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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

By Irwin H. Cornell

BRIEFLY stated, the history of the St. Joseph Lead Co. is the story of how a group of men, working for ten years as officers without salaries and stockholders without dividends, developed a small mine in Missouri into what became a large and prosperous corporation. Their courage and faith in the scattered surface deposits of lead coupled with the management's engineering vision and sound financial judgment should prove an inspiration to present-day mining operators and investors. In 1717, John Law's company, known as "The Company of the West," was formed in France and letters patent were granted, for a period of 25 years by Louis XV, for exploration in the Mississippi River Valley. One of the underlying purposes of the expedition, headed by Mr. Renault and Mr. La Motte, a French metallurgist, was development of the lead mines in the area now known as Southeast Missouri.

Jan 1, 1947

Jan 1, 1970

By Gilbert E. Doan

WHEN metallurgists and other engineers meet their college classmates or former teachers, the conversation will frequently become reminiscent and finally turn to engineering education. These graduates have tested the value of their college training in the hurly-burly of the outside world so respectful attention is due their opinions, which, strangely enough, fall into two opposite categories. A member of one group expresses a deep-seated conviction that engineers should have a fuller foundation of physical chemistry, another asks for a more thorough training in mathematics, others wish a more thorough grounding in refractories, a series of courses in petroleum engineering, or in electric welding. Each alumnus of this group

Jan 1, 1937

By L. C. Graton

At the Tenth International Geological Congress, Mexico, 1906, Waldemar Lindgren presented "The Relation of Ore Deposition to Physical Conditions." Retrospect ranks it as the outstanding offering at that Session and as the most fundamental contribution up to that date on the philosophy of ore deposition. Elaborating thereon in his text-book "Mineral Deposits," Lindgren analyzed ore-forming processes under conditions prevailing from great depth up to surface; explained the nature of deposition in each environment; and developed a comprehensive genetic ore classification, which brought wide acceptance and enriching contributions by many. Since Lindgren's latest edition (1933), have come wealths of material relevant to ore genesis, particularly through amazing renaissance and proliferation throughout science. Current publication regarding ores now emanates largely from a generation caught in pressures of the breathless modern tempo, which tempts scant reflection upon earlier truths. Consequently, today's thrilling output contains not a few offerings that need challenge because supplanting interrelationship and system by what seems, collectively, an assemblage of strange, ad hoc and often self-contradictory concepts. From these latter some merit may eventuate but at the probable cost of present confusion and delayed progress. The following pages, naming numerous post-Lindgren advances, record the conviction, held by many, that Lindgren's philosophy, progressively improved, remains the soundest approach to understanding ore genesis.

Jan 1, 1968

The income of the Institute is derived from dues, subscriptions to MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization and at a minimum of expense. J. V. W. Reynders is chairman of the Endowment Committee.

Jan 1, 1923

By V. C. Perini

The 1943 designation of districts for the Transactions† has caused some confusion because of the elimination of the West Central Texas district and the allocation of the counties of this district to the North Texas district and the North Central Texas district. The North Central Texas district as herein defined includes the counties of Brown, Callahan, Cole-man, Comanche, Coryell, Eastland, Erath, Fisher, Hamilton, Hood, Jones, Lampasas, Mills, Nolan, Palo Pinto, Parker, San Saba, Shackelford, Stephens, Stonewall, Summerville, Taylor, Throckmorton and Wise. These counties as listed are the counties of District 7B, State Railroad Commission. This district covers the south central crest and the west flank of the Bend flexure north of the Llano uplift. The west flank of the Bend flexure is on the east boundary of the Permian Basin of West Texas. The North Texas district, District No. 9, State Railroad Commission, includes the counties of Archer, Clay, Cooke, Foard, Hardeman, Jack, Knox, Montague, Wichita, Wilbarger and Young. The area of this district covers the crest and south flank of the Red River uplift and the north central crest of the Bend flexure. The greater part of the oil and gas produced in the past from the North Central Texas district has been from Pennsyl-vanian strata. Some oil and gas has been produced from the lower Permian (by the latest selection of the Pennsylvanian-Permian boundary') and minor amounts from the Mississippian and Ordovician sediments. Increasingly important quantities of oil and gas are to be expected from the older sediments by deeper development in proven fields and by new discoveries. Most of the oil and gas in the district has accumulated in localized, well-defined structural traps in limestone and sandstone reservoirs and in traps due to stratigraphic changes in sedimentation, mainly porosity traps in limestone and sandstone lenses, both usually associated with some structural feature. The Stripper Well Premium Plan as adopted by the office of the Federal Price Administrator has been an aid to the producers of stripper wells. The producers are pleased to receive the subsidy to prolong the plugging of wells, but they are not too pleased with the subsidy plan in principle. Most independent operators are in favor of, and think they are entitled to, an increase in the market price for oil. The price is not adequate to meet the requirements of the average independent operator with the continued advance in production, development and wildcatting costs. Old and new pipe lines for oil and gas leading out of the state are removing reserves at an alarming rate. Curves showing the rate of discovery versus production and pipe-line deliveries in and out of the state make a cross that sooner or later will be fatal to the state. Wildcatting not only needs a price increase but every other available incentive and encouragement.

Jan 1, 1945

Jan 1, 1968

Executive SCOTT TURNER, Chairman FREDERICK M. BECKET JOHN A. MATHEWS H. A. GUESS WILLIAM WRAITH Finance HENRY KRUMB, Chairman PAUL D. MERICA ROBERT E. TALLY Admissions JOHN M. LovEJOY, Chairman GEORGE D. BARRON ERLE V. DAVELER WILLIAM H. BASSETT W. D. B. MOTTER, JR. Alternates HENRY B. FERNALD F. JULIUS Polls AMOR F. KEENE

Jan 1, 1932

By AIME AIME

HOLDING the annual dinner-dance of the Institute at the Waldorf-Astoria had become such a tradition that there was widespread regret when it became known that the demolition of the building to make way for a huge office structure would perforce bring to an end the long and enjoyable series of gatherings our Institute had held there. This year the . Commodore was the place at which it was held and the commuters on the New York Central and the New Haven railroad systems, at least, found it a more convenient place for them. Except for the famous "Hoover" dinner, which will probably set a mark for all time, it was the largest dinner the Institute held, 1000 being present, and it taxed the facilities of the hotel to the utmost.

Jan 1, 1930

Jan 1, 1970

By F. Weinberg, L. MacAulay

DAVIS,' in an investigation of solute redistribution along molten rods of dilute silver in tin, concluded that at horizontal temperature gradients below approximately 5°C per cm very little convective mixing takes place. Cole and winegard2 observed temperature oscillations in horizontal melts of tin, with temperature gradients of several deg per cm. They associated the temperature oscillations with the presence of convective flow in the melt. At temperature gradients less than 1°C per cm they did not detect convective flow. In the present work, direct measurements of con-vective flow in liquid tin have been made using a radioactive tracer technique. The results indicate that extensive convective flow occurs at temperature gradients below those previously reported. The apparatus used to determine the extent of con-vective flow is shown in Fig. 1. The graphite boat Fig. l(a), has two rectangular channels both of which contain molten tin. Radioactive Ag110 in the form of Sn-0.2 pct Ag alloy was introduced at the end of one channel, by rotating the cylinder shown. A series of fixed thermocouples were positioned along the center of the second channel to determine the temperature gradient. It was assumed that the two channels had identical temperature distributions. The graphite boat was inserted into a vycor tube which was surrounded by a multiple winding tube furnace as shown in Fig. l(b). The tin was melted in an argon atmosphere. The distribution of Ag110, as a function of position along the boat at a given time after introduction of the ~g"', was determined with the

Jan 1, 1970

Jan 1, 1966

Official Program

Jan 8, 1950

By Marcus A. Grossmann

The Institute has established this lectureship to honor the memory of a great American metallurgist, one whose fame has continued long after his passing. As one scientist recently stated it, "All metallurgical texts gradually become outdated and outmoded, except those of the great Henry Marion Howe." It seems fitting, then, that, once every year, we shouId review, in his honor, some aspects of the science in which he was such a distinguished leader, and also discuss any new data that may help to clarify our concepts. It is my privilege, for which indeed I express the deepest appreciation to this Institute, to offer for consideration a few thoughts on the toughness and fracture of hardened steels. Before proceeding to the data, I wish to express my great indebtedness to many associates whose stimulating discussions, generous contributions of data and cooperation in experiments are gratefully acknowledged. (But I wish to absolve them of any blame that may arise from the way in which their discussions and data have been used!) First, Dr. Edgar C. Bain, Vice President, Carnegie-Illinois Steel Corporation, whose amiable but merciless criticisms and always constructive and thoughtful suggestions help unfailingly to guard against pitfalls. Then to associates at Gary Steel Works, especially Mr. H. B. Wishart, Mr. W. K. Smith and Mr. V. Elliott, for great assistance in securing data. Also to Col. C. H. Greenall, Director of Laboratories, Frankford Arsenal, and his metallurgical staff, including Messrs. J. K. Desmond, H. Markus, D. F. Armiento, H. Rosenthal and Henry George, for numerous data and illustrations. Further to Dr. J. R. Low and Dr. M. Asimow, for helpful discussions of effects of states of stress during deformation and rupture, to Mr. J. M. Hodge for discussions and data, to the staff of the U. S. Steel Corporation Research Laboratory for advice and data, and to the Metallurgical Staff at Duquesne Steel Works. The individual acknowledgments will also be found under illustrations. Acknowledgment is also due to Mr. S. C. Snyder for incredibly meticulous scrutiny of manuscript. To all of these, grateful thanks. Introduction The discussion to be offered here will deal with quench-hardened steels only, and may perhaps be considered under three headings: 1. It was found that, when ferrite was precipitated in the (prior austenite) grain boundaries of hardened steel, the notch-bar toughness was much less than in pieces fully hardened. The fracture took place in the ferrite, and the loss in toughness is attributed to the lower cohesive (cleavage) strength of the ferrite, as cornpared with martensite. 2. When notch-bar impact test pieces of quenched and tempered steels were examined as to their mode of fracture, it

Jan 1, 1947

By Marcus A. Grossmann

The Institute has established this lectureship to honor the memory of a great American metallurgist, one whose fame has continued long after his passing. As one scientist recently stated it, "All metallurgical texts gradually become outdated and outmoded, except those of the great Henry Marion Howe." It seems fitting, then, that, once every year, we shouId review, in his honor, some aspects of the science in which he was such a distinguished leader, and also discuss any new data that may help to clarify our concepts. It is my privilege, for which indeed I express the deepest appreciation to this Institute, to offer for consideration a few thoughts on the toughness and fracture of hardened steels. Before proceeding to the data, I wish to express my great indebtedness to many associates whose stimulating discussions, generous contributions of data and cooperation in experiments are gratefully acknowledged. (But I wish to absolve them of any blame that may arise from the way in which their discussions and data have been used!) First, Dr. Edgar C. Bain, Vice President, Carnegie-Illinois Steel Corporation, whose amiable but merciless criticisms and always constructive and thoughtful suggestions help unfailingly to guard against pitfalls. Then to associates at Gary Steel Works, especially Mr. H. B. Wishart, Mr. W. K. Smith and Mr. V. Elliott, for great assistance in securing data. Also to Col. C. H. Greenall, Director of Laboratories, Frankford Arsenal, and his metallurgical staff, including Messrs. J. K. Desmond, H. Markus, D. F. Armiento, H. Rosenthal and Henry George, for numerous data and illustrations. Further to Dr. J. R. Low and Dr. M. Asimow, for helpful discussions of effects of states of stress during deformation and rupture, to Mr. J. M. Hodge for discussions and data, to the staff of the U. S. Steel Corporation Research Laboratory for advice and data, and to the Metallurgical Staff at Duquesne Steel Works. The individual acknowledgments will also be found under illustrations. Acknowledgment is also due to Mr. S. C. Snyder for incredibly meticulous scrutiny of manuscript. To all of these, grateful thanks. Introduction The discussion to be offered here will deal with quench-hardened steels only, and may perhaps be considered under three headings: 1. It was found that, when ferrite was precipitated in the (prior austenite) grain boundaries of hardened steel, the notch-bar toughness was much less than in pieces fully hardened. The fracture took place in the ferrite, and the loss in toughness is attributed to the lower cohesive (cleavage) strength of the ferrite, as cornpared with martensite. 2. When notch-bar impact test pieces of quenched and tempered steels were examined as to their mode of fracture, it

Jan 1, 1947