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By FREDERICK MCAKCCOY

THE production of tin from Mexico has never reached the point of being considered a national industry, but the distribution of tin ores is so widespread that there are possibilities that one day it may become of importance. Of the twenty-seven states of the Republic, tin claims have been taken up in sixteen. In all there had been taken up to the end of 1926, two hundred and twenty-five claims, of a total area of about 7400 acres. The first historical mention of tin in the Americas is found in a letter of Cortez to the Emperor, Charles the Fifth, of Spain, which is as follows: Speaking of his manufacture of some small cannon, he says: "For these reasons I took considerable pains to get copper from some provinces of this country, and bought it at a high price in order to get it quicker.

Jan 1, 1929

CYRIL STANLEY SMITH, Chairman CARL E. SWARTZ, Past-Chairman ARTHUR PHILLIPS, Vice-Chairman E. E. SCHUMACHER, Vice-Chairman H. A. MALONEY, Treasurer FRANK. T. SISCO, Secretary 9 West 39th Street, New York, N. 1. Executive Committee 1944 1945 WILLIAM C. ELLIS C. S. BARRETT ALAN MORRIS T. A. WRIGHT KENT R. VAN HORN L. L. WYMAN

Jan 1, 1943

By Cleland N. Conwell

Coals are found in all parts of Alaska, ranging in geologic age from Carboniferous to Tertiary, and grading from lignite through anthracite. Only the Matanuska and Nenana coal fields have been extensively developed. Nenana Field Today roughly 94% of the coal mined in Alaska comes from the Nenana field near Healy. The coal-bearing horizons in the Nenana field are found in a sedimentary sequence of Tertiary age approximately 2800 ft in thickness. The sediments rest directly on schists of possible Precambrian age. Individual coal beds in the field have been designated by both letters and numbers, starting with the alphabetical designations from A to G, and the numbers 1 to 6. Of these coals, the principal beds that are mined are F, 1, 2, and 3. These vary greatly in thickness, e.g., bed 1 ranges to over 50 ft, and beds 2 and 3 to 30-40 ft.

Jan 10, 1972

By J. L. Kenty, J. P. Hirth

The concept of a critical super saturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, is discussed with reference to vapor-solid nucleation. The necessary and sufficient conditions deduced for observations of this type of behavior are: 1) the nucleation rate must exhibit a sharp dependence on super saturation, 2) the growth rate must be sufficiently large that nuclei become observable in the time period of the experiment, and 3) the number of highly preferred nucleation sites must be small. Experiments reveal that the nucleation of silver on sodium chloride is visually detectable at all experimentally accessible super saturations and does not exhibit critical nucleation behavior. Failure to observe a critical super saturation is attributed to the insensitivity of nucleation rate to supersaturation as a consequence of the particular values of the contact angle and the surface free energy for this system. THE concept of a critical supersaturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, arises naturally in homogeneous nucleation theory. Experimentally this type of behavior has been found by Volmer1 and others for water and other low surface tension liquids, as reviewed by several authors.2'3 The same type of behavior has been predicted and observed for heterogeneous nucleation of solids by Yang et al.4 and others,596 as also recently reviewed.2,7,8 In the work reported here on the heterogeneous nucleation of silver on NaC1, however, no critical super-saturation was found. Similar observations have been made recently for other systems.9-11 These results led to a reexamination of nucleation theory which revealed that there are conditions for which critical behavior is not predicted, either for homogeneous or heterogeneous nucleation. Although heterogeneous nucleation is of primary importance in this paper, some insight into critical behavior for such a case can be gained by considering homogeneous nucleation. Accordingly both types of nucleation theory are reviewed briefly. The requisite conditions for critical supersaturation behavior are then considered. The experimental results for the nucleation of silver on NaCl are presented and interpreted in terms of the theoretical presentation. REVIEW OF NUCLEATION THEORY There are essentially two approaches to nucleation theory, the so-called classical theory involving the concepts of bulk thermodynamics, and the statistical mechanical theory in which nuclei are regarded as macromolecules. The classical theory is based on the work of Volmer and Weber12,13 and Becker and. Doring14 and has been extended by Pound et al.15 The crucial assumption in the classical theory is that the small clusters or nuclei can be characterized by the same thermodynamic properties as those of the stable bulk phase. Thus, the nuclei are assumed to have a surface free energy, y, and a volume free energy of formation (relative to the vapor phase), ,, identical to that of the bulk. For deposition under low super-saturation conditions, the nuclei are large and this assumption is satisfactory. However, in many cases of interest, the nuclei contain only a few atoms and this assumption is highly questionable. The statistical mechanical models originated, for the specific case of a dimer as the critical nucleus, with the work of Frenkel16 and were extended later to larger sizes by Walton,17,18 Hirth19 and, more recently, Ht Zinsmeister. These models describe the nucleus in terms of a partition function, the estimation of which is tractable for clusters of 2 to 10 atoms, but extremely difficult for clusters larger than 10 atoms. Although the classical and statistical mechanical models are expected to apply for the limiting cases of large and small nuclei, both are uncertain for intermediate sizes. In this paper we shall treat only the classical model, recognizing that it is exact only for large nucleus sizes and regarding it as a phenom-enological description for small nucleus sizes. When analyses of experimental data using bulk properties show the nucleus size to be small, the resulting parameters should be regarded as largely empirical parameters describing the relative nucleation potency of the system. Considerable justification for the continued use of classical theory is provided by its general success in predicting nucleation behavior as a function of supersaturation and temperature. We emphasize that the qualitative features of the statistical mechanical models, particularly the critical super-saturation behavior that is central to the present work, are the same as those of the classical model. Of course, potential energy terms and surface partition functions replace the volume and surface energy terms of the latter model. The most recent versions of classical nucleation theory have been extensively reviewed.2,3,7 so that only the results are presented here. For homogeneous nucleation of a condensed phase from the vapor phase, the volume free energy change is ?Gv=vrT = =^ln£ [1] where v is the molecular volume of the condensing species. The supersaturation ratio,

Jan 1, 1970

By Scott Turner

GOLD AND SILVER, the monetary metals, have presented in the last year a striking contrast; gold has experienced unusual prosperity, while silver has been depressed more severely than ever before. Gold mining has been hailed as the only basic industry that is able to thrive on depression; the new gold produced is thought by many to be the most important material for the reconstruction of prosperity. Silver production, meanwhile, has been sinking to its level of 40 years ago, and its price to a level never before recorded. These factors have reduced the value of silver produced in 1932 to about the value of the average annual production more than a century ago, that of the decade 1801-1810. No other major commodity in world trade appears to have suffered a greater decline during the present depression.

Jan 1, 1933

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 George M. Fowler

MINING geology is a progressive study, so we must look to the future for the solution of many of its most significant problems. These problems, world-wide in scope, offer ample opportunity for the exercise of the utmost skill and intelligence by all that attempt to solve theta, as it is generally recognized that many ore deposits of the future will he found only by months or years of combined intelligent effort by the several engineering groups. Renewed appraisals are continually being made to better understand the relationship of physical-chemical processes to ore deposition and other mineralization and to interpret the findings of the geophysicists and others in terms of economic results. A study of current geologic activi¬ties clearly reflects the growing tendency for cooperation between the different branches of geology in order to appraise their united efforts. In line with these activities arrangements have been made to transfer the geophysical section of the U. S. Bureau of Mines to the Geological Survey.

Jan 1, 1936

By T. C. M. Pillay, John Chipman

The Si-0 equilibrium in liquid iron was investigated in some detail by Gokcen and Chipman1 who reported equilibrium constants of the following reactions: In each case the thermodynamic equilibrium constant K was obtained by extrapolating K' to infinite dilution. Their results on reaction [I] were consistent with those of earlier observers, and there seems to be little doubt as to the approximate validity of the equilibrium product determined. On the other hand, the results on reactions [2] and [3] indicated unusual curvilinear relationships between the activity coefficients of silicon and of oxygen and the silicon concentration. Since a linear relation is observed in all other similar instances, it was concluded that some source of error had affected the gas-metal equilibrium relationships. Recently the authors undertook a restudy of these equilibria with the view especially to establishing the equilibrium constant of reaction [2]. Their experiments, however, were discontinued before a tbroughly satisfactory answer had been obtained and consequently have remained unpublished until the present time. Quite recently Matoba, Gunji, and Kuwana2 published the results of a very thorough study of these equilibria. It is the purpose of the present note to Compare these three sets of experimental data, a comparison which leads to Confirmation of the results of Matoba and coworkers. The experimental arrangements described by Dutilloy and Chipman were employed. A controlled mixture of Hz, H,0, and argon was led into the induction furnace over the surface of the Fe-Si melt contained in a silica crucible. On account of the slow approach to equilibrium, runs were continued for at least 8 hr and, in some cases, as much as 12 hr. Samples were taken by means of silica tubes at the start and during the final 4-hr period of each run. Out of twelve runs only seven appeared to have approached equilibrium with sufficient certainty to be reported here. The results of these experiments, all at 1600°c, are shown by the triangles in Fig. 1. Equilibrium was approached from both oxidizing and reducing conditions and the direction of approach is indicated by the shape of the triangle. Attempts to extend the study to higher silicon concentrations were unsuccessful on account of the transfer of silica from the metal bath to the upper portions of the crucible by means of a silicon-monoxide mechanism. Matoba, Gunji, and Kuwana used similar methods and approached equilibrium from both sides. Their results at three temperatures are shown by the solid lines of Fig. 1. A line corresponding to 1600 deg is interpolated from their equations and is shown by the dotted line. The results of Gokcen and Chipman at 1600 deg in the range 0.02 to 2.0 pct Si are also shown. At concentrations up to about 0.6 pct Si, these investigators approached equilibrium from both directions, and their results in this range appear to be trustworthy. Above 1 pct Si, however, all of their experiments involved oxidation only, as shown by a decrease in the silicon content of the bath. It now seems certain that they failed to reach equilibrium at these higher silicon concentrations and that the curvilinear relation shown by their results is incorrect. It is evident that their results in the lower silicon range are in good agreement with those of Matoba and coworkers. In fact, a straight line drawn through their results would parallel the dotted line and would differ from it by only 0.05 in log K. The new data also lie close to that line. It may thus be concluded that the three sets of data are in good agreement and that the equations proposed by Matoba and coworkers for reaction [2] are satisfactory . They take the limiting value of log K', at 0 pct Si as log K ,. The slope of each line gives the value

Jan 1, 1962

By W. A. Anderson

IN the pressure die-casting of zinc alloys it is customary to force the molten alloy under high pressure into a permanent steel die by means of a plunger moving in a bushing that has a clearance on the diameter of the order of 0.002 in. Successful operation of the plunger type of machine requires the presence in the zinc alloy of certain percentages of aluminum. Without these aluminum additions, the normal reaction of molten zinc on ferrous materials causes sticking of the plunger and a complete shutdown of the equipment. All of the zinc alloys used for pressure die-casting today contain approximately 4 per cent of aluminum, which is more than sufficient to make plunger operation feasible. The clearance between the plunger and its bushing is an important matter. As the space becomes larger, there is a loss in effective metal pressure. Ordinary gray cast iron served fairly well and is still used in some machines. However, the rate at which the plunger clearance increases with this material is considered by many to be far too great. There is, therefore, a serious interest in finding new materials more capable of retaining the desired clearance during long periods of use. Today many die casters are using special materials for plungers and bushings selected by the somewhat expensive and time-consuming test of actual experience. An analysis of the problem reveals two possible end points of plunger operation: (1) the building up of zinc-alloy plunger-material reaction products in sufficient bulk to cause sticking and (2) rapid solution, wear or erosion, all of which will increase the clearance to an undesirable extent. If neither of these takes place, the plunger will operate for a long time, of course. The authors have developed a laboratory apparatus in which the action of a plunger moving in a bushing immersed in molten zinc alloy could be simulated closely. Such a machine made possible a more rapid and less expensive survey of the available construction materials and an analysis of the specific alloying reactions taking place in the clear-ance area.

Jan 1, 1939

Jan 1, 1968

By J. J. Bowman, E. H. Dix

A lack of experimental data illustrating the effect of composition, particularly in respect to impurities, on the mechanical properties and corrosion resistance of aluminum-alloy die castings induced the authors and their associates to undertake a limited study of these relations. A number of commercial alloys and several experimental variations of a commercial alloy were used for the investigation. Mechanical property, growth, steam, paraffin, salt spray and atmospheric exposure tests were employed. This paper deals with the more accelerated tests and the results they have produced. It is concluded that a high-silicon alloy with all impurities except iron strictly limited to small amounts will develop an excellent resistance to corrosion and retain satisfactory mechanical properties and casting characteristics. As a direct result of this investigation an alloy of this character with superior corrosion resistance is now available commercially. In general, copper increases the strength and decreases the elongation and corrosion resistance. Tin reduces the mechanical properties and the resistance to corrosion. Iron reduces the elongation and, if excessively high, may adversely affect the tensile strength. Even excessively high iron contents do not affect the corrosion resistance, which is fortunate for the die caster as it is this element that is the most difficult to control. Nickel and zinc in limited amounts do not seem to affect the properties or corrosion resistance of at least the high-silicon alloy. Growth tests have confirmed the previous common belief that dimensional changes under either dry or wet conditions at 100" C. are too small to be of practical importance. Introduction The technical literature contains numerous papers describing die castings, their production, compositions and uses, but nearly all of these

Jan 1, 1935

By J. J. Bowman, E. H. Dix

A lack of experimental data illustrating the effect of composition, particularly in respect to impurities, on the mechanical properties and corrosion resistance of aluminum-alloy die castings induced the authors and their associates to undertake a limited study of these relations. A number of commercial alloys and several experimental variations of a commercial alloy were used for the investigation. Mechanical property, growth, steam, paraffin, salt spray and atmospheric exposure tests were employed. This paper deals with the more accelerated tests and the results they have produced. It is concluded that a high-silicon alloy with all impurities except iron strictly limited to small amounts will develop an excellent resistance to corrosion and retain satisfactory mechanical properties and casting characteristics. As a direct result of this investigation an alloy of this character with superior corrosion resistance is now available commercially. In general, copper increases the strength and decreases the elongation and corrosion resistance. Tin reduces the mechanical properties and the resistance to corrosion. Iron reduces the elongation and, if excessively high, may adversely affect the tensile strength. Even excessively high iron contents do not affect the corrosion resistance, which is fortunate for the die caster as it is this element that is the most difficult to control. Nickel and zinc in limited amounts do not seem to affect the properties or corrosion resistance of at least the high-silicon alloy. Growth tests have confirmed the previous common belief that dimensional changes under either dry or wet conditions at 100" C. are too small to be of practical importance. Introduction The technical literature contains numerous papers describing die castings, their production, compositions and uses, but nearly all of these

Jan 1, 1935

By David L. Holt

The contribution of grain boundary shear to total elongation, CS/E&apos;, has been measured in an Al-Zn eu-tectoid alloy that was quenched from above the invariant temperature, then annealed at 250° C to a grain size of&apos; 1.8 p. At 250°C, ks/E&apos; is low at both high and low strain rates, but reaches a maximum, estimated as 60 pct at an intermediate rate of 5 X 10 per rnin. Rate sensitivity, as measured by the index m = a log a/a log E&apos;, follows the same trend, and furthermore the maximum values of m and -cur at approximately the same strain rate. This result, combined with the metallographic observation that boundary migration enhances boundary shearing, is interpreted as supporting a previous suggestion that the high rate sensitivity characterizing super-plasticity is the result of combined boundary shearing and migration. It is suggested that the latter event relieves stress concentrations at triple points, and smoothes boundaries so that stress is governed largely by a viscous boundary shear. GrAIN boundary shear has been considered in relation to superplasticity in several recent papers.&apos; The problem has been to explain the high strain rate sensitivity of flow stress, and the variation of rate sensitivity with strain rate (E&apos;) and grain size (L). The requirements for superplasticity, small L and high T, suggest the reasonableness of an approach to high rate sensitivity involving grain boundary shear. Further support came from experiments on the A1-Cu eutectic alloy,&apos; where it was found that strain rate sensitivity of cast material annealed to produce an equiaxed, micron-size grain is always low; taking as an index of rate sensitivity m = a log a/a log <, m < 0.3. However, m in hot-worked alloy of comparable grain size can be as high as 0.7. In the cast and annealed material, each phase is a single crystal, the only boundaries are interphase boundaries, and it is, consequently, geometrically impossible for boundary shear to contribute to deformation in any major way. Other observations (for hot-worked material) were a-L at constant (low) strain rates and indications that the rate of recrystallization was enhanced as strain rate increased. As a result of this work, it was proposed that high rate sensitivity arises from a deformation mode of boundary shear associated with boundary migration. Migration serves to relieve stress concentrations at triple points, and smoothes boundaries so that they assume properties of fluid films. On the other hand, the low rate sensitivity observed at high and low strain rates reflects deformation of bulk material. Measurement of the variation of grain boundary shear with strain rate and m have not yet been made. Such measurements are important, especially in view of a proposal, differing in detail from the above, that high m arises merely from a transition between a grain boundary shear mode of deformation at low rates to a transgranular mode at high rates.2&apos;4 In the present work, the contribution of boundary shear to total deformation is measured and in addition metallographic observations are made on surfaces of deformed specimens to look at the interaction between boundary shear and migration. The Al-Zn eutectoid alloy was chosen for its homogeneous, fine-grained structure, which is obtained readily without hot-working. It has also been the subject of a previous phenom-enologically directed study. EXPERIMENTAL Material. Compression specimens, cross section 4 by + in., length \ in., were machined from a sand-cast ingot of composition 77.5 wt pct Zn, 22.5 wt pct Al. (The melt was prepared from 99.9 pct Zn and 99.99 pct Al.) After homogenization at 375°C for 50 hr, the specimens were quenched in brine and removed before the heat evolution that accompanies de -composition of the high-temperature phase.5&apos;6 The resulting microstructure, see Fig. l(a), was too fine for grain boundary sliding to be easily studied; coarser structures were obtained by annealing for various times at 2 50°C. Annealing was terminated by a brine quench. Final average intercept lengths between all grain boundaries (both interphase and those lying in a phase), L, were: 0.5 p [annealed for 15 min, Fig. (a)], 0.8, 1.1, and 1.8 p [Fig. l(b)l. Testing Procedure. An Instron machine was used for most of the compressive deformation. Tests were of two types: those in which crosshead velocity was changed in steps to measure m as a function of strain rate15 and tests at constant velocity to a fixed (engineering) strain of -0.2 (20 pct). Stress reached a steady-state value (a) which was plotted, on a logarithmic scale, against log strain rate (E&apos;). An alternate and equivalent evaluation of m was to take the slope of the log o vs log 6 curve. Time at temperature before testing was 15 min. Strain rates covered by the Instron (4 x lo-&apos; to 4 x 10&apos; per min) were insufficient; at a higher rate of 5 x lo2 per min a gas-operated testing machine was used, the gas driving a piston to compress the specimen at a controlled velocity.&apos; To obtain points on the log a vs log E&apos; curve at low rates, specimens were compressed by a dead weight. strain rate was an average value computed by dividing strain at the end of test by loading time. In some tests strain was measured at fractions of the loading time; creep rate was found to be reasonably constant.

Jan 1, 1969

In 1973, US Borax & Chemical Corp. began investing three days wages and about $20 in training materials in every new employee before having him report to his first job. The result? Accidents involving new employees in the past two years have dropped by more than half from the 1972 level. What made this success possible was safety training done with programmed instruction materials-which, incidentally, US Borax also uses for vocational training.

Jan 4, 1976

The pellet plant, built by Dravo Corp, in Groveland, Mich., for the Hanna Mining Co., is now in full operation. Although using jasper, a type of iron ore with low iron content (approximately 28% Fe), the plant has a rated capacity of 1,250,000 tans of pellets per year. In its four years of existence, the nearby concentrating plant has seen its capacity increase from 700,000 tons to 1,500,000 tons a year as part of a major expansion program at Groveland. Utilizing the Dravo-Lurgi continuous grate process, the pellet plant produces %a-in. pellets of more than 60% iron content. The fully-hooded pelletizing grate, largest in the U.S., is 9 ft. 10% in. wide and 223 ft. 1% in. tong over 34 windboxes, with an effective hearth area of 2195 sq. ft. Drying, firing, and cooling functions are all carried out on this single piece of equipment.

Jan 4, 1964

Discussion of the paper of Frederick Laist, presented at the Butte meeting, August, 1913, and printed in Bulletin No. 79, July, 1913, pp. 1147 to 1162. J. C. DICK, Salt Lake City, Utah :-I would like to ask Mr. Laist why a 10 per cent. salt solution was used. MR. LAIST :-The reason for using salt in the solution is to get .the sulphur. The solution of dilute sulphuric acid has no solvent action on the sulphur even after roasting, and the addition of the salt is made primarily to dissolve the sulphur chlorides. MR. DICK:-I would like to ask also if you made any experiments as to grinding fine your calcines, rather than leaving the coarse material. MR. LAIST :-We have not made any experiments along those lines except in the laboratory, but the objections which we have to grinding are that the difficulties of roasting are very much greater when roasting finely ground material than when roasting coarse material, and the difficulties of leaching are somewhat increased; the percolating system is simpler and easier to manipulate, particularly when acid solutions are used, so that we prefer from our experience not to grind. STUART CROASDALE,* Denver, Colo. (communication to -the Secretary +) :-In order to meet the conditions involved in his ore-treatment problem, Mr. Laist has developed a very interesting and apparently successful metallurgical hybrid which he calls the oxychloridizing roast. The lower floors of the MacDougall furnaces are made to accomplish what used to be done on the " cooling floor" in the old days of salt roasting and " hypo " or brine leaching of silver ores.

Jan 11, 1913

By Marius R. Campbell

VARIOUS classes of coals are recognized in this country at the present time. These classes depend largely upon physical characteristics rather than upon chemical composition, and consequently they cannot be accurately defined. The divisions into anthracite, semi-anthracite and semi-bituminous are fairly satisfactory; but the term bituminous embraces so large a variety of coal that it is of little value, and the term lignite is so loosely applied that it has little or no place in a scientific classification. At present there is no way of accurately defining the vari¬ous classes of coal, because no adequate scheme of classification, which applies to lignites as well as bituminous coal and anthracite bas been proposed. The object of this paper is to present such a scheme, which is based upon data obtained dur¬ing the past year by Prof. N. W. Lord,1 in charge of the chemical laboratory of the United States Geological Survey coal-testing plant at the Louisiana Purchase Exposition, St. Louis. All the classifications of coals proposed prior to 1877 were based either on physical characteristics or on proximate analyses, including all of the impurities. These schemes were illogical and highly unsatisfactory, for the physical properties of a coal give little indication of its true composition; and impurities, such as ash and sulphur, are largely the results of acci-

Sep 1, 1905

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&apos; 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&apos; curve is equal to unity.

Jan 1, 1949