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By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

By E. T. Turkdogan, L. S. Darken

Using the quadratic formalism, thermodynamic equations are derived for the composition dependence of the heat and entropy of mixing. The applicability of these equations is confirmed by available experimental data on the activities and heats of mixing for binary metallic systems of Group ZZB elements. In a recent paper arkeen' introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. That is, in the terminal region, which may extend to as much as 60 at. pct, the logarithm of the activity coefficient, log y,, of component 2 is a linear function of (1 - N,)' where N2 is the atom fraction of component 2. Similarly, for the other component, log yl is a linear function of (1 - N,)'. A number of iron-base binary liquid alloys were shown to obey this quadratic formalism. arkeen' extended this formalism also to any corner of a ternary system and showed that the activity coefficients of the components 1, 2 and 3 (1 is taken as the solvent) can be represented by quadratic terms involving five parameters, four of the binaries and one for the ternary system. Numerous examples given by arkeen' demonstrated the general applicability of the quadratic formalism to iron-base systems over a wide composition range. In this paper further examples are given of binary liquid systems (Group IIB elements, Zn, Cd, and Hg) and of several solid solutions, again demonstrating the appropriateness of this concept. A further purpose of this paper is to extend the quadratic formalism to the enthalpy and excess entropy of binary metallic solutions and to test the equations so found using available experimental data. QUADRATIC FORMALISM FOR HEATS AND ENTROPIES OF MIXING OF BINARY METALLIC SOLUTIONS The following equations, reproduced from Darken's paper, are for the two terminal regions of binary systems. at infinite dilution and a's are temperature dependent parameters to be determined from the experimental data. Although the quadratic formalism is an assumed representation of the data, Eqs. [I] to [4] are thermo-dynamically consistent with the Gibbs-Duhem relation and satisfy Raoult's and Henry's laws as limiting cases. As pointed out previously,' the following form of the Gibbs-Duhem equation facilitates the integration in general but particularly in regions I and 11, where each of the derivatives is constant. The partial molar enthalpy of solution i, (and i; the value of i, at infinite dilution) are related to the activity coefficients y, and y," by the thermodynamic relation Differentiating Eq. [l ] with respect to 1/T and substituting the above thermodynamic relation gives for region (I) It is reasonable to assume that over a temperature range of experimental interest, the enthalpy of mixing is essentially independent of temperature, implying from Eq. [7] that the derivative da,,/d(l/) is also independent of temperature. On the basis of this argument, the temperature dependence of a has the form where £ and S have the units of enthalpy and entropy respectively; they are characteristic parameters for a terminal region of a binary system, e.g. for region (I), C12, S12 and for region (II), d:,,, S2,. Using this equation gives for dff ,/ d(l/), From Eqs. [7] and [9] an expre_ssion is obtained for the composition dependence of L,. Similar calculations are made for El and the results are summarized below for the two terminal regions. For region (I), The corresponding expressions for the molar heat of solution, AHM, are readily obtained from the above equations for the two terminal regions: For region (I),

Jan 1, 1969

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By D. G. Westlake

Resistance was measured as a function of temperature, 77° to 350°K,for niobium with hydrogen concentrations up to 3.76 at. pct. Cooling curves exhibited a discontinuity in slope that was attributed to the initiation of hydride formation. A thermal hysteresis was explained in terms of diffusion and the effects of mechanical constraint on nucleation and growth. The heat of solution of hydrogen in saturated Nb-H solid solution was 2. 737 * 0.045 kcal per g-atom, including an unknown stress contribution. The critical ternperatures for hydride formation during cooling and for embrittlement are correlated but not coincident. This, too, has been explained in terms of mechanical constraint and stress-itlduced tratzsfomtation. Nb-H alloys undergo a ductile-brittle transition with decreasing temperature.'-3 Similar behavior has been noted for v-H.1,5 For the latter system, there is evi-dence6 suggesting coincidence of the temperature of minimum ductility and the critical temperature T, for initiation of metal hydride precipitation during cooling. A decrease in ductility due to the presence of brittle hydride particles is readily explainable. The fact that ductility begins to decrease at some temperature higher than T,4,5 has led us6 to suggest that precipitation may be strain-induced locally during tensile testing. Wood and Daniels' have reported that a plot of temperatures for 10 pct reduction in ductility vs hydrogen concentration in niobium is not coincident with, but parallels, the solvus.7,8 They believe this indicates a correlation of precipitation and embrittlement. Unfortunately, the two reported solvuses 7,8 to which Wood and Daniels refer are not in agreement with each other. Furthermore, neither solvus was determined experimentally: each was a plot of calculated solubilities. Thus. neither is highly dependable for determining whether embrittlement coincides with initiation of hydride precipitation. Longson 9 studied phase relations in the Nb-H system between 77° and 473°K by dilatometry. Comparison with metallographic observations convinced him that discontinuities in the slopes of his dilatometric plots were coincident with the initiation of hydride precipitation. Plotting the logarithm of the hydrogen concentration vs the reciprocal of the temperature at which precipitation was initiated during cooling, he obtained a straight line shown in Fig. 1. Walter and chandler,'' using X-ray techniques to detect the for mation of a second phase? have obtained three experimental points in the temperature range 295° to 338°K which fall within Longson's experimental error for this plot. A similar plotg of temperatures at which dissolution was completed during heating was a parallel line shifted toward higher temperatures. A straight-line plot was obtained, also, for the temperatures of the ductile-brittle transitions,9 but it was shifted toward still higher temperatures. Longson calculated an activation energy of 2.980 * 0.300 kcal per mole for the hydrogen embrittlement mechanism, compared with 3.180 * 0.400 kcal per mole for hydride formation. Despite this agreement, he concluded, "It seems unlikely that embrittlement results from hydride formation..." because hydrogen embrittlement was observed at temperatures above the solvus. It is our contention that embrittlement is correlated with precipitation of the hydride.6 Because only Longson has investigated Nb-H phase relations at sub-ambient temperatures, we deemed it advisable to re-determine the temperature dependence of the solubility using the resistometric technique already proven successful for the V-H system.6 Coincidence of our solvus with temperatures for embrittlement would

Jan 1, 1970

By H. H. Rachford, D. W. Peaceman

A system of partial differential equations describing miscible displacement of fluids in porous media is derived The system takes into account the influence of gravity, the spatial distribution of permeability, diffusion, and fluid viscosities and densities. A numerical procedure for approximating solutions to the differential systems has been tested for a horizontal two-dimensional geometry. In end-to-end displacements of oil with less-viscous solvents, the numerical solutions exhibited fingering qualitatively similar to that observed in laboratory models. Small random spatial variations in permeability about the mean value are sufficient to initiate fingering. Quantitative comparisons of computed results with laboratory data show good agreement. INTRODUCTION Miscible flooding of oil by solvent is receiving increasing consideration for field use.1-4 Unfortunately, such floods potentially present severe problems in loss of recovery through the by-passing of oil by expensive solvent. Consequently, their economic evaluation requires sound techniques for predicting recovery. The purposes of this work are to present a finite-difference method for calculating the multidimensional displacement of oil by solvent and to investigate the validity of the method by comparing results of calculations with data from displacements in laboratory models.5 The formulation of the method to simulate the model experiments treats a case of limited scope in the description of solvent flooding in the reservoir. The model experiments were carried out with fluids that were assumed to form an incompressible, ideal, two-component system with constant diffusivity. Establishing the validity of the method even in its present form provides a major step toward the goal of quantitatively evaluating individual solvent flooding projects. First, it demonstrates the fea- sibility of calculating the course of displacements which are dominated by an inherent macroscopic instability, i.e., viscous fingering. In addition, the method provides almost the only practical means of examining the effect of the size and extent of reservoir inhomogeneities on the development and propagation of the fingers, taking into account the important influences of diffusion and gravitational segregation. It might be inferred that such studies cannot yield results of practical value because in displacements dominated by macroscopic instability the pattern of finger development and the resulting performance should depend critically on small variations in the geometric distribution of reservoir inhomogeneities. The present method offers the capability inherent in computational techniques of predicting performance reproducibly with any arbitrary distribution of reservoir properties and, as such, provides a means of evaluating the sensitivity of behavior to uncertainties in reservoir definition and, thus, assessing the reliability of prediction of performance. THE PHYSICAL PROBLEM DATA USED FOR QUANTITATIVE TESTS OF CALCULATIONS In this work, a calculation for treating the miscible-displacement process is tested by comparing calculated results with experimental data. The experiments chosen for comparison have been described in detail,5 and the quantitative features are summarized in a later section. Briefly, oil was flooded by solvent of equal density from a thin rectangular channel in Lucite packed with uniform Ottawa sand. Under these conditions, two-dimensional geometry is considered adequate to represent the process. Inasmuch as the present work is concerned with testing of the method by comparison with specific two-dimensional data, the system of equations presented in the succeeding section will be oriented to defining the physical system specifically. THE DIFFERENTIAL EQUATIONS Suppose x, y to be a Cartesian co-ordinate system and define h(x, y) to be the height of a point above a horizontal reference plane. It will be assumed

In the special number of the magazine Ocl und Kohle (Oct. 22, 1940) dedicated to the petroleum industry of southeastern Europe, there appeared several articles relating to Yugos1avia.t In the first article the author calls attention to the fact that there are two fields in Yugoslavia that have been explored and exploited by more than 100 wells at variable depths during the last 50 years. These are on the Island of Mura, at the confluence of the Mura and the Drave. Additional exploration drilling in various other parts of the country has been without result, but certain ones of these explorations have revealed the existence of gas horizons that have some value, which are being used for industrial purposes. Table I shows the production of oil and gas between the years 1900 and 1939. TaBle —Production of Oil ad Gas in Yugoslavia . n,i Natural Natural Years oil Years Gas, Cu. Years Gas, Cu. Meters Meters T900-1929 10,000 1923 507,000 1934 1,388,000 1930 277 1924 567,000 1935 1,401,000 1931 202 I92S 691,000 I936 1,483,000 t932 289 19261 1.472,000 1937 1,841,000 1933 629 1927! 1,732,000 193s 2,431,000 1934 324 1928 2,515,000 1939 2,628,000 1935 260 1929 4,700,000 1936 137 I93O 5.345,200 1937 463 1931 6,376,153 1938 1,091 1932 1,661,737 1939 1,114 1933 959,574 The number of wells drilled from 1884 to the present time was in the neighborhood of zoo and the total footage drilled was 65,000 m. up to July I940 They may be divided roughly as follows: 12 wells in the region produce natural gas; 134 wells in the two old fields of the Island of Mura and about zo wells for the exploration of the zone of the Flysch, in Bosnia. The depths of 50 of these wells was roo to 200 m.; the depths of 50 wells oil the Island of Mura ran from zoo to 500 m.; of 2 ; wells, 500 to I000 m.; of ro wells from rooo to 2000 meters. The deepest well drilling in Yugoslavia has reached 2000 in. In the Valley of Morave, in the region of Selnica, I00 km. south of Nish, there have been discovered asphalt-bearing limestones, which contain about 15 per cent asphalt and are associated with bituminous clays. Later, at Paclenica, important deposits of natural gas were found. A zone rich in gas and oil seepages runs through Pracec, Miklenska, Bujavica, etc. The author studied these regions from the point of view of stratigraphy and tectonics. The anticlines and gas-bearing domes are concentrated in two zones: the region of the Drave (Island of Mura) and the region of the Save, southeast of zagreb, which contains the gas field in exploitation in the region of Bujavica. A full description of the productive region of the Island of Mura has been given by Egon Bohm, a geologist, in the second article mentioned. This includes a history of the exploration and exploitation that took place under Hungarian rule in this region. The most important exploration was effected between 1884 and 1885 by Stavenov and Stinger, of Vienna. In 1927 work was done in the same region by Anton Raky, a well-known explorer who makes work of this kind his specialty.

Jan 1, 1941

In the special number of the magazine Ocl und Kohle (Oct. 22, 1940) dedicated to the petroleum industry of southeastern Europe, there appeared several articles relating to Yugos1avia.t In the first article the author calls attention to the fact that there are two fields in Yugoslavia that have been explored and exploited by more than 100 wells at variable depths during the last 50 years. These are on the Island of Mura, at the confluence of the Mura and the Drave. Additional exploration drilling in various other parts of the country has been without result, but certain ones of these explorations have revealed the existence of gas horizons that have some value, which are being used for industrial purposes. Table I shows the production of oil and gas between the years 1900 and 1939. TaBle —Production of Oil ad Gas in Yugoslavia . n,i Natural Natural Years oil Years Gas, Cu. Years Gas, Cu. Meters Meters T900-1929 10,000 1923 507,000 1934 1,388,000 1930 277 1924 567,000 1935 1,401,000 1931 202 I92S 691,000 I936 1,483,000 t932 289 19261 1.472,000 1937 1,841,000 1933 629 1927! 1,732,000 193s 2,431,000 1934 324 1928 2,515,000 1939 2,628,000 1935 260 1929 4,700,000 1936 137 I93O 5.345,200 1937 463 1931 6,376,153 1938 1,091 1932 1,661,737 1939 1,114 1933 959,574 The number of wells drilled from 1884 to the present time was in the neighborhood of zoo and the total footage drilled was 65,000 m. up to July I940 They may be divided roughly as follows: 12 wells in the region produce natural gas; 134 wells in the two old fields of the Island of Mura and about zo wells for the exploration of the zone of the Flysch, in Bosnia. The depths of 50 of these wells was roo to 200 m.; the depths of 50 wells oil the Island of Mura ran from zoo to 500 m.; of 2 ; wells, 500 to I000 m.; of ro wells from rooo to 2000 meters. The deepest well drilling in Yugoslavia has reached 2000 in. In the Valley of Morave, in the region of Selnica, I00 km. south of Nish, there have been discovered asphalt-bearing limestones, which contain about 15 per cent asphalt and are associated with bituminous clays. Later, at Paclenica, important deposits of natural gas were found. A zone rich in gas and oil seepages runs through Pracec, Miklenska, Bujavica, etc. The author studied these regions from the point of view of stratigraphy and tectonics. The anticlines and gas-bearing domes are concentrated in two zones: the region of the Drave (Island of Mura) and the region of the Save, southeast of zagreb, which contains the gas field in exploitation in the region of Bujavica. A full description of the productive region of the Island of Mura has been given by Egon Bohm, a geologist, in the second article mentioned. This includes a history of the exploration and exploitation that took place under Hungarian rule in this region. The most important exploration was effected between 1884 and 1885 by Stavenov and Stinger, of Vienna. In 1927 work was done in the same region by Anton Raky, a well-known explorer who makes work of this kind his specialty.

Jan 1, 1941

By Mary Barrett, Walter Rose

INTRODUCTION The conventional way to program reservoir problems* for solution on the electric analyzer1 is one which concentrates the block units towards the inner radius of the prototype system being represented by the analog model. This is achieved by the device of considering block units of equal value radial resistance, leading to the consequences: (1) the ratio of the external to the internal radius of each block unit is a constant (i.e. r1/ri-l = constant a); (2) the external radius of the nth block unit is equal to the innermost radius of the system times the constant a raised to the nth power: (3) the capacitance of the block units increase by a factor of a2 going out radially from the innermost to the outermost boundaries of the system; (4) given n block units in the radial direction, the capacitance ratio of the outermost to the innermost block unit is a (2n-2); and (5) the vertical resistance of the block units decrease by a factor of a going out radially from the innermost to the outermost boundaries of the system, such that the ratio of the maximum to minimum vertical resistance is also given by the factor a(2n-2) PRESENT PROGRAMMING METHOD While this conventional way of programming problems is quite adequate for routine uses of the electric analyzer, it leads to difficulties in those cases where the inner radius of the prototype system (e.g., the well-bore) is small compared to the external radius (e.g.. the external reservoir boundary). To handle such a case by the conventional method would require either that a large value be selected for the constant a or that a large number n, of radial block units be chosen. In consequence, the capacitance and vertical resistance ratios become impossibly large, as will be evident from the relations given above. In any event, the size of the smallest and largest capacitors will always be limited by the size of commercially available components, and the analyzer itself will determine how many mesh points are available for radial block units. For example, it can be shown that if the maximum capacitance ratio which can be electrically handled is a factor of l04, the maximum external radius of the system which can be considered (assuming an internal wellbore radius of 0.25 ft is: It is thus seen that in direct consequence of having the inner wellbore radius small compared to the external radius, models extending beyond 30 to 40 ft are not possible when the capacitance ratio is limited to l04. (NB. A value of 10-9 farads can perhaps be taken as the minimum electrical capacitance possible if corrections for the capacitance of the lead wires are to be avoided. Values greater than 10-5 farads would require the use of unstable and inaccurate electrolytic capacitors). On the other hand, models extending out to 500 to 5,000 ft may be desired in single-well problems, and hence the need for a revised method of problem programming. * REVISED PROGRAMMING METHOD The revised method of programming is one which attempts to retain the desirable features of the conventional method (viz. concentration of block units towards the inner boundary, simplicity in computation, etc.) without having as a consequence that impossible capacitance and vertical resistance ratios will be required. Other advantages will also be achieved by the revised

Jan 1, 1957

By H. M. Davis, T. S. Jones

A methodfor accelerating the reduction of a metal oxide by carbon monoxide is to incorporate in the reduction system a nonreducible oxide which has a strong affinity for carbon dioxide and will remove it from the product gases. The effectiveness of this method was investigated by veduction experiments on specially prepared powder mixtures of SrO-ZnO ("active'.) and SrCO3-ZnO (reference). Measurements at 750o and 677°C showed that the rate of reduction of ZnO by CO was as much as an order of magnitude greater in the presence of SrO. Under the experimental conditions at least as much CO2 as generated by veduction was absorbed when SrO was present. Enlzancernent of the veduction rate by SvO resulted from modification of' gaseous djfitsion processes. THE specific question posed in this investigation was whether the reduction reaction CO + ZnO - Zn(g) + COa [1] could be accelerated by incorporating strontium oxide into the oxide charge undergoing reduction. Provided the strontium oxide was active enough, it could remove carbon dioxide from the product gases of ( 11 and form strontium carbonate, thus modifying Reaction [ 1] to CO + ZnO + SrO = Zn(g) + SrCO3 [ 2] This study of the comparative rates of Reactions [ I] and [2] can be considered as a particular case of a general scheme for increasing the rates of reduction of metal oxides by carbon monoxide. The limits of applicability of this scheme are indicated in the simple thermodynamic analysis presented in the appendix. This analysis primarily dictated the choice of the system, CO-ZnO-SrO, employed in this investigation. In addition, it was thought that a study of this scheme by use of the CO-ZnO-SrO reaction system would be of special interest in view of indications in the literature1-3 that the gaseous reduction of zinc oxide is prone to rate control by diffusion in the gas phase. The distinction should be pointed out between this and other efforts to increase the rates of reduction reactions through the use of addition agents. Additions of a wide range of chemicals have been tried with de- grees of apparent success varying from slightly negative to highly positive. The reasons for making additions have included the use of salts to produce effects akin to catalysis,4, 5 the alteration of the microstruc-tural details of the reduction process (including solid-state diffusion),6-8 and the conversion of an en-dothermic reaction into one that is exothermic or autogenous.9-12 The means used to attempt alteration of the enthalpy change has commonly been to incorporate lime into the charge, so that heat is generated by reaction with either of the reaction products, carbon dioxide or water. The use of lime in this way makes endeavors such as that of Edstrom and Wiberg similar to the present one. Furthermore, the basic principle behind the present work has previously been set forth.13 However, a detailed investigation of the type of reaction described in this work does not appear to have been conducted. EXPERIMENTAL PROCEDURE From both conceptual and physical standpoints, Reaction [2] is to be considered as the sum of two reactions:

Jan 1, 1968

By A. L. Labbe, J. J. Donoso

Hard-won experience in the operation of smelting plants has pointed the way to the most efficient design and economical operation of a baghouse system for recovery of metallurgical fumes. This paper treats of the principles governing bag filtration and the factors most directly affecting bag life. Methods for temperature conditioning of smoke previous to filtering are described and the evolution of bag shaking mechanisms is brought up to date. THE history of the bag filter process, as applied to the recovery of metallurgical fumes, goes back to 1876, when the Lone Elms Works of Joplin, Missouri, erected a two-section baghouse for filtering fumes from Scotch Hearth lead smelting furnaces. By modern standards this installation was crude, but the basic operating principles remain essentially the same today. Great progress, however, has been made in the mechanization of the process by the use of devices for mechanically and automatically cleaning bags of adhering fumes, in the use of instruments for recording and controlling the variables affecting baghouse operation, and in the conditioning of the smoke previous to filtering. The principles governing bag filtration of fumes were investigated in 1929 by A. J. Seitz of American Smelting and Refining Co., and he arrived at the following conclusions: 1. Pressure on Bags at Constant Volume: The rate at which the pressure builds up in a bag with constant volume is directly proportional to the time, with the same kind of smoke and dust burden (fig. 1). 2. Pressure on Bags for Change in Volume: With equivalent smoke and dust burden, the bag pressure increases with the square of the increase in volume. The rapid increase in pressure is due to (1) increase in volume, (2) increase in amount of dust on the bag, and (3) more intense packing of the dust at higher velocity (fig. 2). 3. Effect of Intensive Filtering on Pressure: Since the pressure builds up directly as the square of the volume, with the same smoke and dust burden, it is necessary to shake the bags in that increased ratio, and vigorously, to keep the pores of the bag open and pressure down. This increases the wear on the bags and the dust losses. 4. Effect of Shaking on Dust Losses: The losses are in direct proportion to the frequency of shaking because the loss takes place immediately after shaking, before the bag seals itself. Tests show that with hand shaking the last 20 pct of the removable dust requires seven times more shaking per unit weight of dust than the first 80 pct. 5. Effect of Fineness of Dust on Losses: The fineness of the dust particle increases the loss in two ways: (1) When the bag is clean a greater percentage of it will pass through before the bag seals itself; (2) fine material penetrates farther into the bag pores, building up pressure faster and necessitating more shaking, thereby increasing the loss. The physical principle of operation of the bag filter is simply the separation of solids from a gaseous carrier through a porous medium, and is analogous to the filtration of solids from liquid carriers. Basically, the mechanics of the process are as follows: Fume-laden gases drawn from the operating fur-

Jan 1, 1951

By Y. L. Yao

A scale based on existing data for the mutual solid solubilities of metals in binary systems has been compiled. This scale is useful for estimating the relative magnitude of two solubilities, provided that these two metals do not form a continuous series of solid solutions. In his classic work on the theory of metallic solid solutions, Hume-Rothery proposed that, other things being equal, a metal of lower valency should be regarded as more likely to dissolve one of higher valency than vice versa. He called this the "relative valency effect". Later he found that the application of this general principle was limited to the three univalent metals: copper, silver, and gold. In dealing with alloys of these metals with metals of higher valency, Hume-Rothery stated, it is usually found that the solid solution of the univalent metal is of the greater extent.&apos; The question of whether there is a systematic trend in comparing the relative magnitude of mutual solubilities, if valency is not considered a criterion, naturally arises. The present paper proposes a "mutual solid solubility" scale on an empirical basis. The order of its arrangement is determined by the relative magnitude of mutual solid solubilities. Some applications of and inferences from this scale are given. ORIGIN AND SCOPE OF THE SCALE An extensive survey of over 400 binary phase diagrams shows that, with certain exceptions and within certain limitations, metals can be arranged in the following order: Na Zn Cd Ga Bi Ge Sb As Hg Sn Si Mg Li Ba In Tl Pb Al Ca Be Mn Cr Re W Mo Cu V Ta Fe Ru Cb Co Ti Hf Ni Os Zr Ir Pt Au U Rh Ce Pd Ag Th so that a metal higher on the scale tends to have a higher solubility in a metal lower on the scale than vice versa. some experimental solubility data are given in Table I. These data, unless otherwise specified, are taken from Hansen and Anderko.6 Throughout this paper, the term "solubility of A in B" is taken to mean the maximum solid solubility of A in B in atomic percent, while the maximum solid solubility of B in A in atomic percent is called "reciprocal solubility". The exceptions found in the above-mentioned survey are: Al-Ag system, 20.34 at. pct Al in Ag, 23.8 Ag in Al; Mg-Pb system, 5.9 Mg in Pb, 7.75 Pb in Mg; As-Sn system, vanishingly small amount of As in Sn, a large As primary solid solution; Cd-Hg system, Cd in Hg <Hg in Cd; Mg-T1 system, 5(?) Mg in ßT1, 15.4 T1 in Mg; W-Ti system, -21 W in ßTi, -25 Ti in W; Zr-Ag system, probably small amount of Zr in Ag, 20 Ag in ßZr.7 Considering the large number of examples, the exceptions are few. It is remarkable that metals may be so arranged without considering other factors such as size, crystal structure, electronic structure, and so forth. A limitation to the use of the scale is the fact that it cannot be tested for two metals forming a continuous series of solid solutions. It is interesting to point out that when the continuous solid solutions have a miscibility gap the critical composition is

Jan 1, 1961

By H. J. Engell, W. Frank, A. Seeger

SWISHER and ~urkdogan&apos; have determined the solubility of oxygen in a iron. They found it to lie between 7 and 10.5 at.-ppm at 881°C. Using earlier work on the permeability of oxygen in bcc iron,&apos; they arrived at the following expression for the diffusion coefficient of oxygen in bcc iron (k = Boltzmann&apos;s constant, T = absolute temperature): where The present authors3 have estimated the activation energy QD for the diffusion of oxygen in bcc iron in two different ways from various experimental data.2&apos;4"6 In the first method QD + QS (QS = heat of solution for oxygen in bcc iron in thermodynamic equilibrium with solid FeO) was determined either from data on the reduction of FeO with hydrogen4 or from measurements of the internal oxidation of silicon in a iron.5 Using an estimate of QS from investigations of the oxygen solubility in 6 iron2 (in thermodynamic equilibrium with molten FeO) Q = 0.97 ev or Q~ = 1.06 ev were obtained. From the magnitude of these values it was concluded that oxygen migrates interstitially in bcc iron and that consequently the activation energy QD for diffusion of oxygen has to be identified with the migration energy E~ of the oxygen atoms. Therefore, for a second estimate of QD from the diffusion coefficient of oxygen in 6 iron at 1450" ~,~ we used the theoretical expression:3 (a = length of elementary cube edge, m = mass of interstitially diffusing atom, sM = migration entropy), applicable to diffusion via the octahedral interstices in bcc lattices. Taking sM = 3.8 k (migration entropy of carbon in a iron), one gets Q = 0.90 ev. Hence, in Ref. 3 Q = (0.98 *0.1) ev was proposed as a plausible value for the diffusion energy of oxygen in bcc iron. sM + 9 (9 = solution entropy for oxygen in bcc iron) can be determined from permeability measurements.4 Using the above-mentioned estimate for QS , the following expression for the solubility c (atomic concentration) of oxygen (in thermodynamic equilibrium with solid FeO) in bcc iron was derived: From [4] the solubility of oxygen at 881°C in a iron is calculated to lie between 0.6 and 12 at.-ppm. We see that the solubility determined by Swisher and

Jan 1, 1969

[†ADAIR, ARTHUR C., Corp 4th Co., 1st. Training Bat., 154th Depot Brigade. ADAMS, HENRY, Major Chemical Warfare Service. ARLUCK, A. A Headquarters, 1St Corps of Artillery. ASKIN, THOMAS B. H Ensign.] [ ]

Jan 1, 1925

By J. W. Downey, J. B. Darby, L. J. Norton

THE only previous investigation of the phase equilibria in the Ta-Pd system was reported by Greenfield and Beck.1 Their work (actually a portion of a much broader survey) was limited to the composition range 50 to 75 at. pct Ta and to a single temperature, 1000°C. The results indicated that no intermediate phases were present at this temperature. They pointed out that this was an unexpected result in view of the fact that niobium, which belongs to the same group in the periodic table as tantalum and has essentially the same atomic size, forms a o phase with palladium.&apos; Also, tantalum in combination with rhodium,&apos; iridium,&apos; or platinum&apos; stabilizes the s phase. By analogy, the Ta-Pd system would also be expected to contain a s phase. The present investigation was therefore undertaken to explore more fully the phase relationships in this system. Alloys were prepared by arc melting on a water-cooled copper hearth in an argon-helium atmosphere. The purity of the starting materials was greater than 99.9 pct. The weight losses on melting were less than 1 pct and therefore the alloys were not analyzed chemically. Specimens were wrapped in molybdenum foil, encapsulated in quartz capsules under a vacuum of at least 1 x 10-5 mm of Hg, annealed as indicated in Table I, and water quenched. Optical and X-ray metallography were used for identifying the phases present in the annealed and quenched alloys. The alloys were resistant to attack by several acids; however, a sodium cyanide electroetch and an immersion etch containing 1 part HF, 1 part HNO3, 2 parts H2SO4, and 5 parts H2O by volume were found satisfactory. The X-ray diffraction patterns were taken with a Straumanis-type Debye-Scherrer camera and filtered copper or chromium radiation. A summary of the phases found in this investigation is presented in Table I. No attempt was made to determine the composition limits of the various phases. The present results indicate that this system consists of two terminal solid solutions separated by at least four intermediate phases at the approximate compositions Ta3Pd, -TaPd, TaPd,, and TaPd3. The Ta-rich solid solution, containing less than 10 at. pct Pd at 1150°C, is in equilibrium with a o phase which is stable in the vicinity of 25 at. pct Pd. The latter phase is also in equilibrium with a bct phase at the equiatomic composition. At high temperatures it appears that the Pd-rich solid solution extends to at least 66.6 at. pct Pd and is in equilibrium with the bct phase. When annealed at 900°C, a sample containing 66.6 at. pct Pd transformed to an unidentified phase designated as X. An X-ray diffraction pattern of this phase contained sharp low-angle lines while the high-angle lines were characteristically diffuse. The observed d-spacings and relative intensities for lines in the low-angle region are presented in Table 11. In the vicinity of 70 at. pct Pd an intermediate phase having the TiA13-type structure is formed. It is stable to at least 1100°C, and presumably dissolves congruently into the ter-

Jan 1, 1963

By E. S. Lenker, H. J. Van Hook

A complete swies of solid solutions has been found between the compounds InAs and GaAs Below the solidus. The melting relations determined by differential thermal and static quenching technzques, indicate that the liquidus and solidus are of the simple ascendant type. No evidence of unmixing of the homogeneous solid solutions was observed at sub-solidus temperatures. A quenching method for locnting the solidus, using X-ray diffraction techniques, is described in some detail. THE semi-conducting properties of compounds formed by various combinations of the less familiar intermetallic elements have created an increasing interest in the phase relations in systems involving these elements. The complete phase diagram of such a system, containing a compound of special interest, will often provide information as to the most favorable conditions for preparing large crystals from a melt, as well as specifying the temperature stability of the crystalline phase or phases produced. In view of the current importance of gallium arsenide in semiconductor research and of the structural similarities of indium arsenide, it was thought that the complete phase relations of the system InAs-GaAs should be investigated. Previous work on the system Ga-As by Koster and homa&apos; and on In-As by Liu and peretti2 has shown that GaAs and InAs are the only compounds formed, having melting points of 1238° and 942°C, respectively. In a survey of various systems of elements from groups IIIb and Vb, spengler3 also re- Mines Ltd., for his continuing encouragement and for permission to publish the results of this work. ports complete miscibility of gallium, indium, and arsenic in the liquid state. In a partial investigation of the InAs-GaAs system, Woolley and smith4 found extensive solid solution throughout the alloy range. Their subsolidus work, however, was inconclusive at temperatures below 900" and they did not determine the liquidus relationships of the system. PRESENT INVESTIGATION The starting materials used were high-purity gallium, indium, and arsenic. The method of preparation of the compounds follows that devised by M. Shafer and is described in detail in a paper by Shafer and eiser.&apos; The end-member compounds, GaAs and InAs, were first prepared by reaction of the elements in the desired proportions in evacuated silica glass vials. The vials were rotated in a furnace as the temperature was slowly raised to insure rapid and complete reaction at low temperatures. Thereafter the starting materials, GaAs and InAs, were melted by heating the sealed vials to 1300" and 1000°C, respectively; the vials in this case were filled as completely as possible to keep the vapor space small and thereby minimize the loss of arsenic to the vapor phase. Ten binary mixtures of these compounds were then prepared by reaction of the powdered material in the solid state just below solidus temperatures. At 900C preparations containing 3, 5, 8, 10, 25, 35, 50, and 75 mol pct GaAs were found to be single homogeneous phases, indicating a complete series of solid solutions between GaAs and InAs. Moreover, it was discovered that the homogeneity of any crystalline binary preparation could be very accurately checked by X-ray diffraction because of the large differences in unit cell dimensions of the end membe5s. The cubic lattice constant ofor GaAs is a = 5.652A and that of InAs is a = 6.061A

Jan 1, 1963

By C. H. Gorski

A method for preparing titanium tetrachloride is described which consists of reducing rutile with coke and chlorinating the reduced product at 200° to 500°C. The crude distillate is purified by treatment with copper powder and distillation. Recoveries, exceeding 90 pct of the titanium in the rutile, were obtained. IN recent years considerable interest in metallic titanium has been aroused because of its outstanding physical and chemical properties. The present commercial processes for preparing titanium are modifications of the Kroll1 process and consist essentially of the reduction of titanium tetrachloride with magnesium in an inert atmosphere to produce metallic titanium with magnesium chloride as a byproduct. At present,&apos; commercial titanium tetrachloride costs $0.32 a pound, which makes the price of the included titanium $1.28 a pound. As the titanium tetrachloride must be purified further before processing into metal, its ultimate cost obviously will be higher. Consequently, one of the prime requisites for the production of lower cost titanium metal is a source of low-cost titanium tetrachloride. Recently, Knickerbocker, Gorski, Kenworthy, and Starliper3 escribed a method for preparing titanium tetrachloride from low-grade Arkansas rutile by smelting the rutile with pyrite and coke to form a titanium matte and then chlorinating the titanium matte to prepare a crude titanium tetrachloride. This process had several inherent advantages. Low-grade rutile concentrates were utilized, the chlorination temperature was relatively low (approximately 200°C), and the reaction was strongly exothermic. However, this process had several disadvantages, chief of them being the rather low recoveries of titanium tetrachloride (65 to 81 pct) and the difficulty in purifying the crude titanium tetrachloride obtained. Because of the high-titanium and low-iron con- tents of rutile as compared to ilmenite, rutile should be of greater potential value as a source of titanium tetrachloride than ilmenite. Rutile, however, is not chlorinated directly in commercial practice, because reaction temperatures above 700 °C are required, at which point chlorine attacks most of the common materials of construction. The process now in use consists of converting the titanium in rutile to the cyanonitride by high-temperature reduction in an electric furnace, and then chlorinating this compound. The disadvantages of this process are the difficulty of producing the cyanonitride, the use of high-grade rutile concentrates in the charge, and the presence of several percent of silicon tetrachloride in the finished product. It would be of considerable interest to develop a new process for the preparation of titanium tetrachloride from rutile by chlorination at 200" to 500°C. Process Development Several investigators&apos;-&apos; have studied the reduction of titanium dioxide with carbon in an effort to prepare titanium monoxide. Invariably, the titanium monoxide formed in this manner was not pure, as it contained titanium carbide and one or more of the lower oxides of titanium. As these lower oxides of titanium are more reactive chemically than rutile, and as it is known that titanium carbide may be chlorinated readily, a study was made of the chlorination of carbon-reduced rutile. A sample of rutile concentrates from Hot Spring County, Ark., containing 76.19 pct TiO,, 5.65 pct Fe2O3, 4.18 pct SiO2, and 2.88 pct Al2O3, was used for this investigation. The experimental procedure consisted of making an intimate mixture of —100-mesh rutile and petroleum coke, adding water and molasses as a binder to foi-m a paste, charging into a graphite crucible that was covered, except for a vent to allow the

Jan 1, 1952

By E. A. Elevatorski

Wollastonite, named after William H. Wollaston, an English chemist, is a calcium metasilicate, CaSiO3. It has a short history as an industrial mineral. The earliest production of wollastonite is reported to be from a deposit near Code Siding, located north of Randsburg, Calif. At this locality small tonnages of wollastonite were quarried during 1933-34 and 1938-41, and processed into mineral wool. This operation was largely experimental and virtually no United States production was again reported until the 1950s when a large deposit near Willsboro, N.Y., was developed by the Cabot Corp. A processing plant was placed on-stream in 1953, with nearly continuous production to date, and it is currently operated by Interpace Corp. Since 1958, wollastonite deposits in the Little and Big Maria Mountains of Riverside County, and in the Panamint Range of Inyo County, both in California, have operated intermittently for production of both ornamental and commercial wollastonite. During 1973, the United States was the major producing country, furnishing about 75% of the world&apos;s output. Recent production also has come from Finland, Mexico, and Kenya. Small amounts have been shipped intermittently from India, USSR, New Zealand, Republic of the Sudan, Republic of South Africa, and South-West Africa. The principal use of wollastonite is in the manufacture of ceramics, especially wall and floor tiles. Other uses are for paints, fillers, adhesives, reinforcing agents, plastics, fluxes, and glazes. Mineralogy Pure wollastonite, CaSiO3, has the composi¬tion of 48.3 % CaO and 51.7 % SiO,. However, it is seldom found in the pure state due to the ease with which it takes into solution the metasilicates of manganese, magnesium, iron, and strontium. Predominantly, wollastonite occurs as a contact metamorphic deposit forming between limestones and igneous rocks. Commonly associated minerals are garnet, diopside, epidote, calcite, and quartz. It has a specific gravity of 2.8 to 3.0, and hardness of 4.5 to 5 on Mobs&apos; scale. When pure, it has a brilliant white color, but with impurities it may be grayish or brownish. Luster is vitreous to pearly. Melting point of wollastonite is about 1540° C. Wollastonite occurs in coarse-bladed masses, rarely showing good crystal form. It is usually acicular or fibrous, even in the smallest of particles. The most unique property of crushed and ground wollastonite is its cleavage. Fragments of crushed wollastonite tend to be needle-shaped, imparting a high strength, and this property is the basis for many of its uses. The fiber lengths are commonly in the ratio of 7 or 8 to 1, length to diameter. Some crystals of wollastonite fluoresce under short-wave or longwave ultraviolet light, or both; colors ranging from yellow-orange to pink-orange. Specimens may also show phosphorescence. The brightness of wollastonite is a property of considerable importance to the paint industry. Material, 99% pure, with a size of -325 mesh, has a General Electric reflectance rating of 92 to 96%. Chemically, wollastonite is inert and this property makes it useful as a filler and reinforcing agent. There are two polymorphs of calcium silicates: wollastonite, a low temperature form, and pseudowollastonite, a high temperature form. Inversion of wollastonite to pseudowollastonite occurs at about 1120° C, resulting in an increase in the coefficient of expansion and a color change. Pure white wollastonite, on inversion, may change to a cream tint, or various shades of red or brown. The color change is thought to be due to the presence of iron and strontium.

Jan 1, 1975

By R. W. Armstrong, P. C. Jindal

WE should like to point out that Hu and cline.1 in their study of the recrystallization of titanium, have obtained data which appear very important for accurately determining the dependence of hardness on grain size for this material. It has been proposed2,3 that the macrohardness. H. of a poly crystalline material should depend on its average grain diameter, l. in accordance with the relationship: H =H0 + kHl-1/2 [1] where Ho and kH are experimental constants. This relationship follows from the hardness dependence on yield stress or flow stress4 and. thence. the Hall-Petch stress-grain size relations.5&apos;6 Fig. 1 shows the Diamond Pyramid Hardness. Dph. values vs the reciprocal square root of the average diameter of the recrystallized grains, taken from the titanium data reported by Hu and Cline. The data in this figure give a linear relationship for the hardness over a wider range of grain diameters than anyone has previously measured. The data are not linear, for example. on an I-1 or l-1/3 scale. At the very large grain sizes the data are in reasonable agreement with measurements earlier reported by Holden, Ogden, and Jaffee.7 For the grain sizes smaller than 1 µ, which correspond in Fig. 1 to hardness values greater than 150, the material was reported as not being completely recrystallized and, therefore, these data appear less meaningful as far as the hardness dependence on grain size is concerned. However. it has been suggested by other investigators that deformed materials exhibit strengthening due to an effective grain size refinement even in the unrecrys-tallized condition.8-10 Also. Hu and Cline have shown that a change in texture occurs for titanium during the recrystallization process and. especially. following it. The influence of this texture change on the hardness-grain size relation would be expected to be less than that reflected in the unidirectional stress-strain behavior, even for an hcp material. because of the actual combined stress system which applies for the hardness test. For, at least, certain combined stresses, average values of the orientation factors should still occur in the stress-grain size analysis of a material exhibiting a preferred orientation.&apos; We previously suggested3 that the experimental constants. H0 and kH. from the Meyer hardness-grain size relation should be correlated with the Hall-Petch constants, uoy and ky.5,6 Our recent study" of the Hall-Petch relation and the hardness-grain size results which obtain for a number of polycrystalline materials shows that: The inequality [2] is explained by noting that the hardness should be correlated. perhaps, with the flow stress at some value of strain, as suggested by Dugdale,12 and. also, that the influence of strain on the Hall-Petch relation is to increase uo and not change k very much." Normally. Dph values and Brinell hardness values are nearly equivalent to each other and to the Meyer hardness number. For the case of titanium, then. the inequality [2] may be evaluated using the experimental values of ao = 8.0 kg per sq mm and ky = 1.3 kg per mm3/2 obtained from the experiment of Guard.6,13 Thus, (Ho/uo) = 12 and (kH/k3) = 1.3. This research has been supported at the University of Maryland through the Center of Materials Research by the Advanced Research Projects Agency of the U.S. Government.

Jan 1, 1969

AN announcement of the annual meeting to be held in New York, Feb. 14 to 17 inclusive is being mailed to all members. Particular attention is called to the necessity of asking for certificates when you purchase your ticket in order that all may secure reduced return fares.

Jan 1, 1927

By Jed H. Mosgrove, Paul M. Budzak

INTRODUCTION Good mine ventilation starts at the drawing board. A coal mine will either be adequately ventilated or not, depending upon how good a job was done in the planning. Poor planning will not only result in inadequate ventilation, but may also lead to low productivity. A mine foreman cannot achieve high productivity while trying to maintain 4.2 m3/s (9000 cfm) of air at his last open crosscut. PLANNING What will provide adequate ventilation? A rule of thumb in laying out a coal mine is to provide enough entries in the main entry system to keep air velocities at 2.5 m/s (500 fpm) or less; at this rate of flow, good ventilation may be expected. The intake and return air courses of a coal mine do not improve with age. Entries will deteriorate, ribs will slough, roof will fall, and clutter will accumulate. The resistance offered to air travel will continue to increase with each passing year. Providing enough airways for the present and the future cannot be emphasized too strongly. In order to better appreciate good planning and bring it into better focus, assume a hypothetical mine has the following features: entries 1.5 m (5 ft) high and 6.1 m (20 ft) wide; one intake and one return entry; the mine development is 4.8 km (3 miles) from the intake and upcast ventilation shafts; and the ventilation requirement is 141.6 m3/s (300,000 cfm) . Air travel of 4.8 km (3 miles) into a mine and the same distance back to the fan is not unusual. However, to do so with one intake and one

Jan 1, 1981