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The Raymond Memorial Volume, which the Members of the In-stitute have been so anxiously awaiting since the beloved man's death, is nearly ready for publication. It will contain about 45,000 words and some illustrations and a frontispiece portrait. This book promises to fill every expectation of the contributors to the volume and the host of admirers of the genius who so long guided the destiny of the Institute. It will contain one of Doctor Raymond's best stories, entitled "James and Jim;" his famous article on "Job on Mining;" and one of his poems entitled "The Grand Canyon." A biography of Doctor Raymond has been written by his daughter, who is the wife of a member of the Institute. The memorial addresses delivered by Dr. Henry F. Drinker and T. A. Rickard at the annual meeting in New York in 1919 will be included. There will also be very interesting reminiscences by H. M. Howe, A. S. Dwight, C. W. Goodale, R. W. Hunt, Lyman Abbott, J. F. hemp, T. A. Rickard. The volume has been edited by T. A. Rickard, which promises all that can be wished for the volume from a literary standpoint. The edition will he limited so that it is very desirable that orders for this volume be sent in to the Institute as promptly as possible. The price will be $5.00.

Jan 12, 1919

By W. L. Martin, J. N. Dew, H. B. Steves, M. L. Powers

This paper presents and discusses the results obtained during a pilot test in the Loco field in southern Okla homa. The test was conducted in a 2%-acre pattern that was part of a 20-acre conventional waterflood pilot area. The conventional flood was well past its economic limit when the hot waterflood was initiated to obtain technical information and operating experience. Temperature data from nine observation wells showed that about 75 percent of the pattern was affected by heat, and that heat losses were severe in the pilot pattern. About 60 percent of the injected heat was lost to overburden and underburden zones during hot-water injection. Wellbore heat losses were held at tolerable levels at the shallow depth of the test by providing a low-pressure air annulus between the injection tubing and well casing. Hot water provided water injectivity increases of 200 to 400 percent. The hot water channeled across the lower portion of the oil sand in three directions through zones of relatively high water saturation. There was no conclusive evidence that natural fractures or pressure partings aflected the flow of fluids in the pilot pattern; however response undoubtedly was aflected by localized pressure gradients and by injection-production rate ratios. The results showed that hot waterflooding increased oil recovery in a reservoir containing 600 cp oil. The total tertiary oil production from the pilot pattern area was 3,896 bbl or about 156 bbl/acre-ft swept by heat. The corre.sponding WOR was about 34:I. Description of the Hot Waterflood Process To hot waterflood an oil reservoir, water is injected that has been heated to a temperature substantially higher than the original reservoir temperature, but lower than the vaporization temperature of water at the prevailing pressures. In the reservoir the hot water flows continuously into cooler sand and rapidly loses heat to the sand until it has been cooled to the original reservoir temperature. Thus, a heated zone and a region or "bank" of cooled water begins to accumulate immediately after hot water injection is started. This bank of cooled water continues to grow ahead of the heated zone, which also grows, but at a slower rate. This occurs because heat transfer is almost instantaneous, and the ratio of heat capacities of water to rock is such that two or three unit PV of hot water must be injected to heat a given unit bulk volume of the reservoir. The primary displacement mechanism is the same for both hot and conventional cold waterfloods; i.e., "piston" displacement occurs at the original reservoir temperature. The incremental benefits of hot waterflooding usually occur long after the breakthrough of cold water at producing wells, and the increased oil recovery necessarily is accomplished with high WOR's (water-oil ratios). Heat decreases the viscosity and density of oil and water. These effects result in more rapid and increased recovery of secondary or tertiary oil. If the cost of the required heat is low enough, the ultimate oil recovery of a hot waterflood should be increased substantially over what would be expected at the economic limit of a conventional cold waterflood. The economic benefits of any hot-fluid injection project depend primarily upon the cost of the heat required to produce more oil at an increased rate. This cost depends in part upon the amount of heat lost to surrounding formations. Heat loss depends upon reservoir thickness, water injection rate and temperature, the depth of the formation, well spacing, and the characteristics of the reservoir rock and surrounding formations. In general, percentage heat losses decrease as injection rate and reservoir thickness increase. Although it is an old idea, hot-water injection has not received widespread field application in the oil industry as a drive process. Much of the original field work with hot water was done in Pennsylvania fields where water permeabilities and injection rates are low. In these cases, hot-water injection was used primarily as a means of increasing in-jectivities — not as a recovery process. Ramey' recently has published an excellent review of the development of hot fluid injection processes. Recent publications"' and our own experiences now indicate that hot water or steam injection also can effectively increase the oil recovery from reservoirs containing viscous crudes. However, the economics of these methods as displacement processes have not been established. Several theoretical predictive techniques have been published (for a review see Ramey'), but simplifying assumptions make

Jan 1, 1969

By S. C. Lindsay, D. J. I. Evans

With each year that passes hydrometallurgical processes are being more widely used to recover base metals from ores and concentrates. Generally these processes involve liquid-solid separation of metal-bearing liquors from barren residues. This may be done by countercurrent decantation, thickening and filtration, or filtration or centrifuging only. Choice of method is governed by chemical and physical characteristics of the pulps; cost of labor, power, materials, and waste disposal; and even by the amount of capital available when building plans are under way. Since all these controlling factors change with time and location and with technological advances, the separation method must be re-evaluated when new plants or expansion programs are contemplated. At the Sherritt Gordon refinery in Fort Saskatchewan, Alberta, an ammonia pressure leaching process recovers nickel, copper, and cobalt from the nickel concentrate produced at Lynn Lake, Manitoba.' Pregnant liquors are separated from the barren leach residues in a thickener-filter liquid-solids circuit. The decision to use this type of separation was based on a summation of economic factors during the pilot plant and design stages. Although countercurrent decantation was not incorporated in the refinery flowsheet, the problems solved in thickening the leach residues and the experience gained in operating the commercial plant are pertinent to countercurrent decantation, particularly where it is applied to slow-settling leach slurries or slurries having a relatively high vapor pressure of a valuable, obnoxious, or poisonous vapor. The nickel sulfide concentrate is leached under pressure with air and ammonia to dissolve the nickel, copper, and cobalt and most of the sulfur, leaving a residue of iron and siliceous material to be discarded.2,3 During a subsequent distillation stage to recirculate part of the ammonia used for leaching, copper is recovered from the solution as a high-grade sulfide. After further purification to remove traces of copper and undesirable sulfur compounds, the nickel is precipitated by hydrogen under pressure at an elevated temperature. The cobalt, together with unreduced nickel, is precipitated as a mixed metal sulfide by hydrogen sulfide for eventual cobalt recovery. The end solution is then evaporated to produce a crystalline ammonium sulfate byproduct. As shown in Fig. 1, the nickel concentrate is leached in a continuous, two-stage, countercurrent circuit. In the first stage, or adjustment leach, the fresh concentrate is partially leached (60 pct) in the liquor produced in the second stage, or final leach. This system is necessary to produce a solution suitable for treatment in the copper sulfide precipitation step. Both stages are carried out at 170" to 180°F under a total pressure, with air, of 100 to 120 psig in large, horizontal, water-cooled autoclaves. The autoclaves are divided by overflow weirs into four compartments to give a certain amount of staging during leaching. In each compartment a relatively slow-speed (100 to 150 rpm) agitator maintains the nickel concentrate in suspension. Adjustment leaching, carried out in two autoclaves in parallel, is followed by a thickener-filter liquid-solids separation. Final leaching is done in two parallel trains of three autoclaves using aqueous ammonia to extract metal values from the adjustment leach residues. This too is followed by a thickener-filter circuit. Here the residues are repulped once with aqueous ammonia and twice with process water and refiltered after each repulping stage, to insure a maximum recovery of soluble metal, before being discarded to the tailings pond. The adjustment leach is followed by a seven-disk Dorr-Oliver American filter, with an agitator in the filter boot to keep the residues in suspension. Agitators have also been installed beneath the four ten-disk filters following the final leach thickener. Slurry Characteristics: A typical analysis of the Lynn Lake nickel concentrate, produced by differential flotation,' is given in Table I. The concentrate comprises 35 to 49 pct pentlandite, (Fe, Ni)S; 3 to 6 pct chalcopyrite, CuFeS,; 1 to 4 pct pyrite, FeS2; and 24 to 42 pct pyrrhotite, Fe1-2S (where x varies between 0 and 0.2) together with various siliceous minerals such as actinolite, hornblende, and talc. During leaching, the sulfur in the pentlandite, chalcopyrite, and part of the pyrrhotite is successively oxidized through the thiosulfate and poly-thionate radicals to sulfate and sulfamate." Simultaneously the nickel, copper, and cobalt are converted to soluble ammine complexes and the iron in the pentlandite, chalcopyrite, and part of the pyrrhotite is oxidized to a spongy hydrated iron oxide. The hydrated iron oxide is readily broken down by the agitation needed to sustain the concentrate in suspension and to maintain a satisfactory mass transfer of the oxygen from the air to the slurry. Table I shows typical chemical, screen, and

Jan 1, 1961

By G. R. Belton, R. J. Fruehan

The Knudsen cell-mass spectrometer combimtion has been used to study the Fe-Al and Ag-Al liquid alloys. By application of the recently developed integration technique to the measured ion-current ratios, activities have been derived for the Fe-A1 system at 1600° C and for the Ag-Al system at 1340"C. The results are partially represented by the following equations: Internal consistency between the data on silver-rich and iron-rich alloys is demonstrated by application of the literature measurements on the distribution of aluminum between the nearly immiscible liquids iron and silver. The usual restrictions on the ratio of the mean free path of the escaping atoms to the orifice diameter of the Knudsen cell are shown not to be limiting in this technique. DESPITE the importance of a knowledge of the activity of aluminum in understanding deoxidation equilibria in molten steel, no direct studies have been made of activities in liquid Fe-A1 alloys at steel-making temperatures. Lower-temperature direct studies have, however, been carried out on aluminum-rich liquid alloys by Gross, Levi, Dewing, and Eilson' at 1300°C and by Coskun and Elliott' at 1315°C. Apart from phase diagram calculations by Pehlke, other determinations have been indirect and were made by measurement of the distribution of aluminum between iron and silver475 and combination of these data with extrapolated activities in the Ag-A1 system.~-% ecently, however, Woolley and Elliott have made a significant contribution by directly measuring heats of solution in the Fe-A1 system at 1600°C. The present authorslo have recently employed a Knudsen cell-mass spectrometer technique in a study of activities in iron-based liquid alloys. In this technique activities and heats of solution are determined from a series of measurements of the ratio of ion currents of the components; and since ion-current ratios are used, problems caused by changes in instrument sensitivity or cell geometry are overcome. Results obtained for the Fe-Ni system were found to be in excellent agreement with previous work, thus demonstrating the reliability of the method. The present paper describes a similar study of activities in the liquid Fe-A1 and Ag-A1 systems, this latter system being included in order that a meaningful comparison can be made with the above-mentioned indirect studies. INTEGRATION EQUATIONS A detailed derivation of the equations used to determine the thermodynamic properties from the measured ion current ratios has been given elsewhere;'' however it is useful to summarize them here. By the combination of the Gibbs-Duhem equation with the direct proportionality between ion-current ratios and partial pressure ratios, it was shown that for a binary system at constant temperature and pressure: where al is the activity of component 1 with pure substance as the standard state, N, is the atom fraction of component 2 in the solution, and I; and t'2 are ion currents of given isotopes of the components. The activity coefficient is given by: this latter equation being more suitable for graphical integration. Combination of Eq. [l] with the Gibbs-Helmholtz equation gives an expression for the partial molar heat of mixing: EXPERIMENTAL A Bendix Time-of-Flight mass spectrometer model 12! fitted with a 107 ion source and a M-105-G-6 electron multiplier, was used to analyze the vapor effusing from the Knudsen cell. The arrangement of the Knudsen cell assembly was essentially that of the commercial instrument (Bendix model 1030) but with several modifications. Instead of heating with a single tungsten filament, a cylindrical tantalum-mesh heater was employed. Up to 1400°C simple resistance heating was used but above this temperature electron bombardment between the tantalum mesh and the tantalum cell susceptor was necessary. The temperature was measured by means of a Leeds and Northrup disappear ing-filament type optical pyrometer sighted on an essentially black-body hole in the side of the cell. Details of the temperature control, temperature measurement, and in situ calibration of the optical pyrometer can be found elsewhere.I0 In the investigation of the Fe-A1 system the Knudsen cells were constructed of thoria crucibles with fitted thoria lids (Zircoa). The cells employed in investigating the Ag-A1 alloys were made up of high-purity alumina crucibles (Morganite) with lids of recrystal-lized alumina (Lucalox). The cells were 0.370 in.

Jan 1, 1970

By A. H. Larson, L. G. Twidwell

The influence which Au, Ag, Sb, Bi, Sn, and Cu have, both individually and collectively, on the activity coefficient of sulfur in liquid lead at 600"C zuas studied by circulating a H2S-Hz gas wlixture over a specific lead alloy until equilibrium was attained. Subsequently, the H2S concentration in the equilibrium gas mixture and sulfur concentration in the condensed phase were deterruined. The elements gold, silver, and antinzony (above 8 at. pct) increased the activity coefficient of sulfur. Bismuth had no apparent effect. Tin (above 3 at. pct) and copper decreased the coefficient. The influence of an individual element, i, on sulfur is best reported as the interaction parameter, riS, which is defined as The values o these first-order interaction zus are: ESzu = —55.0. These interaction parameters are used to predict the activity coefficient of sulfur in six fouv-component alloys and one seven-component alloy. Comparisons are made with direct experimental determinations. INTERACTIONS in dilute solution have been studied by many investigators. Most of the experimental work has been confined to solute-solvent interactions in simple binary systems and solute-solute interactions in ternary systems. Dealy and pehlke"~ have summarized the available literature on activity coefficients at infinite dilution in nonferrous binary alloys and have calculated from published data the values for interaction parameters in dilute nonferrous alloys. Interaction parameters are a convenient means of summarizing the effect of one solute species on another in a given solvent. Only a few investigators have studied interactions of the nonmetallic element sulfur in a metallic solvent. They are as follows: Rosenqvist,~ sulfur in silver; Rosenqvist and Cox,4 sulfur in steel; chipman, sulfur in alloy steels; Alcock and Richardson,% ulfur in copper alloys; Cheng and Alcock,' sulfur in iron, cobalt, and nickel; Cheng and ~lcock,' sulfur in lead and tin. The only reported work on the Pb-S system in the dilute-solution region is that of Cheng and Alcock.' Their investigation involved a study of the solubility of sulfur in liquid lead over the temperature range 500" to 680°C. The results may be summarized by the following relationship: S (dissolved in lead) + Pb(1) = PbS(s) log at. %S = -3388/T + 3.511 Experimentally, it was found that Henry's law was valid up to the solubility limit of sulfur in lead, i.e., at 600°C up to 0.43 pct. Their investigation did not include the study of sulfur in lead alloys. More accurate calculations could be made in smelting and refining systems if activity coefficients of solute species could be accurately predicted in complex solutions. One of the objectives of this study was to compare the experimental data with the values calculated from the equations derived from models for dilute solutions proposed by wagner9 and Alcock and Richardson. A temperature of 600°C was chosen as the experimental temperature to attain reasonable reaction rates and to minimize volatilization of the condensed phase. EXPERIMENTAL Materials. The Pb, Au, Ag, Sb, Bi, Sn, and Cu used for preparation of the alloys were American Smelting and Refining Co. research-grade materials. All were 99.999+ pct purity except the antimony and tin which were 99.99+ pct. The initial alloys prepared for this study consisted of twenty-one binary alloys, eleven ternary alloys, and one six-component alloy. The constituent elements were mixed for each desired alloy and were placed in a crucible machined from spectrographically pure graphite. The crucible was placed in a vycor tube which was evacuated with a vacuum pump and gettered by titanium sponge at 800°C for 8 to 12 hr. After the gettering was completed, the chamber containing the titanium was sealed and removed. The remaining sample chamber was placed in a tube furnace at 800°C for 2 hr and quenched in cold water. The final operation consisted of homogenization of the alloy for 1 to 2 weeks at a temperature just below the solidus for the individual system. The resulting master alloys were sectioned into small pieces and a random choice made for individual equilibrations. Cobalt sulfide (Cogs8) used to control the gas atmosphere in the circulation system was prepared by passing dried HzS for 24 hr over a Co-S mixture heated to 700°C in a tube furnace. This material was then mixed with cobalt metal to give a two-phase mixture which, when heated in hydrogen to a particular temperature, produced a desired H2S/H2 gas atmosphere in the circulation system. A Cu2S-Cu mixture also used in this study was prepared in a comparable manner. Apparatus for Equilibrium Measurements. The experimental technique of this study required apparatus

Jan 1, 1967

By Rex O. McLellan

The formation of a monovacancy in a metal is simulated in an elastic model by the displacement of the surface of a small spherical cavity in a large elastic continuum. The application of linear elasticity to this distortion results in a well- known formula for the energy and an expression for the concomitant entropy change due both to the shear strain in the continuum and also to the dilation of the solid resulting from the boundary conditions at the surface of the solid. Elastic data (the sliear modulus and its temperature coelficient) are used to calculate the entropy and energy of formation for many metals. Despite the simplicity of the assumptions involved, the agreement between the calculated entropies and energies and experimental values is remarkably good. In recent years there has been a large increase in measurements of the absolute concentration of mono-vacancies in metals as a function of temperature. Hence new data for both the energy and the noncon-figurational entropy of formation of monovacancies has become available. Recent measurements&apos; of the anomalous (non-Arrhenius) self-diffusion in many bcc metals has also focused interest on the prediction of the thermodynamic parameters of mono- and multi-vacancies in those metals for which no data are available. Damask and Dienes&apos; have discussed the various theoretical calculations of the energy of formation EL, of a monovacancy. These include simple models involving the breaking of atomic bonds on moving atoms from the interior of a crystal to the surface, models combining elastic calculations with surface-energy terms and detailed quantum mechanical calculations. The simler models give the correct order of magnitude of &, but tend to overestimate it by a factor of about two. The quantum mechanical calculations4"7 have been carried out for the noble and alkali metals with generally reasonably good agreement with the available Ef data. The calculation of entropy of formation Sfv14 lnvolves a fundamental calculation of the perturbation of the phonon spectrum caused by the creation of a vacancy. Huntington, Shirn. and wajda8 have given an approximate evaluation of sJV by considering an Einstein model for the localized vibrations in the immediate neighborhood of the defect and then using elastic theory to calculate the entropy associated with the shear stress field in the distorted crystal (as originally proposed by Zenerg). They also included a term due to the dilation of the crystal. They obtained a value of 1.47k for copper, in good agreement with the experimental value (1.50k). However, Nardelli and Tetta- manzi1° have recently shown that neglecting the coupling between atoms (Einstein Model) may lead to a serious error so the agreement may be somewhat fortuitous. In this work simple linear elastic theory is used to calculate the entropy and energy of formation of mono-vacancies. Despite the simplicity of some of the assumptions involved, the agreement with the available experimental data is remarkable. However. the reasonable degree of success in the application of linear elastic calculations to the excess entropy of a solute atom in a dilute solid solution1&apos; indicates that the application of elastic theory to vacancies. where the interaction of different atomic species is not involved, may not be inappropriate. THE ELASTIC MODEL The metal is assumed to be a spherical elastic continuum. A small spherical cavity of volume V = 4i;v:&apos;/3 is cut from the center. removed. and dissolved rever-sibly in the bulk of the material. TO a good approximation no net atomic bonds are broken and the material does not undergo a volume change although the externally measured volume of the body would increase by V. The radius of the sphere of metal is much larger than r Next a negative pressure is applied to the cavity causing its surface to be displaced inward by an amount simulating the relaxation of the lattice around a monovacancy. In this model the energy and entropy accompanying the distortion are taken as 4, and <. As a first approximation the equation of state for the solid is taken as: r = ro(i + *~D LiJ where K is the bulk modulus. P the hydrostatic pressure. Vo the volume of the material at 0°K and zero pressure. and d+/dT = 30. where 0 is the linear thermal expansion coefficient. The variation of entropy with hydrostatic pressure is given by the Maxwell equation: These equations give the entropy change resulting from increasing the hydrostatic pressure from 0 to P as: and since • we have: This is the entropy arising from the dilation resulting

Jan 1, 1970

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett&apos;, Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,&apos;. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett&apos;, Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,&apos;. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By John L. Miles

John L. Miles (Arthur D. Little, 1nc.)—Pollack and orris" have reported measurements on electron tunneling through A1-A12O3-A1 sandwiches in which the oxide was formed by gaseous oxidation in a glow discharge. From these measurements they deduced the asymmetry of the barrier and, since this is small, conclude that the mechanism suggested by Mott19 for the growth of oxide in thin A12O3 films is inapplicable. In earlier papers20 Pollack and Morris report similar work for oxide films grown thermally. In this case they find a greater asymmetry and conclude that the Mott mechanism is valid. I would like to point out that both these conclusions are quite unjustified. Mott suggests that the growth of the oxide film on aluminum results from the passage of ions through the already present film of oxide under the action of an electric field. This field results from a constant voltage which is in effect a contact potential between metal on one side of the barrier and adsorbed oxygen ions on the other side of the barrier. The theory does not require that the oxide grown is nonuniform either in stoichiometry or structure. It does however specifically assume that the partial layer of ionized oxygen on the surface remains adsorbed on the surface of the growing oxide. In other words, the so-called "built-in field" remains in the oxide only as long as the ionized oxygen is present. When a counter electrode of aluminum is deposited on the oxide, it will react with the adsorbed oxygen on the surface of the oxide, thus forming a small additional amount of oxide. It is clear, then, that there is no requirement in the Mott theory of oxide growth which would necessitate tunneling currents through an Al-A1203-A1 sample to be different when the polarity is reversed. Neither does the theory eliminate the possibility that some additional mechanism could cause the tunneling barrier to be asymmetric and hence tunneling currents to be a function of polarity in such a sandwich. Thus these tunneling-currents measurements are not germane to the question of whether the Mott mechanism is the true method of growth of aluminum oxide films. In fact, it is not surprising that there should be a difference between the oxide properties at the two interfaces (with resulting asymmetry in the tunneling barrier) since the growth conditions and growth rates must have been quite different at these two positions. S. R. Pollack and C. E. Morris (authors&apos; reply)— The point raised by Miles above is one has caused some confusion in the past. The following is an attempt to clarify this point. The built-in field which is responsible for the growth of the thermal oxide at low temperatures arises, according to Mott, because of the passage of electrons from the Fermi surface of the oxidizing metal to surface states introduced by the adsorbed oxygen. It is assumed that the energy of these surface states lies below the Fermi energy of the metal. Electrons therefore continue to flow from the metal to the surface until the built-in electric field raises the potential energy of the surface states to the value of the Fermi energy in the metal, at which time equilibrium is obtained between the surface states and the metal. That is in equilibrium as many excess electrons pass from the metal to the surface per unit time as vice versa. The surface of the oxide prior to deposition of a metallic counterelectrode can then be pictured as follows. The Fermi energy lies in the energy gap of the oxide and is essentially pinned at the energy of the oxygen surface states. The vacuum work function of the oxide is then given by the sum of the electron affinity of the oxide (i.e., the difference in energy between the vacuum and the conduction-band minimum) plus the energy difference between the conduction-band minimum and the Fermi energy. The deposition of a metal onto the surface of the oxide can result in a transfer of electrons across the extremely thin oxide only if there is a contact potential difference between the deposited metal and the parent metal or oxide. That is if the vacuum work function of the deposited metal differs from that of the parent metal, then charge can be redistributed across the oxide in order to equilibriate the Fermi energy across the structure. (It should be

Jan 1, 1965

By B. Ramaswami, U. F. Kocks, B. Chalmers

The latent hardening of silver and an Ag-Au alloy was investigated by lateral compression, overshoot in tension and cormpression, and the stability of multiple-slib orientations. The latent hardening of a secondary slip systenz depends on its relation to the primary slip system. For most secondary slip systems the latent hardening is larger for Ag-10 at. pct Au than for pure silver. The maximum increase in. flow stress on a secondary slip system over that of the primary slip system was 40 pct. The work hardening during the lateral-compression test on the latent system after prestress on the primary system is iuterbreted in terms of the preferential distribution of barriers to dislocation movement with respect to the active slip system in work-lzardened fcc crystals. The work-hardening in fcc crystals is mainly due to the dislocation interactions and the barriers to dislocation movement formed as a result of reactions between dislocations of different slip systems. The operation of sources on the latent system depends on the flow stress of those systems; hence, the increase in flow stress of a latent system due to glide on an active system, which is called latent hardening, is an important element in understanding the phenomenon of work hardening. The problem of latent hardening has attracted the attention of many investigators in the past. For example, a theoretical study of the elastic latent hardening of the latent systems due to glide on an operative system has been made by Haasen&apos; and ~troh. These calculations, however, neglect the stress required for the intersection of forest dislocations by the glide dislocations, a factor which would be important for producing macroscopic strains on the secondary slip systems. The importance of this factor will become evident from the results presented here. Attempts have also been made to determine the latent hardening of different slip systems by experimental means by the methods summarized in Table I.3-9 The experimental methods used have been subject to certain limitations. For instance, in the method used by Hauser,9 frictional constraints between the specimen and the compression platen were not eliminated by proper lubrication (see Hos- ford10). Secondly, with the exception of Kocks,6 Hauser,9 and Rohm and Kochendorfer,11 latent-hardening studies have been made on only one of the slip systems, i.e., on either the conjugate or the coplanar slip system; hence, extensive results are not available on the latent hardening of different slip systems in the same materials, with the exception of aluminum.6 It was therefore decided to study the latent hardening of the conjugate, critical and half-related slip systems in silver. Similar experiments were done in Ag-10 at. pct Au to study the effect of solute (gold) on the latent hardening of silver. Lastly, indirect evidence can be obtained by a study of the orientation stability of crystals of multiple-slip orientations in tension and compression. This method has been used by Kocks6 to supplement his studies of latent hardening in aluminum. Similar studies were made at room temperature in single crystals of silver. EXPERIMENTAL PROCEDURE The single crystals of the desired orientations were grown and the tensile test specimens were prepared as described in Ref. 12. The compression tests were made on 1/4-in.-cube specimens. The specimens were cut from single crystals, in the Servomet spark-erosion machine.13 The two cut surfaces were planed using the lowest available planing rate in the machine to minimize the deformation layer. A brass strip was used as the planing tool. This method of preparation ensured plane parallel faces for the compression tests. The deformed material was removed by prolonged etching in a weak etching solution. A weak etching solution was used to prevent pitting of the surfaces and to ensure uniform etching. About 25 to 50 µ of material were removed from all faces by the etching treatment. The specimens were then annealed for 24 hr at 940°C in oxygen-free helium and cooled in the furnace to room temperature over a period of 7 hr. After annealing, the orientation of the specimens was determined by Laue back-reflection technique to make sure that no recrystallization had occurred on annealing. The compression-test technique and setup are described in Ref. 14. The Laue back-reflection technique was used to study the overshoot in tension, the overshoot in compression, and the stability of the axial orientation in tension and compression. The tests were interrupted after every few percent strain to determine the axial orientation. In investigating the overshoot in compression, the operative system was determined by studying the asterism of the Laue spots.

Jan 1, 1965

By S. D. Baumer, P. M. Hulme

IN the late thirties, the National Carbide Co. cooperated with C. E. Wood, of the U. S. Bureau of Mines, in his investigation of the relative merits of various desulphurizers, including soda ash, caustic soda, and calcium carbide. Laboratory tests showed that carbide, when it could be made to react, is an excellent desulphurizing agent for molten iron. Sulphur content can be driven to lower levels and higher extractions obtained with carbide than with actionsany of the more common reagents. Wood&apos;s results1 are shown in Table I. Unfortunately, as the Handbook of Cupola Operation puts it, the chemical fact that carbide is a good desulphurizer was of only academic interest because it was found to be extremely difficult to devise a practical means to make it react with molten iron. Calcium carbide is formed in the electric furnace at 4000°F and above, and its softening point is probably at least 500 °F above the usual working temperatures encountered in iron and steel practice. Consequently, carbide does not form a true slag but floats as a dry powder on top of the metal and only a very small portion of it ever comes in actual contact with the iron. Stirring with a rabble, or pouring the metal over the carbide, increases the efficiency only slightly. Extractions of 20 to 30 pct can be obtained in this manner, but conventional soda slag treatment can do better than this and do it more cheaply. All attempts to lower the melting point of carbide in order to obtain a reactive, liquid slag have so far proved fruitless. Directly under the arc in a metallurgical electric furnace, carbide becomes highly reactive. Excellent sulphur removal can be obtained without any slag other than a thin layer of carbide." imilarly, good results are obtained by adding small amounts of carbide to the finishing slag in double-slag arc furnace practice. To react a liquid with a solid, it is axiomatic that the liquid has to wet the solid before anything can happen. If the solid is heavier than the liquid, the problem is easy, but it becomes more difficult when the solid is much lighter than the liquid, as in the case of carbide and liquid iron. Wood recognized this problem and solved it in a unique fashion. The results shown in Table I were obtained by spinning the carbide beneath the surface of the molten iron by means of a refractory centrifuge. This technique allowed each particle of the finely divided carbide to come into intimate contact with the metal and to be wetted thereby. Wood&apos;s centrifuge technique was successful in the laboratory where it achieved excellent and consistent results. Some attempts were made to expand this method to commercial practice, but serious difficulty was encountered in obtaining a refractory centrifuge head that would be economically feasible. About this time the war intervened and the project lay dormant for several years. In 1944, it was revived. It was suggested that the carbide could be blown into the metal with a carrier gas in an attempt to eliminate the necessity for the expensive and brittle centrifuge. The idea was first tried out in a fairly large ladle of iron using natural gas as the carrier. Considerable sulphur was removed, but it was quite obvious that the use of natural gas was not practical. Attempts then were made to blow carbide into molten iron using, in turn, nitrogen, argon, carbon dioxide, air, and oxygen. The latter two gases proved unsatisfactory. Calcium evidently prefers oxygen to sulphur because in the tests calcium oxide and carbon dioxide were produced, the sulphur still being untouched in the iron. Nitrogen, argon, and carbon dioxide gave much better results, although the efficiencies and extractions were erratic, and only a few isolated tests approached the results obtained by Wood. Table II shows typical results obtained with these gases. The sulphur removals were interesting, sometimes even encouraging, but it is evident that such erratic behavior could not be tolerated in commercial practice. A number of different types of equipment, such as sand blasting machines, refractory guns, and the like can used to blow the solid into the metal. All types required relatively large quantities of gas in order to maintain the flow of solid carbide through the system and into the metal. It was observed that the bubbles of gas breaking through the surface of the metal contained quantities of unreacted carbide. The liquid metal never came in contact with these particles and if it cannot wet them it cannot react with them. The initial work had shown that carbide had great possibilities as a desulphurizer. In practice

Jan 1, 1952

By R. G. Treuting, W. C. Ellis

The twinned state is characterized by a lattice of coincidence sites. Imperfections are required at stable lateral twin interfaces. Twinned regions can occur with relative ease in the diamond cubic IN recent contributions1,2 on the origin and growth of cubic annealing twins, attention has been directed to the orientation relations between such twinned components and their parent matrix. There are some aspects of twinning which may be illuminated by a more detailed consideration of the twinned state" alone. As an extreme example, the dense twinning in cast ingots of germanium,&apos; as contrasted with the rarity of twins in cast face-centered cubic metals, is yet to be accounted for. It has been this that has led us to the present work, which, it will be noted, uses methods and constructions in many respects similar to those of Kronberg and Wilson.&apos; In the cubic systems, a 70" 32&apos; rotation about a <110> axis is angularly equivalent, as to twinning, to the more usually considered 180" rotation about a <111> axis. Figs. 1 and 2 show a (110) projection of a twinned face-centered cubic lattice and a twinned diamond cubic lattice. In both figures, the two adjacent planes A and B, shown by the larger and smaller circles, are sufficient to represent the entire array. In each case a section of lattice, the original atom sites of which are shown by open circles, has been rotated as indicated through 70" 32&apos; to bring an original. [112] direction into coincidence with the [112] diiection. The latter is the intercept on the (110) projection of the (ill) plane normal thereto, the twinning plane. In the face-centered cubic case the rotation can be performed about an axis passing through an atom-site; the mirror plane then is also a composition plane containing atoms common to both twinned and untwinned lattices. The diamond cubic lattice may be construed as two interpenetrated face-centered lattices. Its (111) planes recur in a sequence of alternately short and long interspacings. Consequently a mirror plane for twinning cannot be a composition plane, but must be the bisector of one of the spacings. When the longer spacing is selected, the closest distance of approach across the mirror plane in the [ill] direc- tion is identical with that in the untwinned structure. In each case periodically recurring (ill) planes (parallel with the twinning plane) are found, on which there is coincidence of atom sites of the pre-twinned and twinned orientations; these are indicated by the cross-hatched circles. In the face-centered lattice there is such coincidence every third (ill) plane; in the diamond cubic lattice, on two adjacent planes in every six. At the twinning interface in the latter, there is on each side of the mirror plane a (ill) plane of atoms common to both twin components. Conceivably, there is little influence on a plane of atoms about to be adhered to such a pair of coincidence planes, whether it be laid down in a normal or in a twinned position with respect to the previously formed structure. Slawson% as attributed the high incidence of twinning in diamond to this boundary state. Further examination shows that the motion of intermediate planes can consist of various pairs of equal and opposite translations, for example of (ill) planes in the [l&apos;;i2) direction, the familiar twinning shear, indicated in the small schematics in the figures. Since the translations form a system of shears of alternating sign between coincidence planes, twinning could take place by such a mechanism over an extended region without extensive shear; in fact, in this case any atom moves but the distance in the [1i2] direction. One alternative construction for the face-centered cubic lattice leading to the same end result is illustrated in Fig. 3. The plane (711) with respect to the pretwinning orientation (the twinning plane of Fig. 1) is given, the twinned region arbitrarily bounded by <110> and <112> directions. The coupled shear is identical to that of Fig. 1. The "rotational" movement about coincidence sites generating the same twinned position could consist as shown of the translation a,/d% for each atom of a group of three in the B layer in a different one of the three <112> directions, and a similar translation of the underlying three atoms in the C layer in either the same or the opposite sense. This is not dissimilar to Kronberg and Wilson&apos;s construction for their 22" rotation of three adjacent (111) planes.

Jan 1, 1952

By P. G. Shewmon

A novel technique for determining the surface energy (?) and its derivative with respect to orientation, (?&apos;) is described. Essentially it involves the &apos;floating" of a wedge on the substrate, said wedge being made of a material which is not wet or only slightly wet by the substrate, i. e., as a greased needle "floats" on water. A thermodynamic analysis of a system in which the wedge is supported entirely by surface energy is given. If the original suyface is not at a cusp orientation, the surface tension is directly measurable from the groove angle formed. If the original surface is at a cusp orientation, there may or may not be a groove depending on the relative value of ?&apos; and the weight of the wedge. Experiments primarily on copper and silver showed that sapphire, quartz and refractory metal wedges were wet while graphite wedges were not. The technique was demonstrated to work using graphite wedges, but the results obtained were not as eccurate as those obtained by other workers using the wire-creep experiments. It is concluded that the technique might prove most useful with non-metals where ?&apos; is large and filament creep experiments would be quite difficult. If an absolute value of the surface free energy (?) of a metal is to be determined, the most reliable methods used to date measure an average over the various orientations exposed on a polycrystalline sample. For example, ? for silver, gold, and copper have been measured by determining the force required to just keep a thin wire,&apos; or foil,&apos; specimen from contracting under the influence of ?. Herring 3 has predicted and experiment confirms, that the sensitivity of this method is inversely proportional to the grain size.&apos; Thus it cannot be used to measure ? for a particular orientation by using a foil single crystal or a very coarse-grained specimen. An accurate value if ? for tungsten averaged over a range of orientations has been determined using a field emission technique. The same techniques cannot or have not been used to measure ? for non-metallic solids, and as a result the values available are much less accurate.4 This Paper resents a means of making an absolute determination of ? for a particular surface orientation on any solid, as long as the given surface orientation does not break up into other orientations during an anneal. Experimentally ? is found to vary with orientation and at a few low index orientations it is found to have a cusped minimum, i.e., the derivative of ? with respect to the orientation of the surface changes discontinuously at the low index orientation, see Fig. 1. The slope of a plot of ? vs orientation (herein designated ?&apos;) is called the torque on the surface, since it tends to rotate the exposed surface toward the low index orientation, or if the surface is at the cusp orientation it opposes any force tending to rotate the surface out of the low index orientation. The ratio ?&apos;/? has been determined for a few metals, but in cases where this ratio is high there is presently no means of determining either ?&apos;/? or the absolute value of ?&apos; for the orientations present on an annealed surface. The technique discussed herein also provides a means of determining an absolute value of ?&apos; for those orientations which deviate only infinitesimally from a cusp orientation. It should work best on surfaces where ?&apos;/? is large; that is, for cases where no other technique is available for measuring ?&apos;. Aside from trying to learn more about surfaces through measuring ? and ?&apos;, the primary reason for wanting values of ? or ?&apos; is to study adsorption. From measurements of the variation of ? for a particular orientation with the concentration of an impurity, one can obtain the number of impurity atoms adsorbed per unit area (Ti) on that orientation using the Gibbs adsorption equation.&apos; where µi is the chemical potential of the adsorbed impurity. Thus, if absolute values of ? could be obtained for the free surface of a given surface orientation as a function of µi, ri could be determined for the given orientation. Furthermore, by equilibrating a grain boundary with the given surface at various values of ki, one could also determine ri for the grain boundary. Similarly Robertson 6 has pointed out that if y is taken to be a continuous function of and µi, then a2 ?/a @a µ2 = a2 ?/a pi a +. Thus, at all orientations away from cusps the following equation holds From a measurement of ?&apos; vs ki, it is thus possible

Jan 1, 1963

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By I. R. Kramer, L. J. Demer

T. H. Alden and R. L. Fleischer (General Electric Research Laboratory)— The authors&apos; results indicate clearly and, we believe, significantly that during tensile deformation the surface layers of an aluminum crystal are hardened more severely than the interior of the crystal. A probable explanation of this effect, as the authors indicate, is that dislocations in the primary slip system may be obstructed at the surface or, it should be added, near the surface. The intent of this discussion is to show that the oxide film on aluminum is not likely to be responsible for this effect, but that the results can be understood if it is assumed the secondary slip is more active in the surface layers than in the interior. Prior study has shown that the principal mechanical effect of an oxide film on a single crystal is to raise the yield stress while leaving the rate of strain hardening during the initial deformation relatively unaffected.33 Since the yield stress is unchanged during polishing in the present case, we conclude that continual removal of the oxide film exerts a small effect on the plastic hardening.* It appears that the hardening interactions are occurring not only at the immediate surface, but to an appreciable depth below it, although with decreasing severity. For example, Kramer and Demer found that with removal of 0.004 in. from a specimen, the easy glide region was extended somewhat; but the yield stress did not decrease. The initial yield stress was recovered only after 0.041 in. was removed. Since a very brief polish would permit dislocations trapped behind a surface film to run out,34 extra dislocations must, instead, be trapped to a considerable depth below the surface. The same conclusion is drawn from the observation of decreasing hardening slope with increasing surface removal rates. If the hardening interactions were only at the immediate surface, a full softening effect would be observed at some small removal rate. The view is taken here that strain hardening is principally caused by small amounts of secondary slip.35 The secondary dislocations will interact in various ways with the primaries, interfering with their motion and causing them to accumulate in the crystal. Prior studies of easy glide have shown Diehl&apos;s model of hardening to be qualitatively consistent with the effects of impurities,36 of temperature,36 and of crystal size.37 On this basis the enhanced hardening of the surface layers in aluminum arises from increased secondary slip at and to some depth below the surface. Selective removal of this hardened layer is expected to decrease the measurable "bulk" hardening, the effect increasing with the removal rate and decreasing with the applied strain rate. We suggest that the stress on secondary systems is raised by the bending moments arising from interactions with the grips during the deformation. This stress from the grips has been shown to be a maximum37 near the surface, and hence, increased secondary slip should result. Prior investigations of grip effect:; indicate that as the grip stresses are raised by changing the crystal shape, the easy glide slope increases while the extent of easy glide decreases.38-40 It has been shown also that bending moments superimposed during tensile testing may either decrease easy glide, when supporting the moments caused by gripping, or increase it, when cancelling the gripping moments.38 This interpretation of the authors&apos; results, emphasizing the special importance of secondary slip near the surface, is also consistent with the earlier results of Rosi.41 Copper crystals alloyed with silver in the surface layer show greatly increased easy glide compared with pure copper. In addition, the easy glide slope is reduced. The effect of bulk alloying in extending easy glide has been well established and has been interpreted as indicating the relative difficulty of secondary slip in alloy crystals. Since non-basal glide is difficult in zinc crystals, the effects of surface removal during deformation may be less important. Experiments to test this idea are in progress. I. R. Kramer and L. J. Demer (authors&apos; reply)—The authors wish to thank Dr. Alden and Dr. Fleischer for their discussion. Our interpretation of the data in the paper is that dislocation motion is obstructed by "debris" which starts to form at the surface and extends towards the interior of the crystal with further plastic deformation. The fact that we did not find a reversion from Stage II to Stage I by surface removal shows that in Stage II the "debris" fills the entire cross-section of the specimen. Drs. Alden and Fleischer take the view that bending stresses due to the grips are responsible for the

Jan 1, 1962

By A. M. Sarem, J. M. Campbell

Molecular refraction is introduced as a new and improved third parameter for prediction of the PVT behavior of hydrocarbon systems. This parameter, characterizing the complex as well as the pure hydrocarbon systems (1) is a direct measure of London dispersion forces which affect the PVT behavior; (2) can be measured directly, accurately and easily for complex as well as pure hydrocarbon systems; (3) varies significantly between the reference substances thus allowing accurate interpolation of PVT properties; and (4) has a fundamentally sound basis. Molal average molecular refraction was used with the pseudocritical mixing rule proposed by Leland and Mueller to predict the molal volume of liquid and vapor for 84 published data points on nC4-nCI0, Cl-nC5, Cl-nC4-nC10 systems in the region of coexisting vapor-liquid and at the critical point. The same technique was applied to predict the densities of liquid hydrocarbon mixtures in the two-phase and single-phase regions near the critical point for seven different systems each having different properties of the heptanes-plus fraction, but all simulating the fluids of either gas-condensate or volatile oil reservoirs. A modification of the Leland-Mueller mixing rule for the determination of pseudocritical properties is also presented which yields more accurate liquid density predictions than the original form when used with the proposed third parameter. INTRODUCTION The PVT behavior of multicomponent systems has received widespread attention in the literature in recent years. A large portion of the reported work has stemmed from attempts to overcome the inherent difficulties encountered when using the standard compressibility-factor chart which shows 2 as a function of reduced temperature T, and and reduced pressure p,. This chart assumes that z, is constant for all systems. The error in this assumption is not pronounced for pipeline-type gases high in methane and low in heavy ends, particularly when contained at moderate pressures. For such gases the error in the calculated z is usually less than 2 to 3 per cent. However, the reliability of this approach becomes somewhat nebulous for gas condensate and volatile oil systems at high pressure. One logical approach has been to recognize the variation of 2,. This idea was first suggested by Meissner and Seferianl and used by Lyderson, Greenkorn and Hougen2 to prepare extensive tables of thermodynamic properties. Other third parameters have been proposed by Stockmeyer, Kihara, Riedel, Lightfoot, Bloomer and Pitzer. These were tested by Satter and Campbel13 for many gas mixtures and it was shown that they were inter-related. All of these third parameters have a common fault — they cannot be directly evaluated for the heptanes-plus fraction. Consequently, one necessary requisite of an improved method for predicting the density of multicomponent hydrocarbon systems, was development of a third parameter that could be evaluated for that fraction. PREVIOUS MULTICOMPONENT DENSITY PREDICTION METHODS Sage and Lacey4 suggested a method of using partial molal volumes for computing the density of hydrocarbon gas mixture for pressures to 3,000 psi. In this technique, they approximate the complex multicomponent gaseous mixtures by a quarternary system of methane, ethane, propane and butane. Sage, Hicks and Lacey5 suggest a method of using partial molal volumes for computing the density of hydrocarbon liquids. The results agree within 3 per cent of the experimental values. However, the composition range is limited to about 10 per cent by weight of methane. Consequently, this correlation does not cover the low-molecular-weight liquid similar to natural gasoline and high-pressure gas condensates.

Jan 1, 1966

By D. G. Westlake

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

Jan 1, 1970

By R. W. Fountain, W. D. Forgeng

A new constitutional diagram is presented for the cobalt-rich end of the cobalt-titaniurn system. The modifications result from the presence of a new, intermediate, fcc phase, ?, the existence and homogeneity limits of which were established by metallo-graphic and X-ray studies of alloys containing from about 3 to 30 pct Ti. The precipitation of the ? phase from supersaturated solid solution was studied by hardness and electrical resistivity measzsrements, and two distinct stages in the process were observed. COBALT forms the base for a number of precipitation -hardenable alloy systems which may be divided into two distinct categories of practical interest, a) those hardened by intermetallic compounds and b) those hardened by carbide formation. The precipitation of intermetallic compounds from solid solution in cobalt-rich alloys has, however, received very little attention. Although the phase diagrams for some binary systems capable of precipitation have been determined,&apos; there is an almost complete lack of data on the property changes associated with the precipitation, and even less information on the kinetics of the reactions or morphology of the products. More information is available on the precipitation of carbides because of the practical significance in superalloys. A survey of cobalt binary phase diagrams suggested that the cobalt-titanium alloys might provide interesting and useful precipitation-hardenable alloys. The equilibrium diagram as proposed by Wallbaum2 is shown in Fig. 1. Köster and wagner3 have indicated that the maximum solubility of titanium in cobalt is about 10 pct at the eutectic temperature (1135oC), and this decreases to about 7.2 pct at room temperature. The temperature of the allotropic transformation in cobalt is lowered by the addition of titanium, about 5 pct being sufficient to retain the high-temperature fcc modification to room temperature. Wallbaum and Witte 4,5 have indicated that the precipitating phase in alloys containing up to about 29 pct Ti is Co2Ti, a hexagonal Laves phase of the MgNi, type. With slightly higher titanium contents, they also report a cubic modification of Co2Ti of the MgCu2-type Laves phase. Duwez and Taylor6 confirmed the existence of the hexagonal (MgNi2) modification but not the cubic (MgCuz) modification of Co2Ti and suggested that existence of the cubic form may have resulted from impurities in Wallbaum&apos;s alloys. In their work on Laves-type phases, Elliott and Rostoker 7 reported the cubic modification of Co,Ti, but did not confirm the existence of the hexagonal modification. However, Dwight8 in a discussion of the work of Eliott and Rostoker again showed the existence of both modifications of Co2Ti, a result which was confirmed at that time by Elliott and Rostoker. As a result of a study on the iron-cobalt-titanium system, Köster and Gellers suggested the existence of a Co3Ti phase isomorphous with Fe3Ti. Witte and Wallbaum,&apos; however, established the fact that no compound, Fe3Ti, exists in the iron-titanium system, and in a later publication, wallbaum2 stated that Kitster and Geller&apos;s reasoning was not valid, and no compound, Co3Ti, exists. This conclusion was later acknowledged by Köster.10 Preliminary experiments by the present authors to determine the precipitation-hardening characteristics of the cobalt-rich, cobalt-titanium alloys re-

Jan 1, 1960

By J. Paces, E. Miller, K. L. Komarek

The resistivity was determined as a function of temperature over the composition range from pure cadmium to 40 at. pct Cd. Melts with cadmium contents less than 85 at. pct had negative temperature coefficients of resistinity. On cooling below a transition temperature close to the liquidus temperature, the slope of the resistivity-temperature curve changed sharply. The activation energy calculated from the slope was 0.07 ev above the transition temperature and 0.14 ev below. The resistivity vs composition curve shows two maxima corresponding in composition approximately to CdSb and Cd3Sb2. THE relationship between the structure of a liquid and that of the crystal formed on solidification is at present not well-under stood. Various experimental determinations of the properties of liquids indicate that deviations from random atomic arrangements in liquids occur and that the properties of a solid and of its melt are closely related. Thermody-namic activities of liquids usually show negative deviations in systems where compound formation occurs in the solid,&apos; and X-ray data indicate that close-packed solids and their melts frequently have nearly the same coordination number. Electrical resistivities and viscosities of liquids frequently exhibit maxima at compositions corresponding to compounds in the solid state. It should be of interest to study systems which have both stable and metastable compounds in the solid, and to determine if the short-range order in the liquid is affected by the existence of the metastable solid phase. The Cd-Sb system exhibits such a metastable phase. The phase diagram is shown in Fig. 1.3 The stable system has one intermetallic compound, CdSb, crystallizing in the orthorhombic crystal structure, with a melting point of 456°C. The metastable system also has one compound, Cd3Sb2, melting at 420°C and crystallizing in the monoclinic structure. Metastable alloys transform to the stable crystal structure in the temperature range from 250o to 350°C. Several distinct indications of very strong short-range order in the liquid phase have been reported in this system, with a close relation between the ordering in the liquid and the existence of both the stable and metastable solid phases. Scheil and Baach4 have observed distinctly different vapor pressures for liquid Cd-Sb alloys depending on whether the liquid solidified to the metastable- or stable-phase configuration. They observed an unusually sharp increase of the activity in a limited temperature interval immediately above the liquidus temperature of stable alloys, followed by a sudden decrease in slope to what they considered normal values. On cooling, the activity data reproduced the values in the normal range but then deviated from the values obtained on heating. They also observed that specimens of the stable phase upon melting and resolidifying always crystallized in the stable crystal structure as long as the melt was not heated to more than 485° to 525°C; otherwise solidification to the metastable phase occurred. However, in a later investigation, these results were not reproduced (13). The resistivity of liquid Cd-Sb alloys has been investigated by Matuyama 5, Oleari and Fioram, 8 and Belaschenko (141, but only above 500°C, the temperature region where Scheil and Baach observed no vapor-pressure anomalies. The data of Matuyama and of Oleari and Fiorani are reproduced in Fig. 5 and show a maximum in resistivity at 50 at. pct Cd. The data of Oleari and Fiorani, however, show the maximum as being rounded, and their values in general are slightly higher than those of Matuyama.

Jan 1, 1964