
0.0001
0.0000
0.0000
0.1584
0.0372
0.0101
0.0030
0.0009
0.0003
0.0001
0.0000
0.0000
POWER OF 10
0.1355 0.1162
0.0325 0.0284
0.0090 0.0079
0.0026 0.0024
0.0008 0.0007
0.0003 0.0002
0.0001 0.0001
0.0000 0.0000
0.0000 0.0000
0
0.1000
0.0249
0.0070
0.0021
0.0007
0.0002
0.0001
0.0000
0.0000
0.0863
0.0218
0.0062
0.0019"
0.0006
0.0002
0.0001
0.0000
0.0000
0.0746
0.0191
0.0055
0.0016
0.0005
0.0002
0.0001
0.0000
0.0000
0.0647
0.0167
0.0048
0.0015
0.0005
0.0002
0.0001
0.0000
0.0000
0.0561
0.0146
0.0043
0.0013
0.0004
0.0001
0.0001
0.0000
0.0000
-------
TABLE 2
VALUES OF ERF(X)
0.0
0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
GO
ro
1
2
3
4
5
6
7
8
9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
POWER OF
0.1125
0.2227
0.3286
0.4284
0.5205
0.6039
0.6778
0.7421
0.7969
0.0
POWER OF
0.8427
0.8802
0.9103
0.9340
0.9523
0.9661
0.9763
0. Q838
0.9891
0.9928
POWER OF
0.9953
0.9970
0.9981
0.9989
0.9993
0.9996
0.9998
0.9999
0.9999
1.0000
10 =
0.1236
0.2335
0.3389
0.4380
0.5292
0.6117
0.6847
0.7480
0.8019
0.0100
10 =
0.8468
0.8835
0.9130
0.9361
0.9539
0.9673
0.9772
0.9844
0.9895
0.9931
10 =
0.9955
0.9972
0.9982
0.9989
0.9993
0.9996
0.9998
0.9999
0.9999
I. 0000
-1
0. 1348
0.2443
0.3491
0.4475
0.5379
0.6194
0.6914
0.7538
0.8068
0.0200
0
0.8508
0.8868
0.9155
0.9381
0.9554
0.9684
0,9780
0.9850
0.9899
0.9934
0
0.9957
0.9973
0.9983
0.9990
0.9994
0.9996
0.9998
0.9999
0.9999
1.0000
0.1459
0.2550
0.3593
0.4569
0.5465
0.6270
0.6981
0.7595
0.8116
0.0300
0.8548
0.8900
0.9181
0.9400
0.9569
0.9695
0.9788
0.9856
0.9903
0.9937
(MULT I
0.1569
0.2657
0.3694
0.4662
0.5549
0.6346
0.7047
0.7651
0.8163
0.0400
(MULT I
0.8586
0.8931
0.9205
0.9419
0.9583
0.9706
0.9796
0.9861
0.9907
0.9939
PLY TABULAR VALUES
0.1680
0.2763
0.3794
0.4755
0.5633
0.6420
0.7112
0.7707
0.8209
0.0500
0.1790
0.2869
0.3893
0.4847
0.5716
0.6494
0.7175
0.7761
0.8254
0.0600
PLY TABULAR VALUES
0.8624
0.8961
0.9229
0.9438
0.9597
0.9716
0.9804
0.9867
0.9911
0.9942
0.8661
0.8991
0.9252
0.9456
0.9611
0.9726
0.9811
0.9872
0.9915
0.9944
(MULTIPLY TABULAR VALUES
0.9959
0.9974
0.9984
0.9990
0.9994
0.9997
0.9998
0.9999
0.9999
1.0000
0.9961
0.9975
0.9985
0.9991
0.9994
0.9997
0.9998
0.9999
0.9999
1.0000
0.9963
0.9976
0.9985
0.9991
0.9995
0.9997
0.9998
0.9999
0.9999
1.0000
0.9964
0.9977
0.9986
0.9992
0.9995
0.9997
0.9998
0.9999
0.9999
1.0000
BY 1.
0.1900
0.2974
0.3992
0.4937
0.5798
0.6566
0.7238
0.7814
0.8299
0.0700
BY 1.
0.8698
0.9020
0.9275
0.9473
0.9624
0.9736
0.9818
0.9877
0.9918
0.9947
0000)
0.2009
0.3079
0.4090
0.5027
0.5879
0.6638
0.7300
0.7867
0.8342
0.0800
0000)
0.8733
0.9048
0.9297
0.9490
0.9637
0.9745
0.9825
0.9882
0.9922
0.9949
0.2118
0.3183
0.4187
0.5117
0.5959
0.6708
0.7361
0.7918
0.8385
0.0900
0.8768
0.9076
0.9319
0.9507
0.9649
0.9755
0.9832
0.9886
0.9925
0.9951
BY 1.0000)
0.9966
0.9979
0.9987
0.9992
0.9995
0.9997
0.9998
0.9999
1.0000
1.0000
0.9967
0.9980
0.9987
0.9992
0.9995
0.9997
0.9998
0.9999
1.0000
1.0000
0.9969
0.9980
0.9988
0.9993
0.9996
0.9998
0.9999
0.9999
1 .0000
1.0000
-------
TABLE 2
VALUES OF ERFCX)
0.0
0,1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000
GO
CO
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
a
9
i
2
3
4
5
6
7
8
9
POWER OF 10 =
0.0113 0.0124
0.0226 0.0237
0.0339 0.0350
0.0451 0.0463
0.0564 0.0575
0.0677 0.0688
0.0790 0.0801
0.0903 0.0914
0.1016 0.1027
POWER OF 10 =
0.0113 0.0124
0.0226 0.0237
0.0339 0.0350
0.0451 0.0463
0.0564 0.0575
0.0677 0.0688
0.0790 0.0801
0.0903 0.0914
0.1016 0.1027
POWER OF 10 =
0.0113 0.0124
0.0226 0.0237
0.0339 0.0350
0.0451 0.0463
0.0564 0.0575
0.0677 0.0688
0.0790 0.0801
0.0903 0.0914
0.1016 0.1027
POWER OF 10 =
0.0113 0.0124
0.0226 0.0237
0.0338 0.0350
0.0451 0.0462
0.0564 0.0575
0.0676 0.0687
0.0789 0.0800
0.0901 0.0912
0.1013 0.1024
-5
0.0135
0.0248
0.0361
0.0474
0.0587
0.0700
0.0812
0.0925
0. 1038
-4
0.0135
0.0248
0.0361
0.0474
0.0587
0.0700
0.0812
0.0925
0.1038
-3
0.0135
0.0248
0.0361
0.0474
0.0587
0.0700
0.0812
0.0925
0. 1038
-2
0.0135
0.0248
0.0361
0.0474
0.0586
0.0699
0.0811
0.0923
0.1035
0.0147
0.0260
0.0372
0.0485
0.0598
0.0711
0.0824
0.0937
0.1049
0.0147
0.0260
0.0372
0.0485
0.0598
0.0711
0.0824
0.0937
0.1049
0.0147
0.0260
0.0372
0.0485
0.0598
0.0711
0.0824
0.0937
0.1049
0.0147
0.0259
0.0372
0.0485
0.0597
0.0710
0.0822
0.0934
0.1046
(MULTIPLY TABULAR VALUES BY 0.0010)
0.0158 0.0169 0.0181 0.0192 0.0203
0.0271 0.0282 0.0293 0.0305 0.0316
0.0384 0.0395 0.0406 0.0418 0.0429
0.0496 0.0508 0.0519 0.0530 0.0542
0.0609 0.0621 0.0632 0.0643 0.0654
0.0722 0.0733 0.0745 0.0756 0.0767
0.0835 0.0846 0.0858 0.0869 0.0880
0.0948 0.0959 0.0970 0.0982 0.0993
0.1061 0.1072 0.1083 0.1095 0.1106
(MULTIPLY TABULAR VALUES BY 0.0100)
0.0158 0.0169 0.0181 0.0192 0.0203
0.0271 0.0282 0.0293 0.0305 0.0316
0.0384 0.0395 0.0406 0.0418 0.0429
0.0496 0.0508 0.0519 0.0530 0.0542
0.0609 0.0621 0.0632 0.0643 0.0654
0.0722 0.0733 0.0745 0.0756 0.0767
0.0835 0.0846 0.0858 0.0869 0.0880
0.0948 0.0959 0.0970 0.0982 0.0993
0.1061 0.1072 0.1083 0.1095 0.1106
(MULTIPLY TABULAR VALUES BY 0.1000)
0.0158 0.0169 0.0181 0.0192 0.0203
0.0271 0.0282 0.0293 0.0305 0.0316
0.0384 0.0395 0.0406 0.0417 0.0429
0.0496 0*0508 0.0519 0.0530 0.0542
0.0609 0.0621 0.0632 0.0643 0.0654
0.0722 0.0733 0.0745 0.0756 0.0767
0.0835 0.0846 0.0858 0.0869 0.0880
0.0948 0.0959 0.0970 0.0982 0.0993
0.1061 0.1072 0.1083 0.1094 0.1106
(MULTIPLY TABULAR VALUES BY 1.0000)
0.0158 0.0169 0.0181 0.0192 0.0203
0.0271 0.0282 0.0293 0.0305 0.0316
0.0384 0.0395 0.0406 0.0417 0.0429
0.0496 0.0507 0.0519 0.0530 0.0541
0.0609 0.0620 0.0631 0.0642 0.0654
0.0721 0.0732 0.0744 0.0755 0.0766
0.0833 0.0845 0.0856 0.0867 0.0878
0.0946 0.0957 0.0968 0.0979 0.0990
0.1058 0.1069 0.1080 0.1091 0.1102
0.0214
0.0327
0,0440
0.0553
0.0666
0.0779
0.0891
0.1004
0.1117
0.0214
0.0327
0.0440
0.0553
0.0666
0.0779
0.0891
0.1004
0.1117
0.0214
0.0327
0.0440
0.0553
0.0666
0.0779
0.0891
0.1004
0.1117
0.0214
0.0327
0.0440
0.0552
0.0665
0.0777
0.0890
0.1002
0.1113
-------
XD=
XD =
CO
X0=
XD'
Y0=
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
I
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
TABLE 3
VALUES OF SIGMA (PSEUDO SKINt VERTICAL FRACTURE)
POWER OF 10 APPLICABLE TO YD= -2
0.0 1.000 2,000 3.000 4.000 5.000 6.000 7.000 8.000 9.000
POWER OF
0.0
•0.000
•0.000
•0.000
•0.001
•0.001
•0.002
•0.002
•0.003
•0.004
0.0
•0.005
•0.020
•0.046
•0.082
•0.131
0.193
•0.270
•0.368
•0.495
-0.000
-0.000
-0.000
-0.001
-0.001
-0.001
-0.002
-0.003
-0.003
-0.004
-0.000
-0.005
-0.020
-0.046
-0.082
-0.131
-0.193
-0.271
-0.368
-0.495
-0.000
-0.000
-0.000
-0.001
-0.001
-0.001
-0.002
-0.003
-0.003
-0.004
-0.000
-0.005
-0.020
-0.046
-0.083
-0.131
-0.193
-0.271
-0.369
-0.496
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
POW
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
.000
.000
.001
.001
.001
.002
.002
.003
.004
.005
ER OF
.000
.005
.021
.046
.083
.131
.193
.271
.369
.497
POWER OF
0.0
:****.*
1.648
•2.079
2.376
2.603
•2.787
2.942
•3.077
3.195
0.0
3.301
3.995
4.401
4.689
4.912
5.094
5.248
5.382
5.500
-0.000
-0.701
-1.648
-2.079
-2.376
-2.603
-2.787
-2.942
-3.077
-3.195
-0.000
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
-0.000
-0.709
-1.648
-2.079
-2.376
-2.603
-2.787
-2.942
-3.077
-3.195
-0.000
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
-0
-0
-1
-2
-2
-2
-2
-2
-3
-3
POW
-0
-3
-3
-4
-4
-4
-5
-5
-5
-5
.000
.717
.648
.079
.376
.603
.787
.942
.077
.195
ER OF
.000
.301
.995
.401
.689
.912
.094
.248
.382
.500
10 APPLI
-0.001
-0.001
-0.001
-0.001
-0.002
-0.002
-0.003
-0.003
-0.004
-0.005
10 APPLI
-0.001
-0.006
-0.021
-0.047
-0.083
-0.132
-0.194
-0.272
-0.370
-0.499
10 APPLI
-0.001
-0.724
-1.648
-2.080
-2.376
-2.603
-2.787
-2.943
-3.077
-3.195
10 APPLI
-0.001
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
CABLE
-0.001
-0.001
-0.001
-0.002
-0.002
-0.003
-0.003
-0.004
-0.004
-0.005
CABLE
-0.001
-0.006
-0.021
-0.047
-0.084
-0.132
-0.195
-0.273
-0.371
-0.501
CABLE
-0.001
-0.732
-1.648
-2.080
-2.376
-2.603
-2.787
-2.943
-3.077
-3,195
CABLE
-0.001
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
TO XD=
-0.002
-0.002
-0.002
-0.002
-0.003
-0.003
-0.004
-0.004
-0.005
-0.006
TO XD=
-0.002
-0.007
-0.022
-0.048
-0.084
-0.133
-0.196
-0.274
-0.373
-0.503
TO X0=
-0.002
-0.740
-1.649
-2.080
-2.376
-2.603
-2.787
-2.943
-3.077
-3.195
TO XD=
-0.002
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
-2
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-1
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
0
-0.
-0.
-1.
-2.
-2.
-2.
-2.
-2.
-3.
-3.
1
-0.
-3.
-3.
-4.
-4.
-4.
-5.
-5.
-5.
-5.
002
002
003
003
003
004
004
005
006
007
002
007
023
048
085
134
197
275
375
505
002
748
649
080
376
603
787
943
077
195
002
301
995
401
689
912
094
248
382
500
-0.003
-0.003
-0.003
-0.004
-0.004
-0.004
-0.005
-0.006
-0.006
-0.007
-0.003
-0.008
-0.023
-0.049
-0.086
-0.135
-0.198
-0.277
-0.376
-0.508
-0.003
-0.755
-1.649
-2.080
-2.376
-2.603
-2.787
-2.943
-3.077
-3.195
-0.003
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
-0.004
-0.004
-0.004
-0.004
-0.005
-0.005
-0.006
-0.007
-0.007
-0.008
-0.004
-0.009
-0.024
-0.050
-0.087
-0.136
-0.199
-0.278
-0.378
-0.511
-0.004
-0.763
-1.649
-2.080
-2.376
-2.603
-2.787
-2.943
-3.077
-3.195
-0.004
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.3R2
-5.500
-------
XD=
XD=
CO
en
XD =
Y0 =
0
I
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
I
2
3
4
5
6
7
8
9
0.0
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
1.000
POWER OF 10 APPLICABLE TO Y0= -2
2.000 3.000 4.000 5.000 6.000 7.000
6.000
9.000
0.0
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
0.0
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
0.0
•10.210
-10.903
•11.309
- 11.597
-11.820
-12.002
- 12.156
-12.290
-12.408
-0.000
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.000
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.000
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-0.000
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.000
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.000
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
POWER OF
-0.000
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
POWER OF
-0.000
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
POWER OF
-0.000
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
10 APPL
-0.001
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
10 APPL
-0.001
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
10 APPL
-0.001
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
ICABLE
-0.001
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
ICABLE
-0.001
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
ICABLE
-0.001
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
TO X
-0
-5
-6
-6
-6
-7
-7
-7
-7
-7
D=
.002
.605
.298
.704
.991
.215
.397
.551
.685
.802
TO XD=
-0
-7
-8
-9
-9
-9
-9
-9
-9
-10
TO X
-0
-10
-10
-11
-11
-11
-12
-12
-12
-12
.002
.908
.601
.006
.294
.517
.700
.854
.987
.105
D—
.002
.210
.903
.309
.597
.820
.002
.156
.290
.408
2
-0.
-5.
—6 .
-6.
—6 «
-7.
-7.
-7.
-7.
-7.
3
-0.
-7.
-8.
-9.
-9.
-9.
-9.
-9.
-9.
-10.
4
-0.
-10.
-10.
-11.
-11.
-11.
-12.
-12.
-12.
-12.
002
605
298
704
991
215
397
551
685
802
002
908
601
006
294
517
700
854
987
105
002
210
903
309
597
820
002
156
290
408
-0.003
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.003
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.003
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-0.004
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.004
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.004
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-------
XD=
xo=
CO
XD=
XD=
YD=
0
I
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
I
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0.0
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
POWER OF 10 APPLICABLE TO YD= -1
1.000 2.000 3.000 4.000 5.000 6.000 7.000
8.000
9.000
0.0
-0.000
-0.000
-0.000
-0.001
-0.001
-0.002
-0.002
-0.003
-0.004
0.0
-0.005
-0.020
-0.046
-0.082
-0.131
-0.193
-0.270
-0.368
-0.495
0.0
*******
-1.648
-2.079
-2.376
-2.603
-2.787
-2.942
-3.077
-3.195
0.0
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
-0.005
-0.005
-0.005
-0.005
-0.006
-0.006
-0.007
-0.007
-0.008
-0.009
-0.005
-0.010
-0.025
-0.051
-0.088
-0.137
-0.200
-0.280
-0.381
-0.513
-0.005
-0.770
-1.650
-2.080
-2.376
-2.603
-2.787
-2.943
-3.077
-3.195
-0.005
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
-0.020
-0.020
-0.020
-0.020
-0.020
-0.021
-0.021
-0.022
-0.023
-0.024
-0.020
-0.025
-0.040
-0.067
-0.105
-0.156
-0.221
-0,304
-0.408
-0.540
-0.020
-0.845
-1.655
-2.082
-2.377
-2.604
-2.788
-2.943
-3.077
-3.195
-0.020
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
POWER OF
-0.043
-0.043
-0.043
-0.044
-0.044
-0.044
-0.045
-0.046
-0.047
-0.047
POWER OF*
-0.043
-0.048
-0.065
-0.092
-0.131
-0.184
-0.251
-0.335
-0.439
-0.564
POWER OF
-0.043
-0.918
-1.663
-2.085
-2.379
-2.605
-2.788
-2.943
-3.078
-3.196
POWER OF
-0.043
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
10
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
10
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
10
-0
-0
-1
-2
-2
-2
-2
-2
-3
-3
10
-0
-3
-3
-4
-4
-4
-5
-5
-5
-5
APPLICABLE
.074
.074
.074
.075
.075
.076
.076
.077
.078
.079
APPLI
.074
.080
.096
.125
.165
.218
.286
.370
.470
.586
APPLI
.074
.987
.674
.089
.381
.606
.789
.944
.078
.196
APPLI
.074
.302
.996
.401
.689
.912
.094
.248
.382
.500
-0.112
-0.112
-0.112
-0.112
-0.112
-0.113
-0.114
-0.114
-0.115
-0.116
CABLE
-0.112
-0.117
-0.134
-0.163
-0.203
-0.257
-0.324
-0.405
-0.501
-0.986
CABLE
-0.112
-1.055
-1.687
-2.095
-2.384
-2.608
-2.791
-2.945
-3.079
-3.197
CABLE
-0.112
-3.302
-3.996
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
TO XD= -2
-0
-0
-0
-0
-0
-0
-0
-0
-0
-0
.154
.154
.154
.154
.155
.155
.156
.156
.157
.158
-0.199
-0.199
-0.200
-0.200
-0.200
-0.201
-0.201
-0.202
-0.203
-0.204
-0.247
-0.247
-0.248
-0.248
-0.248
-0.249
-0.249
-0.250
-0.251
-0.252
-0.297
-0.297
-0.297
-0.297
-0.298
-0.298
-0.299
-0.299
-0.300
-0.301
TO XD= -1
-0
-0
-0
-0
-0
-0
-0
-0
-0
-1
.154
.159
.176
.205
.245
.298
.363
.441
.531
.059
-0.199
-0.205
-0.222
-0.250
-0.289
-0.340
-0.403
-0.477
-1.078
-1. 129
-0.247
-0.253
-0.269
-0.296
-0.334
-0.383
-0.443
-1.108
-1.150
-1.195
-0.297
-0.302
-0.318
-0.344
-0.380
-1.119
-1.147
-1.181
-1.218
-1.259
TO X0= 0
-0
-1
-I
-2
-2
-2
-2
-2
-3
-3
.154
.120
.703
.101
.388
.610
.792
.946
.080
.197
-0. 199
-1.183
-1. 722
-2. 109
-2.392
-2.613
-2.794
-2.948
-3. 081
-3.198
-0.247
-1.243
-1.741
-2.118
-2.397
-2.616
-2.796
-2.949
-3.082
-3.199
-0.297
-1.302
-1.763
-2. 127
— 2.402
--2. 619
-2.799
-2.951
-3.083
-3.200
TO XD= 1
-0
-3
-3
-4
-4
-4
-5
-5
-5
-5
.154
.303
.996
.401
.689
.912
.094
.248
.382
.500
-0. 199
-3.303
-3.996
-4.401
-4.689
-4.912
-5.094
-5.249
-5.382
-5.500
-0.247
-3.304
-3.996
-4.401
-4.689
-4.912
-5.094
-5.249
-5.382
-5.500
-0.297
-3.305
-3.996
-4.401
-4.689
-4.912
-5.094
-5.249
-5.382
-5.500
-------
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
XD=
CO
XD=
Y0=
0
1
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
I
2
3
4
5
6
7
8
9
0.0
1.000
POWER OF 10 APPLICABLE TO YD= -1
2.000 3.000 4.000 5.000 6.000 7.000
8.000
9.000
0.0
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
0.0
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9,987
-10.105
0.0
•10.210
-10.903
-11.309
•11.597
-11.820
-12.002
-12.156
-12.290
•12.408
-0.005
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.005
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.005
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-0.020
-5.605
-6.298
-6,704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.020
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.020
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
POWER OF
-0.043
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
POWER OF
-0.043
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
POWER OF
-0.043
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
10
-0
-5
-6
-6
— 6
APPLI
.074
.605
.298
.704
.991
-7.215
-7
-7
-7
-7
10
-0
-7
-8
—9
-9
-9
-9
-9
—9
-10
10
-0
-10
-10
-11
-11
-11
-12
-12
-12
-12
.397
.551
.685
.802
APPLI
.074
.908
.601
.006
.294
.517
.700
.854
.987
.105 -
APPLI
.074
.210 -
.903 -
.309 -
.597 -
.820 -
.002 -
,156 -
.290 -
.408 -
CABLE
-0.112
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
CABLE
-0.112
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
10.105
CABLE
-0.112
10.210
10.903
11.309
11.597
11.820
12.002
12.156
12.290
12.408
TO XD=
-0
-5
-6
-6
-6
-7
-7
-7
-7
-7
.154
.605
.298
.704
.991
.215
.397
.551
.685
.802
TO XD=
-0
-7
-8
—9
-9
-9
-9
-9
-9
-10
TO X
-0
-10
-10
-11
-11
-11
-12
-12
-12
-12
.154
.908
.601
.006
.294
.517
.700
.854
.987
.105
D=
.154
.210
.903
.309
.597
.820
.002
.156
.290
.408
2
-0.199
-5.605
-6.298
-6. 704
-6. 991
-7.215
-7.397
-7.551
-7.685
-7.802
3
-0. 199
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9. 854
-9.987
-10.105
4
-0.199
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12. 156
-12.290
-12.408
-0.247
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.247
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.247
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-0.297
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-0.297
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-0.297
-10.210
-10.903
-11 .309
-11.597
-11 .820
-12.002
-12.156
-12.290
-12.408
-------
XD=
XD=
CO
00
XD=
XD=
YD=
0
1
2
3
4
5
6
7
8
9
0
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0.0
TABLE 3
VALUES OF SIGMA (PSEUDO SKINt VERTICAL FRACTURE)
POWER OF 10 APPLICABLE TO Y0= 0
1.000 2.000 3.000 4.000 5.000 6.000 7.000
8.000
9.000
0.0
-0.000
-0.000
-0.000
-0.001
-0.001
-0.002
-0.002
-0.003
-0.004
0.0
-0.005
-0.020
-0.046
-0.082
-0.131
-0.193
-0.270
-0.368
-0.495
0.0
*******
-1.648
-2.079
-2.376
-2.603
-2.787
-2.942
-3.077
-3.195
0.0
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5.500
*******
-1.132
-1.132
-1,132
-1.132
-1.133
-1.133
-1.133
-1.134
-1.134
*******
-1.134
-1.142
-1.154
-1.171
-1.193
-1.219
-1.249
-1.283
-1.319
*******
-1.358
-1.785
-2.138
-2.408
-2.623
-2.801
-2.953
-3.085
-3.201
*******
-3.306
-3.997
-4.402
-4.689
-4.912
-5.094
-5.249
-5.382
-5.500
-1.732
-1.732
-1.732
-1.732
-1.732
-1.732
-1.732
-1.733
-1.733
-1.733
-1.732
-1.733
-1.736
-1.741
-1.748
-1.757
-1.767
-1.779
-1.793
-1.808
-1.732
-1.825
-2.040
-2.278
-2.493
-2.679
-2.841
-2.982
-3.108
-3.220
-1.732
-3.321
-4.000
-4.403
-4.690
-4.913
-5.095
-5.249
-5.382
-5.500
POWER OF
-2.117
-2.117
-2.117
-2.117
-2.117
-2.117
-2.117
-2.117
-2.117
-2.117
POWER OF
-2.117
-2.117
-2.119
-2.121
-2.124
-2.129
-2.134
-2.141
-2.148
-2.156
POWER OF
-2.117
-2.164
-2.288
-2.445
-2.608
-2.761
-2.901
-3.028
-3.144
-3.248
POWER OF
-2.117
-3.344
-4.006
-4.406
-4.692
-4.914
-5.096
-5.249
-5.383
-5.500
10
-2
-2
-2
-2
-2
-2
-2
-2
-2
-2
10
-2
-2
-2
-2
-2
-2
-2
-2
-2
-2
APPLI
.397
.397
.397
.397
.397
.397
.397
.397
.397
.397
APPLI
.397
.397
.398
.399
.401
.404
.407
.411
.415
.420
10' APPLI
-2
-2
-2
-2
-2
-2
-2
-3
-3
-3
10
-2
-3
-4
-4
-4
-4
-5
-5
-5
-5
.397
.425
.503
.611
.733
.856
.974
.086
.190
.286
APPLI
.397
.376
.015
.410
.694
.915
.097
.250
.383
.501
CABLE TO XD=
-2.616
-2.616
-2.616
-2.616
-2.616
-2.616
-2.616
-2.616
-2.616
-2.616
-2.796
-2.796
-2.796
-2.796
-2.796
-2.796
-2.796
-2.796
-2.796
-2.796
CABLE TO XD=
-2.616
-2.616
-2.617
-2.618
-2.619
-2.621
-2.623
-2.625
-2.628
-2.631
CABLE TO
-2.616
-2.635
-2.688
-2.766
-2.858
-2.956
-3.055
-3.151
-3.244
-3.331
CABLE TO
-2.616
-3.413
-4.026
-4.415
-4.697
-4.917
-5.098
-5.251
-5.384
-5.501
-2.796
-2.796
-2.797
-2.798
-2.799
-2.800
-2.801
-2.803
-2.805
-2.807
XD=
-2.796
-2.810
-2.848
-2.906
-2.977
-3.056
-3.138
-3.221
-3.302
-3.381
XD =
-2.796
-3.456
-4.039
-4.421
-4.700
-4.919
-5.099
-5.252
-5.385
-5.502
-2
-2.
-2.
-2.
-2.
-2.
-2.
-2.
-2.
-2.
-2.
-1
— 2 .
-2.
-2.
-2.
-2.
-2.
-2.
-2.
-2.
-2.
0
-2.
-2.
-2.
-3.
-3.
-3.
-3.
-3.
-3.
-3.
I
-2.
-3.
-4.
-4.
-4.
-4.
-5.
-b.
-5.
-5.
949
949
949
949
949
949
949
949
949
949
949
949
950
950
951
952
953
954
956
957
949
959
988
032
089
153
222
292
364
433
949
502
053
428
704
922
101
253
386
503
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.082
-3.083
-3.083
-3.084
-3.085
-3.086
-3.087
-3.088
-3.082
-3.090
-3.112
-3.147
-3.192
-3.245
-3.303
-3.364
-3.426
-3.488
-3.082
-3.550
-4.070
-4.435
-4.708
-4.925
-5.103
-5.255
-5.387
-5.504
-3.199
-3.199
-3.199
-3.199
-3il99
-3.199
-3.199
-3.199
-3.199
-3.199
-3.199
-3.199
-3.200
-3.200
-3.200
-3.201
-3.201
-3.202
-3.203
-3.204
-3.199
-3.205
-3.223
-3.251
-3.289
-3.333
-3.382
-3.434
-3.489
-3.544
-3.199
-3.599
-4.088
-4.444
-4.713
-4.928
-5.105
-5.257
-5.388
-5.505
-------
xo=
XD=
CO
vo
XD=
YD=
0
1
2
3
4
5
6
7
a
9
o
i
2
3
4
5
6
7
8
q
0
1
2
3
4
5
6
7
8
9
0.0
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
POWER OF 10 APPLICABLE TO YD= 0
1.000 2.000 3.000 4.000 5.000 6.000 7.000
8.000
9.000
0.0
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
0.0
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9,987
•10.105
0.0
•10.210
•10.903
•11.309
•11.597
•11.820
•12.002
•12.156
•12.290
•12.408
*******
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
*******
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
*******
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-1.732
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
-1.732
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-1.732
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
POWER OF
-2.1 17
-5.606
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
POWER OF
-2.117
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
POWER OF
-2.117
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
10
-2
-5
-6
-6
-6
-7
-7
-7
-7
-7
10
-2
-7
-8
-9
-9
-9
-9
-9
-9
-10
10
-2
-10
-10
-11
-11
-11
-12
-12
-12
-12
APPLICABLE
.397
.606
.299
.704
.992
.215
.397
.551
.685
.802
APPLI
.397
.908
.601
.006
.294
.517
.700
.854
.987
.105 -
APPLI
.397
.210 -
.903 -
.309 -
.597 -
.820 -
.002 -
.156 -
.?90 -
.408 -
-2.616
-5.606
-6.299
-6.704
-6.992
-7.215
-7.397
-7.551
-7.685
-7.802
CABLE
-2.616
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.354
-9.987
10.105
CABLE
-2.616
10.210
10.903
11.309
11.597
11.820
12.002
12.156
L2.290
12.408
TO XD=
-2.796
-5.607
-6.299
-6.704
-6.992
-7.215
-7.397
-7.551
-7.685
-7.802
TO XD=
-2.796
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
TO XD=
-2.796
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
2
-2.
-5.
-6.
-6.
-6.
-7.
-7.
-7.
-7.
-7.
3
-2.
-7.
-8.
-9.
-9.
-9.
-9.
-9.
-9.
-10.
4
-2.
-10.
-10.
-11.
-11.
-11.
-12.
-12.
-12.
-12.
949
608
299
704
992
215
397
551
685
802
949
908
601
006
294
517
700
854
987
105
949
210
903
309
597
820
002
156
290
408
-3.082
-5.608
-6.299
-6.704
-6.992
-7.215
-7.397
-7.551
-7.685
-7.802
-3.082
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-3.08?
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-3.199,
-5.609
-6.299
-6.704
-6.992
-7.215
-7.397
-7.551
-7.685
-7.802
-3.199
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-3.199
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-------
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
XD =
XD =
XD =
xo=
YD =
0
I
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
a
9
0
L
2
3
4
5
6
7
8
POWER OF
0.0 1.000 2.000 3.000
10 APPLICABLE TO YD= 1
4.000 5.000 6.000 7.000 8.000 9.000
0.0
•0.000
•0.000
•0.000
•0.001
•0.001
•0.002
•0.002
•0.003
•0.004
0.0
•0.005
•0.020
•0.046
•0.082
•0.131
•0.193
•0.270
•0.368
•0.495
0.0
c*****
•1.648
•2.079
•2.376
•2.603
•2.787
•2.942
3.077
•3.195
0.0
•3.301
3.995
•4.401
4.689
4.912
•5.094
•5.248
•5.382
•5.500
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.304
-3.305
-3.305
-3.305
-3.306
-3.307
-3.307
-3.308
-3.304
-3.309
-3.324
-3.347
-3.378
-3.415
-3.457
-3.502
-3.550
-3.599
-3.304
-3.649
-4.107
-4.454
-4.719
-4.932
-5.108
-5.259
-5.390
-5.506
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.996
-3.997
-3.997
-3.997
-3.997
-3.996
-3.997
-4.001
-4.007
-4.016
-4.026
-4.039
-4.054
-4.070
-4.088
-3.996
-4.108
-4.342
-4.585
-4.800
-4.986
-5.147
-5.288
-5.412
-5.524
POWER OF
-4.401
-4.401
-4.401
-4.401
-4.401
-4.401
-4.401
-4.401
-4.401
-4.401
POWER OF
-4.401
-4.401
-4.401
-4.401
-4.401
-4.402
-4.402
-4.402
-4.402
-4.402
POWER OF
-4.401
-4.402
-4.404
-4.406
-4.410
-4.415
-4.421
-4.428
-4.436
-4.444
POWER OF
-4.401
-4.454
-4.585
-4.748
-4.912
-5.066
-5.206
-5.333
-5.448
-5.552
10 APPLICABLE
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
10 APPL
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
-4.689
10 APPL
-4.689
-4.689
-4.690
-4.692
-4.694
-4.697
-4.700
-4.704
-4.709
-4.714
10 APPL
-4.689
-4.719
-4.801
-4.912
-5.035
-5.159
-5.278
-5.390
-5.494
-5.590
-4.912
-4.912
-4.912
-4.912
-4.912
TO XD=
-5
-5
-5
-5
-5
-4.912 -5
-4.912
-4.912
-4.912
-4.912
ICABLE
-4.912
-4.912
-4.912
-4.912
-4.912
-4.912
-4.912
-4.912
-4.912
-4.912
ICABLE
-4.912
-4.912
-4.913
-4.914
-4.915
-4.917
-4.919
-4.922
-4.925
-4.928
ICABLE
-4.912
-4.932
-4.986
-5.066
-5.159
-5.259
-5.358
-5.455
-5.547
-5.634
-5
-5
-5
-5
TO X
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
.094
.094
.094
.094
.094
.094
.094
.094
.094
.094
0=
.094
.094
.094
.094
.094
.094
.094
.094
.094
.095
TO XD=
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
TO X
-5
-5
-5
-5
-5
-5
-5
-5
-5
-5
.094
.095
.095
.096
.097
.098
.099
.101
.103
.106
0=
.094
.108
.147
.206
.278
.358
.441
.524
.605
.684
-2
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-1
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
0
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
1
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
-5.
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
249
250
251
252
254
255
257
249
259
288
333
390
455
524
595
666
736
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.382
-5.383
-5.383
-5.384
-5.385
-5.386
-5.387
-5.388
-5.382
-5.390
-5.412
-5.448
-5.494
-5.547
-5.605
-5.666
-5.729
-5.791
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.500
-5.501
-5.501
-5.502
-5.503
-5.504
-5.505
-5.500
-5.506
-5.524
-5.553
-5.590
-5.634
-5.684
-5.736
-5.791
-5.846
-------
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
XD =
XD=
X0 =
YD =
0
I
2
3
4
5
6
7
8
9
0
I
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
3
9
POWER OF 10 APPLICABLE TO Y0= 1
0.0
0.0
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
0.0
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
0.0
- 10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
- 12.290
-12.408
1.000
-3.304
-5.610
-6.300
-6.704
-6.992
-7.215
-7.397
-7.551
-7.685
-7.802
-3.304
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-3.304
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
2.000
-3.996
-5.625
-6.303
-6.706
-6.993
-7.215
-7.397
-7.551
-7.685
-7.803
-3.996
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-3,996
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
3.000
POWER OF
-4.401
-5.648
-6.309
-6.709
-6.994
-7.216
-7.398
-7.552
-7.685
-7.803
POWER OF
-4.401
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
POWER OF
-4.401
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
4.000
10 APP
-4.689
-5.679
-6.318
-6.713
-6.996
-7.218
-7.399
^7.553
-7.686
-7.803
10 APP
-4.689
-7.909
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
10 APP
-4.689
-10.210
-10.903
-11 .309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
5.000
LICABLE
-4. 912
-5.717
-6.329
-6.717
-6.999
-7.220
-7.400
-7.554
-7.687
-7.804
LICABLE
-4.912
-7.909
-8.601
-9.007
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
LICABLE
-4.912
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12. 156
-12.290
-12.408
6
.000
TO XD=
-5
-5
-6
-6
-7
-7
-7
-7
-7
-7
TO X
-5
-7
-8
-9
-9
-9
-9
-9
-9
-10
.094
.759
.341
.723
.003
.222
.402
.555
.687
.805
D=
.094
.910
.601
.007
.294
.517
.700
.854
.987
,105
TO XD=
-5
-10
-10
-11
-11
-11
-12
-12
-12
-12
.094
.210
.903
.309
.597
.820
.002
.156
.290
.408
7.
2
-5.
-5.
-6.
-6.
-7.
-7.
-7.
-7.
-7.
-7.
3
-5.
-7.
-8.
-9.
-9.
-9.
-9.
-9.
-9.
-10.
4
-5.
-10.
-10.
-11.
-11.
-11.
-12.
-12.
-12.
-12.
000
249
805
356
730
007
224
404
556
688
805
249
910
602
007
294
517
700
854
987
105
249
210
903
309
597
820
002
156
290
408
8.000
-5.382
-5.853
-6.373
-6.738
-7.011
-7.227
-7.406
-7.558
-7.690
-7.806
-5.382
-7.911
-8.602
-9.007
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-5.382
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
9.000
-5.500
-5.902
-6.391
-6.747
-7.016
-7.231
-7.408
-7.559
-7.691
-7.807
-5.500
-7.912
-8.602
-9.007
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-5.500
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-------
XD-
XD=
ro
XD=
X0=
YD=
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0.0
TABLE 3
VALUES OF SIGMA (PSEUDO SKINt VERTICAL FRACTURE)
POWER OF 10 APPLICABLE TO YD= 2
1.000 2.000 3.000 4.000 5.000 6.000 7.000
8.000 9.000
0.0
-0.000
-0.000
-0.000
-0.001
-0.001
-0.002
-0.002
-0.003
-0.004
0.0
-0.005
-0.020
-0.046
-0.082
-0.131
-0.193
-0.270
-0.368
-0.495
0.0
: ******
-1.648
-2.079
-2.376
-2.603
-2.787
-2.942
-3.077
-3.195
0.0
-3.301
-3.995
-4.401
-4.689
-4.912
-5.094
-5.248
-5.382
-5,500
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
— 5. 60 1>
-5.605
-5.605
-5.605
-5.605
-5.605
-5.605
-5.606
-5.606
-5.606
-5.607
-5.608
-5.608
-5.609
-5.605
-5.610
-5.625
-5.648
-5.679
-5.717
-5.759
-5.805
-5.853
-5.902
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.298
-6.299
-6.299
-6.299
-6.299
-6.299
-6.299
-6.298
-6.300
-6.303
-6.309
-6.318
-6.329
-6.341
-6.356
-6.373
-6.391
POWER OF
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
POWER OF
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
POWER OF
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
-6.704
PPwER OF
-6.704
-6.704
-6.706
-6.709
-6.713
-6.717
-6.723
-6.730
-6.738
-6.747
10
-6
-6
-6
-6
-6
-6
-6
-6
-6
-6
10
-6
-6
-6
-6
-6
-6
-6
-6
-6
-6
10
-6
-6
-6
-6
-6
-6
-6
-6
-6
-6
10
-6
-6
-6
-6
-6
-6
-7
-7
-7
-7
APPLICABLE
.991
.991
.991
.991
.991
.991
.991
.991
.991
.991
APPLI
.991
.991
.991
.991
.991
.991
.991
.991
.991
.991
.APPLI
.991
.991
.991
.991
.992
.992
.992
.992
.992
.992
APPLI
.991
.992
.993
.994
.996
.999
.003
.007
.011
.016
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
CABLE
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
CABLE
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
-7.215
CABLE
-7.215
-7.215
-7.215
-7.216
-7.218
-7.220
-7.222
-7.224
-7.227
-7.231
TO XD=
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
TO xn=
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
TO XD=
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
-7.397
TO XD =
-7.397
-7.397
-7.397
-7.398
-7.399
-7.400
-7.402
-7.404
-7.406
-7.408
-2
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-1
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
0
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
I
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
-7.
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
551
552
553
554
555
556
558
559
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.685
-7.635
-7.685
-7.685
-7.685
-7.686
-7.687
-7.687
-7.688
-7.690
-7.691
-7.802
-7.802
-7.802
-7.802
-7.802
-7-.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.802
-7.803
-7.803
-7.803
-7.804
-7.805
-7.805
-7.806
-7.807
-------
xo=
XD=
CO
X0=
0
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
POWER OF 10 APPLICABLE TO YD= 2
0.0 1.000 2.000 3.000 4.000 5.000 6.000 7.000
POWER OF 10 APPLICABLE TO XD=
8.000 9.000
0.0
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
0.0
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9, 987
-10.105
0.0
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.2^0
-12.408
-5.605
-5.952
-c.410
-6.756
-7.022
-7.234
-7.411
-7.561
-7.692
-7.809
-5.605
-7.913
-«. 602
-9.007
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
-5.605
-10.210
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-6.298
-6.410
-6.645
-6.888
-7.103
-7.289
-7.450
-7.590
-7.715
-7.826
-6.298
-7.927
-8.606
-9.009
-9.295
-9.518
-9.700
-9.854
-9.988
-10.105
-6.298
-10.211
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-6.704
-6.756
-6.888
-7.050
-7.215
-7.368
-7.509
-7.635
-7.750
-7.855
POWER OF
-6.704
-7.951
-8.612
-9.011
-9.297
-9.519
-9.701
-9.855
-9.988
-10.106
POWER OF
-6.704
-10.211
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.403
-6.991
-7.022
-7.103
-7.215
-7.338
-7.462
-7.581
-7.692
-7.796
-7.893
10 APPL
-6.991
-7.982
-8.621
-9.015
-9.299
-9.520
-9.702
-9,855
-9.988
-10.106
10 APPL
-6.991
-10.211
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-7.215
-7.234
-7.289
-7.368
-7.462
-7.561
-7.661
-7.757
-7.849
-7.937
I CABLE
-7.215
-8.019
-8.631
-9.020
-9.302
-9.522
-9.703
-9.856
-9.989
-10.107
ICABLE
-7.215
-10.212
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-7.397
-7.411
-7.450
-7.509
-7.581
-7.661
-7.744
-7.826
-7.908
-7.986
TO XD=
-7.397
-8.061
-8.644
-9.026
-9.305
-9.524
-9.704
-9.857
-9.990
-10.107
TO XD=
-7.397
-10.212
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-7.551
-7.561
-7.590
-7.635
-7. 692
-7.757
-7.826
-7. 898
-7.969
-8.039
3
-7.551
-8.107
-8.659
-9.033
-9.309
-9. 527
-9.706
-9. 859
-9.991
-10.108
4
-7.551
-10.213
-10.904
-11.309
-11. 597
-11.820
-12.002
-12. 156
-12.290
-12. 408
-7.685
-7.692
-7.715
-7.750
-7. 796
-7.849
-7.908
-7.969
-8.031
-8.094
-7.685
-8.155
-8.675
-9.041
-9.314
-9.530
-9.708
-9.860
-9.992
-10.109
-7.685
-10.214
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12,290
-12.408
-7.802
-7.809
-7.826
-7.855
-7.893
-7.937
-7.986
-8.039
-8.094
-8.149
-7.802
-8.204
-8.693
-9.049
-9.319
-9.533
-9.711
-9.862
-9.993
-10.110
-7.80?
-10.214
-10.904
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-------
xo=
XD=
XD =
XD=
YD =
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
o
7
8
9
0
1
2
3
4
5
6
7
8
9
0.0
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTUP-E)
POWER OF 10 APPLICABLE TO YD= 3
1.000 2.000 3.000 4.000 5.000 6.000 7.000
8.000
9.000
0.0
-0.000
-0.000
-0.000
-0.001
-0.001
-0.002
-0.002
-0.003
-0.004
0.0
-0.005
-0.020
-0.046
-0.082
-0.131
-0.193
-0.270
-0.368
-0.495
0.0
*******
-1.648
-2.079
-2.376
-2.603
-2.787
-2.942
-3.077
-3.195
0.0
-3.301
-3.995
-4.401
-H.689
-4.912
-5.094
-5.248
-5.382
-5.500
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7. 90S
-7.908
-7.908
-7.903
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
•7.90rt
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.908
-7.909
-7.909
-7.910
-7.910
-7.911
-7.912
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-8.601
-3.601
-8.601
-8.601
-8.602
-3.602
-B.6U2
POWER OF
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
POWER OF
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
POWER OF
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
-9.006
POWER OF
-9.006
-9.006
-9.006
-9.006
-9.006
-9.007
-9.007
-9.007
-9.007
-9.007
10 APPL
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
10 APPL
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
10 APPL
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
10 APPL
-9.294
-9.?94
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
-9.294
ICABLE TO X0= -2
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517-
-9.517
-9.517
-9.517
ICABLE TO
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
ICABLE TO
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
ICABLE TO
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9.517
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
X
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
.700
.700
.700
.700
.700
.700
.700
.700
.700
.700
D= -1
.700
.700
.700
.700
.700
.700
.700
.700
.700
.700
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-0.
-9.
854
854
854
854
854
854
854
854
854
854
854
854
854
854
854
854
854
854
854
854
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
XD= 0
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
.700
.700
.700
.700
.700
.700
.700
.700
.700
.700
-9.
-9.
- 9
-9l
-9.
-9.
-9.
-9.
-9.
-9.
854
854
854
854
854
854
854
854
854
854
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
XD= 1
-9
-9
-9
-9
-9
-o
-9
-q
-9
-9
.700
.700
.700
.700
.700
.700
.700
.700
.700
.700
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
854
854
854
854
854
854
854
854
854
854
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-9.987
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-10.105
-------
VALUES OF SIGMA
TABLE 3
(PSEUDO SKIN,
VERTICAL FRACTURE)
X0 =
XD=
en
XD=
YD =
0
I
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
I
2
3
4
5
6
7
8
9
POWER OF 10 APPLICABLE TO YD= 3
0.0 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000
0.0
-5.605
-6.298
-6. 704
-6.991
-7.215
-7.397
-7.551
-7.685
-7.802
0.0
-7.908
-8.601
-9.006
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
0.0
-10.210
-10.903
-11.309
-11.597
-11.820
-12.002
-12.156
-12.290
-12.408
-7.908
-7.913
-7.927
-7.951
-7.982
-8.019
-8.061
-8.107
-8.155
-8.704
-7.908
-8.P54
-8.712
-9.059
-9.324
-9.537
-9.713
-9.864
-9.995
-10.111
-7.908
-10.215
-10.905
-11.310
-11.597
-11.820
-12.002
-I2.15b
-12.290
-12.408
-8.601
-8.602
-8.606
-8.612
-8.621
-8.631
-8.644
-8.659
-8.675
-8.693
-8.601
-8.712
-8.947
-9.190
-9.406
-9.591
-9.752
-9.893
-10.018
-10.129
-3.601
-10.230
-10.908
-11.311
-11.598
-11.821
-12.003
-12.157
-12.290
-12.408
POWER OF
-9.006
-9.007
-9.009
-9.011
-9.015
-9.020
-9.026
-9.033
-9.041
-9.049
POWER OF
-9.006
-9.059
-9.190
-9.353
-9.517
-9.671
-9.811
-9.938
-10.053
-10.158
POWER OF
-9.006
-10.253
-10.915
-11.314
-11.599
-11.822
-12.003
-12.157
-12.290
-12.408
10 APPLICABLE
-9.294
-9.294
-9.295
-9.297
-9.299
-9.302
-9.305
-9.309
-9.314
-9.319
10 APP
-9.294
-9.324
-9.406
-9.517
-9.641
-9.765
-9.883
-9.995
-10.099
-10.195
10 APP
-9.294
-10.285
-10.923
-11.318
-11.60?
-11.823
-12.004
-12.158
-12.291
-12.409
-9.517
-9.517
-9.518
-9.519
-9.520
-9.522
-9.524
-9.527
-9.530
-9.533
LICABLE
-9.517
-9.537
-9.591
-9.671
-9.765
-9.864
-9.963
-10.060
-10.152
-10.239
LICABLE
-9.517
-10.322
-10.934
-11.323
-11.604
- 11.825
-12.006
-12.159
-12.292
-12.409
TO XD=
-9.700
-9.700
-9.700
-9 . 70 1
-9.702
-9.703
-9.704
-9.706
-9.708
-9. 711
TO XD=
-9.700
-9.713
-9.752
-9.81 1
-9.883
-9.963
-10.046
-10.129
-10.210
-10.289
TO XD =
-9.700
-10.364
-10.947
-11.329
-11.608
-11.827
-12.007
-12. 160
-12.293
-12.410
2
-9.
-9.
-9.
-9.
-9.
— 9
-9T
-9.
-9.
-9.
3
-9.
-9.
-9.
-9.
-9.
-10.
-10.
-10.
-10.
-10.
4
-9.
-10.
-10.
-11.
-11.
-11.
-12.
-12.
-12.
-12.
854
854
854
855
855
856
857
859
860
862
854
864
893
938
995
060
129
200
271
342
854
410
961
335
612
829
009
161
294
411
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-9.
-10.
-10.
-10.
-10.
-10.
-10.
-10.
-10.
-9.
-10.
-10.
-11.
-11.
-11.
-12.
-12.
-12.
-12.
987
987
988
988
988
989
990
991
992
993
987
995
018
053
099
152
210
271
334
396
987
458
978
343
616
832
Oil
163
295
412
-10.105
-10.105
-10.105
-10.106
-10.106
-10.107
-10.107
-10.108
-10.109
-10.110
-10.105
-10.111
-10.129
-10.158
-10.195
-10.239
-10.289
-10.342
-10.396
-10.452
-10.105
-10.507
-10.996
-1 1.352
-11.621
-11.836
-12.013
-12.164
-12.296
-12.413
-------
TABLE 3
VALUES OF SIGMA IPSEUOO SKIN, VERTICAL FRACTURE)
XD=
XD=
XD =
XD=
YD=
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
a
9
POWER OF 10 APPLICABLE TO YD= 4
0.0 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000
POWER OF 10 APPLICABLE TO XD= -2
0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
0.
0
000
000
000
001
001
002
002
003
004
0
005
020
046
08?
131
193
270
368
495
0
V ******
-1.
-2.
-2.
-2.
-2.
-2.
-3.
-3.
0.
-3.
-3.
-4.
-4.
-4.
-5.
-5.
-5.
-5.
648
079
376
603
787
942
077
195
0
301
995
401
689
912
094
248
382
500
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10,210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10.210
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
-10
•
•
«
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
*
•
•
•
•
•
•
•
•
*
•
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
903
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820-12.002
-11.309 -11.597 -11.820 -i?.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
POWER OF 10 APPLICABLE TO XD= -
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
POWER OF 10 APPLICABLE TO XD=
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
POWER OF 10 APPLICABLE TO XD=
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-11.309 -11.597 -11.820 -12.002
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
1
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
0
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
1
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
-12.
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
156
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
-12
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
.290
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12,408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-12.408
-------
xo=
XD=
YD =
0
1
2
3
4
5
6
7
8
9
0
1
2
-\
4
5
6
7
8
9
0
I
2
3
4
5
6
7
8
Q
0.0
TABLE 3
VALUES OF SIGMA (PSEUDO SKIN, VERTICAL FRACTURE)
POWER OF 10 APPLICABLE TO YD= 4
1.000 2.000 3.000 4.000 5.000 6.000 7.000
8.000 9.000
0.0
-5.605
-6.298
-6.704
-6.991
-7.215
-7.397
-7.551
-7.68U
-7.802
0.0
-7.908
-8.601
-9.000
-9.294
-9.517
-9.700
-9.854
-9.987
-10.105
0.0
- 10.210
-10.903
-11.309
-11.597
- 11.820
-12.002
-12.156
-12.290
-12.408
-10.210
-10.210
-10.211
-10.211
-10.211
-10.212
-10.212
-10.213
-10.214
-10.214
-10.210
-10.215
-10.230
-10.253
-10. 285
-10.322
-10.364
-10.410
-10.458
-10.507
-10.210
-10.557
-11.015
- 1 1 . 3 62
-11.627
-11.839
-12.016
-12.166
-12.2^3
-12.414
-10.903
-10.904
-10.904
-10.904
-10.904
-10.904
-10.904
-10.904
-10.904
-10.904
-10.903
-10.905
-10.908
-10.915
-10.923
-10.934
-10.947
-I0.
-------
VALUES OF PD
TABLE 4
WITH CAPROCK
LEAKAGE
TD=
1.0000 2.0000 3.0000 4.0000 5,0000 6.0000 7.0000 3.0000 9.0000
R/B=
R/B=
oo
R/B=
0.02
0.04
0.06
0.08
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.02
0.04
0.06
0.08
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
I. 00
0.02
0.04
0.06
0.08
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.0124
0.0124
0.0124
0.0124
0.0124
0.0124
0.0124
0.0123
0.0122
0.0121
0.0120
0.0119
0.0117
0.0115
3.5210
0.5216
0.5211
0.5205
0.5196
0.5119
0.4995
0.4827
0.4622
0.4386
0.4126
0.3350
0.3564
0.3275
1. 5664
1.5611
1.5523
1.5400
1.5246
1.4063
1.2445
1.0722
0.9122
0.7745
0.6593
0.5650
0.4863
0.420?
0.0732
0.0732
0.0732
0.0732
0.0731
0.0728
0.0723
0.0717
0.0708
0.0698
0.0686
0.0673
0.0658
0.0642
0.8109
0.8106
0.8092
0.8074
0.8050
0. 7852
0.7537
0.7125
0.6641
0.6111
0.5561
0.5012
0.4431
0.3980
1.9048
1.8937
1.8754
1.8504
1.8193
1.5987
1.3404
1.1095
0.9233
0.7774
0. 6604
0.565?
0.4863
0.4202
POWER
0. 1428
0.1458
0. 1458
0. 1460
0.1460
0. 1451
0.1437
0.1418
0. 1393
0.1363
0.1329
0.1290
0.1246
0.1197
POWER
0.9939
0.9928
0.9906
0.9875
0.9834
0.9509
0.9002
0.8358
0.7630
0.6867
0.6112
0.5396
0.4735
0.4141
POWER
2. 1035
2.0866
2.0590
2.0218
1.9762
1. 6740
1.3630
1.1133
0.9244
0.7775
0.6604
0.5652
0.4863
0. 42 02
OF 10 =
0.2135
0.2157
0.2156
0.2157
0.2156
0.2140
0.211*
0.2078
0.2033
0.1979
0.1917
0.1849
0.1772
0.1690
OF 10 =
1. 1276
1.1259
1.1227
1.1183
1.1127
1.0673
0.9981
0.9126
0.8193
0.7252
0.6359
0.5542
0.4817
0.4184
OF 10 =
2.2444
2.2217
2.1851
2.1362
2.0771
1.7098
1.3694
1.1144
0.9244
0.7775
0.6604
0.5652
0.4863
0. 42 02
-1 (APPL
0.2773
0.2795
0.2794
0.2793
0.2791
0.2766
0.2727
0.2672
0.2603
0.2522
0.2429
0.2327
0.2216
0.2097
0 (APPL
1.2329
1.2306
1.2265
1.2208
1.2135
1.1555
1.0686
0.9642
0,8537
0. 7464
0.6477
0.5603
0.4846
0.4197
1 {APPL
2.3534
2.3250
2.2795
2.2195
2.1480
1.7284
1.3714
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
IES TO
0.3359
0.3372
0.3370
0.3369
0.3365
0.3331
0*3276
0.3200
0.3106
0.2996
0.2370
0.2733
0.2586
0.2431
IES TO
1.3199
1.3170
1.3119
1.3049
1.2960
1.2255
1.1217
1.0004
0.8759
0.7535
0.6538
0.5629
0.4857
0.4201
IES TO
2.4421
2.4031
2.3540
2.?833
2.2005
1.7386
1.3721
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
TO ONLY)
0.3885
0.3896
0.3893
0.3890
0.3885
0.3842
0.3770
0.3673
0.3552
0.3410
0.3252
0.3079
0.2896
0.2704
TD ONLY)
1.3938
1.3903
1.3844
1.3760
1.3655
1.2827
1.1631
1.0267
0.8906
0.7657
0.6567
0. 5641
0.4861
0.420?
TD.ONLY)
2.5170
2.4773
2.4143
2.3340
2.2406
1.7444
1 . 3 72 3
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
0.4365
0.4373
0.4370
0.4366
0.4360
0.4306
0.4217
0.4097
0.3948
0.3775
0.3583
0.3375
0.3156
0.2931
1.4582
1.4542
1.4472
1.4376
1.4254
1.3305
1 . 1 960
1.0462
0.9005
0.7702
0.6584
0.5647
0.4862
0.4202
2.5815
2 . 5 36 3
2.4656
2.3753
2 . 2 72 1
1.7477
1.3724
1.1 145
0.9244
0.7775
0.6604
0.5652
0.4863
0.420?
0.4304
0.4812
0.4807
0.4802
0.479.5
0.4730
0.4623
0.4480
0.4303
0.4098
0.3872
0.3630
0.3377
0.3118
1.5152
1.5106
1.5027
1.4918
1.4779
1.3712
1.2227
1.0609
0.9074
0.7728
0.6593
0.5649
0.4863
0.4202
2.6383
2.5876
2.5088
2.4094
2.2972
1.7496
1.3724
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
-------
VALUES OF
TABLE 4
PO WITH CAPROCK LEAKAGE
TD =
1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000
R/B=
R/B=
-P.
IO
R/B =
0.02
0.04
0.06
0.08
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.02
0.04
0.06
0.08
0. 10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.02
0.04
0.06
0.08
0. 10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
I. 00
2.6889
2.6327
2.5462
2.4380
2.3176
1.7508
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
3.6773
3.2934
2.9298
2.6474
2.4271
1.7527
1.3725
1. 1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.420?
4.0266
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
3.0155
2.9077
2.7531
2.5777
2.4026
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
3.8732
3.3315
2.9328
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0. 6604
0.5652
0.4863
0.4202
4.02R4
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4363
0.4202
POWER
3.1990
3.0443
2.8369
2.6202
2.4206
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0. 5652
0.4863
0.4202
POWER
3.9493
3.3358
2.9329
2.6475
2.4271
I. 7527
1.3725
1. 1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
POWER
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0. 6604
0.5652
0.4863
0.4202
OF 10 =
3.3241
3.1268
2.8782
2.6360
2.4252
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
OF 10 =
3.9853
3.3364
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
OF 10 ^
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
2 (APPL
3.4173
3. 1813
2.9006
2.6424
2.4265
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
3 {APPL
4.0041
3.3365
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4 (APPL
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
IES TO
3.4905
3.2192
2.9133
2.6452
2.4269
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
IFS TO
4.0143
3.3365
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4363
0.4202
IES TO
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
TO ONLY)
3. 5499
3.2465
2.9208
2.6464
2.4270
1.7527
1.3725
1. 1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
TO ONLY)
4.0201
3.3366
2.9329
2. 6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0. 5652
0.4863
0.4202
TD ONLY)
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
3.5994
3.2667
2.9254
2.6470
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0234
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
l.l 145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1 . 3 72 5
1.1145
0.9244
0.7775
0 . 6 604
0.5652
0.4863
0.4202
3.6413
3.2819
2.9281
2.6473
2.4271
1.7527
L.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0254
3.3366
2.9329
2.6475
2.4271
1.7577
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
-------
TABLE 4
VALUES UF PO WITH CAPROCK LEAKAGE
TD'
1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000
R/B=
R/B=
en
o
R/B =
0.02
0.04
0.06
0.08
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.02
0.04
0.06
0.08
0. 10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.02
0.04
0.06
0.08
0.10
0.20
0.30
0.40
0.50
0. 60
0.70
0.80
0.90
1.00
4.0285
3.3366
2.9329
2 . 64 75
2.4271
1.7527
1.3725
1. 1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5552
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4363
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4363
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
I. 1145
0.9244
0.7775
0.6604
0.5652
0.^863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.486 '3
0.4202
POWER
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1. 1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
POWER
4.0285
3.3366
2.9329
2.6475
2.42.71
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
POWER
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
OF 10 =
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
OF 10 =
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
OF 10 =
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
5 (APPLIES TO
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
6 (APPL
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
7 (APPL
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4363
0.4202
IES TO
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
IES TO
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4363
0.4202
TD ONLY)
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
TD ONLY)
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
TD ONLY)
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1 145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
4.0285
3.3366
2.9329
2.6475
2.4271
1.7527
1.3725
1.1145
0.9244
0.7775
0.6604
0.5652
0.4863
0.4202
-------
APPENDIX B
PROGRAMMABLE DESK CALCULATOR PROGRAMS
1. Exponential integral
2. Error function
3. Single or multiple wells, constant injection or pumping rate
4. Single or multiple wells, variable injection or pumping rates
5. Single vertical fracture, well bore case
6. Single vertical fracture, general case
7. Single horizontal fracture
8. Partially penetrating wells
9i . Semiconfined reservoirs
151
-------
PROGRAM TITLE: Exponential Integral
PARTITIONING: Normal
PROGRAM DESCRIPTION:
Evaluates the exponential integral (National Bureau
of Standards, 1964), which is a part of numerous
pressure buildup solutions.
Program calculates:
r-u
ir
du = -0.5772 - In x -
Note: Results are accurate to ± 0.1% for 0 < x < 5.
USER INSTRUCTIONS
STEP
1
1
PROCEDURE
To calculate E (x) when only the program
for E (x) is being used
To calculate E. (x) when any program
incorporating E (x) as a subroutine is
being used
ENTER
X
X
PRESS
RST
RST
R/S
R/S
DISPLAY
EI(X)
E^x)
152
-------
PROGRAM
LOG
000
001
002
003
004
005
006
007
008
009
010
Oil
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
CODE
42
30
53
23
85
93
05
07
07
02
54
42
33
03
05
42
00
01
42
32
06
42
03
93
00
00
01
32
86
05
53
03
06
KEY
STO
30
(
In x
+
.
5
7
7
2
)
STO
33
3
5
STO
00
1
STO
32
6
STO
03
.
0
0
1
x£t
2nd Stflg
5
(
3
. '6
LOG
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
CODE
75
43
00
54
42
31
53
43
30
45
43
31
55
43
31
55
53
43
31
65
43
32
54
42
32
54
87
05
00
68
86
05
61
KEY
-
RCL
00
)
STO
31
(
RCL
30
yx
RCL
31
V
RCL
31
T
(
RCL
31
X
RCL
32
)
STO
32
)
2nd Ifflg
5
0
68
2nd Stflg
5
GTO
LOG
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
0°4
095
096
097
098
CODE
00
72
22
86
05
94
53
24
85
43
33
54
48
33
97
03
01
02
22
87
05
01
02
53
24
55
43
33
75
01
54
50
22
KEY
0
72
INV
2nd Stflg
5
+/-
(
CE
+
RCL
33
)
2nd Exc
33
2nd Dsz
3
1
02
INV
2nd Ifflg
5
1
02
(
CE
•i-
RCL
33,
-
1
)
2nd x|
INV
LOG
099
100
101
102
103
104
105
106
107
108
109
CODE
77
01
06
97
00
00
30
43
33
94
92
. KEY
2nd x>t
1
06
2nd Dsz
0
0
30
RCL
33
V-
INVSBR
153
-------
PROGRAM TITLE: Error Function
PARTITIONING: Normal
PROGRAM DESCRIPTION: Evaluates the error function (National Bureau of
Standards, 1964), which is a part of several
pressure buildup solutions.
Program calculates:
2 fx -t:
VFj 6
erf (x) =^ I e dt
0
o _~, / -i \n 2n+l
2 » (-1) x
Note: Results are accurate to ± 0.1% for x < 5.
USER INSTRUCTIONS
STEP
1
1
PROCEDURE
To calculate erf (x) when only the program
for erf (x) is being used
*
To calculate erf (x) when any program
incorporating erf (x) as a subroutine
is being used
ENTER
x
x
PRESS
GTO
SBR
110
110
R/S
DISPLAY
erf (x)
erf(x)
154
-------
PROGRAM
LOG
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
CODE
42
34
42
35
86
03
01
42
36
93
00
00
01
32
09
08
42
06
53
09
09
75
43
'06
54
42
38
53
43
38
65
02
85
KEY
STO
34
STO
35
2nd Stflg
3
1
STO
36
•
0
0
1
x?t
9
8
STO
06
(
9
9
-
RCL
06
)
STO
38
(
RCL
38
X
2
+
LOG
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
CODE
01
54
42
39
53
43
35
45
43
39
55
43
39
55
53
43
38
65
43
36
54
42
36
54
87
03
01
76
86
03
61
01
80
KEY
1
)
STO
39
(
RCL
35
X
y
RCL
39
-r
RCL
39
V
(
RCL
38
X
RCL
36
)
STO
36
)
2nd If fig
3
1
76
2nd Stflg
3
GTO
1
80
LOG
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
CODE
94
22
86
03
53
24
85
43
34
54
48
34
22
87
03
02
06
53
24
55
43
34
75
01
54
50
22
77
02
10
97
06
01
KEY
+/-
INV
2nd Stflg
3
(
CE
+
RCL
34
)
2nd Exc
34
INV
2nd If fig
3
2
06
(
CE
V
RCL
34
-
1
)
2nd |x
INV
2nd x>t
2
10
2nd Dsz
6
1
LOG
209
210
211
212
213
214
215
216
217
218
219
CODE
28
53
43
34
65
02
55
89
34
54
92
KEY
28
(
RCL
34
X
2
•i-
2nd IT
v£
)
INV SBR
155
-------
PROGRAM TITLE: single or Multiple Wells, Constant Injection or Pumping
. Rate.
PARTITIONING: Normal
PROGRAM DESCRIPTION: Solves for pressure buildup (decline) at any point
in a fully confined infinite reservoir as a result
of injection (pumping) at a constant rate into
(from) a single completely penetrating well. The
program will also calculate the combined effects
of multiple wells, where all wells are operating at
constant injection or pumping rates and are com-
pletely penetrating.
Program calculates:
2
m 70.6q y $, ( (39.5 <|>u cr -v
P , p. + I 3LIUL E v ° n + 2 S
r i n^ kh [ l[ ktn J n
where:
E
= exponential integral—see exponential integral program
156
-------
USER INSTRUCTIONS
STEP
1
2
3
4
5
6
7
8
9
10
11
12
13
PROCEDURE
Enter number of wells
Enter initial reservoir pressure
Enter injection or pumping rate of
well n
Enter radial distance from well n
to point of investigation
Enter time since injection into or
pumping from well n began
Enter average horizontal reservoir
permeability
Enter reservoir thickness
Enter reservoir porosity
Enter viscosity
Enter system compressibility
Enter formation volume factor
Enter skin factor for well n
Start execution of calculation
ENTER
m
P±(psi)
q (STB/D)
r (ft)
n
tno»
k(md)
h(ft)
(j>( fraction)
iMcp)
c (1/psi)
8 (RB/STB)
n
S
n
PRESS
A
B
C
D
E
STO
STO
STO
STO
STO
STO
STO
2nd
1
1
1
1
1
1
2
E1
4
5
6
7
8
9
0
DISPLAY
m
P.
i
qn
r
n
t
n
k
h
<{>
Vn
c
«n
S
n
P
NOTE: Calculated pressures are accumulative. For second and subsequent
wells enter only data which have changed, then press 2nd E1 . If it
is desired to restart a series of calculations before m calculations
have been made, P. must be reentered as the original value.
157
-------
PROGRAM
NOTE:
Program steps 000-109 are separately documented as the E.(x)
subroutine. Enter this subroutine, then enter the remaining
steps listed here.
LOG
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
CODE
76
11
42
05
91
76
12
42
10
91
76
13
42
11
91
76
14
42
12
91
76
15
42
13
91
76
10
53
KEY
2nd Lbl
A
STO
05
R/S
2nd Lbl
B
STO
10
R/S
2nd Lbl
C
STO
11
R/S
2nd Lbl
D
STO
12
R/S
2nd Lbl
E
STO
13
R/S
2nd Lb]
2nd E1
(
LOG
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
CODE
43
10
85
53
53
03
09
93
05
01
65
43
16
65
43
17
65
43
18
65
43
12
33
55
43
13
55
43
KEY
RCL
10
+
(
(
3
9
.
5
1
X
RCL
16
X
RCL
17
X
RCL
18
X
RCL
12
2
X
~
RCL
13
•
~
RCL
LOG
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
CODE
14
54
71
00
00
85
02
65
43
20
54
65
43
11
65
43
17
65
43
19
55
43
14
55
43
15
65
07
KEY
14
)
SBR
0
00
+
2
X
RCL
20
)
X
RCL
11
X
RCL
17
X
RCL
19
•
RCL
14
V
RCL
15
X
7
LOG
194
195
196
197
198
199
200
201
CODE
00
93
06
54
97
05
12
92
KEY
0
•
6
)
2nd Dsz
5
B
INV SBR
158
-------
PROGRAM TITLE:
Single or Multiple Wells, Variable Injection or
Pumping Rates
PARTITIONING:
Normal
PROGRAM DESCRIPTION:
Solves for pressure buildup (decline) at any point
in a fully confined infinite reservoir as a result
of injection (pumping) at variable rates into (from)
a single completely penetrating well. The program
will also calculate the combined effects of multiple
completely penetrating wells.
Program calculates:
m n 70.6fa, -q, ,
> = P + y Y 1 ba ^a-
r i ,>„ *•„ kh
39.
E
b=l a-1
1 k
cr.
+2s
where:
E = exponential integral—see exponential integral program
b = well number
a = rate number of well b
159
-------
USER INSTRUCTIONS
STEP
PROCEDURE
ENTER
PRESS
DISPLAY
1
2
3
4
8
9
10
11
12
13
14
15
Enter number of wells
Enter number of injection {pumping)
rates for well b under considera-
tion.
Enter initial reservoir pressure
Enter injection (pumping) rate of
well b at time period a
Enter radial distance from well b
to point of investigation
Enter number of days of injection
(pumping) at rate a
Enter total number of days of
operation of well b at all rates
Enter average horizontal reservoir
permeability
Enter reservoir thickness
Enter reservoir porosity
Enter viscosity
Enter system compressibility
Enter formation volume factor
Enter skin factor
Start execution of calculation
m
n
Pi(psi)
qba(STB/D)
rb(ft)
"ha™
GTO
R/S
A
B
C
k(md)
h(ft)
<(>( fraction)
C(l/psi)
3(RB/STB)
S
STO
STO
STO
STO
STO
STO
STO
2nd
1
1
1
1
1
2
2
E1
R/S
5
6
7
8
9
0
1
n
P.
i
fcb
k
h
4>
y
C
B
s
NOTE: Pressures are calculated and displayed cumulatively for each rate
and for each well. After rate 1 has been calculated for well 1,
proceed to rate 2 and time period 2, etc., until all rates for
well 1 have been calculated. For well 2, enter the number of
rates, then the rates and times for well 2, until all rates and
times have been used. A final pressure is displayed after all
wells and all rates and time periods have been taken into account.
At the end of all rate calculations for all but last well, the cal-
culator will display zero. To read the cumulated pressure, when the
display is zero, press RCL 10. If a series of calculations is aborted,
and it is desired to begin over, reenter the m,n, and Pi- A value for
m,n and Pi must be entered for each new series of calculations, even
though the numbers may be the same as for the previous series of
calculations.
-------
PROGRAM
NOTE:
Program steps 000-109 are separately documented as the E., (x)
subroutine. Enter this subroutine, then enter the remaining
steps listed here.
LOG
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
CODE
76
33
42
05
76
22
43
22
42
14
00
42
25
91
42
06
91
76
11
42
10
91
76
12
42
11
91
76
KEY
2nd Lbl
2
X
STO
05
2nd Lbl
INV
RCL
22
STO
14
0
STO
25
R/S
STO
06
R/S
2nd Lbl
A
STO
10
R/S
2nd Lbl
B
STO
11
R/S
2nd Lbl
LOG
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
CODE
13
42
12
91
76
14
42
13
91
76
15
42
14
42
22
91
76
10
53
43
11
75
43
26
54
42
25
53
KEY
C
STO
12
R/S
2nd Lbl
D
STO
13
R/S
2nd Lbl
E
STO
14
STO
22
R/S
2nd Lbl
2nd E1
(
RCL
11
-
RCL
26
)
STO
25
(
LOG
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
CODE
53
53
03
09
93
05
01
65
43
17
65
43
18
65
43
19
65
43
12
33
55
43
15
55
43
14
54
71
KEY
(
(
3
9
.
5
1
X
RCL
17
X
RCL
18
X
RCL
19
X
RCL
12
2
X
•
RCL
15
-r
RCL
14
)
SBR
LOG
194
195
196
197
198
| 199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
CODE
00
00
85
02
65
43
21
54
65
43
18
65
43
20
65
43
25
55
43
15
55
43
16
65
07
00
93
06
KEY
0
00
+
2
X
RCL
21
)
X
RCL
18
X
RCL
20
X
RCL
25
-r
RCL
15
T
RCL
16
X
7
0
*
6
LOG
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
CODE
54
44
10
43
13
22
44
14
43
11
42
26
43
10
97
06
11
00
42
26
97
05
22
43
10
92
KEY
)
SUM
10
RCL
13
INV
SUM
14
RCL
11
STO
26
RCL
10
2nd Dsz
6
A
0
STO
26
2nd Dsz
5
INV
RCL
10
INV SBR
161
-------
PROGRAM TITLE: Single Vertical Fracture, Wellbore Case
PARTITIONING:
Normal
PROGRAM DESCRIPTION:
Solves for pressure buildup at the well bore for a
well with a single vertical fracture passing
centrally through the wellbore (Gringarten, et. al.,
1974).
Program calculates:
P = p + p
WB
141.2qyB
where:
'WD
j. niJ
/TTtD erf
[ kh
> «
1
L2/r\
J
+ 2 El
1
KJ
and
6.33xlO~3kt
4>uc(xf)2
NOTE: Programs for exponential integral, E.(x), error function, erf(x),
are documented separately.
162
-------
USER INSTRUCTIONS
STEP
1
2
3
4
5
6
7
8
9
10
11
PROCEDURE
Enter initial pressure
Enter fracture length
Enter injection rate
Enter injection time
Enter permeability
Enter reservoir thickness
Enter porosity
Enter viscosity
Enter system compressibility
Enter formation volume factor
Start execution of calculation
ENTER
P±(psi)
xf(ft)
q(STB/D)
t(P)
k(md)
h(ft)
4>( fraction)
y(cp)
c(l/psi)
$ (RB/STB)
PRESS
GTO
A
B
C
STO
STO
STO
STO
STO
STO
2nd
2
X
1
1
1
1
1
1
E1
R/S
4
5
6
7
8
9
DISPLAY
P.
i
Xf
q
t
k
h
4>
y
c
6
PWB
NOTE: For next well or data, enter only data which have changed.
163
-------
PROGRAM
NOTE: Program steps 000-109 are separately documented as the E (x) sub-
routine and steps 110-219 are documented as the erf(x) subroutine.
Enter these two subroutines in order, then enter the remaining
steps listed here.
LOG
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
CODE
76
33
42
10
91
76
11
42
11
91
76
12
42
12
91
76
13
42
13
91
76
10
53
93
00
00
06
KEY
2nd Lbl
2
x
STO
10
R/S
2nd Lbl
A
STO
11
R/S
2nd Lbl
B
STO
12
R/S
2nd Lbl
C
STO
13
R/S
2nd Lbl
2nd E1
(
*
0
0
6
LOG
247
248
249
250
251
•252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
CODE
03
03
65
43
14
65
43
13
55
43
16
55
43
17
55
43
18
55
43
11
33
54
42
20
53
53
53
KEY
3
3
x
RCL
14
x
RCL
13
V
RCL
16
T
RCL
17
~
RCL
18
•
•
RCL
11
2
x
)
STO
20
(
(
(
LOG
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
CODE
53
24
34
65
02
54
35
71
01
10
65
53
89
65
43
20
54
34
54
85
53
43
20
65
04
54
35
KEY
(
CE
&
x
2
)
1/x
SBR
1
10
x
(
2nd IT
x
RCL
20
)
&
)
+
(
RCL
20
x
4
)
1/x
LOG
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
CODE
71
00
00
55
02
54
65
01
04
01
93
02
65
43
12
65
43
17
65
43
19
55
43
14
55
43
15
KEY
SBR
0
00
-r
2
)
x
1
4
1
.
2
x
RCL
12
x
RCL
17
x
RCL
19
•
RCL
14
•
RCL
15
164
-------
o>
01
LOC
328
329
330
331
332
CODE
85
43
10
54
92
KEY
+
RCL
10
)
INV SBR
LOC
CODE
KEY
LOC
CODE
KEY
LOC
CODE
KEY
-------
PROGRAM TITLE: Single Vertical Fracture, General Case.
PARTITIONING:
Normal
PROGRAM DESCRIPTION:
Solves for pressure buildup (decline) of any point
in an infinite confined reservoir as a result of
injection (pumping) at a constant rate into (from)
a well with a single vertical fracture passing
centrally through the wellbore (Gringarten, et al,
1974).
Program Calculates:
P = p.
.
xy i D [ kh
where:
P -
and
6.33xlO~3kt
cf>llc(xf)2
At 2yD tan~1(2yD/r^-l) >_ 0
(xD-l) in (yj + (xD-l)2] - 12.5 (r + —)
166
-------
USER INSTRUCTIONS
STEP
1
2
3
4
5
6
7
8
9
10
11
12
13
PROCEDURE
Enter initial pressure
Enter fracture length
Enter distance to point of
interest in x direction
Enter distance to point of
interest in y direction
Enter injection or pumping
rate
Efiter time since injection
into or pumping from well
began
Enter average horizontal
reservoir permeability
Enter reservoir thickness
Enter reservoir porosity
Enter viscosity
Enter system compressibility
Enter formation volume
factor
Start execution of
calculation
NOTE: For next well or
data set, enter
only data which
have changed.
ENTER
P. (psi)
xf(ft)
x(ft)
y(ft)
q(STB/D)
t(D)
k(md)
h(ft)
4>( fraction)
y(cp)
c(l/psi)
3 (RB/STB)
PRESS
GTO
A
B
C
D
E
STO
STO
STO
STO
STO
2nd
2
X
1
1
1
1
2
E1
R/S
6
7
8
9
0
DISPLAY
P.
l
Xf
XD
YD
q
t
k
h
4>
y
c
e
p
xy
167
-------
PROGRAM
LOG
000
001
002
003
004
005
006
007
008
009
010
Oil
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
CODE
76
33
42
10
91
76
11
42
11
91
76
12
53
24
55
43
11
54
42
12
91
76
13
53
24
55
43
11
54
42
KEY
2nd Lbl
2
X
STO
10
R/S
2nd Lbl
A
STO
11
R/S
2nd Lbl
B
(
CE
RCL
11
)
STO
12
R/S
2nd Lbl
C
(
CE
•r
RCL
11
)
STO
LOG
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
CODE
13
91
76
14
42
14
91
76
15
42
15
91
76
10
70
00
32
53
53
53
53
93
00
00
06
03
03
65
43
16
KEY
13
R/S
2nd Lbl
D
STO
14
R/S
2nd Lbl
E
STO
15
R/S
2nd Lbl
2nd E1
2nd Rad
0
x+t
(
(
(
(
.
0
0
6
3
3
X
RCL
16
LOG
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
CODE
65
43
15
55
43
18
55
43
19
55
43
20
55
43
11
33
54
23
85
02
93
08
01
54
55
02
85
53
53
53
KEY
X
RCL
15
•
RCL
18
•
•
RCL
19
RCL
20
•
RCL
11
2
X
)
In x
+
2
•
8
1
)
•r
2
+
(
(
(
LOG
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
CODE
43
12
75
01
54
33
85
43
13
33
54
23
65
53
43
12
75
01
54
75
53
53
43
12
85
01
54
33
85
43
KEY
RCL
12
-
1
)
2
X
+
RCL
13
2
X
)
In x
X
(
RCL
12
-
1
)
-
(
(
RCL
12
+
1
)
2
x
+
RCL
168
-------
LOG
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
CODE
13
33
54
23
65
53
43
12
85
01
54
75
53
53
02
65
43
13
55
53
43
12
33
85
43
13
33
75
01
54
54
22
KEY
13
2
X
)
In x
X
(
RCL
12
+
1
)
-
(
(
2
X
RCL
13
•f
(
RCL
12
2
X
+
RCL
13
2
X
-
1
)
)
INV
LOG
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
CODE
30
65
02
65
43
13
54
77
44
00
76
44
54
55
04
54
65
01
04
01
93
02
65
43
14
65
43
19
65
43
KEY
2nd tan
X
2
X
RCL
13
)
2nd x>t
SUM
0
2nd Lbl
SUM
)
T
4
)
X
1
4
1
*
2
X
RCL
14
X
RCL
19
X
RCL
LOG
182
183
184
185
186
187
188
189
190
191
192
193
CODE
21
55
43
16
55
43
17
85
43
10
54
92
KEY
21
•
RCL
16
V
RCL
17
+
RCL
10
)
LOG
INV SBR 1
n
CODE
KEY
169
-------
PROGRAM TITLE: Single Horizontal Fracture
PARTITIONING: Normal
PROGRAM DESCRIPTION: Calculates the pressure buildup at any location for
a well intersected by a single horizontal fracture
(Grtngarten, and Ramey, 197*0-
Program calculates:
U.
P
r,z i kh
where:
a(rD'ZD'tD)
and
6.33x!0"3kt
At t ^ 12.5(2r*+l) and tD ^ 5 -|:
IT
PD = jtln tD-H.8l-rj;] for 0 < r^ < 1
and
PD =inn(tD/r)+0.8l] for
170
-------
When:
r > r. = r, — /k /k , a - 0
i f TT r z
For r = 0 (at well bore)
22
nir
where:
K.(x) S - for x < 5
I y\
and
Kl(x) = l"
for x 5
171
-------
USER INSTRUCTIONS
STEP
1
2
3
4
5
6
7
8
9
10
11
12
13
14
PROCEDURE
enter initial pressure
enter injection rate
enter distance from well
enter injection time
enter radial length of fracture
enter radial permeability
enter vertical permeability
enter reservoir thickness
enter distance from bottom of reservoir to
center of fracture
enter porosity
enter viscosity
enter total system compressibility
enter formation volume factor
start execution of calculation
NOTE:
For next calculation re-enter only data
which has changed.
z, is needed at r = 0 only.
Final display of a flash followed by 0 indic-
ates violation of some condition. If x £ t
causes same display as Rcl 00 increase r.
If x :£ t does not cause same display as Rcl
00 increase t.
ENTER
P;(psi)
qf(STB/D)
r(ft)
t(D)
rf(ft)
k=k (md)
k (md)
h(ft)
zf (ft)
( fraction)
U(cp)
c(l/psi)
B(RB/STB)
PRESS
GTO
A
B
C
D
STO
STO
STO
STO
STO
STO
STO
STO
E
Inv
1
1
1
1
1
2
2
2
R/S
5
6
7
8
9
0
1
2
DISPLAY
P.
i
If
r
t
rf
k
k
z
h
zf
y
c
B
P or 0
r,z
172
-------
PROGRAM
LOC
000
001
002
003
004
005
006
007
008
009
010
on
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
CODE
76
22
42
10
91
76
11
42
11
91
76
12
42
12
91
76
13
42
13
91
76
14
42
14
91
76
15
53
93
00
KEY
2nd Lbl
INV
STO
10
R/S
2nd Lbl
A
STO
11
R/S
2nd Lbl
B
STO
12
R/S
2nd Lbl
C
STO
13
R/S
2nd Lbl
D
STO
14
R/S
2nd Lbl
E
(
•
0
LOC
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
CODE
00
06
03
03
65
43
15
65
43
13
55
43
19
55
43
20
55
43
21
55
43
14
33
54
42
26
53
01
02
93
KEY
0
6
3
3
X
RCL
15
X
RCL
13
•
•
RCL
19
•r
RCL
20
V
RCL
21
T*
RCL
14
x2
)
STO
26
(
1
2
•
LOC
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
CODE
05
65
53
53
43
12
55
43
14
54
42
24
33
65
02
85
01
54
54
32
43
26
22
77
02
22
53
05
65
53
KEY
5
X
(
(
RCL
12
•f
RCL
14
)
STO
24
2
X
X
2
+
1
)
)
Xjt
RCL
26
INV
2nd x>t
2
22
(
5
X
(
LOC
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
1 111
112
113
114
115
116
117
118
119
CODE
43
17
33
55
43
14
33
65
43
15
55
43
16
54
42
23
55
89
33
54
32
43
26
22
77
02
22
00
32
43
KEY
RCL
17
2
X
-r
RCL
14
2
X
X
RCL
15
T
RCL
16
)
STO
23
•
2nd IT
2
X
)
*tt
RCL
26
INV
2nd x>t
2
22
0
x£t
RCL
173
-------
LOG
120
121
122
123
124
125
126
127
128
129
130
131
132
133
13^
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
CODE
12
67
02
27
53
43
14
85
01
00
65
43
17
55
89
65
53
43
15
55
43
16
54
34
54
42
00
32
43
12
KEY
12
2nd x=t
2
27
(
RCL
14
+
1
0
X
RCL
17
-r
2nd IT
X
(
RCL
15
•
RCL
16
)
&
)
STO
00
x*t
RCL
12
LOC
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
CODE
22
77
02
22
01
32
43
24
77
01
79
53
53
43
26
23
85
01
93
08
01
75
43
24
33
54
61
01
95
53
KEY
INV
2nd x>t
2
22
1
*tt
RCL
24
2nd x>t
1
79
(
(
RCL
26
In x
+
1
•
8
1
-
RCL
24
2
X
)
GTO
1
95
(
LOC
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
CODE
53
53
43
26
55
43
24
33
54
23
85
93
08
01
54
65
07
00
93
06
55
43
15
55
43
17
65
43
11
65
KEY
(
(
RCL
26
T
RCL
24
2
X
)
In x
+
•
8
1
)
x
7
0
•
6
•
RCL
15
•j.
RCL
17
x
RCL
11
x
LOC
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
CODE
43
20
65
43
22
85
43
10
54
61
02
26
00
35
66
25
92
70
53
02
55
03
65
43
23
65
53
01
75
03
KEY
RCL
20
x
RCL
22
+
RCL
10
)
GTO
2
26
0
1/x
2nd Pause
CLR
INV SBR
2nd Rad
(
2
•r
3
x
RCL
23
x
(
1
1
• i'
3
174
-------
LOG
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
CODE
65
53
43
18
55
43
17
54
42
25
65
53
01
75
43
25
54
54
54
42
29
05
00
42
00
53
05
01
75
43
KEY
X
(
RCL
18
V
RCL
17
)
STO
25
X
(
1
-
RCL
25
)
)
)
STO
29
5
0
STO
00
(
5
1
-
RCL
LOC
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
CODE
00
54
42
32
53
53
24
65
89
54
39
33
55
43
32
65
43
25
65
53
53
43
32
65
89
55
43
23
34
54
KEY
00
)
STO
32
(
(
CE
X
2nd IT
)
2nd cos
2
X
•
•
RCL
32
X
RCL
25
X
(
(
RCL
32
X
2nd ir
•
RCL
23
&
)
LOC
300
301
302
303
304
305
306
307
^308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
CODE
42
31
05
32
43
31
77
03
13
35
61
03
41
53
53
89
55
02
65
43
31
54
34
65
53
01
85
03
55
08
KEY I! LOC
STO 1 330
31
5
x*t
RCL
31
2nd x>t
331
332
333
334
335
336
3 f337
13
1/x
GTO
3
41
(
(
2nd ir
•
2
X
RCL
31
)
y^X
X
(
1
+
3
•
8
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
CODE
55
43
31
54
65
43
31
94
22
23
54
54
65
04
55
89
65
43
23
34
54
94
53
24
85
43
29
54
48
29
KEY
•
•
RCL
31
)
X
RCL
31
+/-
INV
In x
)
)'
X
4
-r
2nd IT
X
RCL
23
&
)
+/-
(
CE
+
RCL
29
)
2nd Exc
29
II
175
-------
LOG
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
CODE
32
93
00
00
01
32
53
24
55
43
29
75
01
54
50
22
77
03
83
97
00
02
65
53
43
29
65
02
85
01
KEY
xtt •
*
0
0
1
x£t
(
CE
™
RCL
29
-
1
)
2nd |x|
INV
2nd x>t
3
83
2nd Dsz
0
2
65
(
RCL
29
X
2
+
1
LOC
390
391
392
393
39*»
395
396
397
398
399
400
401
402
1 ' ;~
CODE
93
08
01
85
43
26
23
54
53
24
61
01
95
KEY
•
8
1
+
RCL
26
In x
)
(
CE
GTO
1
95
LOC
CODE
KEY
i
LOC
CODE
KEY
176
-------
PROGRAM TITLE:
Partially Penetrating Wells
PARTITIONING:
Normal
PROGRAM DESCRIPTION:
Solves for pressure buildup at any location in
an infinite confined reservoir as a result of
injection at a constant rate into a well that
partially penetrates the reservoir or a well that
fully penetrates the reservoir and is only perforated
or screened through part of the reservoir (Hantush, 1961)
Program Calculates:
P = P. + P^
r i D
141.2
kh
where:
PD=2
(l/4tD) + f
and
For
6.33xlO~3kt
2
ycr
, 2
2V
< 1
f .
4h
TT(l-d)
n=l
mrr
irnl . Trnd) nffz
sin — sin —r— cos -r—
h hi h
where
K (x) z. In
for x < 0.5
Note: Program for exponential integral, E (x), is documented separately.
KO (x) is the modified zero order Bessel function of second kind.
177
-------
USER INSTRUCTIONS
STEP
1
2
3
4
5
6
7
8
9
10
11
12
13
14
enter injection (pumping) rate
enter time since injection into or
pumping from well began
enter radial distance from well to
point of investigation
enter vertical distance from top
of reservoir to point at which
buildup pressure is to be calcu-
lated
enter reservoir thickness
enter length of penetration of well
enter depth to top of perforations
or screen
enter average horizontal reservoir
permeability
enter initial reservoir pressure
enter reservoir porosity
enter viscosity
enter system compressibility
enter formation volume factor
start execution of calculation
NOTE: For subsequent calculations
re-enter only data that
have changed, then press E.
ENTER
q(STB/D)
t(D)
r(ft)
z(ft)
h(ft)
Kft)
d(ft)
k(md')
P. (psi)
4>( fraction)
y (cp)
c(l/psi)
&(RB/STB)
PRESS
A
B
C
D
STO
STO
STO
STO
STO
STO
STO
STO
STO
E
1
1
1
1
1
1
2
2
2
4
5
6
7
8
9
0
1
2
DISPLAY
q
t
r
z
h
1
d
k
P.
i
4>
y
c
0
p
r
178
-------
PROGRAM
NOTE: Program steps 000-109 are separately documented as the E (x) sub-
routine. Enter this subroutine, then enter the remaining steps
listed here.
LOG
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
CODE
76
11
42
10
91
76
12
42
11
91
76
13
42
12
91
76
14
42
13
91
76
15
70
53
53
03
09
93
KEY
2nd Lbl
A
STO
10
R/S
2nd Lbl
B
STO
11
R/S
2nd Lbl
C
STO
12
R/S
2nd Lbl
D
STO
13
R/S
2nd Lbl
E
2nd Rad
(
(
3
9
.
LOG
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
CODE
05
01
65
43
19
65
43
20
65
43
21
65
43
12
33
55
43
17
55
43
11
54
42
24
65
04
54
35
KEY
5
1
X
RCI
19
X
RCI
20
X
RCI
21
X
RCI
12
2
X
-r
RCL
17
•r
RCL
11
)
STO
24
X
4
)
1/x
LOG
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
CODE
42
33
53
43
24
65
43
14
33
55
43
12
33
65
02
54
32
01
77
01
92
00
35
66
24
92
09
08
KEY
STO
33
(
RCL
24
X
RCL
14
2
X
T
RCL
12
2
X
X
2
)
x£t
1
2nd x>t
1
92
0
1/x
2nd Pause
CE
INV SBR
9
8
LOG
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
CODE
42
00
00
42
04
42
06
53
53
09
09
75
43
00
54
42
01
65
89
55
43
14
54
42
02
93
05
32
KEY
STO
00
0
STO
04
STO
06
(
(
9
9
RCL
00
)
STO
01
X
2nd TT
•
RCL
14
)
STO
02
.
5
x£t
179
-------
LOG
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
CODE
53
53
43
01
35
65
53
43
02
65
43
12
54
42
03
22
77
02
73
53
53
89
55
02
55
43
03
54
34
65
53
01
75
53
KEY
(
(
RCL
01
1/x
x
(
RCL
02
x
RCL
12
)
STO
03
INV
2nd x>t
2
73
(
(
2nd IT
7-
2
-r
RCL
03
)
&
x
(
1
-
(
LOG
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
CODE
08
65
43
03
54
35
54
65
43
03
94
22
23
54
61
02
83
53
01
93
01
02
55
43
03
54
23
32
93
00
00
01
32
42
KEY
8
X
RCL
03
)
1/x
)
X
RCL
03
+/-
INV
In x
)
GTO
2
83
(
1
.
1
2
T
RCL
03
)
In x
x£t
.
0
0
1
x?t
STO
LOG
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
CODE
05
53
24
85
43
06
54
48
06
53
24
55
43
06
75
01
54
50
77
03
14
00
42
00
43
05
65
53
53
43
02
65
43
15.
KEY
05
(
CE
+
RCL
06
)
2nd Exc
06
(
CE
-r
RCL
06
-
1
)
2nd |x
2nd xj>t
3
14
0
STO
00
RCL
05
x
(
(
RCL
02
x
RCL
15
LOG
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
CODE
54
38
75
53
43
02
65
43
16
54
38
54
65
53
43
02
65
43
13
54
39
54
54
44
04
97
00
02
01
53
43
04
65
04
KEY
)
2nd sin
-
(
RCL
02
x
RCL
16
)
2nd sin
)
x
(
RCL
02
x
RCL
13
)
2nd cos
)
)
SUM
04
2nd Dsz
0
2
01
(
RCL
04
x
4
180
-------
LOG
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
CODE
65
43
14
55
89
55
53
43
15
75
43
16
54
54
53
53
53
24
85
43
24
71
00
00
54
55
02
65
43
10
65
43
20
KEY
X
RCL
14
-=-
2nd IT
V
(
RCL
15
-
RCL
16
)
)
(
(
(
CE
+
RCL
24
SBR
0
00
)
•
•
2
X
RCL
10
X
RCL
20
LOG
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
CODE
65
43
22
55
43
17
55
43
14
65
01
04
01
54
85
43
18
54
92
KEY
X
RCL
22
V
RCL
17
•
RCL
14
X
1
4
1
)
+
RCL
18
)
INV SBR
LOG
CODE
KEY
LOG
CODE
KEY
181
-------
PROGRAM TITLE:
Semiconfined Reservoirs
PARTITIONING:
4 2nd Op 17
PROGRAM DESCRIPTION:
Solves for pressure buildup (decline) at any point
in an infinite reservoir with a leaky confining
bed or beds as a result of injection (pumping)
at a constant rate into (from) a single fully
penetrating well (Hantush and Jacob, 1955).
Program Calculates:
p = p + p
r i DL kh
where:
PDL 2
,I0(r/B)-l|
I u J-
- e [0.5772 + In
•4B
-l/u
6 n
, n+m
(-1)" "'(n-m+1) !
I I
n=l m=l (n+2)I 2un"m
for
1.0
or
P = -=•
DL 2
- u +
r2/4B2u
4B
- e
6 n
(r^/4B"
, n . n+m , . n » ,
(-1) (n-m+1) !
n=l m=l (n+2)! u
2 m— n
4B
+ KQ(r/B)
for u < 1.0
and:
B =
for leakage in one direction, or B =
khh h1
c c
k'h +k h'
c c c c
for leakage
in two directions.
u =
kt
182
-------
Ifi(x) = zero order modified Bessel function of the first kind
6
y*> .i + i-
u , 1=1 a
K (x) = zero order modified Bessel function of the second kind
o
2
K (x) = *- + 0.02344X - I (x)[0.5772 + In (^
o 4 0 2
183
-------
USER INSTRUCTIONS
STEP
1
2
3
4
5
6
7
8
9
1°
11
12
13
PROCEDURE
Enter injection or pumping rate
Enter radial distance from well
to point of investigation
Enter time since injection into
or pumping from well began
Enter initial reservoir pressure
Enter average horizontal re-
servoir permeability
Enter average vertical per-
meability of leaky confining
bed (see note below)
Enter reservoir thickness
Enter confining bed thickness
(see note below)
Enter reservoir porosity
Enter viscosity
Enter system compressibility
Enter formation volume factor
Start execution of calculation
NOTE: For leakage in two
directions enter ,. , , .
(h x h')
c c
for h and (k1 h + k h1 ) for
c c c c c
k .
c
ENTER
q(STB/D)
r(ft)
t(D)
P±(psi)
k(md)
k (md)
c
h(ft)
h (ft)
c
(f> (fract)
U(cp)
c (1/psi)
3 (RB/STB)
/
PRESS
A
B
C
D
STO
STO
STO
STO
STO
STO
STO
STO
E
1
1
1
1
1
1
2
2
4
5
6
7
8
9
0
1
DISPLAY
r
t
P.
i
k
k
c
h
h
c
y
c
B
p
r
184
-------
PROGRAM
LOG
000
001
002
003
004
005
006
007
008
009
010
Oil
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
033
CODE
42
30
32
01
00
32
22
77
00
12
00
92
53
23
85
93
05
07
07
02
54
42
33
03
05
42
00
00
42
34
01
42
32
02
KEY
STO
30
xtt
1
0
*Jt
INV
2nd x>t
0
12
0
INV SEE
(
In x
+
•
5
7
7
2
)
STO
33
3
5
STO
00
0
STO
34
1
STO
• 32
2
LOG
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
CODE
42
38
06
42
03
93
00
00
01
32
86
05
53
03
06
75
43
00
54
42
31
53
43
30
45
43
31
55
43
31
55
53
43
31
KEY II LOG
STO 068
38 069
6 1 070
STO
03
•
0
071
072
073
074
0 I 075
1 1 076
xjt
2nd Stflg
5
(
3
6
077
078
079
080
081
082
I 083
RCL 084
00
)
STO
31
085
086
087
088
( 089
RCL
30
X
y
RCL
31
•r
RCL
31
-r
090
091
092
093
094
095
096
097
098
099
100
101
CODE
65
43
32
54
42
32
54
87
05
00
87
86
05
22
86
04
61
00
93
22
86
05
86
04
94
53
24
85
43
33
54
42
39
87
KEY
X
RCL
32
)
STO
32
)
2nd Ifflg
5
0
87
2nd Stflg
5
INV
2nd Stflg
4
GTO
0
93
INV
2nd Stflg
5
2nd Stflg
4
+/-
(
CE
+
RCL
33
)
STO
39
2nd Ifflg
LOG
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
CODE
06
02
15
53
53
43
31
85
02
54
65
43
38
54
42
38
43
31
42
01
42
37
43
32
42
36
53
43
31
75
43
01
85
01
KEY "
6 j
2
15
(
(
RCL
31
+
2
)
X
RCL
38
)
STO
38
RCL
31
STO
01
STO
37
RCL
32
STO
36
(
RCL
31
-
RCL
01
+
1
185
-------
LOG
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
CODE
54
42
35
53
53
43
27
65
43
26
54
45
43
31
87
01
01
56
43
35
65
43
36
55
43
26
45
53
43
01
75
01
54
87
01
KEY
)
STO
35'
(
(
RCL
27
X
RCL
26
)
X
y
RCL
31
2nd Ifflg
1
1
56
RCL
35
X
RCL
36
-r
RCL
26
X
y
(
RCL
01
-
1
)
2nd Ifflg
1
LOG
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
CODE
01
74
94
55
43
38
33
54
87
04
01
89
86
04
22
61
01
92
22
86
04
44
34
53
43
36
55
43
37
54
42
36
53
43
37
KEY
1
74
+/-
~
RCL
38
X
)
2nd Ifflg
4
1
89
2nd Stflg
4
INV
GTO
1
92
INV
2nd Stflg
4
SUM
34
(
RCL
36
RCL
37
)
STO
36
(
RCL
37
LOG
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
CODE
75
01
54
42
37
97
01
01
28
43
39
48
33
97
03
02
43
86
06
22
87
05
02
43
53
24
55
43
33
75
01
54
50
22
77
KEY
-
1
)
STO
37
2nd Dsz
1
1
28
RCL
39
2nd Exc
33
2nd Dsz
3
2
43
2nd Stflg
6
INV
2nd Ifflg
5
2
43
(
CE
•
"•"
RCL
33
-
1
)
2nd x
INV
2nd x>t
LOG
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
:ODEJ
02
47
97
00
00
46
43
33
94
92
76
11
42
10
91
76
12
42
11
91
76
13
42
12
91
76
14
42
13
91
76
15
22
86
01
KEY
2
47
2nd Dsz
0
0
46
RCL
33
V-
INV SBR
2ndLbl
A
STO
10
R/S
2ndLbl
B
STO
11
R/S
2ndLbl
C
STO
12
R/S
2ndLbl
D
STO
13
R/S
2ndLbl
E
INV
2nd Stflg
1
186
-------
LOG
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
CODE
22
86
02
22
86
03
53
43
11
33
55
43
14
55
43
16
55
43
17
65
43
15
54
34
42
25
42
30
32
00
32
22
67
03
13
KEY
INV
2nd Stflg
2
INV
2nd Stflg
3
(
RCL
11
2
X
•
™
RCL
14
-r
RCL
16
~
RCL
17
X
RCL
15
)
&
STO
25
STO
30
xtt
0
xjt
INV
2nd x=t
3
13
LOG
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
CODE
86
02
06
42
02
01
42
32
42
33
53
07
75
43
02
54
42
31
53
53
43
30
33
55
04
54
45
43
31
55
53
43
31
65
43
KEY
2nd Stflg
2
6
STO
02
1
STO
32
STO
33
(
7
-
RCL
02
)
STO
31
(
(
RCL
30
2
X
•
*
4
)
X
y
RCL
31
•r
(
RCL
31
X
RCL
LOG
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
CODE
32
54
42
32
33
54
44
33
97
02
03
21
43
33
42
28
53
03
09
93
05
01
55
43
14
55
43
12
65
43
18
65
43
19
65
KEY
32
)
STO
32
2
X
)
SUM
33
2nd Dsz
2
3
21
RCL
33
STO
28
(
3
9
•
5
1
•
"•"
RCL
14
•
RCL
12
X
RCL
18
X
RCL
19
X
LOG
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
CODE
43
20
65
43
11
33
54
42
26
42
23
32
01
32
22
77
04
01
86
01
53
43
25
33
55
04
55
43
26
54
42
27
42
22
87
KEY
RCL
20
X
RCL
11
2
X
)
STO
26
STO
23
x£t
1
x£t
INV
2nd x>t
4
01
2nd Stflg
1
(
RCL
25
2
X
•7
4
RCL
26
)
STO
27
STO
22
2nd Ifflg
187
-------
LOG
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
CODE
01
04
37
22
87
02
04
29
22
86
02
86
03
43
26
42
22
43
27
42
23
53
53
87
03
04
72
43
28
65
43
23
86
KEY
1
4
37
INV
2nd Ifflg
2
4
29
INV
2nd Stflg
2
2nd Stflg
3
RCL
26
STO
22
RCL
27
STO
23
(
(
2nd Ifflg
3
4
72
RCL
28
X
RCL
23
2nd Stflg
LOG
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
CODE
06
71
00
00
22
86
06
87
02
05
19
85
53
93
05
07
07
02
85
43
22
23
85
43
22
71
00
00
87
03
05
25
75
KEY
6
SBR
0
00
INV
2nd Stflg
6
2nd Ifflg
2
5
19
+
(
.
5
7
7
2
+
RCL
22
In x
+
RCL
22
SBR
0
00
2nd Ifflg
3
5
25
LOG
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
CODE
43
22
85
53
43
28
75
01
54
55
43
23
54
65
43
23
94
22
23
94
85
43
34
65
43
26
33
22
87
01
05
19
34
KEY
RCL
22
+
(
RCL
28
-
1
)
-r
RCL
23
)
X
RCL
23
+/-
INV
In x
+/-
+
RCL
34
x
RCL
26
2
x
INV
2nd Ifflc
1
5
19
^
LOG
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
:ODE
94
35
22
23
54
87
01
05
25
94
55
02
54
42
34
87
03
05
79
87
01
05
79
53
43
25
33
55
04
85
43
25
45
KEY
+/-
1/x
INV
In x
)
2nd Ifflg
1
5
25
+/-
V
2
)
STO
34
2nd Ifflg
3
5
79
2nd Ifflg
1
5
79
(
RCL
25
2
x
v
4
+
RCL
25
x
y
188
-------
LOG
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
CODE
04
65
93
00
02
03
04
04
75
43
28
65
53
93
05
07
07
02
85
53
43
25
55
02
54
23
54
54
24
44
34
53
KEY
4
X
•
0
2
3
4
4
-
RCL
28
X
(
•
5
7
7
2
+
(
RCL
25
-r
2
)
In x
)
)
CE
SUM
34
(
LOG
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
CODE
43
34
65
43
10
65
43
19
65
43
21
65
PI
04
01
55
43
14
55
43
16
85
43
14
54
92
KEY Hi LOG
RCL
34
X
RCL
10
x 1
RCL
19
x
RCL
21
x
1
4
1
-r
RCL
14
•
~
RCL
16
1
+
RCL
13
)
INV SBR
CODE
KEY II LOG
J
CODE
KEY
189
-------
DIMENSION RADSKNtlO) XF( 10) . PERMZUO) , ZF J10), ANSC2 ), BNDYf 2 )
DIMENSION XDUMUO,25 , TlTLEt 171, YDUMC 10, 25)
COMMON/DATA/TIMEC20),LWN(10),NRATE(10),BW(10),VIS(10),PERM(10),
1THKI10),POR|lO)fCOMPliO),SKINl10),Q( 10,15),QTIMEf10,151,RADIUSC
20,25),RW(10),X<10).Y 10) .DPENT C10 )
COMMON/VAR/DELH<25)fCUMlho*20),TSTART
-------
920
930
940
V£>
60
70
80
WRITE<6,920) IPENT , ANSU51 , IFRAC , ANSI! 6) , IREF
FORMATIT15,' IPENT=» ,T22 ,110,T34 ,' WELLS PARTIALLY PENETRA',
1'TING BED?',A4,/,T15,» IFRAC=»,T22,110,T34,• FRACTURE ANALYSIS?'
2,A4,/,T15,« IREF=»,T22,I10.T34,• REFERENCE WELL FOR PRINTING1)
WRITE(6,930) CAPKT,CAPHT,CAPKB,CAPHB.ANGLE
FORMAT(////,T10»• GENERAL DATA CORRESPONDING TO OPTIONS SEL',
1'ECTED:' ,//,T15,' CAPKT=»,T23,F10.3,T34,« PERMEABILITY OF',
.,' CAPHT=',T22,F10.2,T34,' THICK'
t./.Tiu.t CAPKB=•*T23tF10.3tT34v
« ./.T IR. I "
2' OVERLYING BED (MD)',/,1^ .
3'NESS OF OVERLYING BED (FT)',/,T15, .._.,._.. .
4' PERMEABILITY OF UNDERLYING BED (MD)•,/,T 15, • CAPHB=',T22,
5F10.2.T34,' THICKNESS OF UNDERLYING BED (FT)•,/,T15,' ANGLE=»
6,T22,F10.2,T34,' ANGLE OF BOUNDARY INTERSECTION (DEG)')
WRITE(6,940) IBl,BNDY(17),IB2,BNDY(18).PI,DW
FORMAT(T15,' IB 1=',T22,110,T34,• BOUNDARY i SEALING OR ',
1'LEAKING?',1X,A4,/,T15,' IB2=•,T22,110,T34,' BOUNDARY',
2' 2 SEALING OR LEAKING?«,IX,A4,/,T15,' PI=',T22,F10.2,
3T34,• INTIAL RESERVOIR PRESSURE (PSI)',/,T15,' DW=«.T22,
4F10.2,T34,« DENSITY OF RESERVOIR FLUID (LB./CU. FT.)')
DO 30 I=l,NW
READ(5,40) LWN(I),NRATE(I),RW(I),TSTART(I) ,VISN(I),
1TINS(I),RADSKN(I)
FORMAT(10X,2I5,6FIO.O)
IF(IPENT.EQ.l) READ(5,20) PARTHK(I),DPENT( I)
IF(LWN(Il.EQ.O) LWN(I)=I
IFIRADSKN(I).EQ.O.O) RADSKN( I) = 100.
IF(IMAGE.NE.O) READ(5,20) X(I).YU)
READ(5,20) BW(I),VIS(I),PERM(I),THK(I),POR(I),COMP(I),SKIN(I)
COMP(I)=COMP(T)*l.E-6
IF(RWd).EQ.O.O) RW(I)<3.0
RW(I)=RW(I»/12.
QT!ME(I,1)=0.0
NR=NRATE(im
DO 70 K=2,NR
READ(5,60) Q(I,K),QTIME(1,K)
FORMAT(10X,2F10.3)
CONTINUE
IFdMAGE.EQ.O.AND. IFRAC.EQ.O)
FORMAT(IOX,7F10.3)
IF(IFPAC.EQ.O) GO TO 540
IF(IFRAC.NE.i) GO TO 530
READ(5,80) XF(I)
DO 500 KCK=i,NRAD
READt5,80) XV,YV
XDUM(I,KCK)=XV
YDUM(I,KCK)=YV
XXD=XV/XF( I)
YYD=YV/XFU)
RADIUS!I.KCK)=SIGMA(XXD,YYD)
READ(5,80) (RADIUS(I,K),K=l,NRAD )
00000500
00000510
00000520
00000530
00000540
00000550
00000560
00000570
00000580
00000590
00000600
00000610
00000620
00000630
00000640
00000650
00000660
00000670
00000680
00000690
00000700
00000710
00000720
00000730
00000740
00000750
00000760
00000770
00000780
00000790
00000800
00000810
00000620
00000830
00000840
00000850
00000860
00000870
00000880
00000890
00000900
00000910
00000920
00000930
00000940
00000950
00000960
00000970
00000980
-------
500
530
550
540
30
370
360
810
820
to
ro
890
830
CONTINUE
GO TO 541
READ(5t80) XF( I) ,PERMZ { I I ,ZF( I)
RE AD I 5, 80) I RADIUS (I ,KCK) ,KCK=l,NRAD)
DO 550 KCK=l.NRAD
RADIUS(ItKCK)=RADIUS( I,KCK )/XF(I )
CONTINUE
DO 30 K=1,NRAD
IF (RAOIUS(ItK) .LE. 0.0) RAO IUS ( I , K ) =R W( I )
CONTINUE
IF ( IMAGE. NE.l) GO T0 360
DO 370 K=l ,NRAD
READ(5,80) XPm,YP(K)
CONTINUE
IF{ IDIP.NE.OI READ(5t80) ( DELH ( J ) , J=l , NRAD )
DO 800 I=1,NW
WRITE(6,810) LWN(I)
FORMAT('1',////,T40,» RESERVOIR DESCRIPTIVE AND WELL COMPLETION1
it/,T48,« INPUT DATA FOR WELL»,I4,//)
WRITE (6, 820) TSTARTt I),PARTHK(I) ,PEP MZ ( I 1 , RADSKN ( I ) f PERM (I ),
INRATEt I) ,VIS(I),SKIN(I)»PORU)fTINS(I) ,THK(I) , VI SN ( I ) t BW( I ) ,
2COMP( I),RW(I ) ,X( I)
FORMAT(T15i' _TSTART=',F11.2,T34, ' TI ME TO START OF FIRST RATE '
1 1
2,
3,
4,
(DAYS)
(FT)' ,/
ITY (MD)
'/T15
PARTHK=',F1U2,T34,' LENGTH OF WELL PENETRATION'
,T15,» PERMZ='tF12.2rT34,' VERTICAL RESERVOIR PERMEABIL
•/T15,' RAOSKN='tFll,2tT34,' RADIUS EFFECTED BY SKIN'
(FT)',/,Tl5,» PERM=',F13.2,T34,' AREAL RESERVOIR PERMEABILITY'
^, (MD)'/T15,« NRATE = ' ,I12,T34,' NUMBER OF RATES ' t /» Tl 5,' VIS='
6,F14.3,T34t' VISCOSITY OF RESERVOIR FLUID (CP)'/T15,' SKIN=«,
7F13.2,T34,' SKIN FACTOR AT WELLBORE',/,T15,' POR=•,F14.3,T34,
8' RESERVOIR POROSITY ( FRACT I ON)' /T 15 , • T.I NS = ', F13 .2 ,T34,
9' TIME TO START OF NEW FLUID INJECTION (DAYSI•,/,T15, • THK=',
1F14.2,T34,' RESERVOIR THICKNESS (FTP/IIS, • VI SN= ' ,F 13. 3, T34,
2' NEW FLUID VISCOSITY (CP)'./,Tl5,• BW=«,F15.2tT34,• FORMATION',
3' VOLUME FACTOR (PB/STB)'/T15, ' COMP=•,F13.8,T34,• SYSTEM',
4' COMPRESSIBILITY t1/PSI)',/,T15t' RW=',Fl5.3,T34,« WELLBORE',
5' RADIUS (FT|'/T15,« X=',F16.2,T34,« REAL WELL X-LOCATIQN (FT)')
WRITE(6,890) XF(I),Y(I I.ZF(I)tDPENTI I)
ZF=« ,F15.3,T34
FOP.MAT{T15, • XF = » ,F15.3,T34,« FRACTURE LENGTH (FT)'/T15,f Y='
1F16.2,T34,' REAL WELL Y-LOCATION (FT)',/,T15,
2' DISTANCE FROM HORIZONTAL FRACTURE',
2/T34,' TO BOTTOM OF BED
-------
KK=K-l
WRITE<6,850) KK,QtI,K),QTIME(I,K)
850 FORMAT(T40,I3,T50,F10.2,T67,F10.2)
840 CONTINUE
800 CONTINUE
IPEND=NW
IFUMAGE.EQ.il IPEND=1
DO 950 IC=1,IPEND
IFUMAGE.EQ.l.OR.IFRAC.EQ. 1) GO TO 951
WRITE(6,952) LWN(IC)
952 FORMAT(///,T44,» DISTANCE TO POINT X FOR WELL ',I4,/,T56,
CO
951
954
953
960
961
962
950
180
190
NUMBER*,T58
.EQ. 2) IPT
1' CHANGE IN',/,T43,«
2/,T42,
IPT^i
IF (IFRAC
GO TO 953
WRITE(6,954I LWN(IC)
FORMAT!///,T44,» DISTANCE
1« CHANGE IN',/,T3i,'
2,T85t -------
3,T89,' (FT)',/)
IPT=0
DO 960
POINT',T56,
1 (FT)',T76,«
« ELEVATION1,T75,«
(FT)',/)
TO POINT X FOR WELL •
..__ - .._f POINT',T46,» ELEVATION' ,T65,'
' Y-LOCATION',/,T30,' NUMBER• ,T48 ,' (FT) "
,I4,/,T46,
~. X-LOCATION'
•,T69,' (FT)'
KC,DELH(KC),RAOIUS(IC,KC)
KC=1,NRAD
IF(IPT.EQ.l) WRITE(6,961)
DUM=RADIUS(IC,KC)*XF(IC)
IF (IPT .EQ. 2) WRITE (6,961) KC,DEL HIKC),DUM
IF(IMAGE.EQ.i) WRITE(6,962) KC,DELH(KC),XP(KC),YP(KC)
IF(IFRAC.EQ.l) WRITE(6,962) KC,OELH( KC),XDUM(IC,KC),YDUM(IC,KC)
CONTINUE
FORMAT(T42,I6,T56,FIO.2,T75,F10.2)
FORMAT(T30,I6,T46,F10.2,T65,F10.2,T85,F10.2)
CONTINUE
IF(IVIS.NE.O) CALL VARVIS
IF(IMAGE.NE.O) CALL DIMGE(ANGLE,IBl,IB2)
DO 90 IT=1,NT
WRITE(6,180) TIME(IT)
FORMAT(lHi,//,20X,17HPRESSURE AT
IF(IFRAC.EQ.O) WRIT6(6,190)
TIME ,F10.3,7H (DAYS))
FORMAT(//,19X,5HPOIMT,7X,11HRADIUS
1/,18X,6HNUMBER,5X,1*HREFERENCE WEL
FROM,7X,8HPRESSURE
DO 100 KK=1,NRAD
IF(IFRAC.NE.O) WRITEC6,15001 KK
ELL,6X,6H(PSIA),/)
1500 FORMAT(/,20X,' RADIUS POINT NUMBER='
1' WELL NUMBERS10X,' PRESSURE (PSIA)
PX=PI
IF( IDIP.NE.O) PX=PX*-(DW*DELH(KK)/144.)
DO 110 IW=l,NW
IF(IFRAC.EQ.O) GO TO 620
X(IW)=PI
,14,/
20X
00001480
00001490
00001500
00001510
00001520
00001530
00001540
00001550
00001560
00001570
00001580
00001590
00001600
00001610
00001620
00001630
00001640
00001650
00001660
00001670
00001680
00001690
00001700
00001710
00001720
00001730
00001740
00001750
00001760
00001770
00001780
00001790
00001800
00001810
00001820
00001830
00001840
00001850
00001860
00001870
00001880
00001890
00001900
00001910
00001920
00001930
00001940
00001950
00001960
-------
620
200
210
250
510
560
580
570
600
PX=0.0
CONTINUE
S-SKINUW)
IF(IMAGE.NE.i.AND.RADIUSUW,KK).GT.RADSKNUWM S=0.0
IFUVIS.NE.OI S=S*CJMniW,IT)
RAO-RAOIUS(IW,KK)
IEND-NRATEIIWI+1
DO 200 ICHK=2,IEND
LK=ICHK
U1=QTIME(IW,ICHK)
IF(Ul.GT.TIME(IT)) GO TO 210
CONTINUE
TSUP'TIMElIT)-TSTARTUW)
IFCTSUP.LE.O.OI GO TO 110
DO 220 L=2,LK
LM1=L-1
QTERM=QCIW, LI-QUW.LMi)
TTERM=TSUP-OTIMEUW,LM11
OT=QTERM
IF(IFRAC.NE.i) GO TO 510
TDF=6.331E-3*PERM(IH)*TTERM/IPOR(IWI*VISUW)*COMPUW)*XFUW)**2)
IF(RADIUS(IW,KK).EQ.I.E20) GO TO 591
PD=.5"MAIOG GO TO 520
TDF=6.331E-3*PERM(m*TTERM/(POR(IW)*COMP( IW)*VIS( IW)*XF(
HD-THK(IWI*SQRT(PERM(IW)/PERMZ(IW))/XF(IW)
TC1*12.5*(2,*RAOIUS(IW,KK)**2*1.)
TC2=5.*HD**2/I3.14159**2)
IF(TDF.LT.TC1.0R.TDF.LT.TC2) GO TO 560
RD2=RADIUSUW,KK)**2
PD=.5*(ALOG(TDF)*1.80907-RD2)
IFCRADIUS(IW,KK).GT.l.) PD=.5*{ALOG(TDF/RD2)*.80907)
RTST=XF(IW)+10.*THKUW)*SQRT(PERM(m/PERMZUW))/3.14159
R=RADIUS(IW,KK)*XF(!H>
IFfR.LT.RTST.AND.R,NE.O.O) GO TO 570
SGM=0.0
ZFH=ZF(IW)/THK(IW)
IF(R.EQ.O.O) SGM=SIGHOR(HD»ZFH)
PO=PD*SGM
GO TO 240
WRITE(6,580) IW,T!ME(IT)
FORMAT(/,» APPROXIMATIONS FOR HORIZONTAL
1» TO TD LIMITATIONS FOR WELL ',I4,» TIME'
GO TO 590
WRITE(6,600) IW,R
FORMAT(/,« APPROXIMATIONS FOR
1' RADIUS LIMITATIONS FOR WELL
GO TO 590
FRCTURE FAIL
»,F10.2)
DUE
HORIZONTAL FRACTURE FAIL DUE TO1,
»,I4,« RADIUS=',F10.2)
00001970
00001980
00001990
00002000
00002010
00002020
00002030
00002040
00002050
00002060
00002070
00002080
00002090
00002100
00002110
00002120
00002130
00002140
00002150
00002160
00002170
00002180
00002190
00002200
00002210
00002220
00002230
00002240
00002250
00002260
00002270
00002280
00002290
00002300
00002310
00002320
00002330
00002340
00002350
00002360
00002370
00002380
00002390
00002400
00002410
00002420
00002430
00002440
00002450
-------
RADSKNdWI )
ID
cn
591 WRITE(6,592I IW,KK
592 FORMAT!/,• APPROXIMATION FOR VERTICAL FRACTURE PSUEDO'
I1 SKIN FAIL FOR HELLSI4,' RADIUS NO.',14)
590 CONTINUE
520 CONTINUE
IF(IMAGE.NE.l) GO TO 300
IS=NI*(IW-1»
00 220 IK=i,NI
KSUB=IK+IS
IFfIW.EQ.IREF.AND.IK.EQ.l) KPRNT=KSUB
IF(lK.EQ.i.AND.ABS!RADIUS(KSUB,KK)).GT,
IS=S-SKIN(IWI
ISIGN=1
IF(RADIUS(KSUB,KK).LT.O.O) ISIGN=-1
RAD=ABStRADlUS(KSUB,KK)>
QT=QT*ISIGN
300 CALL PRESS(IW1RAD1TTERM,PD,S,fi240)
PX=PX+{70.6*QT*VISUW)*BW( IW)*PD/ ( PERM (I W )*THK( IW) ) )
GO TO 220
240 PX=PX+(PD*QT*VIS( IW)*BW( IW )/( 7.082E-3*PERM (I W)*THK( IWMI
220 CONTINUE
IF(IFRAC.NE.O) X(IHI=X(IW)^PX
IF(IFRAC.NE.O) WRITE(6,1600) IW,X(IW)
1600 FORMAT(20X,I10,11X,F11.2)
110 CONTINUE
IF( INiAGE.NE.l) KPRNT=IREF
IF(IFRAC.EQ.O) WRITE(6,390) KK,RADIUSiKPRNT,KK),PX
390 FORMATa7X,I4,7XfF15.3,3X,F10.3J
100 CONTINUE
90 CONTINUE
STOP
END
FUNCTION EIIZZ)
REAL*8 FACfUtY.RItDC
DIMENSION K(IO)
DATA K/6,8,10,16,l8t20t24,28,32,34/
Z^ABSCZZ)
EI=0.0
IFtZ.GT.lO.) RETURN
C=.5772
U=DBLE(Z)
DC=DBLECC)
Y=-DC-DLOG(U)
FAC=l.DO
IZ=Z
IF(IZ.GT.9| IZ=9
KC=K(IZ*1)
IF(Z.LT.l.E-lO) KC=3
DO 10 1=1,KC
00002460
00002470
00002480
00002490
00002500
00002510
00002520
00002530
00002540
00002550
00002560
00002570
00002580
00002590
00002600
00002610
00002620
00002630
00002640
00002650
00002660
00002670
00002680
00002690
00002700
00002710
00002720
00002730
00002740
00002750
00002760
00002770
00002780
00002790
00002800
00002810
00002820
00002830
00002840
00002850
00002860
00002870
00002880
00002890
00002900
00002910
00002920
00002930
00002940
-------
vc
en
RI=DFLOAT(I)
FAC=FAC*(-RI )
Y=Y-(U**I)/(RI*FAC)
10 CONTINUE
IFIY LT.0.0) Y=0.0
T=SNGUY)
i onjoi-iii
RETURN
END
SUBROUTINE PRESS ( I WN ,RAO ,T , PP ,SKN, *)
COMMON/DAT A/ TIMEt 20) ,L WN( 10) , NRATC ( 10 ) , BW ( 10) , V I S ( 10) , P ERM{ 10 ) ,
ITHKIlOI.PORtlO) tCOMP(10)fSKIN(lO»,QllO,15» , QT IKE ( 10 , 15 ) , RADIUS! 3
20,25) ,RW(10),X(10) ,Y(10) ,DPENT(10)
COMMCN/VAR/DELH(25),CUMI{10,20)tTSTART(10) ,TINS(10) ,VISN(10) »
lPARTHK(10),XP(25),YP(25)»CAPKT.CAPHT,CAPKBtCAPHB .
CCMMON/SWITCH/NT,N^,NRADfIVlS,IMAGE,NI»ILEAK,IPENT,IFRAC
IKEY=0
IF (T .Eti. 0.0) T=l.E-5
IF(ILEAK.NE.l) GO TO 10 ,
TU=0.0
TL=0. 0
IF(CAPHT.NE.O.O) TU=CAPKT/ ( PERM ( I WN) *THK( I WN) *C APHT )
IF
-------
<£>
DO 4 1=1,N2 00003440
4 F2=F2*FLOATd) 00003450
IF(U.LE.L.O) GO TO 120 00003460
SUMM=SUMM+( ( -1. )** {N+M) )*Fi*d (RB8**2)/4. )**N)/ 00003470
' H(F2**2)*(U**(N-M))) 00003480
GO TO 2 00003490
120 SUMM=SUMM+U-1.)**(N + MJ)*F1*U (RB8**21/4. I**M)*(U**{N-M)) 00003500
1/(F2**2) 00003510
2 CONTINUE 00003520
3 SUMN=SUMN*SUMM 00003530
IF(U.LE.l.O) GO TO 130 00003540
TER=0.0 00003550
IF(U.LT.174.) TER=EXP(-U) 00003560
SUMN*SUMN*TER/(U**2) 00003570
PR=(SUMN+DUM)/2.+(2.*SKN) 00003580
GO TO 500 00003590
130 SUMN=SUMN*(U**2) 00003600
TER=0.0 00003610
IFCRB2.LT.174.) TER=EXP<-RB2) 00003620
T3=DUM+TER*(T2-SUMN) 00003630
PR=T3/2.*(2.*SKN) 00003640
500 CONTINUE 00003650
IFdPENT.NE.il RETURN I 00003660
IKEY=1 00003670
10 RTEST=l.5*THK(IWN) 00003680
IFdPENT.NE.l.QR.RAD.GT.RTEST) GO TO 20 00003690
U = PORdWN)*VISI IWN)*COMP< I WN )*RAD**2/ ( 2. 532E-2*PER M{ I WN) *T ) 00003700
IFUKEY.EQ.l) GO TO 30 00003710
PR = PARPENtU,RAD,THM IWN) ,PARTHKdWN) fOPENT {I WN) t IKEY) 00003720
RETURN 1 00003730
30 PR = PR + PARPEN(U,RAD,THKdWN) f PARTHK (I WN) , DPENT (IWN ) t IKEY) 00003740
RETURN 1 00003750
20 IF
-------
oo
10
100
20
50
TANG*TAN C(THETA/57.29578))
SLPE*-1.0/TANG
A*i.O+SLPE**2
DO 10 IW=1,NW
R2=XUW)**2«-YUWI**2
XIUW, 1)=X(IW)
YKlMiD-YIIWI
XI(IW,2)=X(IW)
YI(IW,2)=-Y(IWI
IFCNI.LE.2) GO TO 10
DO 10 IM=3tIEND
IM1=IM-1
IP1=IM+1
B*2.*-YIUMtIM)
CONTINUE
00 20 I*lfN«
IS=NI*(I-i)
DO 20 K*1,NI
KSUB=K*IS
ISIGN=1
IF(K.EQ.1) GO TO 40
IF(IKZB.EQ.l) GO TO 100
IFHBONDl.EQ.i.AND.YH lWtK I .LT.O .0 ) ISIGN=-1
IF(IBOND2.NE.l) GO TO 40
YTEST=TANG*XI(IW,K)
IFIYTEST.LT.YUIW,K)) ISIGN=-1
GO TO 40
IF{IBONDl,EQ.l.ANO.K.GE.5) ISIGN=-1
IF(IBOND2<.EQ.i.AND.K.LE.4) ISIGN=-1
CONT INUE
DO 20 J=1,NRAD
RDUM=(XP(J)-XI (IW,KI)**2-»-(YP(JJ-YI(lW,K})**2
RAD1US(KSUB,J)=SQRT(RDUM)*ISIGN
IF (RADIUS(KSUB,J).EQ.O.O) RADIUS(KSUB,J)=RW{I)
CONTINUE
RETURN
CONTINUE
XL=X(1)
00003930
00003940
00003950
00003960
00003970
00003980
00003990
00004000
00004010
00004020
00004030
00004040
00004050
00004060
00004070
00004080
00004090
00004100
00004110
00004120
00004130
00004140
00004150
00004160
00004170
00004180
00004190
00004200
00004210
00004220
00004230
00004240
00004250
00004260
00004270
00004280
00004290
00004300
00004310
00004320
00004330
00004340
00004350
00004360
00004370
00004380
00004390
00004400
00004410
-------
70
to
10
60
110
10
50
XR=Y(i)
X< 1)=0.0
Y(l)=0.0
xiii,u=o.o
YIU,1)=0.0
DO 60 IH=1,NW
IFUW.EQ.ll GO TO 70
XI (IW, 1)=XUW)
= XL-XUW)
ADR=XR-X(IW)
XI
XI
XI
XI
XI
XI
DO
IW,2)=XR+ADR
IW,3) = XI(IW,2H2.*ABS
-------
ro
o
o
IFtT.EQ.TIMEUTI) GO TO 20
30 CONTINUE
20 CONTINUE
00 60 IW=1,NW
IF(VISNUW).EQ.O.O) GO TO 60
FAC = 5.615*BWUW)M3.1416*THKIIW)*POR(IW)
PF = RWUW)**2
PERMN=PERM(IW)*VISnW)/VISN
-------
ro
o
SUM=SUM*2.*H/PI/RL
Z=(SUM*YJ/2.
PARPEN=SNGL(Z)
RETURN
10 • SUM=0.0
00 20 1=1,100
RI=DFLOATU)
AUG«PI*RI/H
A=DSIN
LIM=2**N-1
DO 10
10
15
20
22
25
26
28
*u j—1,LIM
X=XO+DFLOAT(J)*H
S=S*2.0*FCT(X,C»
TCN+ll = (H/2. )*(S*FCT(B,O)
IF
-------
30 IF (DABStT(K)-T 50,50,35 00005890
35 M=M+l 00005900
K=K-l 00005910
GO TO 28 00005920
40 N=N+l 00005930
IF (N-NMAX) 26,26,45 00005940
45 DEL=DEL/2. 200SI25°
GO TO 5 00005960
50 CONTINUE 009352I°
Q=T(K) 00005980
GO TO 65 00005990
60 CONTINUE 00006000
Q=T(N+1) 00006010
65 RETURN 00006020
END 00006030
SUBROUTINE DEUU.Y) 00006040
IMPLICIT REAL*8(A-H,0-Z) 00006050
DIMENSION K(10) 00006060
DATA K/6,8,10,16,18,20,24,28,32,347 00006070
U=DABStU) 00006080
Y=0.0 00006090
IFCU.GT.IO.I RETURN 00006100
DC=,5772 00006110
Y=-DC-DLOG(U) 00006120
FAC=1.DO 00006130
IZ=U 00006140
IFdZ.GT.9) IZ=9 00006150
KC=K(TZ+1) 00006160
IFIU.LT.l.D-10) KC=3 00006170
00 10 1=1,KC 00006180
RI = DFLOAT«n 00006190
FAC=FAC*(-RI) 00006200
Y=Y-(U**I)/
-------
10
PO
o
CO
20
IF(XMI.EQ.O..AND.YO. EQ.O..OR.XP1.EQ.O. .AND.YD.EQ.O
A=XM l*ALOG(YD**2+XMl**2)
B=XP1*ALOG(YD**2+XP1**2)
DEM=RD 2-1.0
IFCDEM.EQ.0.01 GO TO 10
RATIO=2.*YD/DEM
C=2.*YD*ATANCRATIO)
IFIC.LT.0.01 C*0.0
SIGMA=(A-B-C)/4.
RETURN
SIGMA=1.E20
RETURN
END
FUNCTION SIGHORIH,Z)
IMPLICIT REAI_*8 CA-H.O-Z)
REAL*4 H,Z»SIGHOR
PI =3. 141 592654
I GO TO 10
ZFH=CBLECZ)
A=U-(3.*ZFH*Cl.-ZFHH
A=2.*A*HD**2/3.
SIGHOR=SNGLCAI
IFCHD.LT.UO) RETURN
SUM=0.0
00 20 I=li20
R!*OFLQATm
AUG=RI*PI*ZFH
B=(DCOS(AUG))**2/Rl
T=RI*PI/HD
BES=l./T
IF tT.GT.5.) BES=OSQRTtPI/{2.*TJJ*(l.*C3./(8.*TJ))*OEXPt-T)
B=B*BES
SUM=SUM+B
SUM=SUM*4.*HD/Pl
SIGHOR=SNGLC A-SUMt
RETURN
END
00006380
00006390
00006400
00006410
00006420
00006430
00006440
00006450
00006460
00006470
00006480
00006490
00006500
00006510
00006520
00006530
00006540
00006550
00006560
00006570
00006580
00006590
00006600
00006610
00006620
00006630
00006640
00006650
00006660
00006670
00006680
00006690
00006700
00006710
00006720
00006730
00006740
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/2-79-170
3. RECIPIENT'S ACCESSIOt*NO.
4. TITLE AND SUBTITLE
RADIUS OF PRESSURE INFLUENCE OF INJECTION WELLS
5. REPORT DATE
August 1979 Issuing date
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Don L. Warner, Leonard F. Koederitz,
Andrew D. Simon, and M. Gene Yow
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
University of Missouri at Rolla
Rolla, Missouri 65401
10. PROGRAM ELEMENT NO.
1CC824
11. CONTRACT/GRANT NO.
Grant No. R-805039
12. SPONSORING AGENCY NAME AND ADDRESS
Robert S. Kerr Environmental Research Lab,
Office of Research & Development
U.S. Environmental Protection Agency
Ada, Oklahoma 74820
- Ada, OK
13. TYPE OF REPORT AND PERIOD COVERED
Final (3/77 - l/~"
14. SPONSORING AGENCY CODE
EPA/600/15
15. SUPPLEMENTARY NOTES
16. ABSTRACT
It is often necessary, in injection well design, to predict the
probable rate of pressure increase in the injection reservoir that would
be expected to result from a proposed injection program. Areas of appli-
cation include oilfield brine injection, waterflcoding for secondary oil
recovery, industrial wastewater injection, uranium leaching, etc.
This report presents a number of available analytical solutions that
can be used for pressure buildup calculation and three methods of per-
forming such calculations. The methods are: manual calculation, calcu-
lation by programmable desk calculator, and calculation by digital
computer. Programs for the desk calculator and for the digital computer
are presented and examples of their use are given.
17.
KEY WORDS AND DOCUMENT ANALYSIS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
a.
DESCRIPTORS
Ground Water
Hydrogeology
Injection Wells
Models
Salt Water
Industrial Wastes
48 G
r18. DISTRIBUTION STATEMENT
Release to public.
19. SECURITY CLASS (ThisReport)'
Unclassified
21.NO. OF PAGES
216
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
204
ft U.S. GOVERNMENT PRINTING OFFICE: 1MO-657-146/5710
------- |