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By John C. Long

The advantages of firebrick regenerative hot-blast ovens being thoroughly appreciated by those engaged in modern blast-furnace practice, the important question now is to obtain the best and most efficient apparatus. The apparatus invented by the writer, and described in this

Jan 1, 1885

By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By J. D. Doherty

That America's great coal deposits eventually will be our principal source of liquid as well as solid fuels is generally accepted. Moreover, the day when synthetic oil from coal will begin to supplement our petroleum supplies does not appear to be far off. The American petroleum industry has not spared effort or expenditure in its attempt to keep pace with the demand for oil, and recent production has exceeded expectations. However, the rapidly rising demand for liquid fuels plus the increasing difficulty of finding and developing the new oil needed even to maintain present production rates make it highly unlikely that oil from domestic wells can fully meet future oil requirements. Therefore, it appears that one or more of the following courses must be followed: 1. Curtail oil consumption. 2. Increase imports. 3. Develop new sources such as synthetic liquid fuels.

Jan 1, 1949

By Thomas L. Watson

My thanks are due to Mr. Frank Firmstone, Easton, Pa., who has called my attention to the statement in my paper' that " Barite, fluorite and quartz, thougll not observed in the Tennessee area," ... as possibly misleading to the reader, if construed to mean that such a discovery had never been made. Mr. Firmstone is correct in assuming that this statement referred only to the study of the worked areas of the metallic ores, especially zinc, made in the course of the survey upon which my paper was based. The occurrence of barite and fluorite with lead-ores in Tennessee was reported by Prof. Safford? in 1869, and by Safford and Killebrew? in 1887, with the further statement that about 1,000,000 lb. of barite were annually mined in Greene, Washington and Jefferson counties, Tenn., and that considerable deposits occur also in McMinn, Smith and other counties. It is also noted that the barite " usually occurs in veins, associated with galena." The present worked areas of barite are, however, distinct barite propositions, without workable quantities of either lead or zinc, so far as mining operations have gone, and the areas are more or less removed from the present areas of zinc-ores. Mr. Firmstone informs me also that, in 1892, he observed, in the magnesian limestone at Watauga Point, in Carter county, on the left bank of the Watauga river, a little below the mouth of Buffalo creek, small quantities of galena and some fluorite.

Jan 1, 1907

By J. F. Wilson

An experimental investigation has been made of gas-driven slug displacements in a system of high gas saturation to evaluate the process for use in a California reservoir. Fluid compositions, temperature, pressure and core permeability duplicated reservoir conditions as closely as possible. The temperature was above the critical of the slug materials. The slug composition required for 100 per cent oil recovery in the linear flow systems was found to agree with that determined from equilibrium phase studies. A qualitative theory for the slug displacement of two-phase systems is proposed and found to be in general agreement with the observed flow behavior. The theory predicts that the length of the reservoir fluid-slug transition Zone will increase with increased initial gas saturation and decrease with increased oil swelling accompanying the composition change from reservoir oil to the critical composition. The precipitation of small amounts of an asphaltic phase during the formation of the transition zone had no adverse effects on the flow behavior of otherwise miscible systems. INTRODUCTION Despite the large number of recent publications relating to oil recovery by miscible displacement, little information is available concerning the behavior of crude oil-natural gas systems at conditions likely to be encountered in field application. The laboratory data reported here were obtained during an investigation of the possibility of using a gas-driven LPG slug in a partially depleted California reservoir. Seven gas-driven slug displacements employing slugs of different compositions and sizes were made in 26- to 27-ft long sandstone cores. The equilibrium phase behavior of the systems was also determined. The features of primary interest in this study are the following. 1. Data were obtained on the displacement of reservoir fluids at reservoir conditions. 2. A high gas saturation existed in the long cores at the start of the displacements. 3. The temperature of the studies was above the critical of the slug materials. 4. A comparison between the flow behavior and equilibrium phase behavior, as illustrated by a pseudo-ternary phase diagram, is afforded for a system of considerable complexity. THEORY Phase Behavior The use of the pseudo-ternary phase diagram to illustrate the phase behavior in miscible displacements has been discussed by Clark, Schultz and Shearin. Sie-vert, Dew and Conley and Arnold, Stone and Luffel' have presented both phase equilibrium and flow data for true ternary systems. For the true ternary, the application of the theory is straight-forward; for a reservoir system represented as a ternary, the theory undoubtedly gives a qualitatively correct picture. One purpose of this investigation was to see if the pseudo-ternary phase diagram could be used to predict with reasonable accuracy the conditions necessary for miscible displacements with actual reservoir systems. MiscIBLE Displacement of Two-Phase System A large number of papers "I3 have treated the miscible displacement of a single-phase fluid from both an experimental and a theoretical viewpoint. However, the normal field application of the process will be in a partially depleted reservoir. Often the state of the system will be such that the mobility of the gas phase is greater

By J. R. Campbell

A DOZEN years or so ago, the general superintendent of our company, now the president, Mr. W. H. Clingerman, detailed me to make a study of the coal-washing problem and collect data, which threw me into contact with the best washery men of the country. and took me to those districts where the washing of coal for metallurgical purposes is carried out. I investigated many kinds of coal-cleaning schemes, made numerous tests on them, and collected voluminous data, yet I confess frankly that I have had but little practical washery experience and that little has been at the Middlefork washery of the United States Fuel Co. at Benton, Franklin Co., Ill., which was put in operation last fall. While this wash-cry installation may not be the "last word," I am quite sure it embodies some long steps in advance over older designs and constructions. From the washery man's standpoint, the removal of pyrites, or marcasite, a disulfide of iron, is the one vital problem, and the one productive of the most beneficial results, so far as elimination of sulfur is concerned. Sulfates and so-called organic sulfur occupy quite a secondary -position and are generally lost sight of in coal washing: The elimination of sulfur in coal in the past has usually been accomplished by jigging in water, but lately the use of concentrating tables has been employed with good success, and some mention may be made of the flotation process on fine coal, though hardly considered practicable. Coal washing, is rapidly coming into its own, due to the depletion of low-sulfur coals for coking purposes, and before many years we predict as careful attention being given to the design and construction of coal washeries, ,as is now being given to byproduct plants and other allied industries. Heretofore, coal washing has been considered only as an incidental and a necessary evil-instead of the big problem it is one worthy of the most careful study by men well trained along technical lines and capable of delving into the fundamental principles.

Jan 9, 1919

By Walter Wood

The specifications for cast-iron pipe that have been submitted at this meeting are practically the outgrowth of those which were originally adopted, about 1860, by Mr. Kirkwood of Brooklyn, N. Y. They have been changed but little since that time, the mode of testing pipe in the hydraulic press, as well as the method of coating, not having departed from the original practice. The chief addition to the specifications has been in the adoption of a test-bar 2 in. by 1 in. in crosa-section, broken between 24-in. supports by a transverse strain applied on the flat side. Test-bars were first introduced into pipe-specifications about 1870. At that time a satisfactory test-piece had to stand a tensile strain of 16,000 lb. per square inch. The present test-bar was adopted in order to give some idea of the deflection of the iron that was being used. These deflection-tests have been so satisfactory to both engineers and manufacturers, and have met the requirements of the pipe-trade so accurately, that it is considered best to hold to the . 2-in. by 1-in. bar instead of adopting the short " Arbitration Bar," which yields but little information from the stand-point of deflection. The new feature in these specifications is the effort to reach standards to which pipe shall be cast in the future, thus permitting the manufacturer to make up stock and the purchaser to find material on hand when he asks for deliveries. Heretofore there has never been ally standard weight for pipes? although in some sizes certain weights are more frequently asked for than others. The fixing of standards for pipes permits the adoption of definite standards for fittings. It has been aimed to secure such uniformity for fittings as will permit the same class of fittings to cover two or more classes of pipe. In order to accomplish

Jan 1, 1905

By Harry Tufft

FOR many years the treatment of mine timbers with preservatives was confined to a few pioneer plants in the United States, and it is only in the past few years that the practice has grown appreciably. In a field study of the mine timber situation in Illinois, Pennsylvania, and further study of the situation in the country as a whole, I found that most mine operators did not keep records on mine timber that would afford the necessary data for determining the possible savings from preservative treatment. Some primary questions the mining engineer should be able to answer before making his decision on preservative treatment. for a particular mine are: (1) Quantity and cost of timber going into permanent workings annually; (2) quantity and cost of annual replacements due to decay; (3) life of untreated timber in different places; (4) desired life of timber. With the necessary facts in hand, he can then con-fidently select a method of treatment and preservative that is best suited to his needs. In former years when timber was cheap and an abundant supply could be had close at hand, as was the case in the majority of mining regions, the mine op-erator did not concern himself much except to see that enough was supplied to keep the workings safe. The cost figure for timber and labor, distributed to cost per ton of ore, was all the bookkeeping necessary. With present costs of timber, labor, and increasing length of haul to the mine, many operators are paying closer attention to timbering costs and studying them in. more detail. Some of the larger and more progressive opera-tions now keep detailed' figures that give information on all phases of their timber problems. However, at the majority of mines the data available do not permit such analysis. Checks as to where the different con-signments are placed, the date of setting, and the period

Jan 6, 1927

By John B. Pearse

IN order to get an idea as to the strength of steel rails, it will be well to review the tests to which iron rails have been subjected. In England, Mr. Ashcroft found that the best 80 pound rails broke under a 300 pound weight, falling 15 feet. In Germany the Society of Railway Managers determined on and have long applied a test of 1000 pounds falling 101 feet, as the standard which all first-class iron rails must reach. In this country no inspection nor test is applied, but tests made show that iron rails from our most reliable makers, break under a 6 foot fall of a 1500 pound drop as an extreme test, most of those tested breaking under a far less test; some breaking with less than a 3 foot fall of the same weight. Everywhere where steel has been used, engineers have come to the conclusion that some test is required to show the regularity and strength of the product. As compared with iron, the tests which steel will stand are wonderful. After numerous experiments partially based on the experience of the rail-mill at Graz, belonging to the Southern Railway of Austria, the Society of German Railway Managers fixed upon a test of 2000 pounds falling 13 1/2 feet. They found that this test represented the steel which suited their necessities, and also found that with steel of otherwise average purity, this test represented about one-half per cent. of carbon, and made it a rule to take no steel containing under three-tenths of a per cent, of carbon, because it was too soft. They expressed a hope that a harder steel could soon be made tough enough to stand the same test. In England, a test was adopted of 2240 pounds, falling 15 to 17 feet on the rail on heavy bearings. This test has been found satisfactory under heavy traffic on average road-beds, and has been invariably

Jan 1, 1873

By John B. Pearse

IN order to get an idea as to the strength of steel rails, it will be well to review the tests to which iron rails have been subjected. In England, Mr. Ashcroft found that the best 80 pound rails broke under a 300 pound weight, falling 15 feet. In Germany the Society of Railway tyfanage1-s determined 011 and have long applied a test of 1000 pounds falling 101/2 feet, as the standard which all first-class iron rails must reach. In this country no inspection nor test is applied, but tests made show that iron rails fro; our most reliable makers, break under a G foot fall of a 1500 pound drop as an extreme test, most of those tested breaking under a far less test; some breaking with less than a 3 foot fall of the same weight. Everywhere where steel has been used, engineers have come to the conclusion that some test is required to show the regularity and strength of the product. As compared with iron, the tests which steel will stand are wonderful. After numerous experiments partially based on the experience of the rail-mill at Graz, belonging to the Southern Railway of Austria, the Society of German Railway Managers fixed upon a test of 2000 pounds falling 138 feet. They found that this test represented the steel which suited their necessities, and also found that with steel of otherwise average purity, this test represented about one-half per cent. of carbon, and made it a rule to take no steel containing under three-tenths of a per cent. of carbon, because it was too soft. They expressed a hope that a harder steel could soon be made tough enough to stand the same test. I n England, a test was adopted of 2240 pounds, falling 15 to 17 feet on the rail on heavy bearings. This test has been found satisfactory under heavy traffic on average road-beds, and has been invariably

By J. R. Thoenen

IF ASKED whether limestone production was a mining problem I would; not hesitate to answer emphatically in the affirmative. The question, "When is a quarry a mine?" is familiar. The immediate mental picture induced by the thought of limestone production is that of an open quarry. All are familiar with the open pit in the iron-producing districts of Minnesota and Michigan and the open cuts of the so-called "porphyry" coppers of the West. If these are mines, they differ little from limestone quarries in general mode of operation; if quarries, why do they need the attention of mining engineers? During 1923, the United States produced in round numbers 70,000,000, tons of ore. The limestone production of the United States for the same period was something over 100,000,000 tons. In tons, it about equals the oil production of the United States. The uses of limestone are legion. A paper read by a prominent engineer of Chicago, at the meeting of the National. Crushed Stone Association held last February in St. Louis says: "There is no industry in the United States today that is more basic in its operation or by itself controls. more industries. There is hardly a chemical operation, hardly a metallurgical operation or building operation that a crushed-stone man does not control if he will jump in and make the full utilization of it." Some of the many uses are for road metal, concrete, railway ballast, building stone, riprap, and rubble, the manufacture of iron and steel, alkalies, calcium carbide, magnesia, carbolic and carbonic acids, asphalt filler, mineral wool, poultry grit, sulfuric acid, phosphates, nitrates, soap, baking powder, the purification of copper and prevention of coal-mine explosions, to say nothing of the quantities used in the making of lime and cement. It has been said that without iron we would revert to the Stone Age; how much iron would we have without limestone? From the point. of view of the mining engineer, using the term in its broad sense to include geologists and metallurgists, the production of limestone is important because of its occurrence, volume, commercial importance, and the problems presented by its recovery and treatment.

Jan 2, 1925

By J. R. Thoenen

If asked whether limestone production was a mining problem I would not hesitate to answer emphatically in the affirmative. The question, "When is a quarry a mine?" is familiar. The immediate mental picture induced by the thought of limestone production is that of an open quarry. All are familiar with the open pit in the iron-producing districts of Minnesota and Michigan and the open cuts of the so-called "porphyry" coppers of the West. If these are mines, they differ little from limestone quarries in general mode of operation; if quarries, why do they need the attention of mining engineers? During 1923, the United States produced in round numbers 70,000,000 tons of iron ore. The limestone production of the United States for the same period was something over 100,000,000 tons. In tons, it about equals the oil production of the United States. The uses of limestone are legion. A paper read by a prominent engineer of Chicago, at the meeting of the National Crushed Stone Association held last February in St. Louis says: "There is no industry in the United States today that is more basic in its operation or by itself controls more industries. There is hardly a chemical operation, hardly a metallurgical operation or building operation that a crushed-stone man does not control if he will jump in and make the full utilization of it." Some of the many uses are for road metal, concrete, railway ballast, building stone: riprap, and rubble, the manufacture of iron and steel, alkalies, calcium carbide, magnesia, carbolic and carbonic acids, asphalt filler, mineral wool, poultry grit, sulfuric acid, phosphates, nitrates, soap, baking powder, the purification of copper and prevention of coal-mine explosions, to say nothing of the quantities used in the making of lime and cement. It has been said that without iron we would revert to the Stone Age; how much iron would we have without limestone? From the point of view of the mining engineer, using the term in its broad sense to include geologists and metallurgists, the production of limestone is important because of its occurrence, volume, commercial importance, and the problems presented by its recovery and treatment.

Jan 1, 1925

By Charles D. Walcott

The following acts of the Directors are reported for the information of members At a meeting held June 20, 1907, Dr. Charles D. Walcott, Director of the U. S. Geological Survey, Washington, D. C., having been recommended by unanimous vote of the Council, was unanimously elected an Honorary Member of the American Institute of Mining Engineers, in recognition of his personal services to American geology, and of his generous co-operation with this Institute, to the Transactions of which he has not only himself made valuable contributions, but has also encouraged the preparation of such contributions by the members of the U. S. Geological Survey under his charge, his liberal policy in this respect having gone so far as to permit the preliminary publication by the Institute of important results reached by the geologists of that Survey, even before their final and full publication as public documents. This wise and generous course has not only brought the U. S. Geological Survey into intimate and sympathetic relations with the mining industry of the world, but has also enriched the Transactions of the Institute, especially in the department of the science of ore-deposits, with many valuable papers. At a meeting held Jan. 14, 1908, Mr. Charles Kirchhoff was unanimously re-elected a Trustee of the United Engineering Society, to serve for a second term of three years. At a meeting held Feb. 18, 1908, directly after the adjournment of the annual meeting of the Institute, the following officers were elected for the ensuing year: President, James Gayley: Vice-President, James Douglas; Secretary, R. W. Raymond; Treasurer, Frank Lyman.

Mar 1, 1908

The Manufacturer's Viewpoint A prominent manufacturer of mining 'machinery not long ago expressed himself as being confident that he was securing the best kind of publicity for his product through the advertising pages of the monthly Bulletin of the American Institute of Mining Engineers. Such an expression coming from such a man is highly gratifying; yet it is justifiable when the high quality of reader and subscriber is taken into consideration. In fact, the majority of those using our advertising pages feel the same. It is to be regretted, of course, that others catering to our field do not realize the means at their disposal for presenting the points of interest of their product to the mining man. The question has been asked, " Do your members read their Bulletin?" They not only read the editorial pages, but they "admit being up-to-date enough to peruse the advertising section to "see what is new." The next question the prospective advertiser asks is, " Will the Bulletin bring inquiries?" The answer to this question holds good for any publication having as subscribers those who have purchasing or recommending power-yes, if the article advertised is not a stock one, that has been before the public for any length of time. To secure inquiries on, say, a standard centrifugal pump or any other standard product, the features of which are well known, is a most difficult proposition. Yet, of course, some inquiries are secured, but mostly from those having use for the catalogue or trade literature for reference purposes. It is safe to say that the traceable returns from advertising in trade publications hardly, if at all, pay for the advertising. The real returns are intangible, and result from the constant publicity, and keeping ?everlastingly at it." Who can say what subconscious effect is taking place when an advertisement is "glanced at," to say nothing of the effect produced when the copy is attractive and interests the reader. Time after time it has been proved that sales have been secured as a result of an advertisement, yet no inquiry had been made directly traceable to advertising.

Jan 8, 1915

By Wm. A. Haven

As soon as the likelihood of American participation in the war was established, and in spite of the fact that we can produce almost as much as all other countries combined, the demand for prompt deliveries of iron and steel products from American factories began to exceed their utmost capacity, and, after fifteen months of practically full operation, has continued to do so. Therefore, it would seem worth while to review some of the aspects of the supply and demand for steel as well as the efforts that are being made to bring them into balance. It is still being debated as to whether the situation should be defined as a real shortage that will persist through the emergency period or as a temporary one than can be relieved by less drastic measures than a Government-sponsored program of expanding existing plants and building new ones.

Jan 1, 1942

By A. E. Outerbridge

I had the honor to present to the American Institute of Mining Engineers at the Pittsburg meeting, February, 1896, a paper having the foregoing title, in which I said : " It has generally been accepted as a fact that cast-iron, under the influence of repeated shocks, becomes brittle, and will finally break under a blow which otherwise it would have withstood. It will probably surprise metallurgists, therefore, to learn that experiment disproves the supposed fact, and establishes exactly its opposite. " The result of about a thousand tests of bars of cast-iron of all grades, from the softest foundry mixtures to the strongest car-wheel metal, enables me to assert with confidence that, within limits, cast-iron is materially strengthened by subjection to repeated shocks or blows." Three tables were appended showing increase of strength

Jan 1, 1905

By L. W. Pommier, L. R. Plitt, F. B. Brien

L. R. Plitt (Assistant Professor of Mining and Metallurgy, University of Alberta, Canada.) — It is indeed encouraging to see rheological studies being carried out in a mineral engineering school. The bulk of the work being done today in applied rheology seems to be concerned with the behavior of polymeric solutions and thus has limited application to the solid-liquid systems encountered in mineral beneficiation. The authors have approached the problem by carrying out a dimensional analysis which showed that for power law fluids the drag coefficient, Ds, must be some function of a generalized Reynolds number which has the form: If the power law adequately describes the behavior of a fluid, the dimensional analyses predicts that the Ds - RN function should hold for all values of n' or any other dependent variable. The experimental evi-

Jan 1, 1968

By E. C. Barfield, D. G. McCarty

Two-dimensional analyses offer considerable promise in providing the basic information required to effect more precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-qreed digital computer. The general approach is to (I) develop a representative numerical model of the reservoir and (2) employ a suitable numerical technique to solve the basic equation of flow and to develop the required engineering information for the particular case represented by the model. This technique has been used to calculate pattern performance in connection with several field projects involving water injection into oil reservoirs. This type of analysis involves sequentially (I) calculating the pres-' sure distribution in the reservoir and (2) tracking the progress of the interface between the displaced and displacing fluids in a step-wise manner to provide a depletion history of the operation. The particular analysis presented in this discussion is subject to the restriction that the mobility of the displaced and displacing fluids be equal and assumes that the fluids are incompressible and that gravity and capillary pressure do not affect the shape of the flood pattern. Complete two-dimensional .flexibility is maintained with regard to definition of reservoir rock and fluid characteristics, placement of physical restrains and boundary conditions, investigation of flow characteristics in the reservoir, and movement of the displaced and displacing fluid interface. The results of these studies indicate that the highspeed digital computer is well suited for conducting reservoir performance studies in two-space dimensions and that dependable numerical techniques are available for making such analyses. INTRODUCTION One of the problems facing petroleum engineers is that of providing more precise engineering control over reservoir operations at all stages during the depletion cycle. The most direct approach to this problem is to simulate the reservoir with some type of physical or mathematical model and use the information developed from the behavior of the prototype to predict the performance of the actual reservoir. This principle is, of course, not new, and a variety of simulation techniques have been developed to provide information on the behavior of oil and gas reservoirs. One straightforward refinement of present reservoir analysis techniques is the progress from one-dimensional reservoir models to those where the reservoir can be represented in two- and three-space dimensions. Multidimensional reservoir analyses are desired in order to show not only what is happening in the reservoir but in addition to show where in the reservoir the various phenomena of interest are occurring. Thus far, two-dimensional analyses have been confined predominantly to potentiometric and electrolytic model studies. However, when large numbers of wells are involved and where large-scale models are required, such problems become very tedious and instrumentation problems become acute." It is possible through use of numerical methods and general purpose digital computers to avoid many of the instrumentation difficulties and to relax some of the restrictions of previous techniques. The purpose of this paper is to discuss some recent experiences with the use of high-speed digital computers for predicting pattern performance in fluid injection operations and to describe the numerical procedures which have been used for making such analyses. THE NUMERICAL MODEL The problem of representing the reservoir with an appropriate numerical model is composed of at least two important considerations. The first requires that an adequate description of the reservoir mechanism be formulated in the form of the basic differential equation describing the process. The second consideration is definition of the physical characteristics of the reservoir. The latter requires that representative basic data be obtained, examined, and interpreted to provide sufficient detailed definition of the pertinent physical properties throughout the system. The Differential Equation One of the basic assumptions made for the purpose of performing the two-dimensional studies being dis-

By Leo Ranney

ANY years ago a prospector came to a Nevada town and built himself a shack. Day after day he searched the hills for gold -but he found none. He closed his shack and hurried north, where a strike had been made. Next he tried to trap the flour gold that floats down the Snake River. He panned the black sands along the Oregon coast. He ranged over the mountains and up the gulches of far-off Alaska. At last, broken in health, six years ago he came back to his old home in Nevada. There his shack still stood-nobody wanted it. One day he started a garden in the rocky soil that he owned. His spade turned up a chunk of quartz, and in that quartz were stringers of gold. He had found a rich gold vein, running right under his own house. You gas producers who have hurried to Oklahoma, Louisiana, East Texas, South Texas, West Texas, even to California to drill wildcat holes a mile or two miles deep-why not, like the old gold prospector, have a look in your own back yard? Some of your coal seams contain 20,000,000 cu. ft. of natural gas per acre.

Jan 1, 1943

Abramovits, Charles, Student. Case School of Applied Science Cleveland, Ohio. '37 Adams, Benjamin C., Jr Address Wanted. '36 Adams, Ernest C., Student, Univ. of Illinois 908 W. Green St., Urbana, Ill. '35 Adams, George H. 4021 Walnut St., Riverside, Calif. '36 Afshar, Hodji Khan ?A. Box 2072, Norman, Okla. '35 Ahlen, Louis S., Student, Univ. of North Dakota Univ. Sta., Grand Forks, N. D. '37 Ahrenholz, Herman William, Jr., Student, Lehigh Univ Bethlehem, Pa. '35 Alger, Robert P., Student, Missouri School of Mines & Met Rolla, Mo. '36 Alkire, Robert L., Student, Univ. of Pittsburgh Pittsburgh, Pa. '37 Alleman, Virgil C., Student, South Dakota School of Mines Rapid City, S.-D. '37 Allen, C. G., Student, Case School of Applied Science Cleveland, Ohio. '37 Allen, Eugene S., Student, Univ. of California Berkeley, Calif. '37 Allen, George W., Student, Michigan College of Min. & Tech Houghton, Mich. '37 Allen, Harry Berkley, Student, Univ. of California Los Angeles, Calif. '37 Allen, Henry, Jr., Student. Univ. of Arizona Sigma Chi House, Tucson. Ariz. '37 Allen, Paul W., Student, Mass. Inst. of Tech Cambridge, Mass. '35 Allen. R. M.. Jr.. Student. Virginia Polytechnic Inst., "G" Co Blacksburg, Va. '35

Jan 1, 1937