Search Documents

By R. V. Higgins, A. J. Leighton

Interest by petroleum engineers in the flow of three phases—oil, gas and water—in irregularly bounded porous media lies mostly in the performance calculation of water floods of reservoirs that have been partially depleted as the result of expansion of much of the originally dissolved gas. The authors present a method to forecast three-phase flow in complex geometry and explain the details by the use of a specific example of a five-spot water flood of a partially depleted stratified reservoir. In this example, the fluid and rock properties of a field given by Prats, et al,' were used. The computed results fit the field performance more accurately than Prats, et al, and Slider.' The time required for the high-speed digital computer to make the calculations, including the contributions from the different layered zones, is about one minute. INTRODUCTION The declining rate of discoveries of new oil fields in the United States makes the recovery of more oil from known reservoirs more attractive than previously. Water flooding has an excellent proved background for recovering additional oil economically. Accordingly, the main interest of this paper is in this type of recovery. In petroleum engineering studies, commercial interest in three-phase flow is mostly in the water flooding of reservoirs in which the oil has been partially produced by the expansion of dissolved gas. When water is pumped into these reservoirs, three-phase flow takes place. Although this paper is concerned with these conditions, the principles involved could be used for other conditions when and where they come to the fore. Many investigators have made contributions to non-empirical forecast methods using basic scientific engineering principles. Several of these used the oil in place at the start of the water flood and the oil remaining after a large quantity of water has passed through a core for key values in their calculations. Recently, Prats, et al,' and Slider have reduced assumptions by adding the third phase—gas—in their forecasting methods. Slider uses the mobilities in the immediate vicinity of inlet and outlet wells as an aid to simulate the resistance effect in the five-spat pattern of the flow of oil, gas and water. Prats, et al. minimize assumptions by using previously determined laboratory data for determining sweep efficiency in the five-spot pattern. In neither of these papers is the saturation profile continuously affected by permeability-saturation curves. Sheldon and Dougherty- recently described a method that employs continuously changing saturation profiles using permeability curves, has a minimum of assumptions and needs no prior sweep efficiency. The Higgins-Leighton method, described in this paper, has all of these features; however, many of the techniques are different from those of Sheldon and Dougherty. The Higgins-Leighton method, tested in May, 1961, is direct and easy to apply and requires very little computer time to calculate a forecast. The short computer time is especially helpful in the study of a reservoir containing many layers of different relative permeabilities. In the Higgins-Leighton method, the individual pressures do not have to be calculated, as the resistance to flow in each cell in the flow pattern is readily determined without the use of any iterative techniques. The saturation and permeability distributions are readily determined. These data and the shape factor, which is measured only once from the potentiometric model when mobility ratio is one, determine the resistance to flow in each cell. THEORY The authors showed in a previous paper4 that, as an aid to calculating performance, the reservoir can be divided into channels using the streamlines of a potentiometric model as a guide. See Fig. 1. This procedure also was used in this paper. The authors also showed that, by treating conduits as approximately one-dimensional and neglecting pressure gradients transverse to the main flow, the Buckley-Leverett equation may be expressed as The principles expressed by this equation are employed extensively in the three-phase flow, as they were in two-phase flow. In the three-phase flow, the channels (the size and shape of which are taken from a potentiometric model)

By J. A. Bowers

THIS investigation of the effect of bottom shape and life on slag volume was carried out in two Lectromelt top-charge furnaces whose rated capacity is 1000 lb per hour. Unfortunately, just as the work [ ] was started, our steel tonnage was reduced approximately one half, therefore we did not accumulate enough data from which to draw any definite conclusions. Furthermore, the life of the linings in these furnaces was greatly decreased by intermittent operation, which was a further handicap in making a study of this kind. The weight of the heats from which the data were taken varied 1200 lb but all the information was corrected to the standard weight charge for these furnaces of 4500 lb. Almost all the heats were plain carbon; a few contained a small percentage of added copper.

Jan 1, 1947

By Robert W. Shearman

An historical record of the history of iron-and steelmaking in the United States has long seemed a desirable project to many in The metallurgical Society of AIME. Over a period of five years, experts in their fields have been asked to put down on paper their knowledge. The series of historical articles has been published in JOURNAL OF METALS, beginning with A. B. Wilder's article in 1956, marking the first one hundred years of Bessemer Steelmaking. The Electric Furnace Committee honored the first half-century of the use of the electric arc furnace in America during their 1956 Conference, and S. B. Casey, Jr., wrote an appropriate article for JOURNAL OF METALS. The historical series was well underway. Articles soon followed on the history of the blast furnace, on the open hearth furnace, and on ferro-alloy manufacture. The final need was an authoritative article on coke ovens. The publication of the five-part article by C. S. Finney and John Mitchell this summer has concluded our series (but not the march of progress). We now present, between two covers, a comprehensive historical review, the work of 13 authors. We are hopeful that this book will receive a welcome among ironmakers and steelmakers. and that it will be a valuable reference for home or office library. We hope also that students will find the material helpful in their studies of this most important of American industries. Perhaps also, the historian of Americana will learn something new in searching through these pages. We are indebted to our authors who have spent much time on historical research, and to their companies who have supported their endeavors. We acknowledge the support of the National Open Hearth Steel Committee and of the Blast Furnace. Coke Oven, and Raw Materials Committee in jointly assuming the financial risks in publishing this book.

Jan 1, 1961

Take a look at the maintenance force in some of Wyoming's surface coal mines and you'll notice a significant change-the workers are younger than ever and many have had little or no prior experience. The change is quite a departure from industry's previous "experienced only" hiring policy. It results, in part, from a successful training program offered by Casper College in Casper. Wyo..

Jan 12, 1978

By C. O. Bundranl, Peter Dehlinger, W. H. Browne

Brief laboratory investigations are described which attempt to determine optimum .sand concentrations in gel-sand and oil-sand1 well-treatments. The investigations apply to the case where sand acts as a propping agent in formation fractures. Both analytically and experimentally it is demonstrated that optimum sand concentrations can be defined. It is difficult to translate laboratory results to field treatments, however, since the relative distribution of sand and fluid in fractures may not be the same as injected. This is because fluid may penetrate the furtherest narrow portions of fractures, which would not pass sand. Optimum concentration of a monolayer of Ottawa sand in fractures of 0.025-in. width at the usual range of pressures encountered in treatments appears to be about 95 to 2 lb/gal. of gel. An investigation of abrasion of rock-walls by sand in treatments, described in the Appendix, shows that such abrasion is not probable in significant amounts. INTRODUCTION Experience in the Spraberry formation of West Texas, as well as in other formations, has shown that. sand is a necessary and vital part of gel-sand and oil-sand treatments. Many observers of treatments have also concluded that there seems to be an optimum range of sand concentration for these injections. Brief laboratory investigations were made at Battelle Memorial Institute to study flow in fractures with different sand concen- trations. To investigate the existence and range of optimum concentrations in the laboratory, however, necessitates knowledge of the mechanism by which the sand aids in increasing subsequent production. The action of sand in fractures is usually thought to be either that of a propping agent, thus providing a greater effective formation permeability; that of an abrasive in eroding fill material in fractures; or that of an abrasive eroding rock-wall irregularities along fracture surfaces. Investigations described in the Appendix show that sand does not appear to erode rock-wall materials appreciably. In a subsequent paper it is reasoned, at least for the Spraberry formation of West Texas, that the primary action of sand is not in removing fill materials in fractures. In this formation, and probably others, too, the main effect of sand appears to be that of a propping agent. Both analytical and experimental investigations were made for the case of a monolayer of sand acting as a propper, in which sand concentrations were determined that would, after treatment, permit flow of the maximum quantities of oil from the formation into a well. If too few sand grains are injected into fractures in which the bottom hole pressure has decreased appreciably below the original formation pressure, the confining pressure in the formation may become relatively large, thus compress the rock-walls around the sand grains, essentially close fractures, and so decrease the subsequent flow of oil. Similarly, if too much sand is used, the flow of oil will he impeded by the volume of sand present. THEORY Although an analytical approach to determining optimum sand concentrations involves gross assumptions.

Jan 1, 1955

By H. L. Hartman

The drop tester has proved an invaluable tool for the investigation of percussion drilling in the laboratory in "slow motion". It has allowed the process of rock penetration by impact to be studied a single blow at a time. In the present work, the relation of cratering to indexing has been determined under conditions simulating those in the bottom of the hole at atmospheric pressure. Indexed blows form craters which are influenced by others adjacent to them. Two unique effects are involved: (1) the provision of additional free faces in proximity to the point of impact and (2) the creation of subsurface damage by the previous blow(s). Both have a pronounced influence on the volume of rock removed per blow, which governs the rate of penetration in actual drilling. The emphasis in this study was placed on determining effects of index distance and impact energy on crater volume when blows were struck on a previorusly "drilled" or damaged surface, a situation most representative of down-hole conditions. The results indicated that (I) the optimum index distance on a damaged surface is greater than on a fresh, undamaged rock surface; (2) the volume of rock broken at optimum index distance is about the same for both surface conditions with die-shaped chisels but tends to be greater on a cratered surface with wedges; (3) the optimum index distance and maximum crater volume are proportional to the energy level; (4) at a given energy level, the volume of rock broken by dies generally exceeds that by wedges; and (5) maximum crater volume varies, approximately, inversely with width of die but is nearly independent of included angle of wedge. INTRODUCTION This is the third of a series l,2 of papers reporting on one phase of a continuing program of drilling research being conducted in the Rock Mechanics Laboratory at The Pennsylvania State U. The phase under consideration is crater geometry — blow energy relations in percussion drilling. While the previous papers have discussed mainly craters produced by single blows, indexed-blow studies are the subject of this paper. The basic mechanism of drilling under study here — that of penetration of a chisel-shaped bit subjected to impact — is the one employed in probably 90 per cent of all rock drilling in mining, percussion drilling. It also forms the fundamental action in nearly all oil well drilling with the so-called rotary (roller-bit) method. Here, the action is more complex, however, and may in actuality comprise rotary-percussion drilling. Certainly, the down-hole air and mud hammer drills, which superimpose percussion on rotation, belong in this latter category. In any event, impact blows constitute one of the principal mechanisms in the vast majority of drilling, mining or petroleum, and it is essential in drilling research to study percussion in all its basic aspects. Percussion drilling can be simulated in the laboratory by means of an impact drop tester. Striking one blow at a time with chisel-shaped bits, the drop tester permits study of most of the parameters in the drilling process except blow frequency and the interrelationship of certain variables. Single-blow craters, the simplest to produce, allow the determination of basic relationships, such as volume vs blow energy; while indexed craters most closely resemble the action in real drilling and provide data for the establishment of optimum operating criteria. Indexed-blow craters are those which are influenced by others in proximity. The simplest case to visualize, and the one studied in detail here, is that in which a given crater is formed adjacent and parallel to a previous crater, such that the second crater breaks into the first. A more complex situation usually exists downhole, where indexing is achieved by rotation of a radial-winged or rolling-cutter bit. But, admittedly, the phenomenon of indexing is more likely to be understood eventually if it is first studied in its simplest form, that related to parallel craters. Limited research has been conducted on indexed blows. The most complete study was that by Simon, 3,4 who proposed universal indexing curves to relate the important variables. His work, however, was conducted entirely with rows of craters formed on a

SAMUEL L. HOYT,* Minneapolis, Minn. -I was privileged to see the apparatus used by Mr. Scott, which is quite unique. It is, as the author says, a modification of the apparatus designed by Dr. Rosenhain, but it is evidently quite an; improvement. The author is to be congratulated on the fact that lie has given us, with his apparatus, a quantitative thermal analysis of these critical points. I notice the author refers to Ac3, Ac2, and Ac1. His designation of the Ac2 point is all right, but naturally in a steel with as much carbon as this, which would mean a hypereutectic steel, the other point might better be considered as an Ac, point with possibly another point above the Ac, point. Another important point brought out is the fact that, in Fig. 3, the lines representing the Ar1, transformation and the Ac,1_3 transformation do not intersect at the zero rate curve,

Jan 5, 1919

By Chairman Hill H. H.

The Round Table Discussion on Petroleum Engineering Research was planned for two purposes. First, to review the work that has been done by petroleum engineers during the past few years on problems that have confronted the industry and, second, to suggest new studies that should be made either on the problems that have been the subject of research during the past or on problems that have arisen only recently. It was believed that by holding an informal discussion of the problems in which the petroleum engineer is vitally interested it would be possible to bring out new ideas as to the relative importance of the different problems that should be studied and to suggest new methods for attacking some of the problems that have resisted the energies of research workers throughout the industry. It was also believed that by arranging for an exchange of experiences between the different engineers it would be possible to prevent a large amount of duplication of effort in conducting research work. Those engaged in petroleum engineering research realize that there is a broad field for study and by coordinating the work it will be possible to obtain the maximum amount of information in the shortest possible time. In planning the program on Petroleum Engineering Research, nine subjects were selected for discussion and each was assigned to a man who is doing work on that subject. These men were asked to lead the discussion on the problem assigned to each one. An effort was made to choose problems of a practical nature and upon which considerable work is being conducted at the present time. Some of the men who were asked to lead the discussion were unable to attend the meeting but most of them submitted a written discussion- of the subject assigned, with the result that there was a discussion of eight of the nine problems. Professor Uren, who was asked to lead the discussion on the subject of Recent Developments in Methods for Reducing Gas-oil Ratios, was unable to attend the meeting and advised that he did not have any new ideas to contribute.

Jan 1, 1928

By David R. Mitchell, R. B. Hewes

MANY processes for cleaning coal that are in use depend primarily on physical properties of coal and refuse other than specific gravity and surface conditions relating to froth flotation. These properties are shape, coefficient of sliding friction, resilience, friability, magnetic susceptibility, and electrical conductivity. In many of these processes specific gravity does have some effect and many separators are designed to utilize more than one of the physical properties cited. Although the processes described herein do not have a widespread application, yet for specific coals and specific conditions, they are economically important. A problem confronting many coal-mining districts is the marketing of the slacks or screenings and dust passing the final sizing screens. Processes in commercial use installed primarily to increase the form value, and hence the market value, of these slacks and dusts include briquetting, packaging, and low-temperature carborization. MECHANICAL PICKERS Machines utilizing shape, fictional resistance, and differences in resilience of coal and impurities are usually called mechanical pickers. They require a closely sized feed, therefore their use is confined to the pea, nut, and egg sizes. Various types of these devices are described by Berrisford, 1, 2 Taggart, 3 and Peele. 4 Shape In general, coal differs in shape from its accompanying dirt throughout the range of commercial sizes. Coal, breaking into roughly, cubical particles, contains a greater number of axes that are approximately the same length than does the dirt. The latter, consisting of pieces of slate and shale and lenses of pyrite, is flatter in nature. Further, flat coal often has a dirty, slaty appearance, even though of high quality. Mechanical pickers known as flat pickers, or "flatters," are widely used in the Pennsylvania anthracite region to remove flat coal from the final clean coal. This practice greatly improves the appearance of the final market product.

Jan 1, 1943

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere' that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957

By P. J. Spencer, J. N. Pratt

The vapor pressure of manganese over liquid Mn-Sn alloys has been determined by a high-temperature torsion-effusion technique. Alloys containing from 8 to 100 at. pct Mn were investigated in the temperature range jrom 1280" to 1580" and the measured pressure values were used to calculate the partial and integral thermodynamic properties of the liquid alloys. The activities show small negative departures from ideality while the integral heats and excess entropies of mixing are asymmetric inform, changing from positive to negative with increasing manganese content. The possible contribution of various factors to the observed thermodynamic properties is discussed. COMPARATIVELY few thermodynamic data are available for manganese alloy systems.' Therefore, as part of a continuing program of studies of the thermodynamic properties of transition metal alloys, measurements have been made on various binary alloys involving this element. In recent publications,2~3 investigations of liquid Mn-Cu alloys and of the Mn-Au system in both solid and liquid states have been reported. For the first-mentioned system the work suggested that magnetic interactions may be responsible for the observed form of the thermodynamic properties, while in the second the influence of the electrochemical factor appears to be dominant. The present paper describes a similar study of liquid Mn-Sn alloys. Again the thermodynamic properties have been obtained from vapor pressure measurements made by use of a high-temperature torsion-effusion technique.4 A detailed description of the apparatus and of the experimental procedures used in alloy preparation and pressure measurement may be found elsewhere.2'4 EXPERIMENTAL RESULTS Sixteen alloys, ranging in composition from 8 to 100 at. pct Mn, were prepared from spectroscopically standardized manganese of 99.99 pct purity and tin of 99.999 pct purity, both supplied by Johnson-Matthey and Co., Ltd. One-gram samples of the alloys were obtained by carefully weighing appropriate amounts of the pure components into an effusion cell; this was then suspended in the apparatus and the metals melted together in situ by heating under vacuum to approximately 1550°K. After allowing sufficient time for a homogeneous liquid alloy to be formed, vapor pressure measurements were commenced. These were determined as rapidly as possible at a series of steady temperatures within the range of interest. The duration of experimental runs on individual samples was kept sufficiently short to ensure insignificant varia- tion of alloy composition during investigation. After completing pressure measurements, the alloys were rapidly cooled and their compositions checked by weighing or chemical analysis. All experiments were conducted using effusion cells machined entirely from boron nitride. Measurements were made using a variety of cells with orifice areas ranging from 0.0032 to 0.0075 sq cm and lengths of the order of 0.04 cm; the usual effusion correction factors for orifice geometry and molecular distribution were calculated using Freeman and Searcy's equation5 and had values between 0.6 and 0.75 for the orifices employed here. The vapor pressures of manganese over the alloys were measured at approximately 20°K intervals in the temperature range 1280" to 1580°K. In view of the close approximation of the measured pressures to Clausius-Clapeyron behavior in the experimental temperature range, the data for each alloy have been expressed by equations of the form: logp(atm) =-A/T + B A least-squares computer treatment was applied to the vapor pressure values in order to obtain the coefficients A and B with their associated error. The resulting equations are listed in Table I, together with the equation for pure solid manganese obtained from a previous study.4 To minimize the effect of possible apparatus calibration errors, the activities and partial free energies of manganese in the alloys were calculated by initial reference to the latter equation, obtained from identical torsion-effusion measurements. The immediately resulting thermodynamic quantities, based on a solid manganese reference state, were then converted to refer to the more appropriate supercooled pure liquid manganese standard; tabulated values of the free energies of solid and liquid manganese from Hultgren et al.' were used for this purpose. Partial entropies of solution of manganese were calculated from the temperature coefficients of the free energies and partial heats from the Gibbs-Helmholtz relationship.

Jan 1, 1969

By Wm. Metcalf

One point of vital importance has not been touched upon this evening; it is the necessity of having a history of the mode of

Jan 1, 1882

By J. S. Johnson, W. C. McCulloch

ALL phases of plant operation must be synchronized so that the number of interruptions in the flow of material may be reduced to a minimum. In the majority of plants operating under a labor agreement, time lost during the operating shift cannot be made up with overtime. With the work week restricted to 35 hr., the ratio of productive time to total time justifies extra effort in keeping the plant operating at capacity during the productive shift. This does not apply when central plants with adequate storage are operated by multiple shifts. In such installations the problems become similar to those of any factory or mill where added units parallel circuits, or excess capacity serve to maintain the average production during intervals of maintenance shutdown. These plants, by special agreement, may run continuously, barring mechanical interruptions. The control of plant operation is in those procedures that are practiced to obtain from the run-of-mine product a high recovery of clean coal products to meet adopted trade standards and consumer specifications at the lowest possible cost. Correlation of all factors for continuous operation requires more than mechanical perfection in the plant. The run-of-mine coal must be delivered to the preparation plant without delays and the clean coal and refuse products taken away. Power supply and water requirements must be adequate. Signal systems must be established for emergency stops and to facilitate resumption of coal flow. ORGANIZATION Probably the most important item for successful operation of a preparation plant is a capable organization interconnected with the mine organization. A typical organization chart for companies operating in the Pennsylvania anthracite region is shown in Fig. 1. The breaker foreman is in direct contact with the plant preparation operation and reports to the outside foreman, who, in turn, reports to

Jan 1, 1943

By C. E. Cannon, R. C. Craze

This paper discusses the results of a study of reservoir pressures in the Gulf Coast area of Texas and Louisiana, showing the general relation of the reservoir pressure to its subsea depth, as well as excessive reservoir pressures that have been encountered. The latter are particularly important in mud-control work, and the data show why it is necessary to use muds having a relatively high density in many of the deeper wells drilled in this area. Only a comparatively few of the wells drilled in the Gulf Coast that have encountered excessive pressures are discussed, but as far as is known those omitted fall within the range of pressure observed by the writers. Measurement of Pressures The following methods were used to determine the values of the original pressures: 1. Estimation of original pressure from subsequent pressure behavior of fields. This method is not precise, and was used only in a few of the older fields in which better methods of obtaining original pressures were not available. Only normal pressures were determined by this method. 2. Measurement of shut-in pressures soon after completion of the first producing well. With one exception, all pressures measured by this method were normal, this well having a pressure slightly higher than normal. 3. Measurements of pressure in connection with drill-stem tests. 4. Estimates from the maximum hydrostatic head of mud that failed to prevent flow from the high-pressure formations into the hole. This method is not exact, tending generally to indicate low pressures. Normal Pressures All pressure measurements available are plotted in Fig. 1, with original pressure at the water-oil contact as abscissa and subsea depth as ordinate. All producing fields fall close to the solid line, which passes through the origin and has a slope of 0.465 lb. per sq. in. per ft. By way of compari-

Jan 1, 1938

By J. J. Gilvarry

Recently, Gilvarry1,2 has given a rigorous derivation of the proper distribution function for fragment size in single fracture, based on a closely defined physical model and deduced strictly by the laws of probability. The physical point of departure is Griffith's theory of brittle strength, identifying sub-microscopic flaws as the cause of the low strength of a solid in comparison with values implied by cohesive energies. Gilvarry and Bergstrom,4-7 and Gilvarry8 have compared the predictions of the theory with experiment, and have found excellent agreement, in general. The purpose of this communication is to sketch the extension of the theory to the case of comminution, and to indicate the applications to some examples in nature. The present treatment represents an amplification of a brief discussion appearing elsewhere. 9 Although the basic ideas of the Griffith theory are perfectly general for rupture of brittle solids, it was originally formulated with very brittle materials such as glass in mind. Moreover, Griffith's original experimental work was carried out on glass specimens. Recently, however, the theory has been extended by race" to apply directly to rocks. This extension makes the theory immediately applicable to the materials generally of interest from the standpoint of comminution. GENERAL CASE To obtain the distribution function for fragment size in single fracture, three assumptions are made, that: 1) Fracture proceeds by activation of preex-istent Griffith flaws in the volume, faces, and edges of a fragment; 2) the distributions of flaws of these three types are independent of each other; and 3) activated flaws of a particular type are distributed at random, individually and collectively, in the sense of Fry.11 The last assumption implies that each distribution is separately of Poisson type.

Jan 1, 1964

By P. H. Lindon, J. C. Billington

Fe-O melts containing 0.045 pct 0 were deoxidized with Mn-Si-A1 alloys. Product compositions were reluted to the melt and alloy compositions and were found to be most sensitive to the aluminum content of the alloy. Low residual oxygen contents could be obtained when aluminum oxide was present in the Products because of the reduction of silica and manganese oxide activities. Flotation of the Products from a quiescent melt was followed both by analysis of the oxygen content and metallographic measurement of inclusion concentration. MnO-SiO2-A12O3 products were found to float most rapidly when their composition was such that their viscosity may be expected to be low. Changes in the particle size distribution indicates that particle coalescence occurred and differences in the degree of coalescence are thought to be responsible for the different flotation rates observed between products 0f differing composition. Measured flotation rates were slower than those Predicted from a model based on Stoke's Law, although alumina flotation might be reasonably accounted for by this model. Interfacial effects between oxide particles and the melt are believed to be responsible for the discrepancy. It has been recognized that deoxidation products constitute a large proportion of the nonmetallic inclusions present in killed steel. The amount of oxide inclusions which originate as deoxidation products depends largely upon three factors. These may be summarized, according to P16ckinger1 as: 1) Amount of primary products remaining in the steel prior to cooling. 2) Residual dissolved oxygen content of the steel after deoxidation. 3) Amount of secondary products, formed during cooling and solidification, which remain entrapped in the solid steel. In a well-deoxidized steel containing residual aluminum and/or silicon, the equilibrium dissolved oxygen content is usually very low and so the maximum amount of oxide which may be produced as secondary deoxidation products is small in comparison with the amount of primary products. It may be seen, therefore, that the amount of indigenous nonmetallic inclusions may be minimized if a low dissolved oxygen content is achieved by deoxidation and if the primary deoxidation products are efficiently removed. Oxides which originate by reaction of the metal stream with the atmosphere during teeming are not considered in the present study. It is known that two or more deoxidizers may result in a lower equilibrium oxygen content when used in conjunction with one another than when any of the individual deoxidizers are used alone. Equilibrium studies by Hilty and crafts2 and by Bell3 have shown that manganese increases the effectiveness of silicon as a deoxidizer, and Walsh and Ramachandran4 relate this to a reduction in the activity of silica in the products as the manganese :silicon ratio in the steel increases. It was also shown by Herty's work on deoxidation of steel by silico manganese alloys,5 that there existed an optimum ratio of manganese to silicon which gave a minimum inclusion content. This ratio was in the range 4:l to 7:l and the (FeO-MnO-SiO2) products formed by such deoxidation practice were found to lie in a composition range having very low liquidus temperatures (1170 to 1250°C approx). The optimum manganese:silicon ratio was then explained by postulating that these fluid products were able to coalesce and that the larger particles formed floated out of the steel very quickly as predicted by Stoke's Law. The present work examines the effectiveness of various Mn-Si-A1 alloys as deoxidizers and their effects on the composition and removal of primary deoxidation products from a quiescent melt. EXPERIMENTAL TECHNIQUE Approximately 250 g of prepared Fe-O alloy, containing 0.045 to 0.055 pct O, were melted in an alumina crucible and deoxidized at 1550°C by plunging a thin steel cartridge containing the deoxidizer below the melt surface. A high frequency induction furnace supplying current at 8.5 kHz was used to heat a graphite susceptor, the interior of which had been machined to give a wall thickness of 0.85 in. to form a receptacle for the alumina crucible. The iron melt was essentially quiescent as the induced current was concentrated at the external surface of the graphite susceptor by the skin effect. A nonoxidizing atmosphere was maintained over the melt by passing a continuous stream of argon through the lid of the susceptor. The melt temperature was measured before deoxidation, and again at the end of an experiment by means

Jan 1, 1970

By J. S. Levine, M. Prats

A homogeneous and uniform cylindrical reservoir containing oil and gas is fractured vertically on completion and is produced at a constant bottom-hole pressure. The fracture has an infinite flow capacity, is of limited lateral extent and is bounded above and below by the impermeable strata defining the vertical extent of the reservoir. Results show that such a fractured reservoir can be represented by a reservoir of circular symmetry having very nearly the same production history. The well radius of this circular reservoir is about 1/4 the fracture length and is essentially the same as that obtained previously for a single fluid of constant compressibility. At the same value of cumulative oil production, gas-oil ratios of fractured reservoirs producing at constant terzinal pressure are larger than those of reservoirs having no fractures. This leads to more inefficient use of the reservoir energy in fractured wells and results in lower reservoir pressures for the same cumulative oil production. The reduction in operating life due to fracturing a reservoir is not as great as that for a slightly compressible fluid. This diflerence can be accounted for by the lower reservoir pressure in the fractured reservoir and its adverse effect on the average mobility and compressibility of the oil. As anticipated, the reduction in operating life increases czs the reservoir permeability decreases. The type of results presented in this report can be used to determine the economic attractiveness of fracture treatments per se, to setect the initial spacing to be used in developing a field, and to compare the relative merits of fracturing available wells and infill drilling. INTRODUCTION The effect of vertical fractures on a reservoir producing either an incompressible or a compressible liquid has already been discussed in the 1iterature.l,2 Those results indicate that the production history of such a reservoir is essentially the same as that of a circular reservoir having an effective well radius of approximately one-fourth the fracture length. The present work reports on the effect of a vertical fracture on a reservoir producing two compressible fluids —oil and gas—by solution gas drive. Because of the empirical nature of the PVT and relative permeability data used to obtain the performance of such reservoirs, results can only be obtained numerically and with the aid of high-speed computers. Since reservoirs lose their radial symmetry when fractured vertically, pressure and saturation can no longer be given only in terms of distance from the well. Two coordinates (such as x and y) must now be used to describe the pressure and saturation within the reservoir, and, since we are dealing with compressible fluids, time is also a variable. Thus the solution of a vertically fractured reservoir requires finding two unknowns (pressure and saturation) in two space variables (say x and y) and in time (t). Since no means are readily and generally available for solving such problems at the present time, we have used the results of previous work1,2 to approximate the effect of a vertical fracture on a reservoir producing both oil and gas by depletion. The purpose of the present wmk, then, is to investigate the possibility of using available numerical techniques (limited at the moment to one space variable) to study the two-space-variable flow behavior resulting from a vertical fracture. Results obtained in the course of this investigation are also reported and discussed. Input and output data of the numerical methods used are given in practical units: BOPD, feet, psi, cp, and md. Results are discussed fist in terms of specific reservoir and crude properties and geometries. Later, dimensionless parameters are introduced in order to extend results to different values of some of the reservoir and fracture properties. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable, circular, cylindrical outer boundary of radius r,. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below' the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. 1 indicates the general three-dimensional geometry of the fractured reservoir. Gravity effects and the effects of differential depletion resulting from variations in hydrostatic head (pressure) will be neglected. Thus, the flow behavior in the fractured reservoir is described by the

By Avnulf Muan, Egil Aukrust

Activity-composition curves jor cobalt oxide and manganese oxide in solid solutions with spinel-type structure have been determined by studying the equilibrium between the spinel phase and a coexisting solid-solution phase in the tewzperature range 1100" to 1400"C. Within limits of experimental error, the system displays the behavior of a regular solution. The excess integral free energy of mixing is represented by the equation . The standard free energy of formation of cobalt manganite, CoMn,O,, from the oxide components COO mzd Mn2OS at 1200°C is calculated to be -8.6 kcal. AMONG the technologically and theoretically most important oxide phases are those which crystallize with the same structure type as the mineral MgO . A120,. Although the name spinel originally was used only for this mineral, the term is generally used today to designate the whole group of oxide phases with this same structure type. It is in this wider meaning that the term is being used in the present paper. The previous literature on spinels is very extensive. There are two aspects of spinels which have attracted particular attention: the structure, including the nature and distribution of the cations present, and the physical properties (electric, magnetic). The status of knowledge in these fields has been well-summarized in recent review articles.1'2 By contrast, thermodynamic properties of spinels are virtually unknown. Delineation of the activity-composition curve over the whole composition range of a solid-solution series with spinel-type structure is the objective of the present work. The system at elevated temperatures (>1000"C) constitutes such a series. The activity-composition curves for this system can be calculated from a study of the equilibrium between the above spinel solid solution and a solid solution (Co,Mn)O with sodium chloride-type structure. Data for the latter solid solution have become available recently.3 The system, in contact with metallic CO at 1200°C, obeys Raoult's law. The determination of the activity-composition curve for the spinel phase is based on the following relations. Consider the reduction-oxidation equilibrium for cobalt ions according to the equation: Because it is impossible in practice to measure single activities of electrically charged constituents, we will treat the equilibria in terms of electrically neutral components. Eq. [I] can then formally be written as follows: where and the activities of cobalt oxide in the (Co,Mn)O and the spinel solid-solution phases, respectively, K is a constant at constant temperature, and Pa is the oxygen pressure of the gas phase. The numerical value of K can be determined from a determination of the oxygen pressure P& for the equilibrium coexistence of Cos04 and COO in the binary system Co-0. Under these circumstances be set equal to 1, and hence K = [Po Eq. [3] can therefore be written

Jan 1, 1964

By R. T. C. Rasmussen, L. H. Banning, W. E. Anable

In the rapidly growing industry of elemental-phosphorus production from western phosphates, most of the vanadium and chromium contained in the phosphate rock collect in the byproduct ferro-phosphorus. Results are presented of a completed laboratory project, which developed a tristage crystallization and hydrolysis process for recovering strategic vanadium and chromium, as well as a valuable phosphorus product, after extracting these elements from the ferro-phosphorus by roasting and leaching. THE Phosphoria formation in Idaho, Montana, Wyoming, and Utah contains the Nation's largest reserve of phosphate rock. A unique feature of the Phosphoria beds is their content of a fraction of a percentage each of vanadium, chromium, nickel, and molybdenum. Vanadium is the most important as to quantity and value. Small-scale tests by the Bureau of Mines at Albany, Oregon, in 1947, indicated that most of the vanadium in the phosphate rock collects in the ferrophosphorus product of smelting. Subsequent electric smelting operations to produce elemental phosphorus from western phosphate rock (experimentally by TVA and industrially at Pocatello, Idaho) have shown that the vanadium and other metals in the rock are to a large extent recovered in concentrated form in the ferrophosphorus byproduct. This paper reports the results of completed laboratory research on the recovery of vanadium from ferrophosphorus, which was undertaken by the Bureau of Mines at Albany in 1948 as the first phase of a project entitled, "Vanadium and Fluorine from Western Phosphates." The various vanadium-recovery methods investigated, including the roast-leach method that showed most promise and was studied in greatest detail, are discussed in an earlier publication.' Subsequent systematic study of the roast-leach method of extracting vanadium from western ferrophosphorus developed the more effi- cient tristage crystallization process, which is the subject of this paper. Process Development The investigations were made on ferrophosphorus produced in the electric smelting of elemental phosphorus from western phosphate rock. The TVA provided two sample lots of ferrophosphorus produced in pilot plant smelting of phosphatic shale from the Fort Hall Indian Reservation in Idaho. The Westvaco Chemical Div. of the Food Machinery & Chemical Corp. supplied two sample lots of ferrophosphorus produced by its phosphorus smelter at Pocatello, Idaho. The analyses of all four lots are shown in Table I. Westvaco lot B was the starting material for the more recent tests. The roast-leach process for recovering vanadium from western ferrophosphorus, as originally developed, employed the following principal steps: Roasting of a mixture of pulverized ferrophosphorus, soda ash, and salt; extraction of the water-soluble vanadium, phosphorus, and chromium compounds from the calcine by leaching, settling, and decanta-tion of the pregnant solution; primary crystallization of trisodium phosphate from the pregnant solution; purification of the trisodium phosphate crystals by dissolution in water and secondary crystallization; purification of the pregnant vanadium solution from the primary crystallization step by adding calcium chloride to precipitate calcium phosphate; and hydrolysis of vanadium red cake from the puri-

Jan 1, 1954

By A. B. Dyes

In the operation of a water-driven reservoir, a free gas saturation can he established by maintaining production rates fast enough to cause the reservoir pressure to decline below the bubble point. The benefit of such a procedure on the displacement efficiency of the oil by water is illustrated for two types of sandstone samples from one reservoir. Those rock samples showing the poorest recovery to water drive in the absence of a free gas saturation give the most improvement in the presence of a free gas saturation. Employing one type of reservoir fluid (low .shrinkage) the benefit of evolved gas on oil displacement is calculated at several reservoir pressures below the bubble point. This demonstrates the presence of air optimum pressure for water displace,rnent which is .several hundred pounds per .square inch below the bubble point. Displacement of oil at the optimum pressures results in the removal of 7 to I? per cent more oil than would be obtained by displacement at the bubble point pressure. In some instance. this magnitude of increase may be worthy of consideration in establishing the maximum efficient rate of production from many water-driven fields. INTRODUCTION For many years the belief that the use of gas could be combined with that of water to result in a better recovery operation than the use of either of these phases alone has been prevalent in the oil industry. This is evidenced by the several field trials which have employed the injection of gas and water in combination.1.2.v In most cases the small amount of any additional recovery, in combination with the limited knowledge available on the older reservoirs, has left uncertain the influence of gas on recovery in these earlier attempts to combine the use of gas with water. Research studies in recent years have demonstrated through laboratory. floods the magnitude of the benefit of the presence of gas on the displacement of oil from sandstones by water.5,6,7,8,9,10,11 In addition, studies of the distributions of the phases which are present during the displacement process have developed concepts concerning the mechanism by which this benefit is obtained."." It now remains for the engineer to incorporate these findings into the general technology of reservoir operations. It is the purpose of this paper to illustrate that the production of a water-driven reservoir at pressures below the bubble point is one such operation whereby improved oil displacement efficiency can be obtained as a result of gas evolution. The establishment of a gas saturation by evolution of dissolved gas was one of the techniques used by several investigators in the laboratory studies. The possibility of obtaining the benefit of gas evolution in water-driven reservoirs by producing at pressures less than the bubble point has 3150 been pointed out previously." The desirability of this operation has undoubtedly

Jan 1, 1955