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Jan 12, 1959

By Donald C. Moore

INTRODUCTION Published laboratory procedures used by the major crusher manufacturers for estimating crusher size are based upon techniques developed in the mid 1940's. Specifically, the two largest U.S. crusher manufacturers are using the Bond impact procedure. Although the procedure is still in use, there is little confidence in the results. Unless the laboratory results fall within a preconceived range, personal experience is used for selecting the number of crushers and connected horsepower (Coleman, 1978). There have been numerous theoretical studies of the communition of particles. However, no procedure has been widely acclaimed for predicting crusher power requirements. Experimental studies have included breakage by slow compression, slow speed impact and high speed impact. Theoretical results have increased our knowledge of the comminution process, but the procedures have not been capable of analyzing the complex mechanism of industrial crushing machines. The purpose of this chapter is to review the empirical crushing procedures that have been used, including advantages and disadvantages. A new procedure which has been in development at Allis-Chalmers Corp. from 1977 to 1982 is detailed. Actual results of the new procedure on a concentrator feasibility study are included. EXPERIMENTAL GOALS The goals of a laboratory crushability procedure are accurate predictions of: (1) Rock crushability, measured as energy per unit mass. (2) Crusher product size analysis. A procedure capable of predicting these parameters should be inexpensive and require a minimum amount of sample. CRUSHABILITY TESTS Bond Impact Procedure F. C. Bond (1946) detailed the development of the pendulum impact device that is still used by the leading crusher manufacturers (Bond; Rexnord, 1976). The device (Fig. 1) is comprised of two bicycle wheels with 13.6 kg steel hammers tangentially attached to the rims. The hammer faces are 50 mm apart at rest. On opposite ends of the hammers lifting

Jan 1, 1982

By Henry Hanson

A STUDY of the ore to be treated should be the first step in deciding on a machine for crushing or grinding. Coarse crushing is practically confined to the jaw and the gyratory crushers, the large-size jaw type being often employed in large installations as a primary crusher, followed by the gyratory type for secondary reduction. In small plants where mine-run ore is reduced in a single step, either of these machines will do the work. In intermediate and fine grinding, various machines are used. The relative merit of the different types will be governed in no small measure by the size of the installation, the character of the ore to be reduced and the final product desired for subsequent treatment. It should be possible, nevertheless, with the data available, if properly classified, to arrive at an approximation of the relative efficiency of these intermediate and fine grinders. It should be possible, also, to determine the economic grinding range of the different machines. With this in mind, it will be the object of this article to indicate, in rough outline, how the data available may be classified, rather than to attempt to discuss any particular practice and compare the results with other practices. Conclusions or generalizations can not be drawn without an exhaustive classification of data; in fact, many vital points will have to be determined by additional experiments which can be carried on most advantageously in the laboratory. The expense en-tailed in such experiments would be worth while if the data obtained should lead to definite conclusions that would aid in standardizing and simplifying grinding practice.

Jan 2, 1923

By H. Reginald Hardy, Gary L. Mowrey

Field studies were conducted over a longwall coal mining operation to investigate the feasibility of using microseismic techniques to detect and to locate any areas of instability in the vicinity of the longwall. An array of geophones buried at depths of 3 to 8 m from surface were positioned approximately 130 m above the active area of the longwall panel. A mobile microseismic monitoring facility amplified, filtered, and recorded the microseismic activity sensed by the geophones. Microseismic events were detected at depths of at least 130 m and at horizontal distances in excess of 250 m from the source. Most events, which resembled decaying sinusoidal transients, had frequencies of 10 to 100 Hz, and particle velocities of 1 to 8 pm/s. Source locations for the 150 largest events were computed using a least-square travel-time-difference method. Both isotropic and unique wave propagation velocity models were considered when evaluating the source locations. Most of the events were computed to be within ± 30 m vertically of the coal seam and ± 15 m horizontally of the longwall face, when the unique velocity model was employed.

Jan 1, 1980

By Spurr

CONTENTS. [ ]

Jan 1, 1913

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who called at Institute headquarters during the period June 10, 1916 to July 10, 1916: Arthur Adams, Miami, Ariz. John M. Lovejoy, New Rochelle, N. Y. J. H. Batcheller, Mattapoisitt, Mass. J. F. Manning, Seoul, Korea. R. S. Bonsib, Low Moor, Va. E. P. Mathewson, Anaconda, Mont. E. L. Booth, New York, N. Y. Edwin W. Mills, Seoul, Korea. C. L. Bryden, Scranton, Pa. Arthur Notman, Bisbee, Ariz. F. Crabtree, Pittsburgh, Pa. L. B. Reifsneider, Daiquiri, Cuba. L. B. Eames, Pueblo, Colo. W. S. Schuyler, Berkeley, Cal. S. J. Gormly, Guayacan, Chile. 0. N. Scott, Toronto, Ont., Canada. Ernest A. Hersam, Berkeley, Cal. Arthur F. Taggart, New Haven, Conn. A. W. Hudson, Douglas, Aria. Warren D. Thompson, Boston, Mass. Chas. W. Johnston, West Norfolk, Va. Thor. Warner, IGngman, Ariz. Rodolphe L. Agassiz has been chosen president of the Calumet & Hecla Mining Co., an office which has been vacant for over a year. Percy E. Barbour, Managing Editor of the Engineering and Mining Journal, resigned his commission as 2d Lieutenant in the Main Coast.

Jan 8, 1916

By F. R. Pyne

The following notes are presented in an endeavor to point out the disadvantages attending the use of chrome brick in reverberatory furnaces in which are conducted the treatment of materials of such a nature that absorption by the brick is of too great value to be wasted, and these values must be recovered, if possible, in order to prevent metal losses that can not be tolerated. Several years ago one of the large Eastern copper refineries decided to utilize basic material in place of siliceous material in the walls of their reverberatory furnaces for the treatment of very foul blister copper, as the latter rapidly corroded the siliceous linings. It was also expected that there would be less slag formation, with a consequent decrease in the cost of treatment and a reduction in the metal losses. Magnesite brick were first used, but while the corrosive action of the foul material was greatly reduced, and the amount of slag formed was very much less, the magnesite proved to be unsatisfactory in certain parts of the furnace, because of its tendency to crack and spall badly when subjected to the alternate heating and cooling that takes place in a reverberatory refining furnace. This made many repairs necessary, and consequent frequent interruption in the operation of the furnace, which, together with the high price of the magnesite brick, ran up the cost of maintenance to an unreasonable amount. It was, therefore, decided to substitute chrome brick for magnesite brick in the parts of the furnace affected. The results, as far as the reverberatory furnace was concerned, were very satisfactory. The corrosion due to the action of the foul blister was small and the amount of slag formed was no greater than when using magnesite, and the tendency to crack and spall shown by the magnesite was eliminated. Gradually the use of chrome brick was extended to all furnaces, those treating blister copper as well as those melting cathodes, and the results were so satisfactory that the siliceous roofs were replaced by roofs of chrome brick except in certain places where experience showed a more satisfactory performance on the part of the silica brick. It was immediately recognized, for both the magnesite and the chrome brick, that the metal absorption was very heavy, but it was felt that the

Jan 1, 1918

By Orville A. Derby

In view of the recent important discussions before this Institute on the genesis of metalliferous deposits, certain features in the occurrence of gold which seem to be more clearly developed in Brazil than elsewhere can hardly fail to be of interest. As the observations here recorded have necessarily been of a somewhat cursory character, they will be presented in the form of brief notes, without any attempt to draw conclusions as to their genetic significance. Gold in Gneiss.—The statement made by me many years ago† that in the districts of Campanha and S?o Gongalo, in southern Minas Geraes, gold occurs in gneiss, can now be reaffirmed in the most positive manner, on the strength of a recent examination of fresh material, confirmed by the testimony of an experienced mining captain from the Morro Velho mine, who, being skeptical on this point, made a prospectingtour in the district. The specimens examined, though so far decomposed as to be readily disaggregated, were clearly of

Jan 1, 1903

Map

Jan 1, 1941

By Bernard S. Borie

THE U-A1 binary system has been studied by Kaufmann and Gordon.' They have shown that three intermetallic compounds occur in the system: UAl², UAl², and a third compound tentatively identified as UA15. UA1³ is simple cubic, a, = 4.26A. Its unit cell contains one formula weight, and it is iso-morphous with AuCu³. UA1² is face-centered cubic, a, = 7.72A, with eight formula weights per unit cell. Rundle and Wilson have shown that it is iso-morphous with Cu²Mg.² A Debye-Scherrer pattern of the Al-rich compound indicated a more complex structure than either UA1² or UA1³. The following is a report of an investigation of the crystal structure of this compound and a determination of its stoi-chiometric formula. A melt of uranium (99.9 pct pure) and aluminum (99.9 pct pure) was prepared which contained about 25 pct U by weight. It was cooled from 950" to 650°C at a rate of 500" per hr and then taken from the furnace and air cooled. An X-ray diffraction pattern of the ingot showed only lines of aluminum and the Al-rich compound. Filings from the ingot were reacted with a solution of sodium hydroxide, producing a fine black powder, the diffraction pattern of which showed no traces of aluminum. A comparison of the Debye-Scherrer pattern of our sample with the data published by Kaufmann and Gordon1 showed that it is identical with the Al-rich phase which they reported. Single crystals were obtained by cooling the melt more slowly (about 50°C per hr). After reaction with sodium hydroxide, the crystals appeared as small black needles attached to the ingot surface. Cell Size, Space Group, and Uranium Positions A series of Weissenberg photographs for rotation about two of the crystallographic axes, taken with copper radiation filtered through nickel foil, revealed an orthorhombic cell of dimensions: a = 4.41 ± 0.02A b = 6.27 ± 0.02A c = 13.71 ± 0.03A Reflections of the type hkl were observed only if: h + k + I = 2n, of the type hkO only if: h = 2n and k = 2n, of the type h01 only if: h + 1 = 2n, and of the type Okl only if: k + 1=2n. Hence, the cell is body-centered with an 001 glide plane. The evidence for the existence of the glide plane is the observed extinction of 23 possible re- flections of the type hkO with at least one index odd. There are only two space groups consistent with these data: C"" — I2ma and D28 2h — Imma.³ he possible sets of atomic positions for these space groups are: 12ma: (0 0 0; ½ ½ ½) + 4: (a) x 0 %; x % % (b) x ¼ z; x ¾ Z 8: (c) x y z; x y z; x, ½ + y, Z x, M - y, z Imma: (0 0 0; ½ ½ ½) + 4: (a) 0 0 0; 0 ½ 0 (b) 0 0 ½; 0 ½ ½ (c) ¼ ¼ ¼; ¾ ¼ ¼ (d) ¼ ¾ ¾ ; ¾ ¾ % (e) 0 ¾ Z; 0 ¾ z 8: (f) x 0 0; x 0 0; x 1/2 0; x ½ 0 (g) ¼ Y ¼; ¾ Y ¾; ¾ y ¼; 1 y ¼ (h) 0 y z; 0; ;; 0, ½ + y, z; 0, l/2 - Y, Z (i) x 1/4 z; x ¾ z; ¼ z; x ¾ z 16: (j) xy z; x y z; x y z; x y z; x, ½ + y, Z; x,½ - y, z; x, ½ - y, z; 11 1, + y,Z Though density measurements on different samples were found to vary somewhat, they were all within the range 5.7 * 0.3 g per cu cm. If it is assumed that the unit cell contains four formula weights of UAl,, it is 6.5 g per cu cm. If there were as many as eight uranium atoms per unit cell, the

Jan 1, 1952

By Max W. Bowen, A. J. Weinig

The important part that dissolved oxygen plays in the cyanide treatment of gold and silver ores is commonly recognized by most metallurgists and mill men. But heretofore there has been no simple method on which the mill man could rely for determining the amount of oxygen in the various mill solutions. A few methods are adaptable to the laboratory, such as the gasometric1 determination by actually measuring the oxygen, Winkler's2 iodometric method, and Schutzenberger's3 method, which depends on the reducing action of sodium hyposulfite on a blue solution of indigo carmine; but these are not readily adaptable to the needs of the mill man and cannot be applied to cyanide solutions without modification. The gasometric method is the most accurate but it takes too long to complete a determination. White's4 method (a colorimetric method that depends on the degree of coloration imparted to a solution of pyro-gallic acid in the presence of caustic soda) although much more rapid than any of the methods named, often gives misleading results on account of grading of colors of different solutions, which nearly always contain various kinds of salts. The method herein described was devised for the use of the mill man, the aim being to develop a simple, practical, accurate method. It is a modification of the Schutzenberger method and depends on the reducing

Jan 1, 1925

(Under this heading will he published notes sent too the Secretary of the Institute by members or other persons introduced by members.) Management or superintendency desired by member, graduate mining engineer of large practical experience in the details of mining, milling, concentration and cyaniding. Experienced in the efficient mechanical equipment and operation, and in the general business management of a mining property. No. 444. Metallurgist and operator who has specialized in the hydrometallurgy of. gold and silver, particularly stamp milling and cyaniding, desires change from present position. Ten years' experience in Western U. S. Thirty-six years old, married, in best of health and will go. anywhere. Available in 30 days. No. 445.

Jan 4, 1918

By R. D. Vaughn

The limiting cases of non- Newtonian fluids flowing inside a concentric annular duct are developed without using a model of the fluid behavior. The solutions provide limits with which to test the various models of fluid behavior such as the power law and Bingham plastic models. The results of previous theoretical work are discussed in terms of limiting cases. This limiting case study also shows that experimental work on flow of non-Newtonian fluids in annular ducts should be confined to ducts for which the ratio of the radius of the inner wall to that of the outer wall is less than 0.3 and preferably less than 0.2. INTRODUCTION During the last 10 years the problem of laminar flow of non-Newtonian fluids in concentric annuli has received much attention large1y because of its application to the hydrodynamics of the wellbore. Recently solutions utilizing the power law1,2 and Bingham plasticl,3,4 models have been published. In this paper the method of limiting cases, which has been successfully applied to laminar-flow heat transfer516 will be applied to the problem of flow of non-time dependent, non-Newtonian fluids through annuli. This method permits solutions for the limiting cases to be made without using a model of unknown validity. The solutions, therefore, provide limits with which to test the various models which have been or will be proposed. A pertinent conclusion concerning the region of experimental work is also provided. DEVELOPMENT OF LIMITING CASES The limiting cases for the axial flow of fluids in concentric annuli may be defined with reference to Fig. 1. It is possible to define two limiting cases which pertain to the physical dimensions of the annulus. First, the annulus must degenerate to a circular pipe as the radius of the inner wall decreases or, as k = (k R/R) ? 0. Second, the annulus must approach the limit of parallel plates of infinite extent as the spacing between the inner and outer tubes becomes small in comparison with the radius R of the annulus, or as k?1. It is also possible to ascertain three limiting cases which pertain to fluid behavior. With reference to Fig. 2, as a fluid becomes progressively more pseudoplastic, the shear stress-shear rate relationship progressively approaches the indicated horizontal line more closely. At this limit the shear stress becomes independent of the shear rate. At the other extreme of increasingly dilatant behavior, the vertical asymptote is approached. Intermediate between these two limiting cases lies the case of the Newtonian fluid. Fluids which exhibit a yield shear stress also approach the limiting case of "infinite" pseudoplastic behavior. The remainder of the theoretical development is concerned with the description of and the solutions

By G. Thodos, D. E. Matschke

Cansiderable time and effort frequently are expended to establish, with a degree of confidence, the PVT behavior of pure substances. In particular, a great deal of experimental information contributed by a number of investigators is available in the literature. The data of each investigator, although significant in themselves, cannot be used with a high degree of confidence until they are compared with the continuum of information presented by others. Current interest in thermodynamic and transport properties, for not only the gaseous state but the con-densed state as well, requires that PVT infarmation be presented for both regions. The density dependence on temperature and pressure, when presented as a continuum, is of considerable value in itself, especially since the available equations of state fail to properly account for the PVT behavior in the condensed state. For this reason and to incorporate PVT data recently presented in the literature, this investigation was carried out. In their studies concerned with the thermodynamic properties of methane, Matthews and Hurd in 1946 utilized the data of Kvalnes and Gaddy and Olds, Reamer, Sage and Lacey to establish the PVT behavim of methane in the superheated region and the saturated liquid densities of Keyes, Taylor and Smithl in conjunction with the Clapeyron equation to develop the densities for the saturated envelope. Current activity sponsored by API Project No. 44 under the direction of F. D. Rossini has led to a tabular presentation of compressibility factors for gaseous methane in the superheated region.la These values were obtained by using smoothed residuals, developed from experimental data and the Ben edict-Webb-Rubin equation,' to establish internally consistent compressibility factors for the real gas. This approach offers probably the most precise presentation of PVT information for gaseous methane to date. The PVT behavior of methane also can be represented accurately by equations of state such as the Benedict-Webb-Rubin equation or the Martin-Hoa equation.' These equations, although valuable for analytically representing the PVT behavior, lack precision in the compressed-liquid region. The PVT data available in the literature for methane were utilized to obtain reduced densities that are presented in Figs. 1 and 2 as functions of reduced temperature with parameters of reduced pressure. The critical constants utilized for methane are those reported by Kobe and Lynn." These critical values, T, = 191.1°K, PC = 45.8 atm and p, = 0.162 gm/cc, produce a critical compressibility factor, z, = 0.289. The PVT information, as obtained from the literature, in many instances was not presented in an immediately

By Raja P. Upadhyay

An evaluation of the economics of mining the deep, thick oil shale deposits of the central portion of the Piceance Creek basin, Colorado, U.S.A. is presented in this paper. For the analysis, a modified large scale underground mining system developed by Cameron Engineers, Inc. and the Gas Combustion retorting process developed by the U.S. Bureau of Mines were used to determine capital investment and annual operating costs. A modified risk analysis computer program was then used to calculate DCFROI’s for various grades of oil shale and selling prices of partially refined shale oil. Sensitivity analyses were performed to quantify the affect of bonus bid payments, operating costs, capital investment, and all costs on DCFROI. In addition, a probabilistic evaluation was made to determine the risk involved in obtaining desired rates of return. Results of the economic evaluation indicate that for current selling prices of crude oil a high risk is involved in obtaining a DCFROI of 15%, unless only higher grades of oil shale are mined. However, mining only the higher grade oil shales, 125 l/mt (30 gpt) and above, would effectively reduce the potentially mineable resources by 90%. Risk can also be reduced through higher selling prices of shale oil. Sensitivity analyses indicate that the capital investment has a three times greater effect on required selling price than total operating costs.

Jan 1, 1977

By Joseph W. Leonard

The purpose of this paper is to review and discuss some of the less evident and sometimes neglected opportunities for progressive developments in coal research. While a great deal of both promotional and technical information flows from some areas of coal research, output deficiencies in other areas of activity have reached a magnitude where important developments have been, and will increasingly be, unfavorably affected. These areas mainly involve coal mining and preparation. Some recommendations for the intensification of effort in these areas follow: Coal Mining While a huge tonnage of in-the-ground coal is assured, the location and distribution of these tonnages are becoming less favorable. The easy-to-mine coal which is located in or near population centers has been, or is being, mined. The vigor with which the less accessible reserves are recovered by the mining industry depends largely on the condition of the coal market at the time of mining. Hence, during a buyer's market, the commercially oriented mining industry is compelled to mine the easier and less costly reserves. Conversely, during a seller's market, the need to rapidly expand production results in more difficult mining and higher cost coal as few obstacles are encountered in finding markets. Hence, a seller's market tends to enhance the recovery of reserves while a buyer's market does not. One reason for today's fuel supply problems is that the Nation has recently emerged from a long-term coal buyer's market which lasted from about 1950 to 1968. During that period, national policy caused severe production cutbacks which regretably drove the industry to mining only the more accessible and better quality reserves. Often in order to remain in business, many hundreds of millions of tons of more difficult to mine reserves were abandoned and lost behind caved areas. Many of these reserves are close to population areas and would not have been lost in a more stable economic climate. It is difficult to fully account for all the impacts that were caused by the great buyer's market of the 1950s and 1960s. Besides the obvious loss of reserves that were once considered national wealth, the mining of better reserves tended to produce a generation of technically optimistic mining people. Mining people frequently became accustomed to looking at nothing less than outstanding mining conditions as a result of the declining market. Many are now and have long since received a re-education in the other half of mining. Going from many years of mining accessible, select and easy-to-win reserves, to the crash-driving of development entries in reserves that were considered unworthy of mining during 50s and 60s, frequently results in a much higher rate of encounter with in-seam and out-of-seam rock as well as with coal-deficient areas or "washouts." Intensive entry driving activity and compulsory non-selective mining in sometimes lean reserves were brought on by the need to rapidly open up new supplies of coal. Working under these requirements presents a continuing reminder that much more needs to be known about the relatively esoteric art of planning the best direction for driving entries in order to insure that a more consistent and greater supply of coal is available during early mine development. All of the preceding discussion tends to point to a need for a better estimate of those reserves of coal that are likely to be mined in the future. Such estimates should not be limited to the compilation of the amount of coal in the ground; but, where possible, should also include information concerning the capability for producing this coal. After all, a coal seam of ample thickness may have a degree of thickness variability, undulation, bad roof or floor, so as to make what would otherwise appear to be an attractive mining condition untenable. Underlying the problem involving the feasibility of producing known reserves is the need to develop better methods for the characterization of coal seams and associated lithotypes, based on drill core data, once at area is selected for mining. Reserves and their characterization involve aspects of exploration technology that are frequently considered mature. The resulting technological deficiencies may be the main reason why coal exploration frequently does not end with core drilling of a property, as it should, but extends into the mining operation during the driving of development entries. When exploration is extended to the driving of development entries, the near absence of integrated decision-making theory involving mining, geology, mathematics, and economics becomes, once again, all too painfully apparent and frequently results in very costly rationalizations. Hence, by the formal initiation of a concentrated program to combine the cyclical effects of economics with geology and mining, more relevant estimates of reserve distribution, tonnages, and production capability should be forthcoming. Moreover, a similar formal effort is needed to develop a combination of the most advanced concepts of mathematics, geology, and mining to better "see" coal seams as a means to favorably implement many long-range decisions involving mine safety and productivity. Much more applied research needs to be done on coal mining systems for mining in thin seams and/or under bad roof. Current difficulties in both of these areas at recently opened coal mines should provide a sobering glimpse into the future. Full-scale applied research, sponsored by appropriate federal agencies, is urgently needed on a scheme involving a new combination of established mining and preparation elements. The scheme may include: (1) a continuous mining machine remotely operated by a miner stationed at some distance behind the machine using a cord attached control box; (2) hydraulic transport of coal through pipes from the mining machine to a coarse refuse removal grid, crusher, and then on to portable concentrating equipment; (3) the hydraulic transport of clean coal out of the mine in pipes to the surface for thermal dewatering, if neces-

Jan 1, 1974

The election of the following officers of the Council for the fiscal year 1919-1920, was confirmed by the Council on June 12th, 1919. President, S. E. Doane; vice-president, Wm. J. Clark; general secretary, Clarence L. Law; treasurer, L. B. Marks; directors, E. C. Crittenden, F. E. Cady, R. B. Ely. The membership of the Council for 1919-1920 will therefore be as follows: S. E. Doane, G. H. Stickney, George A. Hoadley, Wm. J. Clark, H. A. Horror, Otis L. Johnson, H. K. Morrison, Clarence L. Law, L. B. Marks, Adolph Hertz, S. C. Roger, P. S. Young, John C. D. Clark, Evan J. Edwards, James J. Kirk, E. C. Crittenden, F. E. Cady, R. B. Ely.

Jan 7, 1919

Truman H. Aldrich '78 Andrew S. McCreath '75 W. S. Ayres '73 Walter McDermott '74 A. A. Blair '75 Philip N. Moore '74 Walter M. Brodie '72 Henry S. Munroe '72 H. M. Chance '74 James Wilson Neill '79 Frederick G. Corning '77 I. P. Pardee '73 Henry S. Drinker Founder Edward C. Potter '79 Ernest F. Eurich '74 Alexandre Pourcel '77 W. E. C. Eustis '76 William H. Radford '76 A. Heckscher '79 Robert H. Richards '75 Henry D. Hibbard '79 Albert F. Schneider '74 Julian Kennedy '79 Porter W. Shimer '79 William St. George Kent '72 John Stevenson, Jr '76 Frank Lyman '77 Arthur Thacher '76 John Markle '79 Edward H. Williams '76 Samuel Mather '79 Thomas D. Wood '79

Jan 1, 1929

By A. F. van Everdingen

The pressure drop in a well per unit rate of flow is conrolled by the resistance of the formation, the viscosity of the fluid. and the additional resistance concentrated around the well bore resulting from the drilling and completion technique employed and, perhaps, from the production practices used. The pressure drop caused by this additional resistance is defined in this paper as the skin effect. denoted by the symbol S. This skin effect considerably detracts from a well's capacity to produce. Methods are given to determine quantitatively (a) the value of S, (b) the final build-up pressure, and (c) the product of average permeability times the thickness of the producing formation. INTRODUCTION Equations which relate the pressure in a well producing from a homogeneous formation with pressures existing at various distances around the well are generally used within the industry. The relation ii quite simple when the fluid flowing is assumed to be incompressible. It becomes somewhat more complicated when the flowing fluid is considered compressible so that the duration of the flow can he considered. In each case the major portion of the pressure drop occurs close to the well bore. However analyses of pressure build-up curves indicate that the pressure drop in the vicinity of the well bore is greater than that computed from these equations using the known, physical characteristics of the formation and the fluids. In order to explain there excessive drops it is necessary to assume that permeability of the formation at and near the well bore is substantially reduced as a result of drilling. completion and, perhaps. production practice. This possibility has been recognized in the literature. A method to compute the pressure drop due to a reduction of the permeability of the formation near the well bore. which is designated as the skin effect. S, is given in the following paragraphs. To start, equations normally used to describe flow in the vicinity of a well are given without considering this effect. These equations then are modified to include the effect of a skin on the pressure behavior. Finally a method is given to estimate the effect of the skin on the pressure and production behavior of a well. PRESSURE EQUATIONS Incompressible Fluid Flow If p is defined as the flowing pressure in a well of radius the pressure at distance r from the well has been shown to be:" The total pressure drop between the drainage boundary, and the well bore is given by These equations are valid only if the flow towards the well occurs in a horizontal homogeneous medium and the fluids are incompressible. The assumptions imply that all fluid taken from the well enters the system at r a condition rarely encountered in practice. Compressible Fluid Flow, Steady State A more realistic equation is obtained if it is assumed that the compressibility, c, of the flowing fluids is small and has a constant value over the pressure range encountered. After the well has been producing for some time so that its rate has become constant and steady state is reached, the pressures throughout the drainage area are falling by the same amount per unit of time, and the pressure differences between a point in the drainage area and the well are constant. When these conditions are met. the rate of production, q, from a well is equal to where dp/dt is the pressure drop per unit time. The fluid flowing at a distance from the center of the well is equal to From the last equation and from Darcy's law it can be shown that The equation holds for a depletion-type reservoir of radius drained by a well located in its center, provided the compressibility of the fluid per unit pressure drop is small and constant, and no fluid moves across the boundary Compressible Fluid Flow — Nonsteady State Table 111 of reference (5) shows the relationship between the pressure at the well bore and the reduced time, The pressure-drop function, p represents the drop below the original reservoir pressure, p caused by unit rate of production for several values of R, the ratio of drainage boundary radius to well radius, r In most reservoirs the values of approach infinity. and under these conditions the values of p shown in Table I of reference (5) can be used where p then signifies the difference between the pressure in the well and the prevailing reservoir pressure per unit rate of flow. The total pressure drop below prevailing reservoir pressure amounts to where the factor converts the cumulative pressure drop per unit rate of production to cumulative pressure drop for actual rate. q. For values of T > 100 the P function may be written (equation VI-15 of reference 5) as Using the time conversion the difference in pressure between reservoir and well becomes If values for the physical constants of the formation and the fluids are inserted, it is found that T exceeds 100 after a few seconds of production (or closed-in time), so that the approximation becomes valid almost at once. A simple relation between the pressure in the well and in the reservoir can also be derived by considering the well as a point source"" '" instead of a unit circle source, that is, by using Lord Kelvin's solution instead of the unit circle source

Jan 1, 1953

Jan 1, 1962