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By M. A. Hararah, T. Neesse, M. G. Farghaly, G. Proellss, P. Kaniut, W. Rubarth

ABSTRACT: This paper presents two new options for hydrocyclone control. Volume split control using a control valve in the overflow is applied for the stabilization of separation results at changing feed conditions. Controlled water injection to the conical part of the cyclone leads to the reduction of fine particles in the underflow. Hydrocyclone monitoring in both cases is performed by optical sensors that indicate the spray angle of the underflow. Applications in mineral processing for desliming, classification in closed-circuit grinding, and dewatering are demonstrated.

Jan 1, 2011

By William W. Adams

Progress made by the quarrying and related industries of the United States during 1939 included increases in the number of men employed and the number of man-hours worked and reductions in the death and injury rates per million man-hours of exposure to risk. Forty-seven States reported quarries in operation; in each of 26 States the industry employed 1,000 or more men. Of these 26 States, 16 reported lower accident rates than in 1938. Among the operations of various types for which separate figures are published in this bulletin, the limestone, lime, and cement groups reported lower accident rates. During 1939, 79,449 men were employed in the quarrying industries. The period of operation of the plants averaged 236 clays per employee, with a total working time that equaled nearly 144 million man-hours. Accidents at the plants resulted in 48 deaths and 5,204 disabling injuries among the workers. Expressed as frequency rates, the accidents represented 0.33 fatality and 36.18 injuries for each million man-hours of work performed during the year. The major cause of fatal accidents inside the quarries was falls or slides of rock or overburden; nine deaths were reported from this cause. Four men were killed by explosives and four by falls of persons. Nonfatal injuries inside the quarries were clue chiefly to handling materials; about one-sixth of the total number at all operations in connection with quarries and related plants were in this class. Flying objects also caused numerous injuries, although only about one-half as many as did handling materials. Next in numerical importance were injuries from falls of persons. Then followed accidents caused by falls or slides of rock or overburden and accidents caused by machinery.

Jan 1, 1941

By R. W. Raymond

(Reprinted With some additions and changes from the Engineering and Mining Journal)] THE death of Prof. Samuel Benedict Christy on the 30th of November,. at the age of 61 years, cuts short a brilliant and influential professional career. He was born in San Francisco, Aug. 8, 1853, and was graduated as Bachelor of Philosophy at the University of California in 1874. For the five years that followed, he studied mining and metallurgy as a post-graduate in the same institution, serving also as instructor in analytical chemistry, and becoming in 1879 instructor in mining and metallurgy¬a position which he held until 1885. During this period he became known also by his contributions to technical literature, the earliest of which, perhaps, was his report on the Monte Diablo coals (in 1875); but the first which drew my attention to him was an exceedingly able discussion (in 1879) of the genesis of the quicksilver deposits of California, in which he followed with much acuteness and originality the lead of Professor Becker, who had been teaching at the University of California. The notion of the thermo-aqueous formation of such deposits was then new; and the laborers in a field now familiar to every student deserve the credit due to pioneers. For some years the subject of quicksilver seems to have occupied much of Christy's attention. In 1877, he described the mines and works at Almaden, Spain; in 1884, the Imperial quicksilver works at Idria, Austria; in 1889, the New Almaden mines of California. But his great work was the creation of the school, of mining and metallurgy at the University of California, which may be said to have begun with his occupancy of a full professorship of these branches. It is not necessary here to recount the early difficulties and perils of the University, and its long struggle for academic independence of political control or interference. The battle is over, and the institution is now upheld by the intelligent loyalty of the citizens of California, without regard to party. But while the issue was uncertain, the development of special schools of applied science was scarcely practicable. Doctor Becker and William Ashburner had given up the school of mines as a hopeless task when Christy, younger and less experienced, took it up. As he wrote me in February, 1901-

Jan 4, 1915

By Roger L. Williams

The Zinc Corporation of America Monaca smelter continues to use the St. Joe-developed electrothermic process for producing zinc metal and zinc oxide. As we enter the 1990s, the electrothermic process flexibility permits treatment of larger quantities? and lower-grade zinc-bearing recycle materials. A new sinter plant having one large sinter machine will increase sinter feed production required to meet our capacity target of 150,000 tons per year.

Jan 1, 1990

By David D. Rabb

Under the auspices of the Atomic Energy Commission, the Lawrence Radiation Laboratory of the University of California analyzed an experiment to provide information as to whether the chimney of broken rock produced by a deeply buried nuclear explosive could be "drawn" by conventional techniques. Since many low-grade disseminated ore-bodies occur in a granite media, the experiment took place in a granodiorite-quartz monzonite intrusive porphyry in the Nevada Test Site as a follow-up to the Department of Defense's Hardhat detonation in February 1962. For emplacement of the nuclear device, a 12 ¼ - in. pilot hole was reamed to a diameter of 44 in. and a depth of 950 ft in one pass using a Hughes multiple-cluster rotary bit. It was then cased to 36 in. ID. The center of the explosive device was located 938.85 ft below the collar. The yield of the device was predicted to be 5 kilotons, or an equivalent of 5000 tons of TNT; the yield was later confirmed by chemical means to be 5.4 kilotons.

Jan 3, 1964

By Daryl L. Gusey, John T. Neubert, Matthew A. Sares

The Colorado Geological Survey completed an inventory of environmental degradation associated with abandoned and inactive mines on National Forest System lands in Colorado. In the course of the inventory, areas with naturally occurring acid rock drainage were also noted. Approximately 18,000 abandoned mine- related features were inventoried, including about 900 features that are considered significant enough environmental problems to warrant further investigation. Water quality data, such as pH and conductivity were gathered at all features where water was present, such as draining adits, seepage at the toe of dumps and tailings, and standing water in shafts. Samples were taken where field tests indicated low pH andlor high conductivity, including several areas with naturally occurring acid rock drainage. Samples were analyzed for dissolved and total metals, and for selected anions. All mine locations and data collected by the field geologists were entered on field forms and, subsequently, into a computer database and GIS format. With the information provided by the inventory, the Forest Service, in cooperation with other agencies, has been able to prioritize abandoned mines for reclamation. In most cases, cleanup is approached on a watershed basis. Mines in priority watersheds have been selected for reclamation first. Watersheds where studies prerequisite to cleanup are occurring include the upper Anirnas River, Willow Creek (tributary to the upper Rio Grande), Chalk Creek (tributary to the upper Arkansas River), the Uncompahgre River, and the Alamosa River. During the inventory, evidence of naturally occurring water quality degradation was found in areas where little or no evidence of mining activity exists. These areas include the upper Alamosa River, the Middle Fork of Mineral Creek, Peekaboo Gulch, and Handcart Gulch. Water from these natural sources has been found to significantly exceed Colorado water quality standards for several metals.

Jan 1, 2000

By J. P. Lesley

The old do not love to see the young pass away from the light of the sun before them. Fathers would fain keep their sons by their side to the. end of life ; but the old Greeks, who loved the old gods, were wont to moderate their grief with the sweet superstition that only those whom their gods especially loved died early. The Christian church found consolation in that superstition applied in a new form to its new sorrows, and paid its most enthusiastic devotion to the memories of its young and beautiful martyrs. The natural science of our century is robbing us fast of this and all other superstitions, sweet as well as bitter, and leaving us for consolation to the teaching—colder, yet kinder—of personal fortitude and that optimism Which intelligently translates the Cosmos of Humboldt back into its old name of the Harmonia of Pythagoras. The Homeric Kataclothes, the three fates, are dead and gone for us, with that old world which comprehended none of the laws of cause and effect, and sorrowed for those who were cut off from the land of the living without hope of more than a shadowy existence beyond the river of death. All the more the ancients cherished the memory of their dead and lavished their choicest art upon their monuments. We moderns have lost the monumental arts, but we better keep the monuments which our dead leave behind them. No one of us who has done good work can fail to be remembered; and in an Institute like this, which keeps the press at work, an immortality in the memory of men is more possible, more certain, for every one of its members than the greatest heroes of antiquity could anticipate for themselves. In old apocalyptic times the works of men followed them through death to the throne of God to be their advocates in judgment, but in these modern times our works remain this side the grave, to follow the name of the departed one as it takes its course along the history of his peculiar art or science advancing slowly to perfection. We write the epitaph, not upon the mouldering stone of a tomb, but on the pages

Jan 1, 1890

By F. P. Dewey

The first systematic attempt of the National Museum to gather material representing the economic geology and metallurgy of the country was made in connection with the Centennial Exhibition. The department may be considered as having originated then, althongh it was not formally inaugurated until December, 1882. Previous to the Centennial, all the illustrations of economic geology had been included in the mineral collection, and the illustrations of metallurgy were so very few that they had also been included with the minerals. When the museum began its collections for the Centennial, the subject of the mineral resources of tile United States was placed in the hands of Professor Wm. P. Blake, who was eminently fitted to undertake the work by his experience at various international exhibitions and his extensive acquaintance with the mining industry of the country. Professor Blake prepared a broad and exhaustive plan for this purpose, and the very large collection shown at Philadelphia was well calculated to set forth the vast mineral wealth of the country. The history of the department proper may conveniently be divided into three periods : first, the formative period, during which the Centennial material was mainly administered upon, ending Jnly 1, 1884, with the beginning of the preparation for the New Orleans Exposition; second, the New Orleans Exposition period, from July 1, 1884, to June 30, 1887, during which the collections for the New Orleans Exposition were made, exhibited at New Orleans, returned to Washington, and installed permanently in the museum; third, the southwest-court period, from July 1, 1887, to October 1, 1889, during which the collections were arranged in the southwest court of the museum.

Jan 1, 1891

By Chu-Phay Yap

This is the first of a series of theoretical papers on the iron-carbon system. A simple critical analysis of the ordinary constitution diagram of the iron-carbon system yields valuable information regarding the nature of the equilibria in the liquid and solid states. It is shown, for example, that the solute in the melt is Fe3C, but in solid Fe (austenite) the solute is carbon. The thermodynamic laws of the depression in the freezing point of solid solutions have been developed and discussed. Using the usual method of plotting the logarithm value of the concentration of the solvent (in this case, the ratio of concentrations of the solvent in the liquid and solid phases) against 1/T, curves are obtained. A rigorous thermodynamic analysis of these curves has been shown to yield considerable information regarding the internal equilibria of the system, with which the phase rule does not deal altogether. In this way, it is shown again that the solute in the melt is Fe3C, but in the solid rFe the solute is carbon. Various heats of reaction (fusion and transition) and other thermal data have been derived: and discussed with a view to correlating the conflicting experimental data obtained by different investigators of the system.

Jan 1, 1931

By S. Tiwary, S. Samanta, B. N. Pandey, N. C. Saxena, R. Sinha, B. P. Nandy, B. Singh

Subsidence investigations over one bord and pillar and one longwall caved panel at Dhemomain colliery showed that, although the width-depth ratio (0.82 and 0.83) and working and strata conditions were almost identical, the maximum subsidence over bord and pillar panel was 46.2 per cent of extraction thickness against only 6.9 per cent over longwall panel. The angle of draw was 13O to 210 and 66 to 95 per cent of the subsidence had taken place immediately after extraction. The subsidence profiles were not symmetrical and were of funnel like shape. There was wide variation in subsidence movements over caved faces in India mainly due to difference in the composition of supercumbent strata.

Jan 1, 1983

By L. A. Ayres da Silva, J. P. G. Negri, A. L. M. Ayres da Silva

"Rock hardness is dependent on the type and quantity of the various mineral constituents of the rock and the bond strength that exists between the mineral grains. As the book “The Complete ISRM Suggested Methods For Rock Characterization, Testing and Monitoring:1974-2006” explains, hardness is a concept of material property. As such, the quantitative measure of hardness depends on the type of the test employed.Among the three types of tests that have been used to measure the hardness of rocks and minerals: 1) indentation tests; 2) dynamic and rebound tests; 3) scratch tests, the authors of this paper chose indentation tests, more specifically the Vickers test, and complementary verified the correlation between the results of the Schmidt sclerometer tests (rebound tests) and the Vickers microhardness tests in a set of the same 9 (nine) granite rocks.The objective of this research was to verif y the correlation of one created index, based on the Vickers test that can be able to represent the rock material hardness. We know that Vickers tests determine the microhardness of individual rock minerals. A pyramidal shaped diamond is applied to the surface with a specified force. The area of the permanent residual deformation divided by the applied force is a measure of the hardness. Using the relative participation of the mineral components of the rock, we established a hardness index denominated EVM (Equivalent Vickers Microhardness).The correlation of the EVM with others strength properties and application parameters like UCS (Uniaxial Compressive Strength) to study sawability of granite blocks have presented very good results. The association of equivalent microhardness with others strength parameters, allowed to find powerful algorithms for analyzes of the rock materials behavior under diversified circumstances, as the sawability of granite blocks, as we can see in Fig. 1.Other very interesting correlations were found as the EVM values and that were obtained by the use of the Schmidt impact hammer for the superficial hardness determination."

Jan 1, 2015

By J. Hanna, I. J. Anazia

The Mineral Resources Institute (MRI) has developed a unique process for selective fatty-acid flotation of phosphate minerals from siliceous ores. The process takes advantage of preferential adsorption (over silica surfaces) and high reactivity of fatty-acid collectors toward apatite under slightly acidic conditions (pH 5 - 6.5). The process was successful in upgrading various Florida and North Carolina phosphate samples containing 7.7% to 15.3% P205 and 62.3% to 77.2% siliceous gangue (Insol). The resulting concentrates assayed 28.1 % to 33.1 % P205 and 4.1 % to 9.9% Insol, with high P205 recoveries of 81.8% to 92.2%. Depending on the degree of surface contamination of the silica particles in the flotation feed, one or more cleaning steps, with or without sodium silicate, would be required to achieve higher-grade phosphate concentrates.

Jan 1, 1994

By Ricardo Morales

Reactions between solids and a gas phase have many interesting theoretical aspects as well as technological applications. The present group had carried out experimental investigations as well as theoretical studies of a number of gas-solid reactions over the past decade and was able to derive interesting results. Studies of the decomposition of alkaline earth carbonates were carried out by thermogravimetric analyses. The experiments were carried out using thin powder beds as well as iso-statically pressed compacts with thermocouples embedded in the same. The investigations revealed the complexity of the reactions and the impact of the heat- and mass transfer aspects on the reaction kinetics. In the case of BaCO3, the kinetics of decomposition was complicated by the formation of a liquid phase. In the case of SrCO3, the reaction kinetics could be simulated by theoretical modeling. Gas-solid reactions were also employed as a versatile process tool towards the production of alloys and intermetallics involving transition elements by hydrogen reduction of complex oxides involving transition metals. Thin powder beds were employed to examine the micro-kinetics, while fluidized bed technique was utilized to produce bulk alloys. Preliminary correlations could be drawn between the thermodynamic stabilities of the oxides and the activation energies of chemical reduction steps. Adjusting the process parameters, products at nano-scale could be produced. The structural, mechanical and thermal properties were investigated in the case of these products. The potentialities of this method as a green route to produce industrially important alloys and intermetallics with unique properties are demonstrated.

Jan 1, 2006

By Yu-ichi Kanbe

It becomes more important to control the composition of inclusions with increasing the demand for quality of products in terms of cleanliness. Along with the development of refining technology to make inclusions harmless, a study was made to develop how to predict the quality of final products. At first, observations of a number of defects revealed that the defects were caused by inclusions larger than 100 m in diameter. Therefore it is required to detect relatively large inclusions in steel, whose existence is quite rare, to identify the quality. In order to estimate the maximum size of inclusions in a given sample, the method with statistics of extreme values has been applied for continuously cast (CC) slabs, hot-rolled coils and cold-rolled coils of type 304 stainless steel. For the CC slabs the diameter of inclusions, which were analyzed to be mostly silicate with globular shape, in the specimens was measured. For the coils, the width of inclusions was measured at the unit section perpendicular to rolling direction because it corresponds to the diameter assuming that the width of globular inclusions does not vary with rolled. Then maximum inclusion diameter in a specimen was calculated. As a result, the obtained values in the rolled coils are larger than in the slabs. This may imply that the measurement with the coils gives the values closer to the truth. Besides, the measurement with the coils is even faster than with the slabs due to its simplicity of preparation of the specimens.

Jan 1, 2006

By W. A. Bruce

Studies of reservoir behavior of 12 Smackover limestone oil and condensate pools are presented. Buckner, Midway, McKamie, Magnolia, Mt. Holly, Schuler (Reynolds) and Village are treated in considerable detail and subjected to analysis with an electrical device for analyzing reservoir behavior. Results and comparisons of these analyses are presented. In addition to these reservoir-behavior studies, an attempt is made to assemble trans-missibility and storage data on the Smackover limestone formation from cores and logs taken in dry holes and producers. This together with the behavior of individual reservoirs leads to a better understanding of the formation as a porous aquifer. The ultimate purpose of this type of study is to improve predictions concerning the future behavior of these pools in such a system. Predictions are presented for several pools. Introduction In 1937 the Phillips Petroleum Co. drilled its J. D. Reynolds No. I to the Smackover limestone formation at Snow Hill, Arkansas. This well found oil in the porous, permeable, upper part of the Smackover, thereafter referred to as the Reynolds lime. Since then, six oil pools and six condensate pools have been discovered in the Reynolds lime, and more than 75 dry holes have explored parts of this formation. By the first of 1943, 44 million barrels of oil and 83 billion cubic feet of gas had been withdrawn from the various reservoirs. The original reserves estimated by the Arkansas Oil and Gas Commission were 342 million barrels of oil and rzoo billion cubic feet of gas. So far all of the production has been from anticlinal structures, most of which are asymmetric and have their axes roughly perpendicular to the dip of the formation top. This is indicated in Fig. I, which shows the pools, dry holes drilled, and contours on top of the Smackover.' These pools are of particular interest for reservoir-behavior studies because the production and drilling has been controlled, and in most cases the records of reservoir data are complete. In addition to the excellent production and pressure information available, more than one half of the wells drilled were cored and all of them were electrically logged. All of the pools show evidence of water drive. While this paper is in a sense a collection of reservoir-behavior studies for several different pools, there has been an attempt to go one step further and to show the importance of the iormation as a porous continuum or a single aquifer in which the withdrawals of fluids from any pool has an important effect on the behavior of all of the pools. An effort will be made to show that the water drives of these pools are dependent upon a much larger area of the Smackover limestone than that occupied by the petroleum accumulations.

Jan 1, 1944

Outokumpu Technology’s HSC Chemistry process calculation software enables the user to simulate an entire chemical or physical process. The HSC Chemistry 6.0 contains 21 calculation modules and 11 databases for reaction, equilibrium, heat balance, heat transfer, petrological and simulation applications. Most of the calculation modules automatically utilize the same extensive thermochemical database which contains enthalpy (H), entropy (S) and heat capacity (C) data. This database has been expanded to include more than 20,000 species.

Jan 1, 2007

By C. Arthur Lefler

The Smoky Valley Mine is jointly owned by Louisiana Land and Exploration Company, Felmont Oil Corporation and Case Pomeroy Company. Copper Range Company, a subsidiary of L.L. & E. is the operator of the mine. The mine is located about 60 miles (100 km) north of Tonopah, Nevada on Highway 376 (formerly 8A) in the Big Smoky Valley on the western flank of the Toquima Mountain Range In the shadow of Mount Jefferson. The mine is at an elevation of about 6100 ft. (1860m) and is situated on the southwestern flank of Round Mountain, the hill for which the town of Round Mountain is named. The ore is a rhyolitic iglmbrite with coarse gold occurring along fractures and with fine microscopic gold disseminated in the rock mass. Minor silver is associated nth gold. Annual mining is planned at 5.8 million tons (5.3 million tonnes) per year with 2.2 million tons (2 million tonnes) as ore (7,000 tons or 6,400 tonnes per day).

Jan 1, 1981

By Y. Nien Wang

The Devil?s Slide portion of Highway 1 between Pacifica and Montara is often closed due to the instability of the adjacent slopes. Following many years of public input and careful evaluation of alternatives, Devil?s Slide will be by-passed via two inland tunnels, providing a safe, dependable highway between Pacifica and Montara. For the twin tunnels, each 9m diameter tube will accommodate only one traffic lane. Each tunnel tube will accommodate a 3.6 meter roadway, 0.6 meter and 2.4 meter inside and outside shoulders respectively, and 1.2 meter walkways on each side. Cross passages will connect the bores at about 120 meter intervals and jet fans will provide tunnel ventilation. The twin tunnels are approximately 1,250 meter long and 9 meter wide. Excavation will progress from south to north using tunneling techniques that rely on inherent rock strength for support known as the New Austrian Tunneling Method (NATM). Both tunnels will be excavated at the same time, one tunnel face approximately 40 meters ahead of the other. Staggering the tunnels reduces the likelihood of damage from blasting in alternate tunnels. The work schedule is 24 hours a day, 7 days a week resulting in a 24-month timetable to break through to the north portal.

Jan 1, 2008

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,' the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968

By G. Thodos, W. F. Stevens

The point-source function introduced by Horner' us a solution to the general unsteady-state equation for the flow of fluids through porous media has been utilized to calculate pressure profiles for adjacent wells as a function of time. By trial and error, the time at which the pressure waves meet to cause interference can then be calculated. For this calculation, the time of interference is arbitrarily defined as that time when both pressure waves exhibit a pressure decrease of 25 psi ar the same point within the formation. To illustrate the method, an example involving two adjacent wells producing at different rates has been worked out and is presented in detail. INTRODUCTION The initiation of production of a new well is usually accompanied by pressure drawdown measurements in order to establish the extent and characteristics of the formation. The interpretation of such pressure drawdown data is based on mathematical developments involving a single well in an infinite reservoir. If more than one well is present in a reservoir, the possibility of interaction between wells exists. Therefore, care must be taken in interpreting the pressure drawdown data. It becomes important to be able to determine when this interaction, or interference, becomes significant. This paper presents a method for the prediction of the approximate time of interference between two such adjacent wells. The basic differential equation describing the pressure distribution existing during unsteady-state flow of a slightly compressible fluid has been solved by Hor-ner.' for a constant production rate from a circular homogeneous reservoir of infinite extent. The solution utilizes the point-source function to define the pressure at various points within the formation as a function of time. The resulting expression is: q = production rate, STB/D ,;= formation volume factor, dimension-less µ = fluid viscosity, cp k = formation permeability. md H = formation thickness, ft C - fluid compressibility, psi' F = formation porosity, dimensionless R = distance from centerline of well, ft T = production time, hours Ei(—u) = Ei-function of U Eq. 1 may be used to calculate the pressure profiles generated during production from a single well in an infinite reservoir.