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By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By W. A. Backofen, D. H. Avery, W. F. Hosford

Sheets of the magnesium alloys AZ31B, HK31A, and ZE10A in several different tempers were tested in tension and determinations were made of the ratio of width-to-thickness strain. A marked increase in the ratio with tensile straining and a dependence upon alloy and test direction are rationalized in terms of a balance between the amounts of basal and prism-plane slip. All such variations are related, in turn, to the prevailing crystallographic texture. Fracture appearance is explained on the basis of anisotropy in plastic flow, and implications for developing texture -hardening effects in these alloys are discussed. ThE crystallographic texture or preferred orientation of a given material is determined by details of processing history. Such texture is known to influence many aspects of material behavior, in particular both the yielding and strain-hardening characteristics which are of special interest in the present work. Traditionally, the resulting plastic anisotropy has not been regarded as especially desirable. Earing in drawn sheet is perhaps the most common example of an unwanted effect of texture. However, it has also been recognized that suitable textures may be usefully employed to improve drawability,1,2 as a specific example, and generally to control yielding resistance under combined-stress loading.374 Texture would seem to be a detail of structure not yet exploited to nearly the fullest extent. A convenient basis for characterizing anisotropy in plastic behavior is the ratio of width-to-thickness strains obtained in a tension test;5&apos;6 the parameter is frequently labeled "R" and its value is revealing with respect to the nature of the prevailing texture. R gives a useful measure of a material&apos;s "thinning resistance". For an isotropic material, R = 1. With R > 1 the increased through-thickness strength in a sheet means greater resistance to yielding under biaxial tension, or "texture hardening";3&apos;4 if R < 1 the result may be a "texture softening" under the same loading conditions.4 Most R data relate to steel sheets for deep-drawing applications. Values for steel and other materials of cubic structures are not often much greater than 1 and nearly constant with strain in testing.1,2,7,8 To explore the implications of plastic anisotropy further, it was felt that experiments with much more strongly textured materials would be useful, and this led to the choice of magnesium alloys. The "ideal" sheet texture for magnesium contains the (0001) plane in the rolling plane, which ought to lead to R values approaching infinity. However, departures from the ideal texture, the possibility of slip in non-close-packed directions, and deformation by twinning would all be expected to introduce some range of R. Accordingly, studies on these materials were undertaken. EXPERIMENTAL Alloys in sheet form, Table I, were selected to obtain a variation in crystallographic texture, in the expectation that this would be reflected in differences in plastic anisotropy. Pole figures constructed by the Schulz surface-reflection technique9 were provided with the experimental materials by the Dow Metal Products Co. Profiles of pole density along great circles through the rolling (0 deg) and transverse (90 deg) directions were prepared from the pole figures and are collected in Figs. 1 and 2; considerable departure from the "ideal" (0001) alignment in the rolling plane is evident, with the largest angular spread in both directions being found in the ZEl0 alloy. Results of tensile tests on full-thickness specimens of 6-in. gage length by 1/2-in. width are given in Fig. 3 as engineering stress-strain curves* in rolling and transverse directions. All tests but one were made at a constant drive rate of 0.02 in. per min, and the final values of percent elongation at fracture, over the initial 6-in. gage length, are noted at the ends of the curves; one test on ZE10A-

Jan 1, 1965

By L. F. Mondolfo, F. A. Crossley

SURFACE effects in the brittle fracture of materials such as glass and in the plastic slip of zinc and cadmium crystals are well known.&apos; Recently, another surface effect has been found for zinc monocrystals. It has been observed that certain normally ductile zinc monocrystals become ex- tremely brittle when their surface is coated with a layer of oxide or copper plate.

Jan 1, 1952

By F. L. Wolf, A. A. Grubb

There is a tendency on the part of practical foundrymen to accept with reluctance the results of tests on sands, binders, and such materials made in the chemical laboratory alone. They feel that such tests frequently emphasize and measure properties that are of minor importance and fail to take account of characteristics that are important in determining the value of the material in actual practice. Experience seems to indicate that the most thorough and conclusive test for any new foundry material is an actual run in the foundry alongside of a standard material of known value. Such a test, however, involves certain difficulties and necessitates certain precautions. It is not always easy to obtain a fail trial for a new material. We all have certain prejuclices, which unconsciously affect our judgment to a marked degree. A practical test frequently involves so many workmen, each of whom reacts in a different manner to the test, that the personal equation becomes very complex and the true results of the test are obscured. There are times, too, when a thorough experimental trial of a material would interfere too much with the. rush of work in a department or would hazard the quality of the product to such an extent as to make it inadvisable. Under such conditions a laboratory test is advisable before the material is sent into the foundry. These tests should be made as practical as possible and so closely related to foundry practice as to give a true index to the value of a product for the purpose desired. Core sands and molding sands are as numerous "as the sands of the sea" and valy as much in quality. Old sources of supply are continually failing and new ones must be opened, so that we must continually search for new and better grades of sand. During the past year, the Ohio Brass Co. has developed tests for sands, cores, and binders which bear a close relation to the particular use to which these materials are put in the foundry and which arc fairly indicative of their value. While the tests thus far have been confined to cores and core sands, it is expected that tests for molding sand will bc developed in the future.

Jan 1, 1921

By R. W. Raymond

In a former paper (Trans., xvi., 770) I gave the text of the archaic mining law of the State of New York, together with some comments upon its curious provisions. In that connection I pointed out two facts : first, that the law seemed to have originated in the schemes of private parties, who were satisfied with those parts of it which concerned them particularly; and secondly, that the remaining provisions had been hitherto quite inoperative, for the reason that mines of the character to which they referred had not been discovered in the State. Since 1888, when that paper was written, the New York Legislature has passed several acts relating to mines as follows: 1. Chapter 394, Laws of 1890. This provides for an inspection

Jan 1, 1895

By Charles M. Cooley

In these troubled times free enterprise is maintaining vital molybdenum output, while expanding plant, and bringing in new low grade ore reserves, at Climax, the world&apos;s largest known molybdenum deposit. Climax Molybdenum Co. is putting $25 million into additional surface plant facilities and other millions into underground development. The expansion program to be operating by 1954 includes a new mining level, crushing plant, 4000-ft conveyor, milling units, by-products plant, and housing for 198 families. Completion of this program and low grade plant will add 10,000 tons per day to present capacity and several million tons to ore reserves.

Jan 1, 1953

By A. T. Yu

As the first year of full-scale shiploading operations nears completion, Chile&apos;s twin ports of Chafiaral and Caldera have proved instrumental in promoting the growth of that nation&apos;s iron ore industry. Located on the Iron Coast several hundred miles below Antofagasta, the two ports boast of new conveyor shiploading facilities uniquely adapted to their coastal environment. Until recently, iron ore producers in this region of Chile have been hampered by antiquated methods of loading crushed ore on ships for transportation to foreign buyers. Use of the "truck-to-lighter- to-ship" method, which dominated heretofore, was too slow and costly to permit expansion of productive mines and exploitation of new high-grade discoveries to meet the growing world demand for such ore.

Jan 8, 1960

By C. H. Stein

THE Pennsylvania Legislature, on March 13, 1837, passed an act authorizing the Lehigh Coal & Navigation Co. to construct a railway to connect the North Branch Division of the Pennsylvania Canal with the slack water navigation f the Lehigh River; the navigation company accepted this act on May 10, 1837. Edwin A. Douglas, chief engineer for the navigation company, located the route for this railway from White Haven to Wilkes-Barre, which was called the Lehigh & Susquehanna Railroad. The object was to transport coal from the Wyoming Valley, of Pennsylvania, to the Atlantic seaboard. This railway was considered a marvelous piece of engineering, as it included a tunnel nearly 13 mi. long, and a series of inclines, or planes, up which the cars laden with coal were raised from the vicinity of Ashley to the summit f the mountain near Solomon&apos;s Gap, whence they were taken to White Haven by rail. There the coal was transferred to canal boats. In June, 1862, floods almost completely destroyed the upper division of the canal, so on March 4, 1863, the Pennsylvania Legislature passed an act prohibiting its restoration, but granted a charter for the construction of a railway from White Haven to Mauch Chunk to connect with the line from White Haven to Wilkes-Barre, previously built. On March 16, 1864, a supplementary act was passed extending the Lehigh & Susquehanna Railroad to Easton, Pa. This completed a direct all-rail route from Wilkes-Barre to the New York harbor (by way of the Central Railroad of New Jersey). Up to this time, all freight and passenger traffic passed over the planes, but in 1866 and 1867 there was constructed what was known as the "back track" down the mountain side between Solomon&apos;s Gap and Ashley over which all the passenger traffic and empty cars thereafter passed; it is now known as part of the main line. For the handling of the heavy coal traffic, however, this would have involved a continuous climb from Ashley, 170.27 mi., from New York, to Solomon&apos;s Gap, 157.8 mi. from New York, or a distance of 12.47 mi., and a total ascent of 1,013.75

Jan 9, 1921

By H. Hance James

SOME of the outstanding features of petroleum production in Illinois during 1923 were: (1) Sustained production from the older wells, due to cleaning and deepening; (2) good results from new drilling in a few localities; (3) large percentage of dry holes, many of which were ill advised tests, with a resulting high cost of the new production; (4) decrease in the number of productive wells in the state; (5) low average price of crude petroleum, a serious factor over the entire country. FIG. 1.-ANNUAL TOTALS OF ILLINOIS PRODUCTION. The total production of Illinois for 1923 was 8,710,000 bbl.,1 a decrease of 7.2 per cent. from that of 1922. Of this amount, it is estimated that about 8,500,000 bbl. were produced by old wells, many of which had been cleaned and deepened somewhat, and approximately 210,000 bbl. were obtained from the new wells drilled during the year. About 95 per cent. of the oil comes from the southeastern field in Clark, Crawford, and Lawrence Counties, where production is almost entirely from Pennsylvanian and Mississippian rocks. Extensions of the productive area were made in Clark, Wabash, Marion, and Jackson Counties. Some important gas development has been accomplished near Jacksonville, in Morgan County, and at Gillespie, in Macoupin County.

Jan 3, 1924

By W. R. Foster, J. M. McMillen, A. S. Odeh

The complete equations of average linear momentum balance for a single-phase fluid in an incompreisible, homogeneous, porous medium are derived. The derivation begins with Euler&apos;s equation of motion for a continuum and uses an integral transform recently developed by Slattery. 7 For steady flow of a compressible, Newtonian fluid, the usual equations of motion result. For transient flow, the space-time description of the pressure is determined in the lowest approximation by the telegrapher&apos;s equation. From the analysis a new phenomenological coefficient results which connects the viscous traction to the deriv ative of the linear momentum density. The magnitude of this coefficient determines the velocity of sound through the pore structure in this approximation to the pressure field. INTRODUCTION The modification of Darcy&apos;s law of momentum balance for steady, single-phase flow through porous media has been discussed for many years. The first modification was suggested by Forcheimerl who added terms of higher order in the velocity. These can be expected to appear because the underlying microscopic equations of momentum balance are themselves nonlinear in the point velocity field. The Reynolds tensor pvv, which represents the convective flux of momentum density, appears in the momentum balance equation. Only in rectilinear flow (parallel stream lines) does the divergence of this tensor vanish. Since the steady flow stream lines in most porous media are not parallel, nonlinear dependence of the pressure gradient on the velocity should naturally appear. This nonlinearity has nothing to do with turbulence in the ordinary sense of random fluctuations in the pressure and velocity fields. It arises simply because the stream lines converge and diverge, even for steady flows. Klinkenberg2 demonstrated that the permeability coefficient in Darcy&apos;s law depends on the absolute pressure or, alternatively, on the density field. However, because he neglected inertial terms of the Forcheimer type, his correction coefficient could not be represented by a constant but tended toward a constant as the velocity decreased. Forcheimer&apos;s and Klinkenberg&apos;s modifications can be combined in a rigorous way to account for both inertia and slip during steady flow. This will be shown in a future paper. The transient change of pressure in porous media has been described by the diffusion equation.3 This form results from eliminating the velocity and density fields from a combination of the equations of motion in the form of Darcy&apos;s law, the continuity equation and an equation of state. Fatt4 suggested that the cause of deviations from the prediction of the diffusion equation for pressure transients lies not in the choice of Darcy&apos;s law as the equation of motion but on the existence of dead-end pores which might invalidate the averaged equation of continuity. On the other hand, Oroveanu and Pascal5 noted chat the time derivative of the momentum density must be included in the equations of motion since this measures the local rate of change of momentum density. Their differential equation for pressure is the telegrapher&apos;s equation (neglecting gravity). However, their form of this equation predicts that the speed of pressure propagation through the pore structure is the same as that through the bulk fluid. M. K. Hubbert6 attempted a derivation of Darcy&apos;s law by volume averaging the Navier-Stokes equations. Since these equations represent momentum balance at a point within an open set of points containing the fluid itself, Hubbert&apos;s volume averaging cannot lead to tenns involving transfer of momentum between the fluid and the walls of the pores. Once these viscous tractions are lost by choosing a control volume containing only fluid, they cannot

By C. W. Volek, J. E. Chappelear

The injection of a hot liquid into initially cool porous media, saturated with the same liquid and surrounded by two impermeable but heat conducting media (cap and base rock), has been studied both experimentally and theoretically. The temperature dependence of the viscosity was included in the theoretical model, but it was assumed that the specilic heats and densities of the various materials were independent of the temperature. Solutions to the theoretical model were approximated by numerical methods. Both theoretical and experimental results indicate that center-line temperatures are significantly higher than boundary temperatures. Comparison of experimental and theoretical results with a cold/hot viscosity ratio 01 19:1 were in reasonable agreement. Theoretical calculations show that the effect of the temperature dependence of viscosity was very significant at ratios of 100:l to 1000:1, which are typical of those that occur when injecting hot water to flood heavy oil reservoirs. INTRODUCTION We consider the problem of prediction of fluid flow and temperature distribution in an initially cold-fluid-filled reservoir on the injection of the same hot liquid by the use of mathematical and physical models. The results reported are for a two-dimensional rectangular section of the reservoir, as shown in Fig. 1. The injection and withdrawal faces are assumed to be equipotentials for fluid flow. The ultimate purpose of such models would be to predict hot-water injection performance. However, we note that in the work presented here, one of the most significant aspects of the problem — the instabilities resulting from two-phase, water and oil flow — is not included. We will not give a historical review, but refer instead to the paper of Spillette and Nielsen,1 which contains a rather complete bibliography and critical discussion. The physical problem is exactly the same as Spillette and Nielsen, except for certain simplifications in our assumptions. The mathematical details are somewhat different, and we will present the details of our method here. The mass flow equation, which is elliptic in character, is handled by successive overrelaxation. The heat flow equation, which is parabolic in character, is handled by a straightforward explicit approximation. Some difficulty arose in the over-all heat balance due to small errors in the solution of the mass flow equation, and we feel that a different formulation of the heat flow equation would be desirable for future work. In addition to the mathematical solutions for the temperature distributions in a porous medium due to the injection of hot liquids, experimental data are presented to check the validity of these solutions. A schematic diagram of the model is shown in Fig. 2. Certain qualitative physical conclusions were obtained from our numerical and experimental results. These are: 1. Assuming high (infinite) conductivity normal to the bedding plane in the reservoir is a poor approximation, and may lead to overestimates of the total heat losses (to cap and base rock) of as much as 50 percent. 2. More heat is retained in the reservoir (per unit of heat injected) for higher viscosity changes. 3. Any particular temperature isotherm moves more rapidly along the center line for higher viscosity changes. Consequently, the approximation of temperature independent viscosity is not suitable for obtaining quantitatively correct results. MATHEMATICAL MODEL Our mathematical model is that of a reservoir of thickness 2h. The problem is idealized from that of a linear hot-water drive, and we imagine that the input face is sufficiently far away from the injection wells that the stream lines enter it normally. Similarly the production wells are far enough from the outflow face that the flow lines leave it normally. The reservoir and surrounding cap and base rock

Jan 1, 1970

By B. E. Sundquist

The various methods based on solution models for obtaining free energies of mixing from miscibility-gap data have been applied to a number of binary-alloy systems. For nine of these systems there exist experimental thermodynamic data that permit a comparison of the results to experiment. It was found that the method of van der Toorn and Tiedema almost invariably leads to results that are physically unacceptable and that vary drastically with small changes in the miscibility-gap parameters. The subregular solution model is found in all cases, except the Al-Zn, Fe-Cr, and Cu-Pb systems, to exaggerate the free energy of mixing by 30 pct or more. The model developed by Lumsden is found to give results that are often in excellent agreement with experiment and which exaggerate the free energy of mixing by no more than 30 pct. These results and others give evidence that the Lumsden treatment of the effect of unequal atomic sizes and of imperfect configurational randomness due to deviations of AB bond energies from the mean of AA and BB bond energies is adequate for most systems. ANALYTIC expressions are frequently proposed for the dependence on composition of the activities of the components of a solution. Because the development of solution theory is incomplete, these expressions contain parameters which must be determined by experiment. The measurement of activities is often difficult and consequently such measurements are less readily available than are measurements of phase equilibria which, under certain conditions, can also be used to evaluate these parameters. For example, suppose it is known that two structurally dissimilar phases, each of known composition, in an n-com-ponent system are at equilibrium at a given temperature and pressure. n equations can be set up in terms of these parameters expressing the equality of the chemical potential of each component in the two phases. In addition, one can write the Gibbs-Duhem equation for each phase that also contains these parameters. Thus, if these n + 2 equations contain n + 2 parameters, these parameters can be determined (at the temperature in question) from the phase diagram alone. If the average number of parameters in each expression for the activity of a given component in a given phase is V then there will be 2nV parameters involved. Equating 2nV to n + 2 shows that, for n + 2, V = 1. If the temperature dependence of each parameter were to be expressed in some explicit form one could use equilibrium conditions at a number of temperatures to increase V. The situation is much improved when the two phases in equilibrium are structurally similar. It can then be assumed that, stably or metastably, two phases will become one at higher temperatures. Thus the number of parameters involved becomes nV instead of 2nV. Hence, V = 2 for n = 2 using only one temperature. (It is implied here that the activity expressions used are valid over the entire composition range.) In this investigation only the equilibrium of two structurally similar, two-component phases (miscibility-gap systems) will be considered. The various proposed solution models will be applied to a number of these systems and the results compared with available experimental results. All of the analytic expressions that have been proposed for the free energy of mixing of a two-component system are of the form where ?Gmix is the free energy of mixing per mole of solution, N1 and N2 are the mole fractions of components 1 and 2, respectively, and f(Ni, T) is some function of composition and temperature. In the "ideal" solution model f = 0. In the "regular" solution model f = a constant. Since these two models permit only a symmetric equilibrium diagram they will not be considered further here. The simplest model that permits a nonsymmetric miscibility envelope is the so-called "subregular" solution model proposed by Hardy.1 This model gives where the Ci(T) are functions of temperature only. The same expression for f is obtained from the "linear a function" model proposed by Darken and Gurry2 and applied to miscibility-gap systems by Wriedt.3 This model requires that the a function defined by be a linear function of composition (yi is the activity coefficient of component i). This model is not purely hypothetical for it has been found2 to hold true for a number of systems. It is readily shown3 that the f(Nl, T) obtained from this model is of the form given in Eq. [2]. It will be noted that the subregular solution model contains only two parameters and hence both of them can be determined at any desired temperature below the critical temperature, Tc, for a miscibility-gap systems in the manner described previously. At T, the two constants can be determined by equating the second and third derivatives of ?Cmix with composition to zero. Another two-parameter model was proposed by Lumsden4 who set

Jan 1, 1967

By F. W. Bremmer

THE drilling of constantly deeper oil wells has made it imperative that the manufacturer of casing be ever searching for new methods and new materials to meet the increased demands. One phase of this search constitutes the subject matter of the present paper. Starting from the original Drake well in 1859, the depth of wells has advanced by leaps and bounds, until today depths of 6000 to 8000 ft. are common. Conditions point to the necessity for drilling to greater depths, and it is not at all improbable that much of the future oil produc- FIG. 1.-TREND IN DEPTH OF OIL WELLS. tion will be from, wells around 10,000 ft. deep. The trend to deeper wells is nicely illustrated by the curve in Fig. 1.1 The points plotted are the maximum depths attained in the various pools which were at their peak for the years given. It may be of some interest to observe the change that has taken place in the tensile and collapsing stresses over the last 25 years. The pressure at the bottom of a 900-ft. hole, equivalent to the pressure caused by an equal column of water, is only 450 lb. per sq. in. The equivalent

Jan 1, 1930

By Chairman Hill H. H.

The Round Table Discussion on Petroleum Engineering Research was planned for two purposes. First, to review the work that has been done by petroleum engineers during the past few years on problems that have confronted the industry and, second, to suggest new studies that should be made either on the problems that have been the subject of research during the past or on problems that have arisen only recently. It was believed that by holding an informal discussion of the problems in which the petroleum engineer is vitally interested it would be possible to bring out new ideas as to the relative importance of the different problems that should be studied and to suggest new methods for attacking some of the problems that have resisted the energies of research workers throughout the industry. It was also believed that by arranging for an exchange of experiences between the different engineers it would be possible to prevent a large amount of duplication of effort in conducting research work. Those engaged in petroleum engineering research realize that there is a broad field for study and by coordinating the work it will be possible to obtain the maximum amount of information in the shortest possible time. In planning the program on Petroleum Engineering Research, nine subjects were selected for discussion and each was assigned to a man who is doing work on that subject. These men were asked to lead the discussion on the problem assigned to each one. An effort was made to choose problems of a practical nature and upon which considerable work is being conducted at the present time. Some of the men who were asked to lead the discussion were unable to attend the meeting but most of them submitted a written discussion- of the subject assigned, with the result that there was a discussion of eight of the nine problems. Professor Uren, who was asked to lead the discussion on the subject of Recent Developments in Methods for Reducing Gas-oil Ratios, was unable to attend the meeting and advised that he did not have any new ideas to contribute.

Jan 1, 1928

By P. K. Koh, H. A. Lewis, H. F. Graff

New data on the distribution of silicon between slag and carbon-saturated iron at 1600Oand 1700OC are presented which, in combination with previously published data, permit the determination of silica activities over a broad range of compositions in the CaO-Al2O3-SiO2 system. The distribution of silicon between graphite-saturated Fe-Si-C alloys and blast furnace-type slags in equilibrium with CO has been described in previous publications.1"3 In this past work the silica-silicon relation was established at temperatures of 1425" to 1&apos;700°C for slags containing up to 20 pct A12O3. This paper presents the results of additional studies at 1600" and 1700° C which extend the silicon distribution data at these temperatures for CaO-A12O3-SiO, slags over a range from zero pct Al2O3 to saturation with Al2O3, or CaO.2Al2O3. The upper limit of SiO2 is set by the occurrence of Sic as a stable phase when the metal contains 23.0 or 23.7 pct Si at 1600" or 1700°C, respectively. The activity of silica over the expanded range is determined directly from the distribution data.3 Recently4-7 other investigators have studied the activities of SiO, and CaO, principally in the binary system, using different methods and obtaining somewhat different results. EXPERIMENTAL STUDY The experimental apparatus and procedure have been fully described in previous publications.1, 3 Six new series of experimental heats have been made, four at 1600° and two at 1700°C. Master slags of several fixed CaO/Al203 ratios were pre-melted in graphite crucibles, and these were used with additions of silica to prepare the initial slag for each experiment. Slag and metal were stirred at 100 rpm and CO was passed through the furnace at 150 cc per min. The initial sample was taken 1 hr after addition of slag at 1600°C or 1/2 hr after addition at 1700°C. The run was normally continued for 8 hr at 1600°C or 7 hr at 1700°C, and the final sample was taken at the end of this period. Changes in Si and SiO2 content indicate the direction of approach to equilibrium, and in a series of runs where the approach is from both sides this permits approximate location of the equilibrium line. Fig. 1 shows the results of such a series of 15 runs at 1600°C for slags of CaO/Al,O3 = 1.50 by weight. Figs. 2 and 3 record other series at 1600°C and Fig. 5 a series at 1700°C with fixed CaO/Al0 ratios. The results of the experiments at 162003°C have been reported in part in a preliminary note.3 In the experiments recorded in Figs. 4 and 6, the slags were saturated with A12O3 (or with CaO.2A12O3 within its field of stability) by suspending a pure alumina tube in the melt during the course of the run. The final slag analyses were used to establish the liquidus boundaries8 in the stability fields of CaO.2Al2O3 and of Al20,. ACTIVITY OF SILICA The free-energy change in the reaction has been calculated by Fulton and chipman2 from recent and trustworthy data including heats of formation, entropies, and heat capacities. The more recent determination by Olette of the high-temperature enthalpy of liquid silicon is in satisfactory agreement with the values used and therefore requires no revision of the result which is expressed in the equation: SiO2 (crist) + 2C (graph) = Si + 2CO(g.) [1] &F° = + 161,500 - 87.4T The standard state for silica is taken as pure cristobalite and that of Si as the pure liquid metal. Since the melts were made under 1 atm of CO and were graphite-saturated, the equilibrium constant for Eq. [I] reduces to K1 = asi /asio2. The value of this constant is 1.77 at 1600°C and 16.2 at 1700°C. Through K1, the activity of silica in the slag is directly related to the activity of silicon in the equilibrium metal.

Jan 1, 1960

By F. C. Langenberg, J. Chipman

New data on the distribution of silicon between slag and carbon-saturated iron at 1600oand 1700oC are presented which, in combination with previously published data, permit the determination of silica activities over a broad range of compositions in the CaO-Al2O3-SiO2 system. The distribution of silicon between graphite-saturated Fe-Si-C alloys and blast furnace-type slags in equilibrium with CO has been described in previous publications.1"3 In this past work the silica-silicon relation was established at temperatures of 1425" to 1700°C for slags containing up to 20 pct Al2O3. This paper presents the results of additional studies at 1600" and 1700° C which extend the silicon distribution data at these temperatures for CaO-A1203-SiO2 slags over a range from zero pct A12O3 to saturation with A12O3, or CaO.2A12O3. The upper limit of SiO, is set by the occurrence of Sic as a stable phase when the metal contains 23.0 or 23.7 pct Si at 1600" or 1700°C, respectively. The activity of silica over the expanded range is determined directly from the distribution data.3 Recently, 4-7 other investigators have studied the activities of SiO, and CaO, principally in the binary system, using different methods and obtaining somewhat different results. EXPERIMENTAL STUDY The experimental apparatus and procedure have been fully described in previous publications.1, 3 Six new series of experimental heats have been made, four at 1600° and two at 1700°C. Master slags of several fixed CaO/A12O3 ratios were pre-melted in graphite crucibles, and these were used with additions of silica to prepare the initial slag for each experiment. Slag and metal were stirred at 100 rpm and CO was passed through the furnace at 150 cc per min. The initial sample was taken 1 hr after addition of slag at 1600°C or 1/2 hr after addition at 1700°C. The run was normally continued for 8 hr at 1600°C or 7 hr at 1700°C, and the final sample was taken at the end of this period. Changes in Si and SiO2 content indicate the direction of approach to equilibrium, and in a series of runs where the approach is from both sides this permits approximate location of the equilibrium line. Fig. 1 shows the results of such a series of 15 runs at 1600°C for slags of CaO/Al2O3 = 1.50 by weight. Figs. 2 and 3 record other series at 1600°C and Fig. 5 a series at 1700°C with fixed CaO/Al2O3 ratios. The results of the experiments at 162003°C have been reported in part in a preliminary note.3 In the experiments recorded in Figs. 4 and 6, the slags were saturated with A12O3 (or with CaO.2A12O3 within its field of stability) by suspending a pure alumina tube in the melt during the course of the run. The final slag analyses were used to establish the liquidus boundaries8 in the stability fields of CaO.2Al,O3 and of A120,. ACTIVITY OF SILICA The free-energy change in the reaction has been calculated by Fulton and chipman2 from recent and trustworthy data including heats of formation, entropies, and heat capacities. The more recent determination by Olette of the high-temperature enthalpy of liquid silicon is in satisfactory agreement with the values used and therefore requires no revision of the result which is expressed in the equation: SiO, (crist) + 2C (graph) = Si + 2CO(g.) [1] &F° = + 161,500 - 87.4T The standard state for silica is taken as pure cristobalite and that of Si as the pure liquid metal. Since the melts were made under 1 atm of CO and were graphite-saturated, the equilibrium constant for Eq. [I] reduces to K1 = asi /asio2 The value of this constant is 1.77 at 1600°C and 16.2 at 1700°C. Through K1, the activity of silica in the slag is directly related to the activity of silicon in the equilibrium metal.

Jan 1, 1960

S. LE FEVRE, Forest Glen, N. Y. (communication to the Secretary*).¬F. L. Nason thinks I could not have studied Mr. Witherbee&apos;s paper and doubts the arithmetic used, but in his discussion arrives at practically the same conclusion. He says 10 ft. thickness of ore over a square mile should give 27,878,400 tons, allowing 10 cu. ft. per ton of ore. This is correct, but if he reads carefully he will see that this depth of ore was figured as covering one-tenth of the surface, which reduces the figures to those used by Mr. Nason. I did not say, however, that there were 2,300,000,000 tons of ore in New Jersey, but that applying the same method of computation as used by Mr. Nason, to the area of the iron ore-bearing gneisses in New Jersey, we would get a total of 2,300,000,000. I did say, "In this area are located 366 magnetite mines that have been worked more or less. These lenses may easily be capable of producing (on an average) 1,000,000 tons each, and there are probably double the number listed not opened up." Thus my estimate for New Jersey, as far as any was made, would be: Probable ore 366,000,000 Possible ore in addition 732,000,000 1,098,000,000 Mr. Nason&apos;s final conclusion of his personal estimate was one-half of what he erroneously read to be the estimate given in the paper, or half of 2,300,000,000, which equals 1,150,000,000. So the two estimates seem to differ less than 5 per cent., and we have the two sister States of New York and New Jersey on an equal footing of productive possibilities in magnetic ore.

Jan 6, 1917

Pennsylvania has been a leader in the pageant of industrial America because of her natural mineral re- sources, geographical location, and the ingenuity and industry of her citizens. Brick and other clay products were manufactured in Philadelphia in William Penn&apos;s time. Ores of iron, zinc, lead, and copper were mined and smelted in eastern Pennsylvania long before the Revolution. Coal was mined on a commercial basis in the anthracite region as early as 1820 and in the bituminous fields in 1830. The first canals and railroads were constructed to transport minerals and mineral products. Oil was struck at Titusville in 1859. A significant event occurred in 1855-the establishment of the Farmers&apos; High School-Pennsylvania&apos;s first attempt to provide higher education for its youth. The Farmers&apos; High School included instruction in geology, mineralogy, and assaying. In 1859 the laws of Pennsylvania transferred to the School the state geological and mineralogical collections formerly located in Harrisburg. Well-informed people are familiar with the effects of the Land-Grant Act of 1862. With inspiring words it established state institutions of higher learning where "the leading object shall be, without excluding other scientific and classical studies . . . to teach such branches of learning as are related to agriculture and the mechanic arts . . . in order to promote the liberal and practical education of the industrial classes in the sev-

Jan 1, 1950

By C. M. Marquardt

The minerals industry in general should bow in homage to the uranium milling industry. Those in the uranium milling industry have "spark- plugged" more progress in the application of instrumentation and control in the last 5 years than has been made in 50 years by the industry in general. Part of this real progress in the application of instrumentation and control has been born of necessity because milling processes are more complex. A lot of the impetus for instrumentation and control has come from the fact that the industry is new, the processes are new, and there are no hide-bound conventions to overcome. Part of it comes from the fact that much of processing is more chemical than metallurgical and the thinking of the process chemist has carried over into the plants. One need not elaborate on what instrumentation has done for the process chemical industries. Each new mill that is constructed, if of appreciable size, seems to employ more instrumentation than the previously completed plant. Plant A makes a break-through in the application of instrumentation to a particular part of the process and Plant B accepts this and goes one step farther, while Plant C, anticipating Plant B, makes two or three more steps before Plant B is entirely leveled out.

Jan 9, 1958