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By John Chipman, Wayne L. Worrell

Using recent thermodynamic data for the carbides and oxides of tantalum, columbium, and vanadium, the stable solid phases aboue 1300°K and at 1 atm CO(g) pressure in each M-C-O system have been determined. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures necessary to obtain these metals by carbothermic reduction under reduced pressures. TANTALUM, columbium, and vanadium react with carbon to form the M,C and MC carbide phases. The M,C carbides have narrow homogeneity ranges, but the MC phases possess considerable ranges of homogeneity.' The free energies of formation of the MC carbides were recently measured, and those of MC and M2Ccarbides have been estimated., (The notations MC and MC denote, respectively, the carbide compositions at the carbon-rich and at the metal-rich boundaries of the homogeneous MC phase.) In this paper, these carbide data are combined with thermodynamic data for the oxides to predict the stable phases in the Ta-C-O, Cb-C-O, and V-C-O systems at specified temperatures and oxygen pressures. M-C-O PHASE DIAGRAMS The solid phases in equilibrium above 1300°K for each M-C-0 system are shown in Figs. 1, 2, and 3. Above 1300°K, the vapor would consist entirely of carbon monoxide; and these phase diagrams were obtained by specifying the vapor pressure of CO(g) to be 1 atm. The temperature at which any two solid phases become unstable is specified along the two-phase equilibrium lines in each diagram. To simplify the diagrams, all solid phases in the Ta-C-O and Cb-C-O systems are represented as stoichiometric compounds. However, the homogeneity ranges of VO and VC are indicated, because they form a complete series of solid solutions.3 It also should be noted that the homogeneity range of

Jan 1, 1964

By L. B. Davidson

The petroleum literature contains many reports on the relative permeability properties of porous media. However, only recently have studies of relative permeability at elevated temperatures been made.1 -5 Each of these studies presents relative permeability data on water-oil systems in linear sandpacks or sandstone cores under isothermal conditions. The results of these investigations are dissimilar. Edmondsonl found that in Berea sandstone a temperature-dependent effect was present, while Shilobod,2 using the same material, found no temperature dependence after normalizing for initial water saturation. Workers at Texas A&M U.3-5 found that the ratio kw/ko was temperature dependent in an unconsolidated system. The differences in results of these studies are probably a consequence of differences in the material employed, in the experimental procedures followed, and in the properties of the porous systems used. This paper describes an experimental investigation of permeability ratio temperature dependence, conducted to clarify some of the results obtained by previous workers. Each experiment described in this paper involved the isothermal displacement of Chevron No. 15 white oil by either nitrogen, steam, or distilled water and displacement of water by nitrogen. All permeability ratios were calculated using the Welge procedure. Values of the water-oil permeability ratio were obtained over the temperature range 75OF to 540°F. Results indicate the ratio is temperature dependent at low water saturations, probably due to interfacial effects. However, as the saturation is increased, temperature dependence decreases until, above some minimum saturation, the ratio becomes insensitive to temperature. Previously published work indicates that the dependence reappears at very high water saturations, a region of the ratio curve not completely examined in the present study. It appears that water-oil permeability ratios are temperature dependent at the extremes of the ratio curve where changes in interfacial tension with temperature induce variations in residual saturations. Between the extremes, there is a region in which the permeability ratio is insensitive to temperature. The size and location of this region is probably a function of the characteristics of the porous system. Gas-oil permeability ratios calculated from nitrogen-white oil displacement experiments indicate a definite temperature dependence over the range 75OF to 500°F and over the entire gas saturation range studied. Evidence discussed in this report indicates that this dependence is a consequence of molecular slippage in the gas phase. This is an extension of the Klinkenberg effect6 to two-phase systems at high temperatures (the existence of slippage in two-phase systems at room temperature has been demonstrated7). Evidence for a similar source of temperature dependence in superheated steam-white oil experiments

Jan 1, 1970

By J. N. Van der Merwe

In the process of pillar extraction, pillars are seldom if ever extracted completely. The pillar remnants, or snooks, play an important role in the extraction process. At the working face, they need to be stable to provide a measure of support in the immediate area. Further back, they have to fail in a controlled manner to prevent undue load build-up on the pillars that have not yet been extracted. The stability condition at the working area is the result of interaction between the stability of the pillar and that of the roof rock. It is shown that the primary mode of roof layer failure is by bending induced tension. Direct tension can be excluded in most practical conditions, and only in exceptional cases will the first failure be in shear mode. Panel spans required to cause the first goaf to be formed, predicted using analytical considerations, are of the same order as has been observed in practice. Once the first goaf has formed, the horizontal stress is reduced and failure will occur at more frequent intervals. It is shown that bending induced tension is the most likely mode of failure in an unjointed roof layer. In roof layers with a high frequency of weak or uncemented jointing, failure can be expected to occur at spans equal to the joint spacing. In this context, failure will occur at the smallest of the spans required to induce tensile roof failure and the joint spacing. A fundamental procedure to evaluate the likely roof layer failure in a stacked beam system is developed. This can to be used to estimate the loading condition on snooks. It is shown that snooks assist in stabilizing the immediate roof beam. The sizes and positions of the snooks relative to the position of the next pillar to be stooped, control the magnitude of the contribution to stability. The further the snook is from the next pillar, and the larger it is, the greater the contribution to the stability of the immediate roof. Under the condition of loading by the immediate, continuous roof beam, the position and size of a single snook controls the load acting on it. The closer it is to the nearest solid, provided that the roof overhang extends beyond the snook, the greater the load on it. However, once the immediate roof beam fails, the loading conditions change. The snook is then loaded by the tributary area load. A procedure is developed to assess the condition of snooks for different situations. Using the fundamental considerations developed in this paper, snooks can be designed to be stable during the active mining phase in their immediate vicinity, but to fail once the next line of pillars has been extracted.

Jan 1, 2005

By T. A. Muhlare

"Large quantities of slag are produced every year and dumped on slag heaps around the world, posing a potential environmental threat due to contained heavy metals content. Slags are waste minerals produced during furnace smelting of minerals. The contained values of base metals may be released into the environment under natural weathering conditions polluting ground and underground water. Copper losses into slag are a continuous problem in pyrometallurgical smelting operations. Due to shortage of ore concentrate, various mining operations have initiated the recovery of copper from dumped slag. The typical process uses crushing, milling and flotation. These operations create excessive liner wear rates during crushing and milling because the bond work index of copper slag is 22 kWh/t and this is considered a very hard slag. The process also has reduced flotation recoveries and requires high flotation reagent consumption. The present work shows that digestion of the milled copper slag slurry with concentrated sulphuric acid at a temperature of 250oC forms a solid cake and leaching of the solid cake with water is a possible option. However, the consumption of sulphuric acid can have a considerable cost on the recovery process. This can be limited by producing a leach residue containing gypsum and silicate materials as amorphous silica which are suitable for use as an additive for Portland cement. Laboratory results show that 90% copper recoveries can be achieved. The leaching is conducted to prevent silica gel formation and iron co-extraction. Leaching is optimum if silica gel-free solutions and good filterable residue are obtained. INTRODUCTION Slag is a waste by-product of smelting and converting operations in metallurgical plants. Both smelting and converting operations are aimed at iron separation from base metal sulphides in non-ferrous metallurgy. The iron sulphide component of the ore or concentrate is oxidized to iron oxide at higher temperatures in the molten form, and then fluxed with silica and other oxide rock minerals to produce fayalite (2FeO•SiO2) slag (Schlesinger et al., 2011). Slags are generally deposited on dumps and considered to be unreactive materials. Smelter copper slag contains significant concentrations of several potentially toxic elements, including arsenic, lead, cadmium, barium, zinc and copper. These elements can be released into the environment under natural weathering conditions and cause pollution of soils, surface waters and groundwater (David, 1998)."

Jan 1, 2015

By Richard Peaker, Jens Lichter, Alexander V. Potapov

"The recent combination of Computational Fluid Dynamics (CFD) and Discrete Element Modeling (DEM) can provide considerable insight into the performance of flotation cells. One area of interest from a fundamental equipment design perspective has been the influence of flotation cell size and the inflow rate on the metallurgical performance of the cell. One of the specific design objectives when increasing the size of flotation cells, or increasing the feed flow to the flotation cell, is to ensure that the feed stream flowing into the cell does not have an opportunity to bypass the mechanism.This paper describes the initial modeling efforts to quantify the inter-relationship of cell size, inflow rates, and feed and discharge box placement, on the retention time distribution of solids in the flotation cell, and the fraction of particles that bypass the mechanism on a size by size basis.INTRODUCTIONThe great majority of newly installed cells in mineral processing plants world-wide are of the cylindrical tank design and this tank shape offers a number of hydraulic advantages over the older style of square cells. Cylindrical cells give symmetrical flow patterns and by careful design of the mechanism and tank internals, the flow patterns generated can concentrate the more intense mixing in the lower portion of the cell to promote good solids suspension and particlebubble contact. Simultaneously, cylindrical tank design gives a more quiescent upper zone for particle-bubble transport into the froth zone. These symmetrical flow patterns are naturally disturbed in normal operation by the slurry inflow and outflow from the individual cells. The challenge for flotation cell designers is to determine the magnitude of these flow disturbances, and to assess whether or when the inflow and outflow rates have a sufficient impact on the hydraulic flow patterns so as to potentially affect the metallurgical performance of the flotation cell."

Jan 1, 2007

By R. Bellotti

The theory of cavity expansion in an infinite frictional soil mass whose strength is represented by a curved Mohr-Coulomb failure envelope has been used to predict with some confidence the cone resistance of a clean dry sand. Experimental data were obtained from cone penetration and pressuremeter tests on two sands, conducted in a large calibration chamber (CC) under carefully controlled placement and boundary conditions. A plane strain bearing capacity theory was developed, and to convert the results to axi-symmetric conditions, an empirical "shape factor" was used. In the paper, the theoretical background, experimental data, calculation procedure, and the results of the analysis are presented. In general, a reasonable validation of the cavity expansion approach to the bearing capacity of deep foundations has been obtained.

Jan 1, 1987

Laboratory and pilot plant investigations aimed at recovering gold as an electroformed sheet from gold eluate and gold leach solutions and slurries are discussed. The electrolytic test work undertaken makes use of high surface area electrodes, in particular nickel-chrome foam metal and activated carbon, as well as ultrasonic activation. The process involves initial gold electrowinning (or adsorption onto activated carbon), followed by gold electroforming, both operations being carried out in a specially designed reactor. The pilot plant work mainly involved the treatment of gold eluate solutions from a South African gold mine containing 600 mg/L Au: some tests were also carried out on gold leach solutions containing 6 mg/L Au. In the former case, very efficient gold extraction onto the foam metal cathode was achieved using electrolysis combined with ultrasonics. The polarity of the gold-loaded cathode was then reversed and, using a replacement electroforming electrolyte, gold was electroformed in situ onto a polished stainless steel mandrel, from which gold sheet was subsequently removed. In the case of leach solutions, pilot plant tests confirmed laboratory findings that in the presence of calcium (resulting from the lime used during the leaching process) no electrowinning is possible. Laboratory tests showed, however, that when sodium (in the form of NaOH or Na2CO3) is added to the leach solution, electrowinning can indeed take place. Alternatively, if a special activated carbon electrode is used (without current), the non-ionic calcium aurocyanide complex is adsorbed on to the activated carbon. When a gold-loaded activated carbon electrode is made anodic in a gold electroforming electrolyte, gold electroforming is feasible, although the efficiency is very low. The possible implications of these developments for gold recovery are further examined.

Jan 1, 2007

Characteristics Analysis of a Bastnaesite Rare Earth Mineral for Recovery of Cerium

Sep 13, 2010

By R. A. Bosch, F. V. Lenel, G. S. Ansell

RECENTLY, Ansell and aenel' proposed a dislocation model to account for the yielding behavior of dispersion-strengthened alloys. The criterion for yielding used in this model was that yielding occurs when the shear stress due to arrays of piled-up dislocations fractures or plastically deforms the dispersed second-phase particles. Calculations based on this model predict that the yield strength, uysof a dispersion-strengthened alloy containing particles whose geometry permits them to be considered as straight, i.e. not curved, barriers to dislocations follows the relation where and are the shear moduli of the matrix and dispersed phase respectively, b is the Burger vector of a dislocation in the matrix, A is the mean free path between dispersed phase particles and C is a constant. This yield stress, ys, is closely approximated in polycrystalline alloys by the proportional limit. The offset yield stress, uoy, is the yield stress, uys, plus the increase of stress due to strain hardening in the offset strain increment. Previous investigation1 has shown that Eq. [I] describes the yielding behavior of several different dispersion-strengthened alloys as a function of the mean free path between dispersed phase particles at a constant temperature. The purpose of this investigation was to investigate the temperature dependence of the yielding behavior of dispersion-strengthened alloys. The alloys studied, MD2100 and MD5100, are SAP-type alloys containing flake shaped aluminum oxide particles dispersed in a matrix of commercial purity aluminum. The proportional limit and 0.2 pct offset stress of both of these alloys were determined as a function of temperature over the temperature range from -190" to 500 C. All tests were conducted on an Instron tensile testing machine. Stress was measured by means of the Instron load cell. Strain was measured by means of SR-4 strain gages attached to the tensile specimens. Stress sensitivity was 80 psi. Strain sensitivity was 2 x 10F Fig. 1 shows the values received for the proportional limit and 0.2 pct offset yield stress plotted as a function of homologous temperature for both the MD2100 and MD5100 alloys. Inspection of Eq. [I] shows that of the terms which determine the theoretically predicted yield stress, uy,, only the shear moduli have an appreciable temperature dependence. From Eq. [I] the yield stress at any temperature T, UT, may be predicted from the yield stress at any arbitrary reference temperature, in this case 25 OC, u25, by the relation where the subscripts T and 25 refer to the values of the property at test temperature and at 25"C, respectively. The temperature dependence of the yield stress predicted by Eq. 121, based on the observed value for the proportional limit at 25OC, is also shown in Fig. 1. In evaluating Eq. [2] the following data was used. The values for the shear modulus of

Jan 1, 1962

By David J. Lowell

The gold content of porphyry copper deposits ranges from less than 0.05 g/t to more than I g/t ((0.0017 to 0.035 oz per st) and the average is about 0.05 g/t (0.0017 oz per st) gold. Perhaps the highest grade mineralization found near a porphyry cop¬per deposit is the Ok Tedi Gold Cap ore body whose grade falls in the 2 to 3 g/t (0.07 to 0.1 oz per st) range. It is difficult to define a gold-rich por¬phyry copper deposit. All porphyry copper ore bodies contain some gold, but there seems to be a fairly sharp break in the gold content at about 0.1 g/t (0.003 oz per st) gold. There is also a problem in identifying dis¬seminated gold deposits that may have an indirect relationship to porphyry copper systems. This relationship is clear cut in deposits such as the Ok Tedi Gold Cap, the El Hueso deposit, the Fortitude and West de¬posits at Battle Mountain, NV, and the Sur¬prise deposit at Ely, NV. There are many other bulk disseminated, epithermal-type gold deposits - McCoy, NV, for example - that might be related to a porphyry system but where this relationship is remains very uncertain. In such places as the Goldfields and Tonapah district in Ne¬vada and in the El Indio, Chile district, there may be a vertically stacked ore deposit rela¬tionship between near surface epithermal deposits and disseminated molybdenite and chalcopyrite enargite mineralization at depth that may represent a deep porphyry system. This, however, has not been positively demonstrated. Most of the bulk epithermal gold deposits are probably not related to porphyry copper systems. Exceptions would probably be Ok Tedi, El Indio, El Hueso, Battle Mountain, and Lepanto where vertical or lateral zoning relationships are more apparent. This author believes that porphyry copper systems are related to a relatively unique type of intrusion that is probably distinct from, for example, the McCoy intrusivebody. For that reason, deposits such as McCoy, Chimney Creek, and the like will not be included in the definition of gold-rich por¬phyry copper deposits for this article. The interpretation of the origin of several of the deposits previously mentioned are subject to an unusual amount of contro¬versy. For example, geologists seem to be equally divided about the presence of a porphyry copper deposit below the El Indio deposit. Geologic setting Continental vs. island arc Several geologists have speculated that the gold-rich, moly-poor, porphyries are

Jan 1, 1989

By Hargraves A. J

With increasing depth, stresses and stress phenomena are becoming more important considerations in Australian coal mining.A large number of compressive and tensile strength tests was made on coal and rock cubes cut from samples taken in various Australian collieries. In addition, an empirical impact strength test was carriedout on fragments of the same samples, to obtain a correlation with compressive strength.In one colliery, flat-jack measurements were taken to assess stresses in coal ribs and in the roof.INTRODUCTIONBy world standards, some of the New South Wales collieries are approaching depths of cover considered a maximum for bord and pillar the normal Australian coal mining method. Several South Coast collieries are winning coal at depths of about 1500 ft., and future operations are being planned at deeper cover. Some areas of these deep workings produce considerable quantities of seam gas.Phenomena associated with high stress and copious gas under pressure in the seam violent phenoma presenting a danger and a nuisance in mine working - have occasionally occurred, and the phenomena are being investigated as a whole (Hargraves, 1958), and separately as a gas problem (Bolt and Innes, 1959; Hargraves, 1962) and as a stress problem. This paper relates to the latter - to investigations into the strengths of coals and coal measure rocks, and into the stresses in and about coal seams...

Jan 1, 1962

Plant for the production of sulphuric acid from pyrites flotation concentrates was commissioned at Cockle Creek during 1956, to meet increasing demands for commercial acid and superphosphate. Pyrite was chosen as raw material because of the uncertain supplyposition of imported brimstone and the desirability of utilising domestic sulphur.Desulphurisation of the pyrite is performed by two 40-ton per day roasters of the Turbulent Layer type operated under licence from the Badische Analin and Soda Fabrik (B.A.S.F.) organisation. These units are the first of their kind commissioned in the southernhemisphere. Pyrite is fed to the roasters in the as-received un-dried condition. Waste heat steam production is coupled with electricity generation within the plant. Sulphur dioxide is produced at comparatively high strengths and cleaned by conventional cyclone and hot electro-filter equipment.The acid unit has a capacity of 100 mono tons of sulphuric acid per day and includes cooling and wash towers, mist precipitators, a single stage drying tower, 4-pass oxidation section and absorption system.INTRODUCTIONSulphuric acid has been manufactured at Cockle Creek Works since 1913, when the first chamber nitration plant was commissioned. The raw material was brimstone roasted in Herreschoff furnaces. Since that time three additional chamber units have been constructed and have produced acid from brimstone, zinc concentrates, pyrites and -spent oxide, according to changing economic and supply factors.Three chamber units are still in operation. Contact processes have become increasingly important since the first Schroder-Grillo unit was commissioned in 1923. Six of these 5-ton per day units were operating in the mid-thirties, but have since been demolished. Two 15 ton Chemico hot gas contact units commenced operation in 1937 and 1938, and although modified, are still in service.The increasing demand over recent years for sulphuric...

Jan 1, 1957

By David Arana

The use of gas-water dispersion of a molten material flow onto a vibrating surface is developed as a process to minimize water pumping requirements, minimize the risks of explosions, and minimize the post solidification dewatering and fines handling equipment requirements. The process uses existing vibration transport technologies and common plant utilities. Plant trials using the smaller footprint and the progressive molten particle cooling time have yielded encouraging results. The results are analyzed and reported.

Jan 1, 2006

In 1961, West Australian Petroleum's Eneabba No. 1 bore encountered 22 seams of coal totalling 40 ft in thickness between the depths of 6373 ft and 6441 ft. On analysis, this coal had a similar calorific value (8000-HOOO B.T.U./lb, assuming 20 per cent water) to the coal from the Collie Coalfield, Western Australia's only known area of commercially exploitable coal. Being buried to depths in excess of 6000 ft, the coal at Eneabba had developed weakly-coking properties, and thus, although much younger than the Permian coals of Collie, gave promise of being a major potential source of power for Western Australia.West Australian Petroleum undertook a programme of stratigraphic drilling and shallow test drilling to determine whether this coalhorizon persisted into the outcrop of the Lower Jurassic sediments in the Hill River district, 140 miles NNW. of Perth, and, if it was present, if the quality and quantity of the coal would warrant development of the deposits by open cutting. The coal horizon was identified in the near surface, but the poor quality of the coal and the complexity of the structure made development (in the area examined) uneconomic at the time.A strong seismic reflection in the Eneabba area occurs at the same depth as the Jurassic coals. This event originates within the upper beds of the Lower Jurassic and it is probable that the velocity contrast between the higher velocity siltstones and the very low velocity coals enhances this very strong, distinctive seismic reflection.This event can be followed on continuous seismic data over a large area of the northern Perth Basin, from 13 miles SE. of Dongara to 20 miles SW. of Coorow. It can be followed from a depth of 4000 ftnear Dongara to over 17,000 ft to the SE., so development of thisvast potential source of power will depend on the economics ofprocesses being developed for the production of power from theburning of coal seams in situ.INTRODUCTIONThe discovery of 22 seams of economically useable coaltotalling 40 ft in thickness in the Lower J urassic sedimentsof the Eneabba No. 1 bore (Fig. 1) led to the search forthese seams at economically workable depths. The Ministerfor Mines in Western Australia granted to West Australian1. Supervising Geologist, West Australian Petroleum Pty. Ltd.Manuscript received at The Institute, 25th May, 1964. and presented to the 1964Annual Conference.

Jan 1, 1964

By Erle C. Donaldson

A study of subsurface waste disposal in the United States shows that in eight States a wide variety of industrial wastes are being injected into formations ranging in age from Precambrian to Recent. More than 30 wells ranging in depth from 300 to 12,000 feet are used for waste disposal into subsurface formations which include unconsolidated sand, sandstone, vugular limestone, and fractured gneiss.

Jan 1, 1964

By R. L. Virta

Four companies mined ball clay in four states during 2005. They included H.C. Spinks Clay (owned by Franklin Minerals), Kentucky-Tennessee Clay (owned by Imerys), Old Hickory Clay and Unimin. Production was estimated to be 1.32 Mt (1.45 million st) valued at $53.3 million, based on the results of a preliminary survey of the ball clay industry. Production in 2004 was 1.22 Mt (1.34 million st) valued at $54.1 million. Tennessee was the leading ball clay producer state with 61 percent of domestic production, followed by Texas, Mississippi and Kentucky.

Jan 1, 2006

By D. J. Chaiko

Aqueous biphasic extraction (ABE) processes offer the potential for low-cost, highly selective separations. This countercurrent extraction technique involves selective partitioning of either dissolved solutes or ultrafine particulates between two immiscible aqueous phases. The extraction systems that we have studied are generated by combining an aqueous salt solution with an aqueous polymer solution. We have examined a wide range of applications for ABE, including the treatment of solid and liquid nuclear wastes, decontamination of soils, and processing of mineral ores. We have also conducted fundamental studies of solution microstructure using small angle neutron scattering (SANS): In this chapter we review the physicochemical fundamentals of aqueous biphase formation and discuss the development and scaleup of ABE processes for environmental remediation.

Jan 1, 1996

By Tracy Brettmann

Equipment ? Hollow Stem Auger ? Drill Bits ? Leads/Torque Arm ? Hydraulic Gearbox ? Hydraulic Power Unit ? Grout Pump ? Crawler Crane

Jan 1, 2004

By Erle C. Donaldson

A study of subsurface waste disposal in the United States shows that in eight States a wide variety of industrial wastes are being injected into formations ranging in age from Precambrian to Recent. More than 30 wells ranging in depth from 300 to 12,000 feet are used for waste disposal into subsurface formations which include unconsolidated sand, sandstone, vugular limestone, and fractured gneiss.

Jan 1, 1964

By J. R. Kyte, L. A. Rapoport

The material balance equation for partiai or complete 1:trter-drivc reser1,oir.s been re-arranged to include a pressure irrferferencr ternr. This pressure interfernce term was ohtained from the theory established hy Morinda. A .successful progranl deissed to solve the resrclritlg c,qrration in a few hours on a nleelitr .sizeti, digital compuier. No prior knowdelge of the properties of the eqrrifer is required in the solution. 7' ri~rl calculations areatle using various assumed con!binuiions of value of the constant expretsing the qquifer properties correspoinds to the best fit ohtained between observed and calculated field history. Details of the method of calculaion are illus trated by an example. INTKCDUCTICN A method 01' calculating the material balance equation for a partial water-drive reservoir completed in an aquifer has been described in the literature." Pressure interference i'rc,m other pools iocated in the same nquiucr is not taken into account in this solution. When present, the pres- sure interference effect must be included in order to make a complete performance analysis. A correction for this effect has been developed using the theory cstahlished by Mor-tada.' Manual calculation of the material balance for water-drive reservoirs is a formidable task. Such manual ca1culation when interference eflects are includcd would be impossible to completc in any reasonable time period. However, a medium-sized stored program, digltal conlputer can he used satisfactorily. The method is described in the following sections. THECKETICAL CONSIDEKATIOhS The material balance equation for a reservoir producing by partial or total water drive, as proposed by Van Everdingen, This relationship is linear for Z/a from which thc slopc, Z, and the intercept, N, can be obtained by the least-squares method from the data points. It is not necessary lo know the aquifer properties to uktain oplimum values tor 2nd IV. Various assumptions are made tor At,,: where 11 is production time, seconds (oilfield between the equal successive time intervals into which the history is divided. t,, h It, times the number of equal time periods from i.e.. the total dimen-sionless time interval from It is noted that the dinlensionless time interval, At,,, involves all the relevant aquifer properties. Accordingly, any assunlption of is an assumption of the combined aquifer properties which pertain to the solution of the equation. Deviations of the data points from a straight line arc calculated for each assumption of and the value of A, correspond ing to the minimunl deviation is chosen as the optimum solution. This method is described in Ref. 1 and 2. Thc material balance solution is usually made with an initial assumption that the reservoir being studied is located in an infinite aquifer from which there are no other withdrawals. Deviation of the points by amounts greater than can be attributed to inaccuracies in field data may be the result of: (1) boundary effects of a limited aquifer, (2) pressure interference from othcr pools completed in the .sarne aquifer, and (3) a combination of these effects. Differentiation of these effects can be made only on the basis of geologic data. Pressure interference from other fields will result in a pressure drop at the original oil-water boundary having an interference component, The measured instantaneous pressure drops at the oil-water