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By George A. Grandy, D. W. Fuerstenau

Simulation of nonlinear grinding systems is discussed in the context of the size-discretized batch-grinding model. A linear approximation of environment-dependent (or nonlinear) selection functions is postulated for systems which exhibit feed grinding orders less than unity. For this, a convex linear combination of zero and first-order selection function forms is used to obtain an analytical solution that can be used for simulation. An example in which marked nonlinear behavior occurs is rod-mill grinding. Accordingly, a series of grinding experiments was carried out in a batch laboratory rod mill to test these techniques; agreement between experiment and the model was found to be very good. Recently, significant progress has been made in the simulation of linear grinding systems by using a population balance mathematical model. Herbst and Fuer-stenaul presented a parameter estimation scheme that can be used with the size-discretized batch-grinding model, and Gumtz and Fuerstenau3 have extended these techniques to the simulation of locked-cycle grinding. Grandy et aL." summarized the simulation of linear systems and noted important alternate solutions to the batch-grinding equation. Kelsall et a1.'-" discussed the dynamic simulation of linear batch grinding, as well as linear open and closed-circuit grinding. In all of these, the key word is linear, which certainly restricts the engineer trying to simulate a variety of grinding systems. This paper discusses an approach for the simulation of non-linear grinding systems, particularly those which exhibit grinding orders less than unity. Experimentally, dry rod-mill grinding is used to evaluate the technique presented. Batch Grinding Model The size-discretized batch-grinding model has been discussed in detail by Mika et al.'.' and by Herbst and Fuerstenau,' and therefore, will only be briefly developed here. The model is formulated by making a differential mass balance of each size fraction in such a manner that the equation parameters are precisely defined in terms of selection and breakage functions,' which can be either calculated'.' or estimated1 from experimental data. The model is phenomenological because it averages all stress-application events in the system and, therefore, does not distinguish the manner in which individual particles are stressed.' For this average environment, the resistance of all particles in a size fraction to breakage is defined by that size-frac-tion's selection function; and when fracture occurs from an average event, the breakage product size distribution is defined again by that size-fraction's breakage function. The model is deterministic and is derived in terms of a continuous time variable and a discretized size variable,' i.e., the n mass fractions associated with the n defined size intervals (see Table 1 for nomenclature).

Jan 1, 1971

By C. R. Forbes, J. C. Barton

Many different shapes of drill bits are in use with hammer drills, but little definite information is available whereby to judge which one of these shapes is the best. The following investigation was undertaken in order to determine what effect, if any, the shape of the cutting edge has on the cutting speed and wearing qualities of drill bits. The bits tested were those in common use, namely, the 4-point or cross bit, the 6-point bit, the Z bit and the "Carr" bit. The rock in which the tests were made was the red granite from southeast Missouri. It is a coarse crystalline granite containing an unusually large amount of quartz and is extremely hard, and on account of its uniform texture is admirably adapted to this work. While tests in other rocks might show somewhat different results, nevertheless it is the opinion of the authors that the relative cutting quality inherent in the shape of the bits would be the same in all rocks. Other qualities, such as mudding freely, freedom from fitchering, etc., might make one bit more desirable than another in softer rocks. Description" of Bits Tested 'I'he 4-point bits were the usual shaped bits commonly made on the Leyner sharpener, with 14' taper on the wings and a 90" angle between cutting edges. Some tests were run at 85 Ib. pressure with a 4-point bit made with a 50 taper on the wings; this bit was formed with the Carr bit dies. The 6-point bits were the usual shaped bits made on the Leyner sharpener. The Carr bits were made with a 5º taper and an angle of 100" between cutting edges.

Jan 1, 1918

By W. M. McKewan

Dense magnetite pellets were reduced in hydrogen-water vapor-nitrogen mixtures over a temperature range of 400° to 500° C at a pressure of 0.97 atm. The rate of reduction per unit area was found to be constant with time and directly proportional to the partial pressure of hydrogen at a constant ratio of water vapor to hydrogen. Water vapor poisoned the oxide surface by an oxidizing reaction and markedly slowed the reduction. The enthalpy of activation was found to be + 13,600 cal per mole. THE investigation of the reduction of iron oxides has been the subject of numerous papers. Most of these papers have dealt with the evaluation of various ores, both magnetite and hematite. There have

Jan 1, 1962

By A. W. Farenwald

Fine grinding cannot be accomplished in machines in which the component parts move in definite and restricted paths with respect to each other. Such machines are crushers. A "grinding mill" may be defined as any machine in which the crushing elements are free to make direct contact with each other but are kept from doing so by the sand to be crushed. Such a machine must possess the ability to give numerous contacts per unit of time. Upon consideration, one will see that this definition nearly includes the old Chilean and Huntington mills, the "rolls" and the stamp mill. It definitely includes all forms of ball, pebble and rod mills. The ideal (perfeet) grinding mill may be defined as one in which the crushing elements are identical in shape and substance and possess perfect freedom of motion with respect to one another. Of the mills mentioned, only the ball and pebble mills come under this definition of the ideal mill. Even the rod mill fails to get a place under this definition of the perfect mill. Modern Fine-grinding Mill In current practice fine grinding is performed in rotating cylinders1 partially loaded with hard objects, the agitation of which accomplishes the crushing or grinding of the rock or ore. The hard objects called "grinding media" nearly always are steel or some other alloy of iron. Hard rock (flint pebbles) have been and still are used to a limited extent. When steel is used as the grinding substance, the form is the sphere or "ball." The combination of rotating cylinder and steel-ball grinding media is termed "ball mill." Shapes other than the sphere have been tried. Cylindrical grinding media also have been and are now used in grinding mills. When cylindrical media are used the mill is termed "rod mill." Mechanical Elements of Grinding Mills The mechanical elements of a grinding mill arc: (1) the rotating element, (2) the grinding media, (3) the rotating means.

Jan 1, 1935

By H. W. McCue

In 1945 the number of oil wells drilled was less than in 1944 but the number of gas wells was greater. The oil wells numbered 176, completed for an initial production of 25,214 bbl., an average of 143 bbl. per well as against a total in 1944 of 245 drilled for 32,886 bbl., or 134 bbl. per well. All of these wells were in proven areas and no new discoveries

Jan 1, 1946

By Harrison Souder

In view of the proposed visit of the Institute to Cuba this winter, the following brief sketch of the principal mineral deposits near Santiago de Cuba has been prepared largely from notes taken in February, 1903, during a visit to the mines then in operation in the province of Santiago de Cuba. Westward from Cape Maysi, the most eastern point of the island, the coast is rocky and uninviting. The usual course of the steamers is well in toward the shore, and the lines of stratification of the rocks can be distinguished clearly, the presence of iron or other ores being indicated by frequent blotches of mineral stain. One is impressed with the general rugged character of the southeastern coast-line,—an almost unbroken barrier of coral-limestone bluff's, full of caves and hollows, into which the surf rushes with a roar and bursts into tall fountains of spray. Beyond rises abruptly the Sierra Maestra range, whose sharp, peaked crest-line betrays its eruptive or igneous origin. From a height of about 800 ft. near Cape Maysi, this range gradually rises to the westward, attaining its maximum elevation of more than 8,300 ft. in the Pico Turquino, beyond Santiago. A general resemblance to the mountain-ranges of southern New Mexico is noticeable. At Daiquiri, 20 miles east of Santiago harbor, the extensive

Jan 1, 1905

By K. A. Jackson, J. D. Hunt

A general theory for the growth of lamellar and rod eutectics is presented. These modes of growth depend on the interplay between the diffusion required for phase separation and the formation of interphase boundaries. The present analysis of these factors provides a justification for earlier approximate theovies. The conditions for stability of rod and Lanlellar structures are consitleved in terms of the mechanisms by which the structure can change. The mechanisms considered include both small adjustments to the lnnzellar spacing due to the motion of lamellar faults, and catastrophic changes due to instabilities. It is concluded that stable growth occurs at or near the minimum interface undevcooling for a gizierz growth rate. The conseqrlences of the existence of a diffusion boundary layer at the interface are discussed. The experimental results for the variation of growth rate, undercooling, and Lanzellar spacing are cornpared with the theory. We believe that the theory presented in this paper provides an adequate basis for understanding the complex phenomena of lanzellar and rod eutectic growth. The growth of lamellar eutectics has been the subject of several theoretical and many experimental studies. The foundations for the theoretical work were laid by zenerl and Brandt2 in their analyses of the growth of pearlite. Zener estimated the effect cf diffusion, and took into account the surface energy of the lamellar structure. He found that the lamellar structure could grow in a range of growth rates at a given undercooling provided the lamellar spacing was appropriate for the growth rate. Since pearlite grows with only one growth rate and one lamellar spacing at a given undercooling, there is clearly an ambiguity in the theory. Zener removed this ambiguity by postulating that the growth rate was the maximum possible at the given undercooling. He predicted then that the product of the growth velocity v and the square of the lamellar spacing A should be constant, i.e., A2v = const. Brandt2 started out by assuming that the interface between the lamellae and austenite was sinusoidal. Because of this, the ambiguity encountered by Zener did not arise. Brandt was able to obtain an approximate solution to the diffusion equation, but, since he did not take into account the surface energy, his considerations are incomplete. Tiller3 applied some of these ideas to the growth of eutectics, and proposed a minimum undercooling condition to replace the maximum velocity condition used by Zener. These conditions are formally identical. Hillert4 extended the work of Zener. He found a solution to the diffusion equation assuming the interface to be plane. Taking surface energy into account, and applying Zener's maximum condition, he was able to calculate an approximate shape of the interface. Jackson et al.5 used an iterative method employing an electric analog to the diffusion problem to refine the calculation of interface shape. It was found that the interface shape calculated from a plane-interface solution to the diffusion equation was negligibly different from the exact solution. The method provided an analog only for eutectics for which the volumes of the two phases are equal, growing from a melt of exactly eu-tectic composition. There has also been considerable experimental work on eutectics, Several experimenters8-10 found that A2v is constant as predicted by Zener.1 Hunt and chilton10 demonstrated that ?T/v1/2 is also a constant for the Pb-Sn system as predicted. Lemkey et al.11have recently found A2v to be constant for a rod eutectic. In the present paper, we present the steady-state solution for the diffusion equation for a lamellar eutectic growing with a plane interface, for the general case, that is, with no restriction on the relative volumes of the two phases, and with the melt on or off eutectic composition. A similar solution is also found for a rod-type eutectic. Expressions are obtained for the average composition at the interface and the average curvature of the interface. These equations for the average composition and curvature are similar in form to those derived by Zener1 and Tiller,3 and provide a justification for some of the approximations made by these authors. The mechanisms by which the spacing in a lamellar structure can change are considered. The important mechanism for small changes in lamellar spacing involves a lamellar fault. Examination of the stability of lamellar faults leads to the conclusion that the growth occurs at or near the extremum.* The insta- bilities which can develop in a rodlike structure are also discussed, resulting in the conclusion that this structure also grows at or near the extremum. Comparison of the conditions for rod and lamellar growth permits a prediction of the surface-energy anisotropy required to produce rods or lamellae for various volume-fraction ratios. The diffusion equation predicts the existence of a diffusion boundary layer at the eutectic interface unless the eutectic has 0.5 volume fraction of each phase and is growing into a liquid of eutectic composition. This boundary layer is such as to make the composition in the liquid at the interface approximately equal to the eutectic composition. This boundary layer permits changes in composition during the zone refining of eutectics. Photographs of the eutectic interface of a growing transparent organic eutectic system have been made. Both the components of this eutectic are transparent organic compounds that freeze as metals do.12 The in-

Jan 1, 1967

By A. E. Jenkins, L. A. Baker, N. A. Warner

The electromagnetic levitation technique has been successfully applied to rate studies of the de-carburization of liquid Fe-C alloys from 5.5 to zero pct C at 1660°C using gas mixtures containing 1 to 100 pct CO2 with CO or helium as diluents. The rate was shown to be independent of carbon concen -tration in the melt and only slightly affected by total pressure. The results were shown to be consistent with control either wholly or predominantly by gaseous diffusion. As well as avoiding side reactions with the crucible, levitation allowed precise calculation of reaction rates since the geometry of the system was accurately known. It also enabled interpretation using the established mass-transfer correlations for a gas flowing past a single sphere, The existence of gaseous-diffusion control and the extremely high rates of reaction reported for gas flowing past small spheres are of great practical significance in relation to current investigations into the use of spray-refining techniques in continzcous steelmaking. PREVIOUS work on the kinetics of carbon removal from liquid iron has generally involved the use of oxygen as the gaseous oxidant. Investigations have been made on commercial steelmaking furnaces and in addition laboratory-scale experiments have been attempted with a slag phase present. The general lack of agreement and the obvious difficulty in interpreting the results is at least partly due to the complexity of the systems used. This work has been reviewed by carter1 and more recently by Bods-worth2 and ward.3 The gas-liquid metal reactions have also been studied with slag-free melts by the conventional technique of blowing oxygen onto the melt contained in a crucible. The reaction between the oxidant and carbon could be followed by sampling either the melt or the gas phase. Side reactions with the crucible material have precluded direct interpretation of the results. Fujii, 5-7 using O-A mixtures, attempted to correct for the crucible reaction and reported that the reaction between carban and oxygen occurred at the melt surface and was controlled by gaseous diffusion for carbon contents greater than a critical value and by carbon-diffusion control in the metal for carbon contents less than the critical. The critical value was given as approximately 0.15 pct C. However, whereas this was the case for oxygen contents in the gas stream up to 10 pct, between 10 and 20 pct the rate was found to be approximately independent of oxygen content, and Fujii attempted to explain this observation by postulating the presence of an oxide "film".7 Turkdogan et a1.' have studied iron fuming during decarburizing and suggested gaseous-diffusion control of the reaction above a critical carbon concentration, given as approximately 2 pct C. Filippov9-12 reports in a similar manner to Fujii but makes no mention of the crucible reaction with the carbon in the melt, even though this would be expected with the temperature, crucible material (MgO), and carbon contents used. Both CO2 and O2 were used as oxidant gases. In the present work the decarburization of liquid Fe-C alloys was studied using an adaptation of the electromagnetic levitation technique, and thus the complexities introduced by crucible side reactions were eliminated. In this technique a single sphere of the Fe-C alloy is freely suspended and heated by electromagnetic induction in a flowing stream containing the oxidant gas. The full range of carbon levels up to saturation was studied, the temperature of the melts in this instance being held constant at 1660°C. The oxidant was CO2 which was used either pure or in association with a diluent gas, the total gas pressure being maintained either at 1 atm or at a reduced pressure. Thus the reaction under study was:

Jan 1, 1964

By Edward Steidle

Those who have followed the rapid progress in rock-dusting bituminous-coal mines must admit that opinion crystallized during the year just closed in support of this preventive of coal-dust explosions. Up to 1924 only one mining company in America practiced rock-dusting on a large scale, but during 1924 forty-two companies had adopted this safety measure, and the "boom" is expected to extend over the next two or three years. Alabama is represented by 1 company, Colorado by 3, Illinois by 4, Kentucky by 1, New Mexico by 4, Pennsylvania by 20, Utah by 8, and Wyoming by 1. A total of about 500 miles of entry has been dusted. Illinois leads with 275 miles of dusted entries and Pennsylvania holds second place with about 175 miles. In each case there is a sense of great security, not only on the part of the operator but by the miner as well. It is also interesting to note that during 1924 the compensation rating or inspection bureaus in twelve of our coal-producing states revised their rating schedules so that a credit would be given for rock-dusting. This credit ranges from 10 to 20 cents per $100 payroll. Recent drastic federal and state regulations approved by mine operators made rock-dusting compulsory in bituminous coal mines in Utah, beginning July 1, 1924. Legislative action favorable to rock-dusting may be expected in other states. Colorado has already proposed a change in its laws, and Pennsylvania, Maryland, Washington, and West Virginia are giving the matter consideration. If the rock-dusting problem is handled properly and proves to be entirely successful, no mining man of any standing will delay applying it in his mine. State legislation regarding this matter may or may not solve the problem. At present, the mining companies that are rock-dusting of their own choice are doing it carefully and thoroughly. In Utah, some are doing it conscientiously, trying to get what benefits can be obtained while others are reported to be doing it only to keep within state regulations. In any event, if we are to have new legislation, it is essential that the various states know what they are about and then, if possible, work for uniform regulations.

Jan 1, 1925

By T. A. Wright

The sampling of waste materials containing copper, lead and tin has taken on a new significance within recent years, and is of increasing importance, on account of the entry of some of the copper refineries into this field and the tendency towards consolidations among the smelters. In the past, such material was sold on the basis either of a rough or grat) sample or of casual inspection of the lot. The two principal sources of this waste are the processes of fabrication and the scrapping of automobile, electrical, plumbing, railroad and other equipment. In both cases rnuch material can bc sorted, salvaged and sold by classification and grade to be melted "as is" or with the addition of new or virgin metal. The increasing care in classifying exercised in the large manufacturing plants tends to incrcase the proportion of this usable scrap; on the contrary, the increasing use of more complex and special non-ferrous alloys tends to makc sorting and grading more difficnlt in turnings, borings, clippings, etc., and conseqllcntly is making sampling of more moment. In tin, lead, alumiinum, and zinc furnace by-products such as ashes, drosses, skimmings, etc., the trade practice of evaluation has not varied much. For instance, tin drosscs, battery lcad, and aluminunl skimmings are ordinarily sold on what is called "metallic button" or "metallic recovery" or "metallic yield." Coppcr and Icad wastcl, howcvcr, is being sold more and more on actual copper and lead contents bascd on sarrlple and chemical analysts. This paper will be dcvotctl chiefly to the sampling of niaterials suitablc only for refining and recovery of one or more of the metals present. The methods described are often bascd on thc fact that but one, metal, such as copper, is to be paid for. The loss of volatile constituents in melting does not appreciably affect thc final copper result, as the "after-melting" assay can be readily calculated to the "bcfore-nltltingl' basis, but if smelter efficiency continues to increase, so that in tiltie zinc, for instance, may be rccovrred on a paying basis, thc method of sampling dirty brass, for example, will have to bc changed also. As a matter of fact, we may cxpect that improved refining proresses will make possible the partial reeovrry of lcad and tin which are now lost

By Carlton D. Hulin

The usual concurrence in time and space of intrusive igneous activity, favorable structural disturbance and mineralization, which is so manifest in the mineralized district necessarily indicates a close interrelationship between these events. Evaluation of available evidence leads to the recognition that an appreciable time interval exists between the emplacement of the igneous intrusive and the formation of associated ore deposits. During this interval known portions of the intrusive are completely solidified, highly differentiated magma facies are injected as dikes, and important faulting occurs, which may fracture and shatter the solidified intrusive body. The highly differentiated dike types could only have originated in some deep portion of an underlying plutonic body that had reached an advanced stage of magmatic differentiation. Appearing after these dikes, the mineralizing solutions may likewise be presumed to have originated at great depth. Certainly no source for these solutions can be found in near-by portions of the intrusive igneous body. The association of igneous intrusives and clustering ore deposits must be recognized as resulting from structural control. The emplacemerit and the subsequent solidification and cooling of the intrusive set in operation forces that are responsible for the favorable structural disturbances that control the mineralized district. The emplacement of the body of fluid magma weakens the crustal rocks to the extent that failure due to strains originally present in the rock body may occur. Faulting of any type and of any magnitude may be the result. Subsequently, owing to the change of state from fluid magma to crystalline granitic rock, volume decreases approximating 10 Per cent may Occur, with resultant shrinkage and collapse within the rock body. Following solidification, thermal contraction, induced by cooling of the rock body, causes a further volume reduction of 6 per cent. This thermal contraction, extending over a lengthy period of time, results in a succession of minor fault movements. These small fault movements, occurring progressively throughout the period of mineralization, are responsible for maintaining the permeability of the rock body, without which access of the mineralizing solutions and the formation of the ore deposits of the mineralized district would be impossible. Introduction A proper understanding of the causes that have localized our mineralized districts should be of considerable value to geologist and engineer alike. under current conditions the known ore reserves of productive mining camps are being rapidly depleted. Although ore of the future will be derived in part from deposits now known and from Ore bodies that are still to be discovered within the limits of productive mining districts, in part at least it must come from mineralized districts whose existence or importance yet remain to be recognized. The mining geologist is thus faced with two problems of paramount importance: (I) the location of new ore bodies within known mineralized areas and (2) the location of new mineralized districts within whose confines, previously unknown, valuable Ore deposits may occur. Any contribution to our knowledge concerning the causes for the localization of mineralized districts

Jan 1, 1949

By Wei-Kao Lu, G. Bitsianes

An improved general rate equation for a one-ditnensional gas-solid system has been derived. Fov the veversihle interfacial chemical reaction, there are concentrations of gaseous reactant and product at the reacting zone to be considered. They have been calculated with the velations fuvnished by the constraints on the system, namely, quasi-steady state and equimolal counterdiffusion of the gases. The results of the diffusiori study of Evans, Watson, and ,Mason based on the "dusty gas" model have been applied here. The interfacial chemical reaction is taken as first-order with respect to the concentration of the gases involved. The equation has proper dependence on gas composition and on solid structure through the relative values of Knudsen and normal diffusivities. The existence of the total pressure gradient inside the specimen has been predicted and confirmed experimentally. In a previous communication' we introduced a general rate equation for gas-solid reactions by considering the contributions of chemical reaction at inter- phase boundaries and diffusion through the solid product layer simultaneously. These equations, for one-dimensional and spherical specimens, take care of the whole range continuously from purely diffusion control to purely chemical reaction control. In this paper we study only the one-dimensional system. The corresponding rate equation is reproduced here: Of the two terms on the right-hand side of Eq. [I], the first represents the contribution of interfacial chemical reaction and the second that of gaseous diffusion. The shortcomings of Eq. [I] are that in its derivation the interfacial chemical reaction was assumed to be irreversible and the diffusion rate of gaseous product was not considered. Any pressure effects building up within the porous media were also neglected. Evidently. these simplifying assumptions will limit the general applicability of these equations. The rate of reduction of iron oxide by hydrogen, for instance, is very sensitive to the concentration of water vapor in the main gas stream, as has been reported by cewan' and by Quets et a1.3 Furthermore, the gaseous phase at the reacting interface will contain an appreciable amount of the gaseous product of reaction. If this were not true, a sufficiently high concentration gradient for the outward diffusion of the gaseous product could not be maintained. With these shortcomings in mind, Eq. [1I cannot be rigorously ap-

Jan 1, 1967

By Carlton D. Hulin

The usual concurrence in time and space of intrusive igneous activity, favorable structural disturbance and mineralization, which is so manifest in the mineralized district necessarily indicates a close interrelationship between these events. Evaluation of available evidence leads to the recognition that an appreciable time interval exists between the emplacement of the igneous intrusive and the formation of associated ore deposits. During this interval known portions of the intrusive are completely solidified, highly differentiated magma facies are injected as dikes, and important faulting occurs, which may fracture and shatter the solidified intrusive body. The highly differentiated dike types could only have originated in some deep portion of an underlying plutonic body that had reached an advanced stage of magmatic differentiation. Appearing after these dikes, the mineralizing solutions may likewise be presumed to have originated at great depth. Certainly no source for these solutions can be found in near-by portions of the intrusive igneous body. The association of igneous intrusives and clustering ore deposits must be recognized as resulting from structural control. The emplacemerit and the subsequent solidification and cooling of the intrusive set in operation forces that are responsible for the favorable structural disturbances that control the mineralized district. The emplacement of the body of fluid magma weakens the crustal rocks to the extent that failure due to strains originally present in the rock body may occur. Faulting of any type and of any magnitude may be the result. Subsequently, owing to the change of state from fluid magma to crystalline granitic rock, volume decreases approximating 10 Per cent may Occur, with resultant shrinkage and collapse within the rock body. Following solidification, thermal contraction, induced by cooling of the rock body, causes a further volume reduction of 6 per cent. This thermal contraction, extending over a lengthy period of time, results in a succession of minor fault movements. These small fault movements, occurring progressively throughout the period of mineralization, are responsible for maintaining the permeability of the rock body, without which access of the mineralizing solutions and the formation of the ore deposits of the mineralized district would be impossible. Introduction A proper understanding of the causes that have localized our mineralized districts should be of considerable value to geologist and engineer alike. under current conditions the known ore reserves of productive mining camps are being rapidly depleted. Although ore of the future will be derived in part from deposits now known and from Ore bodies that are still to be discovered within the limits of productive mining districts, in part at least it must come from mineralized districts whose existence or importance yet remain to be recognized. The mining geologist is thus faced with two problems of paramount importance: (I) the location of new ore bodies within known mineralized areas and (2) the location of new mineralized districts within whose confines, previously unknown, valuable Ore deposits may occur. Any contribution to our knowledge concerning the causes for the localization of mineralized districts

Jan 1, 1949

Jan 1, 1946

By H. J. Morel-Seytoux

Methods of predicting the influence of pattern geometry and mobility ratio on water flooding recovery predictions are discussed. Two methods of calculation are used separately or concurrently. The analytical method yields exact solutions in a convenient form for a unit mobility ratio piston-like displacement. A few typical pressure distributions, sweep efficiencies and oil recoveries are presented for various patterns. For non-unit mobility ratio, one may resort to a numerical method, such as that of Sheldon and Douherty. 1,2 Because the domains of applicability of the analytical and numerical techniques overlap, the exact solutions provide estimates of the errors in the numerical procedures. The advantages of the analytical and numerical methods can be combined. To develop a numerical technique as independent of geometry as possible, the physical space is transformed into a standard rectangle. The entire effect of geometry is rendered through one term, the "scale-factor", derived from mapping relations. The scale factor can be calcu-lated from the exact unit-mobility ratio solution for the particular pattern of interest. By this means recovery performances for arbitrary mobility ratio con be obtained for many patterns. A sample of tesults obtained in this manner is presented. INTRODUCTION Pattern geometry and mobility ratio are two major factors in making a waterflood recovery prediction. Because assisted recovery has become increasingly important to the oil industry, pattern configuration and mobility ratio also assume a greater significance in the assessment of the economic value of recovery projects. The influence of pattern geometry and mobility ratio in shaping a recovery curve and on the other quantities of interest to the reservoir engineer is the main subject of this paper. Much effort has already been spent on estimating quantitatively the influence of either pattern or mobility ratio or both on oil recovery. The literature reports many investigations of this nature. 3-9 However, many results or methods of recovery prediction presented in the literature cannot be considered fully satisfactory. Even for unit mobility ratio and piston-like displacement, where analytical solutions are available, the literature shows discrepancies. For non-unit mobility ratio, the divergence in the results is extreme. For infinite mobility ratio in a repeated five-spot, depending on the investigator, the sweep efficiency ranges from 0 per cent to 60 per cent. With respect to the influence of pattern on recovery, only the repeated five-spot has received much attention. Other confined patterns and pilot configurations have received very little attention. Two calculation methods are presented in this paper, either separately or concurrently: the analytical method of potential theory and the numerical method of finite-difference approximation. The analytical method is more restricted in scope than the finite-difference method, but it has the definite advantage of providing exact solutions within its range of applicability. If a unit-mobility ratio piston-like displacement is assumed, the analytical approach is possible. A few typical results are reported in this paper; the detailed description of the general method and of a great variety of results will be the subject of other articles. Fornon-unity mobility ratio, we must resort to a numerical scheme. The numerical technique is that which was described by Sheldon and Dougherty.l,2 It is not limited to piston-like displacement. However, mainly single interface results will be presented here. Because the respective domains of applicability of the analytical and the numerical method overlap, useful comparisons of exact and numerical solutions can be made for a variety of patterns. The advantages of the analytical and numerical approaches can be combined. The reason for the success of this analytical-numerical approach can be summarized in the following two points: 1. The numerical solution for arbitrary mobility ratio can be programmed most efficiently when the physical space in which the displacement actually takes place is transformed into a standard shape; and 2. This can be done with remarkable simplicity whenever an analytical expression for the pressure

Jan 1, 1966

Jan 1, 1946

By C. A. Heiland

For a long time it has been known that it is possible to deduce conclusions about the physical constitution of the interior of the earth from the records of natural earthquakes obtained by stationary seismographs. In view of this fact it is surprising how late, relatively speaking, geologic prospecting by seismic methods has been taken up, although the first suggestion was made 40 years ago—that travel-time curves of artificial explosions might be used for the study of the change of the velocity of seismic waves as depth. Further suggestions of practical applications of artificial explosions for geologic purposes were made by Belar12 by von dem Borne,3 by Benndorf and by Galitzin,5 but it was not .until 1919 that Mintrop obtained a patent on the seismic prospecting method which he has applied commercially on a large scale ever since. Dr. Mintrop came to this country with his method at about 1923. Since that time, several American oil companies have developed seismographs of the mechanical type for the vertical component similar to that of Mintrop's (Humble Oil Co., Dr. Ricker). Other consulting geophysical companies designed other types of seismic devices, the simplest of them for the recording of the first impulse being the geophone (McCol-lum Geophone Co.). The galvanometric recording method as first proposed by Galitzin is being used (Geophysical Research Corpn.?) and use is being made even of the piezoelectric properties of crystals for portable seismographs (F. Rieber). There is such an enormous variety of all kinds of portable seismographs, vibrographs, accelerographs, etc., that it is difficult to decide just what kind is preferable. Unfortunately, nothing has been published as yet about American designs of portable seismographs, except the Wood-Anderson torsion-seismometer. After Mintrop's design of portable seismographs, other constructions were made

Jan 1, 1929

By Robert C. Bolger, John H. Weitz

REFRACTORY clay, one of Pennsylvania's important nonmetallic mineral resources, occurs at several horizons in beds of Pennsylvanian age. The Mercer fireclay, of Pottsville age (Table 1), is the most important of these clays. A study of this fireclay has been conducted by the Pennsylvania Geologic Survey discontinuously over a period of seven years. The work has included field mapping of a rather large area, as well as petrographic, differen¬tial thermal, and X-ray studies of the fireclay. A comprehensive report on the project is now in preparation.

Jan 1, 1952

By C. S. Matthews, P. Hazebroek, H. Rainbow

It ha been suggested that lormation fractures created by well stimulation treatments will adversely affect sweep-out efficrency in injection operations. Fluid-flow model studies involving vertical fractures of various lengths and fluid systems of various mobility ratios have been carried out to study this subject. In addition, limited data have been obtained on one model containing a horizontal fracture. It was found that relatively long and highly conductive fractures (not generally obtained fracturing operations) were required to affect the sweep-out efficiency substantially. In a given case in the field an approximate distinction can be made between the presence of long conductive fractures and shorter or less conductive ones. This is done with pressure build-up analyses along with data on the relationship of fracture length and conductivity to well productivity. This type analysis shows that usually the fractures induced are either short or of limited conductivity and therefore do not damage sweep-out efficiency. INTRODUCTION Improved well productivity and in-jectivity can frequently be exploited in injection operations. Higher total throughput can yield improved economics. On occasion, the achievement of an increased productivity or injectivity in specific wells can bring about a more uniform sweep of the reservoir. Higher rates can be exploited particularly in water floods of "depleted" reservoirs where a rapid "fill-up" is desired and where low pressures contribute to low well productivity. The creation of fractures local to the wellbore is an excellent means for achieving these objectives. Even though fracturing has been employed in some floods with success,1"3 there still seems to be some reluctance to employ this tool for fear of undue damage to the flood pattern and ultimate recovery. We therefore need to examine the influence which fractures of varying length may have on flood performance and then determine the length of fractures which obtain in the field with conventional fracture treatments. A substantial influence of fractures on the recovery obtained at breakthrough of the injected fluid has been presented by Crawford and Collins for equal fluid mobilities for the line-drive pattern.4,5 In addition, the influence which a fracture has on the production performance after breakthrough and on the ultimate recovery warrants consideration in reaching a conclusion concerning the use of induced fractures in flooding operations. This report presents this type of data for the five-spot injection pattern for several fluid mobilities. In arriving at some conclusion concerning the fracture lengths obtained in field operations we must examine the performance characteristic most affected by the fracture. This is the change in the flow system as reflected in the change in productivity and pressure build-up behavior. A study of these changes is also presented in this report. RESERVOIR ANALOGS The X-ray shadowgraph technique, employing miscible displacement in porous models, has been used in the study of the influence of fractures on pattern sweep-out efficiency. The X-ray shadowgraph procedure is described in detail in an earlier report8. Fractures were represented by leaving the proper portion of the model surface exposed to either injection or production. This assumes the fracture resistance to be negligible compared to that of the formation. Actually the flow resistance in propped fractures obtained in the field is sometimes not negligible so that the results with this model indicate the maximum influence of the fracture. Two types of models were necessary to represent vertical fractures in a five-spot flood. These pattern elements are illustrated in Fig. 1. In studying the influence of the horizontal fracture, only one well spacing length to thickness ratio of 50 was used. The pool unit of a Carter Electric Analyzer was used in studying the influence of fractures on productivity and build-up behavior. The square drainage system of a well was represented by a network of 576 elements of equal volume and resistance. One-fourth of this drainage area was studied as a model unit using a network of 144 condensers and resistors. Vertical fractures were represented by a shunt directed from the well perpendicular to the drainage boundary. Horizontal fractures were represented by a circular shunt. Resistance of a shunt was varied in representing different conductivities for the fractures. FRACTURE DIRECTION AND LENGTH The direction at which a vertical fracture extends into the formation and its length and conductivity influence the sweep behavior. The two

By Allan B. Bowman

Several years ago a wealthy Chinese business friend of mine purchased an interest in a pro- posed oil well to be drilled a great distance from his home. A few months later it came in as a producer and proved to be a huge success and materially added to his resources. I asked him why a man of his wealth should be so lucky in a venture outside his sphere of knowledge when most people of modest means never seemed to get ahead. His answer was, "Fat Hoy takes a chance." Even though this was his answer, I knew from my association with him that there were other tempering considerations which Mr. Hoy applied before making up his mind to enter any transaction. First, he was a cautious individual. He was also a great believer in details and insisted on knowing everything possible about a situation, and finally, he was what we call a very solid individual with good basic instincts and judgment. This philosophy of Mr. Hoy may be applied to most any business but especially to those engaged in a search for natural resources such as mining where great risks are involved. This article concerns events in the history and growth of Banner Mining Co., with which I have been associated for 27 years in capacities from mine surveyor to vice president. Mr. Hoy's philosophy has played a significant role in the exploration projects of this company over the years, but what is more important, the officers, directors, and controlling interests in Banner have been aggressive in their search for ore reserves.

Jan 6, 1963