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By R. S. McClellan

Western Talc Company, Inc., with headquarters in Los Angeles, Calif., has just completed an extensive modernization and expansion program at its talc mine near Tecopa, Calif., and at its talc and clay mills at Dunn Siding, Calif., the nearest rail shipping point to the mine. The basic objective of the program was to provide facilities necessary to produce 300 tpd of a wide range of ground talc and clay grades for the ceramic, paint, paper, rubber and other industries. In the planning of the program every effort was made to provide a system which would permit a high degree of quality control and uniformity of the finished products, along with efficient operation. Several years ago, R. T. Vanderbilt Co., Inc. purchased Western Talc Co. after a comprehensive investigation of its properties, including an extensive diamond drilling campaign. Western Talc's properties embraced a number of claims in the Resting Springs mining district in the northern part of San Bernardino Co. and the southern part of Inyo Co., Calif., some seven miles southeast of the town of Tecopa. Operations by the original company were started on a small scale in 1913 and production from that date to the time of purchase of the company by Vanderbilt is estimated at 250,000 tons. The major part of this output was sold to the ceramic wall tile industry.

Jan 3, 1968

By B. C. Allen

Liquid surface tensions of copper and 18 Group IV-A to VIII transition metals (Ti, Zr, Hf, V, Cb, Ta, Mo, W, Re, Ru, Rh, Pd, Os, Ir, Pt, Fe, Ni. Co) have been measured by the static pendant-drop and dynamic drop-weight methods on the same rod sample. The drops were formed by electron-bombardment heating in high vacuum. Application of necessary corrections enabled determination of surface tensions to k2 pct and agreement between methods to * 1 to 4 pct for all the metals studied. Evidence is presented that the liquid surface was well screened by metal vapor, suggesting negligible adsorption of gaseous impurities and that the surface tensions measured are characteristic of the metals involved. Correlations between liquid surface tension and melting point, molar volume, heat of vaporization, and atomic number are presented and discussed. Temperature coefficients of surface tension were calculated using Eötvös' law. SURFACE tension and interface energies of metals are the result of incomplete atomic coordination resulting in a force perpendicular to the boundary, tending to minimize its area. These energies are important in many phases of metallurgy, including microstructure, sintering, joining, electronic emission, and lubrication, which in turn affect many physical and mechanical properties of metals. Liquid surface tension refers to the interface between the liquid and its own vapor or nonreactive atmosphere, and is considered a physical property of the liquid. Since equilibrium shapes can be readily obtained with liquids, the units of surface tension (force per length) and interface energy (energy per area) are interchangeable. Thermo-dynamically, the surface tension ?LV is given by the change in free energy F with surface area A at constant pressure P, temperature T, and composition N: for commercially important refractory metals, vanadium, columbium, tantalum,13,14 molybdenum,14 and tungsten,l5 and none for the rare platinum-group metals and rhenium. Measuring the surface tensions of transition metals is difficult because of their high reactivity and melting points. Of the many techniques available,16-18 the pendant-drop 19-21 and drop-weight methods17,22 are considered superior because they can be modified to eliminate persistent sources of contamination such as supports and capillaries necessary in the popular sessile drop, capillary rise, and maximum-bubble-pressure techniques. The necessary modification is to melt a drop on the tip of a vertical rod, which provides support through a solid of the same composition.13,15 The object of the work was to study the surface-tension behavior of copper and transition metals, having reasonably low vapor pressures. Liquid surface tension of each pure metal was systematically determined by using a combination of the static pendant-drop and dynamic drop-weight methods on the same rod. Liquid drops were formed by electron-bombardment heating in high vacuum. EXPERIMENTAL WORK As indicated in Table I, the metals studied were high purity and generally were obtained in rod form. The exceptions were titanium and zirconium, which were machined from crystal bars, and molybdenum (tot 11, osmium, and ruthenium, which were sintered and arc cast into rods. All the metals were ground or swaged to desired sizes between 1- and 7-mm diam, and centerless ground round and smooth to a finish better than 50 µ in., rms. Each rod was thoroughly cleaned with steel wool, degreased, acid etched, and dried. In a typical run, the rod was vertically clamped in a modified floating-zone electron-bombardment furnace designed after Calverley23 and Carlson.24 The specimen was outgassed and maintained positive at several kilovolts in a dynamic vacuum of 10-5 to 10-7 mm. The bottom end was enclosed by a tantalum pillbox and heated by electrons emitted from a hot concentric tungsten filament mounted on a movable bracket. The bombardment power was slowly raised until melting was observed. Power requirements ranged from 30 w for copper to 1300 w for 4-mm tungsten. The stabilized and out-gassed drop of near-maximum size was photographed at 4. 1X on panchromatic film at desired time inter-

Jan 1, 1963

[United Engineering Trustees, Inc. W. D. B. MOTTER, JR., '40 A. L. QUENEAU, '41 ALBERT ROBERTS, '41 The Engineering Foundation GEORGE D. BARRON, '44 F. F. COLCORD, '42 A. L. QUENEAU, '41 Engineering Societies Library Board J. W. LAIST, '40 A. B. PARSONS, Ex-officio T. T. READ, '42 F. F. SHARPLESS, '41]

Jan 1, 1940

[United Engineering Trustees, Inc. A. L. QUENEAU, '45 ALBERT ROBERTS, '47 RALPH B.. WILLIAMS, '48 The Engineering Foundation F. F. COLCORD, '46 E. A. PRENTIS, JR., '48 A. L. QENEAU, '45, Chairman Engineering Societies Library Board J. W. LAIST, '48 W. A. MUDGE, '45 A. B. PARSONS, Ex-officio T. T. READ, '46]

Jan 1, 1946

By AIME AIME

THE Coal Division holds its fall meeting in the Pocahontas coal field, at the West Virginian Hotel, Bluefield, W. Va., Oct. 9 and 10. The first day will be a busy one-two sessions for the presentation of papers and a dinner in the evening. Hon. E. Fudge, Assistant Undersecretary, Mines Department, and R. V. Wheeler, head of the Mines Research Board of Great Britain, will be the guests of the Division. Mr. Wheeler will discuss the British Mining Act as relates to the coal industry. George S. Rice, Chief Mining Engineer, U. S. Bureau of Mines, will present an account of the recent meeting at Buxton in England, of representatives of England, Germany, France, Belgium and the United States to formulate a plan and to correlate research work now in progress in the various countries. The second day the members will be the guests of the operators on a trip through the Pocahontas field. The work of preparation for the meeting is being actively pushed by committees headed by T. H. Clagett, R. M. Lambie and H. D. Smith, and a good attendance, both local and from the general membership of the Division, is anticipated. Because many will make the trip by car the principal automobile as well as rail-road connections to Bluefield are given here. The program for Friday, Oct. 9, follows:

Jan 1, 1931

By S. S. Marsden, S. A. Khan

Externally generated foam was injected continuously into short porous media. Both flow rate and pressure drop were measured. Liquid saturation was determined by electrical conductivity. Foam yuality I, expressed as the ratio of gas volume to total volume, was varied from 0.70 to 0.96. As measured with a modified fann VG Meter, apparent viscosity of this foam µa decreases with increasing shear rate but usually falls within the range of 50 to 500 cp. At a given shear rate, µa increases almost linearly with I-. When measured with a Bendix Ultraviscoson, kinematic pa is independent of V but absolute pa increases with T from about 3 to 8 cp. The effective permeability -apparent viscosity ratio ke/µa decreases almost linearly with V for porous media of high permeability, but the rate of decrease becomes less for tighter ones. The relative permeability-apparent viscosity ratio kr/µa us V data does not fall on a single line. The kr/µa ratio increases with liquid saturation in the porous medium and with surfactant concentration. Estimates of pa for foam in porous media vary from 30 to 100 cp. INTRODUCTION Although research on the development of a foam-drive, oil recovery process has been going on for almost a decade, most of the significant publications have appeared within the last several years. This illustrates well the rate at which interest in this process is accelerating. Bond and Holbrook 1 were the first to describe the use of foam to improve oil recovery in their patent of 1958. They proposed that an aqueous foaming agent slug be injected into the formation and that this be followed by gas to produce a foam in situ. Fried 2 studied the injection of foam into porous media which had already been subjected to conventional gas or water drives and found that gas could be used to drive a foam bank which would, in turn, displace additional oil in the form of an oil bank. He attributed the increased oil recovery to the high effective viscosity of foam flowing in porous media. His microscopic observations showed the importance of foam generation and regeneration within the porous medium. By injecting both air and aqueous surfactant solution, Bernard3 generated foams within the porous medium in which oil displacement was being studied. In a separate empirical test, he also measured the dynamic foaming characteristics of the same surfactants in water and/or oil. With some exceptions and for the seyen surfactants studied, there seems to be a qualitative relationship between the efficiency of liquid rlisplacrment and the dynamic foaming testtsed. This relationship was not consistent enough to eliminate the necessity of actual foam flood tests in porous media for surfactant selection. In a study basic to gas storage in aquifers, Bennett4 described the displacement of brine by foam in consolidated porous media. Among other things, he stated that the ability of a surfactant solution to foam is more important than the stability of its foam. The presence of a foam bank between the displacing air and the displaced brine improved both breakthrough and ultimate recovery. In a continuation of this work Kolb5 attributed the great reduction in surfactant solution production rate as displacement by air progressed to a decrease in relative permeability to gas. These several effects reported by both Bennett and Kolb can all be attributed to the high apparent viscosity of foam which was obviously flowing in the porous media. Bernard and Holm6 observed that gas permeability in the presence of foam was much less than in the absence of foam when both were measured at the same gas saturations. This reduction in permeability was proportionately greater for more permeable sands and sandstones than for the less permeable. Viscosities of the surfactant solution and air were used for their calculations rather than apparent foam viscosities. The foam stability increased with decreasing permeability, which was probably due to the natural regenerative properties of porous media, and the permeability reduction increased

Jan 1, 1967

By M. A. Childers

Recent work with controlled laboratory tests.' field experience and a new analytical approach indicate that casing centralization, pipe movement and relative rheological properties between the mud and cement (yield point and density) are the three controlling factors in successfu1 primary cementing of dual casing. Turbulent flow has been demonstrated to be unnecessary under the severe displace ment conditions of parallel dual strings of casing. Simultaneous reciprocation of dual casing in directionally drilled boreholes is highly dependent on centralization and on the rapid initiation of pipe movement once the casing has been run to total depth. Successful cementing of 30 out of 32 dual, 3%-in casing wells substantiated these conclusions. A review of 15 dual, 3 1/2-in. casing wells completed prior to the adoption of these principles disclosed only one success. Mathematical and graphical techniques permit the engineer to analyze and anticipate the success or failure of a cementing operation. Standoff, mud displacement and reciprocation can be analyzed mathematically and planned in deep, directional or straight boreholes by review of annular geometry, relative rheological properties between the mud and cement, and forces caused by caring weight, functional drag and differential sticking. Introduction The objective in primary cementing is to displace the drilling fluid with cement that will bond to the formation and casing to prevent communication through the annulus. The predominant cause of failure appears to be channels of gelled mud that remain in the annulus after cementing.1 '* Past investigations have noted many procedures that could improve the displacement process.2-' These procedures include centralization, chemical preflushes, mechanical mud cake removers, controlled flow rates in certain regimes, pipe movement an1 control of mud and cement properties. Not until recently have the effects of many of these procedures been isolated so that their individual importance could be determined. In a recent paper,' a comprehensive and analytical laboratory study of various factors controlling the displacement process concluded that there are three major factors in obtaining complete mud displacement by the cement slurry. 1. Good relative rheological properties between the mud and cement. The cement should be heavier and have a yield point and plastic viscosity higher than the mud being displaced. Buoyancy forces often can dominate the displacement process. 2. High degree of standoff or centralization. The more centered the casing, the greater the likelihood of complete mud displacement and removal. 3. Pipe movement obtained by rotation or reciprocation. Often unfavorable rheological properties between the mud and cement, and poor standoff can be compensated by pipe movement. This work demonstrates the compatibility of the latter concepts with field results extended to the more severe dual casing displacement process. Early Experience With Dual 3'/t-In. Primary Cementing Early slim casing completions in the West Delta Block 73 field, offshore Louisiana, included 17 dual 3%-in., 3 single 3% -in. and 1 dual 2% -in. casing installations. Table I provides data on these earlier wells. Usually, common Class A cement was placed across the pay zone and 12 percent gel cement was placed to a height of 500 ft above the highest productive sand. Centralizers (6%-in. OD maximum expansion) were placed two or three per joint on both casing strings from total depth through the completion intervals and at least one per joint for the remainder of the cement sheath. A number of techniques and procedures were attempted to improve cementing success. Casing was run simultaneously or separately with a number of mud conditioning and circulating techniques. Mechanical aids such as cement bonders, slmiding sleeves, turbulizers and various sizes and strengths of centralizers were used. Common and gel cements were mixed with fresh or sea water with a number of different additives to control retardation and dispersion. Cements were thinned and mixed at high rates to try to induce turbulent flow in the annulus. On one well the "slow flow" method was used." Perforating was accomplished with a jet orienting gun. Unsuccessful cement jobs were indicated by production of extraneous fluids or by pressure communication between zones. On test, five wells flowed water, four flowed sand and six had pressure communication with the other string or the 10%-in. casing. A total of 25 remedial squeeze ce-

Jan 1, 1969

By Daniel R. Shawe

Large tabular beryllium deposits in waterlaid rhyolitic tuff at Spor Mountain, Utah, contain the world's largest known resources of beryllium (as bertrandite). The district also has produced fluorspar and uranium. The largest beryllium deposit is about 2.5 miles long, and known deposits contain many million tons of material with at least 0.5 per cent BeO. The beryllium-bearing tuff (Pliocene?) underlies topaz-bearing rhyolite ( Pliocene?) that contains unusually high amounts of beryllium, fluorine, and uranium, and overlies other volcanic rocks (Pliocene? or Micocene?) and marine carbonate and elastic rocks ( Paleozoic). The deposits occur in hydrothermally altered tuff only where it contains abundant carbonate pebbles eroded from the Paleozoic rocks and where the tuff was deposited as thick layers in now-buried paleovalleys. Basin and Range faults, thrust fa ults, and possibly strike-slip faults formed in this part of the Basin and Range province during the late Tertiary, and volcanic rocks were extruded. Beryllium mineralization probably occurred during this episode. Undoubtedly the beryllium deposits are related genetically to the topaz-bearing rhyolite, but the details of their genesis are not certain and probably are complex. Beryllium deposits are close to major faults, and locally the beryllium is concentrated at faults, indicating fault control of mineralization. Some elements in the deposits, such as lithium, however, are evenly distributed in certain Luff beds and perhaps were introduced prior to faulting. Still other elements, such as manganese and lead, were concentrated in the beryllium deposits and subsequently were leached along late fractures, indicating a period of metal redistribution following mineralization.

Jan 1, 1968

By GEORGE L. CHRISTIAN

T HE Tonopah Extension assay office is a two- story, concrete structure on a solid foundation of andesite, situated about 100 yd. from the company's mill, so that it will not be affected by the stamps or the tube-mills; also it will not be affected by under- ground blasting. On the second floor are the mine superintendent's office and drafting and blueprint rooms. On the ground floor are the assayer's office,' mixing room, furnace room, crusher room, chemical laboratory, parting room, store room, and change and shower room for the mine superintendent, assayers, and engineers. The crusher room is outside of the main building, and has four concrete walls, thus eliminating the jar of the crusher; it is so situated that the least possible amount of dust spreads through the main building. An 8 by 10-in. jaw crusher, which crushes to ¼ in., was made by a local foundry. Attached to the top is a small galvanized-iron hopper covered with a ¼ in. screen, on to which the sample is dumped. The fines-pass through the screen into the hopper, while the oversize is dumped into the crusher. The crushed sample and fines from the screen drop down to a set .of splits suspended from an iron rod below the crusher jaws. The small sample is caught below in a small pulp pan. The rejects drop from the splits through a 2-in. pipe on to a bucket conveyor, which dumps into a galvanized-iron hopper in an upper corner of the room. The rejects drop through a 2-in. pipe to a reject bin outside the build- ing. This bin is constructed high enough for a truck to be loaded from it by means of a chute door on the side.

Jan 1, 1921

ALABAMA Anniston. Carrington, F. G. Ashland.-Herr, I. Auburn.-Brown, R. L. Bessemer.-Abbott, C. E. Dobbs, G. G. Ferguson, V. Salmon, H. S. Schaber, C. F. Birmingham.-Adams, J. H. Aldrich, T. H. Aldrich, T. H., Jr. Allen, A. W. Ball, E. M. Bonnyman, J. Bowron, J. Bush, M. W. Crawford, G. G. Crockard, F. H.

Jan 1, 1917

By Roger L. Goin

Maintaining smooth haulage roads is a key to significant cost savings at Kennecott Copper Corp.'s Bing- ham Canyon copper mine, located near Salt Lake City, Utah. The truck operations section of the mine moves an estimated 300,000 tpd of waste plus some ore to maintain a balanced production cycle. A three-year truck replacement program has produced a dramatic new look in both size and capacity of the truck fleet. Currently there are 95 haulage trucks in the Bingham fleet with capacities up to 150 t. The trend towards the larger haulage units places greater importance on overall truck availability. The impact of a 150-t truck being out of service is far more critical than with the former 65 or 85-t units.

Jan 12, 1974

Extractive Metallurgy Division Institute of Metals Division Iron and Steel Division Council R R McNaughton, Chairman (EMD), Ernest O Kirkendall, Secretary, J H Scaff, (IMD), Morris Cohen, (IMD), T J McLoughlin, (ISD), J S Marsh, (ISD), P T Stroup, (EMD), R D Parks, (MED), D S Eppelsheimer, (MIED) Journal of Metals Editorial Advisory Committee J S Smart, Jr, Chairman, W A Dean, T D Jones, Evan Just, J C Kinnear, Jr, J S Marsh, M Tenenbaum Pacific Northwest Regional Meeting F X Cappa, General Chairman, W W Wiltschko, Chairman (Metals Branch), Program Chairmen H E Lee (EMD), S E Maddigan (IMD), G R Heffernan (ISD), L C Richards (Ind Min Div), James Bell (Finance Committee), Ed Vestica (Registration), Donald Johnson (Special Events)

Jan 1, 1954

By Charles R. Keyes

I. INTRODUCTION. FOR a period of several years, and in a large number of cases, the Metallurgical Laboratories of the New Mexico School of Mines were employed in umpire work. During this time many important local problems were solved. Against the results of careful chemical analyses of ores, assay-returns were often checked. In many cases the assay-methods of mine and custom-smelter were compared, and both often found faulty for the ore concerned. A wide range of ores was covered. Many of the chemical analyses and assays were made by Dr. F. C. Lincoln, Professor of Metallurgy, now of the Montana State School of Mines. A varied series of instructive assays was prepared by Prof. R. B. Brinsmade, now of the West Virginia State University. Single assays and given series of tests were undertaken by H. T. Goodjohn, now chief chemist to the Cia. Metalurgica de Torreon, Coahuila, Mexico; by H. J. Hubbard, now superintendent of the Butters Divisadero Mines, Jocoro,. San Salvador, C. A.; by E. D. Morton, now superintendent of the Arizona & Nevada Copper Mining Co., at Lunning, Nev. ; and by A. W. Edelen, now superintendent of the Angangueo Unit of the American Smelting & Refining Co., in Michoacan, Mexico. A critical comparison of assay-methods that were found to be followed in the case of certain gouge-ores mined in the Mimbres range in New Mexico, and about which there had been much controversy, was made by D. F. Riddell, then Acting Professor of Assaying, and now superintendent of the Providentia Mines Co. of Parral, in Chihuahua, Mexico. To him is due the credit of much that is contained in the following notes, which be has generously permitted -to be used in advance of the publication of the complete results.

Jul 1, 1911

By AIME AIME

THE fall meeting of the Petroleum Division, held at Tulsa, Okla., on Oct. 11 to 14, devoted two days to technical sessions and two to field excursions. A representative attendance of 250 to 300 engineers and operating officials engaged in oil production marked the sessions and paid close attention throughout to a notable series of highly technical papers. Restricted as the program was to consideration of production problems only, the time proved too short for discussion or even the presentation of the 20 papers submitted. Much informing and pertinent discussion none the less took place, and the sentiment was general to the effect that the meeting was one of the best ever held by the Division. The meetings were held in the auditorium of the Municipal building and local arrangements were well looked after by the Mid-Continent Section of the Institute and the Oil and Gas Association. The combination of the three organizations served to bring together engineers and operators most usefully. F. Julius Fohs, chairman of the Division, presided at the sessions on Monday. Tuesday morning John M. Lovejoy of the local section took over this responsibility in the absence of T. E. Swigart, who was detained in California. The afternoon session was presided over by A. G. Heggam of the Oil and Gas Association and the Tuesday evening banquet by W. C. Franklin of the same organization.

Jan 1, 1926

By A. C. Fieldner

COKE and by-products have prime importance in the war program. The past year was marked by the construction of new and the rehabilitation of old by-product and beehive ovens and by the increase of production from existing plants to practically 100 per cent capacity. W. T. Brown's paper, "Plan to Improve Blast-Furnace Coke," presented at the Fuels Conference in St. Louis, Sept. 30, showed how the blending of low- and high-volatile coal improved the physical properties of coke and that improvement of the quality and uniformity of coke favored an increase of blast-furnace capacity- a vital need in the war program. Others in the industry have likewise increased production of coke or recovery of by- products by various innovations or changes in operation. Recognition of the value of pooling these developments for the benefit of the entire industry led to organization of a survey of coke- oven plants and blast furnaces by the Bureau of Mines in co-operation with the Solid Fuels Co-ordinator with a view to improving metallurgical coke production and recovery of by-products. This survey is being conducted with the help of an advisory committee consisting of representatives of the Bureau of Mines, the Solid Fuels Co-ordinator, the War Production Board, and the blast-furnace, coke-oven, and coal-mining industries.

Jan 1, 1943

[Executive HERBERT G. MOULTON, Chairman WILLIAM WRAITH, Vice-Chairman ,PAUL D. MERICA W. M. PEIRCE H. Y. WALKER Finance H. T. HAMILTON, Chairman ERLE V. DAVELER HENRY KRUMB Admissions FELIX E. WORMSER, Chairman GEORGE D. BARRON, Vice-Chairman CHESTER A. FULTON PHILIP KRAFT EDWARD MEAGHER Alternates P. B. BUCKY LLOYD C. GIBSON F. T. SISCO]

Jan 1, 1940

Executive DONALD B. GILLIES, Chairman WILLIAM WRAITH, Vice-Chairman ERLE V. DAVELER PAUL D. MERICA W. H. PEIRCE Finance H. G. MOULTON, Chairman H. T. HAMILTON HENRY KRUMB Admissions CHESTER A. FULTON, Chairman GEORGE D. BARRON, Vice-Chairman A. B. JESSUP PHILIP KRAFT EDWARD MEAGHER Alternates P.B. BUCKY SAMUEL HASKELL F. T. SISCO

Jan 1, 1939

By W. E. Wrather

SERIOUS consideration was given by the Petroleum Division to a wide variety of subjects, during six busy sessions at the Annual Meeting. Beginning with a joint session on engineering research and production engineering, Tuesday afternoon, conducted by E. A. Stephenson and H. C. Fowler, problems of petroleum technology, domestic and foreign production, proved oil re- serves, economics, and stabilization were mooied almost without interruption until nearly everyone was "talked out,' and the meeting was adjourned at the end of the annual Petroleum Division dinner, late Thursday night.

Jan 1, 1933

By G. W. Nabor, A. S. Odeh

The effect of production history of a well on the results of two-rate flow tests, and conventional build-up analyses was investigated. The effect was examined by means of digital computers and an R-C network model, respectively, for wells with infinite and finite radii of drainage. For systems which behave as infinite, it was found that production history and the duration of production at constant rate prior to the initiation of the test have important effects on the results. During build-up time equal to about one-fourth of the stabilized time, correct permeability-thickness product calculations can be made. For wells with finite radii of drainage, the time was determined during which the straight line can be satisfactorily used for permeability-thickness product calculations in case of drawdowns and build-ups. On build-ups, the dimensionless time (based on the external radius) during which the straight line gives reliable results was detertriined to be about 1/12. This is one-fourth as long as that of the drawdown. The investigation was done theoretically, and subsequently was verified by R-C network model runs. General interpretive rules were formulated which, if not followed, could lead to serious errors. Moreover, a recommended testing procedure is reported. INTRODUCTION The method used by most reservoir engineers for estimating formation characteristics in a producing well is the analysis of pressure build-up data. The method originally devised by Horner' makes use of the point source solution to the diffusion equation. This solution is approximated by a logarithmic function and the superposition principle is employed to arrive at the well known pressure build-up equation:where q, the flow rate, is in reservoir B/D; ft is in cp; kh is in md-ft; At is the shut-in time; and t is the producing time. At and t are in any consistent time units. Ey. 1 is applicable to a well of unlimited drainage radius which produces at a constant rate q from zero to time t and is then shut in. Such a constant production rate seldom obtains in practice. Therefore. a correction term must be applied to Eq. I to account for the varying rate. Two theoretically accurate methods are available for treating the variable rate case. The first, originally derived by Horner,' is based on the application of the superposition theorem. It requires knowlege of production history of the well as a function of time and results in lengthy and laborious calculations. The second t*q* niethod is suited for short production tests and requires that the shut-in time be at least one and one-half times the production time. A third method which is not based on any theoretical justification and which was suggested by Horner as a "good working approximation" is the one used by the majority of reservoir analysts. especially when the well has been producing for a long time and the t*q* method is not practicable. The key to this method is in choosing or determining the t that appears in Eq. 1. Horner suggested using a corrected time t, in place of t. t, is calculated by dividing the total cumulative production by the last established rate. Therefore, a normal procedure of pressure build-up testing is to stabilize the well at a constant rate for at least 24 hours before shut in and to use the stabilized rate to calculate t,. The analysis is then made by plotting either or P. and examining the resulting plot for the expected straight line to calculate kh and the original reservoir pressure. Recently, Russell" proposed a method for determining formation characteristics from two-rate flow tests. His method reduces to pressure build-up if the second flow rate is zero. Russell uses the Horner simplified procedure for calculating a corrected t,. His method also requires the stabilization of the well at a constant rate q which is used to calculate t,. Theoretically, the above procedure is valid for a well with an unlimited radius of drainage or with a limited radius as long as the boundary effect has not been felt by the well. Several authors'' derived formulas which allow the estimation of time during which limited reservoirs behave as infinite ones and, thus, can be treated by unsteady-state mechanics. One equation derived by Swift and Kiel' terminates the application of unsteady-state theory when the drainage radius reaches one-half the reservoir radius. Thereafter, steady-state behavior obtains. Another equation derived by Jones'" initiates steady-state

Jan 1, 1967

ALABAMA Aldrich -Thomas, D A Altoona -Cain, J Anmston-Cowie, L K Walmsley, W N White, H E Bankhead -Terentieff, V E Bessemer -Abbott, C E Ball, E M McKenzie, W C, Jr Mitchell, F R Morgan, C Thompson, N E Birmingham -Adams, J H Adler, J E Aldrich, T H Aldrich, T H , Jr

Jan 1, 1923