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By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-' the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:' and, if some simplifying assumptions about particle shape are allowed, the total number of particles.'2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.' Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968

By T. K. Prentice

ABSTRACTED AND REVIEWED BY E. W. DAVIS,* MEMBER A.I.M.E. THE January-February number of the Journal of the Chemical Metallurgical and Mining Society of South Africa is made up entirely of a discussion of Ball Wear in Cylindrical Mills. Following the principal paper by T. K. Prentice are several remarkably pertinent and carefully prepared discussions. Few persons in this country would be likely to see this publication, and since the information presented is new and of current interest, it seems desirable to abstract and review this publication for the benefit of the members of the A.I.M.E. The purpose of the investigation is stated in the first two paragraphs of Prentice's paper, as follows: Early in 1941, The Chamber of Mines Steel Products, Limited, initiated a series of tests under semi-working scale conditions to determine, if possible, those physical and chemical properties of a ball which make it resistant to wear when used in a cylindrical mill as a grinding medium, with the primary object of incorporating those beneficial qualities in the balls being produced at their works. This paper describes the tests carried out and discusses the results obtained. From these results it was possible to formulate a new theory relating to ball wear in cylindrical mills. This theory is presented in the second portion of this paper. PRACTICAL BALL-MILL TESTS IN A CYLINDRICAL MILL Part I of the paper begins with a discussion of the methods used for the manufacture of grinding balls in South Africa. The following paragraph is of particular interest. The cast steel ingots, 4 ¼ - in. square by 3 ft. 6 in. long, are re-heated in a gas-fired sloping stationary-hearth furnace and then rolled in a six-pass continuous mill into 2 5/8 in. round billets. Some of these billets are then removed and cut into suitable lengths for forging into 4 in., 3 ½ in., 3 in. or 2 ½ in. balls by means of three Drop and two Beché hammers, but the greater number, whilst still at about 1,000 ºC., pass directly into a set of scroll rolls which produce, in an ingenious manner, finished 3 in. balls direct from the 2 5/8 in. billets. Except in special cases, all balls are allowed to cool in the atmosphere and are not water quenched. Details of the Tests In order to enable the reader to evaluate properly the results and conclusions in the rest of the paper and in the discussions following the paper, most of the information presented by the author under this heading is quoted: ….. The testing unit was a nominal 30 in. diameter and 18 in. long centre discharge Denver Ball Mill. The ore pulp to the ball mill comprised a small portion of the normal feed to one of the fourteen City Deep 5 ft. 6 in. X 22 ft. tube mills, and the grinding media consisted of the balls under test plus other balls to give the desired load. The running time of the test-mill was divided into approximately equal periods of five days 13 ½ hours each. The usual procedure was to examine and make up the load

Jan 1, 1944

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By T. D. Mueller, H. Dykstra

This paper describes a method for obtaining compositions of gas and oil phases in equilibrium with each other at a given reservoir temperature and pressure as lean or enriched gas is injected into a reservoir oil not in equilibrium with the gas. The method is based on calculation of equilibrium constants, K, from the equation log Kp = A + B F, where p is pressure and F is component characterization factor. A and B are constants that vary with a composition parameter. The paper explains how A and B could be determined with a minimum amount of data. The method consists of calculating equilibrium constants as a function of liquid composition and using the K's to calculate changes in compositiort of injection gas as it successively contacts original resetvoir oil at the gas-oil front and the change in composition of reservoir oil as it is successively contacted by the injection gas in the vicinity of an injection well. An iterative process is required. Two examples of the method are given which show how oil and gas compositions and properties are calculated with the aid of a computer. INTRODUCTION The calculation of recovery from lean-gas or enriched-gas injection into a saturated or under-saturated reservoir oil requires a knowledge of how phase properties change in a reservoir between injection well and producing well. To determine the phase compositions or properties experimentally would be difficult and time consuming, especially if one wanted to look at the effect of various injection gas compositions. For some fields an engineer would want to make preliminary calculations on the economics of gas injection before he makes the decision to spend a corrsiderable sum of money for laboratory work to obtain the necessary fluid properties. A method for calculatine compositions and properties based on a minimum of laboratory data is described. The minimum amount of data required is injection gas and reservoir oil composition and injection gas solubility as a function of pressure for an undersaturated oil, or the compositions of mixtures of reservoir fluid with two or more enriched gases, which mixtures have a bubble-point pressure that is the same as the expected average displacement pressure. On the other hand, if the economics appear to be attractive, more laboratory data can be obtained in the form of equilibrium constants for three or more mixtures of the reservoir fluid and injection gases. The method is based on the calculation of K's from the equation, log Kp = A + B F, where K is equilibrium constant, p is pressure and F is component characterization factor. This method of plotting K data by means of the above equation is described by Hoffman, Crump and Hocott.1 A and B are constants that vary with a composition parameter. It is shown how experimental data are used to determine how A and B vary with composition. BASIS OF METHOD EQUILIBRIUM CONSTANTS Equilibrium constant (K) data are required for this method. The K of each component is obtained from an equation that gives the product of K and pressure as a function of component characterization factor. The characterization factor F = b(l/Tb — l/T), where b is a constant characteristic of a given component, Tb is the boiling point in OR at atmospheric pressure of the given component, and T is the temperature of the system in OR. This method of plotting K data is described by Hoffman, Crump and Hocott.l The straight-line equation of the log Kp - F plot is log hp = log Kop +BFi, where Kop is at F =0, i designates the component, and B is the slope of the line. The factor F can be

Jan 1, 1966

By R. Lagneborg, R. Gullberg

An X-ray method for determinig volume fractions of phases in textured materials has been developed. The method involves measurements of the integrated intensities of reflections of each phase for one single orientation of the sample. The method was checked by evaluating the phase contents in samples from two stainless Cr-Ni steels containing austenite and ferrite in known amounts. In the present case measurements of about five reflections from each phase were required. The agreement between calculated and known volume fractions was found to be very close. AN X-ray diffraction method is often employed for determining the amounts of two or more phases in a material. The details of the method have been described at several instances.'" In short, the method is based upon the fact that the integrated intensity of a reflection is directly proportional to the volume fraction of the phase considered. In principle, the method only requires the measurement of the intensity of one reflection for each phase. The most severe shortcoming with this method is that it disregards influences from preferred orientation in the material. In a diffractometer, where this type of analysis is most conveniently carried out, the geometry is such that the diffracting planes for a specific Bragg peak are all parallel to the surface of the specimen. This implies that it must be required that the occurrence of the diffracting planes parallel to the specimen surface must be as frequent as for any arbitrarily oriented physical plane of the sample. This requirement will generally only be fulfilled for a material free of texture. Since all materials in reality always exhibit a preferred orientation to some extent. the deficiency of the method is quite serious. In cold-deformed material the texture is appreciable, but also annealed material will in many cases display a considerable texture. The problem of quantitative phase analysis in textured material is one of obtaining the integrated intensity averaged over all orientations of the specimen with respect to the X-ray beam. Lopata and ~ula~ have shown that this can be accomplished by integration of intensities over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. Hence, in this method the average integrated intensity for a specific reflection is obtained by directly determining the intensity for a sufficient number of physical orientations of the sample. However, since an excess of diffracting planes in a certain surface plane necessarily must be accompanied by a deficiency of another type of diffracting plane, it appears to be possible to obtain the correct average intensity for a specific diffracting plane by performing an appropriate averaging of intensities belonging to a large number of diffraction planes of different hkl when all intensities have been produced from one single orientation of the specimen surface. In the present work such a method has been attempted and tested experimentally for two stainless Cr-Ni steels containing austenite and ferrite. 1) THEORY The expression for the integrated intensity of a Bragg reflection diffracted from a phase in a polycrys-talline sample in a diffractometer is: where C is a constant only dependent on the incident X-ray power and the diffractometer geometry, v the volume of the unit cell, F the structure factor, m multiplicity of the diffracting plane, L Lorentz factor, P polarization factor, e-2 temperature factor, p average linear absorption coefficient of the irradiated vO1umej and V volume fraction of the phase 'Onsidered. Hence, the factor R in the abbreviated form of Eq. [I] can be calculated and depends only on 0 and the diffracting plane {hkl}. For an alloy containing two phases, a and y, we can write

Jan 1, 1967

By R. Kerby, T. R. lngraham

The rates of cadmiuln cementation from buffered solutions were studied on both the cylindrical and circular faces of a rotating zinc disk. The activation energies are equivalent on both surfaces, but the rate is more rapid on the cylindrical face. At higher temperatures and at pH values above 6.4, the rate of deposition increases because of an increase in the cathodic area of the deposit. The rate may also be increased by decreasing the thickness of the diffusion layer by rapid stirring. The presence of small amounts of copper, cadmium, lead, iron, or aluminum in the zinc does not affect the cementation rate, but when srnall amounts of copper, cobalt, and arsenic were present in the solution cadmium deposition ceased shortly after it started. Small amounts of copper in solution become cemented with the cadmium to form a coarse deposit of Cd3Cu. When zinc ores containing cadmium are processed for electrolysis, the cadmium appears with the zinc in the leach liquors. Because of the discharge potential of the cadmium ion and the hydrogen overvoltage on metallic cadmium, the cadmium ion must be removed prior to zinc electrolysis to prevent its codeposition. Cadmium is usually removed from acidic zinc sulfate solutions by cementation on zinc. When zinc sheets are used with the appropriate conditions of pH and temperature, a finely divided, high-purity cadmium powder is obtained; it floats to the surface with attached hydrogen bubbles and, after careful washing, may be processed directly to a marketable product.' The reaction on zinc sheets is relatively slow because of the limited amount of exposed cathodic area on the sheets. A much more rapid reaction is obtained when zinc powders are stirred into the solution, but this procedure does have a potential disadvantage: some unreacted zinc may be trapped in the cemented cadmium and thus lower its grade.1 The equilibrium constant at 25°C for the displacement of cadmium by zinc is of the order of lo", which indicates that at equilibrium the displacement would be essentially quantitative and no back reaction need be considered. This indication is not entirely true, however, because in the presence of oxygen any loose cadmium which is out of contact with metallic zinc tends to redissolve after cementation.' The overall effect is much the same as that to be expected if the equilibrium constant were much smaller. Previous experimental work on cementation reac- tions3 is in general agreement that the rates of cementation usually follow first-order kinetics. The metal on which cementation occurs is considered to consist of anodic areas from which metal dissolves and cathodic areas onto which the reactive metal is cemented. For the reaction to continue, the cemented deposit must remain open and porous for the removal of ions. Usually, the deposited metal influences the rate of cementation; when it blocks the pores in the deposit, the rate of cementation will be decreased. Alternatively, when the cemented metal grows as den-drites or as coarse powder the cathodic area is correspondingly increased and the rate of cementation increases,3 Thus, it is only during the initial stages of cementation, prior to the development of deposit effects, that the kinetic behavior of the reaction may be studied without ambiguity. In this paper, experiments will be described for cementation of cadmium from dilute solutions onto the surface of a rapidly spinning zinc cylinder. The effects of ionic concentration, disk rotation speed, temperature, and impurities will be described. APPARATUS AND PROCEDURE The apparatus used for the experiments was described in a previous paper.4 It consisted of a 2-liter vessel in which the contents were protected, against oxidation, by a stream of prepurified nitrogen. The vessel was immersed in a water bath which controlled

Jan 1, 1970

By E. T. Stephenson

Wert and Marx1 pointed out that a straight-line relationship exists between the activation energy of a relaxation process and the temperature at which the maximum relaxation occurs. The data available at the time indicated that this relationship held for a number of Snoek peaks, several grain boundary peaks, and pair relaxation in a brass. Theoretical justification for the observed relationship was found in the following equation, which Wert and Marx derived from the theory of interstitial atomic diffusion coefficients:' where AH is activation energy, R is the gas constant, T is the internal friction peak temperature, v is the interstitial atomic frequency, f is the frequency of the applied stress, S is entropy of activation. More accurate internal-friction data on interstitial diffusion in bcc metals have become available since Wert and Marx's paper. Table I gives activation energies calculated by several authors from a combination of elastic aftereffect data and the peak temperatures at several frequencies of measurement. (In the case of Fe-C and Fe-N, the referenced authors5'7'8'10 also used high-temperature diffusion data.) However, diffusion experiments at 150°C and above1'-13—rather than anelastic techniques—were used to determine the activation energy of hydrogen diffusion in Fe-H. In order to plot this recent data as a AH vs T graph we calculated the peak temperatures of the systems listed in Table I (with the exception of Fe-C, Fe-N, and Fe-H) by using published values3'' of AH and Do. These calculated peak temperatures varied by only a few degrees from experimentally determined peak temperatures. The calculated values were felt to represent the better average. A number of investigators have found the peak temperatures in Fe-C and Fe-N to be 38 to 40°C and 20° to 24°C, respectively. The values of 39" and 22°C (312° and 295°K in Table I) were determined by carefully executed experiments.6'8 The hydrogen peak temperature has been measured at 1 cps,12 20 cps,14 and 35,000 cps.15 All hydrogen peak temperatures were adjusted to 1 cps for Table I using AH = 3000 cal per mole. As Fig. 1 shows, the data of Table I fit a straight line at least as well as the earlier data used by Wert and Marx. Linear-regression analysis was applied to the data in Table I. The Fe-H data was omitted because the activation energy has not been experimentally determined in the temperature range of the peak. The analysis yields the equation: with a standard error of 860 cal per mole. The agreement of the data in Table I with the Wert-Marx equation is excellent. Strict application of Eq. [I] forces the linear regression analysis through the origin. In this case, the analysis gives a slope of 62.1 cal per mole per deg, and a standard error of *890 cal per mole. With this value, it follows from internal-friction theory that Hence, Do varies by only 30 pct among these bcc-interstitial systems. Thus, a concept suggested originally by Wert and Marx1 is confirmed by recently published data. The

Jan 1, 1965

By C. E. Gregor

Current modern trends in mining show that hoisting shafts are being expected to fulfill an important ventilation function. However, where rigid guides and supporting structures are mandatory, ventilating power costs will be high, unless the transverse structures (shaft sets) are streamlined. In the complex configurations of hoisting shaft furniture patterns, either for original design purposes, or for the adjustment of an existing shaft, a useful degree of aerodynamic optimization, by reduction of overall resistance, can only be effectively evaluated by model studies in a special purpose wind tunnel, as described herein. The author has shown that, in one particular case, an annual power cost saving of more than $50,000 was indicated, mainly by the selection of buntons and dividers of improved aerodynamic profile. Mining companies are now realizing the advantages that can accrue through proper attention to the aerodynamic aspects of mine shaft design. With progressive demands of civilization for an ever greater supply of coal and metals, and with greater depths of working, higher rates of extraction, advanced degrees of mechanization, and improved standards of environmental health and work comfort, shaft design is becoming an extremely important aspect of mining operations. In addition, because the cost of sinking, equipping, maintaining, and operating a mine shaft is continually increasing, there is a greater incentive to use a shaft for the maximum duty, consistent with economy. The current natural tendency is therefore to sink multi-purpose shafts, to install as much equipment as is safely and effectively possible to operate; and then, over and above all these functions, to use the shaft to its maximum possible ventilating capacity, as a major, or auxiliary, airway. Clearly, this latter additional function can only be employed at a significant cost, since the most economic operating airways are smooth-lined and devoid of internal rigid furniture. It is true that hoisting functions can be carried out in such shafts if rope guides are used, but only under restricted conditions. Where a manway must be provided, fixed guides and supporting structures are mandatory, and ventilation costs become accentuated. It is generally recognized that the prime element of cost in ventilating a mine can be represented by the power required to drive the fan unit. It is also known that the largest component of total mine resistance is that of the downcast shaft, where this shaft is equipped with rigid guides for hoisting purposes. The pressure loss varies directly as the resistance of the shaft, in accordance with a modification of the Atkinson equation p = RQ2/3600. Furthermore, the air horsepower drawn is given by the equation AHP = (p x 0/33000. Therefore, the power required to drive the fan unit varies as the resistance of the shaft and the cube of the air quantity. Clearly, if Q is a specified minimum, then the only way to minimize the pressure loss (and the power costs) is to reduce the shaft resistance R. (See Table I for a list of symbols.) The resistance to airflow of a shaft equipped with rigid guides and supporting structural sets consists of two components which, for the sake of analytical simplicity, can be regarded as additive. 1) Frictional resistance, represented by the viscous frictional forces within the boundary layer, as air flows along the surfaces of the walls and the periphery of the vertical elements (guides, pipes, cables, ropes, etc.) of the furniture. The friction loss can be readily calculated by the Atkinson equation, after selection of a suitable value for the friction factor K from the McElroy compilation.' KxLxO xQ2 5.2 xA3 Friction loss can be minimized by lining the shaft walls (particularly if of circular or elliptical cross-section) with a smooth continuous lining of monolithic concrete.

Jan 1, 1968

By Rex E. Cheek, Donald E. Menzie

The fluid mapper, a model relatively new to the petroleum industry, was used to study the effect of various mobility ratios on the areal sweepout efficiency for two typical spacing patterns. The experiments indicated the areal sweepout for the five-spot pattern varied from 51.8 per cent at a mobility ratio of 0.093 to 89.1 per cent for a ratio of 24.4. In the direct line-drive pattern, the areal sweepout varied from 58.7 per cent at a mobility ratio of 0.089 to 92.0 per cent at a ratio of 24.8. The fluid mapper may prove useful to determine quickly the effective areal sweepout for any well spacing. INTRODUCTION The effect of the mobility ratio on the areal sweepout efficiency during primary depletion of a water drive reservoir and during secondary recovery operations has recently become more widely recognized The mobility ratio, M, is defined as: _ kjp (displaced fluid) k/u (displacing fluid) where k = effective permeability u = viscosity When the displacing fluid is miscible with the displaced fluid, the permeabilities are equal and the mobility ratio may be expressed as a ratio of viscosities: u (displacing fluid) u (displaced fluid) The mathematical analysis for calculating the areal sweepout efficiency with mobility ratio other than unity is quite tedious.5,11 An experimental method by using a potentiometric model2 in a step-wise manner and in using an X-ray shadowgraph model3,12 with continuous fluid flow has been published. Several types of models have been used to study oil and gas reservoir performance. These models may be classified as physical, electrolytic, potentiometric, X-ray shadowgraph, and fluid mapper. The X-ray shadowgraph and fluid mapper are models relatively new to petroleum engineering and have not been used extensively for specific applications. The theory of the fluid mapper indicates it may be adapted to a study of areal sweepout efficiencies for various mobility ratios as well as other complex problems in petroleum engineering. The use of the model and results obtained when using displacing and displaced fluids of equal densities but different viscosities are discussed. FLUID MAPPER DEVELOPMENT H. S. Hele-ShawV eveloped a fluid mapper model based on the hydrodynamic theory. This theory is that in the steady flow of a viscous fluid between horizontal parallel plates spaced a very small distance apart, the effect of viscous shear is of such magnitude in the vertical plane that the motion in the horizontal plane is practically undisbrted streamline flow. Techniques developed by Hele-Shaw were not expanded and no additional developments in fluid mapper models were forthcoming until A. D. Moore, University of Michigan, published a series of papers starting in 1949, which describe the construction of a flexible and inexpensive model'h nd the fluid mapper technique for the solution of certain problems.' The essential components of the fluid mapper as developed by Moore are::.ln 1. A base slab. made of dental stone (calcium sulphate and water). which is shaped to represent the prototype. 2. Plate glass slightly larger than the slab and spaced

Jan 1, 1956

By J. E. Hilliard

AS is well-known, the length per unit volume, Lv, of any lineal feature (such as grain edges in a polycrys-talline specimen) can be estimated from a count of the number of point intersections with a random plane of polish. Specifically:' Lv = 2NA in which NA is the expected number of intersections per unit area of the plane. As with all other measurements in quantitative metallography, the estimation of Lv is subject to a sampling error, the magnitude of which will depend on the number of observations. The analysis is usually performed by counting the number of intersections falling within a closed test figure of known area applied to a succession of different areas on the plane of polish. The test figure can be drawn directly on the screen of a projection microscope or else superimposed on the image of the structure by means of a reticule in a focusing eyepiece of an ordinary microscope. The use of micrographs is very inefficient unless, as in the present study, these are also needed for some other purpose. Consider an analysis in which n applications are made of a test figure within which the expected number of intersections is N. The expected total number of intersections counted is then given by NT = nN If (N) is the standard deviation in N for one application of the figure and if the latter is applied to non-overlapping regions so that the N's are independent in the statistical sense, then the standard deviation in Nt is given by: a(NT) = a(N)vn Eliminating n from Eqs. [2] and [3] we obtain: Thus, k will be a constant for a given specimen and test figure. From Eqs. [ I] and [4] we find As is to be expected, therefore, the fractional error in the estimation of Lv is inversely proportional to the square root of the total number of intersections counted. It is very desirable to have at least a rough estimate of k before starting an analysis, since it will then be possible to decide in advance by use of Eq. [5J how many counts should be made in order to achieve the desired accuracy in Lv. Without such information the investigator, unless lucky, will either do needless (and tedious) work or else obtain a result with too large an error. It is very easy to calculate k for the limiting case of N — 0, i.e., when the test figure is vanishingly small. In this case there is a negligible probability of two or more intersections falling within the figure. There are therefore only two possible outcomes: a count of one with a probability of, say, p and a zero count with a probability of (I-p). Thus and Therefore: We might expect k to depend on N and therefore on the size of the test figure. Such a dependence was observed2 in the analogous case involving the estimation of grain-boundary area per unit volume by a count of the number of intersections of a test circle with traces of the boundaries on the plane of polish. In this case the theoretical value of k at the limit N — 0 was 1.41. It was also predicted that k would display an initial sharp decrease with increasing N. Experimentally, k was observed to decrease to a value of 0.62 at N - 6 and thereafter remain approximately constant. Furthermore, the value of k for N > 6 was found to be insensitive to the form of the structure provided no pronounced anisotropy or grain-size variation was present. In order to determinewhether k would exhibit a similar dependence on N in the estimation of grain-

Jan 1, 1967

By E. H. Crabtree, Neil S. Parker

The custom milling plant of the Eagle-Picher Mining and Smelting Co. is at Sahuarita, Arizona, approximately 20 miles south of Tucson. It is connected by a 2-mile railroad spur to the main line of the Southern Pacific Railroad between Tucson and Nogales. The capacity of the plant is 500 tons per day. The mill is conventional except perhaps in the rather wide variety of ores treated. These vary from straight copper ores, from which only one concentrate is produced, and lead-zinc or copper-zinc ores from which two concentrates are produced, to complex gold-silver-copper-lead-zinc ores, which require the simultaneous production of three or lour concentrates. Custom ores are received in lots varying in size from a few truckloads to several carloads. Similar ores, after crushing and sampling, may be commingled, or individual lots may be milled individually. The ores are first dumped either into one of two 200-ton railroad bins, or into one of the two 75-ton truck bins. From these bins the lot of ore is individually crushed in a 24 by 16-in. jaw crusher to 3-in. size, and then to ½-in. size in a 3-ft Symons shorthead crusher. After crushing to ½-in., the ore is conveyed to the automatic sampling plant. This consists of three Vezin samplers in series, each successively cutting out 10 pct, 10 pct and 5 pct of its feed. After No. I sampler, the material passes through a mixing barrel and is then crushed to -in. in a set of rolls before passing to No. 2 sampler. Between No. 2 and No. 3 samplers, the ore is again mixed in a mixing barrel. The final sample, consisting of one pound per ton of ore, is taken to the laboratory, where it is further crushed to 1/8-in. in a coffeemill, and then riffled down to the size required for grinding in a pulverizer. The capacity of the crushing and sampling plant is up to 100 tons per hour, depending upon the character of the ore. After sampling, the ore is stored in five ore-storage bins, consisting of four 200-ton bins and one 175-ton bin. Each of these bins is discharged by means of belt feeders and conveyor to the ball mills, so that ores may be composited for milling in any required ratio, or milled separately by themselves. Fine grinding is done in one 6 by 4-ft Allis-Chalmers ball mill and one 8-ft by 36-in. Hardinge mill. These two mills both discharge to one 54-in. Akins Simplex High weir classifier. The classifier sands can be returned to either or both mills, so that flexibility in grinding for different ores is easily obtained. Flotation equipment consists of four 66-in. Fagergren machines for copper-lead roughing and six similar machines for zinc roughing. Lead-copper bulk concentrate is cleaned and recleaned in eight No. 18-S Denver machines, and zinc concentrate is cleaned in three 66-in. Fager-grens. Copper-lead differential separation

Jan 1, 1949

By Harvey T. Kennedy, Erasmo T. Guerrero

In this investigation, the effects of the surface tension of brine and the interfacial tension between oil and brine on the recovery of oil by water flooding of Woodbine sand were studied. Variation of the surface forces was obtained by the addition of small amounts of commercially available chemicals, which did not appreciably change the surface tension of the oil. Fourteen surface-active agents, which were found to be effective in lowering the surface and interfacial tensions, were further investigated to determine the extent of their adsorption by the Woodbine Sand cores. It was found that adsorption was sufficient in all cases to prevent any substantial concentration of chemical at the flood front. The flow system was, therefore, brought to equilibrium with definite concentrations in the flood water by circulation before each test. The data thus have no relation to the results obtainable by using the chemicals in full-scale water floods, but should be helpful in predicting the performance of surface-active chemicals which are not lost by adsorption, if such can be found. Flow tests were made on various concentrations 01 six chemicals selected from the 14 investigated for surface activity and adsorption, with and without the presence of gas in the core. It was found that lowering the interfacial tension had a tendency toward reducing the recovery of oil and that the reduction of the surface tension of the brine had little or no effect. A substantial beneficial effect, however, resulted from the presence of gas in the cores. INTRODUCTION The movement and distribution of crude oil in a porous medium are governed by such factors as surfacc and interfacial tensions, viscosity of the oil, pore size configuration, and wetting characteristics of the medium. The knowledge of the part played by each of these factors is limited. If the oil is assumed to be distributed in droplets whose movement is restricted only by the pore openings, the following equation may be applied: ?P= 2r(1/r1-1/r2) .......(1) In this equation ?P is the pressure drop necessary to force an oil droplet through the construction, r is the oil-brine interfacial tension, r1 is the radius of curvature at the forward and smaller end of the deformed droplet, and r2 is the larger radius. This equation neglects the effects of viscosity, as a static or near static condition is assumed. It would apply equally well for a bubble of gas in liquid if r were taken as the surface tension of the liquid. This relation shows that droplets can be more easily displaced if the interfacial tension is decreased. The displacement of oil from the surface of a sand particle may also be considered from the basis of selective wetting assuming that the oil droplets are smaller than the pore constructions and that the sand surfaces may be considered as planes. A relation of the forces involved can be derived from Dupre's equation to give: Wos = row (1 +Cos?)........(2) where Wos = Work of adhesion between the sand and the oil row = Oil-water interfacial tension 0 = Contact angle ros = Oil-solid interfacial tension This equation would indicate that the displacement of oil from a sand surface is more readily obtained when the water-oil interfacial tension is reduced provided the contact angle remains constant. Evidently. however, the values of Cos 0 may vary along with the water-oil interfacial tension due to changes in the other surfaces of the system. The above theoretical considerations suggest that perhaps even the static behavior of a dispersed oil phase in a porous medium is considerably more complex than may be inferred by the simple systems

Jan 1, 1955

By Reed W. Hyde

SOME information has been published on the sulphur dioxide concentration of gases from Dwight-Lloyd machines sintering lead ores but most of this relates to the customary practice in which the charge is relatively high in lead and is sintered in two passes over the machine. It is thought, therefore, that the following observations on sintering in one pass a low-lead, low-sulphur charge may be of interest. The data were obtained in sintering lead sulphide flotation concentrates mixed with minus 20-mesh oxide ore, the mixture carrying 16.8 per cent Pb and 5.3 per cent S. No returns were used because of the limited amount of sulphur available as fuel, but the mixture pelletized readily to make a satisfactorily permeable bed on the sintering machine. As there was a possibility that the SO2 might be utilized, a series of runs was made to determine the concentration of S02 in the gases at different points along the wind box, and the effect on this concentration of changes in the wind-box vacuum. Several runs each were made with vacuums (as measured in inches of water at the wind box) of (1) 2 to 1 1/3 in., (2) 4 to 3 1/2 in. and (3) 6 to 5 1/8 in. The averages of the determinations from each series are platted on the graph (Fig. I). The vertical scale shows the percentage by volume of SO2 (as determined by the Reich method), and the horizontal scale shows the time expressed as percentage of the total sintering time. Sintering was considered to be complete when no S02 could be detected in the gases. In all cases the depth of bed was 4 ½ in. and the weight of dry charge per square foot of hearth area was 45.2 lb. Other data are given in the table. The volume of gases corresponding to the several points along the wind box at which S02 determinations were made could not be measured, but has been calculated from the S02 content and sulphur elimination on the assumption that the volume is uniform throughout the sintering period. This is not strictly true, as with a given vacuum the volume will usually drop slightly toward the middle of the period and increase toward the end. However, this assumption is a reasonable approximation. Several interesting features are brought out by these data. In general, the published data on S02 concentration in sintering under ordinary conditions show a high S02 concentration in the early stages followed by a rapid decrease in concentration and with relatively little SO2 in the gases from the last half or third of the operation. In other words, the greater part of the sulphur elimination is obtained in the first third or half of the period. In these runs, the 6-in. vacuum, which approximates the usual operating condition, gives a curve that follows this customary pattern. Maximum S02 concentration is obtained 2 ½ min. after

Jan 1, 1942

By R. Schuhmann, E. J. Michal

Experimental measurements are reported for the oxygen pressures of iron-silicate slags in equilibrium with solid silica. CO2-CO mixtures were bubbled through the slags in silica crucibles to find equilibrium values of p co2/p co over the entire composition range of silica-saturated slags at 1250°, 1300°, and 1350°C. From the data, the activity vs. composition relationships were calculated for O, FeO, and Fe. SLAGS composed primarily of silica and iron oxides have particular practical importance in copper smelting,' in acid steelmaking, and in accounting for the service behavior of silica refractories. These slags all contain both ferrous and ferric iron, so that, strictly speaking, they are ternary or three-component liquid solutions. For convenience, the components may be taken as the three oxides, FeO, Fe2O3, and SiO2. The constitution of the FeO-Fe,O,-SiO, system at slagmaking temperatures has been studied in a recent investigation described in a separate paper.' This work showed the compositional ranges of iron-silicate melts at temperatures up to 1450°C and also the temperature-composition relationships for melts in equilibrium with various solid phases, including iron, wüstite, magnetite, and silica. Broadly speaking, the compositions of iron-silicate melts at a given temperature should be thought of as varying over a two-dimensional field. In the first place, the silica/total iron oxide relationship varies from maximum silica for silica-saturated melts to minimum silica for wüstite-saturated melts or, at higher temperatures, to zero silica for straight iron oxide melts. In copper smelting, for example, the converter slags approach the low silica limits while the reverberatory-furnace slags have intermediate silica contents, perhaps approaching silica saturation in some circumstances. Liquids formed in the pores of silica refractories presumably are close to silica saturation. The second type of composition variation is in the ferric/ferrous relationship, which depends on how oxidizing or how reducing the process conditions are. Relatively reducing slags, such as acid-steelmaking slags, are lower in ferric oxide and ap- proach saturation with metallic iron. Oxidized slags, such as copper-smelting slags, contain larger percentages of ferric oxides and approach or reach saturation with magnetite. Since these two kinds of compositional variations are closely related to two general properties of interest for all metallurgical slags, basicity, and oxidizing power, it is hoped that the thermodynamic study of iron-silicate slags eventually will throw further light on the significance and nature of these long-recognized but as yet poorly understood slag properties. Measurements of oxygen activity as a function of slag composition, using CO-CO2 gas mixture to fix oxygen activities, afford an experimentally convenient approach to the study of the thermodynamic properties of iron-silicate slags. In a preceding investigation,³ his approach was used in a systematic study of iron-silicate slags in equilibrium with solid iron. The present paper gives the results of a similar study of the iron-silicate slags in equilibrium with solid silica. The experimental work consisted in the determination of CO2: CO ratios in gas mixtures at equilibrium in the system: gas: liquid slag: silica Determinations were made at temperatures from 1250° to 1350°C for slags ranging in composition from iron saturation to magnetite saturation. Also, equilibrium CO,: CO ratios and slag compositions were determined for the univariant systems: gas: liquid slag: silica: iron gas: liquid slag: silica: magnetite Experimental Methods The experimental procedure was essentially the same as that used in the previous study of iron-silicate slags saturated with solid iron," but in order to work with the silica-saturated slags an all-silica crucible assembly was used. A liquid slag was prepared from pure prefused stock materials and brought to equilibrium with the silica crucible at the desired temperature. Then a mixture of CO2 and CO was continuously bubbled through the melt

Jan 1, 1953

By R. S. Rickard, M. C. Fuerstenau

Anodic polarization curves for iron dissolution and cathodic polarization curves for copper deposition and ferric and hydrogen ion reduction were studied. These results were used to predict the relative rates of the reactions: The rates of the first two reactions were found to be first order with respect to the reacting ion, and the rale-controlling step was diffusion of the ions to the callzode surface. The rate of hydrogen ion reduction in an oxygen-free solution is dependent on the reciprocal of the square root of the hydrogen ion activity. In solutions containing oxygen, the rate of hydrogen reduction becomes dependent on the square root of the partial pressure of oxygen. At equal concentrations copper precipitation occurs about twice as fast as ferric ion reduction. In an air-saturated solution containing 0.01 M cupric ion at pH 2, the rate of hydrogen ion reduction zs about 10 times slower than that of copper precipitation. At pH values below 3, the rate of hydrogen reduction in oxygen-free solutions is very slozu. COPPER cementation has been utilized industrially for many years as a means of recovering copper from aqueous solutions. There are many different types of cementation plants, but all simply provide a means of contacting iron with relatively dilute copper solutions. In the past little or no attention has been paid to rates or mechanisms of the reactions involved. As a result, this and other studies'-3 have been undertaken recently to establish the important parameters in this system. The reactions involved in copper cementation by iron are: Since transfer of charge is involved in every case, these reactions should be considered from an electrochemical point of view. In any electrochemical system involving electrolytic conduction, passage of electrons necessitates ion transfer to the respective electrodes according to Faraday's law. The current in the system will be proportional to the rate of ion transfer, and, therefore, when the current in the galvanic cell is known, the rates of the reactions involved can be determined. Galvanostatic electrode measurements5" are applicable for these electrochemical studies, in that with this technique polarization curves (current density vs electrode potential) are established by impressing a constant current through an electrode and measuring the electrode potential. Once the current density, electrode potential, and reacting area are known for each reaction in this cementation system, the rates of the iron-consuming reactions can be determined. EXPERIMENTAL MATERIALS Several metal electrodes were used in this investigation; they are shown in Table I. Solutions were made with reagent-grade salts and conductivity water. Air, nitrogen, and oxygen were employed. All of these gases were saturated with water and degreased prior to use. EXPERIMENTAL PROCEDURE The experimental work was divided into two general areas. The first area involved galvanostatic measurements, which were used to determine the rates of reactions as a function of various parameters. The second area comprised actual cementation experiments to check the rates predicted from the electrode measurements. Galvanostatic Electrode Experiments. Polarization curves were obtained using a standard galvanostatic technique5'= with the apparatus shown in Fig. 1. The various electrode polarization experiments were run the same way except for changes in solution composition, polarity, and type of measured electrode. The general procedure involved the following steps: 1) a solution was made 0.5 M in sulfate ion and to the desired cation concentrations; this solution was placed in a constant-temperature bath and saturated with the desired gas; 2) the electrodes were cleaned and placed in the electrode holder; 3) the previously cleaned apparatus was assembled and immersed in a constant-temperature water bath (temperature controlled to ± 0.05"C); 4) the electrode was then positioned; the solutions were introduced, and the polarization meas-

Jan 1, 1969

By T. H. Alden

T. H. Alden (General Electric Research Laboratory)—This paper as well as earlier ones of Dr. Wood represent an important contribution to the experimental description of fatigue fracture. The mechanism of fracture proposed by the authors, however, is not established by this data nor supported by other data existing in the literature. Although taper section metallography provides a rather detailed picture of fatigue crack geometry, photographs so obtained must be interpreted with care. The narrow bands revealed by etching, frequently associated with surface notches, are labeled by the authors "fissures". Measurement shows, taking into account the 20 to 1 taper magnification, that the depth of these structures is at most 2 to 3 times the width. This distinction is important in the conception of a mechanism of crack formation. It is difficult, for example, to imagine a deep, narrow fissure arising from a "ratchet slip" model. A surface notch, on the other hand, may form easily by this mechanism. The notches observed in the present work are the subsurface evidence of the surface slip bands or striations in which fatigue cracks are known to originate.4-6 It is clear that an understanding of the structure of these slip bands is of key importance in understanding the mechanism of fracture. The evidence presented shows that these regions etch preferentially, possibly because they contain a high density of lattice defects, or as the authors state equivalently, because they are "abnormally distorted." However, it is not possible to conclude that the distortion consists of a high density of vacant lattice sites. The fact of a high total shear strain in itself does not assure a predominance of point defects as opposed to other defects, for example, dislocations. Other evidence in the literature which suggests unusual densities of point defects formed by fatigue7-' refers not to the striations or fissures, but to the material between fissures (the "matrix"). If a choice must be made, the preferential etching would seem to be evidence for a high dislocation density, since dislocations are known to encourage chemical attack in copper;g no such effect is known for the case of point defects. A third alternative is that the slip bands are actually cracked, but that near its tip the crack is too narrow to be detected by the authors' metal-lographic technique. In this case the rapid etching can be readily understood in terms of the increased chemical activity of surface atoms. Unless a vacancy mechanism is operative, the motion of dislocations to-and-fro on single slip planes will not lead to crack growth. Point defect or dislocation loop generation are the principal non-reversible effects predicted by this model. In any case, the nonuniform roughening of the surface in a slip band6 requires a flexibility of dislocation motion which is not a part of the to-and-fro fine slip idea. The same is probably true of crack growth by a shear mechanism. Either some dislocations must change their slip planes near the end of the band and return on different planes,'0 or dislocations of opposite sign annihilate." The mechanism by which these processes occur in copper at room temperature or below is that of cross slip. Thus cross slip appears to be essential to fatigue crack growth.6'10"12 The fact that a tensile stress opens the slip bands into broad cracks does not indicate the structure of the bands or the mechanism by which cracks form. The charactersitic concentration of slip into bands during fatigue shows a low resistance to shear strain in these regions. (This fact in itself may be inconsistent with a high concentration of vacancies.) The authors contend also that continuing shear produces an additional mechanical weakening so that the bands fracture easily (are pulled apart) under the influence of the superimposed tensile stress. It is equally possible that the only weakness is a weakness in shear, that the crack propagates by a shear mechanism, and that subsequently the tensile stress pulls the crack apart. Even the direct observation of bands opened by a tensile stress would not be conclusive since, as argued above, they may be fine cracks. The same argument applies to internal cracks, their existence in the presence of a tensile stress not indicating the mechanism of formation. Internal cracks originating in regions of heavy shear have also been seen following tensile deformation of OFHC copper,13 so that this mode of fracture is not unique to combined tensile and fatigue straining. The authors point out in their companion report14 that 90 pct of the cracks formed during pure tor-sional strain were within 8 deg of the normal to the specimen axis. If the tensile stress were an important factor in crack propagation, it is surprising that the cracks cluster about the plane in which the normal stress vanishes. Similarly, a study of zinc single crystals showed that for various orientations the life correlated well with the resolved shear stress on the basal plane,'= and was not dependent on the normal stress across this plane. W. A. Wood and H. M. Bendler (Authors' reply) -Dr. Alden's discussion emphasizes the essential point in the relation of slip band structure to

Jan 1, 1963

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By Reed W. Hyde

SOME information has been published on the sulphur dioxide concentration of gases from Dwight-Lloyd machines sintering lead ores but most of this relates to the customary practice in which the charge is relatively high in lead and is sintered in two passes over the machine. It is thought, therefore, that the following observations on sintering in one pass a low-lead, low-sulphur charge may be of interest. The data were obtained in sintering lead sulphide flotation concentrates mixed with minus 20-mesh oxide ore, the mixture carrying 16.8 per cent Pb and 5.3 per cent S. No returns were used because of the limited amount of sulphur available as fuel, but the mixture pelletized readily to make a satisfactorily permeable bed on the sintering machine. As there was a possibility that the SO2 might be utilized, a series of runs was made to determine the concentration of SO2 in the gases at different points along the wind box, and the effect on this concentration of changes in the wind-box vacuum. Several runs each were made with vacuums (as measured in inches of water at the wind box) of (1) 2 to 1 3/4 in., (2) 4 to 3 1/2 in. and (3) 6 to 5 1/8 in. The averages of the determinations from each series are platted on the graph (Fig. I). The vertical scale shows the percentage by volume of SO2 (as determined by the Reich method), and the horizontal scale shows the time expressed as percentage of the total sintering time. Sintering was considered to be complete when no SO2 could be detected in the gases. In all cases the depth of bed was 4 1/2 in. and the weight of dry charge per square foot of hearth area was 45.2 lb. Other data are given in the table. The volume of gases corresponding to the several points along the wind box at which SO2 determinations were made could not be measured, but has been calculated from the SO2 content and sulphur elimination on the assumption that the volume is uniform throughout the sintering period. This is not strictly true, as with a given vacuum the volume will usually drop slightly toward the middle of the period and increase toward the end. However, this assumption is a reasonable approximation. Several interesting features are brought out by these data. In general, the published data on SO2 concentration in sintering under ordinary conditions show a high SO2 concentration in the early stages followed by a rapid decrease in concentration and with relatively little SO2 in the gases from the last half or third of the operation. In other words, the greater part of the sulphur elimination is obtained in the first third or half of the period. In these runs, the 6-in. vacuum, which approximates the usual operating condition, gives a curve that follows this customary pattern. Maximum SO2 concentration is obtained 2 ½ min. after

Jan 1, 1942