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By H. O. Jahns, R. A. Greenkorn, R. E. Haring, L. K. Shallenbarger

This paper is a study of the effects of heterogeneity on flow in an analog of porous media, the Hele-Shaw model. l-3 A set of experiments in heterogeneous Hele-Shaw models showed streamlines through and around heterogeneities of various sizes, shapes and levels. (A level, we define as the ratio between the transmissibility of the heterogeneity and that of the rest of the model.) The heterogeneities were restrictions or expansions of the flow stream analogous to variations in the transmissibility of porous media. The experimental data agreed well with numerical results and with an analytical solution, which we derived for a circular heterogeneity in an infinite field. This study considers the flow-stream distortion due to the shape, size and level of heterogeneities. Size and level are much more important than shape provided the heterogeneity is not long and narrow. Our analytical solution shows that a circular heterogeneity in a large field can be replaced by an equivalent circle of either zero or infinite permeability. The radius of the. equivalent circle is a simple function of size and level of the actual circle. INTRODUCTION With the availability of high-speed computers and numerical procedures to predict reservoir behavior, we are faced with an important question. How much information about the reservoir do we need to justify the cost of the computer in any given case? To answer this question, we have to know how various reservoir parameters affect flow behavior. Reservoir heterogeneity is one of these parameters. In this study, we used a simple, two-dimensional model of porous media, the hele-shaw model, to investigate the effect of heterogeneity on flow behavior. We restricted ourselves to linear, single-phase, steady-state flow in a rectangular field with a single heterogeneity at its center. The analogy between flow in Hele-Shaw models and in porous media is easily verified. Let us first consider a homogeneous Hele-Shaw model with constant plate separation h. (The Hele-Shaw model is constructed by placing two plates, usually glass, very close together and allowing liquid to flow between them. Streamlines are made visible by introducing colored fluid into the space between the plates at a number of points across the model.) We assume a cartesian coordinate system with its origin in the middle between the plates and the z axis directed perpendicular to the glass plates (Fig. 1). The fluid flow is always in a direction parallel to the glass plates and varies from a maximum value to zero in the very small distance from the middle (z = 0) to either plate (z = h/2). For slow motion of an incompressible fluid, neglecting inertia and body forces, we have the viscous flow equation: where p is the fluid pressure, p the viscosity, and v the velocity vector with components u, v and w in the x, y and z directions, respectively. In our rase. and the derivatives of 3 with respect to x and y are small as compared with the derivative in the z direction. Therefore, approximately, with Vp and v being two-dimensional vectors in the x-y plane. Two integrations with respect to z give

Jan 1, 1965

By F. Keller, R. H. Brown

BECAUSE of the extensive use of Alclad 24s alloy sheet in aircraft construction, there is much interest in the metallurgical changes caused by heat-treatment of this product.1,2 One of these changes is the result of the diffusion of soluble elements from the core into the coating during treatment. This paper deals with the thermal treatments that may influence diffusion and with the practical effects of diffusion on the serviceability of the product. As is well known, Alclad 24s-T sheet has a core of high-strength alloy combined with surface layers of relatively pure aluminum. The microstructure of a cross section of this product is shown by Fig. I. hot only does the relatively high-purity coating have a high resistance to corrosion, and hence serves as a mechanical barrier between the core metal and the corroding environment, but in addition this coating I exerts electrochemical protection over areas where the core may be exposed, such as cut edges. In addition, the coating affords electrochemical protection to projecting heads of *417S-T, 17S-T and 24S-T rivets, or attached members made from these alloys. Under some conditions of heat-treatment, however, diffusion of copper into the coating will alter the electrochemical relationship between the coating and the core to the extent that only partial protection will be obtained under some corrosive conditions. The reason for the electrochemical protection lies in the fact that the coating layers of pure aluminum are anodic to the alloy core. The addition of copper to aluminum produces alloys in which the potential is lower than that of the pure metal. Moreover, as the amount of copper in solid solution in z4S alloy is increased, the potential of the alloy becomes more cathodic. When heat-treated at 920°F. and quenched in cold water, 24s-T is about 0.16 volt cathodic to pure aluminum. However, copper will diffuse from the core into the coating, and if it reaches the surface the potential will be altered in a cathodic direction. Thus the potential dif-erence between the core and coating may be less than 0.16 volt, depending upon the thickness of the coating, and the time and temperature of heat-treatment. Of the methods available for determining the extent of diffusion of copper from the core into the coating of Alclad 24S-T, two are generally used; namely, the metallographic and the solution potential method.3 METALLOGRAPHIC METHODS Metallographic methods will reveal the progress of diffusion of copper into the coating. For instance, the diffusion zone in the coating intermediate between the coating surface and the core is shown in Fig. I. This photomicrograph is of a polished and etched cross section of 0.040-in. Alclad 24S-T sheet. Diffusion proceeds into the coating more rapidly along the grain boundaries than through the body of the grains. consequently, the diffusion zone is not of uniform width

Jan 1, 1944

By Walter Crafts, C. M. Offenhauer

In a previous study of the carbide phase of chromium steels, it was shown that chromium carbide (Cr7C3) is 2 more stable carbide than cementite (Fe3C) at tempering temperatures above about 500°C. in quenched steels containing from about I to 7.5 per cent chromium. Below this temperature the carbide phase was found to consist of cementite in all of the steels examined. In the present investigation it was found that a similar change in the carbide phase takes place in molybdenum and in chromium-molybdenum steels at approximately the same tempering temperatures. The approximate ranges of occurrence of the alloy carbides Cr7C3, Cr4C, and Mo2C have been determined in steels containing up to 5 per cent chromium, I per cent molybdenum and 0.60 per cent carbon. The experimental steels were made in small high-frequency furnaces from Armco ingot iron, low-carbon ferrochromium and calcium molybdate and were poured into 2-in. ingots, which were forged to I-in. round bars. Sections of the bars were heated to the carbide-solution temperature and cooled rapidly to induce austenite transformation at relatively low temperatures. The steels were subject to some segregation, therefore comparatively high temperatures were necessary to dissolve all of the carbides. The microstructure of the quenched specimens was examined to verify the belief that the carbides had been dissolved, and also to determine the nature of the nonmartensitic structure of incompletely hardened steels. Ferrite and pseudo-martensite were present in some of the specimens, but all specimens were quenched at such a rate that pearlite was not formed, in order to ensure the formation of the carbides at temperatures lower than about 500°C. It had been found previously1 that in chromium steels the chromium carbide could be produced by transformation of austenite in the pearlite range above 500°C., and, in order to start the tempering treatment with the carbide present as cementite, the absence of pearlite was considered to be essential. The specimens were tempered for 64 hr. to permit the formation of the stable carbide. After tempering, the specimens were submitted to microscopic and X-ray examination. The carbides were separated either electrolytically in a 5 per cent HCl electrolyte or with an acidified copper-potassium chloride solution. The crystal structure of the carbide phases was determined by the Debye-Scherrer type of X-ray patterns. The X-ray patterns obtained from specimens near the boundaries between two types of carbides were generally weak and diffuse as compared with the other patterns. For this reason, and because the more soluble components may be masked, the boundaries between the phases could not be determined precisely. However, the X-ray analysis of electrolytically separated carbides has given consistently reproducible results

Jan 1, 1943

By Walter Crafts, C. M. Offenhauer

In a previous study of the carbide phase of chromium steels, it was shown that chromium carbide (Cr7C3) is 2 more stable carbide than cementite (Fe3C) at tempering temperatures above about 500°C. in quenched steels containing from about I to 7.5 per cent chromium. Below this temperature the carbide phase was found to consist of cementite in all of the steels examined. In the present investigation it was found that a similar change in the carbide phase takes place in molybdenum and in chromium-molybdenum steels at approximately the same tempering temperatures. The approximate ranges of occurrence of the alloy carbides Cr7C3, Cr4C, and Mo2C have been determined in steels containing up to 5 per cent chromium, I per cent molybdenum and 0.60 per cent carbon. The experimental steels were made in small high-frequency furnaces from Armco ingot iron, low-carbon ferrochromium and calcium molybdate and were poured into 2-in. ingots, which were forged to I-in. round bars. Sections of the bars were heated to the carbide-solution temperature and cooled rapidly to induce austenite transformation at relatively low temperatures. The steels were subject to some segregation, therefore comparatively high temperatures were necessary to dissolve all of the carbides. The microstructure of the quenched specimens was examined to verify the belief that the carbides had been dissolved, and also to determine the nature of the nonmartensitic structure of incompletely hardened steels. Ferrite and pseudo-martensite were present in some of the specimens, but all specimens were quenched at such a rate that pearlite was not formed, in order to ensure the formation of the carbides at temperatures lower than about 500°C. It had been found previously1 that in chromium steels the chromium carbide could be produced by transformation of austenite in the pearlite range above 500°C., and, in order to start the tempering treatment with the carbide present as cementite, the absence of pearlite was considered to be essential. The specimens were tempered for 64 hr. to permit the formation of the stable carbide. After tempering, the specimens were submitted to microscopic and X-ray examination. The carbides were separated either electrolytically in a 5 per cent HCl electrolyte or with an acidified copper-potassium chloride solution. The crystal structure of the carbide phases was determined by the Debye-Scherrer type of X-ray patterns. The X-ray patterns obtained from specimens near the boundaries between two types of carbides were generally weak and diffuse as compared with the other patterns. For this reason, and because the more soluble components may be masked, the boundaries between the phases could not be determined precisely. However, the X-ray analysis of electrolytically separated carbides has given consistently reproducible results

Jan 1, 1943

By P. H. Dudley

A Discussion of the Paper of Prof. Howe. (Bi-Monthly Bulletin, No. 14, March, 1907, pp. 169 to 274.) P. H. DUDLEY, New York, N. Y. (communication to the Secretary*) :-The characteristics of Prof. Howe's metallurgical papers are, that he is able, from the mass of confusing evidence on the subject, to make an analysis and present hypothetical and essential principles in concrete form for consideration and discussion. I can appreciate, from the practical side of the subject, the arduous labor of collecting and investigating the data that is essential to prepare the paper. Much of the data necessarily came from material of preceding years. of manufacture in which there was allowed time for chemical reactions of the recarburizer, and for the elimination of the oxidation-products before teeming the ingots. This condition gave a favorable tinge-element to free the metal from slag- and other impurities, but, in allowing the. ingot to cool before charging in the furnace, the time-element entered as a detrimental factor in the development of the pipe or shrinkage-cavities, which gave an ingot-structure deficient in soundness. The interpretations from such material must be made with due allowances for the methods of manufacture, and must be given proper weight, as general facts, in subsequent arguments. The difficulties under which investigators labor are not easily surmounted in differentiating between reliable and unreliable data incident to variables of methods of manufacture, chemical composition of the alloys of steel, mediocre practice and that of the highest state of the art. Modern practice and large outputs in Bessemer steel have reversed the effects of the time-element-by cutting short the chemical reactions of the recarburizer and the elimination of

Jan 5, 1908

By P. K. Koh

Chi phase (body-centered cubic, a = 8.89A) was found in as-cast 23 pct Cr-10 pct Mo-Fe alloy as well as in heat-treated 316, 316L, 317, and modified 446 stainless steels. Chi phase resembles sigma phase in its metastability, chemical composition, and brittleness. Microstructure and some of physical properties of chi phase were developed. MOLYBDENUM has been established as a desirable alloying element for the enhancement of corrosion resistance in Cr-Ni steels and creep and rupture strength in high temperature alloys. On the debit side, however, the molybdenum addition has been known to stimulate u formation. When the molybdenum-bearing steels were subjected to prolonged heating at elevated temperatures, losses of corrosion resistance and/or ductility have been observed. Andrews1,2 first found the existence of a new phase among the anodic FeC13 extracts from type 316 stainless steel solution treated and then reheated from 800" to 1100°C. This phase was designated x and was identified by diffraction patterns as of body-centered cubic structure with a value equal to 8.89? and similar to that of a manganese. He found that the x phase in this steel always coexisted with s phase, but failed to distinguish one from the other by metallographic technique. No definite conclusion was drawn regarding the equilibrium temperature ranges of these two phases. The appearance of Andrew's work recalled an un- explained structure observed several years ago at the Allegheny Ludlum Research Laboratories during the investigation of an experimental alloy containing 25 pct Cr, 10 pct Mo, and balance Fe. X-ray diffraction patterns on the as-cast material revealed the presence of a body-centered cubic phase having a lattice parameter of 8.89?. The structure was sufficiently similar to that of y chromium that for a time it was thought that the structure might be caused by the presence of some undissolved electrolytic chromium particles. The alloy as-cast was so brittle that it shattered after the slightest hot reduction by hammer cogging. This paper gives the results of some metallographic and X-ray diffraction studies on x phase as found in several experimental alloys as well as a few molybdenum-bearing commercial stainless steels. The analyses of materials studied were as shown in Table I. Experimental Procedure Metallography: Solid specimens were polished mechanically and etched in boiling 50 pct HC1 solution in order to best delineate x and s phases in the alloys studied. X-Ray Diffraction: The difficulty of satisfactorily developing diffraction lines for s phase in solid specimens has been previously reported by Bindari, Koh, and Zmeskal.V or this reason all specimens used in this investigation were subjected to anodic

Jan 1, 1954

By H. A. Deans

A three-parameter mathematical model for one-dimensional flow in porous media is developed. The objective of the model is to predict accurately the longitudinal dispersion associated with the flow of either gases or liquids over a wide range of Reynolds number. A qualitative analysis of the model parameters is given. Published experimental pulse-response curves are compared with results predicted by the model. Several general types of problems are given for which the model can be used. INTRODUCTION The problem of multicomponent single-phase flow through porous media is encountered in the study of petroleum reservoirs, gas chromatographic and ion-exchange columns, industrial fixed-bed con-tacters and elsewhere. These particular examples span the wide range of flow conditions possible; Reynolds numbers of less than l0-4 are not unusual in oil-production problems, while values in excess of 103 are common in large fixed-bed operations. The study of flow-dependent transport phenomena is complicated both by the changes in the character of the flow over this range, and by the irregularity of the flow boundaries inherent to porous media. Dispersion is one of the important phenomena known to depend fundamentally on flow conditions as well as on fluid and medium properties. As used in this paper, the term "dispersion" refers to the observed mixing of fluid elements of different composition which occurs in flow systems. The actual mechanism may be one or more of a number listed below. Only dispersion in the direction of the mean flow (referred to as axial or longitudinal dispersion, or mixing) is considered here, although lateral dispersion arises as part of certain coupled mechanisms. MECHANISMS FOR LONGITUDINAL DISPERSION A number of distinct mechanisms are known3,5,7,8 to contribute to the phenomenon of longitudinal dispersion. The more important of these are as follows. 1. Molecular diffusion in the flow direction. 2. Turbulent (cell) mixing. 3. Lateral transport processes coupled with velocity and/or residence time distributions, including: (a) "Taylor" diffusion caused by the interaction of velocity profiles in individual voids with lateral molecular diffusion; (b) separation and remixing or interdiffusion of streams having different velocities around particles; and (c) the couplipg of gross velocity profiles, caused by viscous instability or inhomogeneous porosity, with lateral dispersion. 4. Finite mass-transfer rate between a porous matrix and the flowing phase, and finite diffusion rate inside elements of the porous matrix. It is a well documented fact that these mechanisms, whether acting individually or in combinations, produce essentially similar integral effects. The observed dispersion can be described approximately by solutions of the diffusion equation with a properly chosen dispersion coefficient. Necessary conditions for equivalence between dispersion and diffusion are discussed by Klinkenberg and Sjenitzer.7 Apparently these conditions are not satisfied exactly in many real systems. "Best fit" solutions of the diffusion equation often depart appreciably from measured breakthrough curves for the usual pulse- or step-forced experimental systems. In particular, pulse response curves usually show some degree of asymmetry and "tailing" which cannot be reproduced by the one-parameter diffusion model. The three-parameter model proposed herein attempts to produce these effects in a realistic manner. Asymmetry and tailing are predicted for certain sets of parameter values, while for other sets the new model agrees with the diffusion model. VELOCITY DEPENDENCE OF DISPERSION Molecular diffusion apparently controls at sufficiently low Reynolds number in both gas and liquid systems.*l3 At Re > 20, turbulent cell mixing is dominant for gases flowing at low pressure; the data of McHenry and Wilhelm8 show that the mixing cell is approximately 1 particle diameter long in random sphere packs. on the other hand, the data

By L. C. Reese

The ultimate resistance against a rigid cylinder which is moved laterally in a cohesionless soil is a function of the geometry of the cylinder and the properties of the soil. An approximate method is developed for computing this resistance and is tested against results of laboratory experiments. Satisfactory agreement between the method and experiment was obtained. Not only was the ultimate resistance against the cylinder measured, but measurements were made of the shape of the rupture surfaces. These measurements should allow the development of a more rigorous computation procedure. INTRODUCTION A critical aspect in the design of offshore drilling platforms is assuring the stability of the platform during a hurricane. The large horizontal loads from waves and wind make a severe loading condition. Piles are generally employed as the foundation since they can be effective in resisting both horizontal and vertical loads. Spuds are sometimes used with a mat foundation, where the spuds are designed principally to resist horizontal loads and the mat designed principally to resist vertical loads. The research reported in this paper is related to one aspect of the problem of laterally loaded piles or spuds in sand. The complete solution to the problem of the laterally loaded pile in sand would require the prediction of soil resistance against the pile as a function of pile deflection; only the ultimate resistance against short piles is considered in this paper. A considerable amount of additional research will be necessary in order to obtain a complete solution to the problem of the laterally loaded pile in sand; however, the work reported here should be useful as a guide in the performance of some of the additional research. ULTIMATE LATERAL RESISTANCE AGAINST A LONG FALL IN SAND To aid in the understanding of the theory which is developed for a cylinder, the theory for earth pressure against a wall is reviewed. In Fig. l(a), a long wall of height H is shown embedded in soil. Soil resistance will develop as the wall is deflected, and the soil resistance will increase with deflection until some limiting value is reached. In this discussion, and those following, it is assumed that all points on the wall deflect equal amounts. A possible shape of the real curve which relates soil resistance to deflection is shown by the dashed line in Fig. l(b); however, as a means of simplifying the discussion, an idealized curve (shown by the unbroken lines) is drawn. If such a wall as this were furnishing the horizontal support for an offshore structure, the dashed curve in Fig. 1 would be the information needed in performing a foundation analysis, with the idealized curve possibly being an acceptable substitute. For the idealized curve, the soil resistance is linear with deflection for the early portion of the curve such that

By L. S. Darken

IT has been known for sometime that in an ionic lattice, such as that of Ag2S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulfide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulfide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall1 support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffusion proposed by several authors, most recently by Birchenall and Mehl.2 This theory has, however, also been questioned3.4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however, Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz,5 who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a similar mechanism, whatever it may be, at a greater or lesser rate, thus giving rise

Jan 1, 1948

By Cyril Wells, Robert F. Mehl

The practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out.l,13 This importance lies chiefly, though by no means only, in the study of carbufizing and in the study of reactions involved in the eutectoid inversion in steel. The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in ?-Fe and their mutual effects are measured with precision. The present paper reports the results of measurements of diffusion coefficients D of manganese in ?-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients.‡ Data on the rate of diffusion of manganese in ?-Fe have been reported by Fry2 and by Paschke and Hauttmann.3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq, cm. per set. at 960º, which will be shown to be incorrect by many orders of magnitude. Paschke and Hauttmann gave a rough value of 9.6 x 10-8 Sq. cm. per set. at 14000. Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon. Method and Materials Method.—The method employed is identical with that used earlier.5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded. The diffusion anneals were performed in argon, except One (test 18) in which hydrogen was employed for purposes noted below. The temperatures reported are accurate to about 3" and constant within 1°C; the diffusion times are reported to the nearest half hour. The specimens were furnace-coo1ed after the diffusion ation, at about 2° per min. Layers, usually 0.004 in. thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0.I Per cent Mn; the distances of these layers from the interface was measured to ±0.0002 in. The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions.8 The D values calculated by these two methods do not differ appreci000. The Grube solution was used except in tests in which the effect of concentration upon D was greater than so per cent; in such cases the Matano method, which explicitly provides for the variation of D with concentration,' is the more reliable. In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer. In 3 of the 3' tests, however, this is not justified, and the D values

Jan 1, 1941

By Cyril Wells, Robert F. Mehl

The practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out.l,13 This importance lies chiefly, though by no means only, in the study of carbufizing and in the study of reactions involved in the eutectoid inversion in steel. The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in ?-Fe and their mutual effects are measured with precision. The present paper reports the results of measurements of diffusion coefficients D of manganese in ?-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients.‡ Data on the rate of diffusion of manganese in ?-Fe have been reported by Fry2 and by Paschke and Hauttmann.3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq, cm. per set. at 960º, which will be shown to be incorrect by many orders of magnitude. Paschke and Hauttmann gave a rough value of 9.6 x 10-8 Sq. cm. per set. at 14000. Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon. Method and Materials Method.—The method employed is identical with that used earlier.5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded. The diffusion anneals were performed in argon, except One (test 18) in which hydrogen was employed for purposes noted below. The temperatures reported are accurate to about 3" and constant within 1°C; the diffusion times are reported to the nearest half hour. The specimens were furnace-coo1ed after the diffusion ation, at about 2° per min. Layers, usually 0.004 in. thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0.I Per cent Mn; the distances of these layers from the interface was measured to ±0.0002 in. The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions.8 The D values calculated by these two methods do not differ appreci000. The Grube solution was used except in tests in which the effect of concentration upon D was greater than so per cent; in such cases the Matano method, which explicitly provides for the variation of D with concentration,' is the more reliable. In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer. In 3 of the 3' tests, however, this is not justified, and the D values

Jan 1, 1941

By M. C. Leverett

Knowledge of the theory underlying the behavior of mixtures of fluids in reservoir rocks is essential to the proper solution of certain types of problems in petroleum production, but is as yet incompletely developed. The object of this paper is to show the application of well established thermody-namic and physical principles to these problems, and thus to assist in the development of the basic theory. For convenience the problems to be considered here may be divided into two groups: 1. Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids; i.e., gravitational forces. 2. Dynamic problems, involving analysis of the motion oi mixtures of immiscible fluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential. Capillary Equilbrium in Sands Under this heading the static type of problem will be discussed and the results of experimental investigations on the capillary properties of unconsolidated sands will be presented. Although the discussion of this section is, in a sense, prefatory to the treatment of problems of mixture flow, the concepts developed here have considerable intrinsic importance apart from their ap-plication to flow problems. For, it is reason-able to postulate that the reservoir fluids are, owing to their long existence in undis- turbed mutual contact prior to exploitation, in substantial equilibrium. It follows that their distribution in the reservoir at the time of tapping should be entirely predictable from the theory of capillary equi librium, provided certain experimentally measurable properties of the reservoir rock are known. Knowledge of the distribution of the several fluids in the reservoir is, ol course, helpful in the estimation of reserves and in other problems. It is to be emphasized that throughout the discussion of capillary statics it is assumed that the fluids are in equilibrium from the capillary standpoint. Thus, water, where it is referred to as being in a reservoir, will be understood to be interstitial water, present at the time of drilling the reservoir, commonly termed "connate" water. The theory developed here is perfectly general for any porous solid, whether a carefully prepared unconsolidated sand or a natural sandstone from an oil reservoir. At present, however, only problems involving clean, unconsolidated sands can be made to yield numerical solutions, since only such sands have been adequately investigated experimentally. Experimental evaluation of the pertinent properties 01 natural reservoir rocks will permit the extension of the numerical treatment to problems involving these materials. We shall now consider in some detail the static equilibrium of fluid mixtures in porous solids: that is, the manner in which the reservoir fluids are distributed vertically whell the Forces due to capillarity are just balanccd by those due to gravitation.

Jan 1, 1941

By M. C. Leverett

Knowledge of the theory underlying the behavior of mixtures of fluids in reservoir rocks is essential to the proper solution of certain types of problems in petroleum production, but is as yet incompletely developed. The object of this paper is to show the application of well established thermody-namic and physical principles to these problems, and thus to assist in the development of the basic theory. For convenience the problems to be considered here may be divided into two groups: 1. Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids; i.e., gravitational forces. 2. Dynamic problems, involving analysis of the motion oi mixtures of immiscible fluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential. Capillary Equilbrium in Sands Under this heading the static type of problem will be discussed and the results of experimental investigations on the capillary properties of unconsolidated sands will be presented. Although the discussion of this section is, in a sense, prefatory to the treatment of problems of mixture flow, the concepts developed here have considerable intrinsic importance apart from their ap-plication to flow problems. For, it is reason-able to postulate that the reservoir fluids are, owing to their long existence in undis- turbed mutual contact prior to exploitation, in substantial equilibrium. It follows that their distribution in the reservoir at the time of tapping should be entirely predictable from the theory of capillary equi librium, provided certain experimentally measurable properties of the reservoir rock are known. Knowledge of the distribution of the several fluids in the reservoir is, ol course, helpful in the estimation of reserves and in other problems. It is to be emphasized that throughout the discussion of capillary statics it is assumed that the fluids are in equilibrium from the capillary standpoint. Thus, water, where it is referred to as being in a reservoir, will be understood to be interstitial water, present at the time of drilling the reservoir, commonly termed "connate" water. The theory developed here is perfectly general for any porous solid, whether a carefully prepared unconsolidated sand or a natural sandstone from an oil reservoir. At present, however, only problems involving clean, unconsolidated sands can be made to yield numerical solutions, since only such sands have been adequately investigated experimentally. Experimental evaluation of the pertinent properties 01 natural reservoir rocks will permit the extension of the numerical treatment to problems involving these materials. We shall now consider in some detail the static equilibrium of fluid mixtures in porous solids: that is, the manner in which the reservoir fluids are distributed vertically whell the Forces due to capillarity are just balanccd by those due to gravitation.

Jan 1, 1941

By Cyril Wells, Robert F. Mehl

THE practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out 1,13 This importance ties chiefly, though by no means only, in the study of carburizing and in the study of reactions involved in the eutectoid inversion in steel The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in y-Fe and their mutual effects are measured with precision The present paper reports the results of meas¬urements of diffusion coefficients D of manganese in -y-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients [$] Data on the rate of diffusion of manganese in y-Fe have been reported by Fry2 and by Paschke and Hauttmann 3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq cm per sec at 960°, which will be shown to be incorrect by many orders of magnitude Paschke and Hauttmann gave a rough value of 9 6 X 10-8 sq cm per sec at 1400° Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon METHOD AND MATERIALS Method -The method employed is identical with that used earlier 5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded The diffusion anneals were performed in argon, except one (test 18) in which hydrogen was employed for purposes noted below The temperatures reported are accurate to about 3° and constant within I°C , the diffusion times are reported to the nearest half hour The specimens were furnace-cooled after the diffusion anneal at about 2° per min Layers, usually 0 004 in thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0 01 per cent Mn, the distances of these layers from the interface was measured to ±0 0002 in The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions e The D values calculated by these two methods do not differ appreciably 5 The Grube solution was used except in tests in which the effect of concentration upon D was greater than 50 per cent, in such cases the Matano method, which explicitly provides for the variation of D with concentration,1 is the more reliable In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer In 3 of the 30 tests, however, this is not justified, and the D values

Jan 1, 1941

By Charles C. Hawes

DETERMINATION OF SILICA OXIDE iron ores usually are found in intimate association with silica and phosphorus compounds. Their quantitative separation and purification sometimes present difficult problems to the chemist. Silicic acids may represent various degrees of dehydration. They are exeedingly weak, but combine with metallic oxides and form some of the most stable oxides in nature, the silicates. When iron ores are treated with hydrochloric acid, they yield practically all their iron. However, apart from rare exceptions, varying amounts of insoluble residues of silica, alumina, lime, magnesia and compounds of phosphorus, sulphur, titanium, chromium and others will be left. If the oxides of silicon, aluminum and titanium are present in small quantities, the insoluble residue is generally very small, but the presence of these oxides is more usual in larger quantities. Therefore, only a special treatment can break the bond between these elements. Ore Residues Acids remove the soluble constituent of the ore, leaving the insoluble residue, which chemically is rock or gangue and must be treated accordingly. Alkali carbonates are used frequently to break up the residue, but other fluxes have also been recommended, such as a number of lead and boron salts. The introduction 0f these salts, which offers certain advantages, requires, however, their removal before the other constituents can be analyzed, and this elimination is sometimes difficult. Usually in quantitative analysis silicates are dissociated by fusing them in a platinum crucible with sodium carbonate, thereby forming sodium silicate, Na2SiO3, sodium aluminate, Na2Al204, sodium titanate, Na2TiO3, and carbonates of other elements. All the carbonates are soluble in hydrochloric acid, but also some silicic acid is formed that must be rendered insoluble. To this end the solution is evaporated several times, as the first evaporation still leaves as much as 5 per cent of the silica soluble. Even after a number of evaporations, minute quantities of silica may be found with the iron and alumina present. Perchloric Acid as an Agent for Dehydrating Silicic Acid Perchloric acid, HC104, (60 per cent), has been used for years as a solvent, but few chemists have used it to dehydrate silica. It is derived from anhydrous perchloric C1207, which is most unstable and dangerous. Perchloric acid is a strong oxidizing agent, which boils at 203°C. It is more effective in rendering silica insoluble than any other known agent, and most rapid in action. After perchloric acid is added to a mixture containing silicic acid, the resultant solution is

Jan 1, 1945

By Charles C. Hawes

DETERMINATION OF SILICA OXIDE iron ores usually are found in intimate association with silica and phosphorus compounds. Their quantitative separation and purification sometimes present difficult problems to the chemist. Silicic acids may represent various degrees of dehydration. They are exceedingly weak, but combine with metallic acids and form some of the most stable oxides in nature, the silicates. When iron ores are treated with hydrochloric acid, they yield practically all their iron. However, apart from rare exceptions, varying amounts of insoluble residues of silica, alumina, lime, magnesia and compounds of phosphorus, sulphur, titanium, chromium and others will be left. If the oxides of silicon, aluminum and titanium are present in small quantities, the insoluble residue is generally very small, but the presence of these oxides more usual in larger quantities. Therefore, only a special treatment can break the bond between these elements. Ore Residues Acids remove the soluble constituent of the ore, leaving the insoluble residue, which chemically is rock or gangue and must be treated accordingly. Alkali carbonates are used frequently to break up the residue, but other fluxes have also been recommended, such as a number of lead and boron salts. The introduction of these salts, which offers certain advantages, requires, however, their removal before the other constituents can be analyzed, and this elimination is sometimes difficult. Usually in quantitative analysis silicates are dissociated by fusing them in a platinum crucible with sodium carbonate, thereby forming sodium silicate, Na2SiO3, sodium aluminate, Na2A1204, sodium titanate, Na2TiOs, and carbonates of other elements. All the carbonates are soluble in hydrochloric acid, but also some silicic acid is formed that must be rendered insoluble. To this end the solution is evaporated several times, as the first evaporation still leaves as much as 5 per cent of the silica soluble. Even after a number of evaporations, minute quantities of silica may be found with the iron and alumina present. Perchloric Acid as an Agent for Dehydrating Silicic Acid Perchloric acid, HCI04, (60 per cent), has been used for years as a solvent, but few chemists have used it to dehydrate silica. It is derived from anhydrous perchloric C1207, which is most unstable and dangerous. Perchloric acid is a strong oxidizing agent, which boils at 203°C. It is more effective in rendering silica insoluble than any other known agent, and most rapid in action. After perchloric acid is added to a mixture containing silicic acid, the resultant solution is

Jan 1, 1945

By J. S. Kirkaldy, D. G. Fedak

The extra degree of freedonz introduced by a second independetzt concentration in a tenzary system gives rise to the possibility of unstable planar phase interfaces in semi-infinite diffision layer couples. Diffusion paths which pass continuously in and out of too-phase regions of the phase diagram but which are not coincident with tie-lines give rise to super saturated zones which may be either adjacent to or isolated from planar phase interfaces, with corresponding nonisolated or isolated precipitates. Nonisolated precipitates are equivalent to morphological development of the interface. Selected couples in the ternary systems Fe-Ni-Cr and Cu-Zn-Sn have been examined nzetallographically and ifz the latter case both isolated and uo~zisolated precipitates have been observed. The diffusion path in one of the couples showing interface morphological developtnent has been examitled using electron probe microanalysis. IGNORING the spurious effects of preferential grain boundary diffusion and anisotropic crystal growth7 it can be unequivocally stated that it is impossible for a binary isothermal diffusion couple constructed of two unsaturated phases to sustain a nonplanar phase interface. Consider for demonstrative purposes the schematic phase diagram of Fig. l(a). Given an initial flat phase interface, semi-infinite boundary conditions and the internal boundary condition fixed by the constitution diagram, xB = xB(T), the unique solution of the diffusion equation requires a persistent flat interface. No other solution is possible. If, however, we anticipate the involvement of surface tension, then the internal boundary condition must be written xB = xB (T,Y) where r is the radius of curvature of a hypothetical nonplanar interface. The introduction of a new parameter such as r can be equivalent to the release of an internal constraint, so that a stable nonplanar interface may be possible after all. Consider a perturbation to the interface as indicated in Fig. 1(b). According to the Ostwald-Freundlich equation: which is applicable to a system of this constitution, the solubility of A in the matrix ß ,xB (Y), at a point of curvature r is given by where Va is the molar volume of the a-phase, R is the gas constant, and a is the interfacial tension. Since the right hand side is positive, xB(r) >xB cm, as indicated in Figs. 1(a) and 1(c). Accordingly, the perturbation will carry the interface concentration in a direction which is opposite to that which would sustain local equilibrium. Such a perturbation is necessarily moderated and the system is returned to its initial condition. This result is general for all binary couples since we can regard an interfacial perturbation as an attempt to precipitate within un-

Jan 1, 1962

By R. W. Smashey, B. J. Piearcey

The structure, composition, and morphology of the carbide phases present in the nickel-base superalloy, Mar-M200, hare been determined and three carbide phases observed. The MC carbide is a solidification product, and the M23 Co and M6C carbides are both prod~icts of solid-state precipitation. The identity of each phase usas determined by both X-ray and electron-diffraction techn~ques. Compositions of all three carbides were studied using the electron beam micro-probe analyzer and by unalyszs of electrolytically extracted residues. Optical and electron microscopy were employed in order that the time/temperature -dependent behavior of the carbides might be observed. Supplementary studies were completed on thin foils and oriented single crystals to determine the mor-phology and orientation relationship of each phase with that of the matrix. MAR-M~OO* is a high-temperature, creep-resistant superalloy designed for use in the as-cast condition. The "as-cast" microstructure consists of a solid-solution matrix, referred to as gamma (y), which contains a general, coherent precipitate of the inter-metallic Ni3(A1,Ti) referred to as gamma prime (?). As a result of dendritic segregation during solidification, a degenerate, spherulitic ? -?' eutectic constituent is present at the grain boundaries and the in-terdendritic regions, which is nucleated by the y on the dendrite tips. A primary carbide phase, a solidification product, is also present at the grain boundaries and in the interdendritic areas, and an additional carbide appears at the grain boundaries as a fine discontinuous precipitate. The alloy is particularly susceptible to heat treatment. For example, the mechanical properties of the columnar grained mater- ial are substantially improved by solution heat treatment, followed by an intermediate temperature age. Metallographic examination of heat-treated material reveals, however, that exposure to elevated temperatures has a marked effect on the microstructure of the alloy; in particular, it is observed that precipitation of considerable amounts of various carbide phases occur. The following investigation was carried out to determine the morphology, composition, and behavior of the carbides in Mar-Ma00 as an aid to the determination of their effect on the mechanical properties and stability of the alloy. THE PRIMARY MC CARBIDE The MC carbide phase appears in the interdendritic interstices and the grain boundaries. In directionally solidified Mar-M200 the carbide appears as very small particles in the chilled region, Fig. l(a), whereas in material less affected by the chill, it becomes larger and develops a dendritic morphology, Fig. 1(b). Step polishing of metallographic specimens from this region shows that in directionally solidified material the individual carbide dendrites are connected in a dendritic network within the metallic interdendritic interstices, whereas in material from the chilled region and in conventional Mar-M200 they are discontinuous, isolated dendrites. No orientation relationship exists between the primary carbide and the matrix.

Jan 1, 1968

By S. A. Herres, A. R. Elsea

Temper brittleness refers to the loss in the notched-bar impact resistance encountered in most medium- or low-alloy steels when they are tempered within the temperature range of 700 to ll00°F or slowly cooled from a higher tempering temperature. Temper brittleness is important because it impairs the service properties of otherwise suitable steels over the range of hardnesses obtained at medium tempering temperatures and because it is impractical to cool pieces of large section rapidly enough from higher tempering temperatures to prevent temper brittleness. The problem of temper brittleness has always been closely associated with ordnance manufacture because armor plate and gun steels require good shock resistance and are often heat treated in heavy section. However, it is now realized that many brittle failures in structural alloy steel parts are attributable to temper brittleness, and there is little question that it contributes to the low impact resistance of alloy steels used in the hot-rolled or normalized condition which are slowly cooled from the hot-rolling or normalizing temperature. Recently Hollomonl has presented a comprehensive summary of the literature on the subject and an excellent description of the manner in which temper brittleness affects the notched-bar impact resistance and other mechanical properties of steel. Carpenter and Robertson2 have given a good analysis of the probable mechanism of temper brittleness, which is similar in many respects to the precipitation-hardening phenomenon. Fig 1 is their diagram illustrating the response to tempering of a susceptible steel. Three changes are recognized as the temperature of tempering a previously quenched steel is raised: (1) pre- cipitation occurs more rapidly and to a greater extent and the notched-bar impact value falls to a minimum; (2) coalescence of the precipitated particles begins to be effective and the impact values for both rapidly cooled and slowly cooled specimens increase; (3) the precipitate goes back into solution at higher tempering temperatures and the impact values of specimens cooled rapidly enough to retain the solution increase, while reprecipitation occurs in slowly cooled specimens and their impact values decrease again. No change must proceed to completion before the following one begins and there is overlapping in temperature ranges. Although there have been a large number of experimental investigations of temper brittleness, insufficient evidence has been accumulated to permit definite identification of the precipitate wnich causes temper brittleness nor have the specific effects on it of various alloy elements and impurities in steel been definitely established. This lack of evidence is largely a result of the lack of a suitable measure for temper brittleness. Temper brittleness is evidenced by an increase in the temperature of brittle failure of notched-bar impact specimens, but most of the data are in the form of an arbitrary susceptibility ratio of the room-temperature impact value for specimens quenched from a high tempering temper to that of similar specimens furnace cooled from the temper. It is obvious that this numerical ratio is dependent upon the type of specimen used and the specific conditions of testing rather than the characteristics of the steel. In general, manganese, chromium, and nickel alloy steels are most susceptible to temper brittleness and molybdenum has heen used to decrease

Jan 1, 1950

By E. W. Shaw

Continued discussion of the paper of Roswell H. JOHNSON, presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 221 to 226. See also Bulletin No. 101, May, 1915, pp. 1157 to 1162. E. W. SHAW, Washington, D. C. (communication to the Secretary+). -With the word petrology-literally the science of rocks-being used primarily for igneous rocks, and with geophysics coming to mean the study of lavas and the rocks into which they solidify, contributions to the knowledge of the physical chemistry of sedimentary rocks, even though only ideas which may be used as working hypotheses, become most welcome. The forces which control the formation and subsequent history of the stratified portions of the earth's crust are so little known that no one has yet been able to settle finally the questions as to whether petroleum is of organic or inorganic origin; whether it originated far from its present position, or nearby. Yet both the chemical and physical problems of the rocks in which oil occurs seem to be more simple than those of the igneous rocks. The oil-bearing rocks of western Pennsylvania, for example, have in all probability never been subjected to a pressure exceeding 3,000 or 4,000 lb. to the square inch, nor to a temperature higher than 100° or 200° C. These pressures are considerably below the crushing strength of rocks, and the temperature far below their melting point. The igneous rocks,, on the other hand, have been affected by enormous pressures and very high temperatures and yet steady progress is being made in reproducing in the laboratory the conditions of their formation and subsequent modification within the earth. The solution of the sedimentary-rock problems would seem to be fully as important as those of igneous rocks, and yet we must content ourselves with reasoning backward and our inferences as to what has happened are oftentimes little more than guesses.1 One of the fundamental problems is the origin of the salt water in oil fields. Is the salt water fossil sea water; has it been formed by the solution o-f salts of various kinds from distinct beds, from disseminated par-ticles, and from the weathering of suitable grains in the rock; or is it of deep-seated origin? Its general resemblance to sea water points to the first, but the principles held by some concerning the free circulation of water throughout the earth's crust, and certain peculiarities of composition indicated by the few analyses available, seem out of harmony with such an explanation.

Jan 7, 1915