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During the year terminating at the date for the third annual meeting of Engineering Foundation, the Board completed, its undertaking to sustain the National Research Council for one year. Assistance given in the organization of the National Research Council has been amply justified by the results. The Council is now well established in a 4¬story building at 1023 16th Street, N. W., Washington, and has recently secured another similar building near by in order to house its increasing force. The breadth, importance and volume of work done have steadily grown. Foreign offices have recently been established in London and Paris, Dr. H. A. Bumstead being in charge of the former and Dr. William F. Durand of the latter. The total expenditure by Engineering Foundation for the National Research Council was $9,036, derived partly from income of the endowment fund and partly from special gifts from Ambrose Swasey and Edward D. Adams. In May, Walter M. Gilbert was appointed Assistant Secretary of Engineering. Foundation, with headquarters in Washington, his services being contributed by the Carnegie Institution. He also became and has remained to date Assistant Secretary of the National Research Council. In September, resolutions were exchanged between the Engineering Foundation Board and the National Research Council, setting forth a policy of continuing reciprocal relationship, and a conference committee, Chairman M. I. Pupin, Dr. Charles Warren Hunt, and Gano Dunn, was appointed to inform the National Research Council of the readiness of Engineering Foundation to work upon definite problems sug-gested by the Council. No problems have yet been suggested.

Jan 5, 1918

By E. E. Thurlow

The Geology Div. of Northern Pacific Railway Co. has adapted to its exploration efforts field procedures for geochemical sampling and semi-quantitative analysis which have been developed through research by the U. S. Geological Survey. The sampling is done in conjunction with reconnaissance geologic mapping on aerial photographs or during field checking of maps which have been prepared largely by photo-geologic interpretation. Stream sediment or soil samples are taken and readily soluble combined heavy metals are extracted with ammonium citrate followed by colorimetric titration with dithizone at the sample site. The effectiveness of this approach has been demonstrated both in positive and negative results, thereby assisting in the elimination of large areas of land from further immediate attention and in providing targets for followup exploration. An occa sional sample is submitted for spectrographic analysis as a check on the possible presence of other elements of economic significance. Field laboratory procedures are also being implemented for determining molybdenum, mercury, and other metals which may be valuable in themselves or useful as pathfinder elements in outlining mineralized areas. A lead-zinc occurrence in Oregon and a copper deposit in Montana were readily detected and outlined by stream sediment and soil sampling and a heavy metal anomaly that lacks obvious interpretation has been found in northwestern Montana. Detailed mapping and additional sampling are followed by other exploration techniques if warranted. Northern Pacific's program of reconnaissance mineral evaluation of company-owned lands and adjoining areas was outlined in a paper presented at the American Mining Congress meeting in Las Vegas four years ago. That report included policies and procedures with respect to mineral development on Railway Co. lands and may be referred to for information on these matters.1 In a sense this paper is a progress report on the use of geochemical prospecting in Northern Pacific's continuing mineral evaluation program. At this time there are positive results but as yet there is no real success story in the form of a minable ore body. GEOCHEMICAL PROSPECTING PROCEDURES The decision to use geochemistry as a reconnaissance exploration tool must be followed by research into sampling and analytical methods and into the interpretation of results. Various analytical methods were tried and evaluated by the Geology Div., including hot and cold acid extraction with and without fusion of the sample, panning and magnetic separation followed by dithizone testing of the magnetite, and cold aqueous extraction of metallic ions followed by indicator tests. Samples were first sent to the laboratory for analysis; later field laboratories were established and now virtually all testing is done at the sample site. It was concluded that, where applicable, the quickest dependable methods for reconnaissance use are the dithizone field tests for readily extractable heavy metals. This involves the simultaneous treatment of a sample, usually of soil or stream sediment, with two immiscible liquids; one a cold aqueous extractant (ammonium citrate) and the other a solution of dithizone in toluene or xylene.2 Dithizone is a colorimetric indicator that reacts quantitatively with copper, lead, zinc, and several other metals to form colored complexes in organic solvents. Results may be expressed in ml of 0.001 pct dithizone that are required to reach the blue end point, or calibration of the test results can be carried out with standard solutions of zinc; conversion factors would then be expressed in ppm, zinc equivalent. Calibration of dithizone solution with zinc standards indicates that 1 ml of 0.001 pct dithizone is equivalent to approximately 0.25 ppm of zinc. An authoritative report on dithizone field tests authored by H. E. Hawkes in the June-July 1963 issue of Economic Geology* states "The appeal of these techniques has been the simplicity and speed of the determinations as compared with more tedious laboratory determinations of trace metals in weathered rocks, soils, or plant materials. This obvious appeal, however, has often been more than matched by misuse of the method in such a manner that the results are

Jan 1, 1964

Discussion of the paper of FRANCIS S. PEABODY, presented at the St. Louis meeting, October, 1917, and printed in Bulletin No. 125, May, 1917, pp. 775 to 781. THE CHAIRMAN (CARL SCHOLZ, Chicago, I11.).-Coal wastage is undoubtedly one of the most prominent topics before the coal operators of the United States today. Even those who have been in the business only 25 years, like myself, know that the exhaustion of coal is something that should and must, be curbed. If it is not, before long we shall discover that the great coal resources of the country are not what we-thought they were; we have been so accustomed to work at the best and thickest coal alone, that it will be difficult for us to realize one of these clays-and that (lay is not far distant-that we are no longer the rich nation in coal that we thought we. were. In this connection I feel obliged to attach a little blame to the Geological Survey for misleading the people. There are several members ,here who assisted in that work, and I am going to ask them to defend themselves. The Geological Survey deals with coal seams of much less thickness than we could now expect to, mine, particularly with the present high wages, excepting at a prohibitive cost. The Geological Survey, in its estimates, does not discriminate between thick and thin seams, but simply estimates our resources at so many hundred thousand billion tons of coal. I believe they include seams from 15 to 18 in thick, but you all know that a vein below 3.5 or 4 ft. is not considered economical to mine at this time. R. V. NORRIS, Wilkes-Barre, Pa.-Mr. Peabody has evidently been thinking almost entirely of Illinois conditions, with which I regret to say I am absolutely unfamiliar. In some West Virginia mines the total recovery at present is considerably over 90 per cent. and extraction-, as high as 97 or 98 per cent. are claimed.

Jan 1, 1918

By O. F. Walker, W. C. Hahn, V. A. Johnson, J. D. Wood

The diffusion coefficients of zinc in single-crystal zinc and carbon in single-crystal and poly crystalline nickel were measured by means of radioactive tracer techniques both with and without the application of ultrasonic vibrations under conditions such that the temperature of the sample was closely controlled. The results of this investigation indicate no enhancement of diffusion in any of the samples. It is suggested that previously reported enhancement may have been due either solely to temperature increases caused by ultrasonic vibrations or in combination with changes in the boundary conditions. A number of observations have been reported in the literature in which it has been implied or inferred that the application of ultrasonics enhances diffusion (see, for example, Refs. 1-5). The present study was undertaken in an attempt to observe this effect under carefully controlled conditions, particularly with regard to measurement and control of the temperature of the sample. Two different types of systems were studied; these were the self-diffusion of zinc and the diffusion of carbon in nickel. EXPERIMENTAL For diffusion with ultrasonic energy applied, the samples were included as part of a resonant ultrasonic system operating at 58.5 kcps. The ultrasonic generators used were rated at 100 and 250 w and could be tuned over a frequency from 10 to 100 kc. A PZT (lead titanate/lead zirconate) ceramic transducer provided the driving vibration. This system requires no metallurgical joining of the specimen to the acoustical transmission line since the ultrasonic driver and the follow-up section clamp the specimen in position by means of a constant pressure of 50 lb developed by an air cylinder. The ultrasonic driver and follow-up section, both made of titanium, were 4 in. in length from clamping point to the end in contact with the specimen. Using the relationship given by Mason,6 A = V/f, the resonant wavelength, A, in titanium is calculated to be 3.3 in. at a frequency, f, of 58.5 kc, taking the velocity of sound in titanium, V, as 1.95 X 105 in. per sec. The 4-in. driver and follow-up section, therefore, are each 4.0/3.3 =1.21 times the resonant wavelength. Clamping pressure must be applied at stress nodes of the transmission line in order to preserve resonance. Therefore, a specimen length of 0.58 times the wavelength in the specimen was required to place the clamping pressure application points at stress nodes exactly three wavelengths apart. A stress antinode was contained in the center 3 in. of the specimen. A small PZT ceramic disc attached to the follow-up section provided an output voltage proportional to the intensity of the standing wave. This output voltage was monitored on an oscilloscope and the ultrasonic system was tuned to resonance by varying the frequency until the output signal was a maximum amplitude. The amplitude of the output signal was maintained constant throughout the diffusion anneal. A split cylindrical stainless-steel chamber, which was purged with argon prior to and during the runs, was placed around the specimen. The chamber in turn was surrounded by a movable furnace whose temperature could be controlled to 7C. Heat exchangers were used to cool the driver, follow-up section, and ultrasonic transducer. Great care was taken to obtain the true specimen temperature in all cases. Several different methods were tried; the most successful was that in which the thermocouple was held in contact with the midlength of the specimen by means of an asbestos insulating pad and wire straps. In the case of zinc, single-crystal specimens of 99.999 pct purity were used. The samples were 0.25 by 0.25 in. square and of the proper length for resonance, that is 1.1 in. long with the c axis parallel to the long dimension of the specimen for the case of diffusion perpendicular to the c axis and ultrasonic motion parallel to the c axis, and 1.9 in. long with the c axis perpendicular to the long dimension of the specimen for the case of diffusion parallel to the c axis and ultrasonic motion perpendicular to the c axis. In each case, one of the rectangular faces was electroplated with a thin film of zinc containing Zn The constant pressure used to clamp the specimen in place in the ultrasonic system caused some deformation in some of the samples. For these samples the deformation was concentrated in either end of the specimen; thus, for all samples (both zinc and nickel) the center in. was cut from the specimen after the diffusion anneal to be used for sectioning and counting. The nickel single-crystal samples, of 99.999 pct purity, were used in the form of rods 0.25 by 0.187 by 2.07 in. long with the (100) direction parallel to the rod axis. The polycrystalline nickel samples of 99.97 pct purity had an average grain diameter of 0.007 in. and were used in the form of rods 0.25 by 0.125 by 1.87 in. long. The direction of ultrasonic motion was parallel to (100) direction (bar axis) for the single-cqstal samples and parallel to the bar axis for the polycrystalline specimens. A thin film of c14 suspended in methanol was applied to the diffusing face of the specimen. Two specimens were butted together lengthwise for each diffusion anneal to minimize oxidation. After diffusion, a precision lapping device similar to the one described by Goldstein7 and a radiation detector were used to obtain a plot of specific activity vs penetration distance for each specimen. (A scintil-

Jan 1, 1969

By G. H. Gronhovd, W. H. Oppelt

Complete gasification to produce synthesis gas for manufacture of synthetic chemicals and fuels offers possibilities for utilization of the vast lignite fuel deposits in the U.S. The design of a slugging, fixed-bed, pressure gasification pilot Plant is described. Results are presented for initial operation of the plant at moderate pressure and using low-temperature char as fuel. Gasification of solid fuels is becoming increasingly important in the future overall energy picture, both in this country and abroad. Snythesis gas from gasification of coal consists chiefly of carbon monoxide and hydrogen, and after suitable purification and modification this gas can be used in the production of synthetic ammonia, methanol, higher alcohols, and synthetic liquid fuels, or as a reducing gas in the metallurgical field.' Most synthesis gas used in this country is made from natural gas, petroleum oils, and refining tail-gases, but the direct gasification of coal will become more attractive as costs of petroleum oils and natural gas increase.' A gasification process designed for use with brown coal and lignite was developed by the German Lurgi Co. prior to World War 11. In this process a fixed bed of lump-sized fuel is gasified with steam and oxygen at pressures ranging from 370 to 440 psi. Effective heat exchange between the ascending high-temperature gases and the descending solid fuel results in low gas outlet temperatures, high thermal efficiency, and favorable oxygen consumption. Lurgi gasifiers are used commercially for the production of synthesis gas or as a substitute for coal gas in many countries, including Germany, Czechslovakia, Great Britain, South Africa, Australia and Pakistan.3-6 The chief disadvantage of the conventional Lurgi gasifier which operates under nonclinkering conditions is that large quantities of excess steam must be supplied with the oxygen-steam mixture to reduce the temperature in the fuel bed below fusion temperature of the ash. Most of the steam leaves the gasifier undecomposed with the product gas and, after cooling, produces large amounts of dilute liquor. Evaluation of fixed-bed gasification experiments using dry-ash removal indicated that by increasing the oxygen concentration in the oxygen-steam blast the temperature in the combustion zone could be raised high enough to operate under slagging conditions. 7-8 Operation of a fixed-bed pressure gasifier under slagging conditions would reduce the steam requirements and the volume of waste liquor and would increase the steam decomposition, the overall thermal efficiency of the process, and the rate of gas production per unit cross sectional area of the gasifier. Because the Lurgi gasification process, modified for slagging operation, offered possibilities for efficient gasification of American lignite, the Bureau of Mines decided to investigate the process on a pilot-plant scale at the Grand Forks, N. D., Lignite Research Laboratory. DESIGN Description of Pilot Plant: A flowsheet of the Grand Forks slagging gasification pilot plant is presented in Fig. 1. The gasifier unit consits of the coal lock, the gas generator, and the slag lock. The fuel, which is periodically charged to the coal lock, moves by gravity flow into the generator and is continuously gasified by an oxygen-steam mixture introduced at the bottom of the gasifier. Molten slag is formed at the hearth and flows through a central taphole into a water quench bath. The slag-water slurry is periodically discharged from the slag lock. Process steam is generated and superheated in separately-fired, oil-burning units. Oxygen is supplied to the gasifier from a gas storage bank located some distance from the pilot plant. The capacity of the oxygen storage bank is about 130,000 standard cu ft at 2200 psig. Liquid oxygen is delivered by truck and is converted to gas during the filling operation. The superheated steam and oxygen are metered separately, then mixed and fed to the gasifier tuyeres. The gas generator is surrounded by a water jacket. The steam formed is separated in the steam drum and then discharged to the gas offtake, thus equaliz-

Jan 1, 1961

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

By S. Arthur Krom

(New York Meeting, February, 1912.) THE James diagonal-plane slimer is specially adapted to handle the finest slimes, but it will also handle sands as coarse as 40-mesh. The saving efficiency of this machine is due to the original construction of the deck, and to the rapid reciprocating movement imparted to it by the head-motion. The deck consists of a plurality of connected planes, having a certain fixed ratio of inclination one to another. These planes intersect each other diagonally to the stroke-line of the table and are arranged so as to give the pulp on the table a double treatment. This double concentration performed by the diagonal-plane deck produces cleaner concentrates and tailings than those obtained by the operation of two separate machines. The action of the diagonal planes settles, combines, and holds all the concentrates in one compact mass, sharply defined from the gangue, and easily cut away without loss. Many slime-concentrating machines distribute the feed-pulp for a distance of 4 or 5 ft. only, and upon a very limited settling-surface. This results in a thick, heavy deposit, from which it is impossible to stratify the values and wash, away the gangue, the resulting products being dirty concentrates, and tailings carrying high values. The diagonal-plane slimer distributes the feed-pulp for a distance of 10 ft., and upon a settling-surface having an area of 40 sq. ft.; in other words, it spreads the pulp thinly on the table, which allows the metallic values to settle through the gangue quickly, forming a bottom stratum from which the thinly-distributed overlying stratum. of gangue is easily brushed away by the feed-water without disturbing the underlying concentrates. Referring to Fig. 1, plane A is the main settling-section, of the table. The feed pulp flows gently down this plane and is

Jun 1, 1912

By P. E. Arnold, G. S. Ansell

RELAXATION in metals has been studied in detail by many workers in recent years.1-5 These studies have shown that there is an energy-loss peak observed in a metal placed in mechanical resonance at low frequencies which may be correlated with various metallurgical processes. These experiments have been largely used to study single-phase materials. In order to study the effect of a finely dispersed second phase in a metal matrix upon this phenomenon, the relaxation behavior of an aluminum-aluminum oxide SAP-Type alloy in both the fine-grained as-extruded and coarse-grained recrystallized conditions was investigated by the use of internal-friction measurements. The alloys studied, designated MD 2100, consist of a matrix of commercial-purity aluminum containing a finely dispersed second phase of aluminum oxide. The aluminum oxide is present in this alloy in the form of fine platelets approximately 130A units thick and several microns on edge. The mean free path betwen dispersed platelets is approximately 0.5 p. The grain size of this alloy is extremely stable at temperatures as high as the melting temperature of the aluminum matrix. In the as-extruded condition the grain diameter is several microns, while in the recrystallized condition it is several millimeters in diameter. The damping characteristics of the alloy samples were determined using a torsional-pendulum device. The internal-friction constant was determined for this alloy in both the fine-grained as-extruded and coarse-grained recrystallized conditions over the temperature range from 343" to 923°K at frequencies of 0.9, 1.3, and 1.8 cycles per sec. An internal-friction peak was observed in testing the fine-grained alloys which was not observed for the coarse-grained alloys. This peak, which might be associated with a type of grain-boundary relaxation, was observed at each of the three different test frequencies for the fine-grained sample. The temperature at which the relaxation peak occurred for each of the three different frequencies is shown in Table I. From these data an activation energy of relaxation for each pair of frequencies was determined by comparing the temperature shift of the relaxation peak with frequency between each of the test frequencies, assuming that an Arrhenius-type rate equation is applicable. The activation energy of relaxation determined from these data is also shown in Table I. The mean value of the activation energy was about 6 kcal per mole. The activation energy for the relaxation process determined in this investigation indicates that the relaxation associated with the grain boundaries in this aluminum-aluminum oxide SAP-Type alloy is quite a different process than grain boundary relaxation in single-phase aluminum alloys. In these latter alloys, the activation energy for relaxation has been found to be the activation energy for self-diffusion, approximately 36 kcal per mole1,2 Where the activation energy is the same as the activation energy for self diffusion, it has been proposed that the relaxation phenomena is dependent upon vacancy formation and motion. It is apparent therefore, that, in this aluminum-aluminum oxide SAP-Type alloy, the relaxation must be due to another type of atom transport. It has been shown previously in studies of the high-temperature, low-stress, steady-state creep behavior of as-extruded aluminum SAP-Type alloys, that the activation energy for steady-state creep is one that may be characterized by the nucleation of dislocations from the grain boundaries. It is proposed that the relaxation behavior observed here is due to a similar effect. In this case, the internal-friction peak is a resonance behavior due to the time-dependent nucleation of dislocations from grain boundaries in the sample. A process of this type would have an activation energy which is undoubtedly stress-dependent and of the form Q = Q, + (dQ/du)u

Jan 1, 1962

By A. F. Witt, A. M. Gaudin, A. K. Biswas

Finite contact angles in the rutile-water-organic liquid system are traceable to contamination or are due to addition of a surface-active agent. Finite contact angles are invariably accompanied by hysteresis.1-7 Besides surfactant concentration and pH, the nature of the organic liquid is found to be a factor influencing the magnitude of contact angle hysteresis. In a recent paper the authors have reviewed principles and applications of measurement methods for contact angles and their hysteresis.22 In this paper, these methods are applied to a system consisting of rutile, an organic liquid (benzene, decane, or dode-cane) and water. Surfactant (dodecylamine hydro-chloride) was used at various concentrations and various pH values. MATERIALS A synthetic rutile crystal supplied by the Linde Co. was used. It is a cylinder 1/2 in. diam, with faces cut perpendicular to the c-axis. The crystal is stated to be alumina-free and to be 99.9% pure. Rutile is a high surface energy solid, its calculated average field strength being 2.7 x 105 e.s.u.,9 its dielectric constant10 is 114. The zero point of charge of rutile was measured11 and found to be at pH 6.0. The atomic distances and bond angles of the tetragonal crystal of rutile have been precisely determined.l2 The organic liquids were specially purified. Reagent grade benzene was repeatedly shaken with concentrated sulfuric acid to remove thiophene, then neutralized with sodium hydroxide solution, rinsed with distilled water, dried overnight over anhydrous calcium chloride and filtered. The refractive index of this chemically purified benzene was 1.4977 (at 25°C) - very close to that of pure benzene (n25 1.4979).13 Both n-decane and n-dodecane were washed with aqueous sodium hydroxide, concentrated sulfuric acid (repeatedly, until the acid layer was colorless) and again with alkali, to free the organic hydrocarbon from fatty acids and unsaturated hydrocarbons. The organic phases were subsequently washed with distilled water and dried over anhydrous sodium sulfate. The filtered hydrocarbons were then distilled under vacuum (9-10 mm pressure). Decane, thus purified, showed traces of unsaturated and of carboxylic compounds. On gas chromatographic analysis the purified n-dodecane showed the presence of two impurities. However, the relative retention times of these components did not change substantially when measured on a polar or a nonpolar column. This indicates that the compounds were probably in the same polarity class, i.e. the components were nonpolar like dodecane. Conductivity water has always been one of the liquids. Conductivity of the water used was 10-6 ohm-' cm". Dodecyl ammonium chloride was prepared from pure amine (supplied by Armour and Co., Chicago), by Li in the MIT Mineral Engineering Laboratory.14 The critical micelle concentration at 25°C is known, 0.0138 mol per liter15 or 3.06 gpl. All our experiments have been done at concentrations lower than the critical micelle concentration. The glass vessels, glass drop holder and the rutile crystal were all cleaned with hot chromic acid followed by distilled water, concentrated hydrochloric acid, and again distilled water, and conductivity water. During the experiments, a nitrogen atmosphere was maintained. For this purpose, commercially purified nitrogen was further purified by passing it over hot copper wire at 450°C, then through columns of acidic chromous chloride solution, concentrated alkali solution and distilled water. APPARATUS AND METHODS Hysteresis was produced by the "captive drop" or constant volume drop method as well as by the "expanding-contracting drop" or variable volume drop method. The image of the drop while it is expanding, contracting or moving is projected on a screen and photographed. The developed film is projected through an enlarger and the contact angles measured with a protractor.

Jan 1, 1964

By C. W. Hoffman, W. R. Hinken

Probability sizing, a fairly recent development in the field of particle separation, is now under investigation to determine its value to the mining industry. The method employed is probability sizing through a vibrating network of decreasing screen openings. While probability sizing is not new, the possibility of using it for coarse, highly abrasive ores at high tonnage rates has only recently appeared to merit practical consideration. The advantages of probability sizing vs. conventional screening methods are: (1) reduced space requirements for a high capacity unit, (2) fewer moving parts, (3) more versatile product sizing selection, (4) reduced maintenance requirements, and (5) lower power consumption. Screening is a necessary part of virtually every crushing circuit. At some stage in the process, particle separation becomes a controlling factor in the operation. The basic type of screen in use today is the vibrating unit, which usually employs a mechanical vibrator of one type or another to obtain sizing and material transportation across the screen surface. The vibrating screen has its limitations and inherent problems. Operators must live with: (1) high maintenance — worn rods, screen cloth, spacers, cross members, chutes, etc., (2) low capacity in relation to floor space requirements, (3) extreme noise levels, (4) high power consumption, and (5) structural problems in the screens and supporting steelwork. All plant operators have become tolerant of these drawbacks through the years, and little innovation has been developed in screening. The vibrating screens in use today incorporate improved metals, more efficient power sources, better lubricants, and increased manufacturing skill, but the basic machine itself remains unchanged. Screening is a relatively small part of most plants' operating expenditures and gets relatively little attention from research and development. The HiProb sizer is a new approach to the problem of particle separation on a high tonnage basis. Developed by Dr. Fredrik Mogensen (president of Fred-rik Mogensen, A. B. of Djursholn, Sweden), this unit has found its primary acceptance in the sizing of wet or dry materials in the fine ranges. Climax has been working cooperatively with Mine and Smelter Supply Company, the United States licensee, on the adaptation of the sizer to obtain consistent recovery at a high tonnage rate on a — 3/8-in. separation. This was a new application for the sizer and opened up a whole new field of problems. Dr. Mogensen's machine utilizes the control of normal probability of falling particles and is designed to eliminate some of the undesirable features of vibrating screens mentioned earlier. The machine is light, compact, consumes less power than conventional screens and has a low noise level. PRINCIPLES Probability sizing is a process designed to allow solid particles to segregate with a high ratio of the materials reporting into their respective size fractions with a minimum amount of misplaced particles. Sizing is defined in this paper as segregation of dry solid particles into fractions of comparable sizes. Probability is usually estimated as the ratio of the number of ways an event might occur vs. the total number of allowable ways. The probability process described depends upon the fact that particles falling through a network will segregate across the sizing surface even though all openings are larger than the particles. The degree of segregation is dependent upon the particle size and the trajectory applied by the sizing network to each falling particle. Specifically, the process utilizes a maze made up of screen cloth to control the path of a particle in free fall as illustrated in Fig. 1. The usefulness of this probability sizing process is dependent upon the degree of efficiency of an effective maze. Primarily, a maze must be extremely flexible to meet the multi-faceted nature of solid particles and, at the same time, the degree of control must be reproducible so that a desired separation is predictable. Dr. Fredrik Mogensen has formulated a maze that is not only flexible and easily controlled, but, mote importantly, easily adaptable to a working machine.

Jan 1, 1970

By John V. Beall

There was optimism on 14th Street on April 22, Earth Day. We only have the report second hand because the demonstration conflicted with another appointment. Fifth Avenue was closed to vehicular traffic from 14th Street to the Park for a few hours and the crowd that showed up to promenade rivaled anything that can be imagined, even one at a country fair in Merry Old England. Certainly the domestic animals were there and the costumes were wild-as they are almost any day on 5th Avenue. However, the mood was friendly, happy and optimistic according to one of our neighbors who filmed and taped interviews with some of the characters. People think the air is going to be clean, and the water pure in the future. Land is going to be treated with respect. Even if the demonstration temporarily fouled the streets with litter, it served the purpose of dramatizing awareness. In talking to our friend about his experiences we didn't miss the opportunity to sound out his impression of whether or not people recognize that no group of people nor industry has a monopoly on pollution.

Jan 1, 1970

By Friedrich Wellmer

INTRODUCTION The Ramsbeck Pb/Zn Mine is located in the northern Sauerland area of West Germany, 150 km N of Frankfurt and 120 km E of Cologne. This is a vein deposit which has been worked from the middle of the 19th century to 1974. About 15 million tons of ore were mined and milled. The ore district contains several vein deposits and is roughly 14 km in length and 4 to 5 km in width. The host rocks are strata of Lower Middle Devonian age. The strata strike 60° to 70° NE and where overturned have a dip steeper than the veins (Fig. 1). The galena-sphalerite mineralization is in quartz veins, which are mineralized where they cut the "Main Ramsbeck Quartzite" horizon, a very competent host rock. Vein structures strike at 65º to 75º, dip about 20° to 25º SE and cut the quartzite at approximately 60 m intervals. The main or "steep veins" within each vein structure dip at 10º to 80° SE with an average of 30° and are offset by thrust faults dipping 5º N to 40° S with an average of 5º S. "Flat veins" usually weakly mineralized occur in the thrust faults between the "steep veins", thus forming the overall step-like vein structure. The mineralization is very irregular and changes a- long strike and down dip. It consists of thin veins of pure sphalerite and galena with quartz and pyrite. The thicknesses of the pure sphalerite and galena veins

Jan 1, 1977

By S. K. Mitra

A refinement of the Seeger model for intersection process is investigated which is in better agreement with experimental observations than the original. It is shown that, in single crystals, the strain hardening in Stage II is mainly due to the short-mnge interactions when intersection is the rate-controlling process. It is also demonstrated that the creep curves, as predicted by this theory, are in good agreement with the experimental observations. MOTT: Cottrell? and Seeger have developed an approximate theory for plastic deformation of single crystals over the range of variables where the strain rate is controlled by the rate of intersection of dislocations. Although it is now generally agreed that the low temperature deformation of many pure metals is controlled by the intersection mechanism, various dictates of the over-simplified Seeger model are not in good agreement with all the experimental facts. It is the purpose of this paper to reveal that by appropriate extensions of the Seeger model, particularly those suggested by Basinski: a much more reliable theory results. The refined model to be presented here will be shown to account, in a satisfactory way, for the effect of stress, temperature, and strain on the creep rate under constant stress and for the effect of temperature and strain on the flow stress in constant strain-rate tests. EXPERIMENTAL METHOD To Check the theoretical deductions, both creep and tension tests were conducted on single crystals of high-purity Al (99.994 pct Al) so oriented that both the active slip plane and the Burger's vector of the operative dislocations on that plane made angles of about 45 deg to the tension axis. Single crystals of aluminum (5/8 in. by 1/10 in. by 8 in.) were grown in a graphite mold under an inert atmosphere using the Bridgman method. The chemical composition of the aluminum is given in Table I. A common seed was used for all crystals and their orientation is shown in Fig 3. The extensometry consisted of two differential transformers with matched outputs mounted so as to measure the extension in a 2 in. gage length. The amplified difference in output of the two transformers was recorded by a potentiometer. The amplification was calibrated before each run so that one chart division of the recording potentiometer indicated a 105 shear strain on the specimen. Stresses were measured to the nearest 1 x l04 dynes per sq cm. ACTIVATION VOLUME The concept of Basinski that the activation volume is not constant but is a function of the force that aids thermal fluctuation in effecting the cutting of dislocations will be adopted in this section. The force acting due to an applied shear stress on the dislocation being intersected is where L is the mean spacing between the forest dislocations, is the Burger's vector and T is the back stress. A detailed discussion about the origin of back stress will be taken up later in this report. As shown by Basinski, the activation energy, U, that must be supplied by a thermal fluctuation in order to effect intersection, is equal to where x is the distance through which the dislocation must be translated for complete intersection, and Fm is the maximum force encountered in intersection. When the applied stress is decreased abrupt ly F also decreases and the activation energy increases correspondingly as documented in Eqs. [ 1 ] and [2]. The Seeger equation for the strain rate when the deformation is controlled by rate of intersection of where the shear strain rate (per sec) N = the number of points per unit vol at which intersection can take place

Jan 1, 1962

Jan 1, 1934

By H. Wilton Clark

VARYING in thickness and in number from place to place, coal seams in the Canadian Rockies also range in pitch from nearly horizontal to vertical, sometimes with overturns. Over the entire coal-bearing area there are considerable differences of rank in coals of the same geological age, and there are marked differences in ash content and wash-ability characteristics. Correlation of seams at mining operations within a few miles of each other has often proved impossible. These factors influence mining methods, and, of course, production results. The oldest coal formations of western Canada are of Lower Cretaceous age, as the carboniferous sediments are marine and contain no coal. Coal is also present in formations of Upper Cretaceous and Tertiary ages. The rank of coal varies from semi-anthracite in some operations in the Kootenay and Luscar formations of the Lower Cretaceous in the Rockies to lignite in the Tertiary fields of the Saskatchewan prairies. Fig. 1 shows the general extent of the formations. The pitching seams, chiefly Lower Cretaceous, occur in the western belt of the Rocky Mountain foothills and the eastern slopes of the Rockies themselves. (The road to Tent Mt. strip pit, elevation 7000 ft, is shown on p. 832.) Formations extend from the U. S.-Canadian boundary for several bundred miles in Alberta and continue for a similar distance in British Columbia. Present geological estimates show a probable reserve of the order of 25,000 million tons of coal ranging from high volatile bituminous to semi-anthracite, with a large percentage of coking coal, constituting one of the major world reserves of that type. It should be noted that although the quoted estimate probably errs on the conservative side, the question of access to the seams in a mountainous terrain will always be a problem; a wide divergence may exist between actual reserves and the quantities of coal economically recoverable. An excerpt from the Canadian government Report of the Royal Commission on Coal 1946 states that conditions favorable to coal formation were intermittent and these intervals relatively brief in comparison with periods in which no coal was formed. Conditions were favorable to the growth or accumulation of vegetation in one area, while fresh water sediments and marine shales were being deposited in other areas. During periods of emergence the coal deposits were subjected to erosion or were covered by coarse sands and gravels from the mountains, whereas during submergence they were covered by fine clays deposited in embayments of the sea. During some of the periods of coal formation, volcanic activity deposited beds of fine volcanic ash and dust with the coal-forming vegetation. Coal deposits reach their greatest development in the mountains and thin rapidly to the east into the plains area, where they are deeply buried beneath younger sediments. For example, in the Fernie area of southeastern British Columbia there are in places 22 seams having an aggregate thickness of 150 ft in a stratigraphic interval of 3500 ft, whereas at Cole-man in the Alberta Crowsnest area the measures are only 800 ft in thickness and contain a maximum of five seams aggregating about 47 ft of coal. At Belle-vue, 10 miles further east, the measures are reduced to 430 ft with only three seams aggregating about 37 ft of coal. Subsequently the tremendous forces involved in the upthrust of the Rocky Mountains produced great displacement of the coal-bearing formations and at the same time a change in geologically young coals from low to high rank. The floor or footwall of most seams consists of carbonaceous shales, which are almost as adaptable to bending as the coal seams themselves. The seams show very few cleats or cleavage planes and have been so weakened structurally that as mined 50 pct or more will pass through a ¼-in. screen, seldom

Jan 1, 1955

By L. H. Robinson

A proposed method of drilling utilizes sequential detonation of two types of explosive charges delivered to the hole by a conventional drilling fluid through pipe. A shaped charge first produces a long thin hole. A second charge, called a gauging charge, is pumped into the thin hole, explodes, and enlarges it to full gauge. In one suggested configuration, the explosives are contained in cylindrical capsules 4- to 5-ft long. A drilling head is positioned 2- to 3-ft off bottom. When a capsule is pumped to the bottom of the hole and stops, pressure inside the drill pipe increases and differential pressure detonates the explosive. Primacord along the length of the capsule disintegrates the capsule. The debris circulates out of the hole with the drilling fluid. The gauging-charge action was examined using 2-ft cubes of Berea sandstone. The sandstone (18 per cent porosity) was vacuum-saturated with water and surrounded by concrete. To prevent reflected tensile pulses, the acoustical impedance of the concrete matched that of the sandstone. A 750-psig pressure was applied to a drilling fluid within a shaped-charge-formed hole before detonating the gauging charge. In these tests, 190 gm of rock were removed for each gram of explosive detonated. A similar series of experiments on low-porosity (0.40 per cent) metamorphic limestone provided a more rigorous test. Extensive fracturing from the gauging-charge action prevented an estimate of the volume of the expanded hole. The diameter of the hole was irregular, ranging from about 2 to 4 in, or about fivefold larger than the hole created by the shaped charge. INTRODUCTION In the past, explosives have found a varied but somewhat limited use in the oil field. An early well stimulation technique, still in use today, in vo lves shooting ni troglycerin to en large the borehole and to increase matrix permeability near the wellbore. Bullets and jets are now the conventional method of perforating casing and tubing. Detonations are frequently used to "back off" or "shoot off" stuck pipe and, of course, seismo-graphic work has long depended on explosive-generated pulses to find attractive earth structures. Efforts to use explosives in drilling operations have received limited examinations1-3 which, in one respect, is surprising because explosives offer one way to transmit large amounts of energy directly to the bottom of the hole. Recently, Ostrovskii l described a Russian method of drilling with explosives that utilizes small capsules containing explosives which are pumped into the mud stream to the bottom of a borehole. As the capsules leave the end of the drill pipe, a detonation mechanism is armed. Impact detonates the explosive. In another configuration, two liquids (an oxidizing agent and fuel) in the capsule are separated by a frangible membrane. Separately, the liquids are nonexplosive. Near the bottom of the drill pipe, the capsule passes through a narrow constriction which ruptures the membrane. The mixing of the liquids produces an explosive. Impact is again used to detonate the explosive. About the time Ostrovskii was developing his method, Humble Oil & Refining Co. was independently doing research on another explosive drilling concept based on the sequential detonation of two types -of explosive charges. The proposed technique consisted of alternately pumping a shaped charge and then a "gauging charge" down a well. The shaped charge should drill a long, tapered hole, and the gauging charge should expand it to full gauge. This paper presents the visualized drilling concept and gives results of laboratory work which showed that sequential firing of charges can form hole at an attractive charge-to-rock removal ratio. An important finding was that increased environmental pressure, which is to be expected in wells, increases rock removal efficiency of the gauging charge.

Jan 1, 1966

By B. B. Cox

The principal event during 1936 was the sale of Mosul Oilfields, Ltd. to Mosul Holdings, Ltd., a British company with French and American participation, and the expansion of its wildcat activities to untested structures on its West Tigris concession. Mosul Holdings continued the exploration of its low-gravity Qaiyarah-Najmah-Jawan-Qasab field. The Iraq Petroleum Company's systematic exploration and exploitation of its Kirkuk field was continued on a scientific unitized basis. Pressures and gas-oil ratios remained satisfactory. All wells were produced by flowing. A stabilization plant large enough to supply the 4,000,000-ton pipe line to the Mediterranean was completed at Kirkuk about the close of the year and only sweet oil is now being exported. The Khanaqin Oil Co., Ltd., a subsidiary of the Anglo-Iranian Oil Co., Ltd., continued the normal exploitation of its Naft Khaneh oil field, refining and marketing through the Rafidain Oil Co., Ltd. for local Iraq market. This field lies partly on the Iraq side of the boundary and partly on the Iranian side, the latter portion being known as Naft-i-Shah. Only the Iraq side is considered in this paper. Slightly more than 30,000,000 bbl. of crude was produced in Iraq during 1936. The I.P.C. exported all crude sold outside of Iraq and showed an increase of about 2,500,000 bbl. over the preceding year. Crude production in Iraq for export in 1934 was 7,096,669 bbl.'; in 1935 it was 27,014,904 bbl. and in 1936 it was 29,521,053 barrels.

Jan 1, 1937

By W. L. Phillips

Single crystals of aluminum, brass, and copper oriented for (100) and (110) slip were extended at 25°, 400°, and 600°C in simple shear. Aluminum specimens oriented for nonoctahedral slip began to shear at a higher critical resolved shear stress than specimens oriented for octahedral slip. Parabolic stress-strain curves were obtained from zero strain. The initial rate of parabolic hardening was lower for specimens sheared on the (100) plane in a close-packed direction <110>, than for specimens sheared in a nonclose-packed direction <100>. metallographic evidence, however, showed that all slip traces could be explained in terms of (111) <100> slip. All attempts to cause nonoctahedral slip in copper and 70-30 a-brass single crystals were unsuccessful. Instead of shearing, the crystals bent, allowing {111} type planes to come into action. NONOCTAHEDRAL slip in aluminum has been reported under three different conditions: first, as the main mode of slip in tension experiments at elevated temperatures;&apos;-&apos; second, as the main mode of slip in direct shear experiments at room temperat~re; and third, as a minor mode of deformation, i.e., as cross-slip, in tension, shear, and bicrystal experiments at room and elevated temperatures."-l2 However, as far as the author knows, nonoctahedral slip has not been reported in either copper or 70-30 a-brass. The present study was undertaken to determine whether nonoctahedral slip could be obtained in aluminum, brass, or copper at room or elevated temperatures when the shear stress was approximately constant over the cross-section, a maximum at the center, or a maximum at the surface. EXPERIMENTAL PROCEDURE A detailed description of the crystal preparation and shearing apparatus has been given previo~sly. Cylindrical crystals 1/2 in. in diam and 8 in. long were grown from the melt in a temperature-gradient furnace. The aluminum contained 0.001 pct Zn, 0.001 pct S, and 0.001 pct Fe; the 70-30 brass contained 0.015 pct Pb, 0.001 pct Fe, 0.01 pct Ni, 0.02 pct Sn, and 0.005 pct Se; the copper was certified OFHC of 99.98 pct purity. All samples were electropolished prior to testing. The shear apparatus was a modified Bausch type. The strain sensitivity was 4 x lob4 Load was applied by clamping the rods attached to the shear plates in an Instron tensile machine. The rate of loading was 0.02 in. per min. In all cases a 1/8-in. gage length was used. For the tests performed at 400° and 600°C the shear plates, collars, and rods were made of stainless steel. These elevated-temperature tests were performed in an argon atmosphere. A) Aluminum at Room Temperature. Values of a and ß for the various slip planes and slip directions investigated are shown in Table I where a is the complement of the angle between the specimen axis and the slip direction, and ß is the angle between the specimen axis and the normal to the shear plane. The shear stress is a function of a (assuming ß - 0);10 when a is less than 27 deg, the shear stress on the slip plane for which the specimen is oriented has a maximum at the center of the crystal; at a = 27 deg the shear stress is constant across the slip plane; for a greater than 27 deg the shear stress is a minimum at the center. Fig. 1 shows the stress-strain curves for specimens cut from crystals 1, 2, and 5, which were sheared on the (010) plane in the [loll direction at room temperature. These three crystals have shear-stress distributions corresponding to the three dif-

Jan 1, 1962

By P. R. Smith, R. A. Walters

Borates have been mined in the desert areas of California and Nevada for more than 100 years. To about 1890, playa surface mining provided the chief sources of boron minerals. Underground mining of colemanite and later of borax and kernite was predominate until about twenty years ago. Open pit mining of the large deposits of borax and kernite near Boron, California has been most significant for the past twenty years. Mining of colemanite in the Ryan, California area, near Death Valley, began in 1907. Following the discovery of the large deposits in the Boron area (about 1957), mining in the Death Valley area became nearly nonexistent. Only small tonnages were mined for special uses. Little mining was done in the Boraxo area near Ryan. The first claim was made in about 1915. In 1960 the area became the property of the Kern County Land Company, which was acquired by Tenneco Oil Company in 1967. In 1976 the various boiate properties and claims in this region were acquired by American Borate Corporation. The open pit mine is now approximately 122 m (400 ft) deep, 910 m (3000 ft) long and 305 m (1000 ft wide). The borates in the Boraxo pit consist primarily of three minerals. These are about 50% colemanite (CB6011 5H20), about 40% probertite (NaCaB50g 5H20), and 10% ulexite (NaCaBgOg 5H20). The colemanite, along with boric acid and high-grade colemanite ore from Turkey provide the only sodium-free borates for production of textile grade fiberglas. When heated to its decomposition temperature, colemanite decrepitates to a fine powder, which is the basis for the concentration process. The gangue minerals in this deposit are primarily calcite and clays, including bentonite. The ore body has a very low arsenic content, which is a desirable feature. Test work had been done with samples prior to the results discussed herein. This paper will discuss results of test work which were the basis for erection of a plant, and the subsequent plant operations. Laboratory Calcination and Air Tabling Tests Laboratory calcination tests showed that substantial upgrading of the borate could be accomplished by calcining followed by screening of the calcined material. Removal of the + 28 mesh calcine resulted in borate losses of less than 10% with a rejection of 40 weight % or more of the calcine. The minus 65 mesh calcine generally met the requirement of containing 48%, or more, B203. The minus 28 plus 65 mesh material contained an intermediate quantity of borate and would require additional treatment. Testing demonstrated that ore would not have to be reduced to a size finer than 19 mm (3/4 in.) prior to calcination. A temperature range from 400 to 455OC (750 to 850°F) was apparently satisfactory. Calcination at a temperature of 48Z°C (900°F), or higher, was unsatisfactory due to fusion. All laboratory calcination tests were static tests conducted by placing small covered charges in a laboratory furnace for 40 min. In all tests vapor issues from the furnace for 5 to 7 min. Following this period the ore could be heard "popping," due to decrepitation of the colemanite. The reaction generally continued for approximately one-half hour. Various size fractions of the calcination products from laboratory tests were subjected to laboratory air tabling tests, usually after removing the plus 28 mesh material. Laboratory air tabling tests were conducted employing a Whippet V-80 model air table manufactured by Sutton, Steele and Steele Co. now known as Tripple S Dynamics. Variables include both end and side-tilt, speed of vibration, and quantity of air rising through the deck. In addition to the variables in the machine itself, the feed rate is also a rather critical variable. Testing demonstrated that all - 28 mesh size fractions of the calcine could be successfully concentrated to 48% F2O3 or greater. For the finer material recoveries into the concentrate were between 85 and 90% of the borate. With the coarser material a substantial amount of middling was produced which required cleaner tabling. Laboratory calcination and air tabling tests indicated a process whereby the borate could be concentrated to about 50% B203 with borate recoveries approaching 90%. Moreover, the iron content of the concentrate was well below the required specification of 0.3% Fe2O3. Pilot Plant Calcination Following the laboratory test work described above, pilot plant testing was conducted to prove the process, provide data for engineering studies, and provide product for a prospective purchaser. The kiln used was 0.9 m-diam (3 ft) by 9.0 m (30 ft) long and had a belly section 1.2 m-diam (4 ft) by 2.74 m (9 ft) long near the discharge end. The kiln was operated at a speed of 0.7 rpm. Gas was fired into the kiln at an average rate of 27.1 m3/hr (958.4 cu ft per hr). The air to gas ratio used was 10:1. The ore was fed to the kiln countercurrent to the flame and discharged through a hopper into a screw conveyor which discharged to a 1.2 m (48 in.) Sweco separator. The separator had 28, 65, and 150 mesh screen cloths, with the plus 28 mesh fraction being discarded. The minus 28 mesh fractions were later subjected to air tabling. The exit gases, containing some calcine dust, were swept through two cyclones to recover the dust. The gases then were scrubbed in a Ducon scrubber; very little dust reported past the first cyclone. The dust from the first cyclone was also saved in drums. In addition to the gas rate, the flue gas velocity, after

Jan 1, 1981

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by