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By A. Romero-Juarez

This paper is concerned with the effect of propping-agent concentration on flow capacity of a fracture in the case in which there is embedment of the propping agent. Previous published studies have shown definitely that there is a relationship between fracture flow capacity and prop ping-agent concentration, and it has been shown that the theoretical results are confirmed by laboratory experiments. The problem of directly finding sand concentration for maximum flow capacity of a sand-propped fracture is solved, and formulas and charts are given to obtain this concentration under various conditions of effective overburden pressure, medium sand-grain diameter and rock properties. It is shown that, for the same effective overburden pressure and the same rock characteristics, optimum sand concentration in pounds per gallon does not depend on medium sand diameter. For conditions met in bydraulic fracturing operations, it is found that sand concentration in grains per square inch for maximum flow capacity varies within a wide range of values; this indicates the convenience of using data of fracturing pressure and rock characteristics for calculating sand concentration in order to achieve the best results in fracture treatments. INTRODUCTION It has been pointed out in the published literature1 that one important factor controls the success of a hydraulic fracturing operation — the propping of the fracture. The main effect of the propping agent is to hold the fracture open by means of the reaction forces that oppose the pressure due to the overburden. It is assumed in this paper that the propping agent is sand, that the grains are spherical and uniform in size, and that this sand is distributed in a monolayer in the fracture. The existence of a sand concentration value for maximum fracture flow capacity has been recognized since the publication of one of the first studies on the subject.2 In the reference cited, flow capacity was assumed to be proportional to the cube of the fracture volume per square inch not filled by sand. The obtained experimental curves relating to flow capacity and sand concentration had the same appearance as the curves obtained with the afore-mentioned assumption. Recent work3 has shown that fracture permeability, in the case of a monolayer, can be calculated accurately by means of a modified Kozeny-Cacman equation; thus, it can be shown that fracture pqmeability is a function of free volume in the fracture and of the rock and sand wet surfaces. The flow capacity of a fracture is dependent on the permeability of the fracture and on the fracture width. If all excessive quantity of sand is present in the fracture, its width may be large but its permeability i:; low due to the greater flow resistance; too few grains of sand per square inch are present in the fracture, sand embedment in the rock is greater and the width becomes small enough to appreciably decrease the rate of flow. To determine optimum conditions of flow, therefore, it is necessary to know the dependence of fracture width on density or concentration of propping agent. This relation is given in a study4 in which the approach to embedment is similar to the one made in a penetration hardness test of metal. With the equacions presented by Darin and Huitt,3 the number of sand grains per square inch that results in maxirnum fracture capacity can be determined graphically by plotting fracture capacity vs sand concentration. Since the relationship between fracture capacity and sand concentration may be considered known, one is led to formulate the analytical problem of directly determining sand concentration for maximum fracture flow capacity, in order to study the effect of the various quantities that come into the process. The solution of this problem appears to be interesting both from the viewpoint of fluid mechanics and from the practical viewpoint of oil production in hydraulic fracturing treatments. EQUATION FOR FRACTURE FLOW CAPACITY It can be shown3 that the fracture flow capacity of a monolayer is given by the following expression,

By Jr. Ensign C. O., J. W. Trammell

The two principal methods of room-and-pillar mining practiced at White Pine make it important to predict variations in the thickness and rock types of a stratum called the upper sandstone. In full column mining, the nearly barren upper sandstone occurs between two ore horizons (called upper shale and parting shale, respectively), and is mined as a part of the ore column. In general, full column mining is not practiced where excessive upper sandstone thickness causes full column ore grade to be substantially lower than parting shale ore. In parting shale mining, the upper sandstone forms the mine roof. Difficulty in predicting upper sandstone character arose because the extent and directions of its variations were not apparent in the property's diamond drilling, in which holes are spaced on 1000-ft centers. A study of sedimentary features, undertaken to improve the predictability of trends in the upper sandstone, led to an interpretation of the sedimentary environment in which the sandstone was deposited. Ripple marks, mud cracks, and cross-bedding, as well as other, less well known features, such as channel casts, flute casts, and current crescent casts, were mapped or recorded. These data, coupled with the knowledge of regional facies changes gained from studying drill core, show that the upper sandstone was deposited by a series of streams flowing northeastward over the underlying parting shale. Deposition of the lowermost bed of the upper sandstone, near the ancient shoreline, was locally preceded by erosion of the parting shale, and the greatest thicknesses of sandstone are found in channels scoured out of the parting shale. Awareness of the rather strong linear trends in the upper sandstone makes it possible to project continuous areas of thick upper sandstone through apparently isolated "highs" in the upper sandstone thickness contour map, which is based on drill-hole information. Since local exceptions to general stratigraphic trends exist, a method was also needed for esti- mating, in detail, the thickness and degree of shali-ness of upper sandstone forming the roof in active parting shale mining areas. Because locally the parting shale was thinned by erosion during the deposition of upper sandstone, parting shale thickness is inversely proportional to upper sandstone thickness. Utilizing information taken from short drill holes into the roof, curves were constructed for the correlation of parting shale thickness (measurable in the mine) with the upper sandstone total thickness, as well as the thickness of its basal member. The White Pine mine is situated in Ontonagon County, approximately 6 miles south of Lake Superior, in the Upper Peninsula of Michigan (Fig. 1). The orebody mined by White Pine Copper Co. occurs in the lowermost 20 to 25 ft of the Nonesuch formation, a series of middle- to upper-Keweenawan shales, siltstones, and sandstones. This paper discusses the solution of problems in ore grade control and mine planning arising from the presence of an essentially barren sandstone stratum within the orebody. THE OREBODY AND MINING TYPES A brief description of the orebody and mining methods is necessary to show how the upper sandstone affects mine planning and grade control. In the mine, the cupriferous zone of the Nonesuch shale is divided into three major portions, as shown in Fig. 2. Lying conformably on top of the Copper Harbor formation (or "lower sandstone") is the lower part of the orebody, the parting shale. The parting shale is overlain by the upper sandstone. On top of the upper sandstone, the basal portion (8 ft) of the upper shale is quite similar to the parting shale. Both the upper shale and parting shale are divided into a number of smaller stratigraphic units, each having a characteristic copper content, as shown by the histogram of Fig. 2. Other authors1'3 have dealt in detail with the stratigraphy and mineralogy of the orebody. However, in this article, we are concerned with the major subdivisions only, and it will suffice to note the low copper content of the upper sandstone, shown in Fig. 2. At present, two types of room-and-pillar openings are created in the orebody. In one type, called parting

Jan 1, 1964

By R. S. Reed, D. L. Ward

This paper is the result of a study, in 1919, to determine how much surplus power could be produced through the proper utilization of the entire gas flow from the two furnace stacks at the Federal Furnace Plant, South Chicago, 111. Obviously, the problem was to measure the flow of gas through the main beyond the point where the amount necessary for stove operation mas rermoved. In all probability, blast-furnace gas is the most difficult gas to measure, because of the high moisture and dust content, and the widely fluctuating flow from the furnaces. This wide fluctuation of flow forbids the acceptance of any one group of flow road-ings as indicative of normal operating conditions. A study of the conditions showed that a recording device on gas flow was necessary. As the gas at the point of measurement had passed through met washers, and accordingly was saturated with water and contained considerable dust carried past the scrubbers in the form of sludge, no form of Pitot tube could be used, for this sludge would quickly plug the dynamic. and static holes, spoiling the gage readings. An even more serious objection to the use of Pitot tubes was the impossibility of accurately measuring the cross-sectional area of the gas main on the plane of Pitot-tube installation. Given an absolutely clean gas and a perfectly circular pipe, it would be safe to assume, through measurements of the pipe diameter, that the gas main was of a certain cross-sectional area. But the continual depositing of sludge and the fact that the main mas fabricated from riveted sheets led us to discard the idea of using Pitot tubes for. this service. The Venturi tube mas then considered, and had there been a sufficiently long straight run of gas main to accommodate a tube of the required size (72 by 28 in.) such an installation would very likely have been made. A plate with a sharp-edged orifice was eventually accepted as it possesses all the characteristics of a Venturi tube, requires less space, and

Jan 1, 1922

By R. S. Reed, D. L. Ward

This paper is the result of a study, in 1919, to determine how much surplus power could be produced through the proper utilization of the entire gas flow from the two furnace stacks at the Federal Furnace Plant, South Chicago, 111. Obviously, the problem was to measure the flow of gas through the main beyond the point where the amount necessary for stove operation mas rermoved. In all probability, blast-furnace gas is the most difficult gas to measure, because of the high moisture and dust content, and the widely fluctuating flow from the furnaces. This wide fluctuation of flow forbids the acceptance of any one group of flow road-ings as indicative of normal operating conditions. A study of the conditions showed that a recording device on gas flow was necessary. As the gas at the point of measurement had passed through met washers, and accordingly was saturated with water and contained considerable dust carried past the scrubbers in the form of sludge, no form of Pitot tube could be used, for this sludge would quickly plug the dynamic. and static holes, spoiling the gage readings. An even more serious objection to the use of Pitot tubes was the impossibility of accurately measuring the cross-sectional area of the gas main on the plane of Pitot-tube installation. Given an absolutely clean gas and a perfectly circular pipe, it would be safe to assume, through measurements of the pipe diameter, that the gas main was of a certain cross-sectional area. But the continual depositing of sludge and the fact that the main mas fabricated from riveted sheets led us to discard the idea of using Pitot tubes for. this service. The Venturi tube mas then considered, and had there been a sufficiently long straight run of gas main to accommodate a tube of the required size (72 by 28 in.) such an installation would very likely have been made. A plate with a sharp-edged orifice was eventually accepted as it possesses all the characteristics of a Venturi tube, requires less space, and

Jan 1, 1922

By B. H. Mot

Underground water has been one of the greatest problems in sinking mine shafts, sealing existing shafts, and driving headings under streams. In the preparation of a proposed shaft or existing shafts for elimination of water leakage, advances have been brought about through the use of a controlled grouting method. The modern method to divert water from proposed shaft sites is known to us as pre-grouting, and from existing shafts, as controlled pressure grouting. This method involves the solidification of the surface and rock by the injection of a liquid mixture of

Jan 1, 1949

By Henry N. Doyle

Basic procedures in the mining industry have changed only slightly over the centuries since metals and fossil fuels became an essential part of man's economic and cultural life. Mining techniques of the 20th century bear a close resemblance to those of the ancients: exploration, ore breakage and removal, hoisting, and processing. The great advances, however, have been in equipment and machinery of greater size and speed which allow greater efficiency in each of these operations, with a corresponding reduction in manpower requirements. Yesteryear production was measured in pounds per man-day; today a giant and complex, but highly efficient, continuous mining machine can remove as much as eight tons of material a minute from the coal face. If our energy and metal demands of the future are to be met, and at this time it can be assumed that coal will continue to supply a significant part of the energy demand, other dramatic and spectacular technologic advances must be accomplished. Along with mechanization, however, public policy will require the industry to place greater emphasis on health and safety protection, as has been well demonstrated by recent actions of Congress. Together, fossil fuels and metals formed the basis for the industrial revolution-coal to develop power and metals to transform power into useful energy. Strangely enough, however, the mining industry the world over has lagged behind the continuous social changes brought on by the industrial revolution, such as preventive health and industrial hygiene services, and other programs directed to the well-being of the worker. In some countries this resistance, to change may have led in part to the nationalization of the coal industry. Whether this disinclination to social change in the industry of the United States reflects managerial attitudes, inept labor leadership, government neglect, or economic relationship would be the subject of an interesting study. Doubtless the mores of miners and their resistance to change, as well as their geographic isolation from other industrial groups, may have had a strong influence on these factors. In every major coal mining country the accident rate in the coal industry is substantially higher than other industrial groups, and the cost of pneumoconiosis compensation in some countries is greater than the combined costs for all other occupational diseases from all other industries. The high social cost of occupational accidents and diseases may have been a factor in the closing of the industry in at least two countries. Despite diminishing manpower needs, the industry is faced with critical manpower shortages. Miners once reared their sons to be miners; now it appears that the opposite is true. This factor alone, however, does not explain an acute labor shortage in the industry. Traditionally, the industry drew much of

Jan 1, 1976

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemi-sorption. FLOTATION of quartz is of practical importance as something to be avoided in soap-floating many types of ores. Clean, unactivated quartz is not floated with fatty acids and soaps, such as oleic acid and sodium oleate, in the quantities normally used for flotation. However, data in the literature indicate that almost any multivalent cation will activate quartz if given an opportunity. Thus, a common problem is to prevent activation of quartz by the various inorganic cations inevitably present in flotation pulps. Wark and his coworkers1 have demonstrated the reversibility of the chemical reactions and adsorptions involved in the activation, depression, and collection of the common sulphide minerals. The procedure in much of their work was to bring a mineral surface to equilibrium with solutions of known pH, collector concentration, and activator concentration, and then to test the floatability of the mineral by contact-angle measurement. From the data, graphs were constructed with pH and reagent concentrations as coordinates. These graphs show fields of flotation and fields of nonflotation, separated by narrow transition regions whose locations are shown by so-called contact curves. From the shapes and locations of the contact curves, which roughly separate fields of flotation from fields of nonflotation, a quantitative understanding of the interaction of the reagents with each other and with the minerals often can be deduced. The study of quartz flotation to be described in this paper follows in broad lines the approach of Wark and coworkers. That is, pH, activator concentration, and collector concentration were varied to find equilibrium conditions of flotation and non- flotation, and the results are presented graphically by means of contact curves. However, instead of testing for floatability by measuring the contact angle on a polished surface, a simple vacuum flotation technique was developed and used. Purified oleic acid was the collector and terpineol the frother. Barium activation was studied in some detail, and exploratory studies were made of activation with calcium, aluminum, ferric iron, and stannic tin. Preparation of Materials Quartz: Large lumps of high-grade vein quartz were crushed dry in a cone crusher and rolls. The —20, +28-mesh portion was screened out and used in the subsequent steps. This material was passed through a high-intensity magnetic separator to discard iron, then leached twice with hot concentrated HCl and washed repeatedly with distilled water. The cleaned sand was then wet ground with porcelain balls in a porcelain pebble mill, deslimed repeatedly by settling and decantation to discard —800-mesh material, and again washed with hot HCl followed by distilled water. The resulting stock of quartz was stored under water. Chemical analysis gave 99.8 pct SiO2. Table I gives the size analysis of the quartz used for flotation tests. Calculations from these data, using shape factors given by Gaudin and Hukki9 indicate a specific surface of about 500 cm2 per g. Blank flotation tests in distilled water, and in water with added frother, showed the prepared quartz to be completely nonfloatable and thus indicated the absence of organic contamination. Oleic Acid: The preparation of oleic acid was based on fractional vacuum distillation of methyl oleate2,3 followed by regeneration of oleic acid, and finally fractional crystallization of oleic acid from acetone solutions at low temperatures." The pure oleic acid was stored in a refrigerator. The iodine number of the oleic acid was found to be 90.0 (theoretical 89.93). Oleic acid was used in the form of a dilute water solution of sodium oleate, after preliminary flotation tests showed no effects of form of addition and order of addition of reagents when an adequate conditioning time (that is, 30 min) was provided. Other Reagents: Sodium hydroxide solutions low in carbonate were prepared by first making 1:1

Jan 1, 1951

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemi-sorption. FLOTATION of quartz is of practical importance as something to be avoided in soap-floating many types of ores. Clean, unactivated quartz is not floated with fatty acids and soaps, such as oleic acid and sodium oleate, in the quantities normally used for flotation. However, data in the literature indicate that almost any multivalent cation will activate quartz if given an opportunity. Thus, a common problem is to prevent activation of quartz by the various inorganic cations inevitably present in flotation pulps. Wark and his coworkers1 have demonstrated the reversibility of the chemical reactions and adsorptions involved in the activation, depression, and collection of the common sulphide minerals. The procedure in much of their work was to bring a mineral surface to equilibrium with solutions of known pH, collector concentration, and activator concentration, and then to test the floatability of the mineral by contact-angle measurement. From the data, graphs were constructed with pH and reagent concentrations as coordinates. These graphs show fields of flotation and fields of nonflotation, separated by narrow transition regions whose locations are shown by so-called contact curves. From the shapes and locations of the contact curves, which roughly separate fields of flotation from fields of nonflotation, a quantitative understanding of the interaction of the reagents with each other and with the minerals often can be deduced. The study of quartz flotation to be described in this paper follows in broad lines the approach of Wark and coworkers. That is, pH, activator concentration, and collector concentration were varied to find equilibrium conditions of flotation and non- flotation, and the results are presented graphically by means of contact curves. However, instead of testing for floatability by measuring the contact angle on a polished surface, a simple vacuum flotation technique was developed and used. Purified oleic acid was the collector and terpineol the frother. Barium activation was studied in some detail, and exploratory studies were made of activation with calcium, aluminum, ferric iron, and stannic tin. Preparation of Materials Quartz: Large lumps of high-grade vein quartz were crushed dry in a cone crusher and rolls. The —20, +28-mesh portion was screened out and used in the subsequent steps. This material was passed through a high-intensity magnetic separator to discard iron, then leached twice with hot concentrated HCl and washed repeatedly with distilled water. The cleaned sand was then wet ground with porcelain balls in a porcelain pebble mill, deslimed repeatedly by settling and decantation to discard —800-mesh material, and again washed with hot HCl followed by distilled water. The resulting stock of quartz was stored under water. Chemical analysis gave 99.8 pct SiO2. Table I gives the size analysis of the quartz used for flotation tests. Calculations from these data, using shape factors given by Gaudin and Hukki9 indicate a specific surface of about 500 cm2 per g. Blank flotation tests in distilled water, and in water with added frother, showed the prepared quartz to be completely nonfloatable and thus indicated the absence of organic contamination. Oleic Acid: The preparation of oleic acid was based on fractional vacuum distillation of methyl oleate2,3 followed by regeneration of oleic acid, and finally fractional crystallization of oleic acid from acetone solutions at low temperatures." The pure oleic acid was stored in a refrigerator. The iodine number of the oleic acid was found to be 90.0 (theoretical 89.93). Oleic acid was used in the form of a dilute water solution of sodium oleate, after preliminary flotation tests showed no effects of form of addition and order of addition of reagents when an adequate conditioning time (that is, 30 min) was provided. Other Reagents: Sodium hydroxide solutions low in carbonate were prepared by first making 1:1

Jan 1, 1951

By D. A Dahlstrom

THE necessity for slime elimination from valuable mineral and coal products has become increasingly significant within the past 5 years.' , Most of the mechanized mining and present beneficiation methods have resulted in larger tonnages of extreme fines, silts, and clay, commonly called slimes, processed by the preparation plant. Economics in turn have forced the plant operator constantly to lower the bottom size of effective beneficiation, necessitating an almost complete recovery of valuable solids regardless of particle size. When these important factors are considered, the need for an efficient slime removal method for fine solids becomes self-evident. Ordinarily slimes have been classified as ranging from 75 microns, or 200 mesh, down to colloidal dimensions of less than one micron. At the same time there is general agreement that the most troublesome slimes are primarily clays, silts and extreme fines, so that the actual top size may be placed at approximately 30 to 40 microns. This immediately restricts any desliming operation to classification, as screening or other methods would be both uneconomical and grossly inefficient at such dimensions. The liquid-solid cyclone has been recognized as one of the most efficient fine size classifiers available to the mining industry. Applications of cyclones to thickening, high efficiency solid recovery, degritting,

Jan 1, 1953

By D. A. Dahlstrom

THE necessity for slime elimination from valuable mineral and coal products has become increasingly significant within the past 5 years.' , Most of the mechanized mining and present beneficiation methods have resulted in larger tonnages of extreme fines, silts, and clay, commonly called slimes, processed by the preparation plant. Economics in turn have forced the plant operator constantly to lower the bottom size of effective beneficiation, necessitating an almost complete recovery of valuable solids regardless of particle size. When these important factors are considered, the need for an efficient slime removal method for fine solids becomes self-evident. Ordinarily slimes have been classified as ranging from 75 microns, or 200 mesh, down to colloidal dimensions of less than one micron. At the same time there is general agreement that the most troublesome slimes are primarily clays, silts and extreme fines, so that the actual top size may be placed at approximately 30 to 40 microns. This immediately restricts any desliming operation to classification, as screening or other methods would be both uneconomical and grossly inefficient at such dimensions. The liquid-solid cyclone has been recognized as one of the most efficient fine size classifiers available to the mining industry. Applications of cyclones to thickening, high efficiency solid recovery, degritting,

Jan 1, 1953

By F. R. Archibald, F. C. Jackson

The. prospect of winning aluvinum from clay was recorded almost a century ago at a time when the metal was no more than a curiosity.$ As the industry developed, and it has probably developed faster than that of any other metal, the expanding need for raw materials was adequately met by the ample supplies of bauxite ore. As with the other metals older in industry, however, lower grade ores have gradually entered the raw-material field through improvements in ore dressing, insufficienoy of high-grade ore supplies, favorable geographic location, or national necessity for domestic supply. So with aluminum, or alumina, which has been established as the requisite intermediate, the time may have come when a satisfactory process, with favorable location and suitable raw materials, can hold a sound place both in metallurgy and economics. It is the purpose of this paper to describe the Ancor process and its proposed application in treatment of clay in a plant now under construction at Harleyville, South Carolina, by the Defense Plant Corporation. Development of the AncoR Process The Ancor process has developed through successive stages of laboratory investigation, pilot-plant demonstration using neph-eline syenite and pilot-plant demonstration using kaolin-type clay from South Carolina, and is now in preparation for unit trial on an operating plant basis using the latter material. The laboratory studies were carried out over a number of years in the laboratory of the American Nepheline Corporation in Rochester, N. Y., and for the same company in the ore-dressing laboratory of Beattie Gold Mines, Que. Ltd. at Dupar-quet, Quebec. Both companies are associated with Ventures Ltd., Toronto, and its associated American companies. The work was originally undertaken with a view to recovery of alumina and alkalies from nepheline syenite as an adjunct to the American Nepheline Company's established business in the glass and ceramic trades, but as a process developed the possibility of application to clay and other aluminous raw materials became apparent and the laboratory studies were broadened to include these as well. Under the more pressing impetus of wartime needs and possibilities, pilot-plant operations were undertaken at the Canadian Bureau of Mines Ore Dressing Laboratories in Ottawa, and for purposes of demonstration under joint sponsorship of the Canadian Bureau of Mines, The American Nepheline Corporation, and The Aluminium company of canada Ltd. Upon completion of this program, of

Jan 1, 1944

By Alfred James

Some months since, in the Johannesburg gold-fields of South Africa, the attention of the author was directed to certain statements to the effect that the gold-contents of foul or extremely dilute cyanide-solutions could not be effectively precipitated in practice by the usual zinc-method. Such statements caused all the greater surprise, because it is well known that this difficulty is not encountered in other wellknown districts, as, for example, in New Zealand, where solutions containing less than 0.05 per cent. of KCy are regularly reduced in practice to below 1 grain of gold per ton, while in Mexico and the United States almost equally satisfactory precipitations are not uncommon. As a result of these representations, however, the author visited several plants at work in the Transvaal, and noted that while at some few mines the precipitation was really excellent, at others the effluent, after treatment, was much too high in bullion-contents. An investigation into the causes of these unsatisfactory results disclosed the fact that more attention to the close packing of the zinc-shavings in the extractor-compartments tended to improve the results, even with the most dilute solutions. The function of the zinc being one of surface, it stands to reason that a compartment well filled with zinc would be more effective than a half-filled one. Moreover, the quality of the zinc was inferior. This should be in long, tough, thin, light threads; light enough to ignite readily, and tough enough not to disintegrate easily into a slime. The coarse shavings too frequently employed appear to give the reverse of the best practice ; they are brittle, contain less surface, and take up more room. It is almost impossible to pack a compartment properly

Jan 1, 1898

By R. W. Snyder, H. J. Ramey

This paper presents the results of applying the Buckley-Leverett' displacement theory to petroleum reservoirs consisting of a finite number of layers. The layers are assumed to communicate only in the wellbores, and the reservoir may be represented as a linear system. Most previous investigations of this nature were limited by assumptions and by inconsistent calculation techniques. This study improves on previous work by applying the Buckley-Lev-erett displacement theory to a noncommunicating layered system where permeability, porosity, initial saturation, residual saturation and relative permeability vary from layer to layer in a logical and consistent manner. Gravity and capillary-pressure effects are neglected. A modification of the Higgins-Leighton calculation method was used in this study. Waterflood predictions were made with all properties varying, and then with only permeability varying using several inability ratios. These results were compared with the Stiles and Dykstra-Parsons predictions. It is shown that the latter methods generally give poor values for the breakthrough recovery and pessimistic predictions for the performance after breakthrough. Similar results were obtained for a gas-displacement case. lNTRODUCTION Field experience with immiscible displacement usually shows constant producing conditions until breakthrough of the displacing fluid. Then oil production continues at increasing displacing-to-displaced fluid ratios until the economic limit is reached. Three different ideal mechanisms are known that will produce this behavior: (1) relative permeability effects as described by Buckley-Leverett frontal advance theory,' (2) vertical stratification as considered by Stiles,2 Dykstra and Parsons5 and others and (3) different path lengths involved in areal (two-dimensional) flow between wells as described by Dyes et al.4 Without question, a combination of these factors modified by formation heterogeneity and other known and unknown factors actually does control the behavior of real systems. This paper presents results of an investigation of certain factors that should affect performance but which have received little attention to date. In 1944, Law5 demonstrated that porosity and perme- ability are often found to have normal and logarithmic-normal distributions, respectively. throughout cored intervals in natural formations. This led to the concept of the noncommunicating, multilayered reservoir model for immiscible displacement. This model assumes that the reservoir is composed of a number of layers that communicate only at the wellbores. Each layer is individually homogeneous, but may be different from every other layer. Stiles' presented one of the earliest applications of this model to waterflood performance. In addition, Stiles assumed that the initial saturations and relative permeabilities were the same for each layer, porosity was the same. displacement was piston-like, fluids were incompressible and injection into each layer was proportional to that layer's permeability capacity (permeability-thickness product). The last assumption would be true if the mobility ratio for the displacement were unity.21 Dykstra and Parsons" used the same model as Stiles, but rigorously included mobility ratios other than unity for piston-like displacement. Dykstra and Parsons used their general result to produce charts for log-normal permeability distributions between layers. Similarly, Muskat6 Pub1ished analytical solutions for linear and exponential permeability distributions. In 1959, Roberts' described a scheme for calculating water-drive performance for the noncommunicating, layered reservoir model which considered two-phase flow in the displaced region. Roberts used the same model and assumed that the injection rate into a layer was proportional to that layer's permeability capacity, but that flood front locations could be evaluated from the Dykstra-Parsons results. These assumptions are inconsistent, and a material balance cannot be maintained except for a mobility ratio of unity. At the same time, Kufus and Lynch8 coupled Buckley-Leverett displacement theory with the layered model to provide an improvement of the Dykstra-Parsons method that was consistent. In 1960, Higgins and Leighton9 resented a numerical method for calculating waterflood performance also considering two-phase flow in the displaced region. The result was used to investigate variation in absolute permeability and oil viscosity. An excellent, detailed history of using the noncomrnunicating, layered reservoir model was presented by Nielsen.'" The preceding techniques (and many related ones) were similar in that differences in initial saturations, residual saturations and relative permeabilities from layer to layer were neglected. It is well known that the irreducible water saturation is an important function of absolute permeability. Calhoun11 showed that the irreducible water saturation

By J. L. Huitt, D. K. Lowe

This laboratory flow study covers propping agent transporl in horizontal fractures as influenced by the characteristics of the propping particles, fluid and fracture. Correlations are presented for the transport of particles, deposition and fingering through dunes. For particles moving individually, the article velocity in some cases may be low compared to the hulk average fluid velocity; in other cases, the particle velocity may exceed the bulk average fluid velocity. At high propping agent concentration or low fluid velocity, the likelihood of particle deposition and dune formation increases. Fingering and channeling accompany dune formation. Dune formation can be limited to the outer region of tile fracture by adjustment of pump rate, fluid viscosity and particle concentration. A method is presented by which pump rate and fluid vircosity may he selected to control dune formation for given propping agent concentrations. INTRODUCTION The area and flow capacity of a fracture predominantly control the stimulation derived from hydraulic fracturing. Generation of fracture area exposes the rock matrix to a flow channel; the flow capacity of the fracture controls the flow through the channel to the wellbore under a given pressure gradient. This paper pertains to an important factor that affects the flow capacity of a fracture: the transport of the propping particles in the fracturing during the hydraulic fracturing treatment. With a better understanding of particle transport, fracturing treatments may be designed to obtain more effective distribution of the propping agent. RELATED STUDIES In recent years, the approach to obtaining high fracture flow capacity has been partial monolayer propping. Three papers1-3 have dealt with various facets of this concept. However, in some papers dealing specifically with particle transport, the results generally indicate that packing the propping particles within a fracture is inevitable. In early work&apos; with a sand slurry flowing in a pie-shaped flow cell, qualitative results showed that particle deposition in a fracture during transport should be expected. In other studies"" correlations based on slurry flow in vertical linear flow cells showed particle deposition was primarily a function of fluid velocity. In a recent paper the rate of sand advance (movement of dunes) in a horizontal linear flow cell was discussed. Subsequently, a method was given for designing fracturing treatments, based on the extent of sand advance during a treatment. In this work, particles whose diameter was small relative to the fracture width (i.e., dl W< 0.2) were primarily considered. The particle transport approaches that of sand transport in a stream bed. The industry trend, however, has been to use larger size propping agents. That is, particles with diameters approaching fracture widths predicted by Perkins and Kern.&apos;&apos; This trend has led to generally better fracturing treatments with particle relative sizes in the range 0.2 <d/W < 1.0. In all of the particle transport studies previously cited, the fluid characteristics were discussed. However, little or no attention was given to the parzicle characteristics. In this study the particles. as well as the fluid and fracture, are considered. VARIABLES AFFECTING PARTICLE TRANSPORT In the exploratory work to set LIP a program for this study, it was noted that particles within a batch moved at different velocities in a horizontal linear flow cell. In some cases the particles moved independently. In others there was particle interference. Also, particle deposition and fluid fingering occurred in some cases (Fig. 1). As a result of observing the easily distinguishab&apos;le types of particle movement, the particle variables as well as the fluid variables were included. In addition, the fracture width was included because the fluid velocity profile surely must affect the movement of the larger particles differently than that of smaller particles. Particle variables were density, diameter (based on a sphere of equal volumetric displacement), long and short dimensions, drag coefficient and velocity. Fluid variables were density, viscosity, yield shear strength and velocity. Fracture variables were the width and the angle between the plane of flow and a horizontal plane. Two factors which may prove to be important were omitted because of the complexity resulting from the parameters cited above. These are the fracture-surface roughness and gross irregularities that cause changes in the direction of flow. EXPERIMENTAL EQUIPMENT AND PROCEDURE A linear parallel-plate flow cell (Fig. 2) was used in the study. Lucite plates 1 in. thick formed the test section and permitted a viewing section 11 ft long and 10 in. wide. Spacing between the plates was adjusted with shims to give fracture widths 1/36 to 1/2 in. The model could be tilted to an angle of 45" with the horizonltal plane. Fluid flow was maintained with a Moyno positive displacement pump. Single particles were placed in the flow stream with a particle injector. A .4 - in. diameter plunger moving at a constant rate in a

Jan 1, 1967

By William P. Blake

In another paper I have described in general the close association of zinc-blende and iron pyrites in the ore-deposits of southwest Wis consin. These two minerals generally occur together at the same horizon, a sheet of one being overlain by a sheet of the other; and also the pyrites is disseminated through the blende to such a degree that the latter is rendered comparatively worthless for the produc tion of spelter. Ordinarily the pyrites, which is mostly the trimetric marcasite variety, occurs in about equal quantity with the blende and is separated by hand-culliug and chipping; but there are large de posits where the ores are so closely mixed that they can neither be separated by culling nor by any mechanical method. The specific gravity of the two minerals is so nearly the same that attempts often made to effect even a partial separation by jigging have proved un. successful. The smelters of zinc-ores in the Mississippi valley will not take ores which carry more than 7 per cent. of iron; and it is therefore necessary to cull the massive (&apos;jack" with great care and at consid erable expense, in order to bring it up to the market-standard of purity. The results of trials to effect a separation of blende and pyrites in other regions have been equally unsatisfactory. The literature of this branch of metallurgy abounds in examples. In Wisconsin efforts have been made in the past to " burn " the mixed ores in heaps, in order to soften or destroy the pyrites, and facilitate its separation from the massive blende. The same method has also been resorted to when galenite is mixed through the substance of the blende, for the purpose of disintegrating the ore, so that it could be separated by jigging. The custom was to pile the ore and the fuel together. As might have been expected, the results were far from satisfactory. As is usual in heap-roast ing, some portions of the ore were overheated and decomposed; zinc was lost by volatilization; the galenite in some portions was

Jan 1, 1894

By J. R. Thoenen, M. C. Malamphy, G. K. Dale

The beginning of the war and the events leading up to it precipitated a near crisis in the aluminum industry. Demands for the metal reached proportions far beyond the prewar production capacities and, in addition, the submarine menace seriously curtailed the importation of bauxite from South America, hitherto a chief source of high-grade ore. The situation required an intensive search for domestic ore to augment the reserves and in October 1941 Congress directed the Department of the Interior to investigate the extent, mode of occurrence, and quality of bauxite in the United States. In December of that year the Bureau of Mines and the Geological Survey began the search for bauxite in Arkansas, where more than go per cent of the domestic ore had been produced and where the greatest amount of bauxite was known to occur. The program involves the geophysical and geological investigation of the Arkansas bauxite region and the core drilling of areas considered favorable for the occurrence of bauxite deposits. Cores taken from the bauxite-kaolin zone are sampled and analyzed in the Bureau of Mines laboratory in Little Rock. The information from each of the deposits discovered is then assembled, the bauxite is graded with respect to its possible utility, tonnage estimates are made, and the whole is presented in the form of a war minerals report. Thirty-eight new bauxite deposits had been discovered and investigated at the end of the calendar year 1944, and the presence of several others had been indicated by the drilling. More than 5000 holes had been drilled throughout the bauxite region, and more than 60,000 chemical analyses had been made of samples taken from the bauxite-kaolin zone. A study of the chemical analyses led to certain general conclusions not only with regard to the chemical composition of Arkansas bauxite, but also with regard to its component minerals. Charts and diagrams based on these conclusions have been developed for practical use by the Bureau of Mines: (I) to serve as a check against laboratory analyses, (2) to present tonnage estimates of ore bodies based on mineral composition, (3) to illustrate the relationship of tonnages of bauxite to the alumina, silica, and iron content, and (4) to serve as a control for mining operations by providing a means for quick estimates of the value of the ore from a partial analysis of its chemical constituents. The use of charts and diagrams similar to those discussed in this paper-- is not new. The use of the trilinear diagram for studying the ultimate analyses of coals as of proposed by Ralston in Bureau of Mines Technical Paper 93 (1915) showed that the various ranks of coal fell in different areas on the diagram and that volatile matter, calorific value and other properties could also be plotted by the use of contours. A considerable subsequent literature, largely on classification of coals, has accurnulated since then, showing the utility

Jan 1, 1948

By J. R. Thoenen, M. C. Malamphy, G. K. Dale

The beginning of the war and the events leading up to it precipitated a near crisis in the aluminum industry. Demands for the metal reached proportions far beyond the prewar production capacities and, in addition, the submarine menace seriously curtailed the importation of bauxite from South America, hitherto a chief source of high-grade ore. The situation required an intensive search for domestic ore to augment the reserves and in October 1941 Congress directed the Department of the Interior to investigate the extent, mode of occurrence, and quality of bauxite in the United States. In December of that year the Bureau of Mines and the Geological Survey began the search for bauxite in Arkansas, where more than go per cent of the domestic ore had been produced and where the greatest amount of bauxite was known to occur. The program involves the geophysical and geological investigation of the Arkansas bauxite region and the core drilling of areas considered favorable for the occurrence of bauxite deposits. Cores taken from the bauxite-kaolin zone are sampled and analyzed in the Bureau of Mines laboratory in Little Rock. The information from each of the deposits discovered is then assembled, the bauxite is graded with respect to its possible utility, tonnage estimates are made, and the whole is presented in the form of a war minerals report. Thirty-eight new bauxite deposits had been discovered and investigated at the end of the calendar year 1944, and the presence of several others had been indicated by the drilling. More than 5000 holes had been drilled throughout the bauxite region, and more than 60,000 chemical analyses had been made of samples taken from the bauxite-kaolin zone. A study of the chemical analyses led to certain general conclusions not only with regard to the chemical composition of Arkansas bauxite, but also with regard to its component minerals. Charts and diagrams based on these conclusions have been developed for practical use by the Bureau of Mines: (I) to serve as a check against laboratory analyses, (2) to present tonnage estimates of ore bodies based on mineral composition, (3) to illustrate the relationship of tonnages of bauxite to the alumina, silica, and iron content, and (4) to serve as a control for mining operations by providing a means for quick estimates of the value of the ore from a partial analysis of its chemical constituents. The use of charts and diagrams similar to those discussed in this paper-- is not new. The use of the trilinear diagram for studying the ultimate analyses of coals as of proposed by Ralston in Bureau of Mines Technical Paper 93 (1915) showed that the various ranks of coal fell in different areas on the diagram and that volatile matter, calorific value and other properties could also be plotted by the use of contours. A considerable subsequent literature, largely on classification of coals, has accurnulated since then, showing the utility

Jan 1, 1948

By M. Cohen, D. Caplan

The scaling characteristics of three Fe-Cr alloys have been investigated by determining their weight gain vs. time curves at 1600° to 2000° F. The scales formed thereby have been examined using the techniques of X-ray diffraction and spectrographic and metal-lographic analyses in an attempt to explain the discontinuities in the curves and to elucidate the mechanism of scaling. DESPITE the considerable number of investigations that have been carried out on heat resistant alloys, the characteristics of the scales formed at high temperatures are not fully known. The research reported here was undertaken in an attempt to ascertain the mechanism of scaling of the stainless steels. Scaling experiments were carried out first, the weight increase of the specimens being followed continuously with time. It was observed that, as well as showing the expected decrease in oxidation rate with time, the oxidation curves showed breaks corresponding to intermediate periods of accelerated oxidation, after which protectiveness again increased. This phenomenon was observed with austenitic stainless steels (types 302, 309, and 330) and with Fe-Cr alloys (types 410, 430, and 446), but only the latter are treated in this report. An examination of the scales was made using the techniques of X-ray diffraction and spectrographic and metallographic analyses in an attempt to obtain a correlation between the nature of the scales and the oxidation curves. A search through the literature revealed only a very few previous reports of such periods of accelerated oxidation. Dunn&apos; found breaks in the oxidation-time curves of some Cu-Si alloys but saw no rational explanation of the phenomenon. Heindlhofer and Larsen2 attributed a discontinuity in the weight gain-time curve of iron at 1290°F to the formation of blisters, the subsequent cracking of which exposed an unprotected surface and permitted rapid oxidation until a new protective scale had been reestablished. They advanced no explanation, however, for what they termed the peculiar behavior of a 27 pct Fe-Cr alloy at 2000°F which gained weight very rapidly in between two periods of very slow weight gain. Portevin, Pretet, and Jolivet3 in describing breaks in the weight gain-time curves of Fe-A1 alloys suggested that they might be associated with the occurrence of localized and deeply oxidized areas on the specimens. Bandel4 in a general discussion of oxidation curves of heat resistant alloys considered that the discontinuities were due to a local disruption of the protective layer by the growth of iron-rich oxides. Day and Smith" in their report on the scaling of a large number of iron alloys noted but did not explain occasional relatively rapid changes in oxidation rate at higher temperatures. Chevenard and Wache6 found breaks, often two per specimen, in the oxidation curves of an 18-8 type alloy. They suggested that the cause might be a depletion in chromium of the surface layer of metal due to its selective oxidation, the resultant high concentration of iron and nickel in the scale leading to a poorly protective scale. McCullough, Fontana, and Beck&apos; explained the breaks in the oxidation curves of types 304, 430, and 410 alloys as due to mechanical ruptures. Experimental Work Table I lists the chemical compositions of the materials used. Cylindrical specimens 1/4 in. in diam and 11/2 in. long were machined from cold rolled % in. rod. After a fine finish cut with a sharp tool, the specimens were abraded while still mounted on the lathe with Nos. 2, 1, 0, and 00 metallographic grade emery papers. A 3/64 in. hole was drilled at a distance of 1/8 in. from one end to permit suspension in the furnace. Specimen Nos. 1, 2, and 3 were tested with this surface preparation. All others, after being similarly prepared, were electropolished in a perchloric-acetic electrolyte, electrical contact being made by pressing a tapered platinum hook into the drilled hole. The specimens were then washed in hot water, rinsed with distilled water, rinsed with methanol, dried at 120°F, and weighed. Thereafter,

Jan 1, 1953

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By W. H. Fitch

HAVING been asked to make some remarks after the reading of Mr. Dyrssen&apos;s paper, I regret that a test started some months ago has not yet been completed, but some of the things which I can tell you at this time seem interesting and shed a little different light on the idea of a recuperator. The device referred to is becoming more than. a recuperator, largely taking the place of a regenerator. I assume there is familiarity with the sketches that I presented in October, 1926, before the Engineers&apos; Society of Western Pennsylvania, describing our re-cuperator combination with checker chambers, and I have additional ones to show at this time. The follow-ing remarks will deal with modifications that have been made. At that time I suggested the gases leaving the regenerators at, say, 1400°, be reduced to 500° F. The opinion of the operating men consulted since that time is that, under the best operating conditions, the tem-perature may be 750° to 800° F. after the recuperator and on entering the stack. While the lowest final temperature of the gases en-tering the stack is important from the economic stand-point of fuel burning, and operating in general, it is not the whole story. The method of getting the heat out of the checkers is important. It is believed by many with whom we have talked that a better way is by a combination of checkers and a carborundum re- cuperator of the type described as it will stand all tem-peratures met in practice and might be called a super-refractory.

Jan 1, 1928