Chapter 2: Casing Design con't lec ( 7 )


Casing Weights and Grades
Common casing diameters range from less than 4-1/2 in. to over 20 in., and common tubing sizes are from 3/4 in. to over 4-1/2 in. In some high rate wells, tubing may be 5-1/2 in. to over 7 in. and 2-7/8 in. casing is run in tubingless completions. After the size is determined, the grade of the steel must be selected. The grades, along with weight, are based on pressure and corrosion requirements. The grades of steel used in oil industry tubulars
are shown in the following table for API and non-API sizes. The letters are assigned only to avoid confusion. Grades N-80 and stronger are considered high strength steels. Use of the higher strength steels increases cost and decreases resistance to some forms of corrosion. Use of the very hardalloys, such as V-150, makes packer setting difficult since the slips have difficulty setting in the very hard steel of the casing.


The yield and burst strength values for each casing size and weight are available from detailed tables are used for selection of casing once the necessary strength calculations are made. Often, because of economics or efforts to lighten the casing string, lower grade or lighter weight casing may be considered. Because the weight and pressure loads on a casing string change from top to bottom, a well designed string may incorporate several weights and grades of casing.


Casing Design Safety Factors

The design criteria for casing strings depends on the intended use and anticipated stresses. Because variance exists in both pipe manufacture and formation properties, safety factors must be incorporated into a design. The common ranges for safety factors in normal completion are shown b e l ~ w . ~ ~ ~ ~ Factors such as salt flows,7 very high pressures, sour service,8 reservoir compaction loads,g and thermal cycling'0 may change the safety factors.

tension                                               1.6 to 1.8
burst                                                 1.25 to 1.30
collapse                                            1 .O to 1.25



Earth shift forces, such as salt movement or other faulting and folding events caused by tectonic movement or are very difficult to address with a traditional safety factor. These forces have been successfully offset in some cases by designs using very heavy wall pipe or concentric pipe (casing cemented inside casing) over the affected zone. These types of casing designs are rare and most are generated by a series of trail and error approaches.

Load Description


The casing string must be designed for any load encountered from mud or reservoir fluids in placement or during any phase of stimulation or production. The common forces are tension during running, internal pressures during drilling, completion or production, and external pressures caused by drawdown, mechanical loads, and zone pressures. These loads are tension, burst, and collapse. The loads are often applied simultaneously in different parts of the string, and the forces may interact. The tension design of the casing string is made as if it were hanging free in air. A safety factor of 1.6 to 1.8 is applied to make allowances for a number of other tension factor^.^*^^'' These factors are briefly discussed in the following paragraphs. Collapse, burst, and tension forces are explained separately, but all must be satisfactorily accounted for in the final design. The design methods in this book result in a conservative design. Each design method is based on the worst possible case that could
occur during running. Collapse loading is force applied from outside the casing by either fluid pressure in a zone or earth shift forces. Forces from fluid pressure are collapse loadings while earth shift forces produce mechanical crush loadings. The largest collapse load from fluid pressure will usually be exhibited at the bottom of the string where hydrostatic pressure is greatest. The exception is an isolated, very high pressure zone. These zones are usually noted on the drilling record as places where kicks are taken.
The occurrence of earth shift zones from faults or salt movement are much harder to locate, especially on wildcats but may often show up on the drilling record as sticking points (not associated with mud cake buildup) or zones that have to be reamed or redrilled to get back to gauge hole size. The occurrence of salt zones are a very important tip to potential casing problem^.^ In one study area, 87% of the wells around a salt dome suffered some casing diameter reduction due to external, earth shift force.
’In the collapse design for fluid pressure, the worst case loading occurs with the unlikely combination of an empty casing string in a hole full of mud. A proper design, for effects of collapse only, would be a casing string that is strongest at the bottom and weakest at the top. Collapse is also affected by the effects of tension, which reduces the collapse rating or the “set depth limit” of the casing. As an object is pulled, it is more likely to lose diameter as it stretches in length. This thinning is a force in the same direction as collapse forces. Fortunately, the point at which the effect of tension induced “narrowing” of the string is at maximum is at the surface where effects of collapse pressure from hydrostatic pressure are the lowest. Burst pressure is a force applied from inside the casing by produced fluid pressures, hydrostatic mud load or addition of surface pressure during stimulation or workover operations. Since there is usually mud hydrostatic pressure along the outside of the casing before and during cementing, the net pressure or the difference between the pressure inside the casing and outside the casing will be used in the design of the casing. Unlike collapse, however, the shallower casing section is also important in the burst calculations from a safety standpoint. Burst pressures exerted by produced fluids are maximum at the surface (no offsetting hydrostatic load), while those exerted by mud is maximum at the bottom of the well. During fracturing, high burst loads may be exerted all along the string. Because collapse loads offset the burst load at the bottom of the string, the burst calculation is usually important above the “buoyancy neutral point.” This will be developed later. Tension is a force produced by the weight of the casing, the pressure differential, and the mud weights inside and outside the casing. It is largest at the top of the string and decreases with depth toward the bottom of the string. The tension load is partially offset by the buoyancy of the string in mud and is affected by pressure. When the pressure inside the tube rises, the pipe diameter is expanded and the length shortened or the tension is increased in a pipe that is anchored to prevent upward movement. When the pressure outside of a tube rises, the tube is elongated or the compression is increased if the
ends are fixed, Figure 2.6. Buckling failure in casing usually results from axial compression (lengthwise) overloading. The load produces ridges in the casing walls or corkscrewing of the tube. Either of these actions relieve compression, but the pipe is usually permanently yielded. The effects of buckling, Figure 2.7, is critical on the design of the casing string. The neutral point, Figure 2.8, is the dividing line between where buckling may occur and where it cannot occur in a tube that is evenly loaded around its radius. Above the neutral point, the tube is in tension and will not buckle. Below the neutral point, the upward buoyancy of the mud and other forces including pressure and mechanical loading place the tube in compression. Buckling can occur if the compressive load is more than the pipe can tolerate in the wellbore surroundings. The following information describes the neutral point, first in a theoretical manner and then in a practical way. There can be a neutral point in the casing or tubing string described by the formula:’*






When F, is algebraically greater than the right-hanc side of the equation, the pipe tends to be straldht. When F, is less than the equation, the pipe tends to buckle. When F, is equal to the equation, the neutral point is reached. The right-hand side of Eqn. (2.1) may also be referred to as the stability force. The true axial force will vary from point to point in the string, and will also vary over the life of the well. Typical considerations necessary to compute F, include the conditions at the time of cementing the casing or setting the packer in the case of tubing, as well as changes in the environment (temperature and pressure) to which the tubular is exposed. For casing, buckling primarily affects wear, particularly for intermediate strings through which additional drilling will occur. In extreme cases, splitting may
also be common. For tubing, the radial clearance between tubing and casing is usually sufficient to allow corkscrewing, often producing permanent deformation of the buckled portion of the string.

This equation is only appropriate for an open ended tube, clamped at both ends, with PO = 0 and AT = 0 , and ignoring weight. Under the unlikely conditions of a weightless string with no outside pressure, buckling in tension is possible. To illustrate the impact of Eqn. 2.2, consider a weightless tube that is open ended and subject to internal pressure only. For this loading, the only axial force is that due to ballooning given by Eqn. 2.2 and shown previously in Figure 2.6. As the inside pressure is increased, F, increases as 2pPjAis but the right hand side of Eqn. 2.1 increases as PjAi. The tube will not only buckle immediately, but will also buckle in tension.




Each zone or section of the casing string is checked for tensile requirements following collapse and burst calculations. In case of corrections made to a string design to compensate for tension load requirements, the order of selection is usually: (1) stronger connection, (2) higher grade (stronger steel), and (3) higher weight. Increasing connection strength and steel grade is preferred since they increase total string strength without adding significant weight. There are so many “premium” connections available that it is difficult to present a comprehensive data set. Tables of connection specifics are published yearly.37
For the sole purpose of casing collapse strength derating due to the effects of tension, a practical “buoyancy neutral point”, designated N.P., can be estimated by Eqn. (2.4) where:
The collapse resistance values given in the manufacturer tables are for casing that is not affected by axial load. In a well, the casing will be stressed by fluid pressures, Figure 2.9, mechanical bending forces, Figure 2.10, and tensile forces produced by the hanging weight of the casing. In collapse calculations, axial tension produces a reduction in collapse resistance. For purposes of this example, the axial tension is assumed to be from tension loads on a straight, free hanging pipe and not from bending loads.


Designing for forces involving earth shifts, highly deviated hole, sticking, reciprocating and rotating casing while cementing or running stresses, involves field optimization and the criteria for design differ from company to company. Earth shift design usually involves multiple strings of pipe or very heavy wall pipe across the problem zone. Problem zone recognition can often be made from drilling records where bit dragging (nonassociated with mud cake buildup) occurs long after a zone is drilled. Wells near salt domes or flows are considered likely prospects for formation movement.

Physics and Measurement lec ( 1 )



Like all other sciences, physics is based on experimental observations and quantitative measurements. The main objective of physics is to find the limited number of fundamental
laws that govern natural phenomena and to use them to develop theories that can predict the results of future experiments. The fundamental laws used in developing theories are expressed in the language of mathematics, the tool that provides a bridge between theory and experiment. When a discrepancy between theory and experiment arises, new theories must be formulated to remove the discrepancy. Many times a theory is satisfactory only under limited conditions; a more general theory might be satisfactory without such limitations. For example, the laws of motion discovered by Isaac Newton (1642–1727) in the
17th century accurately describe the motion of objects moving at normal speeds but do
not apply to objects moving at speeds comparable with the speed of light. In contrast,
the special theory of relativity developed by Albert Einstein (1879–1955) in the early 1900s gives the same results as Newton’s laws at low speeds but also correctly describes
motion at speeds approaching the speed of light. Hence, Einstein’s special theory of
relativity is a more general theory of motion. Classical physics includes the theories, concepts, laws, and experiments in classical mechanics, thermodynamics, optics, and electromagnetism developed before 1900. Important contributions to classical physics were provided by Newton, who developed classical mechanics as a systematic theory and was one of the originators of calculus as a mathematical tool. Major developments in mechanics continued in the 18th century, but the fields of thermodynamics and electricity and magnetism were not developed until the latter part of the 19th century, principally because before that time the apparatus for controlled experiments was either too crude or unavailable. A major revolution in physics, usually referred to as modern physics, began near the end of the 19th century. Modern physics developed mainly because of the discovery that many physical phenomena could not be explained by classical physics. The two most important developments in this modern era were the theories of relativity and quantum mechanics. Einstein’s theory of relativity not only correctly described the motion of objects moving at speeds comparable to the speed of light but also completely revolutionized the traditional concepts of space, time, and energy. The theory of relativity also shows that the speed of light is the upper limit of the speed of an object and that mass
and energy are related. Quantum mechanics was formulated by a number of distinguished
scientists to provide descriptions of physical phenomena at the atomic level. Scientists continually work at improving our understanding of fundamental laws, and new discoveries are made every day. In many research areas there is a great deal of overlap among physics, chemistry, and biology. Evidence for this overlap is seen in the names of some subspecialties in science—biophysics, biochemistry, chemical physics, biotechnology, and so on. Numerous technological advances in recent times are the result of the efforts of many scientists, engineers, and technicians. Some of the most notable developments in the latter half of the 20th century were
 (1) unmanned planetary explorations and manned moon landings,
 (2) microcircuitry and high-speed computers,
(3) sophisticated imaging techniques used in scientific research and medicine, and
(4) several remarkable results in genetic engineering. The impacts of such developments
and discoveries on our society have indeed been great, and it is very likely that
future discoveries and developments will be exciting, challenging, and of great benefit
to humanity.

1.1 Standards of Length, Mass, and Time

The laws of physics are expressed as mathematical relationships among physical quantities
that we will introduce and discuss throughout the book. Most of these quantities are derived quantities, in that they can be expressed as combinations of a small number of basic quantities. In mechanics, the three basic quantities are length, mass, and time. All other quantities in mechanics can be expressed in terms of these three. If we are to report the results of a measurement to someone who wishes to reproduce this measurement, a standard must be defined. It would be meaningless if a visitor from another planet were to talk to us about a length of 8 “glitches” if we do not know the meaning of the unit glitch. On the other hand, if someone familiar with our system of measurement reports that a wall is 2 meters high and our unit of length is defined to be 1 meter, we know that the height of the wall is twice our basic length unit. Likewise, if we are told that a person has a mass of 75 kilograms and our unit of mass is defined to be 1 kilogram, then that person is 75 times as massive as our basic unit.1 Whatever is chosen as a standard must be readily accessible and possess some property that can be measured reliably. Measurements taken by different people in different places must yield the same result. In 1960, an international committee established a set of standards for the fundamental quantities of science. It is called the SI (Système International), and its units of length, mass, and time are the meter, kilogram, and second, respectively. Other SI standards established by the committee are those for temperature (the kelvin), electric current (the ampere), luminous intensity (the candela), and the amount of substance (the mole).

Length

In A.D. 1120 the king of England decreed that the standard of length in his country
would be named the yard and would be precisely equal to the distance from the tip of
his nose to the end of his outstretched arm. Similarly, the original standard for the foot
adopted by the French was the length of the royal foot of King Louis XIV. This standard
prevailed until 1799, when the legal standard of length in France became the meter,
defined as one ten-millionth the distance from the equator to the North Pole along
one particular longitudinal line that passes through Paris. Many other systems for measuring length have been developed over the years, but the advantages of the French system have caused it to prevail in almost all countries and in scientific circles everywhere. As recently as 1960, the length of the meter was defined as the distance between two lines on a specific platinum–iridium bar stored under controlled conditions in France. This standard was abandoned for several reasons, a principal one being that the limited accuracy with which the separation between the lines on the bar can be determined does not meet the current
requirements of science and technology. In the 1960s and 1970s, the meter was defined
as 1 650 763.73 wavelengths of orange-red light emitted from a krypton-86 lamp. However, in October 1983, the meter (m) was redefined as the distance traveled by light in vacuum during a time of 1/299 792 458 second. In effect, this latest definition establishes that the speed of light in vacuum is precisely 299 792 458
meters per second.
Table 1.1 lists approximate values of some measured lengths. You should study this
table as well as the next two tables and begin to generate an intuition for what is meant
by a length of 20 centimeters, for example, or a mass of 100 kilograms or a time interval
of 3.2 ! 107 seconds.

Mass

The SI unit of mass, the kilogram (kg), is defined as the mass of a specific platinum–iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sèvres, France. This mass standard was established in 1887 and has not been changed since that time because platinum–iridium is an unusually stable alloy. A duplicate of the Sèvres cylinder is kept at the National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland (Fig. 1.1a). Table 1.2 lists approximate values of the masses of various objects.

Time
Before 1960, the standard of time was defined in terms of the mean solar day for the
year 1900. (A solar day is the time interval between successive appearances of the Sun
at the highest point it reaches in the sky each day.) The second was defined as
of a mean solar day. The rotation of the Earth is now known to vary slightly with time, however, and therefore this motion is not a good one to use for defining a time standard.
In 1967, the second was redefined to take advantage of the high precision attainable
in a device known as an atomic clock (Fig. 1.1b), which uses the characteristic frequency
of the cesium-133 atom as the “reference clock.” The second (s) is now defined as
9 192 631 770 times the period of vibration of radiation from the cesium atom.2

To keep these atomic clocks—and therefore all common clocks and watches that are
set to them—synchronized, it has sometimes been necessary to add leap seconds to our
clocks.
Since Einstein’s discovery of the linkage between space and time, precise measurement
of time intervals requires that we know both the state of motion of the clock used
to measure the interval and, in some cases, the location of the clock as well. Otherwise,
for example, global positioning system satellites might be unable to pinpoint your location
with sufficient accuracy, should you need to be rescued.
Approximate values of time intervals are presented in Table 1.3.
In addition to SI, another system of units, the U.S. customary system, is still used in the
United States despite acceptance of SI by the rest of the world. In this system, the units of
length, mass, and time are the foot (ft), slug, and second, respectively. In this text we shall
use SI units because they are almost universally accepted in science and industry. We shall
make some limited use of U.S. customary units in the study of classical mechanics.
In addition to the basic SI units of meter, kilogram, and second, we can also use
other units, such as millimeters and nanoseconds, where the prefixes milli- and nanodenote
multipliers of the basic units based on various powers of ten. Prefixes for the
various powers of ten and their abbreviations are listed in Table 1.4. For example,
10"3 m is equivalent to 1 millimeter (mm), and 103 m corresponds to 1 kilometer
(km). Likewise, 1 kilogram (kg) is 103 grams (g), and 1 megavolt (MV) is 106 volts (V).




Mechanics

physics, the most fundamental physical science, is concerned with the basic principles of the Universe. It is the foundation upon which the other sciences—astronomy, biology, chemistry, and geology—are based. The beauty of physics lies in the simplicity of the fundamental physical theories and in the manner in which just a small number of fundamental concepts, equations, and assumptions can alter and expand our view of the world around us. The study of physics can be divided into six main areas:
1. classical mechanics, which is concerned with the motion of objects that are large
relative to atoms and move at speeds much slower than the speed of light;
2. relativity, which is a theory describing objects moving at any speed, even speeds
approaching the speed of light;
3. thermodynamics, which deals with heat, work, temperature, and the statistical behavior
of systems with large numbers of particles;
4. electromagnetism, which is concerned with electricity, magnetism, and electromagnetic
fields;
5. optics, which is the study of the behavior of light and its interaction with materials;
6. quantum mechanics, a collection of theories connecting the behavior of matter at
the submicroscopic level to macroscopic observations. The disciplines of mechanics and electromagnetism are basic to all other branches of classical physics (developed before 1900) and modern physics (c. 1900–present). The first part of this textbook deals with classical mechanics, sometimes referred to as Newtonian mechanics or simply mechanics. This is an appropriate place to begin an introductory text because many of the basic principles used to understand mechanical systems can later be used to describe such natural phenomena as waves and the transfer of energy by heat. Furthermore, the laws of
conservation of energy and momentum introduced in mechanics retain their importance
in the fundamental theories of other areas of physics. Today, classical mechanics is of vital importance to students from all disciplines. It is highly successful in describing the motions of different objects, such as planets, rockets, and baseballs. In the first part of the text, we shall describe the laws of classical mechanics and examine a wide range of phenomena that can be understood with these fundamental ideas.