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By A. L. Galpin

INTRODUCTION For many tailings ponds, particularly those having substantial watershed areas, the control of pond water levels will be a major factor influencing the operation of the pond and the design and construction of the dam retaining the pond. This paper summarizes the basic factors affecting the control of water in tailings ponds, methods of water control, and methods of estimating the variables involved. The influences that pond water levels can have on the design, construction, and stability of tailings dams are explained in order to emphasize the importance of water control in the overall planning of mine tailings disposal systems. Two examples of pond water control planning conclude the paper. BASIC FACTORS The principal factors influencing the control of water in tailings ponds are illustrated on Fig. 1. Fig. 1 (a) shows the general disposition of the tailings solids and water in the pond; the solids settle from the slurry to form "slimes", deposits sloping down into the pond from the points of discharge; these slimes hold volumes of water in the voids between solid particles; water in excess of this "retained" water forms a pool of "free" water laying over the slimes deposits. In some cases, tailings solids (and water) go to the tailings dam for its construction. Fig. 1 (b) indicates those ways additional to tailings disposal in which the pond gains or loses water. These include surface and sub-surface runoff from the pond watershed, water reclaimed from the pond for ore processing, evaporation, and seepage. Seepage losses sometimes include water draining from tailings sand placed in the dam, but a portion of the total seepage flow is often collected and returned to the pond in order to avoid downstream pollution and to recover water for re-use. PRINCIPAL REQUIREMENTS In relation to the control of water in a tailings pond, the first requirement is usually to maintain a pool sufficiently large to ensure adequate clarification of the free water prior to its reclaim for use in the mill, or its discharge from the pond.

Jan 1, 1972

By R. B. Muter, W. C. Grady, T. D. Wheelock, D. G. Chedgy

INTRODUCTION Topics of special interest, such as preparation plant flowsheets and noise pollution, are described in this chapter along with a discussion of non- state-of-the-art processes such as chemical cleaning, high intensity magnetic separation, and bacterial oxidation. PREPARATION PLANT FLOWSHEETS by RICHARD B. Muter In determining the layout or combination of unit operations to be utilized in a modern preparation plant several factors must be taken into account.

Jan 1, 1979

By Mark R. Lamb

The treatment of slime is of special interest to those engaged in cyaniding gold- and silver-ores. The usual practice is to make as small a percentage of slime as possible. In many instances the slime is given no treatment, but is impounded in dams in the hope that the future will develop some method of economically treating this product. The filter-press was the first step upward from ordinary decantation, but, on account of heavy labor-charge and high cost, its use has been limited to high-grade material. The slime at the Combination mill at Goldfield averages perhaps $20 per ton, and although the values are quickly dis solved the filter-press installation was not entirely satisfactory, resulting in the erection of the canvas-cell filter, developed by Chas. Butters and his staff. This filter is a great improvement over the filter-press, and the following description of it will be of interest to those engaged in treating slime produced in crushing ores, especially in view of the fact that, by the use of this filter, slime can be treated at a lesser cost and with a higher percentage of gold- or silver-extraction than in the ordinary treatment of sand; and, moreover, the initial outlay for an all-sliming plant is less than that for the ordinary sand- and slime-plant. The economy of construction of the Butters filter-plant is clearly shown in Figs. 1 and 2, which illustrate the 20-frame filter of 40 tons capacity, now being installed by the Nevada Goldfield Reduction Co. In this construction the slime-pump is so connected that it call pump to or from either tank or the filter by changing the valve-settinga—a combination which is necessary in this particular installation, since sufficient fall is not available for filling and discharging the filter by gravity. Ordinarily, a slime-plant comprises: a filter-box with frames

Jan 1, 1908

By J. Burns Read, Charles H. Fulton

A previous article1 by the authors contained a general description of the new roasting furnace herein described but it did not go into detail as to the metallurgical behavior or the results obtained. Believing that such information would be of great value, they have elaborated on the subject and have given many unpublished details. The furnace described applies the principle of roasting finely divided zinc-sulfide ores, now produced in large quantity by the flotation process, in gaseous suspension; that is, the ore particles are carried, in suspension, in a current of air and gaseous products of the roast. The relatively great fineness of flotation concentrate presents difficulties and problems of roasting in furnaces of the ordinary type; the fine ore is forwarded through the furnace in the form of a shallow bed and its very fineness leads to dense impervious bedding which prevents oxygen from reaching the interior of the bed, thus unduly lengthening the time of roasting and preventing the elimination of the last of the sulfur. The fineness of the concentrate, normally, should lead to a rapid and complete roast, for the speed of roasting is a function of the surface exposed to oxygen, which surface is greatest, per unit of weight, in very fine material. The difficulty in bed roasting is to get the oxygen to the particle. If the fine ore, during the roasting, could be freely suspended in oxidizing gases, full advantage could be taken of the great surface conferred by its fineness. This fundamental idea, of course, is not new, for the Stedtefelt furnace, familiar to the older metallurgists, is an example of it; but the manner in which this is accomplished may be new. The numerous efforts to roast in gaseous suspension show that the idea is attractive; in fact, an analysis would indicate that it is the most reason-

Jan 1, 1925

By W. Griffith

The purpose of this paper is to make public record of new information in regard to the sustaining power of artificial mine-roof supports (not timber props), the result of investigations recently made in the anthracite coal fields of Pennsylvania. First.—By the "Scranton Mine Cave Commission," appointed to investigate the mining conditions under the City of Scranton. Second.—By the "Pennsylvania Mine Cave Commission," appointed by the Governor to investigate the general subject of mine caves in the anthracite region of Pennsylvania. Third.-—By the personal researches and tests made by the author in an effort to secure a better artificial mine-roof or surface support. During the progress of the work of the Scranton Mine Cave Commission, the Engineers for the Commission, Messrs. Conner and Griffith, being aware of the general lack of exact information in the engineering profession as to the strength of the ordinary artificial mine-roof or surface support, and particularly the stronger kinds, such as mine cogs, rock piers, etc., had tests made at the Fritz Engineering Laboratory at Lehigh University, to determine the sustaining power under various compressions of the several kinds of artificial mine supports in use in the anthracite region of Pennsylvania. A report of these tests wasincluded in the report of this Commission, which was published as Bulletin No. 25 of the United States Bureau of Mines, Washington. A similar series of tests, more extensive and more elaborately planned, were subsequently made for the Pennsylvania Minc Cave Commission at the U. S. Government Testing Laboratory at Pittsburgh, Pa. The report of this Commission was made to the Governor, but has not yet been published. The author, during his connection with the Scranton Mine Cave Commission, observed that of all the various devices employed for sustaining the roof of coal mines, the one universally used and the best

Jan 1, 1918

By W. Francis

OF THE methods that have been used for studying the chemical composition of coal, attack by reagents has not, in general, yielded much information. Most of the reagents used have been strong oxidants such as nitric acid or Schulze's solution. The use of a milder oxidizing agent, such as air at low temperatures, enables progressive changes in the character of the coal substance to be studied and thus helps toward an understanding of its constitution. British bituminous coals frequently have a banded structure. These bands (of four types) can be separated one from another and have been found to possess markedly different chemical characteristics, even when taken from contiguous portions of the same lump coal. It has been found convenient to give each of the ingredients of banded coal a distinctive name, more or less descriptive of its appearance, and the study of the chemistry of bituminous "coal" in England has resolved itself into a study of each ingredient separately. . The coal chosen for this work was taken from the Top Hard seam at East Kirkby colliery, Nottinghamshire, a detailed chemical analysis of which has been recorded by Baranov and Francis.1 The banded structure was well marked and the bands could readily be separated. The research was confined to the brilliant vitreous bands (vitrain), the dull hard bands (durain) and the "sooty partings" (fusain); for previous work had shown that the fourth type, to which the name clarain has been given, is intermediate in character, chemically, between vitrain and durain.

Jan 3, 1925

By Paul Tyler

THE ferroalloying elements are connecting links between the steel industry and the nonferrous metal industries. Although ferroalloys are distinctly nonferrous themselves, they serve the steel industry either in the manufacturing process or in modifying the product-in some cases so that it may compete in the markets with nonferrous metals. Of the 92 elements generally accepted by chemists as constituting the primary building blocks of matter, all but the very rarest have been investigated with a view to employing them in steel manufacture. The surprising thing is that so few have been found commercially acceptable. Despite the relatively small number of elements involved, the employ-ment of alloys in steelmaking is one of the most complicated and probably one of the least well understood of modern industrial enterprises. A great deal has been written regarding the action of individual elements and a profuse and somewhat acrimonious literature covers pretty much the whole field of ferroalloy ore supplies. In the middle ground between the miner and the steelmaker developments are less carefully watched by most observers, and except for an occasional description of the technique of some conversion process or the tariff hearings in Congress, very little is said about them. The purpose of the present paper is to describe in relatively nontechnical terms this highly complex industry and to study its relations to our national progress.

Jan 1, 1933

By Frank R. Barnako

Coal mining is a hazardous occupation, but tremendous progress has been made in reducing accidental injuries and deaths in the mines. Let us take a look at the hazards in coal mining and the accident record. COAL MINE SAFETY TODAY Underground coal mining creates underground open areas, rooms, and haulageways. The roof (top) and ribs (sides) become highly stressed, and because coal and slate are very weak in tension or compression they frequently fail and fall from the roof and ribs unexpectedly. This is the most hazardous condition miners must cope with underground, and it has consistently produced the greatest number of fatal injuries in the coal mining industry. Only very sophisticated equipment, but which is not yet practical for use underground, is able to detect the buildup of stresses that may eventually lead to a roof or rib fall. Today's miner still looks for fresh cracks in the roof or rib, listens for the "drummy" sound, and feels vibrations from loose material in the roof, when tapped with a sounding stick, in order to find material which may fall. Once located, it is barred down, but if this is not possible, it is then secured to prevent it from falling. The next great& hazard is the equipment used to mine or haul coal. It is large, heavy, reacts quickly to its controls and is operated in con- fined areas with low lighting levels. The record of the last few years shows that fatalities attributable to mining and hauling equipment are about equally divided. Thorough training as part of a complete safety program is necessary to teach employees the hazards of loose roof, rib, and machine operation in order that they can work in the safest way possible. Unless there is such a program, the trade is learned by trial and error with a resulting tragic.

Jan 1, 1973

By Van Dyne Howbert, Fred E. Gray

The Presidio mine of The American Metal Co. of Texas is situated 45 miles south of Marfa, Texas, a town on the Southern Pacific R. R., and lies approximately 20 miles north of the Mexican border. Communication with the railroad is maintained over a state highway. All supplies for mine and mill are hauled in by truck from Marfa and precipitates and concentrates are freighted to the railroad by the same means and shipped to Selby and El Paso, respectively. The mill is at the town of Shafter, 1 mile from the mine and at approximately 350 ft. lower elevation. The ore is conveyed to it by an aerial tramway which requires practically no power on account of the difference in elevation. The mill is a countercurrent decantation cyanide and gravity concentrating plant of 200 tons daily capacity. Coarse and fine crushing are done at the mill. Two neal-by shallow wells in the bed of Cibolo Creek furnish an abundance of water. Power is generated for the mill and town by a Diesel engine plant. Ore Treated The ore is oxidized and siliceous. The greater part contains approximately 16 oz. of silver per ton, but mixed with this are many particles of ore of much higher grade, assaying in many instances 100 oz. or more. In the 16-oz. material there is an almost constant amount of silver which is difficult to recover by cyanidation. The high-grade material contains a much greater proportion of silver which is easily amenable to cyanide treatment. Thus, as the grade of ore becomes higher, the percentage of recovery of silver increases rapidly, under equal milling conditions. The silver minerals contained in the ore are principally argentite and cerargyrite, the former predominating The lead minerals, all of which are argentiferous, are chiefly cerussite and galena, with occasionally a little anglesite. The gold is free; most of the ore contains merely a trace

Jan 1, 1935

By P. R. Kalischer

IN the production of alloys by powder metallurgical processes it is often necessary or desirable to include one or more components that tend to form very stable oxides Included in this group of metals are aluminum, manganese, magnesium, silicon, and a few others In many cases it is not necessary for the sintered compact to have full density and the other physical characteristics of a cast alloy and in that event no undue precautions need be taken If, however, it s required that the sintered part be entirely homogeneous, and have maximum density and physical properties, some method must be found to reduce the surface films of oxide, which are always present on the metals, and for the metals mentioned above this is always extremely difficult, if not impossible Since the production of high-density alloys is of particular interest to powder metallurgists, some experiments were undertaken to devise methods of reducing the refractory oxides For this work, alloys of iron, nickel, and aluminum were chosen because aluminum oxide is one of the most stable oxides and because these alloys in the right compositions form excellent permanent magnets All of the pertinent properties of the magnets could be accurately and delicately measured by density measurements and magnetic tests of sufficient scope to give a complete demagnetization curve From such a curve the maximum coercive force, residual magnetism, and energy products could be obtained and compared with the same properties for a cast material Any lack of homogeneity, density, or solid diffusion would be immediately apparent as a decrease in the magnetic properties NATURE AND REMOVAL OF SURFACE BARRIERS The early work of the present investigation was based upon published processes In the published information it was claimed that by intimately mixing iron, nickel, and iron-aluminum alloy (50 per cent Fe, 50 per cent Al) powders, compressing such a mixture into the desired shape and size, and then sintering (heating to a temperature below the melting point of the component metals) in hydrogen at 1200ºC or higher, a sound, homogeneous article could be made having the desired physical size, shape, and strength, and good magnetic characteristics However, this early work showed clearly that something in the powder compress was inhibiting diffusion and the process was almost entirely unworkable In the initial phase of the investigation samples of iron powder, nickel powder, and iron-aluminum alloy powder were pressed into separate bars and sintered in hydrogen Both the iron and nickel powders sintered

Jan 1, 1941

By W. J. Reagan

THE problem of increasing output and decreasing percentage of rejections is a vital one in the manufacture of steel of any kind. The making of basic open-hearth steel for use in rolled steel wheels, tires for locomotive and car wheels, and forgings of various kinds, is a highly specialized industry. The increase in weight of railway rolling stock of all kinds, and the high speed that the public demands of transportation facilities, make it imperative that steel for use in this class of material shall be of the highest quality obtainable. During the past few years it has been the writer's good fortune to have opportunity-to study the defects in basic open-hearth steel, and also the results obtained by various changes in open-hearth practice, on such defects. The opportunity for study and the details available are rarely found in the manufacture of steel of any kind. It seems reasonable to assume that many of the results determined here can be applied to the production of steel of other types with a decided improvement in quality, a decrease in the percentage of rejections and an increase in output. All of the material described is basic open-hearth steel with the following range of analysis: carbon, 0.50 to 0.85 per cent.; phosphorus and sulfur, 0.04 coax.; silicon, 0.15 to 0.35; manganese, 0.50 to 0.75. All of this material is bottom-cast, therefore tapping and pouring temperatures are higher than in top-cast production. Ingots used in this type of work are of standard length with varying diameters. The ingot is known as duodecagonal, or twelve-sided. The standard body length is 88 in. and the hot top length, 14 in. Fig. 1 shows a typical ingot of this type. The diameter varies from 13 to 30 in. Ingots for special forgings, which cannot be made in molds of standard size, are made in molds of various sizes and designs. These ingots are sliced cold, into blocks of various lengths, depending upon the weight of the forging to be made. Fig. 2 shows the ingot-after coming from the slicing lathe. Just sufficient metal remains between blocks to hold the ingot in one piece while it is being removed from the lathe; then steel wedges are inserted between the blocks and the blocks are broken apart. This affords abundant opportunity for inspection, as the interior of the

Jan 1, 1930

By W.M. Peirce

The present work has been done in an endeavor to correlate and complete the data on the constitution of alloys of zinc with other common metals, dealing exclusively, however, with the zinc-rich alloys in which the zinc content is between 90 and 100 per cent. This investigation has included the systems lead-zinc, cadmium-zinc, iron-zinc, copper-zinc, aluminum-zinc, nickel-zinc, manganese-zinc, cobalt-zinc, tin-zinc, and magnesium-zinc. The important ternary system zinc-lead-cadmium and the zinc corners of other ternary systems have been investigated in connection with this work but will not be dealt with here. Zinc does not form a single homogenous zinc-rich solid solution over any considerable range of concentration with any of the metals mentioned. A limited range of solid solubility is said, by previous investigators, to occur in several cases and certain effects on the properties of zinc are attributed (with varying degrees of consistency among different writers) to the presence of certain other metals dissolved in zinc. The increasing use of rolled zinc and the possibilities offered by zinc as a casting alloy in certain fields have made it essential to determine precisely these equilibrium relationships. In carrying out this investigation reliance was placed chiefly on two methods, conductivity measurements and microscopic analysis. The first method proved valuable in determining the existence and extent of solid solubility. The second method stands alone as a means of determining structural characteristics and supplements the first method in the measurement of solid solubility. The scleroscopic hardness of all conductivity specimens was measured partly for its value from the point of view of mechanical properties and partly as a check on the conductivity curves in indicating the limits of solid solubility. No hardness curves are included in this paper, for in no case were they important in arriving at the constitution of any system. Conductivity measurements were in all cases made on cold-rolled strips 0.020 in. thick and 0.5 in. wide, both as cold rolled and after an

Jan 1, 1923

By W. M. Peirce

The present work has been done in an endeavor to correlate and complete the data on the constitution of alloys of zinc with other common metals, dealing exclusively, however, with the zinc-rich alloys in which the zinc content is between 90 and 100 per cent. This investigation has included the systems lead-zinc, cadmium-zinc, iron-zinc, copper-zinc, aluminum-zinc, nickel-zinc, manganese-zinc, cobalt-zinc, tin-zinc, and magnesium-zinc. The important ternary system zinc-lead-cadmium and the zinc corners of other ternary systems have been investigated in connection with this work but will not be dealt with here. Zinc does not form a single homogenous zinc-rich solid solution over any considerable range of concentration with any of the metals mentioned. A limited range of solid solubility is said, by previous investigators, to occur in several cases and certain effects on the properties of zinc are attributed (with varying degrees of consistency among different writers) to the presence of certain other metals dissolved in zinc. The increasing use of rolled zinc and the possibilities offered by zinc as a casting alloy in certain fields have made it essential to determine precisely these equilibrium relationships. In carrying out this investigation reliance was placed chiefly on two methods, conductivity measurements and microscopic analysis. The first method proved valuable in determining the existence and extent of solid solubility. The second method stands alone as a means of determining structural characteristics and supplements the first method in the measurement of solid solubility. The scleroscopic hardness of all conductivity specimens was measured partly for its value from the point of view of mechanical properties and partly as a check on the conductivity curves in indicating the limits of solid solubility. No hardness curves are included in this paper, for in no case were they important in arriving at the constitution of any system. Conductivity measurements were in all cases made on cold-rolled strips 0.020 in. thick and 0.5 in. wide, both as cold rolled and after an

Jan 1, 1923

By D. A. J. Swinkels

The problem of determining oxygen levels in liquid steel to aid in deoxidation control has received general attention for a number of years. Work in this direction started at the B.H.P. Central Research Laboratories early in 1967 with an evaluation of sampling techniques followed by vacuum fusion analysis to determine the oxygen content of the samples (1). It was found that these techniques had a number of drawbacks if they were to be used for deoxidation control. The method of analysis was rather too slow to allow effective control and measured total oxygen level rather than dissolved oxygen. Furthermore, the results were found to be very variable due to slag entrainment in the samples. Attention therefore turned to the galvanic cell method using a solid oxygen ion conductive electrolyte such as cubic stabilised zirconia. The ionic conductivity properties of electrolytes such as (ZrO2) 85 (CaO).15 had been studied by a number of investigators and had already been applied to the measurement of oxygen activity in gases, in lower melting metals such as copper, lead, tin, silver, alkali metals and indeed the first studies in steel had been made (2,3). Since then the results of a number of studies in the development of an expendable oxygen probe for steel have been reported (4-9).

Jan 1, 1972

By Giovanni B. Barla, Stefan H. Boshkov

The block caving method is examined in this paper on the basis of experimental results and observations in the field, and through the use of numerical modeling by the Finite Element Method. The Grace Mine, developed by a panel caving method, served as a reference case. However, the results obtained and the simulation techniques which have been developed may find useful application in more general conditions as encountered in other mining operations by block caving. Following a brief description of the Grace Mine and of the mining method, the problems associated with the behavior of underground drifts at the production levels, during undercutting and caving, are addressed. The most important results obtained through monitoring of strains and loads in the supports of a runway are discussed, while giving relevance to the sequence of mining operations in the immediate vicinity. The most important geomechanical data, as provided for subsequent modeling, are described with reference to: (a) rock mass characterization and (b) in situ state of stress. Then, the numerical modeling procedures, developed by the Finite Element Method in order to predict the caving phenomena and the behavior of underground openings during undercutting, are discussed. Finally, an attempt is made to compare the pre- dictions of the numerical analyses with, the measurements carried out at the instrumented site. Suggestions as to how to improve the results both qualitatively and quantitatively are also given.

Jan 1, 1984

By J. L. Shafer, Christopher L. Caenepeel, Martha L. White

Often an in situ leach is the only practical economic method for copper recovery from small low grade oxide deposits. The decision to develop a copper property by an in situ blast and leach is strongly dependent on ore grade, tonnage, hydrology, and the copper extraction and acid consumption rates. The inherent leachability of the ore will in part determine the desired amount of fracturing of the ore deposit by the blast in order to obtain a copper extraction rate that is economical. For the last several years Occidental Research Corp. (ORC), has undertaken a modest effort to address the question of how to best identify and determine the information necessary to predict and control the operation of an in situ leach for the economic recovery of copper. Modelling of the Leaching Process During the past 10 years the activity in the mathematical modelling of the leaching of copper sulfides in copper dumps and heaps has increased dramatically. The modelling of copper oxide leaching has not received as much attention. The acid leaching of non-sulfide copper minerals while chemically less complex, compared to sulfides, does generate a vertical acid concentration gradient in the ore heap being leached due to the acid-base nature of the reaction. This is generally not observed in sulfide deposits that are biologically active, due to the buffering action of opposing reactions involving the generation of sulfuric acid from sulfide minerals and acid consuming host rock. Thus, the objective of ORC 's copper oxide modelling efforts is to determine the leaching parameters which will account for this vertical acid concentration gradient. Knowledge of this gradient will result in the correct choice of the feed acid concentration to the top of the ore dump or heap, such that the effluent will have the desired pH.

Jan 1, 1980

By H. C. Spaulding

The rapid increase, during the last few years, in the number and magnitude of applications of electric power-transmission to commer cial uses in this country, has been due principally to three causes: first, the ability and enterprise of those who have been identified with the progress of electrical industries, since electric illumination became an economic fact instead of a laboratory-experiment: sec ondly, the readiness of the American people to adopt new and ad vanced methods as soon as their superiority has been fairly demon strated; and thirdly, tile economy and flexibility of the apparatus employed, when properly designed and constructed, and installed under suitable conditions. Basing our judgment on the world's advance in scientific devel opments during the past century, we may reasonably conclude that in no other country would the pioneeis of electrical invention, whose names have now become household words, have received the prompt and plentiful financial support which has enabled them to inaugurate undertakings of exceptional magnitude, even in this era of tremendous monetary organizations. And, on the other hand, we have seen, in the numerous financial and engineering failures inseparable from such rapid development, the natural results of a too implicit faith in electrical omnipotence. It is not to be wondered at that conservative engineers have been slow to adopt this new and mighty agent in the solution of exten sive problems, and under circumstances where a single failure means not only a greater or less financial sacrifice, but the loss, in a greater or less degree, of professional reputation. Be mechanical engineer, while recognizing the fact that thousands of horse-power are to-day transmitted by electrical means, from sunning the lathe in a dentist's office to the operation of a fifty-ton travelling crane; from passing a cooling draught of air through a

Jan 1, 1891

Jan 1, 1902

By M. Sheffield

This paper presents a technique lor predicting the flow of oil, gas and water through a petroleum reservoir. Gravitational, viscous arid capillary lorces are considered, and all fluids are considered to be slightly compressible. Some theoretical work concerning the fluid flow in one-, two- and three-space dimensions is given along with example performance predictions in one- and two-space dimensions. INTRODUCTION Since the introduction of high speed computing equipment, one of the goals of reservoir engineering research has been to develop more accurate methods of describing fluid movement through underground reservoirs. Various mathematical methods have been developed or used by reservoir engineers to predict reservoir performance, 193-5,7,8 The work reported in this paper extends previously published work on three-phase fluid flow (1) by including a rigorous treatment of capillary forces and (2) by showing certain theoretical mathematical results proving that these equations can be approximated by certain numerical techniques and that a unique solution exists. DISCUSSION The method of predicting three-phase compressible fluid flow. in a reservoir can be summarized briefly by the following steps. 1. The reservoir, or a section of a reservoir, is characterized by a series of mesh points with varying rock and fluid properties simulated at each mesh point. 2. Three partial differential equations are written to describe the movement at any point in the reservoir of each of the three compressible fluids. All forces influencing movement are considered in the equations. 3. At each mesh point, the partial differential equations are replaced by a system of analogous difference equations. 4. A numerical technique is used to solve the resulting system of difference equations. Capillary forces have been included in two-phase flow calculations.1,4,8 The literature, however, does not contain examples of prediction techniques for three-phase flow that include capillary forces. Where capillary forces are considered, each of the three partial differential equations previously discussed has a different dependent variable, namely pressure in one of the three fluid phases. Therefore, three difference equations must be solved at each point in the reservoir. Where large systems of equations must be solved simultaneously, an engineer might question whether a unique solution to this system of equations actually exists and, if so, what numerical techniques may be used to obtain a good approximation to the solution. It is shown in the Appendix that a unique solution to the three-phase flow problem, as formulated, always exists. It is also shown that several methods may be used to obtain a good approximation to the solution. The partial differential equations and differenceequations used are shown in the Appendix. Matrix notation has been used in developing the mathematical results. Two sample problems were solved on a CDC 1604. They illustrate the type of problems that can be solved using a three-phase prediction technique. SAMPLE ONE-DIMENSIONAL RESERVOIR PERFORMANCE PREDICTION A hypothetical reservoir was studied to provide an example of a one-dimensional problem that can be solved. Of the several techniques available, the direct method of solution as shown in the Appendix was used. The reservoir section studied was a truncated, wedge-shaped section, 2,400 ft long, with a 6' dip. (A schematic is shown in Fig. 1.) This section was represented by 49 mesh points, uniformly spaced at 50-ft intervals. The upper end of the wedge was 2 ft wide, and the lower end was 6 ft wide. The section

Jan 1, 1970

NORTH AMERICA. CANADA Canadian Army Overseas. Ball, H. D. Bridges. C. Butterill, H. J. If. Ladner, F. E. Lane, H. C. Alillar, W. A. ALBERTA Calgary.-Chonette, W. C. Clark, L. At. Corbett, C. S. de Hart, J. B. Dingman, C. W. Fath. A. E. Fulton. J. If. Cray, J. G. Johnson. R. V. McCutchin, J. A. *Slipper, S. E. Vin Buckirk H. A.

Jan 1, 1944