William lyons standard handbook of petroleum and natural gas engineering

Triangles A median of a triangle is a line segment whose end points are a vertex and the midpoint of the opposite side.. An isosceles triangle has two congruent sides and the angles op

OF PETROLEUM AND NATURAL GAS

ENGINEERING

etroleum engineering now has its own

P true classic handbook that reflects the profession’s status as a mature major engineering discipline

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 com- prehensive 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 hand- book covers the gamut of oil and gas engineering topics to provide a reliable source of engineering and reference informa- tion 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 experts- academia and industry-contributed to this two-volume set to provide the best, most comprehensive source of petroleum engineer- ing information available

STANDARD

Engineering

HANDBOOK OF

ROLEUM

L G A S

Engineering

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 2 Contents

Gulf Publishing Company

Book Division

P.O Box 2608OHouston, Texas 77252-2608

Library of Congress Cataloging-in-Publication Data

[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)

Contributing Authors vii Preface ix

2-General Engineering and Science 135

Basic Mechanics (Statics and Dynamics), 137

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

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

Phillip W Johnson, Ph.D., P.E

University of Alabama

Tuscaloosa, Alabama

vii

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

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

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

STANDARD HANDBOOK OF

Engineering

Consultant Applied Mathematics and Computer Analysis Albuquerque, New Mexico

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

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

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

L = 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

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 con- gruent 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

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 - X I )

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

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,

is rP = (rx,ry) Also see the discussion of polar coordinates in the section

“Trigonometry” and Chapter 2, “Basic Mechanics.”

Lengths and Areas of Plane Figures [ l ]

(For definitions of trigonometric functions, see “Trigonometry.”)

Right triangle (Figure 1-1)

A

c2 = a2 + b2

area = 1/2 ab = 1/2 a2 cot A = 1/2 b2 tan A = 1/4 c2 sin 2A

Equilateral triangle (Figure 1-2)

area = 114 a2 & = 0 43301a2

Any triangle (Figure 1-3.)

Area = a'sin C = 1/2 DID,

where C = angle between two adjacent sides

D,, D, = diagonals

Parallelogram (Figure 1-6)

c

\

area = bh = ab sin c = 1/2 D,D, sin u

where u = angle between diagonals D, and D,

Trapezoid (Figure 1-7)

area = 1/2 (a + b ) h ' = 1/2 D,D, sin u

where u = angle between diagonals D, and D,

and where bases a and b are parallel

Any quadrilateral (Figure 1-8)

area = 1/2 0 rs = xr2A/36O0 = 1/2 r2 rad A

where rad A = radian measure of angle A

s = length of arc = r rad A

Segment (Figure 1-11)

area = 1/2 r2 (rad A - sin A) = 1/2[r(s - c) + ch]

where rad A = radian measure of angle A

For small arcs,

area of ellipse = nab

area of shaded segment = xy + ab sin-’ (x/a)

length of perimeter of ellipse = x(a + b)K,

In any hyperbola,

shaded area A = ab In [(x/a) + (y/b)]

In an equilateral hyperbola (a = b),

area A = a2 sinh-’ (y/a) = a2 cosh-’ (x/a)

Here x and y are coordinates of point P

Surfaces and Volumes of Solids [I]

Regular prism (Figure 1-16)

volume = 1/2 nrah = Bh

lateral area = nah = Ph

where n = number of sides

Any prism or cylinder (Figure 1-18)

N = area of normal section

Q = perimeter of normal section

Hollow cylinder (right a n d circular)

volume = rch(R2 - r2) = nhb(D - b ) = nhb(d + b ) = rchbD' = rchb(R + r ) where h = altitude

r,R, (d,D) = inner and outer radii (diameters)

b = thickness = R - r

D' = mean diam = 1/2 (d + D) = D - b = d + b

Regular pyramid (Figure 1-19)

volume = 1/3 altitude area of base = 1/6 hran

lateral area = 1/2 slant height perimeter of base = 1/2 san

where r = radius of inscribed circle

a = side (of regular polygon)

n = number of sides

s = JTTi7

(vertex of pyramid directly above center of base)

Right circular cone

where B = area of base

h = perpendicular distance from vertex to plane in which base lies

9 Hollow sphere, or spherical shell

Any spherical segment (Zone) (Figure 1-21)

Spherical sector (Figure 1-22)

Note: as = h(2r - h)

Spherical wedge bounded by two plane semicircles and a lune (Figure 1-23)

Spheroid (or ellipsoid of revolution)

By the prismoidal formula:

volume = 1/6 h(A + B + 4M)

where h = altitude

A and B = areas of bases

M = area of a plane section midway between the bases

Paraboloid of revolution (Figure 1-25)

0 # - - 7 - - ,

/ \

#

volume = 1/2 nr2h = 1/2 volume of circumscribed cylinder

Torus, or anchor ring (Figure 1-26)

volume = 2n2cr2

area = 4nr2cr (proof by theorems of Pappus)

ALGEBRA

See References 1 and 4 for additional information

Operator Precedence and Notation

Operations in a given equation are performed in decreasing order of prece- dence as follows:

The notation for the sum of any real numbers a,, a2, , an is

and for their product

The notation ‘‘x = y” is read “x varies directly with y” or ‘‘x is directly proportional to y,” meaning x = ky where k is some constant If x = l/y, then

x is inversely proportional to y and x = k/y

(i.e., a minus sign preceding a pair of parentheses operates to reverse the signs

of each term within, if the parentheses are removed)

Rules of Multiplication and Simple Factoring

(For higher order polynomials see the section “Binomial Theorem”)

a” + b” is factorable by (a + b) if n is odd, thus

a3 + b” = (a + b)(a2 - ab + b2)

and a” - b” is factorable by (a - b), thus

a” - b” = (a - b)(a”-’ + a”- 2b + + abn-2 + bn-1 1

Fractions

The numerator and denominator of a fraction may be multiplied or divided

by any quantity (other than zero) without altering the value of the fraction, so that, if m # 0,

The logarithm of a positive number N is the power to which the base (10 or

e ) must be raised to produce N So, x = logeN means that ex = N, and x = log,,N

means that 10" = N Logarithms to the base 10, frequently used in numerical computation, are called common or denary logarithms, and those to base e, used

in theoretical work, are called natural logarithms and frequently notated as In

In either case,

log(ab) = log a + log b

log(a/b) = log a - log b

completes with the term n,x"

with corresponding formulas for (1 - x)'", etc., obtained by reversing the signs

of the odd powers of x Also, provided lbl < ( a ( :

of terms, the last term is p = a + (n - l)d, the "average" term is 1/2(a + p) and

the sum of the terms is n times the average term or s = n/2(a + p) The arithmetic

mean between a and b is (a + b)/2

In a geometric progression, (a, ar, ar2, ar', .), each term is obtained from the preceding term by multiplying by a constant ratio, r The nth term is a?', and the sum of the first n terms is s = a(r" - l)/(r - 1) = a(l - rn)/(l - r) If r is a

fraction, r" will approach zero as n increases and the sum of n terms will approach a/( 1 - r) as a limit The geometric mean, also called the "mean proportional," between

a and b is Jab The harmonic mean between a and b is 2ab/(a + b)

Summation of Series by Difference Formulas

a,, a2, ., an is a series of n numbers, and D' (first difference), D" (second difference), are found by subtraction in each column as follows:

If the kth differences are equal, so that subsequent differences would be zero, the series is an arithmetical series of the kth order The nth term of the series

is an, and the sum of the first n terms is Sn, where

an = a, + (n - 1)D' + (n - l ) ( n - 2)D'y2! + (n - l ) ( n - 2)(n - 3)D'"/3! +

Sn = na, + n(n - 1)D'/2! + n(n - l)(n - 2)DfY3! +

In this third-order series just given, the formulas will stop with the term in D"'

Sums of the First n Natural Numbers

To the first power:

Solution of Equations in One Unknown

Legitimate operations on equations include addition of any quantity to both sides, multiplication by any quantity of both sides (unless this would result in division by zero), raising both sides to any positive power (if k is used for even roots) and taking the logarithm or the trigonometric functions of both sides

Any algebraic equation may be written as a polynomial of nth degree in x of

the form

aOxn + a,x"" + a2xn-2 + + an_,x + an = 0

with, in general, n roots, some of which may be imaginary and some equal If the polynomial can be factored in the form

(x - p)(x - q)(x - r) = 0

then p, q, r, are the roots of the equation If 1x1 is very large, the terms containing the lower powers of x are least important, while if 1x1 is very small, the higher-order terms are least significant

First degree equations (linear equations) have the form

x + a = b

with the solution x = b - a and the root b - a

Second-degree equations (quadratic equations) have the form