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By D. Havlena, A. S. Odeh

The material balance equation used by reservoir engineers is arranged algebraically, resulting in an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful solution of the material balance equatiott should meet. In addition, this algebraic arrangement attaches a dynamic ineuning to the otherwise static material balance equation. The straight line method requires the plotting of one variable group vs mother variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. Therefore, one cannot progrm the method entirely on a digital computer ar is usually done in the routine solution of the material balance equation. If this method is applied, then plotting and anaIysis are asential. Only the appropriate equations and the method of analysis and interpremtion with comments and discussion are presented in this paper. Illustrative field examples for the various cases treated are deferred to a subsequent writing. INTRODUCTION One of the fundamental principles utilized in engineering work is the law of conservation of matter. The application of this principle to hydrocarbon reservoirs for the purpose of quantitative deductions and prediction is termed "the material balance method of reservoir analysis". While the construction of the material balance equation (MBE) and the computations that go with its application are not difficult tasks, the criteria that a successful solution of the MBE should fulfill have always been a problem facing the reservoir engineer. True and complete criteria should embody necessary and dcient conditions. The criteria which the reservoir engineer uses possess a few necessary but no sufficient conditions. Because of this, the answers obtained from the MBB are always open to question. However, the degree of their acceptability should increase with the increase in the number of the necessary conditions that they should satisfy. Generally, the necessary conditions commonly used are (1) an unspecified consistency of the results and (2) the agreement between the MBE results and those determined volumetrically. This second criterion is usually overemphasized. Actually, the volumetrically determined results are based on geological and petrophysical data of unknown accuracy. In addition, the oil-in-place obtained by the MBE is that oil which contributes to the pressure-production history,' while the volumetrically calculated oil-in-place refers to the total oil, part of which may not contribute to said history. Because of this difference, the disagreement between the two answers might be of paramount importance, and the concordance between them should not be overemphasized as the measure of correctness of either one. In this paper, a third necessary condition of mathematical as well as physical significance is discussed. It is not subject to any geological or petrophysical interpretation, and as such, it is probably the most important necessary condition. It consists essentially of rearranging the MBE to result in an equation of a straight line. This straight line method of the MBE solution has invalidated a few long time accepted concepts. For instance, it has always been advocated that if a water drive exists, but one neglects to take it into account in the MBE, the calculated oil-in-place should increase with time. The straight line method shows that in some cases, depending on the size of the neglected aquifer, the calculated oil-in-place might decrease with time. The straight line method requires the plotting of a variable group vs another variable group, with the variable group selection depending on the mechanism of production under which the reservoir is producing. The most important aspect of this method of solution is that it attaches a significance to the sequence of the plotted points, the direction in which they plot, and to the shape of the resulting plot. Thus, a dynamic meaning has been introduced into the picture in arriving at the final answer. Since the emphasis of this method is placed on the interpretation of the sequence of the points and the shape of the plot, one cannot completely automate the whole sequence to obtain "the best value" as normally done in the routine application of the MBE. If one uses the straight line method, then plotting and analysis are musts. The straight line method was first recognized by van Everdingen, et al,2 but for some reason it was never fully exploited. The advantages and the elegance of this method can be more appreciated after a few cases are carefully treated and worked out by it. SOLUTION OF THE MATERIAL BALANCE EQUATION SATURATED RESERVOIRS The MBE for saturated reservoirs written in AIME symbols is

Jan 1, 1963

By Zay Jeffries

IT HAS been known for centuries that iron and steel could be hardened by cold hammering and that the metal could be restored to the normal condition by heating to a red heat and cooling either rapidly or slowly with nearly pure iron and slowly with steels containing considerable carbon. The art of tempering steels is also very old. When a medium- or high-carbon steel is quenched from a cherry-red heat, the hardness is increased; this hardness can be reduced by heating to various temperatures below the lower thermal critical point, which is near 700° C. The present paper will not consider these old and well-known changes in iron and steel below the thermal critical range but will confine itself to the more unusual changes, some of which have been studied recently. Stromeyer,1 for example, in 1886, reports that both working steel and heat treatment of steel in the blue-heat range are highly injurious. Recently, however, some metallurgists believe that the straightening of warped steel forgings at a blue heat produces a beneficial effect on the metal.2 The Engineering Division of the National Research Council has constituted a committee on Physical Changes -in Iron and Steel Below the Thermal Critical Range, which has the following personnel: R. R. Abbott, H. C. Boynton, William Campbell, J. V. Emmons, F. B. Foley, H. J. French, H. M. Howe, Zay Jeffries (chairman), F.C. Langenberg, J. A. Mathews, P. D. Merica, A. H. Miller, J. H. Nelson, G. A. Reinhardt, W. E. Ruder, H. F. Wood: This committee is studying several aspects of the physical changes in iron and steel. The results, reported in the literature and obtained by recent experimentation, will be given; this will be followed by a general theoretical discussion of the more important

Jan 2, 1920

By Donald W. Scott, Nathaniel Arbiter, A. C. Richardson

This paper describes the application of amine flotation to a specific problem—that of increasing the grade of magnetite concentrates derived from an iron ore requiring extremely fine grinding for mineral liberation. Experiments conducted on an iron ore from Wisconsin had shown that concentrates containing 60 to 62 per cent iron and 12 to 14 per cent silica could be produced by magnetic separation. The residual silica occurred as quartz and hornblende, either entrained or locked with magnetite. Most advantageous utilization of the concentrate, however, necessitated that the silica content be reduced to about 5 per cent, equivalent to an iron content of 67.5 per cent. It had been demonstrated that tabling of the magnetic concentrate removed sufficient quartz and hornblende to yield an acceptable concentrate, but disadvantages inherent in tabling dictated that flotation be investigated as a substitute. The goals set for the flotation investigation were: (I) the production of concentrates of about 68 per cent iron content from the magnetic concentrate; (2) an iron recovery of about 85 per cent of that in the feed to flotation; and (3) minimum reagent cost. Both batch and continuous flotation tests were employed; the former, to establish the procedure and the latter to verify it. Although the data were obtained on a specific ore, and with a commercial application in view, it is believed that they have a bearing on other problems where amine flotation is being used or is anticipated. Samples Two samples, designated "(minus 100-mesh magnetic concentrate" and "minus 150-mesh magnetic concentrate," were used for the batch experimental work. They differed only in the degree to which the crude ore was ground prior to magnetic separation. They were stored moist in steel drums in quantities sufficient for all the experimental work reported. This procedure had the advantage of allowing all tests to be made on common samples, but had the disadvantage that the individual flotation samples, because of the difference in storage time, were subject to various stages of surface alteration. Previous work had indicated that common samples were desirable for the batch studies, and it was decided that if these data appeared sufficiently promising the effect of surface alteration could be checked best by continuous tests. The size distributions and the assays of the samples are given in Table I. The minus 150-mesh magnetic concentrate, on which most of the flotation tests were made, assayed 60.9 per cent iron, 13.3 per cent silica, and 0.016 per cent phosphorus. The minus 325-mesh portion represented 78.I per cent of the sample by weight, and assayed 67.9 per cent iron. Thus, the insoluble, mainly silica, was concentrated

Jan 1, 1947

By Donald W. Scott, Nathaniel Arbiter, A. C. Richardson

This paper describes the application of amine flotation to a specific problem—that of increasing the grade of magnetite concentrates derived from an iron ore requiring extremely fine grinding for mineral liberation. Experiments conducted on an iron ore from Wisconsin had shown that concentrates containing 60 to 62 per cent iron and 12 to 14 per cent silica could be produced by magnetic separation. The residual silica occurred as quartz and hornblende, either entrained or locked with magnetite. Most advantageous utilization of the concentrate, however, necessitated that the silica content be reduced to about 5 per cent, equivalent to an iron content of 67.5 per cent. It had been demonstrated that tabling of the magnetic concentrate removed sufficient quartz and hornblende to yield an acceptable concentrate, but disadvantages inherent in tabling dictated that flotation be investigated as a substitute. The goals set for the flotation investigation were: (I) the production of concentrates of about 68 per cent iron content from the magnetic concentrate; (2) an iron recovery of about 85 per cent of that in the feed to flotation; and (3) minimum reagent cost. Both batch and continuous flotation tests were employed; the former, to establish the procedure and the latter to verify it. Although the data were obtained on a specific ore, and with a commercial application in view, it is believed that they have a bearing on other problems where amine flotation is being used or is anticipated. Samples Two samples, designated "(minus 100-mesh magnetic concentrate" and "minus 150-mesh magnetic concentrate," were used for the batch experimental work. They differed only in the degree to which the crude ore was ground prior to magnetic separation. They were stored moist in steel drums in quantities sufficient for all the experimental work reported. This procedure had the advantage of allowing all tests to be made on common samples, but had the disadvantage that the individual flotation samples, because of the difference in storage time, were subject to various stages of surface alteration. Previous work had indicated that common samples were desirable for the batch studies, and it was decided that if these data appeared sufficiently promising the effect of surface alteration could be checked best by continuous tests. The size distributions and the assays of the samples are given in Table I. The minus 150-mesh magnetic concentrate, on which most of the flotation tests were made, assayed 60.9 per cent iron, 13.3 per cent silica, and 0.016 per cent phosphorus. The minus 325-mesh portion represented 78.I per cent of the sample by weight, and assayed 67.9 per cent iron. Thus, the insoluble, mainly silica, was concentrated

Jan 1, 1947

By A. Lee Barrett

AN accelerated trend toward mechanical mining was noted in 1940, calling for improvements in and better performance of transportation, hoisting, and ventilating equipment. One of the most interesting experi¬ments in transportation is the track shuttle-car operation first put into use by the Princeton Mining Co. in Indiana and later at the Montour 4 mine of the Pittsburgh Coal Co. This system is based on the use of 10-ton drop-bottom mine cars operating on track and han¬dled by an ordinary gathering loco¬motive. These mine cars are loaded and taken in trips of two to a central dumping station which serves four or less loading machines. The dumping station consists of two standard chain-and-flight room conveyors, approximately 50 ft. long placed side by side approximately 4 ft. below the track from which the drop-bottom cars are dumped. These conveyors are operated at low speed and discharge into two similar elevating conveyors which operate at a higher speed and convey the coal to a trip of standard mine cars. A dumping station is usually located so that approximately 500,000 tons of coal may be handled through it before a move is required. This plan appears to have considerable possibilities for the mine equipped with small mine cars and standard locomotives since the advantages of large mine cars can be secured at a fraction of the cost required to install such cars throughout the mine. It appears logical that the future will see a much wider use of this modification in transportation.

Jan 1, 1941

By W. S. Morris

THE East Texas oil field is the largest in the United States and perhaps the largest 'in the world ; likewise, it is one of the most interesting. The East Texas oil field is a water-drive field. Small amounts of salt water were produced from wells on the western side of the field from the bt-ginning of the development. By the end of 1933 (the field having been discovered in September 1930) water production had reached 9000 barrels per day. By the end of 1936, approximately 2000 wells were producing about 45,000 barrels of water per day, and the problem of salt water disposal attracted the serious attention of the operators. Salt water production in the field has steadily increased and today approximately 450,000 barrels of water per day is produced while the oil production averages about 375,000 barrels. The disposal of this salt water has therefore become one of the major operating problems. Various methods of salt water disposal have been tried in the East Texas field. Evaporation in open pits proved

Jan 1, 1944

Jan 1, 1970

By Frank Haas

THE public generally has-become aware that there is something wrong with the coal industry and a clamor has arisen for an explanation if not a remedy for this disorder. It is only reasonable that this Institute be looked to for a diagnosis to show the way for some other .agency to prepare the patient for prescription or operation. The subject is extensive, widely diversified, and beyond the efforts of an individual to cover completely; one of the objects of this paper is the initiating of a symposium on the non- technical factors essential to an understanding of the bituminous coal industry. The present condition of the coal industry cannot be described in a few words but, in effect, it resolves itself into a simple statement: The average coal operator is losing money notwithstanding a firm conviction on the part of the consumer that he pays too much for his coal. Without enumerating the many and varied. factors which contribute to this condition, this paper will be devoted to the interrelation of taxation and ownership of coal and its effect on finance

Jan 1, 1930

ENGINEERS AVAILABLE, (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members) Member, aged 33, technical graduate, B. S. and E. M., soon to complete contract in Spanish America, desires to get in touch with employers. Ten years mine, mill, cyanide and construction experience. Prefers executive position or assistant to executive. No. 352. Member; University graduate, desires responsible position with good company. Married.' Age; 37. Fourteen years' experience in Australia, Mexico and United States, milling, cyaniding and concentrating, gravity

Jan 5, 1917

By Faustino Roel

AMONG the problems confronting the mining engineer in Mexico in recent years, labor conflicts have come to occupy s prominent place. Each day they have become more serious and frequently have caused- the ruin of companies. It is therefore necessary for the engineer to understand the Federal Labor Law, the rights and obligations of companies and of their workmen, and the reasons for conflicts; to keep in mind the expense which may be caused companies; and to endeavor to avoid difficulties as far as possible. Our labor legislation is primarily to protect the workman and the constant tendency of the tribunals, including the Supreme Court of Justice, is to support the work- man in his demands against employer$, even at times granting him more than he asks, with no limit other than the economic capacity of the company to com-

Jan 1, 1937

By S. Leber, R. F. Hehemann

This investigation describes the kinetics of alloying in a (Cb-15 wt pct W. 5 wt pct Mo, 1 wt pct Zr) powder-metallurgy alloy. The degree of homogeneity obtained in hydrostatic ally pressed and vacuum-sintered samples is described by composition distributions resulting from analysis of X-ray dvfraction line profiles. Sintering variables and degvee of powder dispersion were evaluated. The utility of single-value parameters obtained from composition distributions is disaissed. The spatial distribution of composition, as revealed by anodically tinted metallographic sarrzples, was used to provide diffision models based on a concentric-sphere geometry. Diffusion equations developed from these models were found to be in general agreement with experimental results. The powder-metallurgy method for the production of refractory metal alloys has the ability to produce an inherently fine-grained, fabricable structure. The more general use of this method is inhibited, in part, by the presumed difficulty in obtaining homogeneity on a microscale. The degree of homogeneity therefore is an important, but usually neglected, variable in specifying the quality of a powder-metallurgy alloy. Convenient techniques for measuring the degree of homogeneity are now available,' and have been used to develop a model describing the process of alloying in a simple binary mixture.' In this investigation, the process of alloy formation has been studied in a more complex system. PROCEDURE The columbium-based F-48 mixture was prepared from the constituent powders shown in Table I. The particle sizes tabulated were provided by the vendors of the individual powders. Standard laboratory techniques utilizing a jar mill were employed for blending. The blended powders were hydro-pressed into 1-in. diam rods which were then sliced into thin discs for vacuum sintering. All samples were given a preliminary treatment at 1700°C for 2 hr. Varying degrees of homogeneity were obtained using additional treatments at higher temperatures. The degree of homogeneity obtained by a specific sintering treatment was evaluated metallographi-cally using the anodic-tinting technique described by olff,' and quantitatively by the analysis of X-ray diffraction line profiles using the X-ray diffraction technique developed by udman.' The diffraction technique is strictly valid only for binary systems. However, the relatively small difference between the lattice parameters of tungsten and molvbdenum when compared with columbium permitted the treatment of the complex composition of F-48 as a (W, Mo)-Cb pseudobinary. Calculations were weighted in accord with the W-Mo ratio in the F-48 composition. The contribution of the 1 pct Zr was ignored since it could not even be detected in the blended powder. Two factors are required to convert an X-ray line profile into a composition distribution. The variation of these factors with composition is shown in Fig. 1. Curve A was used to convert angular posi-

Jan 1, 1964

By Grimes, J. A.

EXTENSIVE discovery 'and rapid exploitation of orebodies within the past half century have attracted many able geologists to the mining industry and furnished them a wealth of data from which to develop theories concerning ore genesis. By tosting and elimillating theories which are not sufficiently sup- ported by fact, or which are based on inaccurate observation of field data, the trend of geological opinion has . moved strongly in certain directions until, at the present time, large numbers of geologists subscribe to a broad concept of .ore genesis that I would summarize as below:

Jan 1, 1928

By H. E. Strauss

The time-to-fracture test has been applied to pure platinum and to two alloys of platinum under the special conditions of small cross-sectional area of the specimens and of a test temperature above the annealing temperature. While the results are similar in character to those secured with large specimens of steel at temperatures below the annealing temperatures, two differences are noted: (I) an upward inflection in the curves for log stress vs. log time for the alloys, and (2) a sharp break in the curve for log stress vs. log time for pure platinum when single crystals filled the wire. The experiments showed that: (I) platinum and 10 per cent rhodium-platinum maintained their strengths at IIOO°C. better than did to per cent iridium-platinum, and (2) the rhodium-platinum after a time exceeded the iridium-platinum in strength at IIOO°C. Platinum alloys in their service at high temperatures encounter conditions somewhat similar to those that exist in the usual form of the "time-to-fracture"l test with steel. This paper is intended primarily to present results obtained by a "time-to-fracture" test under conditions approximating actual service for platinum (at the temperature IIOO°C. under oxidizing conditions) with three materials, pure platinum (99.99 per cent), a platinum alloy with 10 per cent iridium, and a platinum alloy with 10 per cent rhodium. The experimental procedure differed from that previously used in this type of measurement in that the samples were of small diameter (0.010 in.), were fully annealed, and were tested at a temperature definitely above their annealing points (600°C., IOOO°C. and 1050°C., respectively, for 60 per cent cold reduction and 15 min. heating time2,3). The experimental arrangement was similar to that previously described,' using as heating unit a small, horizontal, platinum-wound furnace, ½ by 12 in., maintained at constant temperature by an automatic controller. The samples were 0.010-in. wires, which had been annealed at 1200°C. by drawing them slowly through the furnace. The time-to-fracture was measured electrically. Elongation was not determined because of the difficulties inherent in the experimental arrangement. Life—that is, the time-to-fracture—was considered the important property in these first tests. No attempt was made to measure the reduction in area, but the types of fracture were noted qualitatively; in the text they are referred to as (I) the normal, plastic, or necked fracture, (2) the knife-edge fracture, and (3) the brittle or intercrystalline fratture with small reduction of area. Results for different constant applied stresses are plotted in Fig. I. In all cases at least two trials were made for each stress, although they cannot always be indicated separately on the curves. The breaking Stresses drop very rapidly to a small frat-286

Jan 1, 1943

By H. E. Strauss

The time-to-fracture test has been applied to pure platinum and to two alloys of platinum under the special conditions of small cross-sectional area of the specimens and of a test temperature above the annealing temperature. While the results are similar in character to those secured with large specimens of steel at temperatures below the annealing temperatures, two differences are noted: (I) an upward inflection in the curves for log stress vs. log time for the alloys, and (2) a sharp break in the curve for log stress vs. log time for pure platinum when single crystals filled the wire. The experiments showed that: (I) platinum and 10 per cent rhodium-platinum maintained their strengths at IIOO°C. better than did to per cent iridium-platinum, and (2) the rhodium-platinum after a time exceeded the iridium-platinum in strength at IIOO°C. Platinum alloys in their service at high temperatures encounter conditions somewhat similar to those that exist in the usual form of the "time-to-fracture"l test with steel. This paper is intended primarily to present results obtained by a "time-to-fracture" test under conditions approximating actual service for platinum (at the temperature IIOO°C. under oxidizing conditions) with three materials, pure platinum (99.99 per cent), a platinum alloy with 10 per cent iridium, and a platinum alloy with 10 per cent rhodium. The experimental procedure differed from that previously used in this type of measurement in that the samples were of small diameter (0.010 in.), were fully annealed, and were tested at a temperature definitely above their annealing points (600°C., IOOO°C. and 1050°C., respectively, for 60 per cent cold reduction and 15 min. heating time2,3). The experimental arrangement was similar to that previously described,' using as heating unit a small, horizontal, platinum-wound furnace, ½ by 12 in., maintained at constant temperature by an automatic controller. The samples were 0.010-in. wires, which had been annealed at 1200°C. by drawing them slowly through the furnace. The time-to-fracture was measured electrically. Elongation was not determined because of the difficulties inherent in the experimental arrangement. Life—that is, the time-to-fracture—was considered the important property in these first tests. No attempt was made to measure the reduction in area, but the types of fracture were noted qualitatively; in the text they are referred to as (I) the normal, plastic, or necked fracture, (2) the knife-edge fracture, and (3) the brittle or intercrystalline fratture with small reduction of area. Results for different constant applied stresses are plotted in Fig. I. In all cases at least two trials were made for each stress, although they cannot always be indicated separately on the curves. The breaking Stresses drop very rapidly to a small frat-286

Jan 1, 1943

By Quentin D. Singewald, B. S. Butler

Some of the broader relations between structure and ore deposition along the London fault, deduced from a thorough study of the geology of the eastern part of the Mosquito Range, should be of general interest to economic geologists. The first part of this paper is a generalized statement of the geology of the region in which the London fault is located; it may be supplemented by reference to several earlier publications by the writers and to the U. S. Geological Survey's Professional Paper 148, on the Leadville district. The second part deals with the structure of both the fault and the disturbed zone adjoining the fault. The third part discusses the salient features of the ore deposits, particularly emphasizing structural control. The two generalized maps are complementary to one another but contain too many data to show on a single small map. The London fault is between Leadville and Alma, and the ore deposits along it are said to lie in the Alma district. Field work in this district, during six summers since 1927, has been a part of the cooperative work of the U. S. Geological Survey, the State of Colorado, and the Colorado Metal Mining Board. The writers have made use of work by R. D. Butler, J. W. Vanderwilt and R. E. Landon. G. F. Loughlin and C. H. Behre, Jr., who have worked on the west side of the range, have contributed valuable suggestions. Mining men of the district have aided in many ways. General Geology Pre-Cambrian Rocks.—The oldest rocks in the district are schists, correlated with the Idaho Springs formation of the Front Range. Quartz-mica schist predominates, but other types occur locally; almost everywhere the rocks show considerable lit-par-lit injection. Intrusive into the schists are two varieties of granite, only one of which is widespread. It is a fine-grained, porphyritie, gray granite correlated with the Silver Plume granite of the Front Range. Near the head of Buckskin Gulch a

Jan 1, 1937

By A. CHESTER BEATTY

MAGNESIUM oxide is by far the most refractory of the common oxides, since it has a melting point of 5072 deg. F. as compared with 3110 deg. F., the melting point of silica (crystobalite) ; 3722 deg. F., the melting point of alumina (corundum) ; and 4127 deg. F., the melting point of chromite (Cr2O33FeO). Its large-scale use in the lining of metallurgical furnaces dates back to the latter part of the nineteenth century, when extensive deposits of magnesium carbonate were discovered in southern Austria in the province of Styria. Before the development of Austrian magnesite, calcined dolomite, a mixture of lime and magnesia, was used in basic steel-making furnaces. The lime in the dolomite was quite objectionable, since it slaked on exposure to the atmosphere, and dolomite therefore could not be made' .into permanent furnace bottoms or into brick. The Austrian magnesite, with its very low lime content, was free from these objections and soon displaced much of the dolomite. With the extensive development of basic steel-melting, the rise of the copper industry, and other metallurgical and chemical processes which dealt with chemically basic substances, the use of magnesite grain and magnesite brick increased rapidly.

Jan 1, 1931

By Arthur A. Center

WAR demand- motivated developments in the zinc industry during 1942. Stocks of Prime Western were built up and High-Grade remained tight. The Prince The Prime Western stocks are expected to be cut down and the demand for High-Grade more easily filled as the Depue reflux plant of the New Jersery Zinc Co. increases - production. Subistition of steel for brass in artillery shell cases will have a considerable effect on the zinc situation of the country one estimate of the saving in zinc in 1943 by this substitution being a little under 100,000 ton, of metal. The metal saved will, of course be High-Grade. If the substitution occurs, the present tight situation in High-Grade may be entirely relieved as new production comes on the market and zinc may find itself approaching a situation as comfortable as that of lead provided the supply of zinc-hearing raw materials is sufficient to keep all reduction plants tip to capacity production. The premium price of the per pound of zinc over set quotas which went into effect early in 1942, helped to bring about the new lead-slag-fuming plant and other new sources of raw materials.

Jan 1, 1943

By F. M. Lewis, J. E. Goodman

A larger, slow-speed, under-loaded ball mill and hydraulic classifier have almost doubled grinding efficiency at the lsabella mill. TENNESSEE Copper Co. operates two ore con-A centrators, the London and Isabella mills near Copperhill, Tenn. In 1948 and 1949 the small ball mills and rake classifiers in the London concentrator were replaced by one large ball mill and one hydraulic classifier. This new ball mill was designed oversize so that it could be operated at slower than normal speed. The proper operating conditions were established and the results published.' Later it was found that this mill operated more efficiently with a small ball charge." While this London grinding practice was being developed, the Isabella grinding circuit was not changed in any way. It remained a conventional two-stage rod mill—ball mill combination, the rod mill in open circuit and the ball mill in closed circuit with a rake classifier. Study of the data indicated that grinding cost could be lowered by converting to the London practice, but not enough would have been saved to warrant the expense of converting. No plan for improving this grinding operation could be developed. In 1953 this study was reopened when plans were made to increase the Isabella mill output from 1150 to 1500 tpd. At this time the grinding circuit consisted of a 6x12 rod mill followed by a 6x12 ball mill in closed circuit with a 6-ft rake classifier. Another 6x12 ball mill and 6-ft rake classifier would have been sufficient equipment and would have been the simplest and cheapest installation. However, this would have offered no improvement in grinding efficiency or operating cost. If, on the other hand, the grinding operation could be converted to the London practice, by installation of one large 101/2x9x9 tricone mill and a 10-ft hydroscillator,2 lower operating costs would justify the additional investment. Economics: Table I presents estimates for the two schemes for enlarging the Isabella mill. In the first scheme, column 1, one 6x12 ball mill and one 6-ft rake classifier were to be added. In the second scheme, column 2, the existing small ball mill and rake classifier were to be retired and one large mill and hydroscillator were to be installed. Estimated savings from the difference in operating costs made an attractive return on the additional investment for the large mill and hydroscillator. Actual costs of carrying out this plan are tabulated in column 3b. It will be seen that these costs follow the estimates in column 3a very Closely. The return on the additional investment is calculated from the difference in the operating cost in column 1 and the actual operating cost in column 3b. This too come very close to the estimate. Power and Steel: Power requirements and steel consumption for the rod mills and ball mills, both actual and estimated, are presented in Table 11.

Jan 1, 1958

By P. K. Foster, A. McNabb

A consideration of the literature shows the inadequacy of Fick's Laws to describe the diffusion of hydrogen in steels below 400°C. These laws are modified an the assumption that hydrogen is delayed at fixed sites in the lattice. Approximate and exact solutions of the resulting nonlinear system are derived for simple geometrical shapes. The results qualitatively account for the observed anomalous behavior. Experimental methods for verifying the theory are suggested. 1 HIS paper presents a new analysis of the diffusion behavior of hydrogen in steel based on a physical model which supposes that hydrogen atoms wander in a random manner through the crystal lattice, but tend to get trapped or delayed at certain fixed sites uniformly distributed throughout the metal. These sites, which will be called traps, are regarded merely as potential wells of significantly greater depth than those encountered in regular regions of the crystal lattices and no assumptions are made concerning their nature or origin. The results of experimental studies of the diffusion of hydrogen in iron and steel have usually been reported in the literature in terms of a diffusion constant D derived under the assumptions that the hydrogen concentration C is governed by Fick's laws.1 Fig. I is a composite of published graphs of the man. ner in which the values of D, so derived, vary with temperature. It is convenient to consider this material in two categories; the high temperature results above 400°C, and the results at lower temperatures. The graphs 2, 3, 4, 5 in the first class lie within a factor of three of each other and are relatively consistent compared with the low-temperature values. There is an increasing divergence in values of D with decreasing temperature till at room temperature they are spread over three orders of magnitude. Small values of D have been obtained for work-hardened specimens.' It is evident that D is a function of other variables besides temperature in this range and that these neglected variables are in some way connected with the work hardening experienced by the specimen. In view of evidence for an interaction between hydrogen in solution and dislocations9'10 and adsorption on crack surfaces,' some doubts must be entertained about the validity of Fick's laws and their associated physical model of noninteracting particles in random motion through the medium. More direct evidence of their inapplicability to the diffusion of hydrogen in steel was first produced by Darken and smith." Consider the permeation of hydrogen through a plate of thickness a under a boundary concentration Co at the ingoing, and zero at the outgoing, face. If Fick's first law1 is valid, the steady state flux P, through unit area is DCo/a. In addition, the concentration C varies linearly throughout and Qo, the mean quantity of hydrogen in the medium, is co/2. Compare Qo with Q1 the mean quantity required to saturate the same specimen to a uniform concentration G. In this case Ql = Co and hence the ratio

Jan 1, 1963