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By D. H. De Jager

Fluorapatite is an important constituent of the greater part of the basic and ultra-basic rock members of the Complex. The evidence for and role of primary magmatic processes in the development of concentric zones of dunite, pyroxenite, syenite and carbonatite and its consequent bearing on the distribution of apatite are discussed. The presence of at least two generations of each of the latter three rock types indicates the cyclical nature of magmatic activity. Pegmatitic-metasomatic phases corresponding to the major magmatic cycles resulted in emplacement of pegmatoidal assemblages. The abundance of apatite in the pegmatoid can be traced to the composition of its parent magma and its cooling history. Approximately 2.5 million tonnes of phosphate concentrate are produced annually from ores containing from 10 percent to 25 percent apatite.

Jan 1, 1978

By Niels Hansen

The substructure formed by drawing at room temperature in aluminum (99.5 and 99.998 pct purity) and in recrystallized aluminum aluminum-oxide products containing from 0.2 to 4.7 wt pct of aluminum -oxide was examined by transmission electron microscopy, and the flow stress of the drawn materials was measured by tensile testing at room temperature. A sub-grain structure was present after a reduction in area by drawing of 10 to 20 pct, and the subgrain size was observed to decrease with increasing deformation. The tensile data show that the increase in flow stress (0.2 pct offset) by drawing from 10 to 95 pct depends on the reduction in area, not on the composition of the materials. Dispersion strengthening and subgrain bowzdary strengtlzening contribute to the flow stress, and these strengthening processes have been found to be linearly additive. The flow stress (0) can be related to the subgrain size &) by the Petclz relation = uo + k . t, where go is dependent on the composition of the products and k is approximately the same far all materials. THE microstructure of dispersion-strengthened aluminum aluminum-oxide products consists of small oxide plates distributed in an aluminum matrix. The matrix structure depends on the manufacturing history, and in hot-worked as well as cold-worked products the matrix is divided by subgrain (or dislocation) boundaries. For hot-extruded products it has been shown1 that dispersion strengthening and subgrain boundary strengthening are linearly additive, and the flow stress (0.2 pct offset.) at room temperature has been related to the subgrain size (ts) by a Petch equation,2,3 s = so + k . ts-1/2, where s0, increases with increasing oxide content. For cold-worked products containing subgrains no systematic work has been reported, and it was the aim of the present study to examine the microstructure and the relationship between the flow stress and the subgrain size for such products. The behavior of' aluminum aluminum-oxide products depends on the purity of the aluminum matrix, and aluminum of the matrix purity (99.5 pct) was included in the investigation. The literature contains few data about the behavior of this impure aluminum, and aluminum of a higher purity (99.998 pct) was therefore also examined. As regards the relationship between the flow stress and the subgrain size in cold-worked dispersion-strengthened products, no systematic work has been reported. For aged cold-worked structures containing fine precipitates (Fe-Mo carbide) a Petch relation has been found,4 and it has been shown that the k value NlELS HANSEN is Head, Metallurgy Department, Danish Atomic Energy Commission, Research Establishment Riso, Denmark. Manuscriot submitted January 9, 1969. IMD is approximately the same as in iron, whereas the s0 value is higher owing to the presence of the precipi-tates. Investigations of metals such as tungsten,' ferrous metals,4,6 and molybdenum7 cold drawn or swaged at room temperature have shown that the flow stress can be related to the subgrain size by a Petch relation when ts is taken as the subgrain size perpendicular to the direction of deformation. For aluminum no work has been reported on the relationship between the flow stress and the subgrain size after deformation at room temperature, whereas for aluminum tensile strained at different temperatures in the range -183" to 375°C a Petch relation has been found by taking ts equal to the subgrain size.' In the present study two aluminum materials (99.998 and 99.5 pct) and three aluminum aluminum-oxide products (containing 0.2, 1.0, and 4.7 wt pct oxide) were drawn at room temperature to reductions in area from about 10 to about 95 pct. The structures were studied by transmission electron microscopy, and the flow stress (0.2 pct offset) was measured at room temperature. EXPERIMENTAL Materials. The materials are given in Table I together with the chemical analysis. The three aluminum aluminum-oxide products were manufactured from aluminum powder that had been compacted and Table I. Chemical Analysis of Materials Al203 Fe SI Material wt pct wt pct wt pct 99.998 pct* - 0.0004 0.0012 Aluminum 99.5 pctt - 0.36 0.16 Aluminum AlMD13† 0.2 0.16 0.12 Aluminum- -Oxide AlMD105† 1.0 0.26 0.18 Products SAPISML960s† 4.7 0.22 0.19 *Other impurities: O.0004 pct max each of Cu and Zn (supplier's analysis). †Other impurities: 0.03 pct max Cu. 0.02 pct max each of Mn, Mg, Zn, Ti. Table 11. Mean Diameter of Aluminum-Oxide Particles in Extruded and in Cold--Drawn Aluminum Aluminum-Oxide Products Mean Diam. of A1203-Plates* Material State A AlMD105 Extruded 540 Cold Drawn 97 pct 510 SAP ISML 960 Extruded 770 Cold Drawn 95 pct 820 *The standard deviation of the mean is approx. 5 ±pct.

Jan 1, 1970

By C. C. Hwang

The Bureau of Mines made time-dependent calculations to determine the size of a stationary source fire within a ventilated duct (or passage-way) necessary to ignite a combustible duct liner. The objective of this work was to gain more understanding of what occurs in duct fires and to determine critical conditions for ignition and propagation of mine fires. Heat transfer to the combustible surface includes both convective and radiated components, while the heat is conducted into the combustible and reradiated to the surroundings. The combustible is assumed to ignite when the net heat transfer to its surface is sufficient to raise the surface temperature to some minimum temperature, defined as the ignition temperature. A nondimensional parameter, which characterizes the source-fire intensity in the presence of ventilation flow, emerges as a parameter for a criterion of the critical conditions. The results of these calculations indicated that the minimum fire size necessary for ignition increases with the ventilation rate and duct cross section. These results are compared with experimental results obtained from fires in a 0.8-by 0.8-by Il-m-long duct and a full-scale gallery (2.4-by 2.4-by 65-m). Agreement between the theory and the experiment is good.

Jan 1, 1988

By Wallace W. Key

The California pesticide industry in 1962 consumed about 30,000 tons of clay, talc, limestone, diatomite, sulfur, and other minerals as fillers (carriers and diluents) in pesticide formulation. This was 10 percent of the U.S. filler requirement for pesticides. About two-thirds of the California total was supplied by a few local mineral producers; the remainder came mainly from Florida, Georgia, and Wyoming. The objectives of this report are to provide data on quantities, sources, specifications, and market conditions for minerals used as fillers by California pesticide formulators. The study disclosed that specifications for mineral fillers have become more rigid and formulators have become more numerous in recent years. During 1962 over 1,200 firms registered 16,000 pesticide products with the Bureau of Chemistry in California. Factors which will tend to diminish future need for mineral fillers include the trend toward greater use of organic sprays rather than dusts and further development of biological controls, such as the development of sterile insect strains.

Jan 1, 1965

By E. J. Bolitho

"The paper covers the activities of the Government Miners' Training-Schools. It argues that its success is proved by the steady demand for miners trained at the Schools; by the large numbers of ex-apprentices who hold responsible official positions in the industry; and bv the probable expansion of the organization in the near future to meet the never-ending call for trained personnel."

Jan 1, 1947

By D. R. Taylor

Treatment of bentonite clay with mineral acids yields a modified clay product of high surface area and acidity which exhibits enhanced adsorptive and catalytic properties. A highly specialized segment of the clay industry based on this process has evolved into worldwide business with a capacity of about one-half million tons/yr. This paper will present data on the chemistry, mining, manufacturing and applications for acid- activated clays.

Jan 1, 1986

By W. C. Hellyer

In an autogenous grinding circuit in which feed at approximately nine inches top size is reduced to a size suitable for subsequent processing, the build- up of a "critical size" fraction in the media causes problems. A "critical size" fraction has been defined as, "media too small to effect reduction by impact grinding of ore coarser than a quarter of an inch and too large to be broken by the largest size of media in the charge. 9, (1) The buildup of a "critical size" fraction reduces the capacity of the mill, increases the grinding power requirements per ton of finished product, and generally produces a finer grind than is desired. It is general practice to overcome this problem by the addition of large diameter steel balls to the grinding charge. This has certain disadvantages, such as; (i) an increase in mill liner wear; (ii) wear on the steel balls, and; (iii) some loss in flexibility in grinding circuit operations resulting from difficulties in removing the steel balls by means other than by grinding out.

Jan 1, 1970

By R. J. Hundermark, K. van der Merwe, L. R. Nelson

Taphole integrity is critical to all furnaces, but it is especially important in high intensity electric furnaces processing matte and metal of high superheat. Key furnace dimensions are the electrode proximity to the taphole, hearth sump below the taphole and the shape and location of the taphole in the furnace wall (e.g., circular versus rectangular furnace). In addition, electric furnace power density needs to be matched appropriately to any configuration to achieve operational reliability and furnace integrity. The role of furnace dimensioning is generically reviewed across many pyrometallurgical processes to explore potential impact on furnace taphole performance. Some empirical furnace dimensions and power density ratios of industrial furnaces are then compared to explore to what extent they may indeed influence taphole integrity.

Jan 1, 2015

By D. E. Cameron

The Cannon mine, located in north-central Washington is mining gold hosted in silicified Eocene-age arkosic sediments arrayed along a regional strike-slip fault system. Branches of the Eagle Creek fault have broken the Chumstick Formation into blocks and wedges, and have caused intense deformation of stratigraphy in the mine. Mineralization at the Cannon mine (B-Reef) and O-Reef (L-O mine) is a bulk silicification with high grade cross-cutting veins containing principally electrum, silver sulfosalts and pyrite in a gangue of quartz, adularia and calcite. Orebodies have very irregular shapes, but tend to follow stratigraphy and high-angle pre-mineral fault breccias and splays developed adjacent to the major faults. Both B-Reef and O-Reef occur at significant bends in the regional trend of major fault strands. Mean gold grades decrease upward from near sea level to the 300 m elevation at the Cannon mine. A new discovery, the A-Reef is hosted by a moderately dipping structure which is at a low angle to bedding. Fluid inclusion studies of B-Reef ore zones indicate dilute ore-bearing fluids boiled at temperatures between 185 and 2850 C at a depth of 1 km. Many ore zones are bounded by sheared mudstone and claystone and a much broader halo of argillic alteration comprising illite, smectite and sericite. Trace and major element analysis by ICP-ES for 33 elements, LECO for S, Hg by CVAA and gold by AA-FA shows dispersion patterns hundreds of meters outward from the known orebodies in the Cannon mine. Geometric mean comparisons, hierarchical R-mode cluster analysis and single element spatial plots show that Hg, As, Sb, S and K/Al compose a suite of elements which are significantly dispersed away from, and increase toward mineralization. Ba, Ca, Na, Mn, V and Zr decrease toward mineralization. The suite is more selective than gold with respect to known mineralization within the exploration area.

Jan 1, 1992

By J. L. Holman

In conjunction with its research program on separation, recovery, and recycling of metal, mineral, and energy-based materials in urban refuse, the U.S. Bureau of Mines is developing means to reuse and recycle plastics discarded in raw municipal waste. Experimental work on plastic waste from a community collection has produced some guidelines for systematic methods of processing, including air classification, cleaning, separation, and use or disposal. Sink-float methods are a practical means of separation into types. Methods for final disposition of the plastic waste include refabrication, thermal decomposition, and incineration.

Jan 1, 1972

By K. F. Veit, R. L. Marovelli, T. S. Chen

There is an error at the bottom of the right-hand column of p. 11, and the top left-hand column of p. 12. The first paragraph of the section EXPERIMENTAL RESULTS should read: "Thermal shock tests were conducted on circular discs of basalt, quartzite, and taconite. Average grain sizes ranged between 0.10 and 0.25 mm. Individual discs were tested only once, either in a cooling or heating shock. Several discs of the same rock type were shocked at a temperature, and the temperature level then was increased for another test by 10° to 20°F until complete fracture occurred when a specimen was quenched. The minimum temperature difference required to initiate cracking, TmiN was observed and used, together with other property values, to compute the dimensionless stress o*max . The observed ?Tmin for cooling shock in different media is tabulated in Table I. The property values E, St, a, and K are shown in Figs. 6, 8, 10, and 11, respectively. Discs of various rocks shocked in different isothermal baths gave o*max values for a wide range of Biot numbers. These o*max values were then compared with the theoretically predicted values."

Jan 1, 1968

By Margaret R. Egan

The Bureau of Mines experimentally burned Pittsburgh Seam coal and other combustible materials found in mines in order to obtain a better knowledge of their emission products. These experiments were conducted in the Bureau's intermediate-scale fire tunnel, which simulates environ-mental conditions in underground mines. Smoke characteristics, gas concentrations, mass loss, and ventilation were measured. From these values, heat-release rates, particle sizes, obscuration rates, combustion yields, and production constants were calculated. This information was sought as part of a comprehensive study of combustible materials that will ultimately advance the design of more efficient fire detection and suppression systems. The coal combustion measurements presented in this report, together with previous analyses of wood and transformer fluid fires form a data base by which future studies of other mine combustibles can be compared.

Jan 1, 1987

By Henry H. Tayler, Eric Sturel

1 Triton Square was originally a six-storey building with a one-level basement located within a commercial development near Euston, London. It was designed and constructed in the 1990s and the foundation scheme comprised straight shafted London Clay piles arranged singly beneath columns. The scheme added three storeys and a five-storey infill in the central atrium area to increase the building floorplate by 70% and maintained the usability of the basement space. As the loads to support the additional floorplate area were greater than the capacity of the existing foundations, an optimised strengthening scheme of small diameter piles installed within the existing basement and a slender retro-fitted raft was installed to augment the existing piles. The re-use and strengthening of almost all of the existing foundations enabled re-use of a very high proportion of the superstructure and in approximately 35,000 tonnes of concrete and 1,900 tonnes of reinforcement and structural steelwork being re-used. The structural embodied carbon for the refurbished building scheme is estimated at an average of 136 kgCO2e/m2, achieving a Structural Carbon Rating Scheme (SCORS) “A” rating with components detailed in the paper.

May 1, 2022

By Alexsandro Berger

Many thickener operations continue to be constrained by their ability to process consolidated underflows with high yield stress and associated rheological characteristics. To maximise separation efficiencies within a thickener operation the use of both engineering and reagents are always considered. BASF is developing a Novel Flocculant Technology (NFT), which combines both of these aspects to enhance the performance of the thickener operation, improving the areas of pumping efficiency, underflow density and throughput. The development progression through stages of laboratory scale batch test work to pilot scale dynamic testing has demonstrated the ability of BASF NFT to maintain effective flocculation performance whilst increasing the rate of underflow consolidation, and significantly reducing the associated underflow yield stress of the treated material. This paper will present application data through full scale dynamic testing conducted on a granite washing circuit to demonstrate the performance benefits that NFT offers to a thickener operation. Compared to the conventional flocculant treatment, within the operation parameters and conditions employed during the full scale trials, the NFT produced a reduction in underflow rheology (yield stress) of around 45 % relative to a given solids and improved the underflow consolidation by providing at least 20% relative higher underflow solids loading than the upper limit of the given typical thickener operation. Keywords: flocculation, thickener operation, rheology, yield stress, underflow density, throughput, slump test

Sep 1, 2012

By Desmond M. Levins, Reginald K. Ryan

"Removal of radium from uranium tailings would substantially lessen their environmental impact because it would eliminate, or greatly reduce, the hazards arising from radon emanation, leaching of radium, dust dispersal and gamma radiation. A process is described to extract radium from tailings by leaching in 3M Nael solution. The radium can be rapidly leached at ambient temperatures by either multi-stage contact in agitated vessels or washing on a tailings filter cake. Extraction efficiencies ranging from 80 to 94% have been measured for tailings derived from a number of Australian ores.Methods for radium recovery from the leach solution by precipitation, ion exchange and adsorption have been examined. Precipitation as barium/radium sulphate appears to be the most suitable approach. A possible flow diagram for the process is proposed which involves recycle of the saline leach liquor.IntroductionDisposal of mill tailings is the most contentious environmental issue facing the uranium mining industry. The conventional approach to managing tailings is to store them in a dam above ground. Attempts have been made to stabilize some tailings piles by physical or chemical methods. In a few cases, the tailings have been covered with earth and revegetated. However, most tailings piles from abandoned mills are in a neglected state and subject to the erosive and dispersive forces of nature. The cost of remedial action is high. The United States Department of Energy (DOE) has estimated that it will cost up to $130 million to rehabilitate abandoned mill sites in the U.S .A..Environmental authorities are now insisting that uranium mining companies improve their methods of tailings disposal. In the United States, the preferred approach is burial, either in mines or in specially excavated pits. Tailings retention systems as operated in Canada are regarded as storage facilities until an acceptable method of disposal is found. In Australia, the Fox Commission recommended that tailings from the Ranger project should be returned to the open-cut mine. Returning tailings to the mine has considerable merit, but it is not always a viable option. In many underground operations, it is not physically possible to fit all the tailings in the worked-out mine. In other cases, the groundwater hydrology of the mine may be unfavourable."

Jan 1, 1980

By Sitotaw Y. Fantaye

"The first segment of the Second Avenue Subway extension is approaching construction completion. The new extension will operate along Second Avenue from 96th Street to 63rd Street, where it will divert west along the existing 63rd Street line, stopping at the Lexington Avenue/63rd Street Station. The new line will have stateof-the-art stations at 96th, 86th, 72nd and 63rd streets.Most of the two-track, twin-tunnel subway was constructed using bored tunnel methods (Figure 1), with a tunnel boring machine (TBM). The launch and retrieving box of the TBM was strategically located at the south end of the 96th Street Station where bedrock exists approximately 70 ft (21.3 m) below street level. The TBM launch box and the 96th Street Station (Figure 2), including the ancillary facilities adjacent to the station, were constructed by the cut-and-cover method. The cut-and-cover work required the contractor to design and implement a stiff, tightlybraced retaining wall, approximately 100 ft (30.5 m) long, to tie the existing tunnel constructed in the 1970s to the new station, temporary street decking over the entire excavation, and a wide range of excavation support systems at various locations.The cut-and-cover construction posed significant challenges including: installation of street decking on busy Second Avenue, relocation and suspension of the myriad utilities beneath the streets, and configuration of a lateral support system that would minimize movement of adjacent structures but not slow down excavation activities. This article describes the innovative solutions developed to manage and facilitate safe and efficient construction without disrupting Second Avenue, a major southbound one-way thoroughfare.The work was performed in several phases involving: (1) preconstruction condition survey of existing buildings, (2) installation of instrumentation and monitoring, (3) major utility relocation efforts to move vital utilities from within the alignment of the slurry wall on both the east and west sides of the avenue, (4) implementation of maintenance and protection of traffic plans, (5) installation of temporary street decking across the entire avenue and over the excavation to allow an orderly movement of traffic and pedestrians, (6) staged excavation and installation of an intricate temporary bracing system beneath the decking (7) step-by-step construction of the new subway station’s structure and (8) staged removal of the bracing as the structure gained sufficient strength to resist the lateral loads. The main focus in this article is the design and construction of the temporary street decking and lateral bracing systems; the utility suspension system and the north tie-in that allowed the daunting task of excavation and construction of a new subway station in bustling New York City, with minimal disruption to the community, businesses and everyday traffic."

Jan 1, 2016

By K. Yoo

Cuprous oxide is one of the oldest antifouling agents and also acts as red pigment in these paints. In printed circuit board manufacturing industries, waste etchant contains a substantial amount of copper ion. In the present study, a process was suggested for recovering cuprous oxides from the waste etchant and optimum conditions were investigated to recover the cuprous oxides. The process consists of two steps: in first step, Cu powder is added into wastewater solution, and cupric ions re-duce into cuprous ions (Cu+Cu2+?2Cu+), where cuprous ions precipitate as cuprous chloride; In second step, cuprous oxide is synthesized by adding NaOH into cuprous chloride solution (2CuCl+2NaOH?Cu2O+NaCl+H2O). Optimum conditions were investigated to recover cuprous oxide in the processes. When copper powder was added into wastewater with copper ions, Cu concentration decreased from 15.6% to 2.6% and ORP decreased from 620 mV to -59.9 mV. This result shows that cupric ions reduced into cuprous ions. XRD data indicated that the precipitate was cuprous chloride powder. Using the cuprous chloride recovered and NaOH solution, cuprous oxide was synthesized. To investigate the optimum condition, various NaOH solutions were added into water with CuCl, and then pH, ORP, Cu concentration, Cu contents in precipitates were analysed. XRD data showed that main component of precipitates was cuprous oxide.

Jan 1, 2014

By Muammer Kaya, Sait Kursunoglu

"The aim of this study was to investigate the effectiveness of ascorbic (C6H8O6) / oxalic (C2H2O4) acid as a reductant for the simultaneous recovery of zinc and manganese from a spent and mixed zinc-carbon and alkaline battery powder in sulphuric acid leaching. The effects of sulfuric acid concentration, ascorbic/oxalic acid dosages, reaction temperature and leaching time on the zinc and manganese dissolutions were investigated according to 2k full factorial experimental design; then, a simple optimization study was carried out for the best reductant. The optimum reductive acid leaching conditions were determined at 3 hours leaching time, 70°C leaching temperature, 0.5M sulfuric acid concentration, 13 g/L ascorbic acid dosage, 1/20 g/mL solid/liquid ratio and 200 rpm stirring speed. Under these conditions, the dissolution efficiencies were 99.9% for Zn and 99.3% for Mn. When our results were compared with the previous results, our findings were better than previous studies.In addition, the manganese dissolution kinetics was undertaken, and the activation energy was found to be 7.04 kJ/mol. Selective precipitations of Zn and Mn from acid solutions were carried out using NaOH and KOH. Using 3M NaOH as precipitating agent at room temperature and at pH 8; 95.4% of Zn and at pH 10; 93.7% of Mn were precipitated from the leaching solution. Under the same conditions, using 3 M KOH at pH 8; 91.6% of Zn and at pH 10, 96.4% of Mn were precipitated. Based on the experimental results obtained, an appropriate flow sheet was proposed to recover zinc and manganese."

Jan 1, 2012

By A. Paulin, J. Roth, S. Spaic

This experiment was carried out to see whether copper-iron ingots from Late Bronze Age hoards could have been produced by smelting ferruginous copper ores. Since ferruginous copper-ores are chalcopyritic, chalcopyritic concentrate from a present day copper mine was dead roasted in our experiment in lieu of a rich chalcopyritic ore. Charcoal was used as a reducing agent in the reduction of calcine (i.e., a product of dead-roasting), and quartz sand was used as a flux. Two separate metallic solutions, a copper-base and an iron-base alloy, were obtained as a result of two factors: the presence of carbon and the miscibility gap in the Cu-Fe-C system. The metallic melts appeared in a form of bigger or smaller droplets, enclosed by a molten slag which, during the cooling, solidified into metallic beads. The presence of both metals was noticed in the majority of the examined beads. It was therefore concluded that calcine consisted of an intimate mixture of oxides of both metals which were simultaneously reduced during the reduction process. Due to the miscibility gap in the Cu-Fe-C system, separate iron and copper regions were formed in the beads. In both regions, sulphide inclusions were found. The formed molten copper and molten iron solution were found to be saturated solutions. The metallographic analysis revealed the precipitation of iron out of copper and that of copper out of iron during the cooling and solidification of melts. The formed slag contained little iron and no copper oxide.

Jan 1, 2001

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. 'The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm' A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955