An industry and academic standard, Applied Drilling Engineering presents engineering science fundamentals as well as examples of engineering applications involving those fundamentals. Two appendices are included, along with numerous examples. Answers are included for every end-of-chapter question. Solutions to Chapter 8 (http://go.spe.org/ADEsolutions)
The complex behavior of most bottom-hole assemblies can be analyzed using the finite-element method. If the wellbore trajectory, hole diameter, fluid density, and assembly dimensions are known, various properties can be determined. The tendency of a bit either to build or to drop angle can be assessed. Introduction Predicting the actual trajectory of a drilling bit is very Predicting the actual trajectory of a drilling bit is very complex. Many variables interact causing the bit to follow a certain trajectory. Assembly configuration and dimensions, lithology, dip, bit, type, hole curvature, magnitude of inclination, bit weight, and rotary speed are some of the more important parameters that control inclination and azimuth of the bit. The drilling industry has been aware of directional problems and the need to understand these problems for problems and the need to understand these problems for many years. The first major approach was presented by Woods and Lubinski, who emphasized the importance of the bottom-hole assembly makeup. First, the "slick assembly" was analyzed to show the importance of the point of tangency, collar diameter, etc. Further research point of tangency, collar diameter, etc. Further research introduced the concept of single stabilizer placement to increase the point of tangency so that the negative or pendulum forces could be increased. Early research pendulum forces could be increased. Early research recommended multispaced stabilizers to increase the bottom-hole assembly stiffness. This commonly was referred to as the "packed-hole assembly." Currently, most assembly designs are based on the slick, single, or multistabilizer configurations. Exceptions are the use of square collars, mud motors, and special directional tools. Field experience is an important aspect of this technology. Actual assemblies and drilling situations are too complex to rely on the simpler idealizations that do not account for varying collar dimensions, material properties, and multistabilizer arrangements. Recognizing this, properties, and multistabilizer arrangements. Recognizing this, new technology is being developed using numerical solution methods and high-speed digital computers. These techniques have been presented in the literature. Fischer and Bradley et al. analyzed various assemblies that had negative side force tendencies, using a finite-difference approximation. They also investigated square collars, hole inclination, and other important effects. Similar computer programs exist. This paper presents a numerical approach that has gained popularity in other engineering applications. This technique, known as the finite-element method, is used to solve four bottom-hole assemblies. One is a moderate building assembly, the others range from a holding assembly with a slight dropping tendency to a stronger dropping assembly. The basic finite-element technique used for analyzing these four assemblies is presented. The method of solution using a general-purpose, finite-element system is described, along with the mathematical idealizations that achieve tangency of the collars with the wellbore. The nonlinear solution for one assembly demonstrates how the collars react as the load is applied to the system. The solutions for each assembly show various reaction forces and displacements. From the side force at the bit, the general inclination tendency can be determined. The effects of large displacement and boundary contact also are discussed. Technical Approach The Finite-Element Method JPT P. 265
Summary This work, which reports on the effect of bottomhole assembly (BHA) dynamics on the trajectory of a bit, is part of an on-going effort to develop a computer model that simulates the three-dimensional (3D) movement of the bit. A theoretical description of the dynamic version of the 3D finite element algorithm is presented. The basic mechanisms associated with pipe rotation are explained by showing the predominant paths of motion of five BHA's as a function of rotary speed, and stabilizer-bit-, and pipe-friction coefficient values.In a parallel test program, five shallow wells were drilled directionally under controlled conditions. Results of these tests are incorporated to demonstrate that dynamic predictions of the bit's tendencies compared well with numerical results predicted by the program.Two other field examples are cited: one from the Gulf of Mexico, and another from Holland. Data from these wells are used to illustrate how the dynamic results can be applied to explain the bit's trajectory behavior.A final section examines the use of the computer-generated results in predicting the tendencies of the bit for the five assemblies. Introduction Directional drilling is the science of directing the bit along some predetermined trajectory toward a target. To do this, the bit must be controlled in the vertical (inclination) and horizontal (direction) planes.BHA's, mud motors with deflection subs, whipstocks, and jetting bits all are used as a means of steering the bit along the prescribed trajectory. However, the BHA is the most popular method of controlling a directional, straight, or deviation control well once the initial orientation (kickoff) has been made.Historically, design and operation of BHA's have been based on experience. Certain basic BHA configurations were used to build, hold, and drop angle. The associated direction change (bit turn or bit walk) was considered a byproduct of the process.BHA design evolved from an art to a science when certain computer programs were developed that predicted the static two-dimensional force-displacement behavior of a BHA. Later, Millheim used a 3D static program to explain the responses of BHA's in various geological situations. The main emphasis in all these efforts has been directed toward determining the inclination response of the assemblies.To predict the direction as well as the inclination tendencies of a bit accurately, the rotation of the drillstring must be considered. The 3D static program presented by Millheim has been extended to include a dynamic capability. This paper presents the basic formulation of the algorithm that serves as the basis for the dynamic model.Having a computer code representing a mathematically rigorous solution, however, does not ensure that the code will represent the actual drilling process accurately in the field. In reviewing the computer results, it has been observed that other effects such as geology and hole conditions have to be taken into consideration to predict the inclination tendencies of a BHA successfully. To predict bit direction, rotary speed dynamics have to be included as well.For nearly 3 years, the dynamic 3D model mentioned earlier has been studied and compared against field results. To test the program's predictions further, an experiment was conducted involving five shallow directional wells drilled under controlled conditions in an area where the geology is known accurately.Results of these tests, which are presented in this paper, verify the predicted bit tendencies as generated by me dynamic program. JPT P. 2323^
The claasic depth versus days plot was the only tool The Drilling Performance Curve (DPC) ia a being used to compare the drilling success (or simple yet powerful tool to assess the drilling per-failure) of a series of wells. Even this was relaformance in any given area where a c,;nsecutive tive to some initial subjective estimate of how long series of similar wells have been drilled. All the it should take to drill a well to a certain depth. information that is needed to perform the analysis When subsequent wells were drilled in less days than is the sequence numbers of the well and the time it the initial wells, there was a general acknowledgetakes to reach a given depth. ment that something happened to reduce the days and/or costs. This might be a better application of This paper presents some typical examples of technology, better'operations, better rigs, better DPC'S covering a study of over 30 different areas (onshore and offshore) including over 2000 wells.
The constant-rate drawdown test performance for a low-permeability, vertically fractured gas well was investigated. A series of gas wells were tested by flowing each well at a constant rate until the data could be analyzed using conventional radial flow theory. Each well was then shut in to build up. After a sufficient buildup was obtained, another flow test commenced but at a higher flow rate than the first test. Again, the well was shut in when radial flow was obtained. This procedure was repeated for three to four different flow rates. Two wells in the San Juan basin were tested using this procedure. Both wells were fractured after completion, cleaned up and then shut in until flow testing commenced. Test designs of both wells permitted investigation of the most realistic values of effective permeability, wellbore radius and turbulence factor. Also, being able to determine the effective fracture flow area and vertical fracture efficiency was inherent with this testing approach. It was observed that fractures in both wells influenced the pressure behavior for approximately 18 to 40 hours (depending on the flow rate) before radial flow was evident. After this time, drawdown data were analyzed using radial flow theory. When a low-permeability gas well has vertically oriented, induced fractures, the early flow geometry is essentially linear. It will be shown how to determine when a flow test has been conducted long enough so that the most representative values of effective permeability, wellbore radius and turbulence factor can be calculated. From the linear pressure data, valuable information about the fracture treatment, such as the effective flow area and vertical fracture efficiency, can be determined for vertically fractured wells. Introduction During tests on gas wells in the San Juan basin, initial transient behavior lasted for many days because of the low permeability of some porous media. As a result, stabilized flow performance could not be obtained. If these wells received some type of stimulation treatment, early pressure behavior deviated from conventional theoretical radial flow. When conventional radial flow theory was used to analyze these low-permeability fractured gas wells, larger values of flow capacity and absolute open flow potentials (AOF) sometimes resulted. Wells were assigned open flow potentials that proved to be 3 to 10 times higher than the well would sustain over a longer period of production. In some cases where the wells had flowed for longer periods of time during a constant-rate drawdown test, it was noticed that the effective flow capacity appeared to be decreasing with time until a certain value was reached. The early nonradial pressure behavior can be explained if linear flow is assumed. Russell and Truitt mathematically investigated the vertically fractured well in a bounded area. They showed that early flow behavior was essentially linear and, for x(f)/x(e) approximately less than 0.10 radial flow was obtained after short periods of time. Then realistic values of effective permeability and skin could be determined. Scott experimentally studied the vertically fractured well with a heat flow analog. He showed that early flow was linear. Both studies indicate that, for small values of x(f)/x(e), linear flow approaches radial flow if the well is tested long enough. To help prove this concept of early linear flow caused by induced vertical fractures, two low-permeability gas wells were tested. Both wells received large fracture treatments prior to testing. A vertical fracture was indicated from the analysis of fracture treatments. As anticipated, tests of both wells indicated early linear flow that was later followed by a period of radial flow. Data collected from each well were analyzed. From the well tests, plus other information on each well, the effective permeability, wellbore radius and turbulence factor were calculated. Effective fracture flow areas calculated from test analyses for each well proved to be approximately one-fourth the created area calculated from classic hydraulic fracturing theory. Other fractured wells that were tested but not presented in this paper also indicated that the effective fracture flow area was one-fourth to one-third the created area predicted from hydraulic fracturing theory. The vertical fracturing efficiency was estimated from the calculated values of effective wellbore radius and fracture flow area. For the two wells tested, calculated fracture lengths x(f) were 112 and 105 ft, and the vertical fracturing efficiencies E(f) were 122 and 183 percent. Development of Flow Model Agnew showed that most induced fractures below 1,500 ft are vertical. Anderson and Stahl indicated that most of the fractures they studied were vertical. The model proposed for early flow in most vertically fractured gas wells is shown by Fig. 1. JPT P. 193ˆ
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