Lyons W.C. (ed.). Standard handbook of petroleum and natural gas engineering.2001- Volume 1
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Contributing Authors
Frederick
E.
Beck, Ph.D.
ARC0 Alaska
Anchorage, Alaska
Daniel
E.
Boone
Consultant in Petroleum Engineering
Houston, Texas
Gordon
R.
Bopp, Ph.D.
Environmental Technology and Educational Services Company
Richland, Washington
Ronald
M.
Brimhall, Ph.D., P.E.
Texas
A
8c
M
University
College Station, Texas
Robert Desbrandes, Ph.D.
Louisiana State University
Baton Rouge, Louisiana
Patricia D. Duettra
Consultant in Applied Mathematics and Computer Analysis
Albuquerque, New Mexico
B.
J. Gallaher, P.E.
Consultant in Soils and Geological Engineering
Las
Cruces,
New Mexico
Phillip
W.
Johnson, Ph.D., P.E.
University
of
Alabama
Tuscaloosa, Alabama
vii
Murty Kuntamukkla, Ph.D.
Westinghouse Savannah River Company
Aiken, South Carolina
William C. Lyons, Ph.D., P.E.
New
Mexico Institute
of
Mining and Technology
Socorro, New Mexico
Stefan Miska, Ph.D.
University
of
Tulsa
Tulsa, Oklahoma
Abdul Mujeeb
Henkels
8c
McCoy, Incorporated
Blue Bell, Pennsylvania
Charles Nathan, Ph.D., P.E.
Consultant in Corrosion Engineering
Houston, Texas
Chris
S.
Russell,
P.E.
Consultant in Environmental Engineering
Grand Junction, Colorado
Ardeshir
K.
Shahraki, Ph.D.
Dwight's Energy Data, Inc.
Richardson, Texas
Andrzej
K.
Wojtanowicz, Ph.D., P.E.
Louisiana State University
Baton Rouge, Louisiana
...
vtaa
This petroleum and natural gas engineering two-volume handbook
is written in the spirit of the classic handbooks
of
other engineering
disciplines. The two volumes reflect the importance
of
the industry
its engineers serve (i.e.,
Standard and
Poor’s
shows that the fuels sector
is the largest single entity in the gross domestic product) and the
profession’s status as a mature engineering discipline.
The project to write these volumes began with an attempt to
revise the old
Practical Petroleum Engineer’s Handbook
that Gulf
Publishing had published since the
1940’s.
Once the project was
initiated, it became clear that any revision of the old handbook
would be inadequate. Thus, the decision was made to write an
entirely new handbook and to write this handbook in the classic
style of the handbooks of the other major engineering disciplines.
This meant giving the handbook initial chapters on mathematics
and computer applications, the sciences, general engineering, and
auxiliary equipment. These initial chapters set the tone of
the
handbook by using engineering language and notation common
to all engineering disciplines. This common language and notation
is used throughout the handbook (language and notation in nearly
all cases is consistent with Society of Petroleum Engineers publication
practices). The authors, of which there are
27,
have tried (and we
hope succeeded) in avoiding the jargon that had crept into petroleum
engineering literature over the past few decades. Our objective was
to create a handbook for the petroleum engineering discipline that
could be read and understood by any up-to-date engineer.
The specific petroleum engineering discipline chapters cover
drilling and well completions, reservoir engineering, production,
and
economics and valuation. These chapters contain information, data,
and example calculations related to practical situations that petroleum
engineers often encounter. Also, these chapters reflect the growing
role of natural gas in industrial operations by integrating natural
gas topics and related subjects throughout both volumes.
This has been a very long and often frustrating project. Through-
out the entire project the authors have been steadfastly cooperative
and supportive of their editor. In the preparation of the handbook
the authors have used published information from both the American
Petroleum Institute and the Society of Petroleum Engineers. The
authors thank these two institutions for their cooperation in the
preparation
of
the final manuscript. The authors would also like
to thank the many petroleum production and service companies
that have assisted in this project.
In the detailed preparation of this work, the authors would like
to thank Jerry Hayes, Danette DeCristofaro, and the staff of
ExecuStaff Composition Services for their very competent prepara-
tion of the final pages. In addition, the authors would like to thank
Bill Lowe of Gulf Publishing Company for his vision and perseverance
regarding this project; all those many individuals that assisted in
the typing and other duties that are
so
necessary for the prepara-
tion of original manuscripts; and all the families of the authors that
had to put up with weekends and weeknights of writing. The
editor would especially like to thank the group of individuals that
assisted through the years in the overall organization and preparation
of the original written manuscripts and the accompanying graphics,
namely; Ann Gardner, Britta Larrson, Linda Sperling, Ann Irby,
Anne Cate, Rita Case, and Georgia Eaton.
All the authors and their editor know that this work is not
perfect. But we also know that this handbook had to be written.
Our greatest hope is that we have given those that will follow us, in
future editions of this handbook, sound basic material to work with.
William C. Lyons, Ph.D., P.E.
Socorro, New Mexico
X
STANDARD
HANDBOOK
OF
Engineering
Patricia Duettra
Consultant
Applied Mathematics and Computer Analysis
Albuquerque, New Mexico
Geometry
.....
,
............................................................................................
3
Sets and Functions
3.
Angles
3.
Polygons
3.
Triangles
3.
Quadrilaterals
4.
Circles and Spheres
4.
Arcs of Circles
4.
Concurrency
5.
Similarity
5.
Prisms and Pyramids
5.
Coordinate Systems
6.
Graphs
6.
Vectors
6.
Lengths and Areas of Plane Figures
7.
Surfaces and Volumes
of
Solids
12.
Algebra
....................................................................................................
18
Operator Precedence and Notation
18.
Rules of Addition
19.
Fractions
20.
Exponents
21.
Logarithms
21.
Binomial Theorem
22.
Progressions
23.
Summation of Series by Difference
Formulas
23.
Sums of the first n Natural Numbers
24.
Solution of Equations in One Unknown
24.
Solutions of Systems of Simultaneous Equations
25.
Determinants
26.
Trigonometry
..........................................................................................
27
Directed Angles
27.
Basic Trigonometric Functions
28.
Radian Measure
28.
Trigonometric
Properties
29.
Hyperbolic Functions
33.
Polar Coordinate System
34.
Differential
and
Integral Calculus
..........................................................
35
Derivatives
35.
Maxima and Minima
37.
Differentials
38.
Radius of Curvature
39.
Indefinite
Integrals
40.
Definite Integrals
41.
Improper and Multiple Integrals
44.
Second Fundamental
Theorem
45.
Differential Equations
45.
Laplace Transformation
48.
Analytic Geometry
....................
.
.............................................................
50
Symmetry
50.
Intercepts
50.
Asymptotes
50.
Equations
of
Slope
51.
Tangents
51.
Equations of a
Straight Line
52.
Equations of a Circle
53.
Equations of a Parabola
53.
Equations of an Ellipse
of
Eccentricity e
54.
Equations of a Hyperbola
55.
Equations of Three-Dimensional Coordinate Systems
56.
Equations
of
a Plane
56.
Equations
of
a Line
57.
Equations of Angles
57.
Equation
of
a Sphere
57.
Equation of an Ellipsoid
57.
Equations
of
Hyperboloids and Paraboloids
58.
Equation
of
an Elliptic
Cone
59.
Equation of an Elliptic Cylinder
59.
Numerical Methods
............
. .
.......................
......
.
.
.
...........
.
.
.......
.
............
.
60
Expansion in Series
60.
Finite Difference Calculus
60.
Interpolation
64.
Roots of Equations
69.
Solution of Sets of Simultaneous Linear Equations
71.
Least Squares Curve Fitting
76.
Numerical
Integration
78.
Numerical Solution of Differential Equations
83.
Applied Statistics
................................................
.
............
.
......................
92
Moments
92.
Common Probability Distributions for Continuous Random Variables
94.
Probability
Distributions for Discrete Random Variables. Univariate Analysis
102.
Confidence Intervals
103.
Correlation
105.
Regression
106.
Computer Applications
.........................................................................
108
Problem Solving
109.
Programming Languages
109.
Common Data Types
110.
Common Data
Structures
110.
Program Statements
112.
Subprograms
113.
General Programming Principles
113.
FORTRAN Language
114.
Pascal Language
124.
System Software
131.
System Hardware
132.
References......
.......................................................................................
133
1
GEOMETRY
See References
1-3
for additional information.
Sets and Functions
A
set
is a clearly defined collection of distinct objects or
elements.
The
intersection of two sets
S
and T is the set of elements which belong to
S
and
which also belong to T. The
union
of
S
and T is the set of all elements which
belong to S
or
to T (or to both, Le., inclusive
or).
A
ficnction
is
a set of ordered elements such that no two ordered pairs have
the same first element, denoted as (x,y) where x is the independent variable
and
y
is the dependent variable. A function is established when a condition exists
that determines
y
for each x, the condition usually being defined by an equation
such as
y
=
f(x)
[2].
Angles
An angle A may be
acute,
0"
<
A
<
go",
right,
A
=
go",
or
obtuse,
90"
<
A
<
180".
Directed angles,
A
2
0"
or
2
180",
are discussed in the section "Trigonometry."
Two angles are
complementary
if their sum is
90"
or are
supplementary
if their
sum
is
180".
Angles are
congruent
if they have the same measurement in degrees
and line segments are congruent
if
they have the same length. A
dihedral angle
is
formed by two half-planes having the same edge, but not lying in the same plane.
A
plane angle
is the intersection
of
a perpendicular plane with a dihedral angle.
Polygons
A
polygon
is the union
of
a finite number of triangular regions in a plane,
such that if two regions intersect, their intersection is either a point or a line
segment. Two polygons are
similar
if corresponding angles are congruent and
corresponding sides are proportional with some constant
k
of proportionality.
A
segment whose end points are two nonconsecutive vertices of a polygon
is
a
diagonal.
The
perimeter
is the sum of the lengths of the sides.
Triangles
A
median
of a triangle is a line segment whose end points are a vertex and
the midpoint of the opposite side. An
angle bisector
of a triangle is a median
that lies on the ray bisecting an angle of the triangle. The
altitude
of a triangle
is a perpendicular segment from a vertex to the opposite side. The sum of the
angles of a triangle equals
180".
An
isosceles
triangle has two congruent sides
and the angles opposite them are also congruent. If a triangle has three
congruent sides (and, therefore, angles),
it
is
equilateral
and equiangular. A
scalene
3
4
Mathematics
triangle has no congruent sides.
A
set of congruent triangles can be drawn
if
one set of the following is given (where
S
=
side length and
A
=
angle measure-
ment):
SSS,
SAS, AAS
or
ASA.
Quadrilaterals
A
quadrilateral
is a four-sided polygon determined by four coplanar points
(three of which are noncollinear), if the line segments thus formed intersect each
other only at their end points, forming four angles.
A
trapezoid
has one pair of opposite parallel sides and therefore the other
pair
of
opposite sides is congruent.
A
parallelogram
has both pairs of opposite
sides congruent and parallel. The opposite angles are then congruent and
adjacent angles are supplementary. The diagonals bisect each other and are
congruent.
A
rhombus
is a parallelogram whose four sides are congruent and
whose diagonals are perpendicular to each other.
A
rectangle
is a parallelogram having four right angles, therefore both pairs
of opposite sides are congruent.
A
rectangle whose sides are all congruent is
a
square.
Circles
and
Spheres
If P is a point on a given plane and r is a positive number, the
circle
with
center
P
and radius
r
is the set of all points of the plane whose distance from
P
is equal to r. The
sphere
with center
P
and radius r is the set of all points in
space whose distance from
P
is equal to r. Two or more circles (or spheres)
with the same
P,
but different values of r are
concentric.
A
chord
of a circle
(or
sphere) is a line segment whose end points lie on the
circle (or sphere).
A
line which intersects the circle
(or
sphere) in two points is
a
secant
of the circle (or sphere).
A
diameter
of a circle (or sphere) is a chord
containing the center and a radius is a line segment from the center to a point
on the circle (or sphere).
The intersection of a sphere with a plane through its center is called a
great circle.
A
line which intersects a circle at only one point is a
tangent
to the circle at
that point. Every tangent is perpendicular to the radius drawn to the point of
intersection. Spheres may have tangent lines or tangent planes.
Pi
(x)
is the universal ratio of the circumference
of
any circle to its diameter
and is equivalent to 3.1415927
....
Therefore the circumference
of
a
circle is nd
or 2nr.
Arcs
of
Circles
A
central angle
of a circle is an angle whose vertex is the center
of
the circle.
If
P is the center and
A
and
B
are points, not on the same diameter, which lie
on
C
(the circle), the
minor arc
AB
is the union of
A,
B,
and all points on
C
in
the interior of
<APB.
The
major arc
is the union of
A, B,
and all points on
C
on the exterior of
<APB. A
and
B
are the end points of the arc and
P
is the
center.
If
A
and
B
are the end points of a diameter, the arc is a semicircle.
A
sector
of a circle is a region bounded by two radii and an arc of the circle.
The
degree measure
(m) of a minor arc is the measure of the corresponding
central angle (m of a semicircle is 180") and of a major arc 360" minus the m
of the corresponding minor arc. If an arc has a measure q and a radius r, then
its
length
is