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By George Stern

The purpose of this investigation has been to study one method for making ordinary carbon steel by the powder metallurgy technique. This method con- sists of pressing and subsequently sintering an intimate mixture of iron powder and gaphite in a suitable atmosphere to Produce a steel. Two types of iron Powder have been studied, electrolytic and reduced. The sinkring of mixtures of loose Car-bonyf iron and carbon black for several hours at I000 to 1100 C. (1830' to 2010°F.), followed by forging of the resultant ingots to bars, has been studied by Offermann.' TrailZ has reported on the properties of hydrogen-reduced and electrolytic iron powders, both containing 0.5 per cent carbon. Methods for making steel bodies by powder metallurgy have also been sug- gested by Goetzel13 who recommends the addition of steel powder of well-defined carbon content to pure iron powder, and Volterra,~ who suggests compaction and subsequent sintering of a mixture of steel powder, iron oxide and iron powder. Additional methods for making steel bodies by powder metallurgy have been reported in the literature by Kohering Allen,6 Balke,7 Wulff,8 Boegehold,9 and others.,0,11,12 It is felt that the method of pressing iron powder and graphite, as described herein, lends itself best to production be-Cause of the lubricating action of the

Jan 1, 1946

By George Stern

The purpose of this investigation has been to study one method for making ordinary carbon steel by the powder metallurgy technique. This method con- sists of pressing and subsequently sintering an intimate mixture of iron powder and gaphite in a suitable atmosphere to Produce a steel. Two types of iron Powder have been studied, electrolytic and reduced. The sinkring of mixtures of loose Car-bonyf iron and carbon black for several hours at I000 to 1100 C. (1830' to 2010°F.), followed by forging of the resultant ingots to bars, has been studied by Offermann.' TrailZ has reported on the properties of hydrogen-reduced and electrolytic iron powders, both containing 0.5 per cent carbon. Methods for making steel bodies by powder metallurgy have also been sug- gested by Goetzel13 who recommends the addition of steel powder of well-defined carbon content to pure iron powder, and Volterra,~ who suggests compaction and subsequent sintering of a mixture of steel powder, iron oxide and iron powder. Additional methods for making steel bodies by powder metallurgy have been reported in the literature by Kohering Allen,6 Balke,7 Wulff,8 Boegehold,9 and others.,0,11,12 It is felt that the method of pressing iron powder and graphite, as described herein, lends itself best to production be-Cause of the lubricating action of the

Jan 1, 1946

By B. G. Hurd

A liquid-Freon permeameter suitable for making routine permeability determinations on small plug samples is described. The instrument is characterized by simplicity of design and ease of operation, and can be assembled inexpensively from stock items of laboratory equipment. It combines the unique advantages of both liquid and gas permeam-eters while eliminating many undesirable features of both general classes of instruments. Precision and accuracy of the specific Freon permeability measurements compare favorably with results of conventional liquid and gas permeameters. INTRODUCTION The liquid-Freon permeameter described in this paper was designed and built for special investigations of the properties of petroleum reservoir rocks. However, its unique advantages over conventional gas and liquid permeameters make it eminently suitable for routine use in the core analysis of small plug samples. In general, gas permeameters are very popular because of their simplicity of design and ease of operation. However, apparent gas permeabilities are normally higher than true specific permeabilities unless special corrections for gas-slippage are applied. Since these corrections require two or more measurements at different internal gas pressures, much of the time advantage of the specific gas permeability measurements is lost. Liquid permeability measurements, on the other hand, require no slip correction, but liquid saturation of the sample is time-consuming and difficult to insure. Often, too, the saturating liquid must be extracted or dried from the plug before it can be used for another experiment. The liquid-Freon permeameter described herein retains the inherent accuracy of the liquid permeameter, while affording the speed and ease of operation of the gas permeameter. Freon-12 (dichlorodifluoromethane) is a haloge-nated hydrocarbon, immiscible in the liquid phase with water. It may be considered as an oil phase in laboratory fluid-flow studies. Like butane and propane, it is a gas at normal room temperatures and atmospheric pressure but can be liquefied at moderate pressures. Complete liquid saturation of a plug sample with any of these fluids can be easily achieved by condensing vapors in the sample and operating the permeameter at a pressure above the vapor pressure of the liquid. Freon-12 is superior to butane or propane for permeability measurements only in that it is relatively nontoxic and completely incombustible, and thus presents no fire or explosion hazard. Freon-12 is believed to be completely nonreactive with most petroleum-reservoir rock samples. It volatilizes immediately from a plug on depressurizing to leave a clean, dry sample suitable for subsequent experiments. Thus, the inherent risk of changing physical properties of rock samples by cleaning and drying operations between permeability measurement and subsequent experiments is eliminated. DESCRIPTION OF THE PERMEAMETER The design of the liquid Freon-permeameter is shown schematically in Fig. 1. Regulated nitrogen pressure caps are used both as a driving pressure

By Edward Saibel

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,' no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3'4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers' that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson's ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,' no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3'4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers' that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson's ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By R. B. Adamson

The fatigue behauior of irradiated copper single crystals is compared to that of unirradiated crystals. Proton or electron irradiation did not substantially change the fatigue-lzj.e, fatigue-hardening-, or slip-line characteristics, while neutron irradiation did appear to alter these parameters. Postfatigue transrrzission electron microscopy did not reveal any marked structural differazces between irradiated and unirradiated specimens. Possible dislocatio~a mechanisnzs to explain the observed behavior are discussed. A LTHOUGH considerable work has been done to ascertain the effects of radiation on the tensile properties of metals (e.g., Refs. 1 and 2), little work of a basic nature has been reported on the effect of radiation on fatigue properties. Since it is known that fatigue properties are sensitive to conditions at the surface of the metal, it was felt that charged particle irradiation, whose penetration into metals is very small, might influence the fatigue behavior. To investigate this surface effect, irradiations with 10 mev protons and 1.5 mev electrons were conducted. The range of 10 mev protons in copper is about 0.236 mm; which is very small compared with the thickness of the specimens used (1.53 mm). The range of 1.5 mev electrons is somewhat larger, on the order of 0.665 mm.4 On the other hand, irradiation with reactor neutrons produces damage throughout the entire specimen, so neutron irradiation can be used to study the effects of bulk damage. The damage introduced by proton and neutron irradiation is expected to con!ist of large interstitial dislocation loops,5 tiny (<25A) vacancy loops," and/or various vacancy-rich regions called depleted zones.&apos; In the case of electron irradiation at about -173°C the damage is expected to consist of isolated Frenkel pairs.&apos; The effect of radiation damage on the fatigue properties of some engineering materials has been reported,g,10 but the results are not clear-cut or consistent. SPECIMEN PREPARATION Zone-refined copper was used to grow single crystals by a modified Bridgeman technique in an inert helium atmosphere. Using a seeding method, single crystals were obtained as bars about 6 in. long with a cross section of 3 by $ in. Immediately upon removal from the split-mold graphite boat in which they were grown, the very soft bars were embedded in a room-temperature setting plastic. They could then be cut into specimen lengths without introducing any long-range damage. Generally, four or five specimens plus one seed were obtained from each bar. The plastic material was dissolved away in acetone and the orientation of each sample was checked by the standard Laue X-ray

Jan 1, 1968

By HENRT M. HOWE

IN my original paper, Piping and Segregation in Steel Ingots, I pointed out1 among other things that, in view of the slighter stretching (virtual expansion) of the crust, and greater opportunity for sagging, there should be less piping in broad than in narrow ingots, and less in slowly-cooled ingots, e.g., those cast in pre-heated sand molds, than in those which cool quickly, e.g., those cast in iron molds. A. A. Stevenson2 said that neither of these predictions agreed with his own experience. In particular, in a picture which he showed of a wide and of a narrow ingot cast from the same ladleful of steel,, the wide ingot had certainly piped much more deeply than the narrow one. At the time I did not see the explanation of these discrepancies, but further reflection makes it evident. One of the most important elements in determining the depth of the pipe is the degree of " top-lag," that is, the degree to which the solidification of the top of the ingot lags behind that of the bottom. &apos;Through this lagging the steel of the upper part of the ingot is able to run down and fill the pipe below as fast as it forms. To the importance of this lagging I called attention in my original paper.&apos; Sand vs. Iron Molds.-If we compare two like ingots, one cast in an iron and the other in a sand mold, we see that the top-lag&apos; is much greater in the former than in the latter, be¬cause in the former the lower part of the ingot is cooling off fast while the metal is running into the upper part. It is perhaps easier to look at this as a case of the solidification of the hot-

Dec 1, 1909

By FREDERICK MCAKCCOY

THE production of tin from Mexico has never reached the point of being considered a national industry, but the distribution of tin ores is so widespread that there are possibilities that one day it may become of importance. Of the twenty-seven states of the Republic, tin claims have been taken up in sixteen. In all there had been taken up to the end of 1926, two hundred and twenty-five claims, of a total area of about 7400 acres. The first historical mention of tin in the Americas is found in a letter of Cortez to the Emperor, Charles the Fifth, of Spain, which is as follows: Speaking of his manufacture of some small cannon, he says: "For these reasons I took considerable pains to get copper from some provinces of this country, and bought it at a high price in order to get it quicker.

Jan 1, 1929

By C. S. Matthews, H. C. Lefkovits

The performance of depletion-type reservoirs at the stage in which the gas is at such low pressure that gravity is essentially the sole driving force has been investigated both theoretically and by use of scaled models. A simple theory is developed which completely explains the scaled model experiments. It also agrees with some field data. When the range of production rates to be considered is less than 25, the theory predicts that the production rate decline curve for homogeneous reservoirs in which there is a free surface will be of the hyperbolic type with n = 2: The theory gives a physical significance to the parameter y. INTRODUCTION This investigation was undertaken to determine a method for prediction of performance of reservoirs where gravity is the sole driving agent. Depletion-type reservoirs fall into this category after the pressure has fallen to some low value. Some examples of this type are found at Healdton (&apos;Oklahoma), Oklahoma City (Oklahoma), Midway-Sunset (California), and East Coalinga (California). Generally the production rate per unit thickness is quite low in such reservoirs, with the conse- quence that this stage is sometimes called the stripper stage. However, per well production rates may be of the order of 50 B/D because of the considerable sand thickness open in some of the reservoirs. In the past, predictions of behavior of such reservoirs have been based on empirical extrapolation of the rate of production to the economic limit. Difficulties arise when new wells are drilled in the field or when production is artificially curtailed, since in such cases the decline rate of individual wells or leases changes and no clear trend can be detected. It was hoped that the present study would lead to improved methods for evaluation of such reservoirs. The study was initiated by building a scaled model for a particular field and by running a number of experiments on this model. Later a simple theory was developed which explained the laboratory results completely. The theory led, as shown below, to a hyperbolic-type decline equation which had been used previously&apos; in a completely empirical manner. THEORY The General Case The problem to be treated here is the following: We are given a homogeneous cylindrical porous reservoir with exterior radius r, wellbore radius r., and height h,, containing, from the bottom up to a height hit oil, some gas, and interstitial water (see Fig. 1 A). The portion of the reservoir between K, and h, is filled with gas at low pressure, with residual oil, and with interstitial water. If at a time t = 0, the level of the oil in the wellbore is lowered to a height h,, what is the production rate from the reservoir at a time to The configuration within the reservoir at some instant

Jan 1, 1957

By Donald M. Liddell, G. C. RIDDELL

THE cosmic ray continues to engage the attention of the physicists, and according to Millikan and Compton, experiments of the past summer indicate that these rays must come from interstellar space, but not from the stars themselves. According to press reports of the International Congress of Physicists at Rome, the view was given there that these rays have an initiating potential of over 750,000.000 volts. In the field of spectrographic investigation great strides have been made. The U. S. Naval Research Laboratories (R. F. Mehl and G. E. Doan of Lehigh) have just finished a year&apos;s work with a "radium torch" or "shadowgraphic apparatus" in the field of the X-ray, that bids fair to displace the latter to a great extent. The torch is more powerful., easier to operate and cheaper. Penetration of 10 in. of steel has been accomplished, which. is much -beyond the- -scope-, of the X-ray..

Jan 1, 1932

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas&apos; which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy&apos;s law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy&apos;s law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas&apos; which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy&apos;s law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy&apos;s law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By B. B. Kunkle

The history of this refinery has been one of expansion. It now has the capacity to produce 240,000 tons of cathodes annually. A general flowsheet and descriptions of the plant layout, operations involved, and equipment used at one of the world&apos;s largest and most modern electrolytic copper refineries are presented. THE El Paso copper refinery of Phelps Dodge Refining Corp. was originally constructed by the Nichols Copper Co., in association with Phelps Dodge Corp. and the Calumet & Arizona Mining Co., in order to refine anode copper produced at the smelters of the two latter companies. Initial production was obtained from the plant in January 1930 and its annual refining capacity was 100,000 tons of anodes. In order to keep pace with Phelps Dodge Corp.&apos;s increasing copper production in the Southwest, it became necessary in 1937 to increase the El Paso plant&apos;s refining capacity to 160,000 tons of cathodes annually. This was accomplished by adding two sections to the electrolytic tank house, increasing the number of anodes placed in each commercial electrolytic tank from 33 to 37, and making changes in the dc circuits which made it possible to put three generators on each of the two circuits instead of two, thus increasing the amperage on each circuit from 10,000 to 14,800 amp. The capacity of the two furnaces from which refined shapes were cast was increased by raising the sidedoor bays on the furnaces 6 in. An increase of 70 pct in the productive capacity of Phelps Dodge Corp.s Morenci Branch in 1942 again made it necessary to expand refining capacity. In order to accomplish this, Defense Plant Corp. set up a project to increase the capacity of the El Paso plant to 240,000 tons of cathodes annually. This project consisted of enlarging the tank house approximately 50 pct, the construction of another wire- bar furnace, and corresponding increases in other departments where necessary. The engineering work on this expansion was begun in March 1942. Actual construction was under way by August 1942, and the work was completed by March 1944. These additional facilities were purchased from Defense Plant Corp. by Phelps Dodge Refining Corp. in August 1949. The plant is in El Paso about eight miies east of the center of the city and near Highway 80 and the main lines of the Southern Pacific and Texas & New Orleans railroads. The plant site covers approximately 494 acres of company-owned land that is ideally adapted for its use, being well-drained sandy soil and having enough slope so that a minimum amount of excavation was required when the plant was constructed. There is still ample room on the plant site for any future plant expansion. The plant is constructed on four different ground levels and so arranged that the unrefined copper is unloaded on the highest level at the north side of the plant and the refined copper is shipped out from the lowest level on the south side of the plant. The receiving or unloading platform, weighing and sampling rooms, main floor of the tank house, acid and condensate storage tanks, and the slimes and copper sulphate plants are on the first or highest level. The tank house basement, yard scales, charging and furnace bays, balloon flue and stack, brick-storage building, substation and power house, boiler feedwater treating plant and pump house, water storage tanks, and change houses are on the second level. This second level also contains ample yard area for setting-up furnace charges, and for storage of custom scrap, cathodes, scrap anodes, blister, coke, and poles. The casting wheels, inspection conveyors, cathode shears, wire-bar scalping machine, slag

Jan 1, 1952

Readers of recent Bulletins have doubtless observed that the problem of improving both material and moral condition of employees is receiving close attention from influential members of the Institute. This will lend interest to certain developments and investigations that have been reported elsewhere.

Jan 5, 1918

By E. B. Mayo

David LeCount Evans (Consulting Petroleum and Mining Geologist, Wichita, Kans.)-—Not only E. B. Mayo but also W. C. Lacy, who apparently urged the preparation of this analysis, is to be commended. Regional thinking of this type is needed to assure future success in the never-ending search for new mineralized and petroliferous districts. As is usually the case, here is a regional study that will be read by the mining geologist alone. It is ironic that several of the trends established in this study have suggested themselves in northern mid-continent, detailed, and regional studies. These, where established, have offered new keys to petroleum exploration and have provided a possible basis for unraveling a number of broad generalities. The oil geologists, active in Colorado, Kansas, and Oklahoma, would find much food for thought in Mr. Mayo&apos;s projections. To be more specific: 1) The parallelism between E. B. Mayo&apos;s Texas Lineament and the Amarillo Uplift, the Wichita Complex and the Arbuckle Complex of the Texas Panhandle and Southern Oklahoma is viewed with interest and appears especially significant when compared with the similar northwest trend of the Central Kansas Uplift, a major trend of production. 2) Considering the various northeast zones of Fig. 2, and with particular reference to Mayo&apos;s C-C, the Jemez Zone is on direct line with one of several northeast-southwest controls which the present writer has been using with some success in Kansas subsurface correlations. Considering zones of shearing, with no apparent vertical displacement, but suggesting strike-slip movement, because of the staggered effect on other features which cross such trends, Mayo&apos;s philosophy presents regional possibilities for lines of weakness, considered to this time of only local significance. 3) And, finally, in an area as distant from the Southwest as central Kansas, the north-south trends of the Fiarport-Ruggles anticline, the Voshel-Hol-low Nikkel-Burrton structures, the Dayton to Stut-gart trend, the north, slightly east trend of the Ne-maha structural complex, and others all seem to approach the north-south alignments, a through f, of Mayo&apos;s Fig. 3. Mayo&apos;s employment of structural intersections to pinpoint crustal weakness, to localize igneous activity and its accompanying mineralization is not, perhaps, a new concept, but it is a 1958 model, produced by tools improved from the ever-increasing accumulation of geological observations. The use of intersecting trends in petroleum geology is not a new idea, since much production in earlier days was encountered via the straight line projections of established trends to centers of intersection. A tragedy in this age of specialization is that iron curtains have been raised between groups, all seeking raw materials, all acolytes at the altar of structural geology, but all smugly content in and protected by the ivory towers of petroleum geology, engineering geology, mining geology, and geophysics. Mayo presents basic ideas which can stimulate mid-continent structural thinking and, in the case of cen- tral Kansas. he provides a key to replace the broad and overworked simple monoclinal, sinkhole-dotted, Karst topography credo, which is not finding its share of new oil in a state where the declining discovery ratio is disconcerting. The American Association of Petroleum Geologists would do well to add E. B. Mayo to its list of Distinguished Lecturers. Evans B. Mayo (author&apos;s reply)—In reply to David LeCount Evans&apos; comments, it is pleasing to learn that some of the elements discussed in my paper may interest petroleum geologists as well as mining geologists. This should not be surprising, however, because the lineaments make up the framework of the continent, and the oil-bearing sediments must reflect to varying degrees adjustments of basement blocks along their boundaries. A further possibility that petroleum geologists must have considered is that the slow escape of heat from buried lineaments and their intersections has aided the separation of oil from the sediments and started the migration into traps. Regarding the specific points listed by Evans, the following are suggested: 1) The branch of Texas Lineament marked 1&apos; (Fig. 3) is thought to extend eastward through the Capitan Mts., New Mexico, through the long Tertiary dikes east of Roswell, and beyond via the Matador and Electra ranges of the Red River Uplift, Texas. Its further continuation might be the eastern flank of the Ouachita Fold Belt. The Amarillo-Wichita-Arbuckle zone of uplifts appears to continue east-southeastward the Spanish Peaks belt (3-5, Fig. 3). The northwest-trending Central Kansas Uplift would not belong to the above set, except insofar as the Central Kansas Uplift is traversed by west-northwest folds, possible continuations of the Uinta belt (5-5, Fig. 3). 2) The possible continuations into Kansas of the Jemez zone are new to me and are most welcome suggestions. 3) Most of the nearly north-south Kansan structures mentioned by Evans are unfamiliar to me, but the Nemaha Uplift itself appears to be part of a very pronounced structure traceable from the Cerralvo Fault Zone, south of the Rio Grande, through the Bend Arch, Texas, and the Nemaha Uplift, into the Pre-Cambrian of Minnesota (?). This nearly meridional zone is crossed and broken by the Rio Grande Embayment and by the Red River-Wichita Syntaxis. Petroleum geologists realize the economic importance of these features. Perhaps it is inevitable that some papers of general interest be buried in the journals of specialized groups. Moreover, papers dealing with regional, or lineament, tectonics and its applications to exploration for economic mineral deposits are as yet few in the American literature. The opportunity to advance this field is open to all those who are not ultra-conservative and who have a lively curiosity, plenty of patience, and not too many business restrictions. In conclusion, much appreciation is extended to D. L. Evans for his comments.

Jan 1, 1960

By M. Muskat

Calculations are reported on the differential sensitivity of the updip invasion of oil strata of varving permeability to the driving pressure differential. It is assumed that the water-oil interfaces advance with sharp fronts, or that the microscopic displacement efficiency is independent of rate and capillary pressure effects. It is found that, under such conditions, limitations of withdrawal rates will not greatly inhibit the "fingering" and bypassing tendency through high permeability strata unless the differential fluid head across the original oil column is of the order of or exceeds about 80 per cent of the driving pressure differential. In practice, such restrictions will be feasible only for oil reservoirs and aquifers of high permeability and dip, but may develop automatically under combined gas injection and water drive operations. INTRODUCTION A commonly expressed view regarding the intrusion of edge-waters into oil producing formations is that the geometry of such advance is rate sensitive. Specifically, it has been suggested that high rates of advance, stimulated by rapid withdrawals, will lead to "fingering" and an irregular type of invasion, whereas at low withdrawal rates the water encroachment will be more uniform. Two factors tend to support this view. One is the resultant effect of capillary pressure and gravity gradients in the displacement processes&apos; involved in water intrusion, which are magnified at low rates of flow so as to improve the recovery efficiency. The other is the direct retarding effect of the rising water head as it advances upslope into the producing area. Capillary pressure forces give rise to a rate sensitivity of the oil recovery by water displacement in uniform strata as well as differential effects in non-uniform formations. These are basically independent of the effect of gravity and would also occur in horizontal beds or when the oil and water have the same density. Unfortunately, however, the fundamental equation describing the displacement process under the action of capillary pressures can be solved only by numerical or graphical procedures, and moreover the solutions are sensitive to the character of the capillary pressure and relative permeability curves.* On the other hand, the direct effect of gravity can be given a formal analytical solution if the simplifying assumption is introduced that the water advances with sharp fronts in the individual uniform strata. It depends on the absolute permeabilities of the water invaded zones and hence results in a rate sensitivity of the differential invasion in stratified media. Although a tieatment of this factor alone will not give a complete evaluation of the effect of rate on water intrusion in non-uniform pays, it should provide at least a semiquantitative measure of the sensitivity of "fingering" to withdrawal rate. Such a treatment will be presented in the following sections. GENERAL THEORY The basic element of the theory is the history of water advance updip in a uniform stratum (Fig. 1). In contrast to the assumption of constant flow rate, generally made in the analysis of displacement processes, we shall assume here that

Jan 1, 1951

By M. Muskat

Calculations are reported on the differential sensitivity of the updip invasion of oil strata of varving permeability to the driving pressure differential. It is assumed that the water-oil interfaces advance with sharp fronts, or that the microscopic displacement efficiency is independent of rate and capillary pressure effects. It is found that, under such conditions, limitations of withdrawal rates will not greatly inhibit the "fingering" and bypassing tendency through high permeability strata unless the differential fluid head across the original oil column is of the order of or exceeds about 80 per cent of the driving pressure differential. In practice, such restrictions will be feasible only for oil reservoirs and aquifers of high permeability and dip, but may develop automatically under combined gas injection and water drive operations. INTRODUCTION A commonly expressed view regarding the intrusion of edge-waters into oil producing formations is that the geometry of such advance is rate sensitive. Specifically, it has been suggested that high rates of advance, stimulated by rapid withdrawals, will lead to "fingering" and an irregular type of invasion, whereas at low withdrawal rates the water encroachment will be more uniform. Two factors tend to support this view. One is the resultant effect of capillary pressure and gravity gradients in the displacement processes&apos; involved in water intrusion, which are magnified at low rates of flow so as to improve the recovery efficiency. The other is the direct retarding effect of the rising water head as it advances upslope into the producing area. Capillary pressure forces give rise to a rate sensitivity of the oil recovery by water displacement in uniform strata as well as differential effects in non-uniform formations. These are basically independent of the effect of gravity and would also occur in horizontal beds or when the oil and water have the same density. Unfortunately, however, the fundamental equation describing the displacement process under the action of capillary pressures can be solved only by numerical or graphical procedures, and moreover the solutions are sensitive to the character of the capillary pressure and relative permeability curves.* On the other hand, the direct effect of gravity can be given a formal analytical solution if the simplifying assumption is introduced that the water advances with sharp fronts in the individual uniform strata. It depends on the absolute permeabilities of the water invaded zones and hence results in a rate sensitivity of the differential invasion in stratified media. Although a tieatment of this factor alone will not give a complete evaluation of the effect of rate on water intrusion in non-uniform pays, it should provide at least a semiquantitative measure of the sensitivity of "fingering" to withdrawal rate. Such a treatment will be presented in the following sections. GENERAL THEORY The basic element of the theory is the history of water advance updip in a uniform stratum (Fig. 1). In contrast to the assumption of constant flow rate, generally made in the analysis of displacement processes, we shall assume here that

Jan 1, 1951