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By Jack L. Taylor

As expected from similar crystal structures and favorable atomic size factors, titanium, vanadium, and molybdenum are completely soluble in one another above the transformation temperature of titanium. The fl phase parameters of the continuous solid solution are shown graphically. Limiting compositions for retained fl phase have been determined. VANADIUM and molybdenum both have body-centered-cubic structures at all temperatures and, from the atomic diameter comparison factor, 3.9 pct, would be expected to form a complete series of solid solutions. The existence of complete solubility has been confirmed by work' at the Jet Propulsion Laboratory. Furthermore, vanadium and molybdenum have favorable atomic size factors to form complete binary solid solutions with the B phase, high temperature form of titanium, which also has body-centered-cubic structure. Pietro-kowsky and Duwez' and Hansen et al." have established the existence of the complete series of solutions in these binary systems. It would be logical, therefore, to expect that p-titanium, vanadium, and molybdenum would be completely soluble in one

Jan 1, 1957

Newmont has been producing gold from the Carlin Trend for over 45 years. Naturally the focus, scale and complexity of the operations have changed considerably over this time. Newmont discovered and developed the Carlin Main ore body which is located about 32 km (20 miles) north of Carlin Nevada. The property was developed as a one mine one gold mill treatment plant operation which produced about 6,200 kg (200,000 Troy ounces) of dorè gold bars per year. The initial mine, mill and gold refining facilities were relatively small in comparison to today?s standards. The milling circuit used the Merrill-Crowe zinc precipitation process to recover dissolved gold and prepare a concentrated precious metal ?precipitate? to be melted into a dorè bar for sale.

Jan 1, 2012

By Jack A. McQuiston, Thomas A. Cross

Corrosion of equipment and machinery in the coal industry is usually the result of three main agents: acids, chlorides, and abrasion. Acids and chlorides are especially troublesome in coal preparation plants where soluble salts and sulfur in the coal produce a highly corrosive wash solution. Abrasion is common in all operations where coal is handled or conveyed. Together, the acid-chloride-abrasion combination results in some of the worst corrosive conditions found in any industry. The variety of equipment and structures in the coal industry calls for different corrosion control techniques. Table 1 lists the areas of concern for a number of items. Just as there is a wide variety of corrosion problems, there is a wide array of coating materials available. Tables 2 and 3 are selection charts to provide guidance in narrowing down the choices. Experience has shown that a limited number of coating systems work best on coal equipment and structures. These systems are described in Table 4. The good-better-best designation in the table refers to coating system longevity. Good indicates the least costly and shortest service life. In nearly all cases the lowest annualized cost can be achieved by using the coating system rated best, due to the avoidance of costly repaints and unnecessary downtime. The most expensive coating system, though, is worthless unless the coating system is properly applied. Field inspection to insure compliance with specifications is an important aspect, and is a service available from many coating suppliers. Even the best coating systems require periodic maintenance to achieve satisfactory results. Spot rusting from mechanical damage should be repaired annually to maximize the coatingsystem's results.

Jan 2, 1980

Mineral Processing Education in China

Sep 13, 2010

By Kathleen M. Kowalski

In emergency management, the effects of stress on the performance of emergency personnel, typically have been ignored or regarded as too enigmatic to quantify. This paper discusses the concept of Critical Incident Stress in responders to emergencies. It presents the rationale for considering stress as a significant factor in the management of emergencies. It is proposed that Critical Incident Stress Debriefing in a disaster can improve the effectiveness of response teams on site, their turnaround time on site, and post-disaster time off the job. Critical Incident Stress intervention also can mitigate potential deleterious emotional effects associated with emergency work. This paper, prepared by a U.S. Bureau of Mines researcher, offers some ideas to the mining industry in general, to mine rescue team trainers, and to developers of program simulations on the specific issue of how people, time, materials and space may be factored into a plan for emergency management. The impact of stress on emergency workers is, presented as a missing component in present emergency management models.

By Euler De Souza

The authors conducted a study of backfill practices in underground mines across Canada to assess the current state of backfill usage and to overview potential hazards associated with backfill practice, from preparation to transportation to placement. The primary aim of this study was to cover each component of a typical mine backfill system, and to identify potential incidents leading to the disruption of backfilling operations and any associated corrective actions. This paper, Part I of the study, deals with surface operations consisting of backfill material supply and backfill plant preparation. Part II of the study, which deals with underground operations consisting of backfill transportation and backfill placement, is also presented in these proceedings. A review of safety measures associated with current backfill operations and recommendations for procedures of best practice that should be implemented to reduce fill-related hazards in all mine backfill workplace environments are presented. In general it has been found that system failures normally lead only to minor losses to the operations.

May 1, 2009

By A. Redman

Aquatic organisms are sensitive to free cyanide (HCN) though the presence of certain metals that can form stable complexes and thereby reducing both the amount of bioavailable cyanide. Recent work has suggested that consideration of HCN rather than total cyanide can provide the basis for water quality criteria. Cyanide is often present in complex effluents that affect speciation and bioavailability. We have developed a model to predict the speciation of cyanide in complex effluents and have shown that this model can predict the toxicity of metal-cyanide complexes in terms of HCN. This study evaluated available cyanide toxicity exposures with this model to assess the role of water chemistry (e.g., metal-cyanide interactions) on the observed. Toxicity endpoints based on total cyanide ranged over several orders of magnitude for a variety of metal-cyanide mixtures. However, predicted HCN concentrations among these same tests described the observed toxicity data to within a factor of 2. Aquatic toxicity can be well described using HCN though in certain metal-cyanide mixtures toxicity was jointly described by HCN and elevated levels of bioavailable metals. This work was performed in support of an industry-sponsored reassessment (Gensemer et al 2006) of the U.S. EPA water quality criteria for cyanide (EPA 1985) using free cyanide as the basis for the re-calculation. The work presented in this manuscript presents technical support for using free cyanide as the preferred basis for this recalculation.

Jan 1, 2011

By Jack Wasserman, Don Wasserman, Logan Mullinix, Shekhar Khanal, Kelly Neal

This paper presents current finding on truck driver average exposure to acceleration for several different manufacturer’s cab-over trucks on a variety of roads in different countries. The predominant time, for this aspect of the study has been spent in the area around London, England and Warsaw, Poland. The ECE directive 2002/44/EC has provided specific guidelines for vehicle operators 8 hour average acceleration exposure. The primary considerations have been on truck design including the air-ride driver’s seat. The truck manufacturers have produced truck cabs that have some separate suspension from the truck frame. The truck seat manufacturers have been producing air-ride suspension seats for the cab. Both of these designs have had the objective of meeting the ECE directive and providing the vehicle drivers with some degrees of comfort. This paper will provide some information on the ability of the vehicles to operate on a variety of roads and meet the objectives. Method The primary method for evaluation of the driver’s exposure has been the use of a seat pad attached to the driver’s seat. Although this sensor system provides the critical information for the driver, an understanding of the reasons for the values requires additional measurements. The initial study in England used both driver and passenger seat pads, as shown in Figure 1, as well as triaxial accelerometers mounted on the base of the seat. The latest studies used significantly more transducers to better understand the relative rotations and translations on the truck frame, the cab, and the driver. [ ]

Jan 6, 2006

By Kim Fagerlund

Boliden Harjavalta Oy operates a copper smelter in Finland, which is based on flash smelting together with Peirce-Smith converting of copper matte. This paper reviews a case study when a high arsenic feed mixture was successfully eliminated in order to guarantee the anode quality. Based on theoretical and practical knowledge in slag chemistry at Outokumpu Research, the CaO-fluxing practice was introduced. Description of a thermodynamic simulation using MTDATA and implementation of the results into converting practice is given. Results showed that the impurity fluctuations in raw materials could be effectively controlled by efficient utilization of different slag chemistry.

Jan 1, 2005

By C. Fairhurst

Most of the papers designated as being within the topic of underground storage at this Symposium are concerned with aspects of radioactive waste isolation. Although this is, unquestionably, an important international application of underground storage, and one involving a considerable number of research investigations, the subject of underground storage is indeed much broader. Several major international conferences have been devoted exclusively to it. Applications include storage, under a range of temperatures and pressures, of oil and liquefied petroleum products, compressed air, heat, foodstuffs of various kinds, hazardous and 'nuisance' industrial by-products, and a variety of special applications, both civilian and military - some in use, others proposed. Storage may be in caverns excavated specifically for the purpose, exhausted mines may be adapted for storage or, in some cases, the material to be stored may be injected under pressure into the pore spaces of porous-permeable formations at depth. A variety of rock types and geological environments are used, e.g. excavations in salted or domal salt, where long-term creep closure of the openings is a concern; massive granite, where fluid loss through fissures may be important. Cavities may have spans of several tens of meters, and there is interest in achieving still larger excavations. As would be expected, this breadth of underground storage applications introduces a similarly broad range of questions in rock mechanics and rock engineering. The report will review these questions and recent developments in rock mechanics research, computational procedures, and design applications - and will also discuss the opportunities for a still greater range of applications of underground storage to current industrial and social problems.

Jan 1, 1989

By Gene R. Reid

The contract objective is the development and in mine testing of an Automatic Fire Control System (AFCS) for mobile underground metal mining equipment. The effort described by this report covers the period from June 21,1975 through June 30,1976 and accomplished the following tasks: ? Preparation of Data Handling Plan and data acquisition which included visits to twenty mine sites in eleven states, visits to Bureau and MESA facilities, and a literature survey. ? Data analysis which determined the most hazardous type of vehicle for use in the demonstration, and design requirements for the AFCS, ? Development of recommended design concepts for the AFCS. ? Design and development of the AFCS including tests on a full-scale mock-up of a load-haul-dump (LHD) vehicle. ? Underground fire tests on an ST-2B-LHD vehicle at the Hecla Lakeshore mine Casa Grande, Arizona.

Jan 1, 1976

By T. Nyabeze

This paper presents the experiences and views of women involved in the mining industry as determined from a questionnaire that was circulated across the Canadian mining industry. Globally, there have been significant studies done to understand the historic and global variety of women?s participation in this industry1. The reason for focusing on women?s experiences here in Canada is because women?s percentage representation at 14.4% in the mineral industry workforce falls below the overall labour force average of 47.4%2. Notably, a recent article in the Globe and Mail newspaper points out that adequate representation of women in leading of organizations is more of a matter of competitiveness and innovation rather than purely a ?women?s issue?3. This paper will provide some insight into the reasons why women join and stay in the mining industry and shed some light into the reasons for the overall low representation in this sector. The authors believe, as stated in a study from the London Business School, that a gender-balanced workforce is one way of providing the best results in areas that drive innovation4. Women represent a key stakeholder group that can help enhance the mining industry?s sustainability through innovation. The women who responded to the questionnaire represent many different areas within the mining industry, including a broad range of roles in industry, government, academia and in the supplies and services sector. The paper is intended to raise awareness about issues that women encounter that contribute or detract from career satisfaction in the mining industry. The survey provides an overall understanding of why women pursue or work in mining, and why women either remain or choose to leave it. The advantages and disadvantages experienced by women are highlighted, along with a summary of the possible initiatives that could be undertaken by employers as opportunities to improve the attraction of the mining industry for career minded women. As well, the survey provides a summary of the top ten features that are already in place at various organizations and community groups that have been identified as key for supporting and encouraging women to join and remain in the industry. Not surprisingly, the survey identifies that one of the key ingredients for retention of women in mining is the provision of mentors and sponsors. Another key aspect for retention is the provision of progressive employment policies that address the need for a degree of flexibility in work hours and a culture of balance between work and personal life demands. The survey and results are portrayed only from a female perspective since it is largely women?s perceptions that will inevitably be transmitted to others who plan on entering the field.

Oct 1, 2010

By Davy A. T, Hansen J. O

The causes of ferrosilicon loss from Dense Media Separation (DMS) plants, and the related properties of ferrosilicon, are identified. Two characteristics, corrosion resistance and saturation magnetisation, are examined in detail. The chemistry of the corrosion mechanism is described and its relationship to plant parameters discussed. Methods of reducing corrosion losses are proposed. Lack of particle homogeneity, and its influence on corrosion and abrasion is noted. The relationship between low magnetic susceptibility-and increased magnetic separator losses is demonstrated experimentally.

Jan 1, 1986

By Albert Musschoot

The expanding applications of vibrating feeders for controlling the flow of bulk materials, and their adaptation for processing requirements, have developed considerable interest in stockpiling and reclaim systems. The general design of these units consists of a material transporting trough, or platform, driven by a vibratory force system. Design flexibility and variety is limited only by engineering ingenuity. The basic motion of the vibratory trough, or work member, is a controlled directional linear vibration that produces a material tossing or hopping action. Material travel speeds vary from 0 to about 30 m/min, depending on the combination of frequency, amplitude, and slope vibration angle.

Jan 6, 1981

By Robert Bakish, William D. Robertson

AFTER more than fifty years of investigation and continuing failure in service, a satisfactory mechanism to explain stress corrosion cracking in homogeneous alloys is still lacking. The relative chemical activity of grain boundaries and adjacent grains, inferred from the boundary structure, has been used to explain intergranular cracking in a brass.' This concept is probably correct as a general hypothesis, but it requires much more extensive development in order to explain satisfactorily the observed phenomena. For example, the specific function of the solute in an alloy must be considered, because intergranular failure does not occur in pure metals,' which are structurally similar to homogeneous alloys. Also, in this connection, an inter crystalline fracture path in binary copper alloys can be changed to a transcrystalline path by relatively small ternary additions.' The fracture path in ß brass is predominantly transcrystalline,' in contrast with an inter crystalline path in a brass. Whether the two different fracture paths are the result of a difference in composition, crystal structure, or the state of long range order is unknown and cannot be determined with ß brass, because only the ordered state can be obtained at room temperature. The study of chemical activity at structural sites in the Cu-Zn system is restricted by the formation of opaque films in an ammonia environment in which stress corrosion cracking is generally observed. Furthermore, both components of the alloy are chemically active and the interpretation of observations is therefore relatively complicated. The Cu-Au system is a better choice for the purpose of studying structural factors. In particular, CuAu is very susceptible to cracking in ferric chloride and opaque films are not formed in this solution; it may be obtained in different states of long and short range order; and, finally, only copper is oxidized in dilute ferric chloride, which considerably simplifies the chemical problem. To provide information necessary for a more general explanation of stress corrosion cracking in homogeneous solid solutions, the following structural factors have been investigated in a Cu-Au alloy having a composition corresponding to Cu,Au: 1) the effect of long and short range order; 2) the structural sites from which copper is removed from the annealed and cold worked polycrystalline alloy; and 3) the effect of annealing time and temperature on structural reactions in the cold worked alloy. Experimental Procedure A Cu-Au alloy of nominal Cu3Au composition was cast from cathode copper and high purity gold and fabricated into sheet and wire. Chemical analysis for copper and gold indicated 48.92 wt pct Cu and 51.01 pct Au. Quantitative spectrographic analysis indicated 0.01 pct Ag, 0.002 pct Pd, 0.001 pct Pb, and 0.002 pct Fe, with traces of magnesium, silicon, and zinc. Presumably most of the remaining 0.055 pct corresponds to the limits of analytical precision. Heat treatments of wire and sheet were conducted in argon or vacuum. Wire specimens, 0.064 in. diam, were heated for 1 hr at 850 °C to establish a definite

Jan 1, 1957

Despite limited discussion, Chemistry of Flotation is a good text and reference 1985 by M. C. Fuerstenau, J. D. Miller, and M. C. Kuhn Society of Mining Engineers Caller No. D Littleton, CO 80127 Softcover, $23.50 (member), $18.50 (student member), $28.50 (list) Review by Richard R. Klimpel Chemistry in Flotation, as stated by the authors, is intended as a textbook for students as well as a reference book for practicing flotation engineers. It covers subject matter related to surface phenomena; collectors and collector salts; natural floatability; the flotation of sulfide minerals, insoluble oxide and silicate minerals, semisoluble salts, and soluble salts; and slime coatings. There are no discussions in the book on practical plant implications of flotation chemistry, such as the influence of rate, particle size effects, dosage, flotation equipment, and methods of chemical addition. The book itself is small (only 177 pages), and, as published, is in an easy-to-handle soft cover. Once one accepts the intent of the authors, this book really does represent a very concise and convenient summary of the chemistry of flotation. It is, however, far from complete in its discussion of concepts and implications of data. Very often in the presentation, key prior knowledge (or at least subject matter awareness) not given in the book, is assumed. Thus, depending on one's familiarity with the specific subject matter, some sections can be easily followed while others could be tough going. Some of the discussion is so brief and terse on important subjects that unless the reader already realizes the meaning of the presentation, the conclusions to be drawn are not always clear. Therefore, if one is not expecting a self-contained primer on flotation chemistry, this book is very useful. To this end, the book is recommended to practitioners of flotation chemistry. The presentation of data in figures and tables is good. It helps considerably in the book achieving its conciseness. The authors certainly are qualified and knowledgeable in the subject matter - apparent in the style of presentation. In summary, this reviewer thoroughly enjoyed this book and will use it as a concise review of flotation chemistry. Richard R. Klimpel, member SME, is a scientist with Dow Chemical Co., Discovery Development, 1776 Building, M. E. Pruitt Research Center, Midland, MI 48640. International Symposium on Blast Furnace Ironmaking, 1985, The Indian Institute of Metals, The Tata Iron and Steel Co., Ltd., Jamshedpur 831007, India, 282 pp., papercover, no price given - Papers from this symposium held in Jamshedpur, India, include the following: determination of coal and coke quality; feed to blast furnaces; burden quality and blast furnace performance; operation of blast furnaces on charcoal; review of cast house slag granulation systems; developments in blast furnace engineering and control; process improvements in blast furnace ironmaking; coal injection into the blast furnace; and coke from stamp charged coal. Advances in Materials Technology for the Process Industries, 1985, edited by H.A. Huskins, National Association of Corrosion Engineers, P.O. Box 218340, Houston, TX 77218, 273 pp., softcover, $20-This book is the proceedings of a meeting held in Atlanta, GA in October 1984. It describes innovations in metallurgy, ceramics, glass, composites, and polymeric materials that impact the integrity and economics of operating systems. It covers biotechnical developments, improvements in membrane systems, or beneficiation processes, as well as developments in electrochemical controls, testing procedures, and surveillance techniques. A Reference Guide to Mining Legislation in Canada, 1985, by B. Barton, B. Roulston, and N. Strantz, The Canadian Institute of Resources Law, Room 430, Bio Sciences Building, The University of Calgary, Calgary, Alberta, Canada T2N 1N4, 120 pp., bound, $US28- This guide provides a ready means of finding how the different jurisdictions in Canada regulate mineral activity. It covers the rights required for exploration, development, and production of mineral metallics and industrial minerals. It does not cover placer mining, petroleum and natural gas, bituminuous sands, coal, or structural materials. Dictionary of Geological Terms, 1985, edited by Robert L. Bates and Julia A. Jackson, The American Geological Institute, 4220 King St., Alexandria, VA 22302, papercover, $7.95 plus $1 for postage - This third edition is for geoscience students, teachers, and rockhounds. It defines the core vocabulary of earth sciences, contains 8000 revised definitions, and includes 1000 new terms. It adds recent terms in plate tectonics, hydrology, and permafrost studies. Accurate definitions are given without technical jargon, cross-references are included, and commonly used abbreviations are provided. Processing and Utilization of High Sulfur Coals, 1985, edited by Yosry A. Attia, Elsevier Science Publishing Co. Inc., 52 Vanderbilt Ave., New York, NY 10017, 787 pp., bound, $142.50-These proceedings comprise the majority of the papers presented at the First International conference. Investigators there reported the latest discoveries, developments in commercial practice, and state-of-the-art reviews of scientific principles and applications of various technologies for handling, processing, and use of high sulfur coals. Sessions were held on: characterization of sulfur in coals; environmental problems and impact of high sulfur on coal use; selective mining and blending; coal desulfurization by physical and chemical cleaning techniques; handling of coal fines; sulfur capture during coal combustion; biological desulfurization of coal; and new applications for high sulfur coal. The Economics of Magnesium Metal, 1985, Roskill Information Services Ltd., 2 Clapham Road, London SW9 OJA England, 129 pp., 71 tables, appendices, bound, $750-Despite setbacks in some major magnesium markets in 1985, Roskill's latest forecast for the last half of this decade is for a 4% to 6% annual growth rate in demand. Growth for magnesium metal is expected in the motor industry for use as a possible substitute for aluminum. Some magnesium producers are altering their marketing strategies to cultivate this market. This study also includes a review of the worldwide magnesium industry, its end uses and consumption, and international trade and price trends.

Jan 7, 1986

The Raub Gold Mines are situated approximately in the centre of the Malayan Peninsula in the State of Penang. Part of the area, now known as "Raubhole," was opencut some 800 years ago by the Mon Khmers, a Cambodian people, whose vestiges mark numerous outcrops in South Eastern Asia. With their decline and extinction the work was abondoned, leaving a large pond in a dense thicket of Beluka (secondary growth).From the year 1885 onwards the history of Raubhole and the water therein records a chain sale starting from an enterprising local "Rajah," who had "assumed" authority, to an equally wakeful Singapore Arab; thence through the agency of a "down-and-out" beachcomber to a hopeful Australian company in the "goldbrick" days. Subsequent catastrophe on a depleted stringer was followed by reconstruction; the deserved reward of a long mining life, and an output of nearly 800,000 ounces of gold. Owing to the loss of notes and data stored in Singapore, this paper is not as complete as it should be, especially in respect to its metallurgical phases. Apologies are therefore tendered in advance for any deficiencies which may be noted.The necessary regional geological data have been taken largely from the admirable investigation of the Raub area by J. A. Richardson, A.R.C.S., B.Sc., F.G.S., of the Malayan Geological Survey*, and, throughout the paper, months represent lunar periods of 28 days and money is expressed in sterling.MINING SECTIONSAs shown hereunder the reef system has been divided by nature into seven isolated sections, which have been of necessity worked as seven separate small mines. From north to south these are:-(a) Sungei Agas consisting of very shallow workings to the south of, and adjacent to, a granite-porphyry mass known as Bukit (hill) Kajang. This area has not been worked for many years.(b) Bukit Malaka which is also shallow.(c) Bukit Jalis.(d) Bukit Koman which, with (c) and (e), consitutes the main workings and which has possibly been determined in depth.(e) Anderson Section.(I) Raubhole Section.(g) The workings under Raub Village.

Jan 1, 1945

Ceremonies for the induction of four mining industry pioneers into the National Mining Hall of Fame will be held Saturday, Sept. 22, 2007 at the Charles F. Barber Pavilion (Museum Convention Center) in Leadville, CO. The four inductees are James Harold Courtright (1908-1986), Dr. Howard L. Hartman (1924-2002), Charles Washington Merrill (1869-1956) and Kenyon E. Richard (1915-1993). The inductions will bring to 197 the number of mining “greats” whose engraved photographs and biographical sketches are installed in the National Mining Hall of Fame.

Jan 1, 2007

By Manuel Gomez

Bituminous coals having maximum fluidity values in the 40- to 25,400-dial-divisions-per-minute (ddpm) range were carbonized in a continuous, entrained-bed reactor. Carbonization was conducted in an 8-inch diameter, vertical reactor at temperatures from 955° to 1,345° F and at air-to-coal ratios ranging from 4.63 to 16.12 scf/lb of moisture-and ash-free coal charged. Carbonization rates from about 118 to 360 lb/hr, as-carbonized basis, were examined. It was demonstrated that carbonization temperature and air-to-coal ratio must exceed minimum values for continuous operation. Within the operating conditions discussed, highly fluid bituminous coal was carbonized to produce tar and nonagglomerated char. The yield of tar ranged from 21.3 to 38.9 gallons per ton and the char yield ranged from 1,109 to 1,563 pounds per ton, all units expressed on a moisture-and ash-free basis. It was demonstrated that the maximum fluidity and the average size of the coal along with the air-to-coal ratio and the carbonization temperature act together to influence the carbonization product yields and certain properties of the products. Prediction equations were developed from the data for product yields and selected properties of the char, tar, and gas.

Jan 1, 1968

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