Search Documents

By L. D. Clark

Pay-out, the ratio of capital expenditure to annual cash return can be very revealing when employed to gage the merits of a proposed mining venture. It is a quantity, numerically but not physically equal to a factor, by which cash return may be discounted to equal required investment. The fewer the pay-out years, the greater the average annual earning power of the project. Considerable material has been written in the past about the most important and difficult problem mining management faces in evaluation of a property: the optimum production rate for the venture. What daily capacity should be adopted for the proposed operation that it may be the most rewarding to those underwriting it? H.C. Hoover has said, "The most important objective is the least cost per ton mined; and minimum working costs can only be gained by the most intensive production." Theoretically and practically, the quicker the ore is removed, the more profitable should be the venture because of the saving in fixed charges, the consequent lower unit costs and the interest unearned by the profit from the unmined ore. Yet, such performance will be tempered by policy and a restraint imposed by the ratio of capital expenditure to annual cash return. * The 'Annual net profit after taxes but including depreciation and depletion allowances. former will be based upon an analysis of the economic climate anticipated, with its many ramifications including the demand for the product, prices, tax laws, the conduct of labor and related wage scales. The variables and intangibles involved in estimating the optimum production rate for a mine do not readily lend themselves to mathematical relationships or equations and the problem can become complex indeed. The more readily applicable and relatively faster appraisal method will be used which, in addition to being reasonably adequate in most cases, will serve as a guide, should a more expanded and detailed estimate be desired. The first question is what is company policy with respect to the rate of investment return? This will depend on that significant period of time referred to as the pay-out, which can be defined as the estimated interval during which capital investment is returned through application of annual cash return to its recovery. Expressed another way, it is the ratio of capital expenditure to the annual cash return. For example, if the capital investment is $C and the annual cash return is $A (after Federal tax), then $C/$A = the pay-out period in years. That is to say, if $C = $1,500,000 and $A = $214,000, then which is the mathematical expression for the period of time it takes to recover the funds originally invested in a mining enterprise. The relationship yp = $C/$A can be useful — an expression which requires only the significant tern yp to be fixed; in other words, the long range investment policy. For what is the pay-out period but an expression of that policy in terms of the speed, within practical limits, with which an individual or company may want to recover capital expenditure? A policy by which pay-out will be fixed is imperative. This ratio must lie within relatively narrow limits governed by what is economically feasible. It cannot be too low, rendering the ratio impractical or absurd, nor too great, delaying the return of capital for reinvestment beyond a commensurate interval. What pay-out will govern this policy? Federal corporate taxes would seem to present the best measure. Consider mining in Canada where new mines are exempt from Federal income tax for 3½ yr from date of first production. This exemption expressly allows The Act states: "A corporation . . . i s not required to include the profits . . . for the period of 36 months commencing with the day on which the mine came into production in reasonable commercial quantites." a company to recover capital expenditure during the early stages of production. With such an incentive, it is logical to strive for as much capital redemption as possible during this period. Thus, 3½ yr would be a major contribution to the pay-out in Canada. Furthermore, it generally takes from 1½ to 3 yr to develop

Jan 1, 1963

By W. M. Wojcik, R. F. Kowal

Oxygen and sulfur distributions in commercial, 5-ton ingots of killed, medium carbon steel are described. Oxygen distribution is found to vary with deoxidation practice. Irregular distribution of oxygen within ingots makes necessary special precautions in sampling of rolled products for analysis of oxygen. Oxygen distribution is discussed in terms of recently published solidification concepts which had been successfully applied to simpler cases of segregation. These concepts have been found inadequate to explain observed oxygen distributions. Convective movements of the liquid metal, as determined by tracer elements, are shown to be capable of accounting for the observed distributions of oxygen. IN an effort to explore the origin of surface and subsurface imperfections in pierced steel products, a study of oxygen and sulfur segregation was made on ingots cast in open-top and hot-top molds. The results of our previous investigations1"3 have indicated the importance of the location and amount of oxide inclusions in an ingot. Inclusions close to the surface of the ingot have been found to contribute greatly to the formation of imperfections in the surface of finished products. This study of the effects of deoxidation and casting practice on segregation and the resulting oxygen distribution in ingots was initiated to determine the parameters controlling the location of inclusions in an ingot. Segregation of solute elements during solidification of low-melting binary alloys has been studied in the past.1, 5 Formation and growth of inclusions in iron melts have been studied under specific conditions."- In spite of these and other recent studies,10-12 segregation during solidification of commercial, killed steel ingots is not well understood. Consideration of solidification rates, of segregation during solidification of the chill, dendritic, and central zones, and of material balances for the segregated elements has indicated that a simplified theoretical solidification model is not adequate. However, the observed high oxygen contents in localized volumes of the dendritic zone can be rationalized if additional effects of convection currents in the ingots, precipitation, and rapid growth of new phases are considered. EXPERIMENTAL PROCEDURE Steelmaking and Processing. A group of nine killed. medium carbon steel heats having compositions listed in Table I have been studied. The deoxidation and mold practices used were varied to give a wide range of steel oxygen contents. The amounts of aluminum added to the ladle and the ingot casting practices (hot top and open top) were the main variables. The steel was made by a duplex practice in 160-ton tilting basic open-hearth furnaces. All nine heats were top-cast into 24 by 24 in. big end down, fluted molds, to a height between 60 and 76 in., using both open tops and exothermic hot tops. The deoxidation practice and the tapping and teeming details for each heat and ingot studied are given in Tables II and III, respectively. Hot-top practice is indicated by the letter H following the heat designation. Furnace and ladle temperatures were measured by standard disposable-tip, Pt/10 pet PtRh thermocouples. Teeming-stream temperatures were obtained as described by Samways et al.,13 by immersing a Pt/10 pet PtRh thermocouple, covered by a silica sheath, into the teeming stream under the nozzle. The output of this thermocouple was recorded with Leeds & Northrup Speedomax potentiometer. Calibration of the latter thermocouples was based on the freezing point of a pure iron/oxygen alloy (2795°F). The accumulated errors of measurements were within ±10°F. The thermocouple measurements were supplemented in this investigation by continuous recording of a ratioing, two-color pyrometer (Shawmeter), protected from smoke by a blast of clean air within the sighting tube, and calibrated to read with better than ±10°F accuracy. Following teeming of three heats, P, R, and T, tracer elements were added to the steel in the molds to obtain a record of the progress of solidification. As soon as the teeming stream was shut off, a 0.010-in.-thick steel can containing a mixture of crushed standard ferro-titanium and ferro-vanadium (0.05 pet of each alloy element) was plunged into the middle of the steel pool to a depth of 6 in. In about 30 sec no indication of the can or its contents remained. The surface of the open-top ingots solidified in 20 to 30 sec. A study of liquid metal movement and the precipitation of oxides was facilitated materially by use of the tracer technique as titanium has a low distribution coefficient between solid and liquid steel while vanadium has a high distribution coefficient.

Jan 1, 1965

By C. C. Miller, A. B. Dyes

The cost of finding and developing new reserves is continually rising. We must meet these rising costs with more economical operations. This can he accomplished if we revise our ideas of proper well spacing and well allowable to consider the concept of optimum well spacing. According to this concept, the optimum spacing is the one which leads to the maximum present worth for a reservoir when ail factors affecting total cost and total revenue are considered and when the wells are produced in the most eficient manner. Application of this principle efficiently utilizes available well potential and properly considers the recovery eficiency in addition to fixing the spacing on the basis of the amount and value of the oil to he recovered. This Study presents an analysis of one producing zone containing low gravity crude to illustrate the effect of these factors on the present worth and on the optimum economic spacing under two production drives—-evolved gas and water drive. The maximum present worth occurs when the optimum number of wells for open-flow operation is employed. Frequently, this optimum development cal1s for very wide spacing and the ideal field rates are not unreasonable. Under other circumstance. where proration is necessary, an optimum combination of well spacing and well allowable exists which permits production at relatively high rates. The optimum well density in a field depends on the recovery efficiency and the valule of the oil. In solution gas-driven reservoirs this optimum spacing for operation at high producing rates can vary from extremely wide spacing to handle viscous low gravity oil in thin formations to relatively close spacing in thick sands where good recoveries are expected. Because of the better recovery from water-driven fields, the optimum spacing in these fields is closer than in solution gas-driven fields. Also, the water encroachment pattern is dependent upon the well spacing, and an adequate numher of wells is needed to assure a good sweep eficiency. The economic optimum well density in a water-driven field is high enough for this purpose. INTRODUCTION From year to year domestic oil becomes more difficult to find. The fields we do locate are frequently smaller and deeper than older fields and the costs for men, material and equipment are continually rising. To replenish our reserves we must continue to search for and develop new fields, but experience has shown we cannot expect prices to rise in proportion to costs. Consequently, we must meet increasing costs by more economical operations. A vigorous effort is being made within the industry to improve exploration methods, to cope with the problems of deeper drilling, and to obtain a secondary yield from older fields. Many significant contributions have resulted from these efforts. The economic operation of new fields can be further improved by developing these fields on optimum spacing and producing the wells at higher rates. This would avoid the drilling of unnecessary wells and provide additional capital for seeking new oil. While the benefits of these practices are obvious, the problem of defining the optimum development of a field for natural depletion can become very complex. A study of the effect of well spacing and several reservoir variables on economic worth of a specific field is reported here to illustrate the problem and to show the magnitude of the benefits to be realized. This study is necessarily limited to the field conditions selected and is not intended as a general solution of the well spacing problem. It does, however, indicate factors to be considered, the trends to be expected, and the direction in which we should proceed in developing new fields. NO consideration is given to land and legal considerations which might arise. METHOD OF ANALYSIS The optimum method of developing and producing a field is to use the combination of spacing and prora-tion which gives the maximum return. In addition, we do not want to lose recovery. These considerations of maximum return and maximum recovery present no serious conflict. The value of each method of operation is conveniently expressed in terms of its present worth. According to the present worth method of evaluation,' an acceptable annual percentage return is assigned to the operation, and all incomes, capital costs, and expenses are discounted at this rate to the start of the operation. This net value is the present worth. If we apply the same discount rate to several alternate methods of operation, the one yielding the greatest present worth is the best method. If we express net income in terms of price per barrel of oil produced, drilling and equipment costs on a well basis, and expenses as cost per well year, this evalu-

By D. Turnbull, R. E. Cech

FISHER, Hollomon, and Turnbull have developed a theory for the nucleation of martensite. They first tested the theory on Fe-C alloys and low alloy steels. The major factor influencing nucleation of martensite was considered to be statistical composition fluctuations occurring in small regions at high temperature and frozen-in on quenching. These local regions of varying size and composition serve as nucleation centers. They become supercritical, one by one, as temperature is progressively lowered, resulting in temperature-dependent or athermal transformation. Fisher next applied nucleation theory to substi-tutional solid solution alloys. Detailed predictions were made for Fe-Ni alloys because of the availability of free energy data on this system. It was shown that composition fluctuations that were significant energy-wise did not occur, and nucleation frequencies could be calculated from average properties of the system. Nucleation was predicted to occur as time-dependent and having the functional relationship to give a C curve of nucleation frequency vs temperature. The analysis further predicted that the nucleation frequency was extremely sensitive to composition. Experimentally, it would be found that the transformation in some compositions is so slow that measurable amounts will not form in a reasonable length of time. With other compositions, only slightly different, the nucleation frequency becomes so great that the material becomes transformed while still distant in temperature from the maximum nucleation frequency. On quenching an alloy of such composition, the observed transformation kinetics would be similar to those found in Fe-C alloys. Cech and Hollomon repeated experiments of Kurdjumov n which the kinetics of transformation were similar to those predicted by Fisher for Fe-Ni alloys. The alloy studied in this investigation contained 73.3 pct Fe, 23.0 pct Ni, and 3.7 pct Mn. Fisher,' using an idealized model for the extent of transformation as a function of the number of martensite crystals per grain of parent phase, derived nucleation frequencies from the transformation curves of Cech and Hollomon. Complicating influences such as coupling effects between grains in the polycrystalline specimens were neglected. Nevertheless, excellent agreement was found between the theoretically and experimentally derived nucleation frequencies. These experiments, however, could not provide a critical test of the theory. Experimental nucleation frequencies could vary widely from those calculated, depending upon the extent of deviation from ideal partitioning and the extent of coupling effects. Further, since the compositions of material theoretically analyzed and experimentally determined were different, the free energy changes involved in the experimental work could only be estimated. Also, the effect of heterogeneities on the transformation kinetics was not considered. For these reasons, it was decided that experiments designed to test the validity of the Fisher analysis must be conducted on binary Fe-Ni alloys, which were the ones considered theoretically by Fisher. The martensite transformation in Fe-Ni alloys has been the subject of considerable study. Machlin and Cohen have shown that transformation proceeds in a manner quite unlike that in any other ferrous alloy system. They found that single crystals would transform to a large extent in a single burst. In large grain polycrystalline specimens, frequently more than one grain and sometimes the whole specimen would transform at the same instant in this manner. Results on filings indicated that different particles would undergo the burst transformation at widely different temperatures. These results support the conclusion that the transformation behavior could not be described by a single nucleation frequency as would be the case if the nucleation were homogeneous. It appeared that further work was necessary to define the factors responsible for burst-type transformation, so that the conditions could be altered to favor homogeneous nucleation of martensite if such could be accomplished. This report summarizes the results of some experiments conducted with powdered Fe-Ni alloys for this purpose and the re-

Jan 1, 1957

By H. W. Hitzrot

SEPARATING a mixture of particle sizes of material suspended in a liquid medium is by no means an exact science. Selecting machines for individual classifying operations is even more difficult. The plant operator's own background is of course invaluable, and considerable help may be obtained from technical articles, talks with sales engineers, and handbooks on ore dressing. These several sources of information, however, are difficult to marshal in proper perspective for the major decision on classification units that an operator may be called upon to make. To the present writer's knowledge this assembly of facts is not available in handbooks, and technical papers are scarce on classification equipment developed in the past five or six years. It is believed that this paper will be helpful to users of classification equipment at this particular period in the development of hydro-classification. For easy reference the following classification units now available and in use in metallurgical and industrial operations are listed below, with a brief description of each. Unit-type classifiers, bowl classifiers, and bowl desiltors are all rectangular tanks, slightly tilted, with reciprocating rakes or screws to remove settled sands. The unit-type classifier, Figs. 1 and 2, is available in widths from 14 in. to 20 ft and lengths up to 40 ft. The shallow bowl of the bowl classifier, Fig. 3, equipped with rotating rakes, is superimposed on the lower end of the tank. Reciprocating rake compartments for this design range from 18 in. to 20 ft wide. Bowl diameters vary from 4 to 28 ft. The flat-bottomed bowl of the desiltor, Fig. 4, of relatively large diameter, is equipped with rakes rotating outward and partly over a pit, which is created by extension of the rectangular tank into and under the bowl section. Bowl desiltors are available with reciprocating rake sections 4 to 20 ft wide and bowls from 20 to 50 ft in diam. The bowl desiltor is used for applications beyond the range of the bowl classifier. The hydroseparator, Figs. 5 and 6, is a circular tank equipped with slowly rotating rake arms, set on a slope, with interrupted rake or spiral blades to move the settled solids to a central discharge cone. Tank diameters vary from 4 to 250 ft. Tank depths at center are 2 to 3 ft for small units and up to 25 ft for larger units. Hydraulic classifiers of the sizer and super-sorter types, Figs. 7 and 8, are narrow, deep, rectangular tanks divided by vertical baffles into a series of pockets. Hydraulic water is added near the bottom of each pocket. Perforated constriction plates, spiral flow arrangements, or jets are used to disseminate the water under pressure (hydraulic water) throughout the bed of material in the pocket. Discharge valves on each pocket are operated automatically by a pneumatic mechanism, a pincer-type mechanism, or a pressure control and motor combination actuated by a hydrostatic tube within the pocket. Hydraulic classifiers are available in 4, 5, 6, and 8-pocket units of varying constriction plate areas to suit conditions. There is now a jet sizer of unit pocket design that can be made up in 1 to 25 sections or more to accommodate sizing requirements. The hydroscillator, Fig. 9, is a rectangular tank set on a slope of 3 to 4 in. per ft. A bowl is superimposed on the lower end. The bowl bottom is an oscillating rubber-covered disk, perforated to allow hydraulic water introduced beneath the disk to set up a teeter bed and thus produce an oversize or rake product exceptionally free of slimes, and material minus the mesh of separation. A shallow dam at the periphery of the bowl allows the coarse or oversize fraction to spill over and drop down into the tank compartment, where it is moved up the deck by reciprocating rakes. The material, minus the mesh of separation, overflows a circular and stationary weir which is several inches higher than the dam on the oscillating disk. It is carried off in a circular launder in the usual manner. These units are available in bowl diameters from 4 to 14 ft and with reciprocating rake compartment widths to suit the tons per hour to be handled. Centrifugal classifiers include the solid bowl centrifuge and the cyclone classifier. The solid bowl centrifuge, Fig. 10, consists of a truncated cone fixed to a horizontal shaft and rotating at high speed. An internal spiral rotating at slightly less speed continuously removes solids deposited on the inner surface of the cone, or bowl. Feed enters the cone by means of the hollow center shaft. Overflow leaves through ports at the large end of the cone, and oversize solids, moved by the spiral, exit through ports at the small end. Centrifugal classifiers of this type are available in cone diameters from 18 to 54 in. The cyclone classifier, Fig. 11, is a stationary cone having a cylindrical upper section and a lower cone section. Feed is introduced tangentially into the upper cylindrical section under pressure from a hydrostatic head or by means of a pump. Centrifugal force thus induced effects a classification within the cone, the fine sizes being carried off in the overflow through an opening at the top of the cylindrical section. Coarse solids at relatively high pulp density exit through a control valve at the apex of the lower cone section. Cyclone classifiers are available in 3, 6, 12, 14, 24, and 30-in. diam. The cone classifier, Fig. 12, is a steel-plate cone with sides usually about 60" from horizontal. It contains no rotating mechanism. Feed enters a feed-well at center and classification is effected by gravity and pulp density. Fines are carried off in the flow over a peripheral weir at the top of the cone. Settled solids exit through an opening at the apex. An apex valve actuated through levers and rods by the pulp density in the lower cone section is usually supplied. Diameters are usually maximum at 8 ft.

Jan 1, 1955

By N. A. D. Parlee

The diffusion rate of hydrogen in liquid iron has been measured by a gas-liquid metal diffusion cell technique. The diffusion cell was formed by immersing an alumina tube containing hydrogen gas at 1 atm in a bath of stagnant liquid iron. The change in the composition of the melt in the cell was determined by measuring the rate of absorption of the gas in the cell. The appropriate solution to Fick's second law was used to examine the data and calculate diffusivi-ties. The absorption of hydrogen in stagnant pure liquid iron has been found to be diffusion-controlled. The results show that the chemical diffusion coefficient, D, of hydrogen in pure iron in the range of 1547" to 1726°C can be represented by the following Arrhenius relation: D(sq cnz per sec) = 3.2 x X exp(- 3300 i 1800/RT) where the uncertainty in the activation energy corresponds to the YO pct confidence level. Oxygen in the melt (above 0.015 pct 2) increased the apparent rate of absorption of hydrogen. The importance of diffusion data on liquid metals for predicting the rates of certain metallurgical processes has been recognized for a long time. Moreover, these data are much needed to test and develop theory for diffusion in liquid metals. Despite this practical and theoretical interest, however, relatively little reliable information about diffusion in liquid metals is available in the literature. This is particularly true for gas components such as hydrogen, oxygen, and nitrogen in liquid metals, where almost no data on chemical diffusion coefficients are to be found. This is probably due to a multitude of experimental difficulties particularly associated with high-temperature melts. In an effort to fill this gap in information, a research program was undertaken to study the diffusivities and rates of solution of gases in liquid metals. This paper presents the results of a study of the diffusion of hydrogen in liquid iron. EXPERIMENTAL METHOD Two methods for the study of the kinetics of dissolution of gases in liquid metals are being employed in this laboratory. Both involve the measurement of the volume of gas absorbed by the melt as a function of time and as such both avoid the uncertainties involved in chemical analyses of quenched samples for relatively small amounts of gas. In the first method, the gas dissolves in an inductively stirred melt and, in the absence of a slow surface reaction, the results are often interpreted in terms of mass transport across a liquid "boundary layer" between the homogeneous gas phase and well-stirred part of the melt. Other interpretations of the results of such experiments have also been described in the literature.1'5 In the second method a gas-liquid metal diffusion cell is used.' The gas dissolves in a cylindrical column of stagnant liquid metal and, in the absence of a slow surface reaction, the results are interpreted in terms of a non-steady-state diffusion solution to Fick's second law. The weakness of the first method is that while it gives information on the mechanism of absorption by stirred melts it yields an overall rate constant which even in the simplest cases depends on the nature and the thickness of the "mass transport layer" or "boundary layer". It yields no values of diffusion coefficients. The second method was used in this research because in many cases it is possible to determine the diffusion coefficient of the gas component in the liquid metal. In this research it has been utilized to measure diffusion coefficients of hydrogen in liquid iron. The apparatus used was essentially the same as that described by Mizikar, Grace, and par lee but certain modifications have been introduced to meet the elevated temperatures and special conditions of this research. Fig. 1 is a schematic drawing of the apparatus and Table I gives the identification of various parts in this figure. The diffusion cell, shown in detail in Fig. 2, was formed by immersing an impervious alumina tube (hereafter called absorption tube) in a bath of pure liquid iron contained in an alumina crucible. Two types of tubes were used, Morganite triangle RR and McDanel AP35. The crucible was contained in a vertical impervious alumina combustion tube (32 mm ID by 914 mm long) which was closed at both ends by water-cooled brass heads employing O-ring compression seals, Fig. 1. A protection tube enclosing a Pt, 5 pct Rh-Pt, 20 pct Rh thermocouple was introduced through the lower end of the combustion tube

Jan 1, 1968

By A. H. Cottrel

SINCE metallurgy exists to provide strong, tough, engineering materials it must inevitably be perpetually concerned with the problem of brittle-ness. The steel-making industry was created because chemically unrefined iron is brittle. The steel-working and alloy-steel industries exist partly because hardness and ductility are mutually exclusive qualities in structurally unrefined steel. Yet, in spite of these immense industries, the brittle failure of steel ships hulls, bridges, pressure vessels, and pipelines, is still a contemporary problem. In fact, brittleness is a normal property of most solids, including metals and alloys, at low temperatures. Only face-centred cubic metals are commonly ductile at the lowest temperatures, and even here exceptions are known.'," Expensive are-melting processes. under inert gases or vacuum, have been developed to overcome brittleness in titanium, zirconium, columbium. and molybdenum. Polycrystal-line zinc, magnesium, and uranium have little ductility at room temperature. Beryllium, chromium, and tungsten have even less; similarly for antimony, bismuth, germanium, silicon, intermetallic compounds, and metallic carbides, nitrides, silicides, and borides. Oxides and other ceramics would be ideal creep-resistant materials but for their extreme brittleness when cold, and great efforts have been made to overcome this problem by mixing ceramics with metals. In fact, the traditional use of the name metallurgy for what is really the science of engineering materials is a recognition that most non-metallic solids have so far been precluded, by their extreme brittleness, from use as major structural materials in mechanical engineering. Most of what we know about brittleness in metals has come from studies of structural steel, and it is this material that shall mainly be considered. The things we have learned from it have a wider application, at least to other body-centred cubic transition metals, although the extent to which similar ideas can be applied to hexagonal metals and other materials is not yet clear. Fracture and Plastic Deformation The theoretical breaking strength of an ideal solid, about E/10 where E is Young's modulus, has been approached reasonably closely in experiments on fibres. But large specimens break at much lower stresses. For example, brittle cracks in large structural steel assemblies have been observed to spread catastrophically at speeds of 6000 ft per sec under stresses of about 10,000 psi, i.e. about E/3000. There are two sources of weakness; stress concentrations, and chemical agents in grain boundaries or on crack faces that lower the surface energy y of the material. Although we shall deal mainly only with the first of these, much of the discussion is also applicable to the second when different values of y are used. Griffith's well-known formula p = [ 2Ey/p(1 - v2)c]1/2 [1] gives the smallest tensile stress p able to propagate an atomically sharp surface crack of length c or interior crack of length 2c through a thick plate (compared with c) of elastically isotropic material of

Jan 1, 1959

By C. M. Loeb, A. M. Gaudin, J. H. Brown

THE object of most size reduction operations in the mineral industry is to liberate the grains of valuable minerals in the ore from those of the gangue. This is usually accomplished by crushing and grinding the entire mass of ore until there is only a small probability that any single particle contains more than one mineral. During this size reduction only limited control exists over size or composition of the particles exposed to the breaking action, and there is no control over the paths followed by cracks generated during the operation. This lack of control usually results in overgrinding and in production of large quantities of very fine material. The first detriment, overgrinding, is costly in itself, but when combined with the second factor it is doubly so. Not only is the fracture of a free particle unnecessary—the fracture of these particles may also make subsequent separation operations difficult, inefficient, and wasteful. It has been pointed out' that if the object of size reduction is to liberate the valuable mineral component of the ore then, ideally, fracture should follow intergranular paths to the exclusion of trans-granular ones. This would result in liberation of the valuable minerals with as little size reduction as possible. This ideal comminution operation is referred to as intergranular comminution, and it was the object of the investigation to determine the extent to which it could be developed by heat treatments. There are many indications in the literature that heating rocks prior to crushing may be favorable. Reports by Holman,2 Yates3 and Myers' are pertinent. These investigators showed that heating certain rocks prior to crushing them did, in fact, improve their crushing characteristics in that fewer fines were produced, although the fact that intergranular comminution was being effected apparently was overlooked. In addition, Sosman noted that if there is appreciable anisotropism in the thermal coefficients of expansion of even a pure mineral, then considerable permanent separation of the grains of the rock can be expected as a result of heating the rock to a high temperature.' By the same token, if there are ap- preciable differences in the thermal expansion coefficients of the various minerals of a multi-component rock, similar results should be obtained by heating this rock. This has been tested, partially, by Brenner," who obtained patents covering the heat treatment of some pegmatitic rocks in order to facilitate comminution of these materials. It has also been demonstrated that this may occur in taconite." Also, the possibility of causing decomposition of one mineral in a rock as a means of promoting intergranular fracture has been considered. Seigle2 and Schiffman et al. have obtained patents on such processes as applied to calcareous iron ores. These reports all indicate that heat treatments prior to crushing may contribute materially to intergranular comminution, but they also indicate that no organized attempt has been made to determine the controlling factors of the method or to determine its applicability in general. The present article is a report on the initial phase of such an investigation. The authors have reviewed the claims of prior investigators and have attempted, also, to establish the factors that might determine the applicability of heat treatments in the mineral industry. In this work 2000-g samples of various rocks were heated in a small laboratory furnace and crushing and sizing operations were carried out in standard laboratory equipment. All samples of each rock were as nearly identical as possible in particle size, grain size, and composition and contained only lumps coarse enough to contain many grains each. Tests on Granite A number of tests were made on a coarse grained Finnish granite obtained in the form of coarse chips from a local monument yard. This rock exhibited little variation from piece to piece in either composition or grain size. The minerals contained were quartz, orthoclase, small amounts of hornblende, and minute quantities of mica. Grain size ranged from about 1 mm to about 3 mm. Temperature of the Heat Treatment: In some cases the granite was heated to a particular temperature and crushed, hot, immediately upon withdrawal from the furnace—in others the rock was allowed to cool before crushing, but without quenching to room temperature after heating. In most tests on granite the heating period was about 2 hr with the furnace at the highest temperature for about 1 hr. Cases in which these periods were varied greatly will be presented separately.

Jan 1, 1959

By G. M. Schwartz, J. N. Gundersen

Utilization of magnetite-bearing taconite from the great Mesabi range of Minnesota is fast becoming a major industry in the state. The planning and early development stages of taconite processing projects have been de-scribed1-3 and an excellent discussion has appeared recently4 concerning the current mining, crushing, concentrating, and pelletizing techniques of the Reserve Mining Co., whose operations lie entirely within the Eastern Mesabi district. The present paper will deal only with some of the geological aspects of taconite utilization in the district, with emphasis placed upon some of the common mineralogical and textural features of the tacon-ites currently being mined or stripped and how these factors generally affect the potential recovery of the iron from the metamorphosed Biwabik iron-formation. The generalized geologic setting of the Eastern Mesabi district is presented in Fig. 1. The small circles on the geologic map, adapted from Grout and Broderick,3 mark the location of drill holes that were available for inspection during this study through the courtesy of Reserve Mining and Erie Mining Cos. The cores from these holes were divided into stratigraphic units and examined for their mineral content. Typical mineral associations and grain fabrics were also determined from hundreds of thin and polished sections. Available metallurgical tests made it possible to determine the probable response of a given variety of taconite to magnetic concentration. The longitudinal section of Fig. 1, projected along the strike of the iron formation, presents the simple stratigraphy of the area. It also shows the uniformly thick nature of the iron formation members in the district as well as a somewhat abrupt thickening of the formation to the west of the probable fault. The stratigraphy of these precambrian rocks has been described5-' elsewhere and need only be briefly reviewed. Historically, the oldest rocks unit, the Giants Range granite (Algoman) was covered by the Animikie group of sediments (Middle Huronian?), consisting of the Pokegama, Biwabik, and Virginia formations. Outcrops of the Pokegama quartzite are locally distributed along the northern limit of the Biwabik iron formation, but they are too limited to depict on the geologic map of Fig. 1. The effects of the intrusion of several small diabase sills within the Virginia and Biwabik formations are obscure because all of these rocks have been subsequently highly metamorphosed, mainly by the Duluth gabbro. The emplacement of the transgressing Duluth gabbro (Middle Keweenawan) and that of numerous peg-matitic veins in the iron formation8 has resulted in extensive contact and metasomatic metamorphism which has locally reconstituted the previously existing minerals of the Biwabik formation, in large part quartz and magnetite, into a wide variety of silicate mineral assemblages9 that have a profound effect upon the re coverability of the remaining magnetite. The entire region has subsequently been eroded and largely buried beneath Pleistocene glacial deposits. Structurally, the strike of the gently dipping Animikie group generally parallels the elongate outcrop pattern of the Biwabik iron formation on the map of Fig. 1. The Animikie group most commonly dips from 5" to 15" to the south-southeast. In this area, the Duluth gabbro pluton is somewhat sill-like, dipping about 30" to the southeast. Projecting these present structures upward, it seems probable that the gabbro once extended over the underlying Animikie group in the Eastern Mesabi district. SELECTION AND PRESENTATION OF DATA Because of the locally intense metamorphic activity in the district, mineralogical variations within the magnetite-bearing taconites are commonly abrupt, both vertically and laterally. Consequently it is difficult to select a single hole or small group of holes whose cores will be entirely representative of all of the district. Two holes have been selected, however, that in a general way represent mineralogical and textural variations that are likely to be encountered in both the eastern and western parts of the district. These recently drilled holes were chosen for discussion because it was possible to log the core and then to place the sample intervals at stratigraphic boundaries prior to preparation of the core for magnetic tube tests.

Jan 1, 1961

By H. C. Fiedler

Heats of high purity iron containing 3.1 pct Si and be -tween 0.0003 and 0.0295 pct N were prepared by vacuum melting ad then pouring while in a nitrogen atmosphere with the pressure between 0 and 90 psi. Strip from a heat with 0.0184 pct N underwent complete secondary recrystallization during the final anneal. Heats with less nitrogen had too few Si3N4 particles to restrain normal grain growth, and the heat with higher nitrogen had too many particles to allow complete secondary recrystallization. In the hot-rolled structure, Si3N4 precipitates only at the grain boundaries, with the consequence that annealing after hot-rolling diminishes the ability to subsequently undergo secondary recrystallization. In contrast to this behavior, ALNprecipitates uniformly in the hot-rolled structure. Under 1 atm of nitrogen, Si3N, in 3.1 pct Si-Fe dissociates between 900" and 950°C; the solubility of nitrogen increases from 0.0010 pct at 900" to 0.0030 pct at 1200°C. The solubility of nitrogen in Si-Fe has been the subject of many investigations. Corney and Turkdogan1 heated a 2.83 pct Si alloy in nitrogen and found the solubility, under 1 atrn of nitrogen, to be 0.0019 pct at 900°C. They claimed that Si3N4 did not form in the alloy above 705°C in 1 atrn of nitrogen. Fryxell et al.2 heated samples of 3.25 pct Si-Fe containing 0.0025 pct N over a range of temperatures and then analyzed for total nitrogen by vacuum fusion and for nitrogen in solution by a modified Kjeldahl technique. At 900°C, they reported the solubility of nitrogen in equilibrium with Si3N4 to be 0.0011 pct. pearce9 found the solubility of nitrogen at 900°C under 0.95 atrn of nitrogen to be 0.0017 pct in a 3.06 pct Si alloy. He reported that Si3N4 does not form above 770°C in 1 atrn of nitrogen. Although internal friction measurements have given somewhat higher values for the solubility,4-6 if the solubility of nitrogen is as low as has been reported by most investigators, and if Si3N4 is stable up to at least 945°C at 1 atrn pressure of nitrogen as reported by Seybolt,7 a small amount of nitrogen in properly processed Si-Fe should be effective in promoting secondary recrystallization. The requirement is that in the final heat treatment there be enough small, well-dispersed particles of Si3N4 to restrain normal grain growth. Fast8 has obtained secondary recrystallization by nitriding high-purity 3 pct Si-Fe after hot-rolling to a thickness of 0.118 in., followed by processing to 0.012 in., and annealing. A large amount of nitrogen, 0.076 pct. was introduced during the nitriding heat treatment, but he has since reported9 that "a few hundredths of a percent" is sufficient. Small amounts of aluminum10 or vanadium" nitride are capable of promoting secondary recrystallization. Heats containing as little as 0.010 pct A1 or 0.042 pct V and from 0.006 to 0.009 pct N underwent complete secondary recrystallization at final gage, whereas heats with lesser amounts of aluminum or vanadium did not.l2 To be reported is the behavior of nitrogen in high-purity 3.1 pct Si-Fe, and the relation of this behavior to the ability to undergo secondary recrystallization. PROCEDURE Ingots weighing 1 lb were made by vacuum melting high-purity electrolytic iron (A104, Glidden Co.) and high-purity silicon (Monsanto Co.). The latter was used in preference to ferrosilicon to insure a low aluminum content. The design of the melting furnace permitted pouring with the furnace atmosphere either below or above atmospheric pressure. Accordingly, at the completion of melting, nitrogen was admitted to the desired pressure and the heat then immediately poured. The ingots were sound, with no indication of porosity. In Table I are listed the heats investigated, the nitrogen pressure at pour, and the nitrogen and oxygen contents as determined by vacuum fusion with a platinum bath at 1850°C, a procedure which insures measurement of the total nitrogen.13 In addition, all heats contained 3.1 pct Si and not more than 0.002 pct C, 0.003 pct S or 0.005 pct Al. It was subsequently found that the quantity of nitrogen contained in the heats in Table I does not necessarily represent that obtained under equilibrium conditions. For example, the ingot poured immediately after 1 atrn of nitrogen was admitted to the chamber contained 0.0093 pct N, whereas an ingot poured 3 min after the nitrogen was admitted contained 0.021 pct N and another poured after a 6-min delay contained 0.029 pct N. While some bleeding of the hot top occurred in the latter instance, the ingot when examined in cross section appeared sound. The ingots were heated to 1325°C in hydrogen and rapidly rolled to 0.080 in. in 3 passes. The roll speed of the final pass was reduced so as to increase the quenching effect of the rolls. The hot-rolled pieces were processed both as-hot-rolled and after heating for 3 min at 900°C in hydrogen. After cold-rolling to 0.026 in., the strips were heated for 2 min at 900°C in hydrogen, then cold-rolled to the final gage of 0.012 in. The loss of nitrogen in going from the ingot to cold-rolled strip was no more than 10 pct. The final heat treatment, which was for the purpose of develop-

Jan 1, 1970

By T. F. Bower, M. C. Flemings

Results are reported of a study of surface dendrilic structure of an Al- Cu alloy solidified against a chill wall. Most primary and secondary "arms " in the surface dendritic structure are arranged orthogonally, giving the impression of strong preferred orientalion on the surface. However, no such preferred orientation exists and it is therefore evident the arms do not represent (100) directions. The primary arms are shown to be interseclions of a (100) plane wilh the chill plane, or, equally often. the projeclion of a (100) direction on the chill plane. Secondary dendrite arms are usually within a few degrees of 90 deg to the primary arm, independent of grain orientalion. Prirary, secondary, and higher-order surface dendrite arms almost always represenl intersections of (100) platzes with the chill surace, or pvojections of (100) direclions. Growlh of secondary arms is favored on the side of the primary arm where a (100) direclion points toward the chill surfAce a1 a Lou, angle. Surface dendrile arms are often observed to be bent. In these cases, the crystal lallice changes orientation; bending is concave to the chill surface. In a previous paper,' a technique was discussed whereby large grains can be obtained at a chill surface. The technique used involves quickly drawing superheated liquid A1-4.5 pct Cu alloy into a thin copper mold, so that the mold is full well before solidification begins. The chill surfaces employed are polished copper blocks coated with amorphous carbon. Shrinkage during solidification between dendrite arms and grains delineates both, without the need for polishing or etching of the cast surface. The grain structure of the chill surface was discussed in a previous paper;' in this paper, the dendrite arms within each grain are examined. Previous work on surface dendrites includes that of Edmunds, who studied the development of preferred orientation in zinc, cadmium, and magnesium.' In zinc and cadmium, he found that the surface region has a (0001) texture (parallel to the chill surface). Walton and Chalmers reasoned that, since the fast growth (1010) directions are in the basal plane, nuclei which have this plane parallel to the mold wall would produce larger grains than nuclei with other orientations. Hence, the texture observed is as expected.3 The same authors, in measurements on aluminum ingots, found no preferred orientation at the mold wall. However, the X-ray technique they used measured the preferred orientation in terms of grain numbers, not grain areas; larger grains were weighted equally with small ones. No preferred orientation is expected on this basis at the chill surface. In a later paper,' Edmunds stated that experiments show a random grain orientation at the surface in die cast aluminum; his technique, also used in his earlier paper, takes account of grain area. Little work has been published on the dendritic structure of metal chill grains. Recent work of Biloni and Chalmers on "predendritic growth" shows the change in morphology from spherical to dendritic during the initial stages of freezing, 5 but this work did not include detailed examination of the fully developed dendrites. Other pertinent work includes that of Lin-denmeyer, who investigated the growth of ice dendrites. 6 When growth was on a substrate, the dendrite axes were bent. The bend corresponded to a change in orientation of the crystal lattice and occurred in such a way as to align the basal plane to the substrate. DENDRITE STRUCTURE Fig. 1 shows the chill surface of a typical casting poured above the critical temperature necessary to produce coarse grains. A cursory examination of these grains shows that the surface dendrite arms within most of the grains are oriented roughly perpendicular to each other. One is tempted to assume that these are (100) directions and that, therefore, marked preferred orientation exists at the chill face. This, however, is not the case. Each of the grains in the casting of Fig. 1 was separately identified, Fig. 2, and its orientation determined by the Laue back-reflect ion method. Results are given in Fig. 3 and it is seen there that no preferred orientation exists. Even when grain area is accounted for, there is no significant preferred orientation. The relationship between surface grain structure and crystal orientation was then obtained by assigning X and Y axes to the casting surface, Fig. 1, and assigning the same axes to the stereographic projections of each grain. Thus, the visible surface structure could be compared readily with grain orientation. This was done for fifty-five of the grains of Fig. 1. Results of this study on three typical grains are described below, and some general observations given subsequently. Fig. 4 shows the structure and stereographic projection of a grain which lies near the (100) zone (with respect to the casting surface). The X and Y directions are marked on the projection, and the photomicrograph mounted with the same orientation. Poles of the stereographic projection represent crys-tallographic directions in the grain which point out of the casting, toward the chill. Two (100) directions are shown in Fig. 4. A line joining the center of the projection and a pole represents the projection of the pole onto the X-Y plane (chill surface). Two such lines are shown in Fig. 4 (solid lines). A line joining the intersection of a great circle with the circumference of the projection gives the trace of a crystallo-graphic plane in the chill surface; two such traces are shown (dashed lines).

Jan 1, 1968

By Victor A. Phillips

A series of strips of a Ni-12.7 at. pct A1 alloy were Prepared containing cubical y'(NisAl) precipitates with edge lengths from 60 to 500A. A particle-free solution-tveated strip was included for cornparison. They weve cold-rolled 95 pct and the effects of particle size on the isochronal (1/2 hr) annealing behavior between 300° and 950°C studied (by hardness and light and electron microscopy). It ulas inferred that the particles deformed with the lnatvix becoming lamellae which remained coherent. Comparison with published data fov pure nickel showed that aluminum greatly re-tavded softening and recrystallization, but it made little difference whether or not particles were present. The presence of pakticles led to a heterogeneous distribution of precipitates after annealing at 700" to 750°C. Recovery was not detected. Recrystallization occurred by the growth of new grains into unrecrys-tallized material. In a previous study by the author,' the growth of Ll2-type ordered yl(Ni3Al) precipitates was followed in Ni-12.7 at. pct A1 alloy as a function of aging at 600" and 700°C. The particles were showo to be cubical in shape in all sizes from 50 to 3000A and remained coherent. This work was used as a guide in preparing the starting structures for the present study of the effect of these particles on the annealing behavior of heavily cold-rolled strip. Another question of present interest was whether dislocation and particle hardening were additive, since the structures before rolling ranged from solution-treated to peak-aged to overaged. Also, precipitation might occur on annealing after cold-rolling. Reference may be made to other papers2"5 for previous work in this relatively unexplored field and only some recent work will be mentioned her:. phillips2 studied the effect of deformable 0 to 590A-diam cobalt particles on a Cu-3.23 pct Co alloy rolled 95 pct and found that the particles, which rolled out into thin lamellae, impeded softening and recrystallization. Tanner and servi3 likewise studied the annealing of cold-swaged Cu-2 pct Co alloy containing 150A-diam particles and found impeding effects. Haessner et a1.,4 on the other hand, found that incoherent 2-p-diam non-deformable particles of B4C (0.04 vol pct) tended to increase the rate of recrystallization of copper rolled up to 95 pct reduction. They attributed this to the formation of new grains at the particle interfaces. Humphreys and artin' found that nondeformable silica particles in copper rolled to 30 pct reduction accelerated recrystallization if the particle spacing was large and retarded it if the spacing was smaller. Haessner et a1 4 also studied a rolled Ni-Cr-A1 alloy; however, the particles of y'(Ni3Al)-type precipitate were not put in before rolling, but separated during the isothermal annealing at 750°C. No previous work appears to have been carried out on the effect of y' (Ni3A1) particles on the annealing of Ni-A1 alloy. Hornbogen and ICreye7 redetermined the solubility c of aluminum in nickel as a function of temperature T and showed that it was given by c = 32.6 exp(-1940/RT). This relation gives aluminum solubilities of 15.1, 14.2, 12.0, and 10.7 at. pct at 1000°, 900°, 700°, and 600°C, respectively. The phase precipitated from the nickel-rich solid solution is fcc y1 (Ni3A1) which has a Cu3Au -type ordered structure8 and remains ordered up to 1000°C.B EXPERIMENTAL PROCEDURE The alloy used was identical with that used before. Chemical analysis showed 6.27 wt pct (12.71 at. pct) Al, the principle impurities being 0.065 pct Fe, 0.022 pct Co, 0.020 pct Cu, and 0.004 pct C. Bar stock of 1 in. diam was cold-swaged to % in. diam, cold-rolled to 0.300-in.-thick strip, and annealed at 900°C in dry hydrogen. It was cold-rolled to 0.100-in. thickness and solution-treated for 1 hr at 1000°C while sealed in a quartz tube in argon, quenching in iced brine with the aid of a device to snap off the nose of the tube. Lineal analysis gave an average grain size of 0.055 mm. Pieces of strip were aged at 700°C in vacuo for 30 min, 51/4 hr, and 1 week to produce nominal average particle widths of 60, 150, and 500A, respectively, as known from the previous work.' The average diamond pyramid hardness was determined. The heat-treated strips were rolled from 0.100 to 0.005 in., a reduction of 95 pct, and the rolled strips stored at about -5°C. Small pieces were annealed within 1 week for 30 min at temperatures from 300° to 950° ±2°C in a horizontal vacuum furnace. Strips were withdrawn into a cooling zone, giving an estimated initial cooling rate from 950°C of about 50°C per sec. Average diamond pyramid hardnesses were determined on a lightly electropolished spot on the surface of each strip using 300-g load. Each point on the softening curves represents a separate annealed specimen. Sections containing the rolling direction were examined by optical metallography. Selected specimens were electrothinned to the center plane' and examined by transmission at 100 kv in a Siemens Elmiskop I electron microscope. It is well-known that changes in the structure tend to occur when a deformed strip is electrothinned below a thickness of a few hundred angstroms, although this is less serious with a material such as nickel which has a high melting point, and also is apt to be less serious when particles are present. Observations were nevertheless confined to thicker regions of the foils with estimated thicknesses over 1000A. No changes were observed due to beam exposure.

Jan 1, 1968

By Andrew Cosgarea, William R. Upthegrove, Morteza Mirshamsi

The capillary-reservoir technique was used with lead-210 and cadmium-115m to determine the self-diffiLsion coefficients of both cadmium and lead in the liquid binary Cd-Pb system. The self-diffusion coefficients of pure cadmium and pure lead were obtained and were compared with the theoretical predictions. Good to excellent agrement between the experimental and predicted values was obtained. The self-diffusion coefficients of cadmium were tneasuved in alloys containing 2.50, 9.13, 17.40, 31.00, 45.00, 69.00, and 97.00 lot pct Cd by determining- the amount of cadniiutn-115m which diffused out of a small-bore capillavy into an infinite reservoir during- a given time peviod. Sinzila7-measurements were made with lead-210 to determine the self-diffusion coefficients of lead in these identical alloys. Diffusivities were determined from measurenzents performed in the temperature interval of 290" to 480°C. The results were correlated with the Ar-vhenius equation, and the maximum variation of the equation parameters (Q and Do) was also inrestigated . THE theory of diffusion in liquids, particularly liquid metals, is relatively undeveloped in contrast to that for the gaseous and solid states. Although the practical application of liquid metals as heat-transfer media has become increasingly important, few liquid-metals systems have been investigated. Experimental data of fundamental significance in this field are not readily obtained, which may explain but not justify the present lack of knowledge. What work has been completed is primarily restricted to liquid diffusion of pure metals; little work has been done in liquid-metal diffusion of binary mixtures. A review of liquid-metal diffusion theory and research is available elsewhere.1-4 In an effort to add to the knowledge of liquid-metal systems and to increase the basic understanding of the diffusion process in liquids, a study of diffusion in the binary-liquid system, Cd-Pb, was undertaken. The capillary-reservoir technique5 was employed to measure the self-diffusion coefficients of cadmium and lead in molten binary alloys. Measurements were made with seven selected compositions and over a temperature range from 290° to 480°C. The experimental apparatus consisted essentially of the following items: constant-temperature bath, diffusion cells, capillaries, capillary-filling device, and a radioactive tracer counting system. EXPERIMENTAL APPARATUS Constant-Temperature Bath. A cylindrical steel vessel, 8 in. in diam and 15 in. deep, surrounded by an insulated heating coil was used with a sodium-potassium nitrate salt mixture heating medium. The bath was maintained slightly below the desired control temperature by the furnace-heating element; and a 250-w heater, actuated by a Bayley proportional temperature controller, was utilized for the final control of the temperature. A constant-speed mixer stirred the salt to insure a uniform temperature within the bath. Four calibrated Chromel-Alumel thermocouples were placed at various positions in the salt bath to verify the absence of temperature gradients. The observed temperature variation during any diffusion run was less than 0.l°C. The entire furnace assembly was mounted on four shock absorbers to exclude building vibrations and the stirrer propeller blades were adjusted so not to induce vibrations within the reservoir. A schematic diagram of the furnace and the constant-temperature bath is shown in Fig. 1. Diffusion Cell. The diffusion cells and associated parts were the same, except for slight modification, as the one used by walls1 in this laboratory, and are shown in detail elsewhere.' A graphite crucible, 4 in. long and 40 mm (1-1/2 in.) ID, enclosed in a 60-mm (2-1/4 in.) Pyrex tube cell about 18 in. long, was used as a container for the melt. The reservoir (molten alloy in the graphite crucible) was usually about 2 to 2-1/2 in. deep. Graphite was used because of its satisfactory nature as a refractory material and the low solubility of carbon in molten Cd-Pb alloy.677 The Pyrex cell was closed at the bottom and fitted at the top (open end) with a 2-in. Dresser coupling. A brass flange was welded to the top of the coupling. The upper part of the diffusion assembly was bolted to this flange with an O-ring seal. The lower part of the diffusion cell was supported in a 3-in. brass cylinder which was open to allow for circulation of salt around the cell. The top assembly consisted of two synchronous motors, a drive shaft, a thermocouple well, and controlled-atmosphere inlets and outlets. One motor was used for rotation of the capillaries at a rate of 1/2 rpm in the reservoir during the diffusion run. The other motor was used for the vertical positioning of the capillaries and the capillary holder by means of a simple screw drive. The capillary holder and drive assembly were lowered into the reservoir for the run and raised after the desired diffusion time at a rate of approximately 0.4 in. per min. Capillary holders were made of graphite. These

Jan 1, 1967

By D. E. Mikkola, G. E. Poquette

X-ray diffraction was used to study the growth of antiphase domains in quenched (or "disordered&apos;? Cu3Au annealed in the range 300" to 385°C. Measurements of the long-range order parameter indicate that a high degree of order is established rapidly at these annealing temperatures. Average domain sizes obtained by Fourier analysis of the superlattice peak profiles show that antiphase domain growth is analogous to classical metallurgical grain growth (i.e.,fol-lows a D2 US kt relation). The activation energy for the growth process, 44 kcal per mole, indicates diffusion control. The anisotropy in the observed effective domain sizes from seven different superlattice peaks can be best accounted for by a configuration involving antiphase domain boundaries on {100 } and (111 ) planes, where the (100) boundary is the low-energy type, {lOO} Type I. The disappearance of the (111) antiphase domain boundary during domain growth is dif-fusion-controlled with an activation energy of 48.5 kcal per mole. On the other hand, the behavior of the parameter representing the amount of (100) Type I boundary indicates that there may be a conversion of the higher-energy boundary types to (100) Type I boundary during the growth process. THE order-disorder transformation in the alloy Cu3Au has been the subject of numerous experimental investigations over the past 40 years, most of which have involved measurements of convenient physical properties such as resistivity and hardness as a function of heat treatment. The interpretation of these data is difficult because measurements of this type have the disadvantage that they yield total changes resulting from several different atomic processes which may be occurring simultaneously. The present study was undertaken to establish by means of X-ray diffraction the kinetic behavior of one of these atomic processes, namely antiphase domain growth. In the completely ordered state Cu3Au has an L12 structure which can be described as an fcc type arrangement of atoms in which the gold atoms occupy the corner sites and copper atoms the face-centered sites. Three other equivalent unit cells can be formed by allowing two gold atoms to occupy opposite face-centered sites and copper atoms to occupy the remaining corner and face-centered sites. These four different unit cells are crystallographically related by a shift of 1/2<110>. Quenching from above the critical temperature (392°C) to room temperature retains the "disordered" structure-a "random" arrangement of copper and gold atoms having the fcc structure. Annealing the disordered alloy below the critical temperature causes ordering to occur through the nucleation and growth of ordered regions at different points throughout the crystal. These small ordered regions, each based on one of the four types of unit cell, grow by consuming the disordered material until they impinge to form a domain structure in which the domains are antiphase by a shift of 4(110). The boundaries between domains are called antiphase domain boundaries (APDB) and they have been found to lie primarily on &apos; {100} planes in highly ordered Cu3Au. Two types of APDB can occur on ( 100) planes. An example of an (001)1/2[110] shear type APDB is shown in Fig. I. Because of the layer of copper atoms separating the domains in this case, there are no near-neighbor violations across the boundary and it has a low surface ener This type of APDB will be referred to as {lOO} Type I. Fig. 2 shows an (001): [011] climb type APDB, (100) Type 11. This type of APDB can be described as resulting from removal of a (200) plane followed by a shift of 1/2<110> to bring the separated regions together. Near-neighbor violations across (100) Type I1 APDB make it a high-energy boundary. There are numerous other possible APDB configurations; however, it is only worth noting that shear type APDB can be produced on the (111) plane by motion of a normal fcc dislocation with Burgers vector 1/2<110> through the ordered structure. A (111); [110] shear type APDB is shown in Fig. 3. Again, because of the near-neighbor violations this type of APDB has a higher energy than the (100) Type I APDB.

Jan 1, 1970

By S. Usui, I. Iwasaki

The effect of pH on the adsorption of dodecylamine at the mercury-aqueous solution interface was investigated by differential capacity and electrocapillary measurements. With dodecylammonium acetate, the differential capacity curves showed two desorption peaks in the cathodic branch with their relative intensities varying with the solution pH. With dodecyltrimethylammonium chloride, only one cathodic de-sorption peak was observed in the same pH range. Through thermodynamic analysis of the electrocapillary curves, the adsorption density of undissociated amine was evaluated separately from that of aminium ion. The adsorption densities of the un-dissociated amine and of the total amine increased with increasing pH. The ratio at the interface of undissociated amine to aminium ion was several orders of magnitude greater than the ratio in the solution and increased with increasing pH. The potential at the closest distance of approach of counter ions to the mercury surface was compared with values of zeta potential on quartz previously reported. The most important variable in the flotation separation of minerals is probably the pH of the pulp, and a number of theories have been proposed to explain its effect on the condition of the mineral surfaces, on the dissociation of collectors and of inorganic and organic species (accidentally present or intentionally added) in the pulp, and on the mineral-collector interaction. In the development of a theoretical background for oxide flotation systems, an experimental approach based on electrokinetic measurements has been of much value, although the effect of pH becomes confounded since it governs both the electrochemical conditions of the oxide surface and the dissociation of the collector. For investigation of the adsorption behavior of long-chain collectors on oxide minerals, however, electrokinetic potential measurements are the most widely used technique. Hydrogen and hydroxyl ions are found to be the potential determining species, thereby governing the interfacial electrical conditions. The electrostatic interaction between the charged mineral surfaces and ionized collectors is regarded as the driving force for the adsorption of the collectors. An association of alkylamine collectors adsorbed on quartz surfaces has been postulated from streaming potential measurements, and a term "hemi-micelles" has been proposed.&apos; The possibilities of coad-sorption of undissociated amine along with aminium ion has been inferred from contact angle measurements? and from adsorption studies.~ Electrochemical titration as applied to silver sulfide provides a more quantitative approach to the analysis of the electrical double layer at an ionic solid-solution interfaceqG and the electrochemical evidence for the adsorption of amine at pH 4.7 indicates a specific affinity of dodecylammonium ion towards silver sulfide surfaces, whereas at pH 9.2 the adsorbed species might be free arnine." A combination of differential capacity and electrocapillary measurements on a dropping mercury electrode was reported to be a sensitive method of provid- ing reliable information on the adsorption behavior of dodecylammonium acetate (DAA) at a natural (near neutral) pH.? It was also shown that there were striking similarities in the properties of the double layer and in the adsorption behavior of the amine on mercury and on such ionic solids as quartz, silver sulfide, and silver iodide. The effect of pH on the differential capacity curves at a mercury-sodium fluoride solution interface has been investigated by Austin and Parsonss who reported that between pH 7 and pH 11 there was very little effect. In the present paper, the adsorption behavior of DAA was investigated as a function of pH through differential capacity and electrocapillary measurements and the information gathered was correlated with that available in literature on quartz and silver sulfide. Experimental The apparatus and the method used for determining the differential capacity and the electrocapillary curves were identical to those described previously.&apos; The ionic strength of the supporting electrolyte was fixed at 0.1 M with potassium fluoride, and the pH of the solution with potassium hydroxide. Only the neutral to alkaline range was covered in order to avoid the dissolution of the glass vessel with hydrofluoric acid. Results In Fig. 1 the differential capacity has been plotted against the applied potential at a DAA concentration of 10-&apos; M at three different pH values. The curves are characterized by one capacity peak in the anodic branch, by two capacity peaks in the cathodic branch, and by a marked depression in capacity between the peaks. The depression indicates an adsorption of the arnine in this potential range. One of the cathodic peaks appears at pH 7.3 near -1.4 v and decreases with increasing pH. The other appears at pH 8.9 near —1.2 v and increases with increasing pH. At pH 9.6 only the latter peak is observed. Beyond the cathodic peaks, all the curves tend to converge with the curve in the absence of DAA, implying that two different species are being desorbed in this potential region. The anodic peak near 0.0 v increases markedly with increasing pH. The well-defined anodic peaks at pH 8.9 and 9.6 were accompanied by an appreciable increase in the current flow (in excess of O.luA), and, therefore, is a "pseudo-capacity"&apos;" due to a

Jan 1, 1971

By F. D. Wright

Production of a coal preparation plant is governed by many restrictions, such as the tonnage of different products and blends that can be sold within a given period, capacities and output proportions of the cleaning and sizing units, blending proportions, quality specifications, and costs and prices for the various products. Determination of the tonnage of each product and blend that should be made in order to obtain the maximum profit can be difficult unless a systematic method such as linear programming is used. In this paper the basic method of linear programming is described briefly. The Old Ben No. 9 preparation plant is used as an example to illustrate in detail how eqwations can be written to form a linear programming model of a coal preparation plant. Three sample problems, each requiring 56 or more equations and 63 structural variables, were solved with an IBM 650 computer. Linear programming is one of several mathematical tools used for operations research. It has been applied to many fields and has been used by a number of industries either to maximize the profits of certain operations or to minimize costs. P. B. Nalle and L. W. weeks&apos; have described the use of the method by the Riverside Cement Co. to minimize the cost of blending raw materials to make portland cement. Their problem is to obtain at minimum cost a mix with certain specifications from a number of possible materials which have various costs and various amounts of CaO, SiO2, Fe2O3, and other constituents. In a paper on the use of linear programming by the National Coal Board in England, K. B. Williams and K. B. Halley2 describe how the transportation method, a variation of linear programming, is used to minimize the cost of sending 37 grades of coal from 28 mines to seven central washing plants which produce coal for furnace coke and foundry coke. The various coals have different percentages of volatile matter, moisture, sulfur, ash, and phosphorous, so there is considerable choice in how they can be blended to meet the specifications of the two products. The purpose of this paper is to show how linear programming can be used to maximize the profits of a coal washing plant which produces individual final products as well as blends. The Old Ben Corp. furnished assumed sample data from their Old Ben Mine No. 9 preparation plant for this investigation. However, the data that have been used are entirely the author&apos;s responsibility. METHOD OF LINEAR PROGRAMMING Numerous articles and books have been written on the theory and applications of linear programming.3-5 However, since the method has not been widely applied by the mining industry, a brief, nontheo-retical discussion of its basic method seems to be in order. Linear programming (Table I) is used to determine the best possible solution to a number of interdependent activities. It is essentially a method for making systematic selections from a number of possible solutions to determine positively the optimum solution. There may be other equally good solutions but no better ones. Each activity must have linear coefficients and there must be a criterion to judge how good the solution actually is. Linear programming is different from the solution

Jan 1, 1961

By Harold M. Feder, Robert V. Schablaske, Irving Johnson, Ewald Veleckis

The stoichiometry, structure, and stability of the internzediate phases formed between zinc and some of the rare earth (RE) metals were systematically exarnined by means of a recording effusion balance and X-ray diffraction analyses. In the La-, Ce-, PY-, Nd-, and Y-Zu systems, at or below about 600 C, the following sequences of phases (REZnx) were found: La, x = 1, 2, 4.0, 5.25, 7.3, 17/2, 11, and 13.0;&apos; Ce, x = 1, 2, 3, 11/3, 4.3, 5.25, 7.0, 17/2,* and 11; Pr,x = 1,2, 3, 11/3 ,* 4.3, 5.3(?), 7.0, 17/2,* and 11; Nd,x = 1,2, 3,* 11/3,* 4.3, 6.5, 8.5,* and 11; Y,x = 1,2,3, 11/3, 4.5, 5.0, 17/2,* and 12.* The structure types of all these phases were classified. In addition, lattice parameters were obtained for the first time for the pluses denoted by asterisks. In the absence of de tectable valency or electronegativity effects the systesnatic trends in the results have been ascribed to the effects of&apos; the lanthanide contraction. For example, the maximum number of zinc atoms in the coordination polyhedron surrounding the RE atom decreases from twenty-four to twenty-two to twenty as the size of the RE atom decreases. THE structures and compositions of a great many intermetallic phases (e.g., the Laves phases) are known to be based primarily, but not exclusively, on the space-filling efficiency of various modes of packing together atoms of different sizes. The valencies and electronegativities of the constituent atoms are, however, also influential. In extreme cases hypothetical intermetallic phases which fulfill the efficient spacefilling requirements may not be present in the constitutional diagram because of thermodynamic instability brought about by the operation of valency or electronegativity factors. Hence, for a detailed study of the influence of atomic size on alloy structure and composition, it would be desirable to minimize variations of valency and electronegativity. The intermetallic phases formed by the rave earths (RE) with some common partner offer an excellent opportunity for isolating the effects of size from those of valency and electronegativity. The rare earths exhibit a large, but smooth, decrease in size (the lanthanide contraction) in the series from lanthanum to lutetium when inter comparison is made for a common valence state, e.g., isolated atoms or trivalent ions. The elements yttrium and scandium are frequently included as pseudo rare earths; their sizes place them in the vicinity of dysprosium and lutetium, respectively. The electronegativities of RE elements vary by less than 10 pet. The trivalent state is the most common; however, the well-known tendency of cerium, praseodymium, and terbium to achieve higher valencies, and of samarium, europium, and ytterbium to seek lower valencies, requires that caution be exercised in the assumption of equal valencies. In the present study the existence, constitution, and structure of each of the numerous intermediate phases formed by zinc with lanthanum, cerium, praseodymium, neodymium, or yttrium were examined systematically and in detail. The investigation was conducted by a recording effusion balance technique and by X-ray diffraction analysis. The results enrich our knowledge of the phase diagrams of these systems. In addition, they present some clear-cut evidences of the operation of the size factor alone. EXPERIMENTAL PROCEDURE Apparatus. The mode of operation of the recording effusion balance and its application to phase studies have been discussed in detail elsewhere.&apos; In this work, an effusion cell containing a finely divided alloy was suspended within an evacuated tube from the beam of an analytical balance. The tube was immersed in a massive molten salt bath whose temperature was controlled to within 0.5o C during each experiment. The loss in weight of the alloy owing to effusion of zinc* was continuously recorded. Two effusion cells, 1/2 in. diam by 1 in. high, were machined from tantalum rods. Two orifices were drilled laterally into the walls of each cell. The orifice areas were determined by calibration with pure zinc: cell A had a total orifice area of 6.5 x 10-41 sq cm, and cell B an orifice area of 9.8 x 10-3 sq cm. By appropriate choices of orifice area and temperature the wide range of volatilities from pure zinc to pure rare earth metal could be investigated. X-ray diffraction powder photographs were made at room temperature with a 114.6-mm Debye-Scherrer camera with both filtered CuKa radiation and filtered CrKa radiation. Lattice parameters were refined by a computer-programmed least-squares analytical treatment which incorporated appropriate extrapolation techniques.2 Frequent use was also made of a special computer program3 designed to generate a powder pattern from an assumed structure in order to verify structural assignments. Materials. Lanthanum, neodymium, and yttrium were purchased from the Lunex Co., cerium from the Cerium Metals Corp., and praseodymium from the St.

Jan 1, 1968

By J. Chipman, T. Fuwa

The effects of various elements on the activity coefficient of carbon in liquid iron have been studied by two experimental methods: 1) equilibration with controlled mixtures of CO and CO2; 2) the solubility of graphite in the melt. Activity coefficient of C is increased by Al, Co, Cu, Ni, P, Si, S, and Srz. It is decreased by Cr, Cb, Mn, Mo, W, and V. THE thermodynamic properties of the iron-carbon binary system have now been fairly well established, although some uncertainty remains with respect to the exact location of some of the phase boundaries. The activity of carbon in ferrite and in austenite has been measured in the classic researches of R. P. smith&apos; while similar measurements by Richardson and ~ennis, and by Rist and chipman3 have established the values of the activity of carbon in liquid iron up to 1760°C. On the other hand, our knowledge of the effects of alloying elements on the activity of carbon in dilute solutions is restricted to Smith&apos;s experiments on systems Fe-C-Mn and Fe-C-Si in the austenitic range and to some more recent experiments of schwarzman4 in the a range. In addition there have been a number of determinations of the effects of various elements on the solubility of graphite in liquid iron, and from these the corresponding effect in saturated solution may be obtained. The purpose of the present study was to extend the investigation of the liquid system to include the effects of alloying elements upon the activity coefficient of carbon, principally in dilute solutions. Equilibrium measurements were made on the reaction C + co, = 2 CO (g) The prepared mixture of CO and CO,, diluted with argon, flowed over the surface of the liquid metal which, after several hours&apos; exposure to the gas, was quenched and anqlyzed. As in the earlier experiments, the principal experimental difficulty was in the deposition of carbon on the parts of the furnace at temperatures slightly below that of the metal bath. In order to minimize this difficulty, the ratio (Pco)2 /PCo2 was restricted to values not much higher than 100 atm, and correspondingly the carbon concentration in the metal seldom exceeded 0.30 pct. EXPERIMENTAL METHODS The method and apparatus were essentially the same as used by Rist and Chipman.3 The gaseous mixture consisting of highly purified CO, CO,, and argon, each controlled by a flowmeter, was led into the furnace and passed over the surface of the liquid-iron melt which was heated and stirred by high-frequency induction. One slight modification was made in that a molybdenum susceptor was placed outside the crucible for the sake of uniformity of temperature and to combat the tendency of carbon to precipitate on the crucible wall. Pure alumina crucibles approximately 25 mm ID were used. The charge consisting of about 30 g was made up of electrolytic iron, the alloying element to be added, and enough graphite to supply slightly more or less than the anticipated equilibrium carbon concentration. All metals used were of high purity. Metallic chromium, columbium, and vanadium were from special lots supplied by the Electro Metallurgical Co. Tin, copper, molybdenum, tungsten, cobalt, and nickel were of purest commercial grades. The electrolytic iron, after being cut to the proper size for charging, was prereduced by hydrogen at 850° to 1000°C to remove surface oxidation. The oxygen content of the reduced material was 0.002 pct. This treatment made it easy to control the carbon content of the initial melt. The charge was melted under the gas mixture to be used for the entire run. In some earlier melts the charge was melted under a stream of argon, but in this case some alumina was reduced from the crucible, and the aluminum thus absorbed in the melt was subsequently oxidized with the formation of a solid film of alumina on the surface of the melt. AS another safeguard against film formation, overheating of the bath was carefully avoided. All runs were made at a temperature of 1560°C. Under experimental conditions a charge of pure iron picked up 0.17 pct C in 3 hr and 0.23 pct C in 6 hr under an atmosphere for which the equilibrium concentration of carbon is 0.27. It is clear that the time required to reach equilibrium from an initially carbon-free melt would be very great. For this reason each experiment was started with a melt of known carbon concentration not far above or below the expected equilibrium value, and each melt was held at temperature for a period of at least 5 hr. Under such circumstances it was possible to chart the approach to equilibrium from both high-carbon and low-carbon materials. Temperature was controlled by frequent optical observation and adjustment and the metls were timed in such a way that the final 2 hr occurred during a time when electric power was steady; for example, 2 to 4 pm or after 11 pm. In melts containine volatile metals such as copper, tin, and mangane\e the time of holding was decreased somewhat in

Jan 1, 1960

By A. U. Seybol

Eight binary iron alloys were examined after ion nitriding experiments to determine the behavior of the following elements: Al, Mo, Mn, Si, Ti, V,Cr, and C. Only Al, Cr, Ti, and V additions caused hardening in binary iron alloys. A few steels were examined to see the effect of Cr, Cr + Al, Cr + Ti, and Cr + V. It is suggested that a useful new class of ni-triding grade steels might be those containing about I pct V. The nitriding of steel, first described by Fry1 about 45 years ago, rapidly attained commercial application with very little knowledge of the fundamentals involved. While Fry,&apos; in describing the status of nitriding in 1932, apparently correctly postulated hardening by precipitated nitrides, the details of the nitriding process were not understood, nor has the situation changed much since that time. It is also interesting to note that the compositions of some typical nitriding steels given by Fry at that time have changed little in the intervening years. Currently used nitriding steels owe their surface hardening to either chromium (as in 4340 steel) or aluminum plus chromium as in the Nitralloy grades, where both CrN and AlN appear to contribute to harden ing. Titanium additions have been studied experimentally, but thus far titanium steels have not won wide commercial acceptance. This subject will be expanded later. The orthodox ammonia nitriding process has been reviewed very adequately many times as in Jenkins3 and Case and VanHorn,4 and their is no need to outline the process here. Ion nitriding is not as well-known, although there have been several descriptions5-9 of the process given, sometimes with comparisons with the ammonia process. Most of these papers are primarily concerned with a description of the equipment, or of the physics or electrical engineering aspects of ion nitriding, but Noren and Kindbom9 gave the results of a metallurgical investigation using both processes. In brief, ion nitriding is carried out in a vacuum chamber from which the air is exhausted and replaced by a N2-H2 mixture, typically containing 10 to 20 pct N2, at about 5 to 10 torr pressure. While ammonia gas has also been used in ion nitriding, there is no evidence that ammonia makes any improvement in the ion nitriding process. A few hundred volts dc is applied between the grounded container wall (positive) and an insulated center post supporting the work (negative) to be nitrided. A glow discharge is created in the ionized gas, accelerating positive nitrogen ions to the work. These ions contain enough energy to form the normally unstable Fe4N "white layer", thus establish- ing surface nitrogen solubility characteristic of the a Fe/Fe4N equilibrium. This creates a substantial concentration gradient, driving dissolved nitrogen into the steel. The temperature employed is in the same range (around 500" to 550°C) as in ammonia nitriding, but because of factors which are not understood at present the nitriding time is ordinarily considerably reduced in ion nitriding. Other advantages have been cited,9 but it is not the purpose of the present work to contrast the two processes. The present objective was to examine the behavior of binary iron alloys during ion nitriding with respect to the microstructure, hardness level, and depth, and to examine some of these factors in steels as well. In this way it was hoped to be able to find out something about the individual role of these elements in steels. While all the work was done by ion nitriding, there seems to be no reason why any conclusions reached would not equally apply to ammonia nitriding, excepting only the kinetic aspects of the process. Another objective was an exploration of the critical-ity of the ion nitriding variables: gas composition, pressure, temperature, and time. EQUIPMENT AND MATERIALS The equipment used was substantially as described by Jones and Martin.8 The vacuum tank was about 12 in. in diam by about 18 in. high, and consisted of water-cooled stainless steel, with a single small window at the top for viewing inside. This sat on a heavy mild steel base equipped with the main pumping port, pressure control port, and vacuum gaging. A series of variable resistances was interposed between the glow discharge and a large-capacity -40 amp variable primary transformer feeding a 1000-v transformer, but 600 v were about the maximum ordinarily used. With the small l-in.-round, 4-in.-thick discs used for nitriding, the electrical load was usually about 500 v at 0.8 amp. The specimen temperature was controlled by a stainless-steel sheathed chromel-alumel couple, whose junction was in the steel stool upon which the flat discs were placed. These were ground through 400 Sic paper. Cycling of the temperature controller caused -0.2 amp variation in ion current, providing an ample control band. The binary iron alloys were made from vacuum-melted hydrogen-deoxidized electrolytic iron and alloys of 99.9 pct purity. Cast ll-lb-square tapered ingots were forged and hot-rolled to about 11/4-in.-diam rounds. Discs of 1/4 in. thickness by about 1 in. diam were machined from the rods for nitriding specimens. The following alloys were prepared: 1 pct each of Mn, Mo, Cr, Ti, Al, V, Si, and an Fe-0.8 pct C alloy. EXPERIMENTAL VARIABLES Of the variables total gas pressure, nitrogen partial pressure, temperature, and time, only nitrogen partial pressure was found to be critical to the operation. A critical nitrogen partial pressure was found corre-

Jan 1, 1970

By T. C. Boberg, R. B. Lantz

This paper presents a method for calculating the producing rate of a well as a function of time following steam stimulation. The calculations have proved valuable in both selecting wells for stimulation and in determining optimum treatment sizes. The heat transfer model accounts for cooling of the oil sand by both vertical and radial conduction. Heat losses for any number of productive sands separated by unproductive rock are calculated for the injection. shut-in and production phases of the cycle. The oil rate increase caused by viscosity reduction due to heating is calculated by steady-state radial flow equations. The response of successive cycles of steam injection can also be calculated with this method. Excellent agreement is shown between calculated and actual field results. Also included are the results of several reservoir and process variable studies. The method is best suited for wells producing from a multiplicity of thin sands where the bulk of the stimulated production comes from the unheated reservoir. The flow equations used neglect gravity drainage and saturation changes within the heated region. INTRODUCTION This paper presents a calculation method which can be used to predict the field performance of the cyclic steam stimulation process. The calculation method enables the engineer to select reservoirs that have favorable characteristics for steam stimulation and permits him to determine how much steam must be injected to achieve favorable stimulation. While the calculation represents a considerable simplification of physical reality and the results are subject to numerous assumptions which must be made about the reservoir, it has been found that realistic calculations can be made of individual well performance following steam injection. The duration of the stimulation effect will depend primarily on the rate at which the heated oil sand cools which, in turn, is determined by the rate at which energy is removed from the formation with the produced fluids and conducted from the heated oil sand to unproductive rock. A complete mathematical solution to this problem is a formidable task, and finite difference techniques would undoubtedly have to be used. The calculation method pre- sented here utilizes analytic solutions of simple related heat transfer and fluid flow problems. The method is sufficiently simplified that it can be used as a hand calculation, although the calculations are somewhat lengthy and laborious. For that reason, the analysis was programmed for an IBM 7044 digital computer. Well responses observed at the Quiriquire field in eastern Venezuela&apos; have been matched using this program after making suitable approximations for reservoir and wellbore conditions. One of the most valuable uses of this calculation method is to assess the effect of reservoir and proc-cess variables on the stimulation response. This paper contains results of several studies made of key reservoir and process parameters. Among the most important of these is the influence of prior wellbore permeability damage. If a well is severely damaged prior to stimulation, a higher stimulation response will be observed than if it is undamaged. If a portion of this damage is removed, a permanent rate improvement will occur. THEORY I)ES(:KJJ&apos;TION OF CALCULATION METHOD The process of cyclic steam stimulation is essentially one of reducing oil viscosity around the wellbore by heating for a limited distance out into the formation through the injection of steam. Suitable modifications of the calculation technique presented here can be made so that stimulation of wells by hot gas injection or in situ combustion can also be calculated. A schematic drawing of the heat transfer and fluid flow considerations included in the calculation method is shown in Fig. 1. In brief, the calculation assumes that the oil sand is uniformly and radially invaded by injected steam. For wells producing from several sands, each sand is assumed to be invaded to the same distance radially. In calculating the radius heated rn energy losses from the wellbore and conduction to impermeable rock adjacent to the producing sands are taken into account. After steam injection is stopped, heat conduction continues and oil sands with r < ra cool as previously unheated shale and oil sand at r > r, begin to warm. The effect of warming of oil sand out beyond r, has little effect on the oil production rate compared to the effect of cooling of the oil sand nearer the wellbore than ra. Thus, in computing the oil production rate, an idealized step function temperature distribution in the reservoir is assumed where the original temperature exists for r > rn and where an average elevated temperature exists for r < rn. The average temperature in the oil sand for the region r < rn is computed as a function of

Jan 1, 1967