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By William E. Ford, Edward Salisbury Dana

The monoclinic Wolframite Group and the tetragonal Scheelite Group are included here. Wolframite Group WoIframite (Fe,Mn)W04 a : b : c = 0.8300 : 1 : 0.8678 B = 89' 22' Hiibnerite MnW04 048362 : 1 : 0.8668 89' 73' WOLFRAMITE. Monoclinic. Axes a : b : c = 0.8300 : 1 : 0.8678; B = 89' 22'. mm"', 110 A 1TO = 79" 23'. ay', 100 A 101 = 62' 54' at, 100 A 102 = 61" 54'. $', 011 A 011 = 81" 54'. Twins: (1) tw. axis c with a (100) as comp.-face; (2) tw. pl. k (023), Fig. 449, p. 171. Crystals commonly tabular (1 a (100); also prismatic. Faces in prismatic zone vertically striated. Often bladed, lamellar, coarse divergent columnar, granular. Cleavage: b (010) very perfect; also parting (1 a (100), and 11 t (102). Fract,ure uneven. Brittle. H. = 5-5.5. G. = 7.2-7.5. Luster submetallic. Color dark

Jan 1, 1922

By Harry W. Brown

This paper presents results of static capillary pressure measprements made both by the restored-state and by the mercury-injection methods, and of dynamic capillary pressure measurements made by the Hassler technique. The results indicate a variation from sample to sample of the factor used to convert capillary pressure obtained by mercury injection to those applicable to a water-gas system. Static capillary pressures measured by the restored-state method were found to be in close agreement with dynamic capillary pressures, indicating that data obtained from static measurements may be utilized with confidenre in the solution of dynamic problems of fluid flow. Experimental data are presented on the use of "J-curves" for the correlation of capillary pressure-saturation relations for a number of cores from a particular geologic formation. It is shown that the correlation was improved in some cases by reqtricting it to rertain lithologic classifications. INTRODUCTION The Meaning and Importance of Capillary Pressure The coexistence of two or more immiscible fluids within the voids of a porous medium, such as reservoir rock, gives rise to capillary forces. Because of the interfacial tension existing at the boundary between two immiscible fluids in a pore space, the interface is curved, and there is a pressure difference across the interface. This pressure difference is termed the capillary pressure. The magnitude of the capillary pressure between two immiscible fluids which together fill a porous medium depends upon several factors: the textural properties of the medium, the wettability of the medium, the interfacial tension between the fluids, the respective saturations of the fluids, and the manner in which these saturations are attained. For a given pair of immiscible fluids in a particular sample of reservoir rock, the capillary pressure is a unique function of the fluid saturation, provided that the saturation of the fluid which wets the rock has previously been decreased unidirectionally from an initially complete saturation. Similarly, for a given pair of fluids at a particular saturation which has been achieved by a

Jan 1, 1951

By Harry W. Brown

This paper presents results of static capillary pressure measprements made both by the restored-state and by the mercury-injection methods, and of dynamic capillary pressure measurements made by the Hassler technique. The results indicate a variation from sample to sample of the factor used to convert capillary pressure obtained by mercury injection to those applicable to a water-gas system. Static capillary pressures measured by the restored-state method were found to be in close agreement with dynamic capillary pressures, indicating that data obtained from static measurements may be utilized with confidenre in the solution of dynamic problems of fluid flow. Experimental data are presented on the use of "J-curves" for the correlation of capillary pressure-saturation relations for a number of cores from a particular geologic formation. It is shown that the correlation was improved in some cases by reqtricting it to rertain lithologic classifications. INTRODUCTION The Meaning and Importance of Capillary Pressure The coexistence of two or more immiscible fluids within the voids of a porous medium, such as reservoir rock, gives rise to capillary forces. Because of the interfacial tension existing at the boundary between two immiscible fluids in a pore space, the interface is curved, and there is a pressure difference across the interface. This pressure difference is termed the capillary pressure. The magnitude of the capillary pressure between two immiscible fluids which together fill a porous medium depends upon several factors: the textural properties of the medium, the wettability of the medium, the interfacial tension between the fluids, the respective saturations of the fluids, and the manner in which these saturations are attained. For a given pair of immiscible fluids in a particular sample of reservoir rock, the capillary pressure is a unique function of the fluid saturation, provided that the saturation of the fluid which wets the rock has previously been decreased unidirectionally from an initially complete saturation. Similarly, for a given pair of fluids at a particular saturation which has been achieved by a

Jan 1, 1951

A severely technical article, however well written, can not be an agreeable form of literature. It suffers from the defects of its qualities. One defect is a congestion of language, due to a multiplicity of adjectival nouns. The sentences are packed with words of unpleasing sound, charged with complex ideas, crowding one another so closely that the phraseology moves like an ice-pack in Bering Sea or a log-drive in a river; the undercurrent of meaning may continue to move, but the surface is obstructed. This verbal congestion is made evident by ugly compoundings, many of which are adopted by the technical writer in the mistaken belief that they give directness to his statements. For example: A unanimously approved scheme "A scheme unanimously approved " The continuous temperature record "The continuous record of temperature " To stimulate interest in synthetic plant construction "To stimulate interest in the construction of synthetic plants " In smelters reverberatory-furnace firing with powdered coal has been practised for a decade. "In smelting, the firing of reverberatory furnaces with powdered coal has been practised for a decade." A tar consumption of one pound per ton "A consumption of tar at the rate of one pound per ton " A mechanical ventilating system

Jan 1, 1931

By M. J. Duggin

Evidence is produced below to show that the carbide "Mn,C," reported by Kw,and ersson' is really a mixture of two carbides. One is an Fe-Mn carbide which is probably isomorphous with hexagonal Mn15C4, reported by Bouchand and Pruchart.' The othev is a tetragonul Fe-Mn carbide with cell dzmensions close to those reported previously by the author3 for an Fe0.1Mno. carbide. IN a recent investigation several Fe-Mn carbide specimens, each weighing about 5 g, were prepared in a manner previously reported.3 Debye-Scherrer X-ray photographs were taken of at least two samples from different parts of each specimen using a 114.6-mm-diam camera. The exposure time was 2 hr using filtered chromium radiation, a tube voltage of 35 kv and a tube current of 10 ma. In the case of one specimen, which contained nominal weight percentages of iron, manganese, and carbon of 9.40, 84. 6,, and 6.0, respectively, duplicate chemical analyses indicated f1.2 and 5.5 wt pct C to be present in the two samples taken of the specimen: no graphitic carbon was detected. One powder-diffraction pattern of this specimen indicated the presence of the tetragons: carbide reported earlier,3 (a = 6.772A, c = 9.427A), plus cementite (O), plus an unknown structure. The second powder-

Jan 1, 1970

By P. de Vitry, Willis P. Mould

The wire saw is a tool not less than 60 years old, probably nearer 100 years old. It was developed in Europe and is reputed to have originated in Belgium. Frombold is said to be the original patentee. Wire sawing equipment, as indicated in Fig. I, is very simple. It consists of a three-strand wire cable, usually pis or 1/4 in. in diameter, or a single flat ribbon of medium hard, tough, alloy steel twisted into a helix of those diameters, made to form an endless belt of any length up to several thousand feet. The wire is guided into the cut by sheaves mounted in slides on steel columns situated close to either end of the cut. The feed motion usually is controlled either by gravity or by hand-operated feed screws. The steel columns or "standards" range from 15 to 30 ft. in length. At the top is a swiveled arm supporting a sheave similar to the traveling sheave below. Immediately under the swivel-mounted sheave is a guy plate or collar with shackles attaching four chain or wire-rope guys with suitable tightening devices, or with two guys and two jack legs for supporting the standard vertically or at any desired anale. The usual drive is by a 10-hp. motor through a gear reducer, on which are Insti- two grooved sheaves, One of which is keyed and the other free running On the shaft. Tension is provided by a car running on a track in line with the driving sheave

Jan 1, 1948

By P. de Vitry, Willis P. Mould

The wire saw is a tool not less than 60 years old, probably nearer 100 years old. It was developed in Europe and is reputed to have originated in Belgium. Frombold is said to be the original patentee. Wire sawing equipment, as indicated in Fig. I, is very simple. It consists of a three-strand wire cable, usually pis or 1/4 in. in diameter, or a single flat ribbon of medium hard, tough, alloy steel twisted into a helix of those diameters, made to form an endless belt of any length up to several thousand feet. The wire is guided into the cut by sheaves mounted in slides on steel columns situated close to either end of the cut. The feed motion usually is controlled either by gravity or by hand-operated feed screws. The steel columns or "standards" range from 15 to 30 ft. in length. At the top is a swiveled arm supporting a sheave similar to the traveling sheave below. Immediately under the swivel-mounted sheave is a guy plate or collar with shackles attaching four chain or wire-rope guys with suitable tightening devices, or with two guys and two jack legs for supporting the standard vertically or at any desired anale. The usual drive is by a 10-hp. motor through a gear reducer, on which are Insti- two grooved sheaves, One of which is keyed and the other free running On the shaft. Tension is provided by a car running on a track in line with the driving sheave

Jan 1, 1948

By Louis Huber

DESPITE the fact that centrifugal fans were first developed for ventilating mines and that artificial ventilation was first practiced in mines, the lack of knowledge of mining men on mine ventilation in general, and on fan performances and characteristics in particular, is very much in evidence today. While it is true that mines are much better ventilated now than they were 20 to 30 years ago, we have made very little progress in the study of mine ventilation, or in mine ventilating fan design. Today the average mine operator is woefully dependent on the engineers of mine fan manufacturers when he is in the market for a fan, and this situation works to the disadvantage of both the operator and the manufacturer. The former may be imposed upon by an unscrupulous sales engineer and induced to buy a fan which is not the proper one for the mine; when it is operating it may be wasteful of power and even accessory to a serious mine disaster. More often, however, it is the fan manufacturer who is imposed on. If the operator asks the manufacturer to build for him a fan that will deliver a certain quantity of air against a certain specified pressure and requiring a specified number of horse power when operating under these conditions, the manufacturer may build a fan that will comply with these specifications to the letter. When the fan is installed it is frequently found that it is delivering a greater quantity of air against a lesser pressure or a lesser quantity of air against a greater pressure, and is requiring more horse power than specified in the first case and less than that specified in the second. In either case the operator usually upbraids the manufacturer for not meeting specifications, and refuses to pay for the fan. The trouble in either case outlined above is that the pressure necessary to force the specified quantity of air through the mine has been estimated incorrectly by the operator or his engineers. When a fan is designed and built to deliver a certain quantity of air against a certain specified resistance it will operate at its maximum efficiency only when it is operating under

Jan 2, 1926

By E. H. Rose

The question is often pondered whether the flotation process is still an art or has become a science. The fact is that flotation is a science in so many variables that only art can blend them. It is demonstrable that no less than one hundred variables are involved in any flotation operation, most of them immeasurable on a routine basis. The behavior of every one of them is always governed by orderly and unchanging law, as no man can doubt. There is nothing truly indefinite about that behavior; the only indefiniteness is in our knowledge of it, either in general or from hour to hour in the circuit. In dealing with a simultaneous equation in, say, one hundred variables, all not only affecting the outcome to some degree but many influencing each other as well, it is small wonder that the mineral-dressing profession presents a case history of debate and controversial opinion. The statement of the subject of this symposium—a symposium on flotation machines—seems to delimit and define the matters to be considered and at least the general nature of the conclusions sought. Nevertheless, in such a meeting it is not possible to meditate upon all the variables that do in one way or another affect performance of flotation machines. To attempt it would be much like trying to operate a hundred-ring circus. Perverse variables being what they are, one could expect the elephant in ring 36 to squirt a trunkful of water at the tightrope performer in ring 37 to ruin that artist's act, just as our learning to depress pyrite in the early 1920's ruined the act of the formerly faithful old Callows. Honest Disagreements Selective flotation dates from 1922 or 1923, when several plants established their regular flotation operations on a selective basis. Since then, two decades of efforr have gone into the development of better and better flotation machines. Many have come and gone. The competition has simmered down to perhaps a dozen machines, each one of which is staunchly defended by some operators as being the best for their particular jobs, and as scornfully dismissed by at least a few others elsewhere as being positively the poorest for theirs. These disagreements are honest disagreements, honestly arrived at after plenty of sweat. In many a flotation plant, one machine has been tried out against another under conditions as fair as they could possibly be made. Sometimes the results are on a par but more often one machine shows a consistent and unmistakable margin of superiority over the other. In equally honest and enlightened tests, machine A may win over machine B in one place, and machine B over machine A by as great a margin in another. This paper purposes to identify some of the more prominent reasons why this is so,

Jan 1, 1947

By E. H. Rose

The question is often pondered whether the flotation process is still an art or has become a science. The fact is that flotation is a science in so many variables that only art can blend them. It is demonstrable that no less than one hundred variables are involved in any flotation operation, most of them immeasurable on a routine basis. The behavior of every one of them is always governed by orderly and unchanging law, as no man can doubt. There is nothing truly indefinite about that behavior; the only indefiniteness is in our knowledge of it, either in general or from hour to hour in the circuit. In dealing with a simultaneous equation in, say, one hundred variables, all not only affecting the outcome to some degree but many influencing each other as well, it is small wonder that the mineral-dressing profession presents a case history of debate and controversial opinion. The statement of the subject of this symposium—a symposium on flotation machines—seems to delimit and define the matters to be considered and at least the general nature of the conclusions sought. Nevertheless, in such a meeting it is not possible to meditate upon all the variables that do in one way or another affect performance of flotation machines. To attempt it would be much like trying to operate a hundred-ring circus. Perverse variables being what they are, one could expect the elephant in ring 36 to squirt a trunkful of water at the tightrope performer in ring 37 to ruin that artist's act, just as our learning to depress pyrite in the early 1920's ruined the act of the formerly faithful old Callows. Honest Disagreements Selective flotation dates from 1922 or 1923, when several plants established their regular flotation operations on a selective basis. Since then, two decades of efforr have gone into the development of better and better flotation machines. Many have come and gone. The competition has simmered down to perhaps a dozen machines, each one of which is staunchly defended by some operators as being the best for their particular jobs, and as scornfully dismissed by at least a few others elsewhere as being positively the poorest for theirs. These disagreements are honest disagreements, honestly arrived at after plenty of sweat. In many a flotation plant, one machine has been tried out against another under conditions as fair as they could possibly be made. Sometimes the results are on a par but more often one machine shows a consistent and unmistakable margin of superiority over the other. In equally honest and enlightened tests, machine A may win over machine B in one place, and machine B over machine A by as great a margin in another. This paper purposes to identify some of the more prominent reasons why this is so,

Jan 1, 1947

By G. H. Tausch, J. R. Dublin, T. A. Huber

Simplified equipment and techniques have been developed to permit cementing a completion interval in a well and recompleting higher, lower, or at the same depth in such a manner as to: 1. Eliminate the need for a conventional drilling or workover rig. 2. Eliminate mud and other cement contaminants which have long interferred with ideal cementing. 3. Eliminate need for drilling out cement. 4. Provide a more satisfactory recompletion. 5. Provide a more economical recompletion. This technique involves the use of a small-diameter, lightweight, tubing extension which is run on a wireline and set in a landing nipple previously installed in the tubing string. Low squeeze pressure and small cement volumes, with their attendant cost reduction, are successfully used when wells are completed and reworked with salt water or other penetrating fluids. Relatively low-water-loss cement is an integral component of the technique which provides that excess cement be reverse-circulated from the well to leave the casing void of cement when recompleting lower or in the same interval. Substantial cost reductions are realized by using the simplified or low-pressure cementing technique, and the ratio of successful squeeze-cement operations has been increased. Squeeze-cementing or recementing is the act of filling a channel behind casing or filling holes purposely placed in the casing. To obtain a satisfactory squeeze-cement job, it is necessary only to fill the channel or the perforation holes with a cement filter cake and to allow it to harden in that position. In the past, the presence of mud in a well has been considered the chief deterrent to obtaining a good cement bond and satisfactory cement job; however, late developments in squeeze-cementing have made it possible to eliminate cement contamination or interference. Since it is possible to form a cement filter cake with a small pressure differential, squeeze-cementing with high pressures may not be necessary in most cases. The amount of cement needed to fill the annulus about the casing and even to fill part of the casing, if necessary, is generally small in quantity. Use of low squeeze-cementing pressures and small quantities of cement provides the following advantages: 1. Longer effective life of well tubing, casing, and other equipment; and less chance of costly equipment failure due to excessive pressure. 2. Monetary savings effected by elimination of retainers and specal squeeze-cementing tools. 3. Monetary savings effected by use of small quantities of cement and fewer squeeze-cementing operations. 4. Future surface squeeze-cementing equipment may be smaller and more economical to operate and maintain.

Jan 1, 1955

By Che, C. W. Spencer, C. A. Steidel, Yu Li

Grain boundary grooving as it occurs in a 5.5-deg simple-tilt nickel bicrystal immersed in a saturated Ni-S liquid has been studied. A 1/3 (t= time) dependence for the depth of the groove indicates that the rate -controlling meckanism for groove developvnent is volume diffusion in the liquid. The activation energy for the diffusive process is estimated at 15 kcal per mole. Using an extended form of W. W. Mullins&apos; analysis for grooving reactions, a computer is employed to fit the appropriate diffusion equation by a numerical method. From the analysis a possible method of measuring L.S. the solid-liquid interfacial tension is demonstrated. WHEN a polycrystalline solid is heated in equilibrium with a saturated fluid phase, grooves will form at the intersections of the grain boundaries and surface. The equilibrium root angle of these grooves is determined by the balance between the grain boundary and solid-fluid interfacial tensions. The grooves deepen and widen with time due to a difference in chemical potential between the flat interface and the curved interface of the groove. In this investigation solid-liquid interaction at a grain boundary is studied, with the object to determine the mechanism of grain boundary grooving in the presence of a saturated liquid. Extension of Mullin analysis then permits the estimation of the solid-liquid interfacial tension. Herring has demonstrated by dimensional analysis that the quasi-steady state change of the dimensions of a small particle during sintering is proportional flow, evaporation-condensation, volume-diffusion, and surface-diffusion mechanisms, respectively, if geometric similarity of consecutive configurations of the particles holds. Mullins has extended this analysis to grain boundary grooving. In the case of shallow grooves he solves the diffusion equations for evaporation-condensation, volume-diffusion, and surface-diffusion mechanisms, and obtains the same time dependence for any linear dimension of a groove as Herring found for the change in dimension of small particles. In Mullins&apos; analysis2&apos;3 grain boundary grooving of a bicrystal by volume diffusion in the presence of a saturated fluid phase was considered. Several assumptions were made prior to the analysis: 1) the solid-fluid interfacial tension is independent of crystallographic orientation; 2) the Gibbs-Thompson equation relating curvature and chemical potential is applicable at the solid-fluid interface; 3) the relaxation time of the diffusion field is small compared with the time for appreciable changes in the curvature of the groove, so that the diffusion is divergence-less; and 4) the groove has a small slope relative to the initial flat interface. Usually this last condition is fulfilled only for solid-gas systems. The solution of the diffusion equation under the above conditions produces a t1/3 dependence for any linear dimension of the groove in the case where volume diffusion is rate-controlling. The t1/3 dependence is valid because geometric similarity of the grooves exists for all time. EXPERIMENT In the experiment a 5.5-deg nickel bicrystal of <100> simple-tilt orientation was used.4 Grooving was studied in the presence of a saturated Ni-S liquid alloy as a function of time at 750°, 800°, 850°, and 900°C. A low-angle bicrystal was chosen for study to insure that 2L.S. > .b., where l.s.

Jan 1, 1964

By S. K. Kawatra, R. A. Seitz

Various mathematical models and expressions to describe the behavior of a hydrocyclone have been presented in the literature (Lynch and Rao, 1977; Plitt, 1976; Plitt and Kawatra, 1977). Two of these models, by Lynch (1977) and by Plitt (1976), have been extensively used for process control studies (Kawatra and Thayer, 1879; Seitz and Kawatra, 1984). However, neither of these models relates the fineness of grind in a hydrocyclone overflow to the corrected efficiency curve of a hydrocyclone. If such a relationship were available, then one could relate fineness of grind to the operating variables using equation (1) or (2). A plant metallurgist is interested in knowing the fineness of grind rather than the dso(c) of a hydro- cyclone. As a consequence, several empirical relation- ships between fineness of grind and hydrocyclone operating variables are available. These relationships (Fewings, Wickham, and Wiseman, 1979; Manning, 1978; Watson, Cropton, and Brookes, 1970; Watts, Thompson, and White, 1978; Wiegal, 1973) have only a limited relationship with each other and have met with varying degrees of success. The object of this paper is to develop a fundamental relationship between fineness of grind and the efficiency curve of a hydro- cyclone

Jan 1, 1986

By J. T. Berling, J. B. Conway

MANY studies have been devoted to the correlation of low-cycle fatigue behavior. Several of these have also been concerned with the identification of an effective approach to the prediction of low-cycle fatigue behavior from short-term tensile data. Perhaps the first such approach was that reported by coffin1 in the form: where is the plastic strain range, Nf is the number of cycles to failure, and c is a constant characteristic of a material. In this analysis by Coffin it was reasoned that in a short-term tensile test the value of Nf could be considered as equal to a , in which case the value of c is interpreted as the tensile ductility, f, measured in such a test. If, therefore, the Coffin equation is assumed to be applicable to a given material, it is a simple matter to predict the low-cycle fatigue behavior. Once the tensile ductility is known, this point is located at Nf = 1/4 on a log-log plot of vs Nf and a line is drawn through this point with a slope of to yield a prediction for the fatigue life. Actually, while this equation is quite useful it is not generally applicable, for experiment has shown that the value of —$ does not reflect the relationship between and Nf for all materials or even for a given material over all temperature ranges. An equation similar to the Coffin equation was prepared almost simultaneously by Manson.2 This expression had the form: In this case the exponent on Nf was not assigned any particular numerical value in accord with the various values of this exponent which had been observed for different materials and at different test conditions. Because of this characteristic it will be recognized that little use can be made of this expression in predicting low-cycle fatigue results. A fairly effective expression for use in predicting fatigue behavior was proposed by Manson3 based on a study of numerous sets of experimental results. This relation (Method of Universal Slopes) makes use of modulus of elasticity, ultimate strength, and tensile ductility, and assumes an exponent on Nf equal to 0.6 in representing the plastic strain range contribution to total strain range. While this equation of Man-Son does not yield completely accurate results it must be recognized as being the best means available at

Jan 1, 1970

By C. R. Hocott

The distribution and movement of fluids in oil reservoirs are influenced to a great extent by capillary forces, which depend upon the size and shape of the pores in the reservoir rock, the surface characteristics of the rock, and the interfacial tension between the fluid phases. This paper presents the results of an investigation of the interfacial tension between salt water and crude oil containing dissolved gas under reservoir conditions. Apparatus and Procedure In the preliminary phases of this investigation, it was found that a scum formed at the oil-water interface, which made measurement of interfacial tension by either the ring or capillary rise methods unreliable. Accordingly, the drop-weight method, in which a fresh interface is continuously formed, was selected. In this method, a tip through which drops of one fluid can be expelled is immersed in a second fluid. At the instant that the drop becomes large enough to fall, the gravitational force tending to pull away the drop exactly balances the interfacial force tending to hold it. From the size of the drop, the dimensions of the tip, and the density of the two fluid phases, the interfacial tension may be calculated. The apparatus consists of a circulating pump for bringing the oil to equilibrium with gas at the desired pressure, a displacement pump for forming the drops, an interfacial tension cell in which the drops are formed, and a density cell to determine the density of the oil. The density of the water is determined separately in another apparatus. A flow diagram of the assembled equipment is shown in Fig. 1. The interfacial tension cell contains a stainless-steel dropping tip suspended from the top and extending below the surface of the oil. The tip is a cylindrical rod with a small hole in the center through which the water was forced to form the drop on the lower face. The walls of the tip were highly polished, to prevent the water on the tip from creeping up the side and increasing the effective diameter. The face of the tip, how-

Jan 1, 1939

By C. R. Hocott

The distribution and movement of fluids in oil reservoirs are influenced to a great extent by capillary forces, which depend upon the size and shape of the pores in the reservoir rock, the surface characteristics of the rock, and the interfacial tension between the fluid phases. This paper presents the results of an investigation of the interfacial tension between salt water and crude oil containing dissolved gas under reservoir conditions. Apparatus and Procedure In the preliminary phases of this investigation, it was found that a scum formed at the oil-water interface, which made measurement of interfacial tension by either the ring or capillary rise methods unreliable. Accordingly, the drop-weight method, in which a fresh interface is continuously formed, was selected. In this method, a tip through which drops of one fluid can be expelled is immersed in a second fluid. At the instant that the drop becomes large enough to fall, the gravitational force tending to pull away the drop exactly balances the interfacial force tending to hold it. From the size of the drop, the dimensions of the tip, and the density of the two fluid phases, the interfacial tension may be calculated. The apparatus consists of a circulating pump for bringing the oil to equilibrium with gas at the desired pressure, a displacement pump for forming the drops, an interfacial tension cell in which the drops are formed, and a density cell to determine the density of the oil. The density of the water is determined separately in another apparatus. A flow diagram of the assembled equipment is shown in Fig. 1. The interfacial tension cell contains a stainless-steel dropping tip suspended from the top and extending below the surface of the oil. The tip is a cylindrical rod with a small hole in the center through which the water was forced to form the drop on the lower face. The walls of the tip were highly polished, to prevent the water on the tip from creeping up the side and increasing the effective diameter. The face of the tip, how-

Jan 1, 1939

By Walter J. Karplus

By means of a finite difference expansion a fluid flow field in cylindrical coordinates with axial symmetry, is simulated by a network of electrical resistors. A series of DC analog computing units, connected to the network bounrlary corresponding to the free surface effectively adjust the network parameterr to satisfy simultaneously Laplace&apos;s equation and the borrndary conditions. The system automatica1ly "re1axes" to the correct boundary shape in a fraction of a second. A detailed application of the method to the water coning problem in oil wells is presented. INTRODUCTION The water coning problem in petroleum production is a prime example of a class of problems known as free surface problems. A free surface arises in fluid flow regions when the shape of the boundary of a single phase flow region is affected in some manner by the pressure or potential gradients within the region. When there exists an interface of two fluids of different densities, the shape of this interface will be determined by the relative velocities of the two fluids and will therefore comprise a free surface. Other free surface problems of interest to petroleum engineers include the gas coning, water injection, and gravity drainage probIcms. In each case it is desired to predict the shape of the boundary of the oil zone as a function of the flow rate, the well penetration and the physical parameters and dimensions of the system. Such problems do not lend themselves to the classical analytical treatments of boundary value problems because in this case the boundary of the potential field and the potential distribution within the field are interdependent and must be calculated simultaneously. A further difficulty arises from geometric considerations. Since the fluid flow is of the radial type in most cases, such effective methods as conformal transformation and the hodograph are not applicable. It is the purpose of this paper to present a method whereby free surface problems of this type may be solved rapidly to the desired order of accuracy by means of a combination of a network of electrical resistors and conventional analog computer units. The water coning problem is treated in some detail. Then the procedure for extending the technique to other free surface problems is indicated. FORMULATION Most commercial oil reservoirs consist of an oil-saturated sand, bounded above by an impermeable strata and below by a water-saturated sand. Gravimetric separation results in a horizontal oil-water interface. When an oil well is drilled so that it partially penetrates the oil zone, and production is initiated at a constant rate, the oil-water interface will assume a new shape as a result of the pressure gradients in the oil zone. It should be emphasized that this is a steady phenomenon. After an initial transient period the water phase will be completely static and only the oil will be in motion. The new steady-state shape of the interface, as shown in Fig. 1, depends upon the depth of penetration, d, the thickness of the oil zone, I, the production rate, q, the hydraulic permeability zone of the sand, k, the viscosity of the oil, µ, and the densities of the oil and water, p.,. and pw.. The problem is to determine this relationship. Darcy&apos;s law + = - (P f g p z).....(1) it.

Jan 1, 1957

This story of the salting of a supposed diamond mine is a part of our Western history and deserves to be recorded in this book. It was more than a local affair, because it was concerned with persons in London and New York, as well as San Francisco. Part of the story has been told by Asbury Harpending in a little book published 12 years ago. Harpending (who died at New York in 1923) was in London in March, 1872, when he received a cable dispatch from William C. Ralston, the president of the Bank of California, stating that "a vast diamond field" had been discovered "in a remote section of the United States". Before starting for San Francisco, Harpending had an interview with Baron Rothschild, who showed a lively interest in the story, which was as follows: two weather-beaten prospectors went to the Bank of California and deposited some uncut diamonds and rubies for safe keeping; these precious stones were estimated to be worth $125,000. The men said that they had found the gems in "a desert portion of the West". They departed quietly, but the story was told in business circles; whereupon George D. Roberts, a mining engineer of wide experience and an associate of Ralston, sought an interview with the prospectors. One of them proved to be a man that had been in the employ of Roberts. Both prospectors, named Slack and Arnold, appeared "coy and cautious"; they were "simpleminded fellows", and were "afraid to trust anyone with the momentous secret ". They refused to divulge the place of discovery and declined "to part with their rights", but later "they became more amenable to reason" and expressed willingness to sell a half interest to

Jan 1, 1932

By P. Rama Rao, D. H. Sastry, T. R. Anantharaman

Deformation (a) and twin (a&apos;) stacking-fault densities in cold - wor ked filings of fcc silver alloys containing 2, 4, and 6 wt pct Sb have been estimated from Debye-Scherrer peak shifts and asymmetries, respectively. Evidence has been obtained for a possible strain-induced transformation in a two-phase alloy containing 9.0 zut pct Sb. Using Fourier analysis of X-ray line profiles, the effective particle sizes and root mean square strains have been determined for the three fcc alloys in the cold-worked condition. The values of the compound fault probability 0.5a + a&apos;) evaluated from peak shifts and asymmetries are in reasonable apeement with those derived from peak broadening. COLD work of fcc metals may produce both deformation and twin (also called growth) stacking faults, which can be detected and quantitatively estimated by X-ray diffraction techniques.&apos; In addition to peak broadening, deformation faults produce a shift in peak positions and twin faults an asymmetry of the Debye-Scherrer reflections. Besides stacking faults, a reduction in the size of coherently diffracting domains and distortion within these also broaden the powder reflections of deformed fcc metals and alloys. Fourier analysis&apos; of peak shapes provides quantitative infor- mation about the effective domain sizes, lattice strains, and also the compound fault probability (1.5a + a&apos;), where a and a&apos; represent deformation-and growth-fault density, respectively. The Paterson method2 for determination of a from peak shifts, the warren3 or wagner4 method for evaluation of a&apos; from peak asymmetries, and the Fourier analysis for quantitative estimates of all the contributory causes of peak broadening have, in the course of the last decade, been extensively applied to obtain data for a number of deformed fcc metals and alloys. One of the useful results of earlier measurements of a in several solid solutions is a correlation between a and the solute valence as well as electron concentration per atom (p) in alloy systems based on a particular solvent. The work of Smallman and westmacott5 on Cu-Zn, Cu-A1, and Cu-Sn, of Foley, Cahn, and ~aynor&apos; on Cu-Si and Cu-Ge, and of Rama Rao and Anantharaman7 on Cu-Si and Cu-Sb has revealed a common trend in the increase of a with p and also a with valency of the solute. Cahn and Davies&apos; and Ad-ler and wagnerg have observed similar trends for silver alloys containing cadmium, indium, and tin. Data on a for silver alloys with a pentavalent solute element are not, however, available. It is primarily to fill this need that the present investigation on Ag-Sb alloys was undertaken. Utilizing the Patersonand Warren methods, values of a and a&apos;, respectively, have been determined in three silver alloys containing 2, 4, and 6 wt pct Sb. By Fourier analysis of the broadening of Debye-Scherrer peaks, effective particle sizes, lattice strains, and the compound fault probability (1.5a +a&apos;) have also been evaluated.

Jan 1, 1967

By Werner Goldsmith

This discussion is confined to the first section of Professor Clark&apos;s paper entitled &apos;Elastic and Nonelastic Waves&apos; and its application to wave propagation in rocks. Some published results by other investigators concerning measured decay of peak strain and variation of pulse duration with travel distance are cited, but the principal subject of this section is a detailed mathematical analysis of spherical (and, to a lesser extent, of plane) wave propagation in various homogeneous, isotropic media. The materials selected include an elastic substance, a Voigt and a &apos;modified&apos; Voigt solid-the latter incorporating the assumption of a constant loss factor (defined here as the product of frequency and the ratio of the imaginary to the real part of the shear modulus)-and a solid friction model. While other possible representations of a solid continuum model are mentioned, corresponding solutions are not presented. The pulse inputs considered comprise exponential decay, a unit step, and steady- state sinusoidal excitation: the process of conversion from one solution to another in the operational plane is indicated. The basic problem relative to the analysis of wave propagation in rocks concerns the specification of the appropriate material behavior, since the equations of motion for a given geometry of the source and medium are well established. In principle, the required information can be deduced from two types of measurement: 1) field observations of underground explosions or seismic disturbances, and 2) laboratory tests on small samples of the pertinent rock. However, in practice both types of approaches are beset with difficulties and subject to valid criticism. Field observations must be carried out under relatively uncontrolled conditions, including, in general, a lack of knowledge of the precise arrangement of the medium, stratification, faulting. inhomogeneities, etc. Specimens investigated in the laboratory can not represent the environment found

Jan 1, 1967