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By A. N. Mitinsky

Discussion of the paper of A. N. MITINSKY, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 104, August, 1915, pp. 1697 to 1705. LAWFORD H. FRY, Burnham, Pa. (communication to the Secretary*). -The author assumes that the proportional limit and the elastic limit are coincident or very nearly so, and then further assumes that the stress corresponding to these two points is the least stress which if repeated will cause failure. The point is extremely interesting and it is to be regretted that the author did not quote experimental data to show the relation between the limit of repeated stress and the other properties of the material. The author's suggestion that a steel of poor quality may have a normal value for the yield point and tensile strength (see Fig. 2) and an abnormally low elastic limit, and that this will correspond to a low resistance to repeated stress, may account for a number of failures of axles in which the tensile tests show normal physical properties. If so and if a determination of the proportional limit would have eliminated the material before it was put into service, this determination will merit most earnest attention. It appears, however, that considerable further research is necessary before any definite conclusion as to the quality of a steel can be drawn from its proportional limit. Mr. Mitinsky's paper is extremely interesting and if it stimulates thought and work along the lines indicated, it may prove of considerable practical benefit. H. V. WILLE, Philadelphia, Pa.-The paper discusses the difference between the proportional limit, or elastic limit, and the yield point, and refers to the fact that much harm results from confusion of the terms yield point and elastic limit. Similar confusion has arisen in this country; the American-Society for Testing Materials does not even consider the elastic limit and proportional limit to be identical and recently adopted the following definitions:

Jan 12, 1915

By D. J. Carney, E. Van Meter, J. J. Oravec

A study was made of combustion-air temperatures and factors affecting air temperatures in the open-hearth regenerative systems. Air-temperature surveys in the regenerative system revealed marked thermal gradients in the air above the checkers. The design of the fantail-uptake region plays a prominent part in increasing the heat recovery of the regenerative system. THE efficiency of the open-hearth regenerative system is one of the most important factors affecting open-hearth performance. Until recently, this factor has not received the attention in the literature given to many other items affecting performance, such as the type of charge, speed of charging, and the mechanical equipment of the open hearth. J. S. Marsh' emphasized the importance of the flame temperature and its dependence upon the combustion-air temperature. By means of measured air temperatures in open-hearth furnaces, data were presented which showed a remarkable degree of correlation between production rate and combustion-air temperature. This correlation was extremely good in view of the numerous factors, other than air temperature, which affect open-hearth production rates. In Marsh's work, a 100°F increase in air temperature reduced the heat time by approximately 45 min. Realizing the importance of combustion-air temperature, it is desirable to know which factors control the regenerative efficiency of the open-hearth furnace. B. M. Larsen recently discussed this subject.' The present paper illustrates a few of the more important items that affect regenerative efficiency and combustion-air temperature. In the latter part of 1951, a study of open-hearth combustion-air temperatures was begun at the South Works of the United States Steel Corp. In the initial work at open-hearth shop X, which produces low carbon steel products, temperatures were measured in the uptake in a manner similar to that used by Marsh' and the results obtained were very similar to the Bethlehem data. When it was decided to expand the study of combustion-air temperatures, open-hearth shop Y was selected because of the greater variety of furnace-design features, types of steel produced, and firing rates used. With the use of aspirating thermocouples, continuous gas analyzers, thermocouple and optical pyrometers, a study was made of: 1—effect of combustion-air temperature on open-hearth production rate, 2—thermal gradients present in various zones of the regenerative system, 3—effect of furnace-design variations on air temperature and heat recovery, 4-—effect of furnace-operating variables on heat recovery, and 5—variation in heat recovery with furnace age during the normal furnace campaign. Data collected on individual heats at 15 min intervals included air-flow rate, firing rate, checker temperature, combustion-air temperature, and furnace pressure. These data were collected on approximately 230 heats of steel. In addition, information was obtained at random on air infiltration and combustion-gas compositions. The data gathered have shown the desirability of closer control of open-hearth firing practices, a need for reducing air infiltration in the uptake zones, and a need for further study of design of checkers and of uptake-fantail areas. Equipment Air is practically a nonradiating medium. Consequently, in the measurement of air temperatures, the principle of heat conduction must be used rather than heat radiation. For this reason, aspirating-type thermocouple pyrometers normally are used to measure air temperatures. With these devices, air

Jan 1, 1956

NORTH AMERICA Number Members Alaska 36 Canada 323 Mexico 184 Newfoundland 3 United States Alabama 40 Arizona 111 Arkansas 8 California 646 Colorado 171 Connecticut 90 Delaware 21 District of Columbia 136 Florida 16 Georgia 7 Idaho 66 Illinois 208 Indiana 66 Iowa 11 Kansas 24 Kentucky 32

Jan 1, 1934

By Charles D. Borror, George K. Foster

The Jeffrey mine of the Canadian Johns-Manville Co., Limited, is in the town of Asbestos, situated approximately 100 miles northeast of Montreal and about the same distance southwest of Quebec, in Richmond County, Quebec. Mining operations were started in 1881 on outcrops on a hill, as a side-hill cut, followed by a second and third cut. This development was the forerunner of the present large open-pit operations, the mine now ranking as the largest open-pit asbestos mine in the world. Operations were first carried on by hand, then by horsepower and later by stem cableways. By 1924 the derrick spans, 2000 ft. or more long, became unwieldy. To overcome this, and also to eliminate hand labor as much as possible, steam shovels and railroad haulage were introduced. The steam shovels were replaced in 1928 by larger electric shovels of the full-revolving type. The Ore Body The ore body is a serpentinized peri-dotite rock mass. The chrysotile fibers form a network of veins throughout, varying from microscopic width to two or more inches measured across the veins (Fig. I). These veins may be continuous for a few or many feet; they may increase or decrease in width within a few feet. The veins in which the fibers occur per- pendicular to the veins are known as cross fiber. Those in which the fibers lay parallel to the veins are known as slip fiber. The cross fibers are of better quality, and more in demand. The majority of the fiber

Jan 1, 1948

By George K. Foster, Charles D. Borror

The Jeffrey mine of the Canadian Johns-Manville Co., Limited, is in the town of Asbestos, situated approximately 100 miles northeast of Montreal and about the same distance southwest of Quebec, in Richmond County, Quebec. Mining operations were started in 1881 on outcrops on a hill, as a side-hill cut, followed by a second and third cut. This development was the forerunner of the present large open-pit operations, the mine now ranking as the largest open-pit asbestos mine in the world. Operations were first carried on by hand, then by horsepower and later by stem cableways. By 1924 the derrick spans, 2000 ft. or more long, became unwieldy. To overcome this, and also to eliminate hand labor as much as possible, steam shovels and railroad haulage were introduced. The steam shovels were replaced in 1928 by larger electric shovels of the full-revolving type. The Ore Body The ore body is a serpentinized peri-dotite rock mass. The chrysotile fibers form a network of veins throughout, varying from microscopic width to two or more inches measured across the veins (Fig. I). These veins may be continuous for a few or many feet; they may increase or decrease in width within a few feet. The veins in which the fibers occur per- pendicular to the veins are known as cross fiber. Those in which the fibers lay parallel to the veins are known as slip fiber. The cross fibers are of better quality, and more in demand. The majority of the fiber

Jan 1, 1948

By Cyril Stanley Smith

THE art of metallography is mature and the forms in which various micro-constituents appear are well known. Investigations almost without end have disclosed the importance of the exact manner of distribution of phases on the physical properties and usefulness of an alloy. Surprisingly, however, relatively little attention has been paid to the forces that are responsible for the particular and varied spatial arrangements of grains and phases that are observed. Like the anatomist, the metallurgist has been more concerned with form and function than with origins. In this paper it is proposed to develop the simple concept that many microstructures result from an attempted approach to equilibrium between phase and grain interfaces whose surface tensions geometrically balance each other at the points and along the lines where they meet. From this follows a number of principles which may prove to be of interest to the metallographer and of practical use in explaining failures and in designing alloys for particular service. In general, the discussion will be limited to structures obtained after full annealing. The simple principles do not apply to structures resulting from Widmanstatten mechanisms in precipitation, or to other structures not in local equilibrium and in which lattice coherency is a determining factor. INTERFACIAL TENSION Much has been written by physical chemists about the free energy of surfaces, which manifests itself as a measurable surface tension. Two- and three-phase interfaces in fluids seek a condition of minimum energy and approach a geometrical configuration in which the various forces are in vectorial balance.* Measurement of the angles established between the interfaces when in equilibrium provides a quantitative value for the relative value of the surface forces involved. The case of two fluids meeting at the surface of a solid (of great importance in connection with the flotation of minerals) has often been studied, but there have been few investigations of the equally definite interface between two or more crystals of a single solid phase, or the more complex cases where crystal grains of more than one phase are involved. The principles are best illustrated by considering first the case of two and three immiscible liquids. If, as in Fig I, a liquid, 2, is dropped into a less dense liquid, I, it will form a sphere-if gravity and viscosity can be ignored-for in this shape the interface has the smallest possible area. If these two phases should together encounter a third phase in which they are both immiscible, the geometry will change to become that which gives the lowest total energy for all three interfaces. Thus, if the spherical drop of liquid, falling through r, eventually reaches the interface between liquids 3 and I (we are assuming that the density of 3 is greater than 2, and 2 than I), it will assume the shape of a lens, the angle

Jan 1, 1948

By RALPH HAYES SWEETSER

IRON ore and bituminous coal are the two basic raw materials for the whole iron and steel industry. The ore furnishes the iron and is absolutely necessary-all iron and steel products come directly or in- directly from the iron ores. The bituminous coal furnishes the carbon needed for the smelting of the ores and for the fuel used in all the processes of iron and steel manufacture. The necessary carbon could be furnished in some other form besides bituminous coal. In fact, it is only since the Civil War that bituminous coal has been the chief source of the carbon for metallurgical fuel. For many years only charcoal made from the forests furnished the carbon for smelting iron ores. About 90 years ago, anthracite coal was first used as blast-furnace fuel and for many years continued to be the chief blast furnace and steel making source for carbon. Even in my own blast-furnace experience, I have used charcoal in Canada and anthracite in Pennsylvania for smelting ores in an iron blast furnace. Bituminous coal, now almost exclusively the source for the carbon used in smelting iron ores, also furnishes most of the heat used in the steel-making processes. It is seldom used in blast furnaces in its natural condition, hut is first coked in beehive, or in by-product coke ovens; such bituminous coal is called "coking coal." Bituminous coal that is suitable for making the producer gas used in the open-hearth steel process is called gas coal. Any bituminous coals suitable for making blast-furnace coke or foundry coke, or that can be satisfactorily used for making producer gas, are classed as metallurgical coals and as such are to be considered in my proposed plan for the evaluation of metallurgical coals. According to Bureau of Mines Bulletin No. 449 these coals comprised 22 per cent of the bituminous coals mined in this country in 1923.

Jan 1, 1926

By Elbert Rowland

THE widespread interest in the alloys of beryllium with copper is due principally to the fact that certain compositions show very favorable precipitation-hardening characteristics and are, in fact, the strongest nonferrous alloys known at the present time. Investigations have been conducted by Masing and Dahl and others on the physical characteristics of ternary beryllium alloys, in an attempt to produce precipitation-hardening effects with a smaller amount of beryllium than that required in the binary copper-beryllium alloys (2.0 to 2.5 per cent Be). The results of these investigations show that ternary alloys of beryllium with Cu-Sn, Cu-Al and Cu-Zn, among others, exhibit promising improvements in physical properties after precipitation-hardening treatment and, while the increases in properties obtained are not as high as those realized from the binary copper-beryllium alloys, excellent properties are obtained with beryllium contents averaging about one-half the amount required in the binary alloys. This paper presents the results of an investigation of the equilibrium relations of certain alloys containing copper, tin and beryllium. The alpha-phase boundary of the ternary system is given for alloys containing from 0 to 1 per cent beryllium. The equilibrium conditions beyond the alpha-phase boundary are presented for alloys containing up to 32 per cent tin and 1 per cent beryllium. The data were collected by means of

Jan 1, 1935

Jan 5, 1976

By C. E. Sims, G. A. Lillieqvist

The following presentation is more a summation of observations made and conclusions drawn over a period of three to four years than a report of experiments made with a definite objective. Tests were made, of course, to verify hypotheses, but the large mass of data was collected incidental to other work. Lack of space forbids the presentation of more than a few of those data. On the other hand, it is unfortunate that some of the most illustrative examples are not available. The work is admittedly incomplete but is presented in the hope that it will stimulate further work along a similar line. The answers to many of the questions left unanswered by this paper will be found only after long and painstaking study, such as is scarcely possible in a commercial laboratory where problems of immediate importance consume most of the time. It is also hoped that this study will in some measure throw light on some of the dark spots of steelmaking, and help to clarify some of the annoyingly vague references to "good practice." Only cast steel was studied and the conclusions apply to cast steel, but it is the authors' opinion that the quality of rolled or forged steel is largely dependent on the quality of the ingot, which is a casting. Although this discussion deals almost entirely with inclusions, it is important that the reader understand that only those natural inclusions which owe their origin to the solubility of certain materials in steel and to the chemical reactions of steelmaking are considered. Accidental inclusions, such as entrapped particles of slag, nozzle, runner, or mold arc outside its province and are not considered. Such accidental inclusions are always dangerous and should be carefully avoided. Relation between Ductility and Nonmetallic Inclusions In September, 1928, an acid electric furnace was put into operation at the Indiana Harbor plant of the American Steel Foundries. Following the usual practice, aluminum additions were made in order to obtain sound castings. Immediately the problem of low ductility arose. Previous to that time, only open-hearth steel was produced, and, aluminum being used rarely in that steel, there had been practically no trouble with low ductility in the lower carbon range.

Jan 1, 1932

By Russell W. Dayton

The metallurgical polarization microscope has been utilized in several researches in the last few years, thus attaining a fair degree of prominence, but little has been written in a manner suitable to a metallurgist concerning the theory of this instrument. In this investigation the theory was carefully studied, and the results are presented here in a detailed manner, yet as simply as possible. The theory is discussed with particular reference to the three chief functions of the instrument: (1) determination of anisotropy; (2) effect of strain; and (3) identification of inclusions. Each of these is investigated experimentally, with especial attention to the mechanism of producing any effect. Where possible, the discussion is supplemented by photomicrographs. The instrument used had numerous defects as a polarization microscope; these and their remedies are discussed. In the microscopic study of transparent mineral sections (chalcography) the use of polarized light has aided tremendously in the identification of a mineral. The determination of strain in transparent substances (photoelasticity) by the use of polarized light has lately become a commercial process, used in testing finished glass articles. The success of the use of polarized light with opaque materials has not been so great. The magnitude of the effects obtained is much less than that of the corresponding effects with transparent materials, and the mechanical difficulties are much greater. Königsberger,"' i in 1909, was the first to apply polarized light to the microscopic study of opaque substances; Endell and Hanemann(2) were the next, in 1913. In 1919 and 1920, Wright(3,4) prepared two papers on the subject. In the first he developed the detailed mathematical theory from the viewpoint of the electromagnetic theory of light, and in the second described the various methods in use, giving improvements of his own. Schwarz(5)

Jan 1, 1935

By Russell W. Dayton

The metallurgical polarization microscope has been utilized in several researches in the last few years, thus attaining a fair degree of prominence, but little has been written in a manner suitable to a metallurgist concerning the theory of this instrument. In this investigation the theory was carefully studied, and the results are presented here in a detailed manner, yet as simply as possible. The theory is discussed with particular reference to the three chief functions of the instrument: (1) determination of anisotropy; (2) effect of strain; and (3) identification of inclusions. Each of these is investigated experimentally, with especial attention to the mechanism of producing any effect. Where possible, the discussion is supplemented by photomicrographs. The instrument used had numerous defects as a polarization microscope; these and their remedies are discussed. In the microscopic study of transparent mineral sections (chalcography) the use of polarized light has aided tremendously in the identification of a mineral. The determination of strain in transparent substances (photoelasticity) by the use of polarized light has lately become a commercial process, used in testing finished glass articles. The success of the use of polarized light with opaque materials has not been so great. The magnitude of the effects obtained is much less than that of the corresponding effects with transparent materials, and the mechanical difficulties are much greater. Königsberger,"' i in 1909, was the first to apply polarized light to the microscopic study of opaque substances; Endell and Hanemann(2) were the next, in 1913. In 1919 and 1920, Wright(3,4) prepared two papers on the subject. In the first he developed the detailed mathematical theory from the viewpoint of the electromagnetic theory of light, and in the second described the various methods in use, giving improvements of his own. Schwarz(5)

Jan 1, 1935

By C. K. Donoho

SILICON is used in almost all commercial steels; up to about 0.20 pct in killed wrought steels and 0.50 pct in steel castings. Above about 0.50 pct in wrought steels and 0.70 pct in cast steels, silicon is considered an alloy. As an alloy, silicon is useful for several purposes: (I) for its effect on magnetic properties of parts for electrical apparatus; (2) for increasing the yield strength of carbon and low-alloy steels without too much sacrifice of ductility and weldability; (3) for adding hardness and toughness to spring and chisel steels; (4) for adding resistance to scaling and carburization to heat-resistant steels; and (5) for its graphitizing effect in graphitic steels. In acid electric steels for casting we are principally interested in the effect listed second; i.e., increase of strength with minimum sacrifice of ductility.

Jan 1, 1947

By Harry E. Cross

Kiln Products commissioned a Waelz kiln 4 metres in diameter by 75 metres long, in South West Africa in March, 1969, to recover nine in a form suitable for the production of electrolytic zinc. The raw material consists of a mixture of zinc silicate concentrates and zinc rich tailings purchased from an adjacent zinc mine - the mixture containing 20% to 25% zinc. The chemical composition of the ore is tabulated and the initial test results are described. Due to the comparatively low temperature at which the ore starts softening the kiln has certain unusual features to enable the temperature to be controlled within the necessary limits. A detailed description of the kiln, the starting-up problems and present operating conditions and results are presented.

Jan 1, 1970

By A. E. Wheeler, H. Y. Eagle

The copper industry in the Province of Katanga, in the Belgian Congo, which is now controlled and operated by the Union Minére du Haut Katanga, had its inception many years ago in the vision of a Scotsman, Robert Williams, now Sir Robert Williams, Baronet. He it was who personally negotiated the mineral concession with King Leopold of Belgium, sent in the prospecting parties who located most of the present mines of the company, later arranged for the Belgian participation from which the present company was formed, and has been its active mentor ever since. The idea back of his efforts was the establishment of an industry on the Congo-Zambezi divide, of sufficient importance to draw up to it the head of the Cape to Cairo Railroad, the dream of Sir Cecil Rhodes, and the consummation of which he had left as a legacy to Mr. Williams, his successor. The reports of the prospecting expeditions showed that copper in profitable quantity was there, but many difficulties lay in the way of the establishment of the infant industry. The isolated location of the mines, various tribal wars, the Boer War, and many other factors contributed to making progress very slow. However, in spite of these difficulties the railroad was finally built and a blast-furnace plant erected at Lubumbashi, near Elisabethville, the capital of the Province. Operations of this plant were started in 1911, treating high-grade oxidized ores and producing pig copper by a reducing smelting. Production has been continuous since that time and the company has grown so that at present it ranks as the largest individual copper producer in the industry. It is a fitting monument to the foresight, optimism and driving force of its founder, and the progressive policies of his Belgian colleagues. In January, 1914, the Union Miniere du Haut Katanga engaged as its consulting engineer, Archer E. Wheeler, metallurgical engineer, at that time general superintendent of the Great Falls plant of the Anaconda Copper Mining Co. Mr. Wheeler was commissioned by the Board of Directors to proceed into Katanga, and make all necessary investigations to enable him to report on a comprehensive development program, and to recommend a scheme of treatment particularly for their low grade

Jan 1, 1934

By Nicholas J. Grant, Oliver Preston

PUBLICATION of data by Irmann' indicating outstanding thermal stability and elevated-temperature strength properties in a sintered aluminum powder product (SAP) stimulated interest in the strengthening of metals by means of a highly dispersed oxide phase. This material was produced by compacting, sintering and extruding a fine flake aluminum powder, resulting in a dense product containing 10 to 16 volume pct alumina, which arises from the thin oxide film on the starting powder, highly dispersed in a matrix of pure aluminum. The method of producing SAP, and the stable high-temperature properties obtained from it, introduced the possibility of developing superior materials for high-temperature service by powder metallurgy methods. The composition of the materials of this type which are presently under consideration is predominantly metallic, containing from less than 1 pct up to about 20 volume pct of the oxide. As a result, other properties of these materials, such as electrical and thermal conductivity, thermal shock resistance, and to a certain extent ductility, notch sensitivity, machinability and hot working properties, are also predominantly metallic. These alloys do not constitute, therefore, a completely new class of materials as do the cermets, but rather present a new means of modifying the properties of a metallic matrix. In this sense, SAP type alloys are more closely analogous to the alloy aging systems. While the strength properties realized in the oxide-pure metal systems at the lower temperatures are substantially less than the best attainable in the aging systems, the thermal instabilities in the latter make them of less value for use at temperature much above their optimum aging temperatures, as indicated in Fig. 1. While the means of obtaining an oxide dispersion are more difficult and costly than conventional aging processes, in the light of the as yet limited understanding of such systems there is considerable promise of improved high temperature properties arising from the thermal stability of these structures. Since the development of SAP in 1946, its properties and the properties of a series of similarAl,O,-A1 products containing from about 1 to 20 pct aluminum oxide have been fairly extensively studied and reported.'- "articular attention has been given to

Jan 1, 1958

By W. A. Doble

Opinions differ as to whether the water-wheel almost universally known as the Pelton type belongs to the impulse, the tangential, the reactive, the jet or the percussion class, or to a cross between two or more of these classes. The fact is, that for an almost infinitesimal part of a second the axis of the jet of water strikes the bucket of this wheel at a true tangent to its base-line. The percussion of the water, striking the bucket, imparts an impulse to the wheel, causing rotation; and generally the bucket is so shaped that the direction of the jet is

Jan 1, 1900

Secondary minerals are the result of a process of concentration and enrichment and are commonly richer than the primary minerals of the same deposit. Secondary ores that contain abundant sulphides are commonly distinguishable in the field from primary ores; this distinction is more difficult with ores that carry a small quantity only of sulphide minerals, and microscopical examination of the ore in thin section is advisable in all doubtful cases. It is frequently difficult, and in some cases impossible, to determine the primary or secondary character of quartzose gold ores. The safest guide is the presence or absence of gaseous or fluid inclusions in association with the ore minerals; such primary association coupled with a lack of traces of oxidation is indicative of primary origin. Any ore that carries traces of oxidation, such as iron stains, endritic oxides of manganese, kaolin and so forth must be considered to have been acted upon by surface agencies, and secondary enrichment must be suspected. Further examination, however, may indicate that the contained value is primary, and, therefore, persistent in its vertical distribution. The manner of occurrence of secondary minerals is frequently characteristic; secondary minerals, being due to the action of surface waters, are commonly found in cracks through earlier minerals, or as crusts lining vugs or surrounding nucleal masses, or in general, in some distribution later than and not conforming to the arrangement of the primary minerals. Secondary sulphides are often found as soft black pulverulent masses or coatings, although they frequently occur well crystallized or as

Jan 1, 1932

By H. C. Spaulding

The rapid increase, during the last few years, in the number and magnitude of applications of electric power-transmission to commer cial uses in this country, has been due principally to three causes: first, the ability and enterprise of those who have been identified with the progress of electrical industries, since electric illumination became an economic fact instead of a laboratory-experiment: sec ondly, the readiness of the American people to adopt new and ad vanced methods as soon as their superiority has been fairly demon strated; and thirdly, tile economy and flexibility of the apparatus employed, when properly designed and constructed, and installed under suitable conditions. Basing our judgment on the world's advance in scientific devel opments during the past century, we may reasonably conclude that in no other country would the pioneeis of electrical invention, whose names have now become household words, have received the prompt and plentiful financial support which has enabled them to inaugurate undertakings of exceptional magnitude, even in this era of tremendous monetary organizations. And, on the other hand, we have seen, in the numerous financial and engineering failures inseparable from such rapid development, the natural results of a too implicit faith in electrical omnipotence. It is not to be wondered at that conservative engineers have been slow to adopt this new and mighty agent in the solution of exten sive problems, and under circumstances where a single failure means not only a greater or less financial sacrifice, but the loss, in a greater or less degree, of professional reputation. Be mechanical engineer, while recognizing the fact that thousands of horse-power are to-day transmitted by electrical means, from sunning the lathe in a dentist's office to the operation of a fifty-ton travelling crane; from passing a cooling draught of air through a

Jan 1, 1891

By A. G. Spillette, R. L. Nielsen

The purpose of this paper is to further the understanding of reservoir response to hot-water injection by desuribing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterfioding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil us continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few." Even if extensive data were available, two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements," laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments — injectivity/productivity tests and pilot floods—results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey" and Spillette' recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery.'."1° Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot-water injection are that (1) no gas phase is present and (2) the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. Darcy's law for multiphase fluid flow relates the velocities of the oil and water phases to the phase pressure gradients by the following relations:

Jan 1, 1969