William lyons standard handbook of petroleum and natural gas engineering

STANDARD

Y
S
F-

MEBX D
21

WILLIAM
C. LYONS
EDITOR


STANDARD HANDBOOK
OF
PETROLEUM
AND NATURAL GAS
ENGINEERING
VOLUME 1

etroleum engineering now has its own
true classic handbook that reflects the
profession’s status as a mature major
engineering discipline.

P

Formerly titled the Practical Perroleurn
Engineer’s Handbook, by Joseph Zaba and W. ’1’.
Doherty (editors), this new, completely

updated two-volume set is expanded and
revised to give petroleum engineers a comprehensive source of industry standards and
engineering practices. It is packed with
the key, practical information and data that
petroleum engineers rely upon daily.
The result of a fifteen-year effort, this handbook covers the gamut of oil and gas
engineering topics to provide a reliable
source of engineering and reference information for analyzing and solving problems. It
also reflects the growing role of natural gas in
industrial development by integrating natural
gas topics throughout both volumes.
More than a dozen leading industry expertsacademia and industry-contributed to this
two-volume set to provide the best, most
comprehensive source of petroleum engineering information available.




STANDARD
HANDBOOK OF

Engineering



STANDARD
HANDBOOK OF

WILLIAM
C . LYONS, PH.D.,P.E.

EDITOR

Gulf Publishing Company
Houston, Texas


STANDARD
HANDBOOK OF
ROLEUM
L GAS

Engineering

Copyright 0 1996 by Gulf Publishing Company, Houston, Texas.
All rights reserved. Printed in the United States of America. This
book, or parts thereof, may not be reproduced in any form
without permission of the publisher.
Volume
Chapter
Chapter
Chapter

2 Contents
5 - Reservoir Engineering
6 - Production Engineering
7 - Petroleum Economics

Gulf Publishing Company
Book Division
P.O. Box 2608OHouston, Texas 77252-2608

10 9 8 7 6 5 4 3 2
Library of Congress Cataloging-in-Publication Data
Standard handbook of petroleum and natural gas engineering /
[edited by William Lyons].
p. cm.
Includes bibliographical references and index.
ISBN 0-88415-642-7 (Vol. l),ISBN 0-88415-643-5 (Vol. 2)

1. Petroleum engineering.
(William C.)
TN870.S6233 1996
665.5-dc20

2. Natural gas. I. Lyons, William
96-13965
CIP

Printed on Acid-Free Paper (-)
iu


Contributing Authors

.................................................

...........................................................................
1-Mathematics .............................................................

Preface

vii
ix
1

Geometry, 3
Algebra, 18
Trigonometry, 27
Differential and Integral Calculus, 35
Analytic Geometry, 50
Numerical Methods, 60
Applied Statistics, 92
Computer Applications, 108
References, 133

2-General

Engineering and Science

...................135

Basic Mechanics (Statics and Dynamics), 137
Fluid Mechanics, 168
Strength of Materials, 185
Thermodynamics, 209
Geological Engineering, 240
Electricity, 278
Chemistry, 297
Engineering Design, 365
References, 386

V


3-Auxiliary

Equipment

...........................

............... 391

,

Prime Movers, 393
Power Transmission, 420
Pumps, 458
Compressors, 476
References, 495

4-Drilling

and Well Completions

..........................

497

Derricks and Portable Masts, 499
Hoisting Systems, 523
Rotary Equipment, 616

Mud Pumps, 627
Drilling Muds and Completion Systems, 650
Drill String: Composition and Design, 715
Drilling Bits and Downhole Tools, 769
Drilling Mud Hydraulics, 829
Air and Gas Drilling, 840
Downhole Motors, 862
MWD and LWD, 901
Directional Drilling, 1079
Selection of Drilling Practices, 1090
Well Pressure Control, 1100
Fishing Operations and Equipment, 11 13
Casing and Casing String Design, 1127
Well Cementing, 1 177
Tubing and Tubing String Design, 1233
Corrosion and Scaling, 1257
Environmental Considerations, 1343
Offshore Operations, 1363
References, 1373

............... 1385
,.........................................
1399

Appendix: Units and Conversions (SI)
Index

.... ...........................

vi

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. Throughout 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 preparation 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 preparation 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.

..........................................................

35

..............................................................

50

Differential and Integral Calculus

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

..........

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.

.........................................................................

108

.......................................................................................

133

Computer Applications

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......

1



GEOMETRY
See References 1-3 for additional information.

Sets and Functions
A set is a clearly defined collection of distinct objects o r 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 o r 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 o r 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 measurement): 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 on the exterior of 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

Geometry

L

=

5

q/l80*nr

Some of the properties of arcs are defined by the following theorems:

1. In congruent circles, if two chords are congruent, so are the corresponding
minor arcs.
2. Tangent-Secant Theorem-If given an angle with its vertex on a circle, formed
by a secant ray and a tangent ray, then the measure of the angle is half
the measure of the intercepted arc.
3. Two-Tangent Power Theorem-The two tangent segments to a circle from an
exterior point are congruent and determine congruent angles with the
segment from the exterior point to the center of the circle.
4. Two-Secant Power Theorem-If given a circle C and an exterior point Q, let
L, be a secant line through Q, intersecting C at points R and S, and let L,
be another secant line through Q, intersecting C at U and T, then

QR

QS

=

QU

QT

5. Tangent-Secant Power Theorem-If given a tangent segment QT to a circle
and a secant line through Q, intersecting the circle at R and S, then

QR

QS

=

QT2
-

6. Two-Chord Power Theorem-If
intersecting at Q, then

QR

QS

=

QU

-

RS and TU are chords of the same circle,

QT

Concurrency
Two or more lines are concurrent if there is a single point which lies on all
of them. The three altitudes of a triangle (if taken as lines, not segments) are
always concurrent, and their point of concurrency is called the orthocenter. The
angle bisectors of a triangle are concurrent at a point equidistant from their
sides, and the medians are concurrent two thirds of the way along each median
from the vertex to the opposite side. The point of concurrency of the medians
is the centroid.

Similarity
Two figures with straight sides are similar if corresponding angles are congruent and the lengths of corresponding sides are in the same ratio. A line
parallel to one side of a triangle divides the other two sides in proportion,
producing a second triangle similar to the original one.

Prisms and Pyramids
A prism is a three dimensional figure whose bases are any congruent and
parallel polygons and whose sides are parallelograms. A pyramid is a solid with
one base consisting of any polygon and with triangular sides meeting at a point
in a plane parallel to the base.
Prisms and pyramids are described by their bases: a triangular prism has a
triangular base, a parallelpiped is a prism whose base is a parallelogram and a


6

Mathematics

rectangular parallelpiped is a right rectangular prism. A cube is a rectangular
parallelpiped all of whose edges are congruent. A triangular pyramid has a
triangular base, etc. A circular cylinder is a prism whose base is a circle and a
circular cone is a pyramid whose base is a circle.

Coordinate Systems
Each point on a plane may be defined by a pair of numbers. The coordinate
system is represented by a line X in the plane (the x-axis) and by a line Y (the
y-axis) perpendicular to line X in the plane, constructed so that their intersection,
the origin, is denoted by zero. Any point P on the plane can now be described
by its two coordinates which form an ordered pair, so that P(x,,y,) is a point
whose location corresponds to the real numbers x and y on the x-axis and
the y-axis.
If the coordinate system is extended into space, a third axis, the z-axis,
perpendicular to the plane of the xI and y, axes, is needed to represent the
third dimension coordinate defining a point P(x,,y,,z,).The z-axis intersects the
x and y axes at their origin, zero. More than three dimensions are frequently
dealt with mathematically, but are difficult to visualize.
The slope m of a line segment in a plane with end points P,(x,,y,) and P,(x,,y,)
is determined by the ratio of the change in the vertical (y) coordinates to the
change in the horizontal (x) coordinates or
m

=

(Y' -

YI)/(X2

- XI)

except that a vertical line segment (the change in x coordinates equal to zero)
has no slope, i.e., m is undefined. A horizontal segment has a slope of zero.
Two lines with the same slope are parallel and two lines whose slopes are
negative reciprocals are perpendicular to each other.
Since the distance between two points P,(x,,y,) and P,(x,,y,) is the hypotenuse
of a right triangle, the length of the line segment PIP, is equal to

Graphs
A graph is a figure, i.e., a set of points, lying in a coordinate system and a
graph of a condition (such as x = y + 2) is the set of all points that satisfy the
condition. The graph of the slope-intercept equation, y = mx + b, is the line which
passes through the point (O,b), where b is the y-intercept (x = 0) and m is the
slope. The graph of the equation
(x

-

a)' + (y

-

b)'

=

r2

is a circle with center (a,b) and radius r.

Vectors
A vector is described on a coordinate plane by a directed segment from its initial
point to its terminal point. The directed segment represents the fact that every
vector determines not only a magnitude, but also a direction. A vector v is not


Geometry

7

changed when moved around the plane, if its magnitude and angular orientation
with respect to the x-axis is kept constant. The initial point of v may therefore
be placed at the origin of the coordinate system a n d ? ’ m a y be denoted by

d=< a,b >
where a is the x-component and b is the y-component of the terminal point.
The magnitude may then be determined by the Pythagorean theorem

For every pair of vectors (xI,yI)and (x2,y2),the vector sum is given by (x, + xp,
= (x,y) and a real number (a scalar) r
is rP = (rx,ry). Also see the discussion of polar coordinates in the section
“Trigonometry” and Chapter 2, “Basic Mechanics.”

y1 + y2). The scalar product of a vector P

Lengths and Areas of Plane Figures [ l ]
(For definitions of trigonometric functions, see “Trigonometry.”)

Right triangle (Figure 1-1)
A

=

a2

+

area

=

1/2

c2

b2
ab

=

1/2

a2 cot A

Equilateral triangle (Figure 1-2)

area = 114 a2& = 0. 43301a2

=

1/2

b2 tan A

=

1/4

c2 sin 2A


8

Mathematics
Any triangle (Figure 1-3.)
A

area

=

1/2 base altitude = 1/2
1/2 {(XIY2 - $yI)

ah

=

1/2

ab sin C

= +
+

+

(XZYS
(XSYI

-

X.SY2)

- XIY,))

where (x,,yl),(xz,yz),(x,,y,) are coordinates of vertices.
Rectangle (Figure 1-4)

area

=

ab

=

1/2

D2 sin u

where u = angle between diagonals D, D
Rhombus (Figure 1-5)

Area

=

a'sin C

=

1/2

DID,

where C = angle between two adjacent sides
D,, D, = diagonals
Parallelogram (Figure 1-6)

c

\


Geometry
area

=

bh

where u

=

=

ab sin c

=

D,D, sin u

1/2

angle between diagonals D, and D,

Trapezoid (Figure 1-7)

area

=

1/2

where u

=

(a

+

b ) h ' = 1/2

D,D, sin u

angle between diagonals D, and D,

and where bases a and b are parallel.

Any quadrilateral (Figure 1-8)

area

=

1/2

D,D, sin u

Note: a2 + b2 +

where m

=

c2

+ d*= D21 + D*2 + 4m*

distance between midpoints of D, and D,

Circles

area

=

nr2 = 1/2

Cr

=

where r = radius
d = diameter
C = circumference

1/4

=

2nr

Cd

=

=

nd

1/4

nd2 = 0.785398d2

9