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By K. Swedburg, M. Samuels

"The New Afton concentrator was commissioned in June 2012, reaching the design milling rate in September 2012. By late 2013, through a campaign of optimization and de-bottlenecking, it was recognized that the installed plant was capable of greatly exceeding the design throughput of 11,700 tpd. Because the value of the metal contained (by increasing the plant feed rate) exceeded the offsetting losses of copper and gold recovery (as the operation moved to a coarser grind), the concentrator feed rate was strategically increased with support of New Gold, while the operations team was given a mandate to evaluate, and then implement, flow sheet options that could re-establish the original design criterion grind target and achieve the corresponding improved recovery. Broadly, the two options implemented were the addition of a tertiary grinding stage consisting of Metso Vertimill® prior to rougher flotation (in order to address the grinding required at increasing throughput by increasing the power), and the addition of three Woodgrove Staged Flotation Reactors (SFR) added to the cleaner circuit after regrind of the rougher concentrate (to address the increased mineral loading to the cleaner circuit). Through test work, it was anticipated that the SFRs would be capable of achieving final concentrate grade in a single pass without the integration of recirculating loads, a strategy sometimes referred to pre-cleaning. This paper describes the expectations generated for the Woodgrove SFR unit operation through pilot plant testing on site, and compares those results with the performance of the expanded circuit that exceeded the original design criterion of P80 160 µm, which was commissioned in the second quarter of 2015.INTRODUCTIONThe New Afton concentrator, located near Kamloops, BC Canada, commenced operation in June 2012. The mill achieved the design throughput of 11,000 tonnes per day average during the month of September 2012 and, following various operational optimization efforts (O’Hara et al, 2015), achieved the design p80 grind size of 160 µm at the design milling rate in July 2013.During August 2013, trials were carried out to determine the throughput rate limits of the mill circuits and to evaluate mill metallurgical performance at higher rates. Milling rates up to 15,500 dmt per 24 hours were achieved during this trial, demonstrating potential capability for sustained milling rates exceeding the nominal design capacity. As was expected, the higher milling rates resulted in a coarsening of the grinding circuit product size, and resulted in marginally lower recoveries in the rougher flotation circuit. Despite the lower recoveries, the higher milling rates resulted in higher metal production and the financial analysis favored running at rates of at least 13,000 tonnes per operating day, with the higher cash flow in the near term offsetting the value of metal production loss at the end of the mine life (due to the short term increase in the rate of reserve depletion). Milling rates were sustained above 13,000 tonnes per day through the second half of 2013, and increased above 14,000 tonnes per day by mid-2014 (Figure 1)."

Jan 1, 2016

By He De-wen

The municipal solid waste is a by-product of the daily life of urban residents. The quantity and ingredients of municipal solid waste has exceeded the current management and disposal ability, which has done a great harm to municipal environment and sanitation quality and threatened people?s health. On the basic of analysis on the amounts and main elements of municipal solid waste of Changsha City, the sanitation landfill, incineration, composting, reclamation and utilization technology of household waste were compared specifically in this paper. Based on the concrete conditions of Changsha City, the paper has proposed a disposal proposal combined with reclamation and landfill of municipal solid waste of Changsha City, and the environmental benefit, social benefit and economical benefit of the prepared processing routes were also analyzed in the paper.

Jan 1, 2009

By J. R. Thoenen, Hugh D. Pallister

"INTRODUCTION The Stone Hill Copper project resulted from the recommendations made in the war minerals report on this deposit by engineers of the Bureau of Mines 4/ and a similar report of the Geological Survey. 5/ACKNOWLEDGMENTSIn its program of investigation of mineral deposits, the Bureau of Mines has as its primary objective the more effective utilization of domestic mineral resources to the end that they make the greatest possible contribution to the national security and economy. The Mining Division, Lowell E. Moon, chief, conducts preliminary examinations, does the actual investi¬gative work, and prepares the final report. The Metallurgical Division, Oliver C. Ralston, chief, analyzes samples and makes beneficiation tests.This report was prepared under the supervision of Paul M. Tyler, former regional engineer, Eastern Region, and is based on the examination and investigation of the deposit by Hugh D. Pallister, mining engineer, made under the immediate supervision of Richard W. Smith, former District Engineer for Alabama and Mississippi.The report was rewritten and prepared for publication by J. R. Thoenen, chief, Tuscaloosa Branch, Mining Division.LOCATION AND ACCESSIBILITYThe Store Hill copper mine is about• 12 miles south of Heflin, the oounty seat of Cleburne County, Ala. Heflin, a town with a population of approximately 1,700, is the nearest shipping point for freight and express. It is on the Southern Railway, between Birmingham and Atlanta. A rural mail route passes within quarter of a mile of the mine. Paved reads from Heflin lead to Atlanta, Birmingham, and Montgomery. The country Toads leading from Heflin are well-maintained but are practically inaccessible during inclement weather. The road crossing the property within a hundred yards of the mine needs grading and repairing (see fig. 1)."

Apr 1, 1948

By Mitsutaka Hino

The contents of gangue minerals, such as Al2O3. P2O5, crystalline water and so forth in the iron ore imported to Japan tend to increase year by year. Though the increments of such gangue contents arc approximately 0.1-0.2 mass%, some problems for the blast furnace operation in ironmaking process have already been reported, In order to clarify the mechanism of harmful effect caused by the small increment of gangue minerals, mainly Al2O3. on the blast furnace operation, the dripping behavior of Fe,O-CaO-SiO2-Al2O3-MgO slag from the iron funnel, which simulated the micro-porosity in sinter ore, has been observed with the wide range of basicity, Al2O3, Fe2O and MgO contents. The effect of MgO on the dripping behavior of slag has been summarized in this paper. It was found that the addition of 2mass% MgO resulted in large increase of hold-up on the most of the conditions. When Fe2O content was less than 20mass% and the basicity was lower than 0.8, MgO lowered the hold-up even if the slag contained 10mass% Ah03. Every slag hold-up showed the minimum at the basicity of less than unity on the conditions of constant Fe2O and Al2O3 contents, This trend became remarkable when the slag contained 2 mass% MgO.

Jan 1, 2003

By E Donskoi

In order to develop downstream processing routines for iron ore and to understand the behaviour of the ore during such processing, extensive mineralogical characterisation is required. To determine mineral associations, mineral liberation and grain size distribution, imaging techniques have to be used. There are two main imaging techniques used for the characterisation of iron ore, ie, Optical Image Analysis (OIA) and Scanning Electron Microscopy (SEM). In this article a QEMSCANTM system is used as an example of SEM methodology and results obtained from it are compared against results obtained by the CSIRO ‘Recognition3/Mineral3’ OIA system.Both OIA and QEMSCANTM systems have advantages and drawbacks. Even though the latest QEMSCANTM systems can distinguish between major iron oxides and oxyhydroxides, it is still problematic for QEMSCANTM to distinguish between iron ore minerals very close in oxygen content, eg haematite and hydroheamatite, or between different types of vitreous goethite.QEMSCANTM also can misidentify minerals with close chemical composition, ie haematite as magnetite and vitreous goethite as haematite. In OIA, iron minerals with slight differences in their oxidation or hydration state are more easily and directly recognisable by correlation with their reflectivity. In both methods, the presence of microporosity can result in some misidentification, but in SEM methods misidentifi cations due to microporosity can be critical. Low resolution during QEMSCANTM analysis can significantly affect the textural classifi cation of particle sections.The main conclusion of this study is that, for low iron content ores or tailings, QEMSCANTM can provide much more detailed information on the gangue minerals than OIA. However, for routine characterisation of iron ores with high iron content and containing a variety of iron oxides and oxyhydroxides, OIA is a faster, more cost-effective and more reliable method of iron ore characterisation. A combined approach using both techniques will provide the most detailed understanding of iron ore samples being characterised.

Jul 11, 2011

By J. S. Young

During 1975, the Reclasource Corporation constructed and commissioned a plant for the recovery of mill scale, coke breeze, blast furnace dust, blast furnace sludge and basic oxygen furnace dust at the site of Crucible Alloy Division, Midland, Pennsylvania. The Reclaform Process was employed as the criteria for plant design. This Process takes the solid in-plant fines as listed above, commonly found in integrated steel mills, sizes and forms them through the use of a carbonaceous binder briquetting system and cures the binder through a final heat-treating step. 15,000 tons of Reclaform briquets have been tested in the Crucible blast furnace in several campaigns structured to assess material handling properties, burden feasibility and finally culminating in an iron and carbon assessment campaign. Data are presented from the records of the blast furnace operation and conclusions are drawn that both iron and carbon utilization have been demonstrated.

Jan 1, 1977

By Eder Salazar

Como parte del desarrollo de sus operaciones de mina de cobre subterránea, la Sociedad Minera El Brocal S.A., desarrolló el método de minado tajeo por subniveles con pilares recorridas con el fin de incrementar su producción actual. En ese sentido, el presente texto señala la implementación de un método de minado conforme a las características geomecánicas del macizo rocoso del yacimiento.

Sep 12, 2011

By Richards S. M

The abundances and abundance relationships of lead, zinc, copper and silver in the major sulphide lenses at Broken Hill are examined, and their possible geochemical significance discussed.When expressed as atoms per cent, zinc is the most abundant base metal throughout the whole .group of orebodies, the highest average lead: zinc ratio (No. 2 lens) being about 0·45, the lowest (No. 1 lensZinc Lode group) being in the 0·12-0 ·14 range. Lead and silver are clearly higher in the lower two orebodies, but the abundance of zinc shows no apparent relationship with stratigraphical position. Among the base metals copper is conspicuously low and remarkably uniform, a feature noted in other conformable orebodies.Although, as has been recognised for many years, abundances of silver and lead, and lead and zinc, are sympathetically related, correlation within the pairs is variable and generally of low degree. Silver and lead show distinctly the better correlation, particularly in No. 3 lens. On the basis of lead: zinc ratios, No. 2' and No. 3· lenses, on the one hand, and the No. 1 lenses, Rhodonitic and Siliceous Zinc Lodes on the other, constitute two groups. However on the basis of silver : lead ratios, No. 3 lens stands alone, No. 2 lens showing clear affinities with the higher layers. Ternary relationships between copper-zinc-Iead and silver-zinc-Iead emphasize the very close constitutional relationship between the No. 1 lenses and the two "zinc lodes".The possible implications of these relationships are then discussed in the light of the' two principal theories-hydrothermal replacement or chemical sedimentation-held for the formation of the Broken Hill ores. It is pointed out that the ratios of the four metals in the ores are rather different from those found in most igneous and sedimentary rocks, and in seawater. For 'example, whereas copper and zinc are present in almost equal amounts in most terrestrial materials, copper in the ores is only about one-hundredth of the amount of zinc. Lead has increased somewhat, but the ratio of silver to lead has fallen; in spite of its recognition as a source of silver, the Broken Hill lode is impoverished in silver with respect to lead as compared with most common terrestrial materials.No solutions are offered to these prob'lems of abundance. Rather it has been the aim of the work to provide data, and to demonstrate the...

Jan 1, 1961

By A. C. Fieldner

"Gas hazards may be divided into two principal classes- namely (1) inflammation and explosions; (2) asphyxiation and poisoning. Inflammation and explosion are prevented first by adequate ventilation so that gas sufficient to propagate flame or explosion can not accumulate, and second, by avoiding sources of ignition such as open lights, flames, sparks, electrical arcs, short circuits, or sparks. Ventilation is also the best preventive measure against asphyxiation and poisoning from toxic gases. When men must enter unventilated or poorly ventilated places containing poisonous or asphyxiating gases, suitable gas masks, hose masks, or oxygen breathing apparatus should be worn. As a rule, loss of life and property from gas hazards is due to ignorance of the properties and hazards of various gases commonly used, and consequently a failure to use proper measures for eliminating and meeting these dangers. It is the purpose of this paper to describe briefly the common gases and vapors with respect to the hazards involved in their use and to discuss the necessary precautions and methods for avoiding these dangersLight, heat, and power are prime essentials of our modern industrial civilization. The combustible gases and vapors used for the production of these necessary elements of our existence comprise the largest and most common group of domestic and industrial gas hazards. Almost every individual in his daily life subject to possible danger from asphyxiation, fire, or explosion due to one or more of these gases. For evidence one need only refer to the daily newspaper where headlines such as the following are frequently seen; ""Family asphyxiated by carbon monoxide from gas heater;"" ""Schoolhouse wrecked by gas explosion in basement;"" ""Man killed by automobile exhaust fumes in his garage;"" ""Fireman overcome by smoke fumes in basement ""Woman"".""Boman severely burned by accidental ignition of gasoline used in cleaning gloves;"" and 'in recent Years we often see ""Building wrecked by explosion of still in residential district.""It will be noted that these accidents are due to inflammation, explosion, or asphyxiation. Any combustible gas or vapor, when mixed, with air or oxygen within certain limiting proportions, will explode on ignition. The violence of the explosion varies with respective proportions of air and gas, and with the degree of confinement of the mixture. For example: Mixtures of natural gas and air containing between 4.5 and 12 per cent natural gas will explode, or propagate flame throughout the mixture without the continual presence of the source of ignition that started the inflammation. The table following gives the explosive limits of the common combustible gases and air:"

Jun 1, 1926

By S. Peterson, E. C. Westman, P. L. Swanson

Coal bumps are brittle, violent failures associated with high stresses and competent host strata. To study bump mechanisms, conditions in the vicinity of a deep longwall mining face in bump-prone strata were monitored using three discrete systems. First, a microseismic monitoring network recorded mining-induced seismic events throughout the mine and surrounding strata. Second, pressure variations and distributions on the longwall shield legs across the face were recorded. Last, tomography surveys imaged seismic transmission properties ahead of the face. Results from the three systems were correlated in an effort to increase understanding of mining-induced stress redistribution and bump potential. An initial, one-week study showed that the correlation between averaged tomogram values and seismically active areas had a coefficient of correlation (R) of 0.89. Further results of these studies demonstrate that the tomography system is capable of imaging heavy shield-leg loading and bump-prone conditions prior to them disrupting the face operations.

By James R. Hein

Rodriguez Seamount, located 150 km off the central California coast at the base of the continental slope, was studied using the ROV Tiburon aboard MBARI?s R/V Western Flyer, October 13-16, 2003. Fe-Mn crust and rock samples were collected along the SW flank of the seamount at water depths from 700 to 2100 m; bottom-water dissolved oxygen content (O2) and temperature were determined at each sample site. Fifty-three samples of bulk crusts, crust layers, and surface scrapes (~0.5 mm) were analyzed for 59 elements. Data allow for the correlation of crust compositions with precisely known water depths and seawater O2 measured at the actual site of sample collection. This is the first detailed study of Fe-Mn crust compositions in a region of strong continental-margin upwelling. Compared to open-ocean seamount Fe-Mn crusts, Rodriguez crusts have significantly higher (2-6 fold) mean concentrations of Fe (26.9%), Al (1.65%), Si (13.0%), Cr (82 ppm), Th (64 ppm), and Ag (1.7 ppm); and significantly lower (2-8 fold) mean concentrations of Ca, P, Bi, Co, Cu, Ni, Tl, and especially Te (8.2 times lower). All but one Fe/Mn ratio are >1 compared to <1 ratios for open-ocean crusts. O2 contents (0.35-2.03 ml/L) are nearly perfectly corrected with water depth and elements correlated with one are correlated with the other. The Fe-Mn surface scrapes represent 60-450 ka (mean 150 ka) of growth, whereas the dissolved oxygen contents of seawater represent an instant in time. Assuming that the entire sample set was affected uniformly by oceanographic changes, we suggest that correlation of elements with O2 may reflect oceanographic processes. O2 has a negative correlation with P, V, As, Fe, U, Be, Pb, Cr, Mg, Y, Bi, Te, and REEs (except Ce) and a positive correlation with aluminosilicate-hosted elements (Al, K, Rb, Cs). This later relationship is related solely to water depth, indicating that detritus shed down the seamount slopes accumulates in greater abundances in deeper-water crusts. Si/Al ratios indicate that the detritus includes a large component of biosilica produced by upwelling-mediated high productivity. These observations are supported by positive correlations of aluminosilicate-hosted elements with crust growth rates (range 1.2-13.0 mm/Myr). In contrast, other elements (Sr, Co, Mn, Mg, Te, As, Mo, V, W, U, Ti, Ni, REEs, etc.) are negatively correlated with growth rates. Growth rate has a weak positive correlation with O2. These compositional characteristics indicate that even though low-O2 seawater acts as a reservoir for Mn and associated elements and produces slow growth rates, which would allow for the concentration of elements and surface oxidation processes to occur, the high rate of input of detritus and high bioproductivity ameliorate the strong concentration of most metals. This dilution is significantly enhanced by the doubling of FeOOH in the crusts--the main cause of the generally high growth rates compared to open-ocean crusts. The high growth rates limit the oxidation of Co, Tl, and especially Te on the crust surface, which is reflected by their relatively low concentrations. Within the range of oxygen contents measured, O2 has less of an influence on crust chemistry than does the availability and incorporation of FeOOH and detritus.

Jan 1, 2004

By Craig Bournes, David Chapman, Michael DiPonio

Historically, boulders are a frequent source of problems in soft ground tunneling. During tunnel construction, the need to manually break and remove boulders as obstructions causes delays to the project. Repairs to a tunnel boring machine (TBM) can also be a source of delays. Managing these problems is difficult since normal soil investigation techniques do not accurately predict the presence or frequency of boulders. This has lead to considerable number of claims for extra costs and delays during the construction of soft ground tunneling projects. These issues are exacerbated in pressurized face tunneling systems where there is limited access to the TBM cutterhead for obstruction removal and/or cutterhead maintenance. The project team that built the Big Walnut Augmentation/Rickenbacker Interceptor (BWARI) Project for the City of Columbus successfully managed the design and construction of a 4,267 mm (14 ft) diameter soft ground tunnel with high boulder concentrations in a complex geologic setting. The management of the boulder issue tookplace during several phases of the project.

Jan 1, 2007

In this paper, geostatistical techniques are applied to forecast the annual copper price in the short and medium terms (from one to five years ahead). These techniques allow the incorporation of monthly and multivariate information in the analysis and provide more accurate results than traditional approaches, especially as far as the one-year forecast is concerned. A second advantage of geostatistics stems from its ability to assess the uncertainty associated with the unknown future prices, thanks to estimation variances or confidence intervals, depending on the technique used. Such an assessment has a crucial importance in decision-making, from both macroeconomic and microeconomic points of view

Sep 1, 2004

By Patrick Polk

For many years, sulfuric acid producers all over the world have been forced to meet ever more strict environmental regulations to reduce SO2 emissions. The sulfuric acid industry has implemented new solutions in order to comply with the new lower SO2 emissions target. Haldor Topsoe (Topsoe) has responded to this challenge by continuously improving the range of VK sulfuric acid catalysts and providing tailor-made catalyst solutions to meet the demands of the sulfuric acid producers for lower SO2 emissions. Reducing emissions through catalysis: requires less capital than installing a scrubber, requires no additional process chemicals, generates no waste or by-product to dispose of. In 1996 Topsoe introduced VK69, a cesium-promoted vanadium catalyst, designed for operation in the pass(es) after the intermediate absorption tower in double absorption plants. The high activity of VK69 allows for a more than 50% reduction in SO2 emissions from existing double-absorption plants. Topsoe currently has more than 110 installations of VK69. To comply with the still more stringent regulations being placed on the sulfuric acid industry to lower SO2 emissions, Topsoe has developed a new sulfuric acid catalyst designated VK-701 LEAP5™. This catalyst was introduced to the market in 2010. VK-701 LEAP5™ is based on a novel technology which circumvents the internal transport deficiencies of existing commercial sulfuric acid catalysts and thereby offers exceptionally high activity in strong, SO3 rich gases. Sulfuric acid plants have used this catalyst to meet emissions requirements lower than previously believed possible with a catalyst only solution. This paper will present examples on how to reduce emissions by implementing a tailor-made catalyst solution using VK69 and VK-701 LEAP5™.

Jan 1, 2014

By Seth L. Pearlman

A major excavation support case history for the Eastern approach to the Third Harbor Tunnel (THT) in Boston, MA is described, which uses an anchored Soil Mixed Wall (SMW). Both general and project specific information is provided regarding the design and construction of SMW walls. In addition, conclusions are presented that discuss the suitability of this particular application and other possible variations.

Jan 1, 1993

By B. Tripp

Utah produces a wide variety of industrial rock and mineral commodities, valued in 2005 at a record $758 million (21 percent of the total non-fuel mineral production of Utah). Major commodities produced in 2005 include salts (halite, potash, and magnesium salts), Portland cement, sand and gravel, carbonates (lime, limestone, and dolomite), phosphate, crushed stone, clays, lightweight aggregate (expanded shale and perlite), gypsum, silica, sulfur and sulfuric acid, and building stone. Commodities produced in smaller amounts include diatomite, pumice, gemstones, ornamental stone, fluorspar, and mineral and fossil specimens. Utah is in a period of rapid growth in industrial rock and mineral production; however, some commodities have grown faster than others. The robust western economy has stimulated production of construction-related commodities like sand and gravel, Portland cement raw materials, lime, and building stone, resulting in exploration for raw materials, development of new quarries, and expansion of existing plants

Jan 1, 2007

By Jeanne A. Smith, Suzanne D. Smith

Annoyance, fatigue, and musculoskeletal pain have been reported during prolonged exposures to propulsion-generated vibration in military propeller aircraft1. The objective of this study was to determine the vibration mitigation properties of selected seat cushions and the effects of occupant seating posture during exposure to higher frequency multi-axis vibration associated with military propeller aircraft. Methods A Navy E-2C Hawkeye crew seat was mounted onto the Six Degree-of-Freedom Motion Simulator (SIXMODE). Six seat pan cushion configurations were tested during exposure to an E-2C vibration signal collected in the field1. Seat pan cushions 1 – 5 were used with the original E-2C seat back cushion. Cushion configuration 6 included seat pan cushion 5 with a prototype seat back cushion. Triaxial accelerometer pads were mounted onto the seat pan and seat back cushions to measure the vibration entering the human. Data were collected for seven subjects seated upright with their backs in contact with the seat (back-on) and not in contact with the seat (back-off). Spectral analysis techniques were used to analyze data at the two dominant frequencies associated with the propulsion system (propeller rotation frequency (PRF) ~18.5 Hz, and blade passage frequency (BPF) ~73.5 Hz). Overall accelerations were also calculated between 1 and 80 Hz. Vibration Total Values (VTVs) were calculated using the weighted seat pan and seat back (back-on only) accelerations and compared to the comfort reactions given in ISO 2631-1: 19972. Results In general, the highest accelerations observed at the seat pan occurred in the fore-and-aft (X) direction at both the PRF and the BPF for all cushions and both postures. The most pronounced effect was at the BPF in the X direction, where all configurations showed significantly lower seat pan accelerations than configuration 1 (original E-2C cushion) with the back-on posture. Configuration 5 was the exception with the back-off posture (Fig. 1A, Repeated Measures ANOVA, P<0.05). The most pronounced effect of posture occurred at the PRF in the X direction, where all cushion configurations showed significantly lower seat pan accelerations with the back-off posture (Fig. 1B). All configurations except configuration 2 showed similar VTVs as compared to Configuration 1 (Fig. 2, P<0.05). Configuration 2 tended to show the lowest weighted acceleration levels. The overall VTVs (back-on only, Fig. 2B) showed significantly higher accelerations as compared to both the back-on and back-off seat pan point VTVs (Figs. 2A &

Jan 6, 2006

There remains considerable controversy in the industry regarding precision type detonators and where the end user can benefit from their use. In spite of the fact that electronic detonators and other prototypes were tested over one decade ago, explosive suppliers have hedged on full scale production for many reasons. Although some of the reasons were based on solid economics, others were strongly influenced by shear internal resistance within the corporate objectives, ultimate fear of market rejection, indecision as to what degree of precision was required and limited data on defining the real benefits to the end user.

Jan 1, 1992

By V Kveldsvik, N Ragvin, T Eiken, G Grøneng, G V. Ganerød

Catastrophic rock slope failures have caused destructive tsunamis in Norwegian fjords. At the Åknes rock slope the tsunami generating potential is large due to the potential large volume involved in a possible catastrophic failure. Widening of the upper crack has been recorded since 1986, and in recent years, a quite extensive investigation and monitorin campaign has been conducted. Data from some of these investigations are presented and analysed with respect to a preliminary evaluation of the stability of the slope.

Jan 1, 2006

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&apos;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&apos; et aL5 assumption of vertical equilibrium and extend the relations to three-phase flow. Coats&apos; 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&apos;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&apos;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