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By G. Caetani

I. INTRODUCTION. WE owe to the courtesy of Mr. R. M. Raymond, Manager of the El Oro Mining & Railway Co., Ltd., the permission of publishing in this paper the results of a series of experiments and tests made in view of determining the economical limit to which the fine grinding of the ore by tube-mills could be carried on. For the sake of clearness, the following definitions are given of certain terms used in this paper, as well as of the units and screens in the experiments. Slime : In a general way " slime" is that mill-product, of which from 90 to 95 per cent, will pass a 200-mesh screen (0.067 mm. aperture), and which is treated as one class of material in the El Oro cyanide-plants. As a screen-product, slime constitutes all material that *ill pass a 200-mesh, screen. In sizing, the following products are distinguished:- Coarse Sand : That material remaining on a 100-mesh (0.111 mm. aperture) screen. Fine Sand : That passing through. 100-mesh and remaining on a 200-mesh (0.067 mm. aperture) screen. Slime: That passing through 200-mesh. Fines, which pass through 200-mesh and settle in 30 seconds, and silt, which does not settle in 1 minute. Sand-index : The number proportional to its total fineness considered from the economical point of view, as explained on page 93. Absolute extraction : The percentage of values actually brought into solution. Actual extraction: The percentage of values actually brought to the ziuc-boxes. Units : Dollars, U. S. Currency; pounds; and short tons (2,000 lb.). Gold is valued at $20.67, and silver at $0.50 per ounce. Screens : In the sizing-tests the screens used were:¬ Mesh (per 1 in.), . 24 30 40 60 80 100 150 200 250 Aperture (mm.), . 0.740 0.515 0.424 0.250 0.159 0.111 0.090 0.067 0.058 Strengths of solution : Strengths are expressed in the percent- . age of KCN contained, though the sodium cyanide, which is

Jan 1, 1906

By C. N. Adams

The purpose of this investigation was to evaluate the physical and mechanical properties of high-purity titanium made by two processes. Sodium-reduced metal with 58 Brinell hardness number (B.h.n.) and electrorefined metal with 60 B.h.n. and 70 B.h.n. were used. Titanium of these hardness levels did not work-harden excessively, and beyond 40 percent cold work the hardening effect was not great. Rapid softening occurred when the metal was annealed at temperature between 300° and 600° C. Full annealing, as determined by property and microstructure studies, was accomplished after 30 minutes at 700° C. A recrystallization diagram is presented which is based on determinations of annealed grain size as a function of rolling reduction and annealing time. For reductions of less than 20 percent, exaggerated grain growth occurred during annealing; for reductions greater than 20 percent, the variation in grain size for each annealing temperature was minor.

Jan 1, 1961

By A. H. Baldo

Covers a very broad spectrum of problems and solutions. The problems are multitudinous and their solutions are sometimes simplistic, sometimes ingenious and sometimes within a very broad interpretation of the law. However, one thing is quite certain: the problems and their solutions will have a direct impact upon corporate and personal well being. First of all, why does one mine in a foreign land? Since the Bronze Age, when ancient man discovered the metallurgy of copper, tin and zinc, intrepid souls have been wandering afield searching for and exploiting those mineral deposits which would create wealth and security for his city-state or community.

Jan 1, 1981

By C. Q. Cupps

n view of increased interest in secondary recovery of oil in the Cut Bank field, Montana, a review has been made of unpublished data obtained during a 1943-44 study of reservoir oil characteristics in this field. Considerable uncertainty was attached to interpretations of subsurface oil sample analyses from six Cut Bank zone wells, one Lander sand well, and one Moulton sand well, because of adverse sampling conditions and wide range in the data. Much of this uncertainty has been removed by this review which has shown two of the Cut Bank zone samples and the Moulton sand sample to be representative of the reservoir oils. Estimates of original reservoir oil characteristics derived from differential-liberation analyses of these samples show that the oil in the Cut Bank zone was initially saturated at the gas-oil contact pres-sure, 750 psia, and the oil in the Moulton sand was undersaturated with a saturation pressure of only 380 psia. The rest of the samples were indicated to be nonrepresentative of the reservoir oils because of a disproportional vaporization of heavier components of the solution gas. The vaporization of these components is believed to be a cumulative effect of contact of the oil with bypassing, light-gravity gas which had been liberated at higher pressures from solution in oil farther back in the formation, or which had come from the gas cap, rather than from the singular effect of gas evolution caused by excessively low bottom-hole pressures. Change of oil composition caused by the latter was found to conform closely to that occurring during a differential liberation of gas in the laboratory.

Jan 1, 1967

By Pei‑liang Xu, Jun Wang, Xi Zhang, Deng‑pan Qiao, Tian‑yu Yang

The surface backfill, serving as the operational platform for continuing mining in upward slicing and filling stopes, is required to possess sufficient strength and thickness. Currently, there are limited model methods for determining the strength and thickness of the surface fill body. By analyzing the mechanical actions on the surface backfill, it is determined that its stability is mainly influenced by the combined effects of normal and tangential uniform loads under full-load conditions of trackless equipment. Assuming a circular contact surface between the tire of the trackless equipment and the surface backfill, and utilizing solutions from elastic mechanics theories such as the Boussinesq and Cerruti solution, the stress and displacement distribution of the surface fill body were obtained. Based on the maximum vertical stress condition, where the surface backfill body undergoes maximum deformation while still in an elastic state, and considering the stress–strain relationship, a model for the strength and thickness of the surface backfill has been established. According to the research findings, the design for the strength and structural parameters of the surface backfill has been developed to meet the full-load operation of the Atlas ST7 scooptram, with a compressive strength of 1.32 MPa and a thickness of 0.5 m. Numerical simulation analysis results indicate that the stress and displacement of the surface backfill align with theoretical analysis results. Practical results from industrial application in the western section of the Dahongshan Copper Mine demonstrate that the designed strength and thickness of the surface backfill meet the operational requirements for trackless equipment, resulting in significant engineering application effects and economic benefits. The research findings hold significant importance for advancing the theory of backfill mining and have high applicability and promotional value for similar mines.

Mar 24, 2024

By Roy T. Sorensen

The Bureau of Mines has investigated the recovery of cell-grade alu-mina by RCI leaching of calcined kaolin in the alumina miniplant at its Boulder City (NV) Engineering Laboratory. Classification and thickening were used for separating aluminum chloride leach liquor from the siliceous residue generated in the acid leaching step of the clay-HCI process. Coarse solids were classified from fines at 115 mesh and countercurrently washed in three additional spiral classifiers. Fines were treated in a conventional five-thickener, countercurrent decantation circuit. When this method was applied to the solids-liquid separation of slurry from RCI leaching of minus lO-mesh calcined kaolin, 75 pct of the residue reported as classifier sands and 25 pct as thickener underflow. Predicted individual classifier and thickener area requirements were 6 and 25 ft2/tpd, respectively. Total thickener circuit flocculant requirement was 2.4 lb/ton solids. Aluminum chloride pregnant liquor was produced that analyzed 8.4 pct A1203 and contained more than 97 pct of the alumina in the liquid phase of the slurry. Bench-scale settling tests were used to correlate fines content of leach residue to thickener area and flocculant requirements.

Jan 1, 1983

The sulphide ore occurring in the North Mine at Broken Hill is of a complex nature, consisting of an intimate mixture of argentiferous galena, marmatite (zinc-iron sulphide), and gangue minerals. A typical analysis of the ore is:Lead 15.2%Zinc 12.0%Iron 5.3%Manganese 0.8%Copper 0.1%Alumina 0.3%Lime 0.9%Sulphur 11.1%Insoluble 53.8%Carbon dioxide 0.3%Undetermined 0.2%Silver 9 oz. per tonTotal 100.0%The metallurgical practice for the recovery of the lead concentrate and zinc concentrate from the crude ore is briefly described in the following pages.(1) COARSE CRUSHING AND FINE GRINDING OF THE CRUDE OREThe crude ore from the mine, containing lumps to the size of, roughly, 10 in. x 8 in., is tipped over grizzlies with the bars spaced 3 in. apart; the oversize gravitating to a...

Jan 1, 1933

By Yael Miron

The presence of pyrite (FeS2) in coal can cause or contribute to several problems for the coal mining industry. These problems, which include spontaneous combustion, roof falls, floor heave, and accidental explosions in coal surface mining when ammonium nitrate fuel oil (ANFO) explosives are used, result from pyrite oxidation. Pyrite oxidizes exothermically in the presence of air and moisture to form a large variety of products, including hydrated ferrous and ferric sulfates, and sulfuric acid. Some of the products are reactive chemicals and strong oxidants. The volume of many of these oxidation products exceeds the original volume of the pyrite; as a result, the adjacent coal disintegrates and its surface increases, rendering it more susceptible to oxidation. The heat from pyrite oxidation raises the temperature of the adjacent coal, accelerating the oxidation and self-heating rates of the coal. These combined chemical, physical, and thermal effects are the cause of the aforementioned problems. When ANFO is used in surface coal mines and contacts ferrous sulfate, a highly exothermic reaction ensiles. Additional hazards are fires or explosions caused by the frictional ignition of methane when the pyrite in the coal is struck by a cutting bit during mining.

Jan 1, 1994

By AIME AIME

SILVER reached a new high, with the ceiling the limit, at the annual Institute dinner at the Commodore on Washington's Birthday night. Carrying along as ballast other commodities, such as rolls, roses and ferns, souvenir boxes and table number placards, hundreds of silvery balloons, cut loose from their moorings at the tables, bounced idly against the plaster decorations high overhead. At the head table, Scott Turner, retiring President, pre- sided as toastmaster, with the new President, Frederick M. Becket, on his right, and the Chairman of the New York Section, Sydney H. Ball, on his left. Many other distinguished Institute members, medalists, and representatives of organizations and committees, ranged to the east and west. Each had the opportunity at least to rise and bow.

Jan 1, 1933

By G. X. Du

Improving reaction effectiveness of asbestos tailings and acid is main means to increase the productivity of magnesium hydroxide and amorphous silica and to reduce production costs. In this paper, the process optimization of acid-leaching reaction process of asbestos tailings is reported. Through the orthogonal experiments of four influence factors, such as acid consumption, reaction temperature, reaction time and initial acid concentration in the leaching reaction. The experiment results indicated that the optimal process parameters were as follows: reaction temperature was 95?, reaction time was 1.5h, acid consumption was 218.9g hydrochloric acid(37%) per 100g asbestos tailings and initial acid concentration was about 25%. The influence significance sequence of the four factors was as follows: reaction temperature > reaction time > mass concentration of hydrochloric acid > hydrochloric acid consumption. Under the optimum process conditions, the leaching rate of MgO was 97.3%, total iron 98.15% and Al2O3 57.9%.

Jan 1, 2014

By W. J. D. Stone

In 1960, Magnetics International Ltd. undertook the development of the Jones High Intensity Wet Magnetic Separator in the Americas. Magnetics International had a number of possible applications in its own projects plus the intention of developing the equipment for sale to others. It was soon recognized that no matter how innovative a piece of mineral separation equipment may be, it takes many years and much finance before it is finally accepted for large scale use. For this reason, many good ideas die in their infancy. One of the chief reasons for such a time lag between conception and large scale implementation is the usual lack of finance to construct and put into operation a large demonstration unit. Even with a large unit for demonstration, the first major user usually requires a guarantee that is not normal in accepted separation equipment. Such problems are also normally accompanied by major design changes from the first conception.

Jan 1, 1971

By J. -F. Lepage, M. A. Tomlinson, K. K. Murray

"The Éléonore mine, located in the James Bay region of Northern Quebec, generates a gold bearing flotation concentrate rich in pyrrhotite. Direct leaching of the finely ground concentrate results in high cyanide consumptions and poor recoveries, so effective pre-treatment to passivate the pyrrhotite is required before leaching. Following a number of process upsets at the mine, test work was performed to better understand the requirements for passivation so a more effective operational strategy could be implemented. This paper outlines the testing and implementation of the new strategy at Éléonore.ÉLÉONORE CONCENTRATOR The Éléonore mine is located 800 km north of Montreal, in the James Bay Region of Quebec, Canada. The ore, containing gold disseminated in sulfide minerals and free fine gold in silicate gangue, is crushed in a two-stage crusher plant before being ground in a single 9,000 kW ball mill. The ball mill is in closed circuit, with about 25% of the cyclone underflow passing through a gravity plant with two, 48” Knelson concentrators. Gold recovery in the gravity circuit varies between 15 and 20%, with gravity concentrate leached daily in an Acacia intensive leach reactor. Cyclone overflow, at a target P80 of 65 microns, flows to the flotation plant where the gold bearing sulfide minerals, mainly pyrrhotite and arsenopyrite, are recovered to concentrate with a mass pull of about 5%. The flotation concentrate, typically containing between 80 and 120 g/t of gold, is thickened and finely ground using a 1500 kW Isa Mill. The finely ground concentrate is diluted, to generate a slurry with about 32% solids by weight, before feeding the leach plant. Initially the concentrate slurry is pre-treated with oxygen and lead nitrate, to passivate the sulphide minerals before cyanide is added for gold dissolution. Gold is recovered from the leached slurry using carbon-in-pulp (CIP). The flotation tailings are also thickened and gold is recovered in a dedicated leach-CIP plant."

Jan 1, 2017

By D. S. Yang, Y. D. Wang, G. Watanabe, A. P. Notaro

"Deep soil mixing (DSM) walls reinforced with steel soldier piles were installed for excavation support and groundwater control for the construction of a grade separation structure at the intersection of Warren Avenue and the Union Pacific Railroad in Fremont, California to mitigate traffic conditions during the busy commute hours and for the extension of San Francisco Bay Area Rapid Transit (BART) system. Instead of treating the DSM wall as a temporary structure, the reinforced DSM walls were integrated in the design of the permanent structures including retaining walls, and the abutments and pier of the railroad and BART bridges. The integration of steel members inside the DSM wall as part of the permanent structures is an innovation which facilitates the use of top down construction techniques to speed construction and utilizes the steel soldier piles that would have been disregarded after the use as a temporary shoring wall. This paper will review the background of the project and DSM method and present the design and construction of the DSM wall composite structure for this grade separation project.INTRODUCTIONUsing the concept of mixed-in-place piles initiated in the 1950’s in the United States, Japanese contractors in the late 1960’s and early 1970’s installed single mixed-in-place soil-cement piles along a row to create a wall for excavation support and groundwater control. Due to the high groundwater conditions in most of the coastal cities in Japan, wall continuity and uniformity became the requirements of soil-cement walls for reliable groundwater control to minimize ground movement and impacts to adjacent buildings and facilities. In late 1970s, Seiko Kogyo, Co. Ltd. developed the Soil Mix Wall (SMW) method, which uses a triple auger mixing tool to improve the uniformity and continuity of soilcement wall. The SMW method is considered a wall installation method in contrast to the Cement Deep Mixing (CDM) method, also developed in Japan, for ground stabilization in soft soils, especially in the marine environment. In the U.S., generic terms like DMM (Deep Mixing Method), DSM (Deep Soil Mixing) or CDSM (Cement Deep Soil Mixing) are used by various government agencies and private organizations to describe the soil mixing technologies without differentiating the origin, procedure and application. The method used in this project is called DSM method by the project owner, Santa Clara Valley Transportation Authority (VTA), to produce a single continuous soil-cement wall for use as shoring wall and composite structure. The mixing tool for DSM wall installation can vary from 3 to 6 mixing augers. Due to the need to install steel soldier piles into the DSM wall for resisting lateral forces, high water cement ratio slurry with bentonite is used to produce low strength soil-cement, generally in the range of 70 to 100 psi (500 to 690 kPa), with high fluidity to facilitate the installation of steel soldier piles. To maintain the wall continuity for groundwater control, overlapping of one full DSM column is made between neighboring elements using two types of installation procedures as illustrated in Figures 1a and 1b. Steel soldier piles, as shown in Figure 2, are used to reinforce the soil-cement wall to resist the lateral shear force and bending moment induced during the excavation."

Jan 1, 2015

By Yuexin Han, Wenbo Li, Xinran Zhu, Pengchao Li

A multi-stage fluidization magnetization roasting is a promising method to treat limonite ore. The dehydroxylation of limonite ore is a key reaction in the pre-heating stage. In this study, the dehydroxylation mechanism of limonite was studied in a laboratory fluidization roasting reactor. The samples were characterized using in situ X-ray diffraction, Fourier transform infrared spectroscopy, and simultaneous thermogravimetry and differential scanning calorimetry analysis. The phase transformation and kinetics analysis were studied. Results indicated that the dehydroxylation occurred at the temperature of 250–350 °C with the vanish of hydroxyl functional groups (-OH). The dehydroxylation kinetics followed the 2-D diffusion (Jander) reaction model G(α) = [1 − (1 − α)1/2]2, and the calculated activation energy was 113.43 kJ·mol−1. This study is conducive to exploiting limonite ore resources using magnetization roasting technology.

Nov 2, 2023

By W. D. Macleod

This paper describes a mineral dressing process for the upgrading of tin ores. The process described is called 'agglomeration' and. is similar in many respects to flotation. Many variables have been examined experimentally both on batch and continuous operations and are reported upon herein... Using a Mt. Pleasant tin ore, assaying 0.5% Sn, an upgrading to 8% Sn, with a recovery of 95% could be obtained by this process.

Jan 1, 1966

By Maciej Korecki

Pyrowear®Alloy 53 steel is an excellent material for the construction of drive transmission components (gears, shafts, etc.) which have to operate in difficult conditions primarily in the aviation industry (Fig. 1.). Among the properties of such items is a high case hardness and abrasion-resistance, while the core remains flexible and is capable of carrying large impact loads. They can work at elevated temperatures with limited lubrication. The thermal treatment of such materials is based on case hardening by means of carburizing. This paper presents the technology of vacuum carburizing of Pyrowear® Alloy 53 steel. It discusses the methods of establishing different profiles of carbon concentration in a layer and their influence on the hardness profile. The effects of sub-zero treatment and tempering on the properties of the hardened case are also considered. It also presents a SimVaC® simulator of vacuum carburizing, designed especially for Pyrowear® Alloy 53 steel, which provides highly accurate predictions of the outcome of the process as the profile of carbon concentration in the layer, or vice versa: establishes the process parameters which will guarantee the required profile.

Aug 16, 2017

By Ye Chen, Jianhua Chen, Meng Liu, Yuqiong Li, Xiao Mu, Cuihua Zhao

"Sulfidization-amine is the most effective method for the recovery of smithsonite (ZnCO3), however the interface interaction details remain unclear. The sulfidization-amine flotation mechanism of smithsonite has been studied by Density Functional based Tight Binding (DFTB+) method in this paper. The slab model of ZnCO3 (101) surface was built and the adsorptions of a monolayer of HS- and S2- ions were conducted to model the sulfidization effect on the ZnCO3 (101) surface adsorption. DDA hardly interacts with the hydrated ZnCO3 (101) surface. Under the low concentration of Na2S, HS- ions form a Zn-SH-SH structure on the ZnCO3 (101) surface, which hinders the interaction between DDA and surface Zn atoms. Under the high concentration of Na2S, a layer of ZnS is formed on ZnCO3 (101) surface, which is favorable for the adsorption of DDA on the surface. This is consistent with the flotation practice where smithsonite flotation requires a large amount of sodium sulfide. The results could provide a microscopic investigation into the sulfidization-amine flotation mechanism of smithsonite.INTRODUCTIONSmithsonite (ZnCO3) is an important and typical oxide mineral of zinc. It is a semi-soluble salt mineral with a solubility product constant of 1.46 × 10-10 (Weast, 1973). The most common and effective method to recover oxidized zinc ores is froth flotation (Caproni et al., 1979; Pereia and Peres, 2005; Kashani and Rashchi, 2008). It is well known that the flotation of oxidized zinc minerals is much more difficult than the flotation of zinc sulphide minerals (Hosseini and Forssberg, 2007).The recovery of zinc oxide ores with poor floatability attracts more and more attention due to the depletion of easy-recovered of zinc sulfide ores.Sulfidization-amine flotation, which using Na2S as sufidizing agent and amine as collector (Mckenna et al., 1949; Rey, 1954; Abramov, 1961; Rey, 1979; Hosseini and Forssberg, 2007). This method is the most successful technology used for zinc oxide minerals flotation in large-scale industrial applications since it was invented in the 1950s (Önal et al., 2005; Pereira and Peres, 2005). There have been numerous experimental researches on the sulfidization-amine flotation of smithsonite. Shi et al., (2013) studied solution chemistry of smithsonite flotation system. Feng and Wen (2017) studied the formation of zinc sulfide species on smithsonite surfaces and its response to flotation performance. Wu et al., (2017) investigated the sulfidization behavior of smithsonite with the use of zeta potential, inductively coupled plasma (ICP), scanning electron microscope (SEM), and X-ray photoelectron spectroscopic (XPS). Their measurement results confirms the chemisorption of sulfur ions and the formation of ZnS film on the smithsonite surface after Na2S treatment, however the influence of HS- ions on the surface and the influence of sulfidization on the amine adsorption have not been discussed."

Jan 1, 2018

By M. Taheri

Multiple Attribute Decision Making (MADM) method is applied to select tailings site of the Gol-e-Gohar Iron Ore Processing Plant in the Kerman province, south-eastern of Iran. To select tailings site, screening is applied on eight location proposed by Binnie and Granges. Consequently three sites identified for further studies. Evaluation factors include only the most important factors such as efficiency ratio, elevation and distance to processing facilities, occurrence of faults and fractures. Crisp values such as efficiency ratio, elevation and distance can be determined by measurements and calculations, but some factors such as occurrence of faults and fractures are presented as linguistic values that can be described with triangular fuzzy numbers. Based on evaluation values obtained an optimal tailings site can be selected using a modified Technique of ranking Preferences by Similarity to the Ideal Solution (TOPSIS) given crisp data and linguistic variables as the alternatives of attributes. Each attribute?s weight is assigned using the analytic hierarchy process. The final ranking order aids in the selection of tailings site. Finally, the stages of modified TOPSIS method were applied and site No.2 situated in 5400m to the mill was selected as the best alternative.

Jan 1, 2014

By W. R. Hardwick

This paper describes block -caving methods and practices of the Bagdad Copper Corp. in Yavapai County , Ariz . It is one of a series being prepared by the Federal Bureau of Mines on mining methods , practices , and costs in various mining districts of the United States . The story of the Bagdad caving operation is of particular interest because the ore body was not as thick as at other mines where the method had been successful . At Bagdad the caving method worked very well as a smallscale operation of 300 tons per day but was abandoned when production was increased to 2,000 tons per day . The Bagdad mine is in western Yavapai County , Ariz . , about 22 miles northwest of Hillside , a station on the Phoenix -Ash Fork branch of the Atchison , Topeka & Santa Fe Railway system ( fig . 1 ) . Copper ore now is mined by open -pit methods . The ore is concentrated , and the concentrates are trucked to Hillside and shipped by rail to a custom smelter . Some molybdenum sulfide is produced as a byproduct . This report gives a brief history of the district , describes the ore de- posit , and outlines the methods of prospecting , exploration , and estimation of ore . Development and former underground mining , including stope preparation , stoping , and transportation , are described . Extraction of ore , production rates , miscellaneous operations related to mining , wage and contract systems , and method of concentration are described . The final section discusses mining costs . The underground mine was visited by the author several times between 1937 and 1942 , and some information has been drawn from personal notes . The property again was visited in June 1957 , and maps and plans for this paper were furnished by the company at that time ; they have been edited to conform with Bureau of Mines format . The underground mine could not be visited then because it had been closed in 1948 when open -pit mining was begun .

Jan 1, 1959

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by