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By Richard Schellinger, Ronald H. Carlson, Robert D. Norris

INTRODUCTION A very important key to the success of an in-situ leach venture is proper choice of well field chemistry, in which type and concentration of oxidant plays a significant role. For proper design of well field and plant, an engineer must be able to estimate uranium production levels and their change with time. The rate controlling step in the uranium leach process is generally acknowledged to be the oxidation step (Goddard and Brosnahan, 1980; McKnight and Anthony, 1979; Mays, 1979). Uranium head grade is very dependent upon concentration of oxidant injected into the ore zone. If oxidant levels are too low, uranium production requirements will not be met; if levels ate too high, excess oxidant will be wasted in side reactions with gangue material and leach economics will suffer. To date, no reliable laboratory technique exists for generating data easily translatable to field conditions. Empirical correlations based upon lengthy field testing have been the major tools avail- able to the design engineer to date. During the past five years, FMC has developed lab- oratory techniques for studying uranium leach chemistry under conditions simulating as closely as possible the field situation. Both agitated batch and consolidated core leach procedures have been developed. Results of FMC agitated batch studies are described in detail in a companion paper (Carlson, et. al., 1980). This paper will focus on the technique developed for leaching consolidated undisturbed core under simulated down-hole conditions. Through use of a follow-up computer model (Winkley, 1980), generated data can be translated to expected field response, thus providing the design engineer with valuable information in a relatively short period of time. CHEMISTRY In addition to uranium (+4), other oxidant-consuming species present in uranium ore are iron sulfides and carbonaceous material. Iron sulfides are usually present in concentrations far exceeding those of the other two materials and, therefore, represent the major oxidant-consuming species present in uranium sandstone ore. Previous studies (Carlson, et. al., 1980) have shown that iron sulfides exist in both Texas and Wyoming ores as a mixture of pyrite and marcasite (FeSz); furthermore, uranium mineralization (existing as uraninite) was shown to exist as a fine granular material coating or imbedded in iron sulfide crystals and sand grains (i.e. quartz and feldspars). The leach chemistry of a uranium ore body can be described by the following equations using hydrogen peroxide (Hz021 as oxidant:

Jan 1, 1980

By P. Barnes

(Read at the Philadelphia Meeting, February, 1878.) SOME statements have already been made to the Institute in reference to the cost of other departments of the above-named works, and some details have been given in tabular form.* For the purpose of the present paper it may be sufficient to say that this converting works is made up of three buildings, a cupolahouse, an engine-house, and a converting-house. The machinery and fixtures comprise two blowing-engines, two pressure-pumps, two five-ton converters, five hydraulic cranes, three pig-iron cupolas, four spiegel cupolas, two lifts for the cupolas, together with the usual arrangements of smaller parts. Every effort was made in the construction to combine efficiency of operation with durability, and the general course of the operation of the works during two and a half years seems to warrant the belief that the large outlay has been fully justified. • In the accompanying tabular statement all items on vouchers less than ten dollars, and all freight items have been omitted. * See Transactions of the. Institute, iv, 105, v, 427; also, Engineering and Mining Journal, vow. xxi, 561, xxiii, p. 439, xxiv, 419.

Jan 1, 1878

By Robert W. Hunt

In 1888 the writer had the honor of submitting to the Institute a paper on " Steel Rails and Specifications for their Manufacture."* In his judgment the specifications were sufficient for "that day and generation." In that paper I said: '' The first duty falls upon the railroad engineer in designing his section. If that is bad, the steel-maker will be heavily handicapped in trying to furnish a satisfactory rail. I suppose it is hopeless to expect the adoption of standard sections."

Jan 1, 1896

By J. W. Bolton

PRODUCTION of sound bronze castings is a matter of great practical interest to users and manufacturers of high-grade non-ferrous engineering specialties. Although there has been much excellent research in this field, there still remains some confusion regarding the fundamental principles underlying production of really sound bronze. The literature of the past 20 years on this subject indicates that the prevailing opinion of metallurgists and foundrymen has been that unsoundness in bronze is due generally to oxidation. The following references are typical.

Jan 1, 1929

By D. L. Johnson

Only general treatment of a subject of such scope can be given in a short paper, therefore, except in a few instances, statistics and descriptions of specific installations are omitted. The earlier applications of electricity to the production of petroleum in the Mid-Continent field were widely separated chonologically, each holding a special interest, and each contributing greatly to the present development. Electric Pumping One of the first installations of electric pumping was on a lease near Jenks, Okla., in the Arkansas River bed, where a difficult problem was solved by the use of motors. The Arkansas River had frequent flood periods which interfered seriously with the use of jacks and pull rods. Small piers were built with old casing used as piling, and upon these were set small jacks driven by 3-hp. squirrel-cage motors. The starting switches were located on a bank and the power was furnished by a small generator, which was driven by an oil country gas engine. This installation was made in 1913 and is, I believe, still in satisfactory operation. In 1914, the Cushing field came in and the Hill Oil & Gas Co. electrified its Shamrock property, using eight-pole Star Delta motors, rated at 10 to 30 hp. and belted through countershafts to the band wheel. Power was furnished by a small generating plant consisting of two 135-kw. machines, gas-engine driven. Considerable difficulty was experienced in the early operation of this station because of low voltage. It is characteristic of small alternating-current generators that voltage regulation will be poor with widely fluctuating loads. This field had three producing sands, and a number of wells were redrilled with the motors, and this, together with a great deal of swabbing, was responsible for the bad load conditions. However, when the wells had settled down to steady operation, the electric equipment functioned satisfactorily, and continued in use as installed until a few years ago when the present owners contracted for service from a central-station company and shut

Jan 1, 1928

By J. Nolan, B. Ande’n, E. Lindgren

Field testing was conducted at the Strassa Iron Ore Processing Plant to evaluate high-gradient magnetic recovery of iron from the plant's tailings. The installation is the first commercial application of the Sala Continuous High-Gradient Magnetic Separator (HGMS) Model 480 Carousel. The objectives of the five-month testing program included optimization of the operating parameters using SSDEVOP techniques to maximize iron recovery, along with establishing a long-term operating history for the SALA 480 HGMS Carousel. The effectiveness of the optimization procedure, the net benefit in term of iron recovery, and equipment performance are discussed in the paper.

Jan 1, 1983

By Jose J. Alvarez

INTRODUCTION Three major plant processes control the operation of an uranium in-situ mining plant. The three pro- cesses can be categorized under the headings termed - loading, elution, and precipitation. All other plant processes can be subcategorized under the three. In summary, the major plant processes in an in- situ mining plant are: 1. Loading - The pregnant lixiviant from the production wells flows through anion exchange resin. The loading of the uranium on the resin is controlled by various factors, such as ionic strength, valence, functional groups, etc. 2. Elution - The uranium-loaded resin is eluted or regenerated by a high ionic strength solution. The effluent from this process is de- fined as the pregnant eluate. 3 . Precipitation - The pregnant eluate is chemically treated to attain the ideal conditions for the selective precipitation of uranium. Hydrogen peroxide is an ideal precipitating agent under URI conditions. This paper will focus on two of the major processes: Elution and Precipitation. For the most part this relatively young industry has grasped the theory of liquids in continuous flow for the operation of the plant processes. Likewise, URI initially operated the two processes of interest with the continuous flow concept. Through laboratory experiments, URI has abandoned the flow concept and operates the eluting and precipitating stages with the concept of "batch" processes, whereby only one container, filled to a specified liquid level, is chemically processed. In the proceeding sections, each of the two pro- cesses will be discussed in detail, from their original concept to the present operation. Only minor modifications were made to the existing circuits for the conversion with results revealing a greater level of efficiency. ELUTION The elution of the loaded anion exchange resin can be achieved by different high ionic strength solutions. The selection of constituents is dependent on both chemical and economic considerations (i .e., efficiency and operating/restoration factors). The regenerant presently used is a pH 9.5 solution containing 7.5% NaCl and a mixture of Na2C03/NaHC03. expressed as 2.5% NaHC03.

Jan 1, 1980

The annual report of the Secretary of the Southern California Local Section for the year ending May, 1919, says that the Section was called upon to give all the assistance possible for the different Liberty Loan drives, for the Red Cross drives and not only in the canvass of our membership, but the canvass of all of the mining companies represented in this city. The committee on the Red Cross drive on which we were represented raised a larger proportion of the total amount than any other in the city. The subscriptions for Liberty Bonds from the members of our' Section that were credited to the Committee of the Joint Technical Societies exceeded in amount the subscription from the members of all the other technical societies combined. Members of our Section slid splendid and efficient work throughout the first half of the year at the Red Cross headquarters in this city, and under the leadership of A. B. W. Hodges and F. B. Close, systematized the work of handling the enormous quantity of material that passed through that organization. Mr. E. A. Montgomery directed the canvass of the mining companies of this city in the bond drives, and the Executive Committee did its part in solicitation among the mining engineers. The Section, together with the local sections of the American Chemical Society, American Institute of Architect, American Institute of Electrical Engineers, American Society of Civil Engineers, American Society of Mechanical Engineers, and the local Engineers and Architects Association, forms what is called the Joint Committee of the Technical Societies. of Los Angeles. The honor of having the first president of this combined organization of engineers was given to us with, the election of Mr. Seeley W. Mudd. Upon Mr. Mudd's entering the service, Mr. George A. Daman of the Electrical Engineers was elected to the position and served splendidly during the latter part of the year. It devolves upon this Section to be represented upon this Joint Committee by three members, and it is our duty to supply a speaker once in six weeks to address the engineers in attendance at the weekly luncheon. During the year not a few of the most prominent men of the engineering professions have spoken upon subjects of the greatest interest to us all. Had it not been for the organized team work in the engineering profession available through this Joint Committee, there would have undoubtedly been passed in the recent session of the legislature of this state a bill for licensing and registering all professional engineers in this state, which, in the opinion of your Executive Committee and a large proportion of the membership of this Section, would have fallen far short of either protecting the engineer or protecting the public from impostors. That the public is awakening to the importance of what our National Society represents in the profession of mining engineering can be well inferred from the increasing number of inquiries your Secretary receives regarding the reputation of mining engineers. The necessary qualifications which a membership in the Institute requires and the membership of an engineer in this National Organization is more and more a criterion as to the ability of an engineer who represents himself as such, to the general public.

Jan 9, 1919

At the University Club, New York, Jan. 23, Chairman George E. Hale and other officers of the National Research Council, gave a dinner to officers of the national engineering and other societies. About thirty persons were present, including officers of the National Research Council, the four Founder Societies, American Society for Testing Materials, Society of Automotive Engineers, Inc., Illuminating Engineering Society, United Engineering Society, and Engineering Foundation. Letters were received from the Western Society of Engineers, which also had been invited. Gano Dunn, vice-chairman of National Research Council, was toastmaster. The proposed permanent organization of the National Research Council and possible methods of connection with the national engineering societies, either directly or through Engineering Foundation, were outlined. It was suggested that not only the four Founder Societies be represented in the Engineering Division of National Research Council, but also that the other national engineering societies be admitted to membership. It was proposed that the Engineering Division should have a chairman who should be an engineer of wide reputation and of the highest professional attainments who should devote his whole time to the establishment and development of the Division. Methods of organizing industrial research were discussed. At a subsequent meeting of the National Research Council, an invitation was issued to each of the national societies to form a research committee encouraging that committee to become active in the promotion of research within its respective field. Due recognition is to be given each committee in the general organization of the National Research Council. Dr. H. M. Howe, in a very interesting and comprehensive address, told of much important work that had been clone by the various sections of the Research Council, as that of mechanical engineering in developing the often rather nebulous devices for helping win the war and putting them in such form that they could be of direct use to the military service. The section on metallurgy, till lately under Bradley Stoughton and now under G. H. Clevenger, did much valuable work in the improvement of helmets and body armor and made very extensive ballistic tests with refractory steels for this purpose. Important work was done in investigating the fatigue of metals and results of great moment were achieved. The committee on ferro-alloys, under J. E. Johnson, Jr., did important work in effecting economy of manganese in steel manufacture with a view to reducing the necessity for importation of manganese ore, thus releasing ships for other purposes. , The section on electric welding has accomplished valuable results in the development of electric welding for ships, a new branch of industry of very great promise.

Jan 3, 1919

By Edgar Kendall

A KNOWLEDGE of the fundamental principles of locating, sampling, testing and evaluating materials is essential in prospecting for mineral aggregates. In this discussion, mineral aggregates will be considered sand, gravel, crushed stone and slag that are used as materials of con-struction. The quantity of mineral aggregates produced in the United States during the year 1935 for such purposes was roughly 165,000,000 tons, about 60 per cent of which was sand and gravel, 37 per cent crushed stone and 3 per cent crushed slag. The total value of this material was approximately $100,000,000. It is apparent therefore that the prospect-ing for suitable mineral aggregates is of considerable economic importance. In prospecting for mineral aggregates, the methods employed are the same whether the organization is large or small. In the large organiza-tion there may be available geologists for locating sources of supply, a land acquisition department to arrange for the necessary options or permits, engineers to do the sampling, a laboratory for testing, and a board of consulting materials engineers to make the final selection. Even small organizations must follow the same general procedure, though the respon-sibility for the selection of aggregates may rest with one man, who may or may not be an engineer, but who must depend entirely upon his own judgment.

Jan 1, 1939

By Eckley B. Coxe

IN making surveys in the anthracite coal regions of Pennsylvania, the ordinary engineer's chain (50 or 100 feet long) is generally used, both above and below ground. Sometimes, where it is difficult to chain, as, for instance, across a chasm, a wire is stretched from one station to the other, the distance is marked on the wire and its length is then measured with the ordinary chain. Having had occasion lately to make some surveys where it was necessary to determine with great accuracy the position of the land or property line, not

Jan 1, 1874

By Eckley B. Coxe

In making surveys in the anthracite coal regions of Pennsylvania, the ordinary engineer's chain (50 or 100 feet long) is generally used, both above and below ground. Sometimes, where it is difficult to chain, as, for instance, across a chasm, a wire is stretched from one station to the other, the distance is marked on the wire and its length is then measured with the ordinary chain. Having had occasion lately to make some surveys where it was necessary to determine with great accuracy the position of the land or property line, not

JUDGE Samuel E. Schull, in the Court of Quarter Sessions of Monroe County, Pa., handed down a decision on July 2, declaring the Pennsylvania law for the Licensing of Professional Engineers and Land Surveyors to be in violation of the Constitution of the State of Pennsylvania and also of the 14th amendment of the Constitution of the United States. The case was that of George E. Stevenson, who was arrested in June, 1922, charged with the practice of the profession of land surveying without first obtaining a state license. Mr. Stevenson had had forty years of practical experience as an engineer and land surveyor, and as set forth in the findings "had attained unusual skill, distinction and reputation in his said profession, and, on said date and for a considerable period thereto-fore and down to the present time, was and is President of the Engineer's Society of Northern Pennsylvania." That part of the decision referring to the unconsti-tutionality of the act is quoted in full as follows: This matter now comes on to be heard on argument as to the constitutionality of the said Act of May 25, 1921, P. I. 1131. The defendant urges that the same is unconstitutional: First: Because it is in violation of Article 3, Section 3, of the Constitution of Pennsylvania, which provides: "No bill, except general appropriations bills, shall be passed containing more than one subject which shall be clearly expressed in its title." Second: That the same is discriminatory and, therefore, in violation of the 14th Amendment of the Federal Constitution. In this case, we: are confronted by the Act of Assembly bearing the title "an act to regulate the practice of profession of Engi-neering and Land Surveying; creating a State Board for Regis-tration of Professional Engineers and Land Surveyors; defining its powers and duties, imposing certain duties upon the Common-wealth and Political subdivisions thereof, in connection with public work and providing penalties." We meet in the title of this act, a recognition of the fact that it is the legislative intent to deal with two professions: First: Engineering. Second: Land Surveying.

Jan 8, 1923

By John Chipman, Karl L. Fetters

Tax relationship between the composition of the slag and that of the underlying metal during the refining of a heat of liquid steel may best be studied in the light of the two broad physicochemical concepts of equilibrium and reaction rate. Actual steelmaking processes, typified by basic open-hearth practice, involve such complexities of operating variables that it is impossible to distinguish with any degree of certainty between the general limiting conditions imposed by chemical equilibrium and the effects associated with rates of diffusion or of chemical reaction. Further advances in the physical chemistry of steelmaking will depend upon our ability to distinguish clearly between these two kinds of effects, and the experimental work that must be done falls naturally into two classifications. The first is the study of chemical equilibrium that cannot be carried out with assurance under operating conditions but must be done in the laboratory. The second is the subject of rates of reaction and diffusion and the mechanism of the process as a whole, which can best be studied under operating conditions. The latter is not entirely independent of the former, since its interpretation often requires a knowledge of the equilibrium state. It is the purpose of this and of several papers that will follow to present the results of laboratory investigations of equilibria involving liquid steel and slag. Open-hearth slag is a complex mixture containing at least eight major components and perhaps twice as many whose influence may be classified as probably minor. It is not surprising that progress toward a complete understanding of such a material at high temperatures has been slow. Attempts to apply the established principles of physical chemistry to the behavior of the individual components of this mixture have been beset by an almost complete lack of data on its chemical properties in the liquid state. This has necessitated the adoption of various methods of approximation based upon such assumptions as, for example, that for a given component the ratio of its mol fraction in the slag to that in the metal is a constant, or that the molecular composition of the liquid slag is the same as its crystalline constitution after solidification. From the thermodynamic viewpoint, such assumptions are merely useful dodges, which enable one to hazard a guess as to the magnitude of the more fundamental quantities, the chemical potentials and activities of the components of slag. The problem of determining the activity of each substance in an eight-component system seems too complex to be undertaken without the aid of generalizations derived from experimental data on similar systems containing a smaller number of components. Accordingly, it was planned in the present investigation to study the equilibrium of molten iron with the simplest

Jan 1, 1941

By Karl Fetters, John Chipman

The relationship between the composition of the slag and that of the underlying metal during the refining of a heat of liquid steel may best be studied in the light of the two broad physicochemical concepts of equilibrium and reaction rate. Actual steel-making processes, typified by basic open-hearth practice, involve such complexities of operating variables that it is impossible to distinguish with any degree of certainty between the general limiting conditions imposed by chemical equilibrium and the effects associated with rates of diffusion or of chemical reaction. Further advances in the physical chemistry of steelmaking will depend upon our ability to distinguish clearly between these two kinds of effects, and the experimental work that must be done falls naturally into two classifications. The first is the study of chemical equilibrium that cannot be carried out with assurance under operating conditions but must be done in the laboratory. The second is the -subject of rates of reaction and diffusion and the mechanism of the process as a whole, which can best be studied under operating conditions. The latter is not entirely independent of the former, since its interpretation often requires a knowledge of the equilibrium state. It is the purpose of this and of several papers that will follow to present the results of labora- tory investigations of equilibria involving liquid steel and slag. Open-hearth slag is a complex mixture containing at least eight major components and perhaps twice as many whose influence may be classified as probably minor. It is not surprising that progress toward a complete understanding of such a material at high temperatures has been slow. Attempts to apply the established principles of physical chemistry to the behavior of the individual components of this mixture have been beset by an almost complete lack of data on its chemical properties in the liquid state. This has necessitated the adoption of various methods of approximation based upon such assumptions as, for example, that for a given component the ratio of its mol fraction in the slag to that in the metal is a constant, or that the molecular composition of the liquid slag is the same as its crystalline constitution after solidification. From the thermo-dynamic viewpoint, such assumptions are merely useful dodges, which enable one to hazard a guess as to the magnitude of the more fundamental quantities, the chemical potentials and activities of the components of slag. The problem of determining the activity of each substance in an eight-component svstem seems too complex to be undertaken without the aid of generalizations derived from experimental data on similar systems containing a smaller number of components. Accordingly, it was planned in the present investigation to study the equilibrium of molten iron with the simplest

Jan 1, 1941

By Karl Fetters, John Chipman

The relationship between the composition of the slag and that of the underlying metal during the refining of a heat of liquid steel may best be studied in the light of the two broad physicochemical concepts of equilibrium and reaction rate. Actual steel-making processes, typified by basic open-hearth practice, involve such complexities of operating variables that it is impossible to distinguish with any degree of certainty between the general limiting conditions imposed by chemical equilibrium and the effects associated with rates of diffusion or of chemical reaction. Further advances in the physical chemistry of steelmaking will depend upon our ability to distinguish clearly between these two kinds of effects, and the experimental work that must be done falls naturally into two classifications. The first is the study of chemical equilibrium that cannot be carried out with assurance under operating conditions but must be done in the laboratory. The second is the -subject of rates of reaction and diffusion and the mechanism of the process as a whole, which can best be studied under operating conditions. The latter is not entirely independent of the former, since its interpretation often requires a knowledge of the equilibrium state. It is the purpose of this and of several papers that will follow to present the results of labora- tory investigations of equilibria involving liquid steel and slag. Open-hearth slag is a complex mixture containing at least eight major components and perhaps twice as many whose influence may be classified as probably minor. It is not surprising that progress toward a complete understanding of such a material at high temperatures has been slow. Attempts to apply the established principles of physical chemistry to the behavior of the individual components of this mixture have been beset by an almost complete lack of data on its chemical properties in the liquid state. This has necessitated the adoption of various methods of approximation based upon such assumptions as, for example, that for a given component the ratio of its mol fraction in the slag to that in the metal is a constant, or that the molecular composition of the liquid slag is the same as its crystalline constitution after solidification. From the thermo-dynamic viewpoint, such assumptions are merely useful dodges, which enable one to hazard a guess as to the magnitude of the more fundamental quantities, the chemical potentials and activities of the components of slag. The problem of determining the activity of each substance in an eight-component svstem seems too complex to be undertaken without the aid of generalizations derived from experimental data on similar systems containing a smaller number of components. Accordingly, it was planned in the present investigation to study the equilibrium of molten iron with the simplest

Jan 1, 1941

COMPLYING with your frequently expressed wish and, your persistent request, I have decided to prepare a brief little book on metallic ores, based on ,the books of the ancient philosophers and on the experience of practicing miners, that will instruct you how to judge from promising indications which rock forma¬tions, which veins, stringers, or mineral matter are likely to bring. forth metallic ores so that it would be promising and gainful to work them. It explains according to the best of my ability, in separate chapters, as much as you need to :know for your, chosen profession or business, about such things as the favorable characteristics of the terrain, the strike, and dip* and outcrop of veins in general, and also about each metal in particular. Young Knappius: † Then it will be explained to me logically in. this little book and I shall be given a reasonable understanding which mines can be worked gainfully so that my investment will not be wasted but will show a profit. Daniel: Everybody should, of course, use his intelligence and should educate himself well and diligently to become able to understand, [2]‡ as far as that is. possible, from what matter, by what means, and where metals are generated by. Nature; and as a mere side issue he should not spurn the profit that ensues there from. But if his aim is solely and predominantly profit and gain rather

Jan 1, 1949

Jan 1, 1971

By M. Prats

Most of the information available on the heat efficiency of hot fluid injection processes, both water and steam, has been obtained from calculated temperature distributions in the pay zone and adjacent formations. The usual approach has been to write the heat balance equations in terms of the temperatures, and then to introduce whatever simplifications are necessary to help obtain an analytical or a numerical solution. In either case, the assumption has often been made that the vertical thermal conductivity in the flooded interval is infinite, so that the temperatures within the flooded interval are then independent of vertical position. Because it was first made by Lauwerier,l and has been used extensively since, this assumption will be referred to as the Lauwerier assumption. Excellent reviews of the literature on the heat efficiency of hot fluid injection processes have been given by Spillette,2 Flock et al.,3 and Ramney.4 Of course, the most significant contributions take into account the effect of a finite vertical thermal conductivity on the vertical temperature profile. The most general analytic expression for the heat efficiency of a hot fluid injection process is that of Antimirov5 who considers injection of a heated incompressible fluid into a reservoir through an arbitrary number of wells. The rate of heat injection into the reservoir, as well as the injection temperature, is an arbitrary function of time. The geometry of the horizontal flow is arbitrary, although the reservoir is considered to be of uniform thickness and properties and to be of infinite areal extent. Heat transfer within the reservoir is by horizontal convection and conduc- tion, and by vertical conduction. In the formations adjacent to the flooded interval, heat transfer is by conduction in any direction. Thus, the available expression for the heat efficiency due to hot water injection has been developed for rather general conditions. This degree of applicability has not been obtained for other thermal recovery processes. By making the Lauwerier assumption we have been able to obtain expressions for the heat efficiency that are essentially independent of the thermal recovery process, be it steam, hot-water, or underground combustion. Clearly, then, the approach followed here is more restrictive than that of Antimirov5 in that it uses the Lauwerier assumption. At the same time less restrictive assumptions are made about the horizontal heat transfer mechanisms, either in the flooded interval or in the formations adjacent to it. The main difference between our approach and that of other investigators is that the heat balance in the pay zone is expressed for the pay zone as a whole rather than for a volume element within it. The Lauwerier assumption is introduced after the problem is developed along these lines as far as possible. The details of the development of the heat efficiency are given in the Appendix, while the main features of the model are discussed in the next section. Results and their implications are discussed later in a separate section. The Model Certain assumptions have been made to determine

Jan 1, 1970