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By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

Jan 1, 1967

By John D. Morgan, Sylvain J. Pirson

An instantaneous and continuous analysis of a mineral suspension should be of great value in controlling various mineral preparation processes. Described herein is a method of analysis based on the use of high-frequency alternating current, which, under certain restrictive conditions, could be of use. Theoretical Considerations In a suspension of conductive minerals, the electrical effect primarily responsible for the variations in electric conductivity is the capacitance. In Fig Ia, let an alternating voltage E be applied across two electrodes F and F', between which are two rows (S and T) of mineral particles, all of approximately the same size, immersed in a fluid. Let the number of rows of particles between the electrodes be R and the number of particles in each row be N. If A is the area of a particle, D is the distance separating two particles, and k is a constant depending on the fluid, the capacity, CO, of the particle system will be given by: KRA C°= ND Referring now to Fig Ib, let R, the number of rows, be held constant, but let N, the number of particles in each row (S and T), be increased X-fold. The capacity, C1, of

Jan 1, 1949

Jan 1, 1967

By E. R. Darby

When bronze is melted in open-flame furnaces a considerable amount of slag is formed during the melting operation. This slag may be incidental to the melting practice or it may be formed intentionally by slag-forming constituents added to the furnace charge to provide a covering for the melted metal When this slag is removed from the furnace, it contains, in addition to the free metal carried with it by the skimming operation, a considerable amount of metal as oxide either combined or mechanically mixed with it. By the usual crushing and washing methods this metallic oxide generally goes to the tailings pile, so diluted by other foundry waste that its recovery is economically impossible. If this furnace slag is not inixed with other foundry waste, practically all of the metal oxide as well as the free metal may be recovered by some form of smelting operation. The first side of the problem to be considered is the amount of slag produced. It may not be true that the majority of foundries have no record of the amount of slag made, but it is certainly true that a very great many either have no record or pay little attention to it. Usually the collection of furnace slag for one normal week's run will be sufficient to determine the advisability of its being handled in a different manner from the crushing and concentrating generally employed. If a large representative sample of the accumulation is crushed and concentrated and the recovery compared with the results of a careful assay, it will be found that a large percentage of the total metal content was lost in the washing process. The percentage of loss will be greater than the metallic oxide content, as some free metal in extremely fine particles always is carried away in grains of slag. From such a comparison, it may be determined whether or not the slag should be melted, sold or treated as before. An example of an actual test of this kind is given below. In a foundry melting 50,000 to 80,000 Ib. of bronze per day, a week's accumulation of furnace slag and ladle skimmings amounted to 16,500 1b.—over three times as much as the foundry superintendent estimated before the accumulation was made. Two tons of this material was taken as representative of the lot. This was ground through a thoroughly cleaned ball-mill and concentrated over a Wilfley table. The

By R. C. Troxell, S. C. Sun

EFFORTS to obtain definite quantitative data when employing the currently used bubble pick-up method1,2 as a pre-flotation investigation tool led to the adoption of the magnifying mirror method and the microscopic method modifications. Quantitative data obtained by these two methods were converted into bubble pick-up indices and bubble pick-up coefficients. Rough correlations were established between the calculated indices and the results of contact angle testing as well as actual flotation under the same conditions. The basic steps of the magnifying mirror method are as follows: 1—mixing 200 ml distilled water, sized and cleaned mineral particles of approximately 0.5 g, pH regulator, and flotation reagents in a glass beaker; 2—swirling the mineral particles to the center of the beaker to leave a clear circumference; 3—pressing an air bubble against the mineral particles for about 1 sec, and then moving the mineralized air bubble to the clear part of the beaker; and 4—dropping all the attached mineral particles of the air bubble by tapping the bubble holder, and counting the number of the dropped particles by looking at the magnified image in the mirror positioned beneath the beaker. This method is impractical for mineral particles which are transparent in water or finer than 200 mesh. The microscopic method is essentially similar to the above described magnifying mirror method, with the exception that the mineralized air bubble was drawn up into the bubble holder and subsequently discharged onto an externally placed watch glass, where the number of pick-up particles was counted with the aid of a microscope or hand lens. Drying was necessary when the discharged liquid interfered with the counting. The results of the bubble pick-up tests can be simply expressed in the form of the actual count. However, this can be misleading because the number of pick-up particles varies not only with the size of bubble but also with the size of particles. This short-coming is largely remedied by the use of the bubble pick-up index. as calculated from the following equation: PI = (pn/p) 100 [1] in which PI and pn are respectively the pick-up index and the number of pick-up particles under any test conditions, and p is the maximum number of pick-up particles of the same mineral under optimum flotation conditions, with the same size holder and particle. The bubble pick-up coefficient is a term coined to denote the difference between the bubble pick-up index of mineral particles in a liquid and that of the same mineral-liquid mixture plus a chemical reagent at the same pH value. For example, the difference between the pick-up index of a naturally floatable bituminous coal in a solution of water and kerosene and that of the same coal in water alone is a bubble pick-up coefficient. Compared with the contact angle method, the quantitative bubble pick-up method is inferior in accuracy but superior in sensitivity. Other advantages of the bubble pick-up method are that the apparatus can be easily assembled, the mineral sample is conventionally prepared, and the test procedure is relatively simple. References S. R. B. Cooke: The Flotation of Quartz Using Calcium Ion As Activator, Trans. AIME (1949) 184, p. 306. 'G. A. Last and M. A. Cook: Theory of Collector-Depressant Equilibrium at Mineral Surfaces. Paper presented at St. Louis Meeting, AIME (February, 1951).

Jan 1, 1954

By Rudolph G. Wuerker

THE Krupp-Renn Process,[1] has been successfully used to treat low-grade iron ores, laterites, titaniferous sands, and other minerals, and before World War I1 25 units were built by the Krupp-Grusonwerk, Magdeburg, Germany. J. J. Howard[2] has shown theoretical advantages of the pyro-metallurgical treatment over conventional approaches; and the process was described by R. Durrer[3].

Jan 1, 1951

Texture Transition in Ordered CuAu, by E. A. Starke, Jr., J. C. Ogle, and C. J. Sparks, Jr., Trans. TMS-AIME, 1969, vol. 245, pp. 169-70. pole figures should have had two parts not one. On the Estimation of Oxygen Absorption by Continuous Molten Metal Streams, by J. Szekely, Trans. TMS-AIME, 1969, vol. 245, pp. 341-44.

Jan 1, 1970

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

Jan 1, 1955

By Lester A. Blackner

Discussion of the paper of LESTER A. BLACKNER, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 102, June, 1915, pp. 1249 to 1290. SIDNEY J. JENNINGS, New York, N. Y.-In the historical part of the development of the caving system discussed by Mr. Blackner, I notice the absence of one man's name, Charles Henroten. Mr. Henroten used the caving system in South Africa in the. Kimberly mines, and realized from his work there that ground would cave when properly prepared. I think it is due him that his name should be mentioned in connection with an exposition of this system in America.

Jan 12, 1915

[JOSEPHSON, W. G.: The Argonaut Mine of Today, M88, 475 JOUET, C. H., biography, M29, 258 Joule-Thompson effect, 98, 381 JOWETT, J. H., biography, M83, 276 JUDSON, S. A.: Operations in the Gulf Coast of Texas and Louisiana for 1926, G26, 659 JUDSON, S. A., EASTON, H. D. JR. AND SCHAEFFER. W. A. JR.: Estimation of Petroleum Reserves in Prorated Fields 114, 11. Abs., YB35, 50 JULIHN, C. E.: Copper---An Example of Advancing Technology and the Utilization of Low-grade Ores. Brookings Lecture, in Mineral Economics (1931 volume, B. W. Mudd Fund)]

Jan 1, 1936

For the benefit of those of our members who are considerable holders of securities,but owing to their isolated situations are not in close touch with the metropolitan market and current quotations, we are publishing two very interesting graphs, showing the course of the bond and stock markets in New York over a long period. These graphs are furnished through the courtesy of the financial department of the New York Tribune.

Jan 11, 1919

US 4,190,434 - In the thermal production of magnesium metal, a mixture of calcined dolomite, an iron- silicon-aluminum alloy as a reductant, and residual slag from the production of ferrochromium is smelted to evolve magnesium vapor, which is then condensed. The use of bauxite is lessened or eliminated because of the relatively high alumina content of the residual slag. R. Bonfils, A. Mena, C. Payn, and L. Septier, assigned to Ste. Francaise d’Electrometallurgie (SOFREM). Feb. 26, 1980. 6 pp. (75-10R). Filed: 6-14-78 (915,387). Priority: France, 6-24-77 (77/20,227).

Jan 1, 1982

Jan 1, 1967

University of Alabama University, Alabama Mining and Metallurgical Society WILLIAM R. HIGGS, President ROBERT E. MEAD, Secretary J. R. CUDWORTH, Faculty Sponsor MILTON H. FIBS, Counselor University of Arizona Tucson, Arizona Miners' Society LEE BLESSING, President R. W. CORY, Secretary E. P. MATHEWSON, Faculty Sponsor B. R. HATCHER, Counselor University of California at Los Angeles Los Angeles, California Student Chapter, A.I.M.E. ARCHER WARNE, President ROBERT JOHNSTON, Secretary E. K. SOPER, Faculty Sponsor EMILE HUGUENIN, Counselor Colorado School of Mines Golden, Colorado Student Chapter, A.I.M.E. J. Ross REED, President ANDREW PERRY, JR., Secretary J. BURNS READ, Faculty Sponsor A. W. NEWBERRY, Counselor

Jan 1, 1936

By Open-Hearth Steel

I received a telegram yesterday from Mr. J. H. Nead saying that he regretted circumstances had come up which prevent his attending the meeting, but that arrangements have been made and Mr. T. S. Washburn, of Inland Steel, will act as the Co-Chairman in his stead. We are sorry, of course, that he cannot be here at this conference. We have, therefore, asked Mr. James J. Bowden, chief metallurgist of Republic Steel Corporation, Cleveland, to act as Chairman and Mr. Tom Washburn to act as Co-Chairman. I will turn the meeting over to these gentlemen at this time.

Jan 1, 1940

Jan 1, 1967