Search Documents

By W. L. McMorris, Shiou-Chuan Sun

The Convertol process was first described in Ger- many by Muschenborn1 in 1952. In the U. S. Fraser2 reported this new process in 1953, and Brisse and McMorris-resented the results of a Convertol pilot plant at the Alpheus preparation plant in Gary, W. Va., illustrating the mechanics of the process by a series of sketches. The purpose of the present investigation was threefold: 1) to determine the relative effectiveness of various oils and hydrocarbons for recovering coal by the Convertol process, 2) to ascertain the behavior of coal pulps in this process under various operational conditions, and 3) to compare Convertol with flotation in the recovery of fine coals.

Jan 11, 1959

By R. Stefanko, Y. J. Wang, H. R. Hardy, R. Y. Kim

Since 1964, the Dept. of Mining at The Pennsylvania State University has been carrying out extensive studies associated with the phenomena of microseismic activity and inelastic behavior in geologic materials. Briefly, the program to date has involved the following stages 1) Study of the microseismic noise and energy rates for selected geologic materials under incremental, uniaxial tension.1,2 2) Investigation of the frequency spectra of microseismic activity of selected geologic materials under incremental, uniaxial tension.3,4 3) Investigation of the time-dependent inelastic deformation of geologic materials and the analysis of such deformation in terms of mechanical models.5, 6 4) Simultaneous study of microseismic activity and time-dependent inelastic deformation in geologic materials under incremental, uniaxial compression.7,8 Details of the research involved in stage 4 of the program constitute the subject of this chapter. It should be noted that the majority of the experimental data quoted in this chapter forms part of a thesis to be presented by one of the authors (Kim) in partial fulfillment of the requirements for the Ph.D. degree in mining engineering at The Pennsylvania State University. During the last two or three years, a number of important papers have been published which deal primarily with the fundamental structure and mechanical behavior of geologic materials. Recent papers 9,10 have provided research workers in the rock mechanics field with a meaningful overall picture of rock as a structural material. The concept that many

Jan 1, 1970

By Paul D. Merica, H. Hanemann

The application of other than mechanical methods to the study of the mechanical-physical properties of metals has become in the last few years a topic of investigation of ever-increasing interest, both from the theoretical standpoint and from that of the engineer and constructor. Besides the investigations which have been made of the magnetic properties of ferromagnetic metals, in their relation to the mechanical properties of these metals, which will be discussed more in detail below, there have been made studies of other phenomena in the same relation, and methods for the mechanical testing 'of metals have even been suggested; for example, the microscopic method of Tammann,' and the thermo-electric method of Turnera for determining elastic limits. The application of all such methods, which are based upon the dependence of some physical, crystallographic, or possibly chemical property, upon the mechanical state of the metal, must be preceded by close and careful correlation of these various "test" properties with the known mechanical state of the different metals or materials. It is with this view that the present work, as well as that of many previous investigators of, what may be termed in the interests of brevity, the mechanical-magnetic properties of ferromagnetic materials of construction, has been done. Previous Investigations of Mechanical Magnetic Properties The effect of mechanical stresses and of deformation, elastic or otherwise, oil the magnetic qualities of iron, steel, and other metals, has been studied by a number of investigators from the time of Joule (1841) to the present. It will, however, for the present purpose be sufficient to give an account only of the principal results obtained in the course of these investigations. It was early noticed (Villari, 1865) that if an iron wire is placed in a

Jan 1, 1916

By Lyall Zickrick

NUMEROUS brands of virgin pig lead are used in the manufacture of lead and lead-alloy cable sheath for commercial cables. In changing from one brand of pig lead to another a readjustment of press operating conditions is nearly always necessary. This is due largely to different flow characteristics, and some brands extrude at a much lower pressure than others; for example, copper-bearing lead requires much more pressure than a low-bismuth lead under the same operating conditions. With the modern type of lead press the extrusion practice in general differs very little. Molten lead at a temperature of 375° to 400° C. (710° to 750° F.) is cast in a water-cooled cylinder and allowed to cool or solidify into a slug for six to nine minutes. . This slug is forced into the die block and around the core tube through which the cable runs. The die block is held at an optimum temperature by means of gas flames, usually 175° to 225° C. (350° to 4.35° F.). Measurements of the tem¬perature of the cable sheath taken at the time of extrusion have covered a range of 190° to 225° C. (375° to 435° F.). According to Tammann, the rate of extrusion for a metal under constant pressure through a simple orifice is almost doubled for each 10° C. rise in temperature. Because of the irregularity of die-block construction, such a great increase is not obtained in lead-cable extrusion practice. To obtain more" definite information about the effect of small per¬centages of metals usually present as impurities in virgin pig lead, a series of compression tests were made covering several different brands of lead and various alloys. Since the usual temperature of the sheath is approxi¬mately 200.° C. as it emerges from the die block, these compression tests were all performed at 200° C. Five different brands of virgin pig lead were selected, as follows: Brand A: A desilverized western lead of very high purity. This lead contains neither copper nor bismuth. Brand B: A bismuth-free southeastern Missouri lead, usually con¬taining 0.05 to 0.08 per cent copper. Brand C: A copper-free mid-western desilverized lead of very good grade, usually containing around 0.06 to 0.10 per cent bismuth.

Jan 1, 1932

By W. O. Crosby

The crystalline belt of the Atlantic Seaboard, south of New York, attains its maximum breadth of 220 miles on the northern border of North Carolina; arid in this State it is most widely characterized by the occurrence of gold in workable deposits. Half a dozen auriferous belts have been recognized by Nitze and Hanna.' These are, in the main, coincident in position and trend with the NE.—SW. zones of metamorphic slates and schists, which, more than any other feature, give character to the geological map of North Carolina. The central gold-belts, accompanying the main zone of slates and as-

Jan 1, 1908

By Lowell B. Page

The White River Shale Project has completed a 5,000-foot production decline and a 30-foot diameter 1,010-foot deep shaft into its oil shale orebody in the Uinta Basin of eastern Utah. This is the first major underground access into these Green River deposits in this basin and provides an opportunity to establish and monitor in-situ rock mechanics stations as input to the mine engineering and planning of this large opening, high-tonnage mine. This paper discusses the history, mine development, and rock mechanics planning for this project.

Jan 1, 1984

By C. Pin, J. Bruce Wagner

In order to demonstrate the role of defect chemistry in the solid state to a process-metallurgy reaction, laboratory experiments were carried aut to remove copper from liquid lead using lead sulfide which had been doped to provide definite concentrations of cation vacancies. The removal of copper decreases in the order: bismuth- or antimony-doped PbS, undoped PbS or tin-doped PbS, and silver-doped PbS. The data are explained using the simple mass -action law and in terms of the exceedingly rapid interstitial diffusion of coppw in PbS to vacant cation sites. Results are in agree-ment with thermodynamic predictions and certain industrial practices that copper may be removed from lead below the limit of its coexistence with pure Cu,S and pure PbS. The role of defects in solids has been exploited in semiconductors and many device applications, in explaining tarnish formation, dissolution rates, and mechanical properties. The application of these principles to many process-metallurgical problems has not received as much attention. It was the purpose of this study to illustrate the role of defect structures of solids in a process-metallurgical application. When lead is refined, the ore, galena (PbS), is reduced by a series of operations to liquid lead (lead bullion) containing impurities such as copper, bismuth, antimony, arsenic, and silver depending on the original composition, the fluxes added, and the particular type of operation, see Fig. 1. In order to produce a pure lead, a series of refining operations are carried out. A typical lead-bullion analysis before drossing is shown in Table I. Copper is removed first as its presence increases the zinc consumption during the desilverizing process. For preliminary copper removal the lead bullion is brought to a temperature of 440°C in a kettle of 60 metric tons capacity. Some tar (or sawdust or resins) is usually added and the kettle is cooled slowly to 400°C while the liquid is stirred. A solid phase, called a dross, floats on top of the liquid and the particles of the solid phase adhere to the tar. This "hot dross" is collected. It contains mostly lead and copper which are partly oxidized and/or sulfurized if the lead bullion contains some sulfur.*

Jan 1, 1963

By Albert Ledoux

SEVERAL years ago my firm was representing the Mt. Lyell Co. of Australia, which was shipping its blister copper to a refining works in the United States. After the contract had been running for many months, the superintendent of these works discovered that if water was poured upon the surface of the bars much of it would disappear into the interior through blow holes. -Some experiments made by him showed that this could be a considerable amount, so that copper which had been rained on before it was weighed, although the surface appeared dry, nevertheless would contain water. It had frequently occurred in our experience-as samp-lers that the drillings from a lot taken by boring would come out quite wet, and in some cases, indeed, water would drip into the sample pan placed below the bars, due to the fact that the drill had penetrated a cavity or cavities containing water, which presumably got into the cavities at the time the copper was water-cooled after casting, there being, perhaps, no outlet to the surface. So far as I know, until this discovery at the refining works, no. one had thought that rain could penetrate into the interior of blister copper; at least in any quantity sufficient to be considered.

Jan 10, 1922

By P. E. Hopkins

Introduction and History IN speaking of the economic geology of southeastern Ontario, W. G. Miller and C. W. Knight' say that "there occurs in southeastern Ontario a variety of minerals and rocks of economic value, probably as great as in any district of like size on the North American continent. Some of these deposits, including marble and trap, are inexhaustible. Others, including talc and iron pyrites, have proved to be of considerable economic importance. From time to time, during the last 50 years, the following minerals and rocks have been mined or quarried with varying success: gold, iron pyrites, zinc blende, copper pyrites, galena, mispickel, magnetite, hematite, talc, actinolite, mica, marble, ophicalcite, feldspar; fluorite, apatite, corundum, graphite and sodalite. All of the economic materials, with the exception of fluorite, appear to be of pre-Cambrian age. The fluorite veins penetrate the Ordovician, Black River, limestone." Accompanying that report was an article by the writer on the Queensboro Pyrite Area which includes one of the two working pyrite properties in southeastern Ontario. In the present paper will be given a brief description' of all the known pyrite deposits in the area which may at some time possess an economic value, with fuller descriptions of the two working mines-The Canadian Sulphur Ore Co.'s mine near Queensboro, and the Nichols Chemical Co.'s property at Sulphide. The earliest mining of iron pyrites in Ontario was done in 1868 on the Billings property near Brockville. The mines were closed down in 1879 under the assumption that they were exhausted. Many other

Jan 8, 1916

By Steven T. Mitchell

INTRODUCTION Mill production from the Homestake Mine in 1979 amounted to 1.29 Mt (1.43 million st) of ore containing 5.9 g/t of gold (0.172 oz per st) compared with 1978 production of 1.44 Mt (1.59 million st) containing 6.2 g/t of gold (0.180 oz per st). The average cost per ounce of gold produced in 1979 rose to approximately $250 contrasted with $176 in 1978. This increase in unit cost is the result of inflation, a diminishing ore grade, and productivity losses related to a shortage of experienced miners as well as compliance with federal regulatory requirements. Together, these factors prompted the investigation of several large-scale, highly mechanized underground mining methods. This analysis indicated Vertical Crater Retreat mining to be one of the safest underground methods known today, yet competitive with all other forms of stoping in terms of cost and productivity. Therefore, the feasibility of applying the VCR stoping method at the Homestake Mine was explored. Vertical Crater Retreat stoping is a recent innovation in large- scale underground mining based on C. W. Livingston's crater blasting theories. Figure 1 illustrates the method which consists of drilling 165.1-mm-diameter (6.5-in.) holes from a topsill down-dip to an under- cut on the level below. The bottom of each hole is then loaded from above with a predetermined charge weight and horizontal slices up to 4.27 m (14 ft) in thickness are blasted into the undercut. Broken ore is extracted from drawpoints located on or below the undercut level.

Jan 1, 1983

By M. Bevis, A. F. Acton, P. C. Rowlands

Defor~nation twinning and transformation twinning modes most likely to be operative in Fe-Ni and Fe-Ni-C martensites have been determined using a new theory of the crystallography of deformation t~inning.~ This analysis shows that potentially important conventional and nonconventional twinning modes1 have been omitted in previous analyses. Discussion is given on the relevance of the predicted twinning modes to the lattice invariant shear associated with the martensite transformation in steels and to anomalous deformation twinning in Fe-Ni-C martensites. THE two most important criteria which appear to govern operative twinning modes in metallic structures1 are that the magnitude of the twinning shear should be small and that the twinning shear should restore the lattice or a multiple lattice in a twin orientation. The latter criterion ensures that the shuffle mechanism required to restore the structure in a twin orientation is simple. These criteria have been adhered to in the prediction of twinning modes2"6 in bcc and bct single-lattice structures with axial ratios in the range y = 1 to 1.09 as, for example, encountered in martensite occurring in steels. Refs. 2 and 3 in particular consider the martensite transformation in steels and the twinning modes in these cases relate to transformation twinning, and hence the lattice invariant shear associated with the martensite transformation. The list of twinning modes which can be compiled from these sources is incomplete and the ranges of magnitude of shear considered could be unrealistically small, particularly in the case of deformation twinning. The latter consideration is supported by the fact that twinning modes with magnitudes of shear large compared with the smallest shear consistent with a simple shuffle mechanism have been established in, for example, the single-lattice structure mercury7 and the multiple-lattice structure zirconium.&apos; In addition the anomalous deformation twins reported by Ftichrnan4 to occur in a range of Fe-Ni-C martensites still remain unexplained. It is clear that a comprehensive analysis of twinning modes likely to be operative in martensite In steels is required. The results of the application of a new theory of the crystallography of deformation twinningg to these structures are presented in this paper. The theory has been used to determine all shears which restore the lattice or a multiple lattice in a new orientation with magnitude of shear up to a required maximum. The orientation relationships between parent and twinned lattices are not restricted to the classical orientation relationships of reflection in the twin plane or a rotation of 180 deg about the shear direction. PREDICTED TWINNING MODES Twinning modes which restore all or one half of lattice points to their correct twin positions will be referred to as m = 1 and m = 2 modes, respectively. These modes are the most likely to describe operative modes in single lattice structures. The bcc m = 1 and m = 2 modes which have magnitudes of shear s in the range s < 2 and s < 1, respectively, have been given10 and are reproduced here in Tables I and 11. Detailed discussion of the crystallography of these modes and cubic modes in general will be discussed elsewhere (~evis and rocker, to be published). The four twinning elements Kl, &,ql,7)2 as well as the magnitude of shear s are given for each twinning mode, and the twinning modes are given in order of increasing shear. Two twinning modes are given in each row of the tables, the twinning mode Kl, Kz, ql, q2 and the reciprocal twinning mode with elements Kl = K,, Ki = Kl, q: = q2, and 17; = ql. The m = 1 and m = 2 twinning modes which describe twinning shears with small magnitudes of shear and simple shuffle mechanisms in bct crystals with -y = 1 to 1.09 are given in Tables I11 and IV, respectively. On increasing the symmetry of the tetragonal lattice to cubic, that is making y = 1, all modes listed in Tables 111 and IV must reduce to crystallographically equivalent variants of the modes given in Tables I and 11, respectively, or become twinning modes with both shear planes as symmetry planes in the cubic lattice and hence not considered in Tables I and 11. With the exception of this last type of mode only those tetragonal twinning modes which reduce to modes 1.1, 1.2, 2.1, and 2.2 of Tables I and I1 are considered in Tables 111 and IV. For values of y in the range -y = 1 to 1.09 the tetragonal modes and the corresponding cubic twinning modes have approximately the same magnitude of shear. The twinning modes listed in Tables 111 and IV are therefore by the criteria given above the most

Jan 1, 1969

By T. A. Rickard

The lodes of Cripple Creek, Colo., partake of the composition of the geological formation which they traverse. The prevailing rocks are andesitic breccia, lying upon granite, and also bodies of phonolite, trachytic phonolite, nepheline-basalt, etc., penetrating both the granite and the breccia. At Kalgoorlie, in West Australia, the prevailing rock is schistose, and has not been certainly identified, though microscopic sections indicate the probability that it was originally an acid eruptive. The lodes are essentially bands, more highly schistose than the encasing rock, and impregnated to a notable degree with disseminated pyrites and secondary calcite. During 1899 Cripple Creek produced 425,590 tons of ore, having a gross value of $15,658,254; during the same period the output of Kalgoorlie was 467,048 tons, valued at $17,724,587. In chemical composition, the ores at Cripple Creek and Kalgoorlie, respectively, present differences equally interesting to the petrographer and the metallurgist. In both cases we have to deal with altered eruptives as the matrix of the ore; but the much older rock of Kalgoorlie has undergone more decompo-

Jan 1, 1901

By J. M. Boutwell

PAGE I. Introduction,.......541 II. General Geography,......542 III. General Geology,......544 1. Sedimentary Rocks,..... 544 2. Igneous Rocks,...... 545 3. Areal Geology,.......546 4. Structural Geology......547 IV. General Character of Ore-Deposits,...548 V. Genesis of the Disseminated Ore in Monzonite,.... 549 1. General,........549 2. Character and Occurrence,... 649 3. Genesis,....... 550 4. Superficial Alteration.....553 5. Conclusion......553 VI. Genesis of the Ore in Fissures,...553 1. Character........... 553 2 Occurrence......554 3. Deposition...... 556 4. Transporting Agent....555 6. Immediate Causes of Deposition..556 6. Superficial Alteration....564 7. Conclusionl ..... 565 VII. Genesis of the Copper-Ore in Limestone...... 566 1. Character......566 2. Occurrencel .....566 3. Deposition......567 4. Relation of Fissures.....569 5. Relation of Intrusives,...571 6. Superficial Alteration....575 7. Conclusion......578 VIII. Periods of Ore-Deposition....578 IX. Dates of Mineralization.....579 X. General Conclusions.....580 I. Introduction. The object of this paper is to present a concise statement on the genesis of the copper- and lead-deposits of the Bingham

Jan 1, 1906

By John Buch

NEARLY 25 years ago operating officials in the northern anthracite field were confronted with the problem of profitably mining virgin beds of thin coal (those 48 in. and under) or destroying them by mining under-lying thick beds. To solve this problem costly hand-mining methods were replaced by cheaper mechanical methods, which eliminated the need for the lifting of bottom or the brushing of top in excessive quantities, which was essential if proper height for hand loading&apos; was to be provided. During this period long-face mining was an outstanding development. In its favor in comparison with any other method were the ease with which undercutting machines could be used, a differential in powder cost of about fifteen cents per ton in favor of this method over mining from a solid chamber or pillar face, and a greater production per day from a single working place, resulting in lower capital expenditures for a given total production, closer supervision and lower transportation cost. The long faces were drilled by jackhammer and undercut by machines. The coal from the cut was loaded into mine cars placed on the gangway road by means of a double-drum mechanical scraper engine and a mechan-ical V-type scoop. A tugger hoist was used to spot empty cars at the loading point from a supply placed at the operation by an electric mine locomotive. During loading the roof was supported by vertical wooden props paralleling the face. After the loading was completed the scraper engine and the ropes that had been used to propel the scoop in the loading of coal transferred the props to and along the face. A row of unfilled cogs was then built parallel to the new face and about 6 ft. from it. These cogs were usually made 6 by 3 ft., the longer dimension paralleling the face; they were placed on an average at 12-ft. centers. These wooden cogs were left in place and were buried later by falling roof. Attempts to remove them were never successful. When a new long face was started, the cog spacing would be increased to about 20-ft. centers. As successive cuts were made, weight would begin on the cogs, and they

Jan 1, 1939

By Carl H. Beal, E. D. Nolan

In February, 1918, the conclusion was published by Lewis and Beal "that wells of equal output on the average will produce equal amounts of oil in the future, regardless of the ages of the wells." This conclusion was based upon the study of data collected principally in Oklahoma and was not known at that time to be true for other oil fields. An abundance of statistical proof was later collected by the senior author of the present paper, which showed that the conclusion was undoubtedly well founded and that it applied to other fields as well. Accordingly, it was later restated2 as the "law of equal expectations" as follows: "If two wells under similar conditions produce equal amounts during any given year, the amounts they will produce thereafter, on the average, will be approximately equal, regardless of their relative ages." Although only scanty data from the California oil fields were available at the time this publication was prepared, sufficient information was analyzed upon which to base the insert on Fig. 80, which showed beyond a doubt that the law held at least for a part of the Midway oil field in California. Recently the authors have collected more complete data in California, and it is the purpose of this paper to explain the method used in demonstrating the truth of the law and, in addition, to give several methods by which curves constructed in accordance with this law can be used in a practical way with ease and accuracy. The Family Curve The law of equal expectations means that each individual of a group of wells producing under similar conditions will decline along approximately the same type of curve, the rapidity of decline varying with the output

Jan 1, 1921

By Frank J. Anderson

IN the cement region of the Lehigh Valley, a difference of 2 to 3 pct in CaCO3 can make or break a new quarry development, and experience of the Dragon Cement Co. has shown that values of calcium carbonate, as reported from churn drill samples, have been increased as much as 6 pct on the average when the same area was diamond drilled. This calcium carbonate increase consequently lowered the values for silica, iron, and alumina, and made these sections much more attractive. Since 1950, the Dragon Cement Co. Inc. has been engaged in extensive diamond drilling in the local limestone of the Northampton, Pa., region, known as the Jacksonburg formation, and in the Lebanon, Pa., region in the Annville limestone, both of Ordovician age.

Jan 12, 1954

By C. Hanford Henderson

The belt of copper-bearing rocks of the South Mountain has attracted Attention principally iii the townships of Hamilton Ban and Liberty in Adams County, Pennsylvania, and in the southeastern portion of Franklin County. As the developments, thus far, have been almost exclusively limited to that area, the examination here described extended only within those boundaries. The region, being one of considerable interest geologically, has been the subject of careful study and description, both on the part

Jan 1, 1884

By G. A. Alers, F. Borik

Rolled sheet products are elastically anisotropic and a large number of measurements of Young&apos;s modulus and rigidity modulus are necessary to completely specify their elastic properties. This paper describes and uses a simple measurement technique to obtain the nine elements of the elastic modulus tensor from which all the elastic The elastic properties of a polycrystalline material are usually specified by giving the Young&apos;s modulus E and the rigidity modulus G. Unfortunately, these two moduli by themselves are insufficient to completely specify the elastic properties because the rolling process introduces a preferred orientation which makes the material properties can be deduced. In particular, the variation of Young&apos;s modulus and the rigidity modulus in the principal planes of a sheet of ausformed steel were deduced. Furthermore, the variation of Young&apos;s modulus in the rolling plane was compared with direct measurements. anisotropic. This anisotropy makes E and G functions of the orientation of the test specimen in the sheet so that a complete description of the elasticity requires many measurements on a large number of specimens. A more fundamental approach to the problem is to consider the sheet as a single crystal and measure the elements of its elastic modulus tensor. Although this appears formidable, there have been developed recently high-frequency ultrasonic techniques which yield these tensor elements directly. The symmetry of a rolled sheet is such that it behaves elastically as if it were an orthorhombic

Jan 1, 1965

By James F. Kemp

In submitting an additional contribution to the discussion on ore-deposits in the recent volumes of the Transactions, it is my desire to adhere closely to matters of material importance as affecting the actual processes. Judging from the discussion by Professor Van Hise, and from one or two reviews or other articles by associates of his in geological work, the impression seems to prevail that, in so far as my paper* referred to his masterly essay, I was guilty of misconceptions regarding both the part attributed by him in it to the igneous rocks and the ubiquitous presence of the ground-water. I should regret extremely to be wanting in these particulars or to have misunderstood one for whose great services in this and other branches of geology no one has a higher esteem than myself. I have, however, in the most careful way, and with these points in mind, read his essay again, and, taking it as a whole, I cannot gain any different impression of relative magnitudes than the one first received. The importance of the igneous phenomena and the restrictive influence of the processes described by " cementation " in their effect upon the ground-water, as set forth in Professor Van Hise&apos;s "Discussion" (Trans., xxxi., 292), impress me as being in very marked contrast with the same things in his first essay. If the point seems to anyone of sufficient importance, it can easily be decided by reading the originals. My paper was the result of some years of observation, reading and reflection, and was meant to be an independent contribution, controversial only in some subordinate particulars. In depicting the drama of the deposition of ores, I cannot but feel that Professor Van Hise assigned to the chorus and the scene-shifters some characters which, it seems to me, should

Jan 1, 1903

By E. J. Bonet, P. B. Crawford

It is fairly common practice to reinject water into the aquifer near the oil-water interface in water-drive reservoirs. There have been many studies of aquifer behavior without reinjection,l-5 but apparently no analytical studies have been made to indicate performance when injection wells are present in the aquifer. The diffusivity equation may be used to describe the pressure behavior in an aquifer. When sources are present it can be written as A general solution of Eq. 1 may be obtained as the sum of two solutions. One is a general solution of the homogeneous equation, obtained by dropping the source term in Eq. 1 and still satisfying the required boundary conditions. Another is a general solution of Eq. 1 satisfying homogeneous boundary conditions.1° The first solution, which corresponds to the aquifer without reinjection, has been given quantitative and qualitative treatment in the literature.l-5,8,9 The latter solution will be treated here. Solutions with variable injection rates are obtained by superimposing solutions with constant rates, so we have considered only the latter. Five cases have been treated here: 1. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The pressure along the line x = 0 is maintained at zero pressure. (See Fig. 1.) Equations showing the pressure distribution, rates, velocity and cumulative influx have been developed. Certain numerical results are shown. 2. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The rate of production along the oil-water water contact is maintained constant. Equations showing the pressure distribution inside the aquifer are presented. 3. A linear aquifer of finite width and extent. Constant pressures are maintained at opposite ends of the aquifer. Water is injected at constant rates at point xo, yo. Equations showing the pressure distribution are shown. 4. A linear aquifer of finite width and infinite extent. The pressure is maintained constant at the oil-water contact. Water is injected at a constant rate at point xo, YO. 5. A linear aquifer of finite width and finite extent. The pressure at the oil-water contact is maintained constant. Water is injected at constant rate per unit length along a line x,. The Linear Aquifer The linear closed aquifer, performing at constant terminal pressure was selected as the first case to be analyzed. The development of the equations is based on uniform injection per unit of thickness, and gravity effects are neglected. In practical application this condition is probably most closely achieved when the

Jan 1, 1970