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By Amitava Gangulee

A recent investigation has shown that solid solution hardening is almost absent in the quasibinary system SnTe-pbTe.1 The lack of solid solution hardening was attributed to the small difference of only about 3 pct between the atomic sizes of lead and tin, and to the fact that the formation of these solid solutions involved changes only in the sublattice occupied by the lead and tin atoms. The investigation reported here is concerned with the quasibinary system PbSe-PbTe which, similar to the SnTe-PbTe system, forms a continuous series of solid solutions2 and has the same NaC1-type (Bl) structure. The size difference between the selenium and tellurium atoms, however, is slightly larger than 7 pct. No indication of any ordering of the lead and tin atoms at. selected compositions had been found in the system SnTe-PbTe, which had been explained by the weak second-nearest-neighbor interactions between lead and tin atoms.' The possible occurrence of an ordering transition in the system PbSe-PbTe was also investigated in the present work. Polycrystalline specinlens of PbSel-1-xTex (x = 0, 0.20, 0.25, 0.33, 0.50, 0.67, 0.75, 0.80, and 1.0) were prepared by melting appropriate amounts of 99.999 pct pure Pb, Se, and Te j.n evacuated and sealed Vycor capsules. The capsules were quenched in water. The solidified ingots were homogenized at 800°C for 14 days. Chemical analysis of the homogenized ingots showed that the deviations from the stoichiometric compositions were less than 0.1 at. pct for each component. Part of each ingot was ground to pass through a 75 g sieve and pressed into 25.4 mm by 12.7 by 2 mm briquettes. Duplicate sets of specimens, each containing at least one briquette and part of the ingot of each composition, were sealed in evacuated Vycor capsules. Both sets were annealed at 500°C for 7 days; one set was quenced in ice-water and the other was cooled to room temperature over a period of 14 days.

Jan 1, 1970

By J. B. Newkirk, R. W. Hendricks, R. Baro

STUDIES of the kinetics of precipitation in binary alkali halide systems are of interest from a theoretical point of view, because of the possibility of controlling diffusion rates by additions of aliovalent impurities. This note reports some preliminary results of a study of the kinetics of precipitation of AgCl from supersaturated solid solutions of AgCl in NaCl containing trace amounts of divalent cation impurities. In their study of the system NaC1- AgC1, Stokes and Li1 derived the phase diagram containing a mis-cibility gap with a broad maximum at approximately 170°C. They found that single crystals quenched from above the miscibility gap and aged at various temperatures within the two-phase region gradually turned light blue, then cloudy white, and finally opaque. The rate of transformation depended markedly on the aging temperature. The light-blue color in the early stages of aging was interpreted to be the result of Rayleigh scattering from precipitated particles less than 0.1 µ in diameter. These qualitative observations have been confirmed by us. However, a more precise tool was needed in order to quantitatively follow the growth kinetics of the precipitate particles. Because of the suspected small size of the precipitate particles and for other reasons, small-angle X-ray scattering was thought to be a suitable technique for this study. Small-angle X-ray intensities scattered from powder specimens were recorded on a General Electric XRD-5 diffractometer using the four-slit geometry described by Neynaber, Brammer, and Beeman.2 The slits were 0.08 mm wide by 10.00 mm high. It was found that, with very careful alignment, meaningful data could be obtained to within 3 min from the middle of the direct beam. Chromium radiation (?Ka = 2.29Å) was used in order to spread the scattered intensity to a relatively high angle, as indicated by Eq. [1]. A specimen containing 21.0 at. pet AgCl was prepared by melting analytic reagent-grade AgCl and NaCl under a chlorine atmosphere in a vycor cap-

Jan 1, 1964

Jan 1, 1884

By C. Scala, M. Gondouin

Published laboratory data have established that very significant streaming potentials can exist across mud cakes subjected to pressure differentials such as exist between a mud column and formation fluids. Since shale is similar in kind and in properties to a well-formed mud cake, it appeared possible that streaming potentials might also arise across shales. A practical consequence would be that the streaming potential contribution to the SP would be smaller than might otherwise be assumed since the SP is measured with respect to the "shale bare line". The resultant contribution would be the difference between the streaming potential across the shale and that across the mud cake. In order to investigate this possibility, a laboratory apparatus was devised for measuring streaming potentials under pressure conditions normally encountered in wells. Reported data on streaming potentids across mud cakes were verified. More important, appreciable streaming potentials were found across shale samples. As in the case of mud cakes, the shale potentials varied with the concentration and nature of the impregnating electrolyte. Dependence on pressure was In a different rela-tion than that for mud cakes, possibly because of the lower compressibility of shales. The differences in streaming potentials between the shales md mud cakes were generally small, although they might vary considerably in practice depending on the relative electro-kinetic properties of the particular shale-mud cuke combination. A "poorly eflective" shale with a "very eflec-tive mud cake" would produce the largest negative addition to the electrochemical component of the SP. Results of field experiments with pressurized wells were considered in the light of the laboratory results. INTRODUCTION Field experiments wherein the pressure of the mud column in a borehole was varied have often indicated the presence of a streaming potential, but its magnitude was not easily predictable and its sign sometimes changed from one formation to another in the same well.' In the interpretation of SP logs from standard surveys, nevertheless, the correct value of R,, is very frequently obtained, within the limits of field accuracy, using only the simple electrochemical expression of the SP provided that proper corrections are made for bed thickness, ion activity, etc.' Accordingly, it was apparent that the streaming potential component of the SP in a borehole was considerably more complex than commonly assumed and clarification was indeed necessary The close similarity in nature and constitution of a shale to a well-compacted mud cake suggested that a streaming potential might also exist across shales as pointed out by M. P. Tixier in 1953 and as recently emphasized by Wyllie." e practical consequence would be that the streaming potential across the mud cake would be canceled, at least in part, on electrical logs since the SP is recorded with respect to the shale potential as a base line. This appeared to be a plausible explanation for many of the effects observed but no supporting data were available. In 1955 preliminary experiments at low pressures were conducted in our laboratories which supported the hypothesis of the shale streaming potential and formed the basis for later studies at borehole pressures.* EARLY LOW PRESSURE EXPERIMENTS The early experiments were conducted primarily to determine the possibility of a streaming potential across shales. The shale used was a compact type designated as No. 7 from Reagan County, Tex. (Permian). Cut samples were saturated for over one month in .2 to 2.0-N NaCl solutions. In order to eliminate all electrode polarization effects, a dynamic method was used. A transient pressure of about 1 atm was applied across

By M. I. Sherman, J. D. H. Strickland

PRELIMINARY experiments in these laboratories showed that whereas pyrite1 produced only sul-fate the action of aqueous chlorine solutions on most other sulfide ores resulted in the formation of a mixture of sulfate and elemental sulfur, the production of the latter being favored by a very dilute solution of oxidant. The reactions taking place were obviously complex and only a detailed kinetic study could be expected to clarify the position and enable a prediction to be made of conditions leading to the rapid formation of metal salt and the economically desirable elemental form of sulfur. Galena was chosen for the first investigation as it is of widespread occurrence and is representative of a simple cubic lattice sulfide containing the monosulfide unit, S2-. Experimental Procedure The apparatus and general technique used in this work have already been described.' Analyses for chlorine and sulfate were carried out by the same methods as those used for pyrite. The lead in 1 ml aliquots of solution was determined polarographi-cally, after destroying chlorine with hydrazine hy-drochloride and making solutions 0.5 molar with hydrochloric acid. A large sample of Kansas galena, assaying at better than 98 pet PbS, was crushed and wet sieved to give fractions of —10 + 14, —20 + 28, —28 + 35, and —48 + 65 Tyler screen. The particles were almost perfect cubes and the apparent surface Per gram was calculated assuming each particle a cube Of side equal to the mean mesh opening. A volume shape factor, calculated as for pyrite, was exactly unity. The main apparatus was unsuitable for direct visual examination of the ore particles during the reaction. For this purpose a small cell from a Spekker Absorptiometer optical flats 1 cm apart) was l by a greased microscope slide after filling with oxidant solution. One or two ore particles were placed in the cell and the solution was stirred by a glass covered speck of iron wire activated by an external rotating magnet. The surface of an ore particle was examined under a binocular microscope at between 10 and 40 magnifications. Results Experiments were made under a wide variety of conditions, the form of presentation of the data being illustrated by Fig. 1, where the concentrations of chlorine, sulfate, and sulfur are plotted against time. The fictitious concentration of solid sulfur is used for convenience and is the molarity of sulfur which would be recorded if the elementary sulfur formed during the reaction were dissolved in the liquid iii the reaction vessel. As some lead sulfate is occluded with the sulfur on the ore particles the amounts of sulfur and sulfate formed during a reaction cannot be calculated

Jan 1, 1958

By Michael J. Messel

W. P. MOULD*—Has consideration been given to the problem of retreating the 4,000,000 ton tailings pile to recover the very considerable amount of asbestos fiber that was lost over the years due to insufficient operation and poor recoveries? Also, what was known about the possible content of chromite and the sulphides of nickel and cobalt? M. J. MESSEL (author's reply)—Consideration was given to the problem but nothing concrete has been done up to this time. W. P. MOULD—I am certain the tail- ings contain a very considerable quantity of fiber, not all of which is in the shortest lengths, because in the milling of talc rock from a neighboring location having a common origin with the asbestos bearing serpentine source of the tailings pile, a concentrate carrying 15 pct Ni and Co in complex sulphides and constituting about 4/10 of 1 pct of the talc rock was recovered. In the belief that the tailings also contained an appreciable content of chromite (then in demand, 1937) it was suggested to the management of the asbestos company that a truck load of the current tailings be sent to the flotation plant of the talc company where it would be put over the concentrating tables in an effort to discover the presence and roughly the percentages of chromite, nickel, and cobalt. Preparations for the test were woefully inadequate and the test was completely snarled up by the surprisingly large quantity of asbestos fiber from 1 in. long down to very short fiber, all of which matted up and plugged launders and pumps with disastrous effects and practically the total loss of the sample. If anything was indicaded by the test, it was that a wet process for milling asbestos was worthy of very serious consideration. M. J. MESSEL—A wet milling process for tailings retreatment only, is at present under study at our plant. One asbestos mining company in Canada has constructed a fairly large test plant for this purpose, but as yet no definite results have been obtained other than in a small test unit plant which were in some respects quite encouraging.

Jan 1, 1950

By Howard Martens

HARDNESS behavior of commercial titanium alloys following various heat treating processes has been studied for some time. However, the hardness of such alloys following a definite measured cooling rate from the single phase region has not been reported. Therefore, a series of experiments was conducted on the three alloys: 150A, 130A, and 130B. The manufacturers gave the following compositions for these alloys: Ti 150A: 0.045 pct C, 0.069 pctN, 1.32 pct Fe, and 2.68 pct Cr; RC 130A: 0.13 pct C, and 7.9 pct Mn: RC 130B: 0.11 pct C, 3.5 pct Mn, and 3.2 pct Al. A method similar to that described by Greninger was used, and the cooling rate varied from 6" to 9200°F per sec. The cooling curves were recorded on a Speedomax or a recording oscillograph, and the hardness was measured on a Tukon hardness tester using a Knoop indentor with a 500 g load. The curves of Fig. 1 show the variation of the Knoop hardness with the cooling rate for these three alloys. The alloys 150A and 130B behave in a similar manner, as shown by the curves. In neither of these alloys was it; possible to retain the high temperature ß phases, even by the most rapid cooling rate. The slow cooling rates produced a typical ß structure in these two alloys. As the cooling was increased, these phalses became more finely dispersed and the hardness increased. This increase in hardness with cooling rate continued for the 150A alloy until a rate of approximately 1000°F per sec was reached. At this cooling rate, the structure showed the result of the dif-fusionless transformation of the ß solid solution to the supersaturated a solid solution which is referred as a'. At higher cooling rates, the structure showed no change and the hardness showed no great change, as indicated by the dotted portion of the curve in Fig. 1. The increase in hardness with cooling rate for the 130B alloy continued until a rate of approximately 300°F per sec was reached. At this rate the structure was produced and the maximum hardness was reached. Higher cooling rates caused no marked changes in hardness or structure. The alloy 130A behaved in a different manner, as shown by the curve of Fig. 1. The structure produced by the slow cooling rates was a typical a+ß structure, which became finely dispersed as the cooling rate increased. The hardness increased with cooling rate and reached a maximum at approximately 120°F per sec. At this maximum hardness, the structure showed the result of the decomposition of the ß phase into the ß + phase structure. As the cooling rate was increased, smaller amounts of the at phase were formed and the alloy became softer. For cooling rates of 3000°F per sec and above, the high temperature ß phase was retained and the hardness of the alloy did not change markedly. Acknowledgment This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. DA-04-495-0rd 18, sponsored by the Dept. of the Army, Ordnance Corps.

Jan 1, 1957

By D. H. Thompson, A. W. Tracy

E. A. ANDERSON*—At the outset, I note that you are using a humid atmosphere containing ammonia but that you make no reference to the variable of carbon dioxide content. Edmunds in his work in this laboratory found very marked effects on the rate of failure due to variations in carbon dioxide in the environment. This point is, of course, strongly related to the overall corrosion rate problem since the role of the carbon dioxide seems to be to permit the formation of hygrogroscopic salts which give a controlled moisture film on the specimen surface, which in turn seems to support the intergranular penetration more consistently than would otherwise occur. (2) Your results with various copper binary systems are very striking. It is curious, however, that the time-to-failure minima all occur at percentages of the alloying element which are considerably below the solubility limits as given in the conventional equilibrium diagrams. If your theory regarding the presence of these impurities in some concentration in the grain boundaries is correct, then either the existing diagrams are not accurate in the room temperature region, or there is a difference in solubility in the grain boundaries as compared -with the grains. A study along these lines might be very revealing. (3) The undesirable effect of silicon in copper calls to mind our own observations on the influence of silicon on the stress corrosion cracking resistance of alpha brass. In this case, silicon was found to have a very marked beneficial effect, particularly when a heat treatment capable of producing a grain boundary constituent was used. I should appreciate it if in the discussion of your paper this point should arise, you would attempt to clarify the difference between the copper-silicon binaries and the copper-zinc-sili-con ternary alloys. D. H. THOMPSON and A. W. TRACY (authors' reply)—(1) We have no data on the constancy of the carbon dioxide content of the air used for the test atmosphere but have believed that the normal carbon dioxide content of the air was as constant as could be obtained by using Edmunds' method of removing carbon dioxide from the air and then adding a measured quantity. In any event, the test atmosphere was the same for all specimens in a test run. We agree with Mr. Anderson that the carbon dioxide content is important in the formation of a hygroscopic film on specimens. (2) We can imagine that there could be a concentration of solute atoms at the grain boundaries which would be so small that present methods would not detect it even if it exceeded the solubility limit of the alloy. There could be somewhat greater solubility at the grain boundaries for an interstitial solute. There is a possibility that phosphorus dissolves in this way but we believe that none of the other solutes studied does. In our present studies we hope to find out something about conditions at the grain boundaries of some of the systems mentioned in the paper. (3) Mr. Anderson points out that silicon brass, which has had a high temperature heat treatment followed by a quench. is highly resistant to stress-corrosion cracking. Although the test conditions used by Anderson* et al were different from our test conditions, it is noted that the silicon brasses which had not had the special heat treatment were less resistant to stress-corrosion cracking than copper containing approximately equal amounts of silicon. G. R. GOHN†—Nonferrous metallurgists and particularly, materials engineers, have been accustomed to thinking

Jan 1, 1950

By R. D. Stover, F. O. Shuck

The variation of binary-diffusion coefficients with composition in the liquid Bi-Sn system at 300°C was measured using the capillary-reservoir technique. The experimental coefficients did not exhibit a simple composition dependence. A number of tests were also made to determine the effect of variation of density with composition on convection within the capillaries. These tests indicate that the density changes arising from composition duferences may give rise to high diffusion coefficients unless care is taken to maintain a stable configuration. In recent years there has been considerable interest in diffusion in liquid metals. However, the bulk of the work done to date has involved measurements of self-diffusion or diffusion of dilute concentrations of "solute" metals. Because there are possible applications to liquid phase processing of metal alloys and since additional data may help to clarify the nature of diffusion in liquid metals, investigations of the concentration variation of diffusion coefficients in binary alloys have been undertaken. Of past studies only two have covered large ranges of binary composition. Niwa et al.' investigated the Pb-Sn, Bi-Pb, and Bi-Sn systems and Grace and Derge2 investigated the Bi-Pb system. Because of the discrepancy between the data of these investigators, it was deemed desirable to check the possibility of convection arising from the variation of density with composition. The capillary-reservoir technique of Anderson and saddington3 was chosen for the present investigation since it has been widely used for measurements involving dilute solute concentrations and it was the technique used by Grace and Derge.2 It was necessary, however, to modify the normal procedure of using a pure metal bath to avoid measurement of integral diffusion coefficients over large concentration ranges. The alloy system chosen for study was the Bi-Sn system for which there are some data available.' EXPERIMENTAL PROCEDURE In order to utilize the capillary-reservoir technique for measurements of diffusion coefficients as a function of composition, it was necessary to modify the normal procedure slightly. This modification consisted of using a reservoir composition which was only slightly different from that in the set of capillaries, in order that the integral coefficients measured might be taken over a small composition range and might thereby be assumed to approximate the differential coefficient at some average composition between that of the capillary and that of the bath. It was found that a composition difference of approximately 0.10 mass fraction provided a satisfactory compromise between a small increment in composition and reasonable accuracy in measuring changes of composition. The alloys were prepared from tin and bismuth of 99.999 pct purity. The materials were first cleaned of surface oxides, then weighed and melted to form a homogeneous alloy in a Pyrex filling apparatus. The capillaries used were of precision bore Pyrex tubing 1.000 *0.005 mm bore. Capillaries of various lengths (from 2.85 to 5.85 cm) were cut and sealed at one end by fusing a 3-mm Pyrex rod to the end. The capillaries were filled by inserting them into the filling chamber, evacuating the chamber, submerging the capillaries, and pressurizing the chamber with argon. Two sets of capillaries were prepared for each run. One set contained an alloy more dense than the bath alloy and one set a less dense alloy. This procedure was followed so that the effect of density difference on the measurement could be determined. After filling one set of capillaries, these were placed open end up in a capillary holder and transferred to the diffusion chamber which consisted of a Pyrex tube inserted into a graphite block. The second set of capillaries was then filled and placed into the diffusion chamber. The reservoir alloy, which had been melted in a separate crucible, then was poured carefully into the diffusion chamber. Sufficient reservoir alloy was used to cover all capillaries to a depth of several centimeters. All of these operations: capillary filling, melting of alloys, and diffusion anneal, were carried out in a fused-salt bath which maintained a temperature of 300"*1°C. All capillaries were permitted to diffuse for approximately 48 hr. At the end of the diffusion period the capillary holder was removed from the bath and

Jan 1, 1969

By Nicholas Kowall, K. L. Clark

Maximum furnace efficiency and close control of final steel composition demand that the steel melter be able to follow closely the variations in the carbon content of the bath. For many years, the fracture test has been used by melters for estimating carbon, because it requires only a very short time to pour a sample into a chill mold, cool it in water, break it with a sledge hammer, and observe the fracture. After long experience gained from the observation of such fractures, most melters are able to estimate the carbon content of steel with amazing accuracy, particularly in the lower carbon ranges. Notwithstanding the utility of the fracture test, there has been widespread interest in other methods for rapid carbon determination to supplement it and to ensure against possible errors in human judgment. Several methods, based upon measurement of magnetic properties as functions of carbon content, have been described in the literature1-6 and have been found to give reasonably reliable results in plant practice when scrap composition is known and controlled. A difficulty encountered in the use of analyzers of the magnetic type is that alloying elements do change the relationship between carbon content and magnetic properties and it becomes necessary to establish calibration curves for all the expected combinations of alloy residuals that are not oxidized in the bath. The work reported here is of an investigation of a method that is independent of alloying elements normally present in constructional steels, being based upon the relatively well-known fact that in plain carbon and low-alloy steels martensitic hardness is a function of carbon content alone. Work oF Other Investigators In I938, Burns, Moore and Archer published & curve? that showed that the hardness of martensite is a function of carbon from 0.10 to 0.50 per cent and is independent of grain size or alloy content, at least within the rallge found in construc-tional S.A.E. compositions. Some of the deeper hardening types investigated, however, contained carbon to a maximum of only o.2o per cent. Using this principle, Kern8 developed a method of rapid carbon determination for S.A.E 43xx steels, His procedure consisted of chill-casting a test bar that was large enough to give a a that could be prepared for Brinell indentations. The test piece was quenched immediately after solidi fication was complete and hardness readings were taken, so that the carbon content could he read from an experimentally determined curve giving the relationship between as-quenched hardness and carbon. Experimental Work Although Kern's work had been done with a relatively deep-hardening steel, it

Jan 1, 1944

By K. L. Clark, Nicholas Kowall

Maximum furnace efficiency and close control of final steel composition demand that the steel melter be able to follow closely the variations in the carbon content of the bath. For many years, the fracture test has been used by melters for estimating carbon, because it requires only a very short time to pour a sample into a chill mold, cool it in water, break it with a sledge hammer, and observe the fracture. After long experience gained from the observation of such fractures, most melters are able to estimate the carbon content of steel with amazing accuracy, particularly in the lower carbon ranges. Notwithstanding the utility of the fracture test, there has been widespread interest in other methods for rapid carbon determination to supplement it and to ensure against possible errors in human judgment. Several methods, based upon measurement of magnetic properties as functions of carbon content, have been described in the literature1-6 and have been found to give reasonably reliable results in plant practice when scrap composition is known and controlled. A difficulty encountered in the use of analyzers of the magnetic type is that alloying elements do change the relationship between carbon content and magnetic properties and it becomes necessary to establish calibration curves for all the expected combinations of alloy residuals that are not oxidized in the bath. The work reported here is of an investigation of a method that is independent of alloying elements normally present in constructional steels, being based upon the relatively well-known fact that in plain carbon and low-alloy steels martensitic hardness is a function of carbon content alone. Work oF Other Investigators In I938, Burns, Moore and Archer published & curve? that showed that the hardness of martensite is a function of carbon from 0.10 to 0.50 per cent and is independent of grain size or alloy content, at least within the rallge found in construc-tional S.A.E. compositions. Some of the deeper hardening types investigated, however, contained carbon to a maximum of only o.2o per cent. Using this principle, Kern8 developed a method of rapid carbon determination for S.A.E 43xx steels, His procedure consisted of chill-casting a test bar that was large enough to give a a that could be prepared for Brinell indentations. The test piece was quenched immediately after solidi fication was complete and hardness readings were taken, so that the carbon content could he read from an experimentally determined curve giving the relationship between as-quenched hardness and carbon. Experimental Work Although Kern's work had been done with a relatively deep-hardening steel, it

Jan 1, 1944

The Engineering Council met on October 11 in the rooms of the American Society of Mechanical Engineers, Engineering Societies Building, New York. The Rules Committee submitted a draft of rules for the admission of other societies to the Council and progress was made in their consideration. The Committee on Public Affairs reported on a number of requests that the Council support pending or proposed legislation. Remedial laws intended to promote hydro-electric development were favored and Council voted to offer its cooperation to the United States Chamber of Commerce which is interesting itself in this matter. A movement to coordinate, unify and strengthen the work of various engineering committees cooperating with the federal authorities at Washington was favorably considered. Messrs. H. W. Buck and Charles. Whiting Baker were appointed Council conferees. CALVERT TOWNLEY, Secretary.

Jan 12, 1917

By Robin P. Gardner

Prior work by the author has established that closedform analytic solutions can be obtained for certain steady-state and transient types of operation of open circuit, continuous ball mills. This is possible when the tanks-in-series concept is used with the segregated flow or lumped parameter milling models. Such models should be useful (whenever they apply) in any calculational application since they are efficient and simple to program for digital computation. For example, they might be used within a computer program such as that developed by Herbst et al. for the calculation of model

Jan 1, 1975

By F. W. Newhall

DURING the latter part of the year 1931, the Republic mine of the Republic Steel Corporation, at Republic, about 4 miles south of Browns-ville, Pa., was mining coal along four rib or fracture lines. One of these lines, the west butt rib line, was retreating towards a concrete-lined air shaft, 320 ft. deep, which had been sunk in 1911 for ventilation purposes. With the normal rate of mining at that time, it was expected that this rib line would pass the shaft in three or four months and the shaft would then be abandoned and allowed to cave. Realizing the opportunity presented for the study of an unusual case of ground movement, the question of conducting the study was presented by the junior author to the chairman of the Institute's committee on Ground Movement and Subsidence, Mr. George S. Rice, who presented the matter to Mr. G. H. Morse, General Manager of the Northern Mines, Republic Steel Corpora-tion, and he agreed to cooperate with the Bureau of Mines in making the study, the results of which are presented in this paper. Acknowledg-ments are due to Mr. Morse for his full cooperation in this work and to Mr. G. S. Rice and Mr. J. W. Paul, both of the U. S. Bureau of Mines, for their advice and guidance during the course of the work. The authors are indebted to Mr. B. F. Herbert, mining engineer, Northern Coal Mines, Republic Steel Corporation, who assisted in all the surveys, and Mr. W. H. Smith, draftsman, U. S. Bureau of Mines, who prepared all illustrations for publication.

Jan 1, 1934

By R. J. Wagner, Jim Douglas Jr., P. M. Blair

The calculation of the behavior of an oil reservoir during a water flood has long been an important problem to reservoir engineers. Buckley and Leverett derived the differential equation which describes the displacement of oil from a linear porous medium by an immiscible fluid, but this equation could not be solved by the methods of classic mathematics. Consequently, in order to integrate the equation over the length of the reservoir, they neglected the effects of capillary pressure. In the present paper, a numerical method has been developed for determining the behavior of a linear wafer flood with the inclusion of capillary pressure. The differential equation which was derived for the case of incompressible fluids is second order and non-linear. This differential equation was approximated by an implicit form of difference equation which is second order correct in both time and distance. An electronic digital computer was used to perform the numerical solution of the difference equation. INTRODUCTION The problem of calculating the flow and distribution of fluids in an oil reservoir subjected to a water flood has long challenged the reservoir engineer. The ability to solve this problem would provide a valuable tool for the design and study of field waterflooding programs. One of the first contributions in this field was made by Buckley and Leverett,'.' who developed a method of calculating waterflood performance in a linear reservoir. Their technique was limited by the practical necessity of excluding quantitative consideration of capillary pressure. It is the purpose of this paper to describe a method for calculating the behavior of a linear water flood with capillary pressure considered. This method, although limited to the linear case, should serve as a step toward the solution of the two- or three-dimensional waterflooding problem which would better describe actual reservoirs. The treatment of the problem has assumed that the reservoir is linear and homogeneous, that both oil and water -are incompressible, and that gravitational forces may be neglected, and that water is injected into one end of the reservoir and oil and water are produced from the other. Though these assumptions may not be directly applied to natural reservoirs, they are closely approached in many laboratory core tests. The physical problem has been represented mathematically by means of a differential equation and suitable boundary conditions. The inclusion of capillary pressure effects causes the differential equation to be second order and non-linear, and it is not amenable to solution in terms of known functions. Nevertheless, the problem may be solved by numerical methods. The authors have successfully calculated several cases from the start of water injection through to depletion of the hypothetical reservoir using realistic capillary pressure and relative permeability characteristics that were chosen so as to put the method to a test. DIFFERENTIAL EQUATION In two- or three-dimensional problems involving the two-phase flow of incompressible fluids through a porous medium, the equations describing the flow can be combined until only two dependent variables remain, the pressure in one phase, and the saturation of one phase. These variables appear in two simultaneous partial differential equations which are derived on the basis of the conservation of mass and Darcy's law as applied to two-phase flow. For a linear reservoir, this system of differential equations can be reduced to a single, nonlinear, second order, parabolic differential equation for one dependent variable, the saturation of one phase. For incompressible water and oil, it can be shown that the conservation of mass for the two phases requires that Where q, and q, are the water end oil flow rates per unit cross-section, s, and so their saturations, +, the porosity, and [ and T, dimensional space and time variables. Darcy's law, as extended to two-phase flow including the effect of capillary pressure,' is as follows:

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By R. J. Sullivan

DURING the past twelve months the Loudon pool of the Eastern Interior Coal Basin has become established as one of the two largest discoveries since the revival of exploitation in the Illinois region and now occupies a position among the important pools of the United States. On Aug. 1, 1939, production averaged 54,000 bbl. per day from 990 wells, having accumulated a total of 10,305,000 bbl. Its very active develop-ment promises to continue for fully another year. It is the site of one of the industry's most singular large-scale gas-injection programs. LOCATION AND RESERVOIR CHARACTERISTICS At present the pool embraces an area 15 miles long by 3 ½ miles wide in eastern Fayette County, along the western rim of the now well-known Illinois Basin's deeper part, through townships 6, 7 and 8 north and ranges 2 and 3 east of the Third Meridian. It is the northernmost, and most prominent, productive structure of a group extending over a 50-mile trend southward to the Dix pool of Jefferson County. Three horizons have been proved to carry production-namely, the Weiler sandstone at 1390 ft., the Paint Creek sand at 1460 ft. and the Benoist or Bethel, at 1500 ft. Geologically, they fall in the Chester series of the upper Mississippian system, where much of Illinois' early-day oil was found, having been laid down in shallow off-shore waters as a part of the vast delta deposit underlying central Illinois and parts of Indiana and Kentucky. As a result of this type of sedimentation, followed by repeated uplifts and warping along an anticlinal axis, differ-ential deposition of sands and shales contributing to great irregularity took place. This is further reflected by wide variations in permeability, porosity and thickness of all the sands and, accordingly, in the producing characteristics of wells. Permeabilities range as high as 550 millidarcies, with the average commonly lying between 60 and 100. For the three pay horizons the mean porosity is 18 per cent, at a calculated water saturation of roughly 30 per cent. The Weiler sand has an average thickness of 25 ft., the Benoist of about 23 ft. and the Paint Creek of approximately 18 ft. Of these three productive formations the Benoist

Jan 1, 1940

By John H. Hollomon

The interpretation of notched-bar impact results has been a matter of controversy since the introduction of more or less standard tests by Fremont,' Charpy2 and others at the turn of the century. Many investigators3-l1 have contributed to the understanding of the significance of such tests. Several symposiums12,13 have been held with the express purpose of discussing the significance and interpretation of the impact tests. It is not the purpose of this paper to review all these contributions to the development of the knowledge on this subject, but rather to present an interpretation of notched-bar impact tests that appears to be in agreement with the available published data. Fundamentally, the interpretation discussed in this paper of the brittle failure of some steels in notched-bar impact test is similar to the qualitative analysis presented by Ludwik3 in the I92o's. Essentially, Ludwik stated that the function of the notch was to increase the tensile stress necessary for yielding, and that brittle failure occurred when the stress necessary for yielding exceeded the normal stress required for fracture (with no plastic deformation). Ludwik, however, had no means of measuring this normal stress necessary for failure of a plastically* undeformed metal, therefore he could not extend his interpretation beyond the qualitative stage. Kuntze14 and recently Mc-Adam15 attempted to determine the effect of deformation on the stress necessary for fracture by testing, in tension, specimens notched to various depths and angles. Because of the uncertainties in Kuntze's (and McAdam's) analysis of the stresses (which have been pointed out by Sachs16) and the inherent nonuniformity in the stress distribution in notched bars, the results of such investigations are difficult to interpret. A more direct method of measuring the effect of deformation on the fracture stress was suggested in previous papers"-18 and has been utilized in the present investigation. The present paper concerns itself primarily with the behavior of notched impact specimens. The effects of strain rate, temperature, and stress distribution, which are discussed with reference to the impact specimen, apply just as well to the behavior of metal at the bases of notches in any engineering structure. All that is necessary is to determine the stress distribution in the structure at the base of the notches.

Jan 1, 1944

By John H. Hollomon

The interpretation of notched-bar impact results has been a matter of controversy since the introduction of more or less standard tests by Fremont,' Charpy2 and others at the turn of the century. Many investigators3-l1 have contributed to the understanding of the significance of such tests. Several symposiums12,13 have been held with the express purpose of discussing the significance and interpretation of the impact tests. It is not the purpose of this paper to review all these contributions to the development of the knowledge on this subject, but rather to present an interpretation of notched-bar impact tests that appears to be in agreement with the available published data. Fundamentally, the interpretation discussed in this paper of the brittle failure of some steels in notched-bar impact test is similar to the qualitative analysis presented by Ludwik3 in the I92o's. Essentially, Ludwik stated that the function of the notch was to increase the tensile stress necessary for yielding, and that brittle failure occurred when the stress necessary for yielding exceeded the normal stress required for fracture (with no plastic deformation). Ludwik, however, had no means of measuring this normal stress necessary for failure of a plastically* undeformed metal, therefore he could not extend his interpretation beyond the qualitative stage. Kuntze14 and recently Mc-Adam15 attempted to determine the effect of deformation on the stress necessary for fracture by testing, in tension, specimens notched to various depths and angles. Because of the uncertainties in Kuntze's (and McAdam's) analysis of the stresses (which have been pointed out by Sachs16) and the inherent nonuniformity in the stress distribution in notched bars, the results of such investigations are difficult to interpret. A more direct method of measuring the effect of deformation on the fracture stress was suggested in previous papers"-18 and has been utilized in the present investigation. The present paper concerns itself primarily with the behavior of notched impact specimens. The effects of strain rate, temperature, and stress distribution, which are discussed with reference to the impact specimen, apply just as well to the behavior of metal at the bases of notches in any engineering structure. All that is necessary is to determine the stress distribution in the structure at the base of the notches.

Jan 1, 1944