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By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970

By K. K. Landes

The north central and northeastern states supply over 50 pct of the chemical and metallurgical limestone produced annually in the United States, and Ontario is the leading source of this material in Canada. About three fourths of the chemical and metallurgical stone produced in this area comes from Michigan, Pennsylvania, Ohio, and Ontario. The specifications, physical and especially chemical, for chemical and metallurgical stone depend upon the end use, but in general the tolerance for impurities is so low as to rule out most limestones and dolomites. Both high calcium limestone and dolomite are used in the metallurgical and chemical industries. The principal metallurgical use is as a flux in iron ore blast furnaces and open hearth steel furnaces. The major chemical uses are in lime burning and soda-ash manufacture. Other important uses include glass manufacture, in making calcium carbide, and in sugar factories. All deposits of high quality carbonate rock are definitely finite. Invariably and inevitably they diminish in either thickness or quality laterally so as to become unworkable as chemical and metallurgical stone. The size of these high quality lenses ranges from a few thousands of tons to hundreds of millions of tons. The best hunting for new supplies is in the geologic formations known to contain premium quality deposits. However, because of high transportation costs, carbonate rocks, to be workable, must be close to market, dollarwise. Definitions: Chemical stone is limestone or dolomite used as a raw material by the chemical industry. The major chemical uses are in lime burning and soda-ash manufacture. Other important uses include glass manufacture, making calcium carbide, and in sugar factories. The specifications for chemical stone depend entirely upon the end product. Some uses require dolomite, some require high calcium limestone; in a few instances, notably in lime burning, either type of carbonate rock can be used as raw material. As a general rule, a fairly pure stone is necessary and for certain particular uses the tolerance for some elements such as sulfur, iron, and phosphorus may be extremely small. Metallurgical stone is used as a flux in furnace operations, especially in the blast furnace where iron ore is converted into pig iron and in the open hearth furnace where pig iron is made into steel. Either limestone or dolomite can be used in the blast furnace, but only high calcium stone is charged in the open hearth (except for rice-size dolomite used as a refractory). There are no rigid chemical specifications for blast furnace stone, but low silica, alumina, sulfur, and phosphorus are desirable. For open hearth use, in addition to low magnesia, a very low sulfur content is also specified by many furnace operators. For furnace use, fluxstone also must be sufficiently shatter resistant that it will remain in lump form during transport and charging into the furnace. Commercial stone is the term applied in the trade for crushed stone used for roadstone and in concrete aggregate. Many of our best chemical and metallurgical limestones are too soft to qualify in the Los Angeles abrasion test for use as commercial stone. However, some limestones, and a higher proportion of dolomites, do qualify for commercial stone and so can be sold to either market. Place Value: Even the highest grade limestone is still a bulk commodity with a relatively low value per ton. As a matter of fact there is very little difference in the average price per ton between high grade chemical and metallurgical stone and crushed limestone used commercially. Most high quality stone is produced in large operations with consequent low cost per ton whereas most commercial stone is produced in relatively small local quarries. As in the case of other bulk commodities most limestone buyers pay more for transporting the raw material than the cost of the stone at its source. For this reason steel furnaces and chemical plants

Jan 1, 1961

By Edward Griffith

The anthracite industry, which produces about 50 million net tons of coal annually, has been talked of as being able to last for another century; but if the water record of the past century continues into the expected century, this expectation of many years production still to come out of the remaining reserves will not be attained. The industry will be a submerged one in fact as well as in name. A recorded forecast of what has since occurred appears on page 34 of the Mine Inspectors' reports of 1897: It should also be noticed that bodies of water had accumulated in parts of abandoned mines before duplicate surveys of the same were required by law; and as a result we have today to contend with bodies of water, the exact location and position of which are not correctly known. Since that date, 47 years ago, the implications of the foregoing comment have grown enormously. This is shown in Fig. I and in the following table showing flooded and partially flooded areas that have come into existence since the early 1930's in the northern anthracite field: Number of Year Flooded Areas 1932...................... 2 1933...................... 3 1934..................... 3 1935...................... 5 1936...................... 7 1937...................... 9 1938.................... 11 1939...................... 11 1940...................... 11 1941...................... 14 1942...................... 14 1944...................... 26 Similar conditions exist in other fields in the anthracite region. In the period between 1923 and 1940, abandonment of collieries in the southern field resulted in the flooding of approximately 60 sq. miles (30 per cent) of the field. The ahandonment of collieries in this field has imposed additional expense for pumping on the collieries still operating. This condition will be aggravated by the extension of developments and cause suspension of operations if economic conditions do not justify the assumption of additional pumping costs. During the years, the region's rainfall has not altered, but the quantity going inside the mines through breakages in the surface, brought about by extraction of the coal, has increased materially, as indicated by the ratio of tons of water pumped to tons of coal produced underground for one of the large companies in the northern anthracite field: Year Ratio 1920................. 8.4:1 1925.................. 10.6:I I930.................. II.4:I 1935................. 26.2:1 1940.................. 32.7: I 1942.................. 30.3:I The data in Table I shows the total amount of water pumped and its ratio to underground production for one of the large companies in the southern anthracite field, and shows a rapidly growing serious situation. Rainfall quickly affects the workings in all the fields. In mine inspection district 7 of the southern field the rainfall in 1935 was 92,083,000,000 gal. The total water pumped was 36,274,000,000 gal. (39.4 per cent of the rainfall). The operating mines

Jan 1, 1947

By Edward Griffith

The anthracite industry, which produces about 50 million net tons of coal annually, has been talked of as being able to last for another century; but if the water record of the past century continues into the expected century, this expectation of many years production still to come out of the remaining reserves will not be attained. The industry will be a submerged one in fact as well as in name. A recorded forecast of what has since occurred appears on page 34 of the Mine Inspectors' reports of 1897: It should also be noticed that bodies of water had accumulated in parts of abandoned mines before duplicate surveys of the same were required by law; and as a result we have today to contend with bodies of water, the exact location and position of which are not correctly known. Since that date, 47 years ago, the implications of the foregoing comment have grown enormously. This is shown in Fig. I and in the following table showing flooded and partially flooded areas that have come into existence since the early 1930's in the northern anthracite field: Number of Year Flooded Areas 1932...................... 2 1933...................... 3 1934..................... 3 1935...................... 5 1936...................... 7 1937...................... 9 1938.................... 11 1939...................... 11 1940...................... 11 1941...................... 14 1942...................... 14 1944...................... 26 Similar conditions exist in other fields in the anthracite region. In the period between 1923 and 1940, abandonment of collieries in the southern field resulted in the flooding of approximately 60 sq. miles (30 per cent) of the field. The ahandonment of collieries in this field has imposed additional expense for pumping on the collieries still operating. This condition will be aggravated by the extension of developments and cause suspension of operations if economic conditions do not justify the assumption of additional pumping costs. During the years, the region's rainfall has not altered, but the quantity going inside the mines through breakages in the surface, brought about by extraction of the coal, has increased materially, as indicated by the ratio of tons of water pumped to tons of coal produced underground for one of the large companies in the northern anthracite field: Year Ratio 1920................. 8.4:1 1925.................. 10.6:I I930.................. II.4:I 1935................. 26.2:1 1940.................. 32.7: I 1942.................. 30.3:I The data in Table I shows the total amount of water pumped and its ratio to underground production for one of the large companies in the southern anthracite field, and shows a rapidly growing serious situation. Rainfall quickly affects the workings in all the fields. In mine inspection district 7 of the southern field the rainfall in 1935 was 92,083,000,000 gal. The total water pumped was 36,274,000,000 gal. (39.4 per cent of the rainfall). The operating mines

Jan 1, 1947

By A. W. Ruff

The seismic wave produced by an explosive is very important in blasting. A true understanding of the wave is only important when considering possible structural damage to buildings located near the blast, but it is also of primary importance when considering rock fragmentation. Because of the importance of the seismic wave to fragmentation, a finda-mental study of the seismic wave and its effect was made at the Cananea Consolidated Copper Co.'s mine at Cananea, Sonora, Mexico. Strain gages were used to measure the strain in the rock when nearby explosive charges were detonated. The variance in the circuit voltage caused by changes in the resistance of the strain gage was measured with an oscilloscope and recorded with a Polaroid camera. CONFINED DRILLHOLE CHARGES To record the seismic wave from a confined drillhole explosive charge, a gage was cemented to the bottom of a 4-in diam drillhole. The horizontal gage hole and nine horizontal charge holes were drilled perpendicular to the center line of the 2-39 drift and 4 ft above the floor. The gage hole was 29 in. deep, and the charge holes were drilled so that each bottomed 1 in. deeper than the gage hole. The gage was installed with its axis horizontal and parallel to the 2-39 drift. The charge holes had the following horizontal distances from the gage: hole 3, 3 ft; hole 4, 4 ft; hole 5, 5 ft; hole 9, 9 ft; hole 10, 10 ft; hole 14, 14 ft; and hole 15, 15 ft. Figs. 1 and 2 show the relationships of the gage and the charge holes. Charges of 80 pct special gelatin, which weighed 50, 100, and 150 g were exploded in the charge holes and the seismic waves were recorded. All charges were stemmed with 200 g of mud and detonated with an electric blasting cap. Fig. 3 shows the recorded seismic waves. The reflected components of the waves were too weak to be objectional on these records. Table I shows the data taken from the wave forms. The approximate average velocity of a wave with a 9-ft travel distance was 12,900 fps. Since different charge weights were used, it was necessary to scale the data. The scaled maximum compress ion-strain data and the scaled maximum tens ion-strain data are shown in Figs. 4 and 5, respectively. Figs. 6 and 7 show the strain-distance data from Figs. 4 and 5 converted to a 1-lb charge. The results showed that the wave consisted of an initial compression pulse followed by a tension pulse. The amplitude of the tension pulse approached the amplitude of the compression pulse as the distance between the gage and the shot increased. The decay rate of the seismic wave is very important in the evaluation of the blasting characteristics of a rock. When high-amplitude stresses are produced, as in rock fragmentation, the rate of decay is much more rapid than when small amplitude stresses are produced. In underground mine blasting, the burdens are usually not greater than 6 ft and the decay is very rapid. The rapid seismic-wave decay rate in the fragmentation range means that in practice, if the minimum weight of powder is used to break a specified burden, only a very

Jan 1, 1961

By T. E. Watkins, M. D. Nelson

A method of determining the lime content of drilling muds proposed by Battle and Chaney* has been examined both in the Field Research Laboratories of Magnolia Petroleum Co. and in field drilling operations. This proposed analytical method is condensed as follows: Titrate one ml of mud and one ml of mud filtrate, each with 0.02 N H2SO4, to the end point with phenolphthalein. The volume of acid in ml required for the mud titration is recorded as Pm and that of the mud filtrate titration as Pf Calculation of the lb lime/bbl mud is accomplished by use of the formula, lb lime/bbl mud = 0.6 (Pm - 1.3Pf) - 0.6 The analytical procedure outlined by Battle and Chaney was found to be quite satisfactory when reasonable precautions are used in mud sampling technique. Calculation of lime concentration by the method proposed in the above publication, however, has given values that varied as much as 100 per cent from the known lime content, for muds of either high or low solids concentration. By use of a formula, lb lime/bbl mud = 0.26 (Pm-F1.Pf), based on chemical equivalents of acid required for titration, both laboratory and field data have been satisfactorily correlated with the known amounts of lime present in the muds. In this formula a correction, F1, or volume fraction of liquid in the mud, is made for the solid content of the mud. Pm and Pf * Paper on "Lime Base Muds," presented by J. L. Battle (Humble Oil and Refining Co., Houston, Tex., and P. E. Chaney (Sun Oil Co., Beaumont Tex.), at the 1949 Spring Meeting of the Southwestern District API Division of Production, Dallas, Tex. The analytical procedure has also had wide distribution in a trade journal, Kembreak, published by the Accuracy Rig and Tool Co., Houston, Tex, †Derivation of equation lb/bbl — grams/350 ml 1 ml 0,02 N acid = 0.000741 grams of lime 1 ml 0.02 N acid/ml lime suspension = 0.26 lb of lime bbl lb of lime/bbl = 0.26 (Pm -F1, Pf ) have the same significance as in the Battle and Chaney equation. Table I shows typical data employing both formulas in calculating the lime content of various lime muds. This suggested procedure ignores lime which is in solution in the mud. The solubility of lime in water, normally about 0.5 lb per bbl, is greatly decreased by the addition of caustic soda, and, in a lime mud, it is probable that the concentration of dissolved lime is of the order of 0.1 lb per bbl. Such an amount of lime can be ignored, since it is within the range of accuracy of the method.

Jan 1, 1950

By F. Petkovich, M. P. Sudbury

Development of a new method of treating flotation concentrates for the preparation of feed suitable for direct charging to blast furnaces or converters is described. The method takes advantage of the fact that pyrrhotite contained in the concentrates can be made to undergo exothermic reactions which, under properly controlled conditions, result information of oxidation products that serve to cement the concentrate particles together. Thus green concentrates either in the form of pellets or briquettes containing 5 to 8 pct moisture not only were hardened, but also completely dried autogenously by continuous countercu,vrent shaft treatment with air. The process was developed through pilot plant operations ranging from 35 1b per hr to 2.5 tph, culminating in products evaluation tests on a railway-car scale. Falconbridge Nickel Mines Ltd., Falconbridge, Ont., have practised sintering, on a travelling grate machine, for many years to prepare a pyr-rhotite-bearing Cu-Ni sulfide flotation concentrate for blast furnace smelting. In recent years the development of new mines, and the construction of concentration plants some 40 miles from the smelter has increased the quantity of concentrate shipped, and encouraged the search for a method of producing dry, hard pellets or briquettes suitable for direct charging to a blast furnace or converter, and capable of withstanding considerable handling. The cementing properties of pyrrhotite oxidation products were discovered during a search for a suitable agglomeration method for sulfide concentrates, and were exploited in a process subsequently developed for autogenously drying and hardening pellets and briquettes of pyrrhotite-bearing Cu-Ni sulfide flotation concentrate. EARLY TEST WORK The production of hard, dry pellets of concentrate filter cake was attempted in the drying plant of one of the new concentrators. While soft pellets were produced containing 5 pct moisture, attempts at further drying resulted in disintegration of the pellets and intolerable dusting. The plant therefore was controlled to produce a concentrate containing about 6 pct moisture. The partially dried concentrate, which was shipped to Falconbridge for sintering, tended to heat spontaneously in transit. An at- tempt to briquette the moist concentrate at Falconbridge, in a plant incorporating a muller, a 20-in. roll briquetting press, and a steam-heated travelling grate oven, was more successful, although the equipment corroded rapidly due to the acid nature of the concentrate after spontaneous heating had occurred. LABORATORY STUDIES OF SPONTANEOUS HEATING OF CONCENTRATE The spontaneous heating of partially dried concentrate was studied in the laboratory. Moist concen-

Jan 1, 1961

By R. L. Grunes, F. K. Kies, C. D&apos, Antonio

THE several studies concerned with the annealing of thin nickel films have largely been restricted to films of a single thickness.1-4 It is well-known, however, that both physical and mechanical properties depend upon film thickness.5, 6 The strength-thickness relations found in vapor-deposited nickel films in the annealed and as-deposited states, as an example, are at least partially due to the density and arrangement of imperfections within the films.7, 8 For these reasons, the annealing characteristics of thin nickel films as a function of thickness were investigated. Electrical resistance was chosen to monitor annealing behavior since resistance changes are partially dependent upon defect structure. In addition, the equations predicting film resistivity as a function of thickness are already available.9, 10 Further advantages afforded by electrical-resistance measurements are its adaption to continuous readings during annealing and its relative simplicity. Nickel films were vapor-deposited, at average rates of 60Å per sec, on Vycor substrates held at room temperature in vacuums of about 10-5 torr. Afterwards, deposition-thickness measurements were made using a multiple-beam interferometric technique. A more detailed description of deposition procedures and the interferometer appear elsewhere.7, 8 The four-probe method was employed in measuring electrical resistance since this technique measures film resistance without contributions from lead wires and contacts. Resistance measurements were made before, during, and after annealing to temperatures of 700°C under vacuums of approximately 10-4 torr. Measurements were made every 25°C or more often when necessitated by unusual resistance changes. Cooling and heating rates were maintained at approximately 5°C per min. Typical resistivity vs temperature curves are shown in Figs. 1 through 4. It is apparent from these

Jan 1, 1965

By A. M. Gaudin

Jan 1, 1962

By Eugene Stephenson

CRITICAL analyses of the work expended in producing oil by the utilization of gas energy have appeared in the publications of Shaw,1 Pierce and Lewis,2 and Herold,3 authors who have ably discussed the factors which must be taken into consideration in comparing energy consumed per barrel in various wells which are flowed by means of gas-lift. However, two distinct phases of oil production are concerned with the ratio of gas energy consumed to oil produced. One of these phases is the gas-lift, which utilizes the differential gas pressures for the purpose of flowing oil, whether these pressures be natural reservoir pressures or be induced by artificial compression of gas or air. The other phase has to do with prorating oil production in pools which are operated either as units, or are subject to such restrictions as those imposed at Oklahoma City by the Corporation Commission, or, by similar controlling groups in other fields. An abundance of literature is available relative to the problems of flowing wells by gas-lift, but the first suggestion that the energy of the gas within the oil and gas pool might serve as a basis for proration, appeared in the timely article by McWilliams.4 Much of the. dissatisfaction with proration in certain fields is because some operators feel that besides the hazard to the wells which accompanies the test, the method of allocating production on the basis of the "potential" gage is inequitable and gives some operators a distinct advantage over others.5 The most severe penalty may be exacted from the most progressive operators or those who attempt to produce their oil with a minimum quantity of reservoir gas. If :no difficulties ever

Jan 1, 1931

By Sumner M. Anderson

Any discussion of outside support to Latin American mineral industries must concede at once the pre-eminent role of U. S. industry and business. American capital has developed the great copper resources of Chile and Peru, the lead-zinc of Peru and Mexico, the bauxite of Surinam and Jamaica, the petroleum and iron ore of Venezuela. American consumers have provided the market for their products. U. S. companies operating south of the border have trained Latin American geologists, engineers, chemists, and skilled labor—including metal, mineral, and fuel technicians—to new and greater competence. The industrial demands of World War II drastically altered world economics and concepts of U. S. foreign mineral requirements. In this country discovery of vital mineral resources fell far behind the alarming depletion rates, and there was new appreciation of the actual and potential importance of the world's less extensively explored areas. During the war and afterward, the task of supplying the nation's mineral requirements became greater than private industry could carry alone, and the Government assumed a position of continuing support. In Latin America, as elsewhere, this support applies in three categories: banking, procurement, and technical assistance. The first two are now generally accepted as necessary Government functions; the third has often been misunderstood and misinterpreted, although it has given rise to legitimate controversy. There have been major accomplishments in all three categories, as well as some errors of judgment. Since the beginning of World War 11, U. S. Government financing, procurement, and technical assistance have been applied on a large scale to a wide range of commodities and services throughout the free world. The present discussion—under the separate headings mentioned—will concern only the support related to a single industrial group in a single geographic area. During the War Federal banking was conducted on an emergency scale by temporary agencies created to meet the abnormal circumstances. Unfortunately, there are no readily available data on these activities that would permit evaluating loans and credits extended for mineral projects in Latin America. The only agency operating in this field since World War II is the Export-Import Bank, under its own authority and to some extent from credits authorized by the Office of Defense Mobilization. The Bank can offer more capital—on more favorable terms—than is available from most Latin American banks, and its staff of engineers evidently can appraise loan applications more favorably than commercial banks in this country are willing to do. The risks seem to be justified, as defaults have been well under 1 pct of total loans. From V-J day 1945 to the end of 1957, mineral loans to Latin America have been authorized for projects totaling $541.63 million in eight countries. In order of magnitude of credits, they have been made to Brazil, Peru, Chile, Mexico, Argentina, Venezuela, Guatemala, and Bolivia. In order of magnitude by industries. they are for development and expansion of steel mills, copper, manganese, nitrate plants, iron ore, zinc plants, sulfur plants, cement plants, tungsten, coal, and lead. Loan Distribution: By far the largest loans have been $307.9 million for iron and steel projects in Brazil, Chile, Mexico, Argentina, and Peru: $100.4 for developing the great low-grade copper deposits of southern Peru; and $55.3 million for developing manganese deposits in the Territory of Amapa, Brazil. Others range from $20.8 million for a zinc smelter in central Peru to $19 thousand for iron-mine trucking equipment in Chile. It has been noted that 59 pct of the loans have been to foreign companies, 14 pct to companies of mixed foreign and American capital, and 27 pct to American mining companies. About 40 pct of the total authorizations has been disbursed so far. In addition to these amounts, the Strategic Materials Division of the Economic Cooperation Admin-

Jan 1, 1959

By F. H. Buchella, J. F. Buchanan

The San Manuel copper deposit is located about 45 miles northeast of Tucson. The concentrator, smelter, administration building, and other plant facilities are located about seven miles southeast of the ,nine area at the new town of Sari Manuel as shown on Figure 1 (Sketch).

Jan 1, 1961

By A. B. Parsons

Jan 1, 1971

By C. David Mann

Metal prices continued to improve in 1964, resulting in the opening of new mines and re- activation of old ones. Larger and deeper shafts are being bored. At the AEC's Nevada Test Site, a 72-in. diam shaft is being bored to 3200 ft. In New Mexico a 1650-ft shaft was bored with a 48-in. bit, then reamed to 124 in. to 935 ft, and 102 in. to 1650 ft. Deviation was only 26 in. In California a shaft sinking machine has been developed which combines drilling and mucking equipment into one mobile, integral unit.

Jan 2, 1965

By J. E. House, C. J. Lewis

In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-pregnant sulfuric acid leach solution is contacted with an organic extractant dispersed in kerosene; the uranium enters the organic phase and associates itself with the organic extractants. Simultaneously an-ions or cations, as the case may be, leave the organic extractant phase and enter the aqueous phase. The two phases are then allowed to separate by virtue of their immiscibility. Based on the data available, a generalized procedure for the recovery of molybdenum from the sodium carbonate scrub liquor of acid leach uranium mills using secondary and tertiary amine extractants is presented, as is another generalized procedure for the recovery of molybdenum from the bleed stream of alkaline leach uranium mill circuits. Such economic appraisal as can be made at this stage of the development is also indicated. Molybdenum occurs in most uranium ores. Whether the uranium is solubilized by the acid leach route or by the alkaline leach process, some of the molybdenum present in the ore is solubilized along with the uranium. Molybdenum in uranium mill pregant solutions may cause processing difficulties, among which may be mentioned the poisoning of resins, the precipitation of organo-molybdenum complexes, or the build-up of molybdenum in recycle streams. While the uranium milling industry has been successful in applying measures to overcome the problems arising from the presence of molybdenum in the circuits, such measures nevertheless add to the cost of producing uranium yellow cake concentrate. Table I shows the analysis of typical uranium pregnant leach solutions. Uranium recovery by solvent extraction is presently practiced only in conjunction with acid leach circuits, and it may be noted that of about 16,000 tons of uranium ore daily processed by sulfuric acid leach, more than half of this tonnage follows the solvent extraction route. Uranium mills leaching ore with sodium carbonate-sodium bicarbonate solution (the so-called alkaline leach circuit) do not use solvent extraction. In this case the uranium pregnant solution is sufficiently pure to permit the direct precipitation of uranium concentrate with subsequent recycle of the alkaline leach solution. While solvent extraction procedures may be developed which are economically attractive for the alkaline leach uranium process, this has so far not been the case. The earlier uranium mill solvent extraction circuits used organo-phosphate extraction reagents, among which di-2-ethylhexyl phosphoric acid was popular. It should be borne in mind that uranium in its sulfuric acid leach solution exists in an equilibrium involving uranium in both anion and cation forms: uo + 2S0 = [uo2(so4)2] For this reason uranium may be extracted by either cation extractors or anion extractors and this is likewise true of molybdenum. However, the organo-phosphate extractants also load ferric iron which is usually present in the uranium acid leach solution. For this reason, it is necessary to reduce this solution substantially to the ferrous state ahead of solvent extraction using organo-phosphate reagents. The amines, being anion extractors, selectively reject iron and thus render the iron reduction step unnecessary. In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-

Jan 1, 1961

By M. Prats

Most of the information available on the heat efficiency of hot fluid injection processes, both water and steam, has been obtained from calculated temperature distributions in the pay zone and adjacent formations. The usual approach has been to write the heat balance equations in terms of the temperatures, and then to introduce whatever simplifications are necessary to help obtain an analytical or a numerical solution. In either case, the assumption has often been made that the vertical thermal conductivity in the flooded interval is infinite, so that the temperatures within the flooded interval are then independent of vertical position. Because it was first made by Lauwerier,l and has been used extensively since, this assumption will be referred to as the Lauwerier assumption. Excellent reviews of the literature on the heat efficiency of hot fluid injection processes have been given by Spillette,2 Flock et al.,3 and Ramney.4 Of course, the most significant contributions take into account the effect of a finite vertical thermal conductivity on the vertical temperature profile. The most general analytic expression for the heat efficiency of a hot fluid injection process is that of Antimirov5 who considers injection of a heated incompressible fluid into a reservoir through an arbitrary number of wells. The rate of heat injection into the reservoir, as well as the injection temperature, is an arbitrary function of time. The geometry of the horizontal flow is arbitrary, although the reservoir is considered to be of uniform thickness and properties and to be of infinite areal extent. Heat transfer within the reservoir is by horizontal convection and conduc- tion, and by vertical conduction. In the formations adjacent to the flooded interval, heat transfer is by conduction in any direction. Thus, the available expression for the heat efficiency due to hot water injection has been developed for rather general conditions. This degree of applicability has not been obtained for other thermal recovery processes. By making the Lauwerier assumption we have been able to obtain expressions for the heat efficiency that are essentially independent of the thermal recovery process, be it steam, hot-water, or underground combustion. Clearly, then, the approach followed here is more restrictive than that of Antimirov5 in that it uses the Lauwerier assumption. At the same time less restrictive assumptions are made about the horizontal heat transfer mechanisms, either in the flooded interval or in the formations adjacent to it. The main difference between our approach and that of other investigators is that the heat balance in the pay zone is expressed for the pay zone as a whole rather than for a volume element within it. The Lauwerier assumption is introduced after the problem is developed along these lines as far as possible. The details of the development of the heat efficiency are given in the Appendix, while the main features of the model are discussed in the next section. Results and their implications are discussed later in a separate section. The Model Certain assumptions have been made to determine

Jan 1, 1970

By J. C. Martin

Equations for three-phase, three-dimensional, compressible flow (including capillarity) are reduced to two-dimensional relations by a partial integration. This reduction allows three-dimensional flow problems to be treated with mathematics for only two spatial dimensions. The results can be used to formulate flow equations for two-dimensional reservoir simulators in which the effects of capillarity and fluid segregation in the third dimension are represented. Such reservoir simulators would retain many of the aduantages of two-dimensional simulators while simulating three-dimensional effects. The principal restriction of the method is that the thickness of the reservoir should be small, compared to the distance across the reservoir. INTRODUCTION In recent years, computers have been used to calculate the performances of many reservoirs. Most of the detailed calculations, however, are based on finite difference solutions of the flow equations, and present day computers are seldom able to handle a sufficient number of cells to produce entirely satisfactory solutions, even for reservoirs represented by two-dimensional arrays of cells. The situation becomes much worse when one wishes to approximate the reservoir by a three-dimensional array. A great saving in computation or a more detailed solution can be obtained for many reservoirs by using the partial integration of the equations of flow presented in this paper. The integration reduces the three-dimensional equations to two-dimensional relations; and, for studies of two-dimensional flows in vertical cross-sections, the equations are reduced to one-dimensional relations. Most reservoir performance calculations currently are based on one- or two-dimensional flow re1ations.l-3 In some cases flow in the third dimension is approximated by assuming a particular type of vertical saturation distribution, such as gravity segregation.l.2. The relations developed in this paper approach those for segregated flow as the capillary pressures approach zero, and they approach those for uniformly distributed saturations as the capillary pressures are increased. For this analysis, the ratio of the reservoir's thickness to the maximum distance across it must be small. The capillary pressures between the oil and water should also be small compared to the maximum pressure difference in the reservoir. This requirement is met by most reservoirs. It is assumed that the capillary-pressure curves are well defined, whether or not hysteresis effects are included. Also, the reservoir must have sufficient vertical permeability to allow the fluids to segregate. The results presented here provide a firm theoretical foundation to Coats' et aL5 assumption of vertical equilibrium and extend the relations to three-phase flow. Coats' assumption of vertical equilibrium, which he verified by calculations and experiment, is developed here mathematically from basic flow equations. DISCUSSION SATURATION AND PRESSURE DISTRIBUTIONS Appendix A presents a mathematical analysis of fluid flow in reservoirs where the ratio of thickness to maximum distance across the reservoir is small. The results indicate: (1) that the fluids along any line perpendicular to such a reservoir's upper surface are in static capillary equilibrium (vertical equilibrium); (2) that, to a first approximation, the fluid pressures and properties are functions of only areal position in the reservoir and time; and (3) that hydrostatic pressure gradients exist along any line perpendicular to the reservoir's upper surface. The results might be expected after studying several physical considerations. First, no flow is allowed normal to the upper and lower reservoir boundaries, which are relatively close together.

Jan 1, 1969

By AIME AIME

FEW mining schools possess an art gallery and certainly none can equal the collection of paintings depicting the mineral industries now hanging in the comparatively new building of the School of Mineral Industries at The Pennsylvania State College. Dean Steidle, who conceived the idea, early this spring boasted of 55 paintings in the collection, by 24 different artists, the gallery being appraised at $18,000. Since then, eleven additional paintings have been added. Opportunity will he presented for an inspection at the meeting of the Industrial Minerals Division, to be held at the College, Sept. 24-26.

Jan 1, 1936

[JOSEPHSON, W. G.: The Argonaut Mine of Today, M88, 475 JOUET, C. H., biography, M29, 258 Joule-Thompson effect, 98, 381 JOWETT, J. H., biography, M83, 276 JUDSON, S. A.: Operations in the Gulf Coast of Texas and Louisiana for 1926, G26, 659 JUDSON, S. A., EASTON, H. D. JR. AND SCHAEFFER. W. A. JR.: Estimation of Petroleum Reserves in Prorated Fields 114, 11. Abs., YB35, 50 JULIHN, C. E.: Copper---An Example of Advancing Technology and the Utilization of Low-grade Ores. Brookings Lecture, in Mineral Economics (1931 volume, B. W. Mudd Fund)]

Jan 1, 1936

Organization Place - Date 1918 American Iron and Steel Institute New York, N. Y. May American Water Works Association :.. St. Paul, Minn. May 20-25 American Institute of Chemical Engineers Berlin, N. H.. June 19-22 American Concrete Institute Atlantic City, N. J. June 24-26 American Society for Testing Materials Atlantic City, N. J. June 25-28 New York Electrical Society New York, N. Y. June National Association of Stationary Engineers Cincinnati, 0. Sept. 9-13 National Exposition of Chemical Industries New York, N.Y.. Sept.23-28 American Chemical Society Cleveland, 0. Sept. National Petroleum Association Atlantic' City, N. J. Sept.

Jan 5, 1918