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By B. Etkin, A. A. Haasz

The Infrasizer Mk III, developed at the University of Toronto, is capable of sizing particles of a few pm to hundreds of pm according to particle terminal velocity, which is a function of particle density, size and shape. The factors limiting the performance of the Infrasizer Mk III have been presented and analyzed. It has been established theoretically and experimentally that the device has excellent potential as a laboratory instrument. The principle is applicable to a continuous production classifier, a prototype of which is now under development.

Jan 1, 1980

By C. S. Duncan, S. Scuro, D. R. Muss

Work is vepurted which was aimed at accentuating the pec14liar attributes of the GaAs laser diode, namely its sutzull size and its high efficiency. This has been done by reducing- transport losses in the bulk p and n regions of the diode and combining many of. these diodes into series stacks with common optical cazlities. The result of this effort is a nearly monochromati source at about 8450A With a luminous areu 0.05 by The GaAs laser diode is an attractive pulsed light source in the near ir because of its ability to emit very large pulse powers and its small size. In addition to this, the device is efficient; and the higher the 0.05 cm emitting peak pulse po we rs at greater than 300 LC at repetition rates below 200 pps into a cone about 0.01 steradians when operated at 77°K. The results of nzeasuvetnents of peak optical power and spectra frorr~ these stacks are reported and some conclusions are drawn about the vole the individual diodes play in the stacked operation. peak output power, the more efficient it is. The limit for the amount of power that these diodes can emit is the transient and average dissipation associated with the pumping pulse. This power dissipation arises primarily from transport across the bulk regions of the diode; this fact, along with the relatively low thermal conductivity of the GaAs, led us to the conclusion that higher power

Jan 1, 1968

By Wilson Blake

Rock deformation and failure taking place around underground openings is usually both accompanied and preceded by the phenomena of rock noise or microseismic activity. These small-scale releases of seismic and acoustic energy can be detected with special geophysical monitoring equipment. Use of this equipment allows one to look inside a rock mass to determine how an opening is behaving under the applied loading system. Microseismic equipment and monitoring techniques are briefly reviewed, and use of the microseismic method as an engineering tool in monitoring rock structure stability is illustrated by case histories. Examples cited range from evaluating roof stability using single-channel portable equipment, to rock burst monitoring using sophisticated computer controlled, multichannel monitoring systems.

Jan 1, 1983

By Hallan Marsh

THE subject of this paper is apt to bring to mind wells ranging from 6000 to over 8000 ft. in depth. However, it is uncommon to pump wells at depths greater than about 5000 ft. Fig. 1 shows the number of wells being pumped at various depths by one company in Southern California. FIG. 1.-NUMBER OF WELLS BEING PUMPED BY ONE COMPANY FROM VARIOUS DEPTHS IN SOUTHERN CALIFORNIA. A few companies have a very few wells pumping at depths greater than this. This paper will deal with wells between 3000 and 5500 ft. in depth. Most California oils at these depths are between 25° and 35 gravity. The subject is so broad that it will be necessary to omit many interesting phases, and to treat others very briefly. Power, power transmission equipment, power efficiency, counterbalancing, sucker rods, pumps and volumetric efficiency will be discussed.

Jan 1, 1928

By Harlowe Hardinqe

ABOUT three years ago a distinctive new type of crushing and grinding equipment, known as the Hadsel mill, was announced. A description appeared in the November, 1932, issue of this magazine. Any machine that would take run-of-mine ore and reduce it, in one operation, and at a reasonable cost, to a size suitable for metallurgical treatment was bound to attract much interest, as the original Hadsel mill did. The first commercial sizes were built with the drum supported by an overhung shaft and partly immersed in a tank. The drum carried inside and outside buckets to lift the ore, which was dropped as the drum revolved onto stationary breaker plates projecting into the drum from the opposite tank wall. The coarser material settled back into the inside buckets. Intermediate sizes were carried into the tank, and this material was scooped out by the outside buckets and deposited hack in the drum for further grinding. The fines were carried out of the mill with the wash water over an adjustable weir at one side of the tank.

Jan 1, 1935

By R. V. McAfee

The fundamentals of vertical-lift performance are examined with the aid of computer-calculated flowing gradient charts. Flowing and gas-lift well performance characteristics are determined from available well test data. The effect of tubing size, gas-liquid ratio and wellhead pressure is discussed for both flowing and gas-lift wells. The effect of gas-injection pressure, formation gas, bottom-hole pressure and valve spacing is also discussed for gas lift wells. From these studies conclusions may be reached for improving or prolonging natural flow, obtaining optimum lift efficiency when natural flow ceases and improving existing gas-lift systems. The techniques perfected satisfy the requirement that the time involved to conduct an evaluation be practical for operating personnel. INTRODUCTION Flowing pressure gradients furnish the key to successful evaluation of vertical-lift performance in producing wells. Command of multiphase flow gradients in some readily usable form is a necessity before operating personnel can competently include vertical-lift performance evaluation of both flowing and artificial-lift wells in their over-all consideration of production efficiency. A readily usable form cannot be overemphasized since most of the decisions which confront the production engineer with a problem well must be made quickly. In moving a barrel of oil from the reservoir to the stock tank, the major portion of energy generally is expended in the vertical-lift phase. This may or may not be of concern during the flowing life of a well, depending upon the production requirements. It becomes of some concern when the flow performance of the well becomes erratic, and a conscious effort must be made to maintain natural flow. It is at this time that the first steps may be taken to modify existing conditions to relieve unnecessary limitations to proper flow. When natural flow ceases and some form of artificial lift must be installed, the amount of energy expended in lifting liquids becomes quite obvious. It is at this time, if no other, that lifting efficiency becomes important because that part which must be supplied from an outside source is now related directly as a cost per barrel of oil produced. Ten years ago, the majority of gas-lift wells were produced with gas-well gas. Today, the majority are produced by closed rotative gas-lift systems. This permits a direct evaluation of well performance in terms of horsepower requirements and has resulted in mixed conclusions as to the success of gas lift based upon the relative efficiency of a particular system. An increased awareness of the need to resolve vertical-lift performance on a readily usable, scientific basis was inevitable. An indication of the need for better applied science in this field is the often-asked question of whether or not gas-lift can efficiently deplete a given well or reservoir. This question cannot possibly be answered without first evaluating reservoir, surface and vertical-lift performance both as encountered today and as anticipated throughout the life of the well or wells. The technique presented in this paper was originally developed to upgrade gas-lift installation design from an applied art to an applied science. It has since been successfully used not only for this purpose, but also for the whole field of vertical-lift performance in its broadest sense. Lift efficiency should be considered important while the well is still flowing, as well as after natural flow ceases. Correct interpretation and proper modification of the vertical-lift performance of a producing well can provide dramatic improvement in production performance and/or efficiency. STATEMENT OF THEORY AND DEFINITIONS Fig. 1 illustrates the three divisions of production which will be used in this paper. The terms are a modified version of those presented in the very fine paper by Gilbert.' The fields of reservoir and surface performance both have been greatly improved over the years. A study of those writings which may be found indicates that the field of vertical-lift performance has not progressed as well. There are two possible reasons for this lack of progress. 1. It has not been recognized as a scientific field in itself by the oil companies, as has reservoir engineering. 2. The equipment companies have confined their efforts to mechanical design research rather than the more basic study of vertical-lift performance of producing wells. Both organizations must have an economic stimulus for doing research in this field, and most of the results obtained in past work has been so erratic as to arouse little enthusiasm. The basic purpose of interpreting vertical-lift performance is to predict operating conditions below the surface of the ground from available data. The success of the interpretation depends upon the accuracy with

By R. B. Sudderth, C. R. Merigold

Greater, emphasis is being placed on recovering nickel from laterite ores by ammonia leaching techniques. New methods are required for lower cost, non-polluting techniques to separate more efficiently the metals of interest. Liquid ion exchange techniques meet these requirements with the added advantage of producing salable electrowon nickel cathodes at the plantsite. A complete solvent extraction- electrowinning process is described, including preliminary engineering and cost data for a typical plant producing 50 million pounds of nickel per year.

Jan 1, 1973

Jan 1, 1904

By R. E. Rowlands, I. M. Daniel

An experimental study is discussed of the state of strain, deformation and fracture around lined and unlined cylindrical cavities in rock under biaxial compressive static loading. The specimens were limestone plates 36 in. high, 24 in. wide and 3 in. thick with a 4 in. diameter hole unlined or lined with hydrostone and aluminum liners. The ratio of horizontal to vertical applied stress was one-third. Experimental techniques used were strain gages, differential transformers and photoelastic coatings. Strain distributions were plotted along the horizontal axis of symmetry for various levels of applied stress. The agreement with theory was good at low stress levels but appreciable deviations occurred at higher levels and near the hole. The experimental strain concentration factor was nearly the same, slightly higher and appreciably higher than the theoretical value for the hydrostone-lined, unlined and aluminum-lined specimens, respectively. Failure modes were splitting along a vertical plane for the unlined and hydrostone-fined specimens, compressive (shear) failure for one unlined specimen and splitting with radial cracking for the aluminum-lined specimen. In the latter, a maximum tensile stress of more than three times the uniaxial tensile strength existed at the interface with the liner at the time of fracture,

Jan 1, 1971

By Eugene P. Pfleider

Research indicates that the cube diamond is a superior stone for drill bits. It can be oriented to combine a long cutting edge with structural strength and high resistance to wear. Test bits set with preferred orientation give double the bit life at astoundingly low diamond loss in comparison to oriented octahedral diamonds. A PROGRAM of research on the orientation of diamonds in drill bits has been under way for several years at both the United States Bureau of Mines Experimental Mine at Mount Weather, Va., and the School of Mines and Metallurgy of the University of Minnesota. Reports on past work done both in the laboratory and the field are available in the technical press.1,3,4 The results of such drilling, done under comparable conditions, show that bits having diamonds oriented in a direction that combines structural strength and greatest hardness not only can advance somewhat faster than random set bits but can do this with a unit diamond loss of 50 pct or less. Several bit manufacturers have initiated the training of diamond setters in the principles of orientation on the basis of the above-mentioned research results. The basic information on the crystallography and hardness variation of the diamond was presented in an earlier paper,' which pointed out that the diamond is several hundred times harder along certain directions and certain faces than on others. The same article discussed the drilling results obtained with a group of nine bits having octahedron diamonds set with on-point, positive (gouge) rake, and negative (drag) rake orientations. The testing of oriented cube diamonds is an extension of this research program, employing the same procedures and equipment (Hy Mac hydraulic drill unit, EXT diamond core bits, St. Cloud Pink granite) as previously described. This current work covers the test experience of seven bits set with cube diamonds running approximately 10 stones per carat. The individual stones were near perfect cubic form; hence it was simple to orient them in any desired direction. The cube is a comparatively rare crystal form of the diamond, although considerable numbers are produced from the Congo. It is understood that most of the cube diamonds are retained in Africa, where they are either used locally for diamond bit manufacture or ground up to make powder. They have been considered to be an inferior stone for drilling purposes.

Jan 1, 1954

By A. E. Belton

The individual projections for large mines in the Pittsburgh coal seam in northern West Virginia are discussed with emphasis on roof control and ventilation requirements. All four mines use continuous miners with panel belts and rail for main line haulage. Both development and retreat-type mining are covered. There are a variety of mining projections being used currently in northern West Virginia. To discuss each would be impossible, so an arbitrary cross section has been selected in an attempt to indicate a fair degree of representation. Four mines, hereinafter referred to as Mines A, B, C and Dl will be discussed separately. The greater part of northern West Virginia coal production is mined from the Pittsburgh seam. This is the seam worked by all the mines discussed here. Although the coal bed outcrops at the eastern and southernmost points, these mines are all working in a depth ranging from 400 to 1400 ft below the surface. Some steep gracles have been encountered but are only considered local in nature; the overall average dip of the seam is 1 1/2 % northwest. In each of the operations the particular mining scheme used has proved advantageous, since they have been designed to satisfy particular equipment and/or physical condition requirements. So regardless whether such projections utilize a partial or full recovery principle, the productivity performances appear better than average. MINE A Full retreat is the basic mining approach for mine A, although current mining is primarily in the entry-driving stages to expand territory in preparation for pillar work. Only one section unit now on retreat. The average clean coal production at this mine is 7000 tons per day. Initially, a ripper-type miner was used for development at this mine. But with a rather weak roof overlying the coal bed and the greater horizontal span left at the top by a ripper machine, roof control became a critical problem. Even though roof bolts were used concurrently in the mining cycle for initial support, the majority of the roof in these entries

Jan 1, 1962

By J. G. Hadley

IN THE early stages of the depression the Utah Copper Co. realized that an unemployment problem would he created which demanded an intelligent and sympathetic solution. The company recognized that as many men as possible must be kept at work on a basis which would ultimately permit of the most efficient reabsorption of displaced labor. The company therefore determined to distribute available work among the greatest number of men and to that end adopted a system of rotating employees on a part-time basis. An employer requires a certain number of days' or shifts' work during the month. Obviously one employee working thirty days or shifts a month is equal to two employees each working fifteen. In principle, therefore, where two employees equally fitted to do certain work are available the work could be divided between them on an equitable basis and twice as many persons would benefit. A rotation plan on this basis was adopted by the Utah Copper, Co. on Jan. 30, 1930. Some variations of the orig¬inal plan have been made from time to time, the reasons for which will be discussed.

Jan 1, 1932

By F. M. Hamilton, H. F. Ameen

Results of a laboratory investigation of some sintering variables are presented. The effect on physical properties of mix component variation and rate of cooling of the sinter is illustrated by crush and tumbler test results and data of reducibility tests and microscopic examination of sinters are shown. The results of using solid additions in the mix to improve bed permeability are given. SOME of the variables encountered in the sintering of iron ores and their effect on sinter properties have been investigated at the Jones and Laughlin Ore Research Laboratory in Michigan. Ores requiring agglomeration before blast furnace utilization may be classed as coarse, intermediate or fine. Coarse iron ore is considered similar to a — 1/4-in. Mesabi wash ore containing some 95 pct of its particles between 94 in. and 100-mesh. Intermediate iron ore is considered similar to our New York State magnetic concentrates in which all the particles are — 20-mesh and about 60 pct are +100-mesh. Fine ores are considered as being at least 100 pct —100-mesh. This paper will deal only with the two coarser classifications. Most of the work has been done in a small experimental batch unit previously described in an AIME1 paper. Results being obtained form a basis for present and future trials in production sinter plants. It is expected that new production units that may be added in the future will benefit from laboratory studies. In general, the results reported here are obtained by laboratory study, but it is Experimental Sinter Machine: The laboratory sinter machine employed in the work consists of a chamber with 1 sq ft of grate area. It is mounted on

Jan 1, 1951

By H. F. Ameen, F. M. Hamilton

Results of a laboratory investigation of some sintering variables are presented. The effect on physical properties of mix component variation and rate of cooling of the sinter is illustrated by crush and tumbler test results and data of reducibility tests and microscopic examination of sinters are shown. The results of using solid additions in the mix to improve bed permeability are given. SOME of the variables encountered in the sintering of iron ores and their effect on sinter properties have been investigated at the Jones and Laughlin Ore Research Laboratory in Michigan. Ores requiring agglomeration before blast furnace utilization may be classed as coarse, intermediate or fine. Coarse iron ore is considered similar to a — 1/4-in. Mesabi wash ore containing some 95 pct of its particles between 94 in. and 100-mesh. Intermediate iron ore is considered similar to our New York State magnetic concentrates in which all the particles are — 20-mesh and about 60 pct are +100-mesh. Fine ores are considered as being at least 100 pct —100-mesh. This paper will deal only with the two coarser classifications. Most of the work has been done in a small experimental batch unit previously described in an AIME1 paper. Results being obtained form a basis for present and future trials in production sinter plants. It is expected that new production units that may be added in the future will benefit from laboratory studies. In general, the results reported here are obtained by laboratory study, but it is Experimental Sinter Machine: The laboratory sinter machine employed in the work consists of a chamber with 1 sq ft of grate area. It is mounted on

Jan 1, 1951

By Donald L. King

This paper has been prepared with the objective of providing basic information on thickening equipment as applied to mineral processing plant design. Thus, by design, the content is elementary, yet sufficiently informative to advise the reader concerning the thickening and clarifying process, equipment configurations, installation and operation. Practical considerations are provided for slurry samples for testing, evaluation of testing, preliminary sizing, duty classification, and thickener selection to enhance operation, see icing and control. Illustrations are provided to both inform and demonstrate present state of the art features and capability.

Jan 1, 1978

By W. J. West, W. W. Garvin, J. W. Sheldon

One of the most important problems of reservoir mechanics is the prediction of the behavior of a gas and oil producing reservoir for a variety of production programs. In the absence of a knowledge of the behavior of even idealized systems, it has been difficult, if not impossible, to determine which production program would yield maximum economic recovery. The problem was formulated mathematically many years ago, hilt a solution of the equations had never been obtained because of their extreme complexity. The solution of the problem became possible, however, with the advent of modern computing machines. This paper describes a digital method of solving the problem and discusses some of the results which have been obtained to date. The IBM Type 701 Electronic Data Processing Machines located at IBM's New York Scientific Computing Service were used successfully to perform the computations. The flow of gas and oil through a reservoir can be described mathematically by two second-order, nonlinear partial differential equations which must be solved simultaneously. All derivatives were replaced by finite differences to bring the equations into a form suitable for digital calculations. A number of finite ditference formulations were investigated and one form was found which resulted in stable, convergent solutions. This form was used to obtain .solutions for both radial and linear systems producing by solution gas drive. The results presented in this paper are: (a) saturation profile within the hypothetical reservoir vs. time, (b) pres.strre profile within the hypothetical reservoir vs. time. (c) gas-oil ratio vs. cumulative recovery, and (d) ultimate recovery. The saturation profile clearly shows the effect of critical gas saturation. The saturation near the well-bore drops quickly to the critical gas saturation and remains essentially at that value until the remainder of the reservoir also has dropped to the critical gas saturation. The pressure profile shows a smooth variation of pressure across the reservoir. The gas-oil ratio drops slightly during the early stage of production until the critical gas saturation is reached, rises rapidly from then on and eventually passes through a sharp maximum just before the economic limit of production is reached. For the radial example presented in this paper, the average oil .saturation of the reservoir at a time corresponding to the limit of economic production was 56.5 per cent and the ultimate recovery was 6.86 per cent. The difference between change in saturation and ultimate recovery is caused by .shrinkage of the oil phase. The solution time with the 701 Computer is sufficiently short to permit an economically feasible investigation of the effects of variation of the many parameters which describe an oil reservoir. In particular, the ultimate recovery for various systems can he determined as a function of rock and fluid properties, of well spacing. and of production rate. INTRODUCTION The effective planning for maximum economic depletion of oil reservoirs is one of the major problems confronting oil producers. The most important part of the planning is prediction of the response of the oil reservoir to a particular production program. The production program can be selected by imposing certain controls available to the operator. Some of these controls are: (a) well spacing, (b) production rate, (c) time

Jan 1, 1955

By K. D. Jacob, W. L. Hill

THE bulk of natural phosphates is comprised of calcium phosphates, which are usually apatites;1 calcium aluminum phosphates such as pseudowavellite;2 and aluminum phosphates, which occur in extensive deposits, notably on Grand Connetable Island.3 Nearly all deposits of current commercial value are apatite, often with admixed material of other classes. In the trade coarsely crystalline material, mainly fluorapatite of igneous origin, moves as apatite, whereas the fine-grained material of sedimentary origin is marketed as phosphate rock. The latter classification includes the phosphate shales in western North America. Although several genetic varieties of phosphate rock are recognized,4 most known reserves are of marine origin. Calcium phosphate is concentrated from Florida land pebble and Florida hard rock deposits and from Tennessee brown rock deposits. Phosphate Rock as a Fluorine Carrier: More than two decades ago Reynolds and Jacob surveyed the fluorine content of commercial phosphate rock from various parts of the world.3,5 Later these samples were reanalyzed by a new and more reliable method of determining flourine.6,7 The revised results with interim additions of new samples, published a few years ago in a brief summary,' are shown in Figs. 1-3. Through the points representing the respective varieties of rock medial straight lines are drawn. In some instances the lines are well defined by the points; in others, where scattering renders the position of the best line uncertain, the greater weight is given points near the end of the covered range. Wherever distinct varieties are not recognized among regional deposits the custom is to identify the sample with the geographical location of the deposit.

Jan 10, 1954

By M. T. Halbouty

The Laredo oil district, South Texas, includes an area of approximately 200 miles long north and south and 75 miles wide, embracing the following counties: Starr, Zapata, Jim Hogg, Webb, Duval and McMullen. The area is relatively old in respect to the production of oil, as the first oil was discovered and produced in the Piedra Pintas field in Duval County on Sept. 10, 1905. Since that date, continuous new discoveries have contributed to the development of this district until, at the present time, it is one of the important oil-producing and gas-producing areas in the world. The year 1937 also had its share of new discoveries in the district, including not only new oil fields but also new sands in already producing pools and important extensions to existing sands and fields. Among the most important field discoveries, by counties, are: Duval County..... Benavides, Sweden, Thomas-Lockhart, Labbe and Lundell fields Jim Hogg County.. Las Animas field McMullen County. Ezzell field Starr County...... El Tanque field Webb County..... Killam and Oilton fields Of these, Benavides, Oilton, Killam and Ezzell have so far proved themselves most important; the Benavides field, Duval County, showing by far the most activity. For the year 1937, therc were 283 wildcat tests drilled in this district, of which 35 were oil producers, 20 completed as gas wells and 228 abandoned as dry holes. Duval County, as usual, received the greatest amount of wildcat drilling, having 21 oil wells, 5 gas wells and 63 dry holes completed during the year for a total of 89 tests. Next came Webb County with 4 oil wells, 4 gas wells and 53 dry holes for a total of 61 tests.The Laredo oil district, South Texas, includes an area of approximately 200 miles long north and south and 75 miles wide, embracing the following counties: Starr, Zapata, Jim Hogg, Webb, Duval and McMullen. The area is relatively old in respect to the production of oil, as the first oil was discovered and produced in the Piedra Pintas field in Duval County on Sept. 10, 1905. Since that date, continuous new discoveries have contributed to the development of this district until, at the present time, it is one of the important oil-producing and gas-producing areas in the world. The year 1937 also had its share of new discoveries in the district, including not only new oil fields but also new sands in already producing pools and important extensions to existing sands and fields. Among the most important field discoveries, by counties, are: Duval County..... Benavides, Sweden, Thomas-Lockhart, Labbe and Lundell fields Jim Hogg County.. Las Animas field McMullen County. Ezzell field Starr County...... El Tanque field Webb County..... Killam and Oilton fields Of these, Benavides, Oilton, Killam and Ezzell have so far proved themselves most important; the Benavides field, Duval County, showing by far the most activity. For the year 1937, therc were 283 wildcat tests drilled in this district, of which 35 were oil producers, 20 completed as gas wells and 228 abandoned as dry holes. Duval County, as usual, received the greatest amount of wildcat drilling, having 21 oil wells, 5 gas wells and 63 dry holes completed during the year for a total of 89 tests. Next came Webb County with 4 oil wells, 4 gas wells and 53 dry holes for a total of 61 tests.

Jan 1, 1938

By C. A. Heiland

The following summary is written for the benefit of the practical operator in the nonmetallic field who wishes to know what geophysics has done and may be expected to do in his line of work. His problem is quite different from that of the geophysicist who has operated with various or all methods and has followed the literature, and who is assumed to be familiar with the geologic possibilities and limitations of each method. This article is not written for the latter, although he may be interested in the four or five hitherto unpublished surveys described. To the operator, on the other hand, geophysics is only secondary. His problem is to determine which geophysical method is best suited to his special needs. If he wanted to know, however, which method could be used to locate a certain material of given physical properties, building stone, for instance, he would have to wade through a tremendous amount of geophysical literature, bibliographies and articles, before he could find what he wanted. Therefore, the purpose of this summary is to present the geological problems first and then to discuss the comparative merits of the geophysical methods that can be, or have been, applied. Choice of Geophysical Methods in Oil, Civil and Mining Engineering In the first two of these fields, the geological problems are not nearly so complex as in the metal and nonmetallic mining fields. The selection of the correct geophysical method in these fields is not nearly so difficult for the operator. For oil prospecting, his problems have been discussed exhaustively by E. DeGolyer.(1) † In civil engineering (foundation and ground-water work), the usefulness of electrical methods has been so well established that there is hardly any choice of other methods at present. The situation may be changed in the future with the perfection of the seismic reflection method for shallow depths. In the mining field the operator and often the geophysicist himself finds difficulty in determining which method is best suited for a given

Jan 1, 1934

By N. E. Truitt, D. G. Russell

The transient pressure behavior of a well which produces a single compressible fluid through a singte-plane wrticat fracture has been investigated mathematically. The fracture is assumed to possess infinite flow capacity, to be of limited mdial extent, and' to penetrate the producing formation completely in the vertical direction. Previous studies of vertically fractured wells have been concerned primarily with production rate performance or semisteady-state pressure behavior. This study was undertaken to ascertain the influence of vertical fractures on transient pressure tests such as pressure build-ups and flow tests. In a vertically fractured system, flow in the region nearest the fracture is practically linear, whereas farther away from the fracture essentially radial flow prevails. Thus, transient pressure analyses based on radial flow theory are somewhat inaccurate. As fracture penetration increases radially, kh values calcutated from pressure build-up and flow test curves become increasingly larger than true values. Failure to consider the effect of fracture penetration also introduces inaccuracies into the catculation of fracture length from the apparent skin factor and into the determination of average reservoir pressure. If the total length of the fracture is 20 per cent, or greater, of the drainage radius of the well, corrections must be made to pressure build-up and flow test results. Methods for correcting such results are discussed in this paper. For wells with prefracturing pressure build-up or flow test data, it is possible to estimate fracture length by comparison with postfracturing build-up or flow test results. In new wells or wells without prefracturing build-up or flow test data, fracture length must be estimated to correct the values obtained from analysis of pressure tests after fracturing. Fracturing efficiency calculations should be made whenever possible to provide an estimate of fracture length. Tables of the dimensionless pressure drop as a function of time and fracture penetration are included in this paper. Using these values should permit analysis of other types of transient pressure behavior in vertically fractured wells. INTRODUCTION Hydraulic fracturing has been used quite successfully for over a decade as a completion and stimulation technique in oil and gas wells completed in low-permeability reservoirs During this period a considerable amount of theory has evolved on the performance of hydraulically fractured reservoirs and on more efficient means of artificial fracturing. Although theory has been developed, no rigorous investigation has been made of pressure build-up and flow test behavior in such wells. Prats et al.1 first discussed the performance of vertically fractured reservoirs for the case of a compressible fluid. Their work was primarily concerned with production performance at constant flowing pressure. These authors also considered large-time (semisteady-state) constant production rate behavior for vertically fractured wells; however, transient pressure behavior at constant rate was not investigated. McGuire and Sikora10 and Dyes, Kemp, and Caudle2 employed an electrical analog to investigate the influence of artificial vertical fractures on well productivity and pressure build-up. They found that fractures which extend beyond 15 per cent of the drainage radius away from the well alter the position and slope of the straight-line portion of the build-up curve. They concluded that these effects must be considered both in the determination of the effective permeability of the formation and in any calculations of final build-up pressure. Although these authors did not undertake an exhaustive study of the influence of vertical fractures on pressure build-up performance, their limited results were quite interesting from the standpoint of the effects they demonstrated. In a more recent paper, Scott- reported the results of an investigation of the effect of vertical fractures on pressure behavior, which was conducted with a heat flow model. Scott's results appear to be consistent with those reported in Refs. 1 and 2. However, the effects of different fracture lengths on performance were not investigated. Pressure build-ups and transient flow tests are among the most diagnostic tools available to the reservoir engineer or production engineer. Since a very high percentage of present-day well completions incorporate the hydraulic fracturing technique, a definite need exists for information on the effect of fractures on transient pressure performance. For these reasons we have undertaken a rigorous study of pressure build-up and flow test behavior in vertically fractured reservoirs. The objectives of this study were (1) to obtain synthetic pressure build-up and flow test

Jan 1, 1965