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By E. C. Lee

THE safety of mine workers has received more attention from both State and Federal law-making bodies than any other industry, a fact that shows clearly the hazardous nature of the industry. The last, but by no means the least, of the measures adopted for the protection of mine workers, is workmen's compensation legislation. This is proving to be a powerful instrument for greater safety in the industries, from the fact that special stress is laid not on how the accident happened or who may have been responsible for it, but on how badly the employee is hurt by it. The injured person does not have to employ lawyers to prove his case, because the mere fact of his employment is proof of his right to compensation. The immediate effect of such legislation is the certainty confronting the mine operator that he must pay out large sums for every accident, regardless of its cause, thus adding materially to the cost of the production of his coal. This fact furnished to the operator the strongest incentive to reduce the causes of accidents; not that the operator has ever lacked reasonable consideration for the welfare of his employees and a proper humane interest in their safety, but his engrossment in earning his daily livelihood has been so great that he has not felt that he had the time to devote to the safety of the operation. This time he must now find because of the actual-cash value of the prevention of accidents in his mines. This agency alone proved inadequate to bring about a material improvement because operators have always been willing enough to improve safety conditions when possible to do so within reasonable limits of their financial ability. The requirement in the Workmen's Compensation Laws of several of the States, that the mine operator shall insure as a guarantee of his ability to meet his compensation obligations, has furnished the needed incentive, moral and financial, necessary to the prompt and effective dissemination of a more general knowledge of the causes and

Jan 10, 1917

By C. S. Smith

The solubility of tantalum at 1100°C is 0.025 pct in pure copper, 1.2 pct with 20 pct Ni, and 2.7 pct with -30 pct Ni. The solubility decreases with temperature, and the alloys are precipitation hardenable. A 79/20/1 Cu-Ni-Ta alloy reaches maximum hardness after aging at about 750°C and, if cold worked, does not recrystal-lize below that temperature. The alloys have good tensile properties at moderately elevated temperatures and, since they can be hot and cold worked nearly as easily as cupronickel, they are suggested for service at temperatures above the usual limits for copper alloys. MASSIVE tantalum dissolves extremely slowly in copper-rich alloys, and tantalum powder forms refractory surface layers which prevent its solution unless special precautions are taken. After many trials, an 80 pit recovery was consistently obtained by using a mixture of a finely divided tantalum powder with two or three times its volume of potassium tantalum fluoride (K2TaF1,-melting point about 750°C) poured in a slow stream directly on to the surface of the molten copper alloy, so that each particle would remain coated with flux and be immediately and individually wetted by the molten metal. A 50-50 nickel-tantalum alloy has a melting point of about 1400°C and small lumps of it slowly but satisfactorily dissolve in molten copper-nickel alloys as does commerical "ferro-tantalum." The high affinity of tantalum for carbon makes it necessary to avoid carbonaceous crucibles. COPPER-TANTALUM ALLOYS Castings with good shrinkage resulted when 0.1 pct Ta or more was added to copper melted under charcoal and cast in air. Copper in two-pound melts to which 0.1, 0.15, and 0.2 pct Ta had been added retained residual amounts, by analysis, of 0.025, 0.023 and 0.026 pct, respectively. The solubility of tantalum in molten copper at about 1200 °C is therefore about 0.025 pct. The electrical conductivity of these three samples was 100.48, 100.00 and 100.20 pct IACS in the annealed condition, and 98.24, 97.98 and 98.08 in the cold-drawn condition. Wires 0.080 in. in diam withstood from thirteen to nineteen reversed bends after annealing for 30 min in hydrogen at 850°C and the metal was therefore completely deoxidized. The annealing temperature corresponding to 50 pct loss of work hardness in 1 hr in a strip cold rolled 77 pct reduction was 175C, compared to 230°C for equivalent undeoxidized material. It is unusual for a decrease of recrystallization temperature to result from an alloying addition, and the tantalum probably combines with and removes some minor impurity in the original copper that restrained its recrystalliza- tion. No difficulty whatever was encountered in hot or cold rolling or drawing these ingots, and were tantalum not so expensive it would make an excellent deoxidizer for copper. COPPER-NIcKEL-TANTALUM ALLOYS Studies were made of the solubility of tantalum in a large number of copper-rich alloys, but of these significant solubilities were found only in the case of an iron alloy (which, however, separated into two immiscible liquid layers) and alloys of copper and nickel, in which tantalum is freely soluble and which were found to have interesting properties. The latter alloys are the subject of U. S. Patent No. 2,430,306 (1947). They are not at present available commercially. The Ternary Constitution Diagram—The copper-rich corner of the constitution diagram was constructed on the basis of microscopic examination of samples of various composition and treatments. The alloys were hot rolled to 0.25 in. from castings 0.625 in. thick, then annealed for 1 hr at 1000°C, quenched, cold rolled to 0.10 in. and finally annealed for various periods of time at temperatures between 800" and 1100°C in a nonoxidizing atmosphere and quenched. When the solid-solubility limit had been transgressed, particles of a compound believed to be Ni2Ta*were

Jan 1, 1960

By C. Graeme-Barber, R. L. Bell, T. G. Langdon

An analysis is made of the formulas and ,methods used to estimate the contribution of grain boundary sliding to the overall strain of a polycrystal. The errors involved in the approximations and/or ,mistakes in earlier work are assessed quantitatively so as to make possible the critical use of previously published data. SINCE it has been found that, under conditions of very slow creep, the strain due to grain boundary sliding (?gb) may contribute as much as 80 pct of the total creep strain,1,2 it is obviously important to have reliable methods for estimating this grain boundary strain. In two recent papers Stevens3,4 has drawn attention to the pitfalls encountered in assessing ?gb. He criticizes 1) the assumptions made in the derivation of some of the formulas for ?gb, and 2) the indiscriminate averaging procedures used for obtaining the quantities substituted in these formulas. These and further criticisms of earlier work are mostly valid. Unfortunately the only formulas and procedures recommended are either impossible or very difficult to apply in practice. Furthermore no attempt is made to assess the errors involved by the earlier approximations or mistakes, and so it is not possible to make critical use of any of these early dab. The present article attempts to improve on these shortcomings by reference to empirical verification of easily applied formulas whose theoretical derivations involve some otherwise unjustifiable assumptions, and by a quantitative assessment of the errors in previous work. DEFINITIONS First it is necessary to define the terms and symbols to be used. The choice of symbols preferred here is a logical combination and extension of the v introduced by McLean5 and the u by Brunner and rant.' In Fig. 1 the two grains X and Y are displaced by the sliding vector AC. u is the component of sliding resolved along the stress axis, v is that measured perpendicular both to the stress axis and to the specimen surface, and w is that measured perpendicular to the stress axis but in the plane of the surface. Two angles define the orientation of the grain boundary: 8, between the stress axis and the surface trace of the boundary, and +, the internal angle on a longitudinal section cut perpendicular to the surface. In computing the strain resulting from the boundary displacement at all the in- dividual boundaries in a polycrystal the components u, v, or w are sometimes averaged along a longitudinal line (i.e., parallel to the stress axis), sometimes along a transverse line, and sometimes at randomly chosen boundaries. Averages obtained in these three ways are given subscripts 1, t, and r, respectively. Stevens rightly calls attention to the possibility of non-equiaxed grain shapes either at the start or at the end of deformation. In this article all values of numbers of grains per unit length will refer to measurements made before deformation. The subscripts 1 and t will be used for the number of grains per unit length obtained along longitudinal and transverse lines, r for that obtained by averaging along a number of randomly directed lines. FORMULAS FOR ?gb ?gt, as a Function of u. An obvious truth is that cgb can, in principle, be obtained by summation of all the v components at the boundaries intersected by a longitudinal line of known length I, viz.: where nl is the number of grains per unit length, parallel to the stress axis, in the unstrained specimen. There are assumptions in the analytic derivation of Eq. [I] due to Brunner and rant' but ~achinger' arrived at Eq. [la] by a rigorous method. Unfortunately the experimental procedure required by Eq. [ la] proves very difficult as boundary migration tends to obscure the points at which the longitudinal line meets the grain boundary and the errors on such measurements tend to be large, see Fig. 2. For example, on a specimen of Magnox AL 80 at a creep strain of 9.7 pct, 300 measurements of u obtained from the points of intersection of a longitudinal line with the grain boundaries gave ul = 8.95 ± 3.58 pm, or an error of ±40 pct, at the 95 pct confidence limit. These large errors due to migration may be avoided by measuring u from the separation of the segments

Jan 1, 1968

By W. L. Crentz, E. E. Donath, D. Doherty

IN 1948, the United States used nearly six million barrels of petroleum products every day. Although substitution of synthetic fuels for the natural petroleum product is not here yet, large quantities of special-purpose coal will be required in ever-increasing volume as the domestic production of oil from other sources fails to meet demand and the production of synthetic fuels begins. Petroleum economists do not agree as to when the shortages of domestic oil will appear; but the increasing per capita consumption of oil, coupled with a constantly growing population drawing on a potential domestic oil supply estimated to be 85 billion barrels, sooner or later will result in demand exceeding domestic supply. When this situation comes about, the excess demand will be either eliminated by curtailment of consumption or the demand met by increasing importation of foreign oil or by the production of synthetic fuels. The first recourse would definitely retard the heretofore unbroken rise in American living standards, while dependence upon a foreign oil supply during a war or other emergency would be dangerous. On the other hand, the enormous coal reserves in the United States, plus sizable deposits of oil shale, indicate adequate means of augmenting a diminishing domestic oil supply. Some idea of the impact of an expanding synthetic liquid fuels program on the coal-mining industry may be gathered when it is considered that to supply just half of our present-day petroleum needs synthetically from coal would increase the coal output by about 500 million tons annually, using an 11,900 Btu bituminous coal as the plant feed. If either a subbituminous coal or lignite were used, the quantity required would be materially increased. Synthetic Fuel Processes: The principal synthetic fuel processes using coal as a raw material are the Bergius, or coal-hydrogenation process, and the Fischer-Tropsch, or gas-synthesis process. These two processes not only produce different end products, but the preparation of the coal used in each presents its own individual problem to the coal-preparation engineer. The hydrogenation process brings together a mixture of dry, finely powdered coal, catalyst, and heavy oil to form a paste. Addition of hydrogen under rather high pressure and temperature conditions brings about transformation of the coal to a liquid product, from which a high-grade gasoline and other motor fuels may be obtained. The Fischer-Tropsch process requires the production of synthesis gas, a mixture of carbon monoxide and hydrogen. At the Bureau of Mines Louisiana, Mo., demonstration plant, this gas is being made by reacting dried pulverized coal with carefully controlled volumes of oxygen and superheated steam. After purification and in the presence of the proper catalyst and suitable conditions of pressure and temperature, the hydrogen and carbon monoxide components of the synthesis gas react to form motor fuel. The two processes are not competitive but rather com-

Jan 1, 1951

By E. E. Donath, W. L. Crentz, D. Doherty

IN 1948, the United States used nearly six million barrels of petroleum products every day. Although substitution of synthetic fuels for the natural petroleum product is not here yet, large quantities of special-purpose coal will be required in ever-increasing volume as the domestic production of oil from other sources fails to meet demand and the production of synthetic fuels begins. Petroleum economists do not agree as to when the shortages of domestic oil will appear; but the increasing per capita consumption of oil, coupled with a constantly growing population drawing on a potential domestic oil supply estimated to be 85 billion barrels, sooner or later will result in demand exceeding domestic supply. When this situation comes about, the excess demand will be either eliminated by curtailment of consumption or the demand met by increasing importation of foreign oil or by the production of synthetic fuels. The first recourse would definitely retard the heretofore unbroken rise in American living standards, while dependence upon a foreign oil supply during a war or other emergency would be dangerous. On the other hand, the enormous coal reserves in the United States, plus sizable deposits of oil shale, indicate adequate means of augmenting a diminishing domestic oil supply. Some idea of the impact of an expanding synthetic liquid fuels program on the coal-mining industry may be gathered when it is considered that to supply just half of our present-day petroleum needs synthetically from coal would increase the coal output by about 500 million tons annually, using an 11,900 Btu bituminous coal as the plant feed. If either a subbituminous coal or lignite were used, the quantity required would be materially increased. Synthetic Fuel Processes: The principal synthetic fuel processes using coal as a raw material are the Bergius, or coal-hydrogenation process, and the Fischer-Tropsch, or gas-synthesis process. These two processes not only produce different end products, but the preparation of the coal used in each presents its own individual problem to the coal-preparation engineer. The hydrogenation process brings together a mixture of dry, finely powdered coal, catalyst, and heavy oil to form a paste. Addition of hydrogen under rather high pressure and temperature conditions brings about transformation of the coal to a liquid product, from which a high-grade gasoline and other motor fuels may be obtained. The Fischer-Tropsch process requires the production of synthesis gas, a mixture of carbon monoxide and hydrogen. At the Bureau of Mines Louisiana, Mo., demonstration plant, this gas is being made by reacting dried pulverized coal with carefully controlled volumes of oxygen and superheated steam. After purification and in the presence of the proper catalyst and suitable conditions of pressure and temperature, the hydrogen and carbon monoxide components of the synthesis gas react to form motor fuel. The two processes are not competitive but rather com-

Jan 1, 1951

By A. S. Appleton, M. B. Bever

The stored and expended energies of an Au-Ag alloy deformed in torsion were investigated as functions of strain, strain rate, and temperature. At room temperature, the stored energy, measured by tin solution calorimetry, increased linearly up to an intermediate strain, above which it was nearly constant; at 78 °K the relation was linear up to fracture. Approximate values of the energy stored at 4 OK indicate a rapid increase below 78 OK. The energy stored by specimens deformed successively at 4o and 78oK changed slowly with increasing second strain from the curve for energy stored at 4 OK (measured after annealing at 78oK) to that for deformation at 78°K. The ratios of the stored to the expended energy at room temperature and 78 oK were unusually large. The additional amount of energy stored at the lower temperature is attributed mainly to an increase in the number and energy of dislocations. The stored energy as a function of strain rate at 4oK (measured after annealing at 78oK) increased to a sharp maximum over a narrow range of strain rates, whereas the expended energy changed only slightly. These effects are explained by the generation of point defects resulting from the enforced nonconservative movement of jogs in fast moving screw dislocations. The effect of straining successively at two strain rates at 4oK was also investigated. Stress-strain curves for 4o, 78oK, and room temperature and the results of micro examination of specimens deformed at these temperatures are also reported. THIS investigation is a continuation of a research program primarily concerned with the effects of variables on the energy relations involved in the deformation of metals. The variables investigated in earlier work have included strain, strain rate, temperature of deformation (room temperature and 78oK), and the type of deformation process. Most of this work has been carried out with Au-Ag alloys. In the investigation reported here, the deformation process was torsion, which had not been used previously in the program. The stored and expended energies involved in the deformation process were measured as functions of strain, strain rate and the temperature of deformation in the range 4" to 373" K. The microhardness and microstructure of deformed specimens were also investigated. The relation between stored energy and strain differs for different deformation processes.1,2 In general, the stored energy increases with strain and may attain a nearly constant value at large strains. This value and the rate at which it is reached, however, depend on the process of deformation. This dependence has been attributed, at least in part, to differences in the effective strain rate and rise in temperature of the specimen during deformation. The effects of the temperature of deformation on both the stored energy and the energy expended in the working process have been the subject of only a few investigations.3-6 Values of these quantities at low temperatures are of special interest as they yield information on point defects which, for many metals, is not obtainable at higher temperatures. The effect of the strain rate on the stored and expended energies has received little attention The strain rate has usually been measured only in relative terms, and hence the interpretation of its effect on the stored energy has been mainly comparative.

Jan 1, 1963

By W. B. Lilienthal, J. C. Melrose

The application of Bingham's law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham's law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn' have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham's law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,' following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham's integration of Bingham's law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning's equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,' the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham's equation is defined

Jan 1, 1951

By J. C. Melrose, W. B. Lilienthal

The application of Bingham's law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham's law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn' have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham's law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,' following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham's integration of Bingham's law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning's equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,' the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham's equation is defined

Jan 1, 1951

By W. T. Weller

In Part I, a study of pressure build-up curves calculated for conditions under which both oil and gas flow led to the conclusion that the presence of a dispersed free gas phase in an oil reservoir must be taken into consideration to estimate accurately average reservoir pressure and permeability from build-up curves. Familiar methods based on the assumption of no free gas can be extended to the two-phase case by using total compressibility and mobility in place of single-fluid compressibility and mobility. These methods give correct values for average pressure and permeability when gas saturation is small. Errors become larger as the gas saturation increases. However, for the use to which the results will be put, the methods are satisfactory for reservoir engineering purposes. An improved method of calculating the performance of depletion-type reservoirs is presented in Part 2. Because the mathematical relationships describing simultaneous flow of oil and gas are quite involved. simplifying assumptions are made to provide means of obtaining approximate solutions of reasonable accuracy. One such approximate method now in use is the constant-GOR solution. It involves the assumption that at any instant, the ratio of total gas flow rate (both free and disolved) to oil flow rate is the same at all points in the reservoir. The approach is not applicable unless the free gar saturation in the reservoir is everywhere greater than the critical gas saturation. This paper presents a modification which, by avoiding the constant-GOR assumption, makes the method applicable to all reservoir conditions, and so far appears to be more accurate than the constant-GOR solution and to he comparable in required compuctation time. PART I— BUILD-UP CURVE ANALYSIS INTRODUCTION Pressure build-up characteristics of shut-in wells have been used for many years by engineers to evaluate average reservoir pressure, effective permeability thickness of the pay section, effectiveness of well completion (skin effect) and reservoir size. A number of methods of analysis have appeared from time to time."" Without exception, these methods are based on the assumption that the reservoir contains but one fluid of constant small compressibility and constant mobility. It has been suggesteda" hat these single-fluid methods may be applied to data from reservoirs containing both oil and gas by substitution of some effective total properties of the multiphase system in place of the corresponding single-phase properties. The present investigation was undertaken primarily to evaluate this approach. METHOD A number of theoretical build-up curves were calculated for conditions of two-phase flow, under the assumption of certain reservoir and fluid properties, and were analyzed by single-fluid methods with appropriate total compressibility and total mobility values for the corresponding single-fluid properties. Results of the analyses were compared with the assumed conditions. The theoretical build-up curves were completed by procedures similar to those of West, Garvin and Sheldon." Since these calculations require a considerable amount of computer time, an attempt was made to derive an approximate calculation method. The attempt was unsuccessful for calculating build-up curves, but the effort did result in a new approximate method of calculating the performance of solution gas drive reservoirs, which appears to be an improvement over the constant-GOR method" used previously (see Part 2). The West, Garvin and Sheldon calculations involved the following assumptions: (1) the reservoir is circular and completely bounded, with a completely penetrating well at its center; (2) the porous medium is uniform and iso-tropic, with a constant water saturation at all points; (3) gravity effects can be neglected; (4) compressibility of rock and water can be neglected; (5) the composition and equilibrium are constant for oil and gas; (6) the same pressure exists in both the oil phase and the gas phase; and (7) no afterproduction occurs, i.e., the well is shut in at the sand face for build-up. These assumptions make it possible to describe two-phase flow of oil and gas by the partial differential equations:

Jan 1, 1967

By H. R. Thresh

An oscillational vis cometer has been constructed to measure the viscosity of liquid metals and alloys to 800°C. An enclosed cylindrical interface surrounds the molten sample avoiding the free surface condition found in many previous measurements. Standardization of the apparatus with mercury has verified the use of Roscoe's formula in the calculation of the viscosity. Operation of the apparatus at higher temperatures was also checked using molten lead. Extensive measurements on five different samples of zinc, of not less than 99.99 pct purity, indicate i) impurities at this level do not influence the viscosity and ii) the apparatus is capable of giving reproducible data. The variation of the viscosity ? with absolute temperature T is adequately expressed by Andrade's exponential relationship ?V1/3 = AeC/VT , where A and C are constants and V is the specific volume of the liquid. The values of A and C are given as 2.485 x 10-3 and 20.78, 2.444 x 10-3 and 88.79, and 2.169 x 10-3 and 239.8, respectively, for mercury, lead, and zinc. The error of measurement is assessed to be about 1 pct. Prefreezing phenomena in the vicinity of the freezing point of the zinc samples were found to be absent. AS part of an over-all program of research on various phases of melting and casting nonferrous alloys, a systematic study of some physical properties of liquid metals and their alloys was undertaken in the laboratories of the Physical Metallurgy Division.1,2,3 The most recent phase of this work, on zinc and some zinc-base alloys, was carried out in cooperation with the Canadian Zinc and Lead Research Committee and the International Lead-Zinc Research Organization. One of the properties investigated was viscosity and the present paper gives results on pure zinc; the second part, on the viscosity of some zinc alloys, will be reported separately. Experimental interest in the viscosity of liquid metals has virtually been confined to the past 40 years. The capillary technique was already established as the primary method for the viscosity of fluids in the vicinity of room temperature; all relevant experimental corrections were known and an absolute accuracy of 1 to 2 pct was possible. Ap- plication of the capillary method to liquid metals creates a number of exacting requirements to manipulate a smooth flow of highly reactive liquid through a fine-bore tube. Consequently, the degree of precision usually achieved in the high-temperature field rarely compares with measurements on aqueous fluids near room temperature. However, the full potential of the capillary method has yet to be explored using modern experimental techniques. As an alternative, many investigators in this field have preferred to select the oscillational method. Unfortunately, the practical advantages are somewhat offset by the inability of the hydrodynamic theory to realize a rational working formula for the calculation of the viscosity. In attempting to overcome this restriction many investigators have employed calibrational procedures, even to the extent of selecting an arbitrary formula for use with a given shaped interface. However, where calibration cannot be founded on well-established techniques, the contribution of such experiments to the general field of viscometry is questionable. A critical appraisal of the viscosity data existing for pure liquid metals reveals a somewhat discordant situation where considerable effort is still required to establish reproducible and reliable values for the low-melting point metals. The means of rectifying this situation have gradually evolved in recent years. Here, the theory of the oscillational method has undergone major advances for both the spherical and cylindrical interfaces. The basic concepts of verschaffelt4 governing the oscillation of a solid sphere in an infinite liquid have been adequately expressed by Andrade and his coworkers.5,6 Employing a hollow spherical container and a formula, which had been extensively verified by experiments on water, absolute measurements on the liquid alkali metals were obtained. The extension of this approach to the more common liquid metals has been demonstrated by culpin7 and Rothwel18 where much ingenuity was used to surmount the problem of loading the sample into the delicate sphere. Because of the elegant technique required to construct a hollow sphere, the cylindrical interface holds recognition as virtually the ideal shape. On the other hand, loss of symmetry in one plane increases the complexity of deriving a calculation of the viscosity. The contributions of Hopkins and Toye9 and Roscoe10 have markedly improved the potential use of the cylindrical interface in liquid-metal viscometry. The relatively simple experi-

Jan 1, 1965

By D. E. Coates, G. R. Purdy, S. V. Subramanian

The morphological stability of the planar solid-liquid interface in dilute ternary alloys, undergoing steady-state unidirectional solidification, is analyzed in terms of both the constitutional supercooling principle and the perturbation methods recently developed by Mullins and Sekerka. First, various steady-state solutions for the two solute distributions ahead of a planar interface are examined. The nature of the solutions depends on the size and concentration dependence of the off-diagonal diffusion coefficients. W~thin the framework of the constitutional supercooling principle, a cumulative contribution to instability frorn the two solutes is found to exist in the absence of diffusional interaction. It is shown that the latter can produce a further enhancement of instability or can have a stabilizing influence, depending on the form of the liquidus surface and on the sign of the solute-solute interaction. A perturbation analysis, which ignores diffusional interaction, verifies the cumulative influence of lhe solute fields and demonstrates that the Mullins-Sekerka stability criterion for binary systems (with capillarity accounted for) can be readily extended for application to ternary systems. SOME time ago, Tiller et al.' calculated the solute concentration distribution ahead of the planar solid-liquid interface of binary alloys undergoing steady-state unidirectional solidification. An earlier qualitative proposal that the transition from planar to nonplanar growth morphologies is associated solely with the onset of constitutional supercooling in the liquid layer ahead of the moving interface2 was used in conjunction with this calculation to put the now well-known constitutional supercooling (C-S) stability criterion into quantitative terms. Mullins and Sekerka,3 in a recent and very elegant analysis, established a more complete criterion (hereafter referred to as the M-S criterion). Interfacial stability was investigated by determining the time derivative of the amplitude of a sinusoidal perturbation of infinitesimal amplitude which had been introduced into the originally planar shape of the moving interface. Of particular importance is the fact that capillarity was included in the boundary conditions of their calculation. The purpose of the present paper is to extend all of this earlier work on dilute binary systems for application to dilute ternary alloy solidification. The analysis is divided into three sections. In the first the two solute distributions ahead of a moving planar interface are considered. Mathematical solutions are de- termined for situations in which: a) diffusional interaction is negligible, 6) diffusional interaction must be considered but circumstances permit use of constant diffusion coefficients, and c) the concentration dependence of off-diagonal diffusion coefficients can be described by first-order dilute solution approximations. In the next section, a stability criterion analogous to the C-S criterion is developed and the influence of diffusional interaction on interface stability is analyzed. Finally, the perturbation formalism of Mullins and Sekerka, with capillarity included in the boundary conditions, is extended for analysis of ternary systems in which diffusional interaction is negligible. The study of interface stability in binary systems usually commences with the assumption that the equilibrium distribution coefficient and the slope of the liquidus line are constant at values corresponding to infinite dilution. Similar assumptions have not been introduced into the present treatment; that is, we do not assume planar solidus and liquidus surfaces joined by tie lines which yield constant distribution coefficients. The latter involves the assumption of no ther-modynamic interaction between solute species in both the solid and liquid. We consider a ternary phase diagram for which the solidus and liquidus surfaces are, in general, nonplanar and of course pass through the corresponding binary solidus and liquidus lines. These lines are not assumed to have constant slope. In the dilute regions we are concerned with, the following assumptions are made: i) The solidus and liquidus surfaces are of a form such that both the solidus and liquidus temperatures are monotonically varying functions of each solute concentration. ii) The tie lines are such that the equilibrium distribution coefficient of a given solute is greater than unity for every point on the solidus (or liquidus) surface or it is less than unity for every point. STEADY-STATE SOLUTE DISTRIBUTIONS IN THE LIQUID As will be demonstrated in the next section, a knowledge of the steady-state solute profiles is not a necessary prerequisite for the formulation of a ternary C-S stability criterion. However, in that details, such as the complete description of the equilibrium liquidus temperature profile, require an evaluation of the solute distributions, the overall treatment is enhanced if these distributions are determined. Consider a ternary system (solvent plus solutes 1 and 2) for which a planar solid-liquid interface is in unidirectional motion at constant velocity V. At this stage it is unnecessary to limit ourselves to dilute solutions. For a stationary frame of reference the generalized forms of Fick's equations are:

Jan 1, 1969

William Metcalf, Pittsburg, Pa. (communication to the Secretary*): I am greatly pleased that some one has at last reached what I have long regarded as the only rational explanation yet given of the reasons why steel hardens. Mr. Field claims originality; and doubtless he is entitled to it, but not to priority, mhich must be granted to Prof. John W. Langley.' The difference between them is that Langley says " Tension, probably molecular," and Field says " Tension, probably atomic "; in either case the vital thing after solution is tension. Mr. Field's argument carries with it the idea of increase of density with hardness; if he mill study the facts farther he will observe that the case is just the reverse; that is, the greater the hardness the less the specific gravity; it was just this fact that led Langley to his conclusion, in mhich I have always concurred. Field agrees with Langley that the first requisite for perfect hardening is complete solution of the carbon, not combination; and all of the facts agree with this conclusion. The fact that increase of hardness causes reduction of density was first brought to my notice some 40 years ago, when Major William Wade was testing Jones & Laughlin's cold-rolled iron, and I mas his assistant. We found the well-known increase of tenacity, compressive strength, torsional resistance, and hardness. Specific-gravity tests showed that the cold-rolled iron was less dense than the hot-rolled bars. Major Wade was so surprised at this result that he gave me a lot of samples to weigh, saying that he was not satisfied with

Jan 1, 1904

By J. G. Y. Chow, S. B. McRickard

The tensi1e properties of Ferrovac iron have been studied from 4° to 300°K. The stress required for macroscopic yielding was found to he constant below approximately 50°K. The effect of mechanical twinning on this low -temperature stress plateau was investigated. The onset of twinning occurs in this iron between 130° and 150°K and depending on its previous thermal history the twinning-stress curue may drop below or remain above the vield-stress curves as the temperature is lowered. Twinning has been shown to initiate slip in quenclzed iron at low temperatures. In no instances, however, did the onset of twinning alter the continuity of the yield stress -tempwature curve. Our data shows that carbon inhibits twinning and slip at low tem-peratures. This observation nay be used to explain the ductile-to-brittle transition in iron. The effect of fast neutron irradiation on yielding and embrittlement in iron and Fe-C alloys is offered as supporting evidence for this viewpoint. THE mode of yielding in iron at low temperatures was studied in an attempt to find an expression based on a single mechanism to describe the thermal dependence of the yield stress of iron. There are two types of inflections observed in the variation of the yield stress with temperature in iron and Fe-C alloys. The first is associated with ductile behavior and consists of a region extending 50" to 100°K above absolute zero in which the yield stress is independent of temperature. The second is observed in more brittle materials such as Fe-C alloys and irradiated iron and consists of an abrupt discontinuity in the yield curve as the temperature is lowered through a ductile-to-brittle transition point. The temperature dependence of the yield stress for iron with four grain diameters as found in this study is shown in Fig. 1. To varying degrees all the curves appear to flatten or approach an asymptotic value as the temperature is lowered below 50°K. Several other investigators1,2 have observed a plateau in the yield stress of iron and steel at low temperatures and in 1956 Louat3 presented a theory which contained an explanation for this behavior. In a subsequent exchange with Erickson and Low4'5 who attributed the plateau to the onset of mechanical twinning Louat8 showed that twinning first occurs in iron and steel tested in tension at temperatures as high as 140°K which is well above the observed plateau in yield stress. Furthermore he pointed out that both twinning and slip are basically dislocation processes and that with modified parameters his original theory still applied when deformation is initiated by twinning. Variables which affect the ductile-to-brittle transition in iron are test temperature, strain rate, composition and grain size.7 LOW,8 Hahn et al.,9 and Hull10 have provided evidence which links brittle fracture at a given temperature with the specimen grain size and the onset of twinning. In fact, Hull equates the brittle fracture stress to the twinning stress. On the other hand brittle fracture has been observed in the absence of twinning and priestnerl1 has given a fracture criterion which is valid whether or not fracture is preceded by extensive twinning. The data presented here clarify the role of twinning in the low-temperature deformation of iron. Strong evidence is given that the amount and distribution of interstitial impurities such as carbon are of

Jan 1, 1965

By P. W. Gilles, B. D. Pollock

THE pioneering work of Steinitz1 and Steinitz, Binder, and Moskowitz2 has shown conclusively the existence at high temperature of two additional phases in the molybdenum-boron system and thus brings to a total of six the number of structures appearing in this system. To the structures Mo2B, MOB, and Mo2B5 they have added MO3B2, a new -MOB form, and have shown that MOB,, which has the same range of composition as Mo2B5, is only a high temperature structure of the latter. This solid solution, interestingly enough, includes neither of the compositions corresponding to the stoichiomet-ric compounds, MOB, or Mo2B5, but rather at all temperatures has intermediate values of composition. These workers have also, in the course of their work, measured melting points, transition temperatures, eutectic and peritectic points in the system and have shown that Mo3B2, because of its dispro-portionation at low temperature to Mo2B and MOB, is stable only in a limited high temperature range. During the course of the present work on the vaporization properties of the molybdenum-boron compounds, a few transition temperatures were observed. When the report of the other workers appeared, it was decided to repeat, in part, their study of the system. As a result, considerable evidence has been obtained that substantiates the specific kinds of melting processes they report as well as the general features of their diagram. However, a marked difference was found between the temperatures they report and the ones observed in this study, with the latter being higher. The purposes of this paper are to present the evidence obtained in this laboratory that verifies their diagram of the system, to give some important temperatures in the system, to compare them with those previously published, and to seek an explanation of the difference. Samples The metal starting material was 400 mesh molybdenum powder with a purity stated by the manufacturer to be 99.9 pct. The initial treatment, designed to remove volatile contamination, consisted of heating in a vacuum for 10 min to a temperature of from 800" to 1000°C during which a loss of 0.3 to 0.4 pct occurred. An assay following this treatment showed it to be 99.4 pct pure, with the principal impurity probably being oxygen. The boron starting material was obtained from the Cooper Metallurgical Laboratories and the Fair-mount Chemical Co. as 325 mesh powder with manufacturers' analyses of 99 pct or better. Initial treatment consisted of heating in molybdenum in a vacuum at about 1700°C for 10 min. During this time a loss of 3.5 pct occurred. An assay following this treatment showed the different samples to have purities ranging from 95.5 to 99.0 pct with iron and carbon as the principal impurities. Following the initial treatment, the elements were combined to form stocks of Mo2B and MOB by heating pressed mixtures in a vacuum to 1100" to 1200°C to accomplish reaction and to 1500" to 1900°C for a few minutes to evaporate the more volatile impurities. Analysis of the two compounds for boron by a modification of the method of Blumenthal3 and for molybdenum by the lead-molybdate method indicated them to have purities greater than 99 pct. The individual samples to be studied had compositions in the Mo2B-MOB range and consisted of mixtures of the stock compounds. Procedure As is usually the case in high temperature work the selection of containers for the samples posed some problems. For vapor pressure studies tantalum crucibles, allowing little contact with the pressed samples, were used and some of the observations made during these experiments are pertinent to the study of the phase diagram. Most of the experiments, however, were performed in graphite containers, as were those of the previous authors. Two kinds of spectroscopic grade graphite crucibles were used. One was a % in. cylinder, 3/4 in. high, containing seven 3/16 in. holes drilled 1/2 in. deep into which were packed samples of the different mixtures weighing 250 to 500 milligrams. The other, consisting of separate crucibles, was prepared by drilling 3/16 in. holes, 1/2 in. deep into 1/4 in. graphite rods % in. long. The 7/8 in. cylinder was heated directly by induction while the small crucibles were packed in a tantalum heating element for induction heating. All heating was done in a high vacuum system in which the pressure was generally less than 1x10-5mm and never rose above 2x10-5mm when the samples were hot. The general pattern of the heating in graphite was to heat rapidly to a temperature somewhat below the desired one, then to raise the temperature slowly. The samples were held for 2 to 5 min at the maximum temperature, which in all cases was far higher than that needed to produce reaction. The short time was employed to reduce possible contamination by the crucible material and to reduce composition changes that would occur because of vaporization. After examination following the heating, the samples were reheated to a higher temperature. Temperatures were measured with a Leeds and Northrup disappearing filament optical pyrometer, certified by the National Bureau of Standards, by sighting through a window at the top of the vacuum

Jan 1, 1954

By E. R. Borcherdt

IT is notable that the first large-scale mine operation equipped entirely with detachable bits was the Badger State mine of the Anaconda Copper Mining Co. in Butte, Montana, just 30 years ago. This mine in 1922 was producing approximately 1200 tons of ore per day. Much of the data presented in C. L. Berrien's article' describing the development and installation of the Hawkesworth detachable drill bit were obtained from these operations. As in any pioneering effort, no precedent existed and many difficult problems required solution, so that the changeover to detachable bits at all Butte hill mines was not completed for 6 years. There was widespread disbelief as to the probable efficiency of the new installation. Some attempts were made in 1931 by the owners of the Hawkesworth patents to interest Ontario gold mine operators in the bit. These efforts were not successful, but they undoubtedly stimulated thinking which resulted in the invention and patenting of several well-known Canadian detachable bits, one of which is now a widely used throwaway bit. The success of the Butte installation also led to the development of the threaded type of bit connections by several well-known manufacturers, and in 1935 these bits were introduced to the mining industry on a national scale. The original Hawkesworth bit was not provided with a water hole but, depended upon water passing through the clearance opening between the tongue in the bit and the groove in the rod to flush cuttings from the drill hole, see Fig. 1. In December 1935 it was found that this method of introducing drilling water to the bit face resulted in high dust counts. To correct this a water hole was drilled on the central axis of the bit, passing through the tongue. Unfortunately, quenching water would rise through the small water hole, spot-hardening the tongue to cause breakage, never completely eliminated. In the fall of 1936 large-scale tests indicated that savings would be effected by use of a threaded type of bit, which was therefore adopted as standard for all Butte mines. This type of bit was used until 1947, when it was superseded by a one-use slip-on type. Since the first use of the Hawkesworth bit every detachable bit of importance has been investigated, and where advantages which might reduce costs or increase efficiency were indicated, substantial tests of the bit were carried on in the Butte mines. When tests demonstrated the advisability of changing from one kind of detachable bit to another the change was made at one level or in one area each day until the new rod and bit equipment was used throughout the mine. This involved a minimum of cost and disruption of drilling. Intelligent selection of a detachable bit to obtain optimum results requires careful consideration to achieve a balance between the three principal types of equipment used in the drilling process: 1—drill bits, 2—drill steel, and 3—drilling machines. Optimum results imply maximum output and minimum cost per unit of output. Since every rock type differs in drillability and it is generally impractical to provide equipment for more than one or two types of rock which may occur in one operation, selection of equipment must encompass average drilling conditions. However, on exceptional occasions several widely differing conditions may make it mandatory to provide equipment best suited to each condition. The choice of rock-drilling equipment is a most controversial subject and one that is further complicated by unreliable and frequently misleading performance claims. Small operators without the means for making accurate evaluations of equipment frequently suffer from these over-enthusiastic claims. It is apparent from experience in rock drilling throughout the world that rock drillability is not alike in any two places, and that selection of proper equipment can only be made after conducting thorough trials of various types of equipment. Some recent drilling tests in tactite and hornstone at the Darwin, California mine of the Anaconda Co. present some interesting clues on rock drillability. Microscopic examination of thin sections of these rocks reveals that mineral composition and rock texture are equally important in governing drillability. The Darwin hornstone is at times so abrasive that the carbide bit cutting edges become flattened to 3/32 in. in 2 to 4 ft of drilling, and some carbide bits were dulled to this point after 9 to 10 in. of drilling. This wear was determined to be the proper point for resharpening to eliminate carbide insert breakage or breakage of the steel rod when drilling with 1½ to 1?-in. bits, with a drifter of 2 3/4-in. diam and 90 to 100 psi air pressure, see Supplement A. Before considering the merits of various bit designs it may be well to review the mechanics of drilling rock with percussion drills. A sharp bit cuts by penetration and chipping. The amount of penetration governs the amount of chipping and depends upon the contact area of the cutting edge, the foot-

Jan 1, 1954

By N. K. Chen, R. Maddin

In the extension of molybdenum single crystals at room temperature, the slip planes were found to be of the type (1101; the slip direction <111>. Theories of plasticity of body-centered cubic metals have been examined, and an explanation based upon planes of highest atomic density seems plausible to explain the plastic behavior of molybdenum single crystals. IN body-centered cubic metals, slip has been reported to occur on several planes; these are of the type {110), {112), and (123). Andrade has correlated&apos; the operative slip planes in body-centered cubic metals with the testing temperature relative to the melting point. In this correlation, if T is the absolute temperature at which slip takes place and Tm the absolute melting point, then the acting slip planes in body-centered cubic metals may be arranged as shown in Table I. However, deviations from this correlation have been reported in iron and iron-silicon alloys2 and also in molybdenum deformed at a temperature around 2400°C." In the case of iron and other body-centered cubic metals or alloys in which all three slip planes have been reported to be active at any one temperature, the crystallographic mechanism of slip is not well understood. Numerous investigators in this field have assumed that the resolved shear stress is a deciding factor. Such considerations were given by Gough in his experiments with repeated torsion of iron single crystals4 and recently by Opinsky and Smoluchowski in their study of iron-silicon alloys," and will be dealt with later in this report. A third possibility is that slip lines in body-centered cubic metals may be formed by alternate slip on nonparallel (110) planes and not by slip on any plane of higher indices. This was advanced by Elam in the case of ß brass." Since (1101 planes are planes of highest atomic density in the body-centered cubic structure, this hypothesis would be in accordance with the plastic behavior of metals in other systems, namely, face-centered cubic and hexagonal close-packed. Experimental evidence in support of this hypothesis is lacking. Nevertheless the work of Barrett, Ansel, and Meh12 has definitely demonstrated that the slip resistance on {110} planes in iron is very much smaller compared with that on (112) and (123) planes. In the present investigation, molybdenum single crystals were carefully documented as to the operative slip planes and lattice reorientations after plastic extension at room temperature. In three crystals studied, (110) planes were found to be active invariably rather than the (112) planes, which were previously reported for molybdenum at this temperature&apos; and predicted by Andrade&apos;s theory.&apos; In two other cases (112) and (123) planes seemed to operate together with (110) planes as active slip planes. However, it is believed, after careful analysis of crystallite and lattice rotations, that slip on (112) and (123) planes may be spurious. Particular reference will be made to the formation of asterism, lattice rotation, and crystallite rotation in an attempt to show that slip apparently observed on {1121} and (123) planes is actually slip on nonparallel {110} planes. Materials and Treatment Sintered molybdenum rods ? in. in diam, obtained from the Fansteel Metallurgical Co., were reported to have a purity of 99.9 pct.* One specimen, Mo-13, ¼ in. in diam, was supplied by Westinghouse Electric Corp. Single crystals were prepared, using the technique devised by Chen, Maddin, and Pond." Mo-13 was ¼ in. in diam x 7 in. long with a reduced gage section of 0.200 in. in diam x 3 in. long. The center of

Jan 1, 1952

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By C. F. Allen, G. B. Walker

K. F. TROMP*—In dealing with the question of the most suitable kind of solid media for heavy density suspension processes Walker and Allen point out that the particle size of the solid media should not be taken too fine, as the viscosity increases with the area of the solid media and a low viscosity is essential lor high tonnage and accurate separation. A coarser particle size of the solid media will, in their opinion, of necessity give rise to a differential density in the bath (higher gravity at the bottom of the bath than at the top) but they advocate acceptance of the differential density rather than a higher viscosity. Though I fully agree with the choice the authors have made, I cannot subscribe to their view that only by accepting a differential density in the bath a coarse particle size of the solid media can be used. There certainly is another alternative: stronger agitation. Applying sufficiently strong vertical currents, a uniform gravity can be obtained quite well in a suspension of a coarse solid media. Of course, this is not a very attractive solution, for it means a degradation of the true gravity separation and a step backwards to hydraulic classification, which makes the washing dependent on size and shape of the particles. However, to a greater or lesser extent, this is what actually takes place in all the heavy density suspension processes relying on a uniform gravity in the bath. The so-called "stable" suspension processes make no exception. They all "stabilize" their suspensions by introducing or creating vertical currents, be it upwards or downwards or both, be it by hydraulic or by mechanical means. In fact, there is no such thing as a "stable" suspension in gravity separation, as the very reason for the use of suspensions in this field is the property that the solid media is able to settle and so facilitate the recovery. I have been enlarging on this point because the characteristics of the various processes can only be well understood and viewed from the same angle (from Bar-voys up to Chance) when the fact is recognized that mechanical or hydraulic agitation is a condition sine qua non for obtaining a uniform density from top to bottom in a suspension. Is a Cone-slraped Vessel Essenlial? Of the two alternatives for getting a low viscosity Walker and Allen have preferred correctly the sacrifice of uniform gravity in the bath instead of increasing further their vertical current arid agitation. The resulting differential density of the bath brings the problem of bow to prevent accumulation of intermediate gravity products in the bath, an accumulation which, if not prevented, would ultimately plug their cone. According to the authors an open-top cone combined with a downdraft current of the bath liquid would he the only suitable way to cope with such suspensions and they assume as a fact that "in any vessel other than a cone, such a differential density could not be tolerated." My experience is quilt: different. In my process, which has been in successful operation for more than a decade, differ-ential density of the suspension is applied ranging from values below 0.1 up to differentials above 0.5, according to the prevailing requirements of the individual plant. In this process, which is charac-terized by the use of horizontal currents in a suspension of differential density, the form of the vessel is of secondary importance and different types are in operation. It so happens that none of these are in the, form of a cone. The fact that 24 washboxes on my process have been installed and 12 others are under construction may constitute sufficient proof against the opinion that only a cone-shaped separator would be suited for differential density separation. Horizontal Currents in Differentia1 Den-sity Sepparation I myself have some doubts as to the suitability of a cone with downdraft for dealing with differential density (or, for that matter, any other washbox relying on vertical currents for removing the intermediate gravity products). It ap-pears to me that it is restricted to feed of small size only and even then with watch-fulness. If we take, for example, a piece of 2 in., the draft necessary to pull such a piece down to a zone wherein the den-sity of the suspension is, say, 0.03 higher, is quite considerable. For a suspension of, say, 1.6 sp gr the downdraft will have to be in the region of 3 in. per second. Unfortunately. most of the differential in density is in the part immediately below the reach of the top current which transports the floats. Consequently, we need the downdraft where we like it least: in the upper part of the cone. This entails the risk that light float particles are carried away with the downward current. This current of, say again, 3 in. per second would carry particles up to 1.3 sp gr and 3/8 in. size into the 1.6 gravity zone. This is prohibitive. It is also prohibitive because a downdraft of 3 in. per second in the upper part of the cone would require a tremendous circulation of medium. IIalf way up a 20 ft diam cone, a downdraft of 3 in. per second would correspond with 8500 gpm. With the downward current following the way of least resistance, the strength of the downdraft will not be exactly the same at different places of a cross area. If, as I anticipate, the center of the cone is favored, the strength of the downdraft will fall below the critical value near the

Jan 1, 1950

By James A. Lewis

It is the purpose of this paper to show the importance of sand characteristics, when combined with other physical data, in evaluating production obtained by secondary recovery operations, and to indicate the benefits to be gained from the application of these principles to primary production. Introduction During the past 10 years there has been a growing interest within the industry regarding the movement of fluids through oil reservoirs. A number of research projects have been directed toward the development of the physical laws governing this movement. In the period 1933 to the present, correlations between laboratory analysis of cores, reservoir fluids and well performance have been established and have been applied to successful secondary water-flooding recovery operations; and to the completion, production, reconditioning and evaluation of wells in new fields. The application of these data to water-flooding, either natural or artificial, is comparatively new, but the principlcs involved were set forth in 1880 by John F. Carll,1 who said: The flooding of an oil district is generally viewed as a great calamity, yet it may be questioned whether a larger amount of oil cannot be drawn from the rocks in that way than by any other, for it is certain that all the oil can-not be drawn from the reservoir without admission of something to take its place. If one company owned all of the wells drawing upon a pool, and had accurate records of the depth and characteristics of the oil producing stratum in each well, it is quite possible that some system might be devised by which water could be let down through certain shafts, and thus the rocks be completely voided of oil and left full of water. As it is, however, no systematized plan of action can be adopted. The careless handling of one well. by which water is let down to the oil rock, may spoil several others belonging to different parties. A clashing of interests at once arises and is likely to result in disaster to the whole district. In judging of the probable effects of the intro-duction of water into any particular oil district several things are to be considered. (1st) The time of flooding—whether early in the progress of development, while yet a large percentage of oil remains unexhausted or at a later period after the supply has suffered from long continued depletion. (2nd) The structure of the rock—whether regular and homogeneous throughout, or composed of fine sand inter. bedding connected and irregular layers of gravel, sometimes lying near the top and at others near the bottom. (3rd) The shape of the area being flooded. (4th) The position of the point at which water is admitted. in relation to the location of the surrounding wells still pumping oil. (5th) The height (which governs the pressure) of the column of water obtaining admittance. (6th) The duration of the water supply. Although we may take exception to part of Carll&apos;s reasoning, particularly " and thus the rocks be completely voided of oil and left full of water," we must give him credit for pointing out the increased effectiveness of water encroachment in displacing oil from a sand and for his recording six of the present seven considerations necessary for evaluation of production of oil by water

Jan 1, 1942