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By G. O. Hiers

THE object of the experiments reported in this paper is to determine the eutectic composition of copper and tin and to determine the location of the part of the liquidus line immediately above the eutectic composition in copper. Three methods were used in the investigation: (1) the method of dissolving copper in a bath of molten tin at constant temperature, with the idea that when the bath was saturated with copper its copper content, by analysis, together with the temperature at which the saturation took place would locate a point on the liquidus line (2) the method of the differential cooling curves, and (3) the method of microscopic examination. This paper is principally concerned with the results of the last two methods mentioned. The results of the first method, that of dissolving copper in molten tin, did not agree with the .results of Miller,1 by the same method, nor with the results of other investigators by other methods, nor yet with the results of the cooling-¬curve experiments and microscopic examination reported here.

Jan 1, 1929

By William H. Shockley

There was an extensive mining and industrial exploitation of Russia, about 20 years ago, by Belgian, French and British capitalists; but the results were discouraging. It is said that the Belgian and French public together lost approximately $400,000,000, chiefly in the coal and iron industry of southern Russia. This loss is largely accounted for by the fact that most of the companies were formed, as usual in " boom" times, to sell stock; and that thorough investigations were not made. I11 1906, renewed interest was taken in Russian mines, especially in those of gold and copper, and a considerable literature is growing on this subject; but as yet I have seen no account of one of the large Russian mining estates. The following notes on such property, where the conditions are so different from those in the mining regions of the United States, should be of interest: This inadequate and probably somewhat inaccurate account is made up, partly from my own notes made on the ground, in the summers of 1904 and 1905, and partly from a volume on the geology and resources of the estate issued several years ago, containing surface- and mine-maps, and from a pamphlet published in 1904, giving a general account of the condition and prospects of the property. This pamphlet includes a report made in 1899 by Arthur L. Pearse, a member of this Institute. Both these books are in Russian, and were prepared by the Bogoslovsk Mining Co., which owns and operates the property. Articles in many other languages have appeared dealing with various matters connected with the estate; but I know of no other general account of it. In numerous books and articles on the Urals and Siberia, however, localities are described in which somewhat similar conditions prevail. Recent papers by

Jan 1, 1909

THIS chapter and the one following deal with the heat quantities involved in open-hearth steelmaking, including the thermal efficiency of the furnace as a generator of high-temperature heat, the heat storage in the steel and slag produced and in the furnace walls, and the heats of the various chemical reactions involved in combustion, in the formation of slag, and the refining of steel. The fundamental laws to be considered are the simplification of the first two ' laws of thermodynamics as applied to problems involving sensible and potential (or latent) heat only 1. Heat input equals heat outflow plus storage. 2. Heat may be transferred only from a hotter body to a colder one. The first of these laws relates to the various heat quantities or the "heat balance" of the process. No one has as yet made an open-hearth heat balance that came out almost exactly balanced, and we assume that the cause lies in the difficulties of accurate temperature and flow-rate measurements at the high temperatures involved and the inherent complexities of flow distribution, air leakage, etc., present in any real, open-hearth furnace system. Some idea of the magnitude of the heat quantities involved can be obtained- by a brief, crude outline of the heat balance of a 90-ton heat of steel. We will assume a 60 to 70 per cent hot-metal charge in a fairly fast working and only moderately efficient furnace, burning fuel oil, with a fuel consumption of around 4 million B.t.u. per net ton. of ingots produced. The time from start of charge to tap is 9 hr. During this period, the oil burned represents 360 million B.t.u., and the sensible heat in the preheated air at the port ends is 117 million B.t.u. so that the total heat input at the ports is 477 million B.t.u. Heat stored in the steel and slag at the end of the heat, plus the various amounts absorbed by certain bath reactions, amounts to a total of 195 million B.t.u., but 120 million of this is supplied by the heat in the hot metal and by various heat--evolving reactions in the bath, so that only 75 million B.t.u. need be supplied to the bath by the flame.

Jan 1, 1944

By Walter R. Hibbard

THE increased strength of a polycrystal-line metallic aggregate compared with that of its individual crystals generally has been associated with complex stress distributions at the grain boundaries resulting from atomic irregularity between grains. This disregistry, together with the necessity for adjacent crystals to deform 'compatibly regardless of the single crystal crystallographic strain mechanism, complicates this mechanism so as to increase the metal's resistance to deformation. Although Taylor1 has shown from purely mechanical considerations the requirement for at least five active slip systems to absorb the complexities during the homogeneous deformation of polycrystalline face-centered cubic metals, experimental studies by Barrett and Levenson2 indicate that this is feasible only in a qualitative sense because of deviations from homogeneous deformation. Seitz and Read in their review3 state: "Unfortunately . . . present knowledge of the grain boundary influence is not sufficient to complement the work in single crystals and provide us with a good foundation for treating polycrystals." The purpose of this investigation was to attempt to clarify the gap between single crystals and crystalline aggregates by an analysis of the effects of deformational stresses. Some of the results were described by C. H. Mathewson in his 1943 Campbell Memorial Lecture.21 PREVIOUS INVESTIGATIONS Since the performance of single crystals deformed under pure stresses has been relatively thoroughly investigated, the most significant researches are concerned primarily with deviations from single crystal behavior of large grained specimens. Qualitative grain boundary effects involving the observed amount of slip were reported by Carpenter and Elam5 in 1921. Individual crystals in a two or three grained aluminum specimen deformed by tension acted in the normal manner described by Taylor and Elam4 except for marked modifications at the grain boundaries. There the power to withstand deformation was considerably increased, leaving a ridge on the specimen where decreased slip occurred, often noticeable 34 in: from the boundary. Adcock,6 Yamaguchi,7 Seumel,8 Hirst9 and others have also reported this phenomenon as a qualitative trend. Yet attempts by O'Neill10 and Ljunggren11 to measure a difference in hardness at grain boundaries in undeformed specimens were unsuccessful. Miller12 measured quantitatively the reduction in slip near the boundary between the single crystal and polycrystalline areas of zinc specimens. These effects consisted of two parts: I. Next to the polycrystalline interface the distribution of stresses was so altered

Jan 1, 1948

By Basil Prescott

Resume.—The district of Santa Eulalia lies 12 miles to the southeast of the city of Chihuahua, Mexico. The ore deposits occur in a Cretaceous limestone of unknown thickness, overlain by a series of rhyolitic tuffs and flows. The limestone is very gently folded and is cut by several systems of fissures, of which only those with a general north-south strike are pre-mineral and control the deposition. The deposits are of two main types; the earlier silver-bearing iron sulphide type occurs as high-grade tabular bodies resembling veins and as large masses of relatively low-grade ore, The gangue of this type is composed of lime-iron silicates that point toward a close association with an igneous rock mass which has not yet been encountered. In the later silver-lead-zinc type the ore occurs in vertical chimneys and horizontal mantas, principally as oxides, though at a depth of 1,500 ft. some sulphides have been encountered. During oxidation the ore chambers have increased in size owing to the solution of the walls by the sulphuric acid generated in the process, and a substitution has taken place of nearly one-half part by weight of the original constituents of the ore, by newly introduced elements and radicals. Both types are believed to have come from greater depths than those yet reached by mining, and their ultimate source, from a consideration of similar deposits, is believed to be an igneous rock in contact with the limestone at some horizon below. The deposits are believed to have been formed at unusually great depths, as indicated by the proved great vertical range of the silicate minerals coupled with the absence of the igneous rock, and by the practically unchanged character of the silver-lead-zinc ores as far as developed. The volcanic capping is believed to be distinctly later than the economically important ore deposition. Introduction The Santa Eulalia district is situated in the State of Chihuahua, Mexico, and lies about 12 miles southeast of the capital, the city of Chihuahua. (See map, Fig. 1.) The district embraces the Sierra de La

Jan 1, 1915

By J. B. Newkirk

IN 1939 Bitter and Kaufmann1 suggested that iron, precipitating from a copper-rich, Cu-Fe solid solution, appears initially as coherent particles of r-Fe which transform to the body-centered-cubic form of iron when the alloy is cold worked. Since then there has been considerable discussion, supported only by indirect evidence, regarding the validity of the concept. For example, Reekie, Hutchison, and Hether-ington2 interpreted the changes in electrical resistance accompanying the aging of Cu-Fe specimens in terms of a coherent 7-Fe precipitate which transformed to the incoherent a-phase during long aging or cold working. Greninger- ound that Cu-Fe alloys which had been water quenched from 1050" and then held at 650°C for 3 hr changed from weakly to strongly ferromagnetic as the aged wire was subsequently cold worked. He also found diffraction lines corresponding to body-centered-cubic iron in Debye-Scherrer patterns given by aged and worked specimens but lines corresponding to only one face-centered-cubic phase in specimens which had been aged but not worked. Knoppwost,' and later Cech and Turnbull,5 found that aged Cu-Fe specimens showed a slight increase in ferromagnet-ism after they had be? cooled in liquid nitrogen. Very recently Denney6 followed the kinetics of the precipitation reaction as indicated by the saturation magnetization, hardness, and diffuse X-ray effects. The experimental results reported by all of the authors mentioned above are readily explained in terms of the Bitter and Kaufmann concept. However, most of the evidence is indirect when used to define the structural changes involved. It was the aim of the present investigation to determine the mechanism of precipitation of iron from a Cu-Fe solid solution in the light of available published information and with additional new and more direct experimental data. Experimental Method At 1060°C copper will contain up to 3 atomic pct Fe in equilibrium solid solution.7 The solvus slopes rapidly toward lower iron concentration, so that at 600°C only about 0.5 pct Fe remains in solution at equilibrium. Below the eutectoid temperature (850°C), the iron-rich phase in equilibrium with the copper-rich solid solution consists of body-centered-cubic a-Fe. Above 850 °C the equilibrium iron-rich phase is face-centered-cubic r-Fe. The alloy to be studied was made by melting electrolytic iron and OFHC copper by induction under vacuum in an Alundum-lined crucible. The metal was held molten for about 5 min, after which time the power was turned off and the crucible was tipped about 70" to promote directional solidification. The resulting ingot, containing 2.5 wt pct Fe by analysis, was clean, large grained, and free of gross segregation. Slices % in. thick were cut from the ingot, rolled to 1/8 in. in thickness, homogenized in hydrogen at 1060°C for 24 hr and, finally, quenched in cold water. Specimens for all subsequent tests were made from these slices. Squares measuring about 1 cm on a side were cut from the slices to make specimens for studying hardness and microstructure. Wires (0.020 in.) for the Debye-Scherrer survey were drawn from 1/8 in. sq rods which had been cut from the homogenized slices. Large crystals for observing diffuse X-ray diffraction effects were prepared by mechanically

Jan 1, 1958

By B. H. Bergstram, C. L. Sollenberger

When glass spheres are crushed by slow compression loading, the outer lune-shaped fragments resulting from the fracture consistently fly outward at high velocity. About 45 pct of the strain energy fed into the sphere-platen system reappears in the form of the kinetic energy possessed by these fragments. These measurements were obtained from high-speed photographs. This kinetic energy can be utilized for addtional comminution if the fragments are allowed to impact against a suitable structure. Comminution theory has advanced considerably in recent years by the study of this unit operation under laboratory conditions. Some of the parameters have been isolated, but the experimental measurements of the pertinent quantities, such as energy, particle size, etc., are still only made prior to and after the conclusion of a fracture sequence. The catastrophic fracture process itself has not been adequately studied from a comminution point of view. It has recently been suggested by Gilvarry that the fragments which result from the free crushing of a single glass sphere by slow compression contain a considerable amount of kinetic energy after fracture. This kinetic energy, if properly directed, possibly can be partially utilized to cause additional fracture. In this paper a hypothesis will be presented which suggests that this kinetic energy is necessarily present and that its dissipation is the process by which a large part of the thermal energy imparted to the crushed product is generated. Evidence supporting the existence of kinetic energy and its utilization for secondary fracture will also be presented. THEORETICAL A previous paper4 has shown that the load-deformation curve of a system composed of an elastic sphere gripped by a pair of parallel platens, can be predicted by a consideration of the theories of Hertz as summarized by Timoshenko.' The deformation A, of one half of the system is given by which states that the deformation is a function of the mutually applied load, P, the radius of the sphere, R; and the respective physical properties of Poisson's ratio, v, and Young's modulus of elasticity, Y. The shape of experimental load-deformation curves conform to this relationship. The energy input to the sphere-platen system, can be predicted from the integral of the load acting through the appropriate distance, dA. Since dA can be evaluated in terms of P from the derivative of Eq. 1, this integral can be integrated between limits of 0 and P. The test sphere, however, is loaded at not one but at two points of contact, i.e., at both ends of a diameter, and hence the total energy input, E, is twice the energy input at each end, or The energy input to the system calculated from this equation corresponds to the energy computed from the measured area under the load-deformation curve. Timoshenko, considering the impact of two perfectly elastic spheres, has shown that the inter-penetration distance A is given by - m f (D (^ * ^t w as modified for the special case where one sphere is of infinite radius, i.e., its surface is a plane; where M is the mass of the finite sphere of radius R, and V is the velocity of approach at the start of an impact and also equals the final velocity of separation for perfectly elastic bodies. Because A is also a function of the load and the elastic properties, as shown in Eq. 1, the velocity, V, can also be calculated in terms of the elastic properties and maximum load, P, or

Jan 1, 1961

By Leonard Logan

Production control in the petroleum industry may be discussed under three general heads: engineering, legal, and economic. Though the problems that fall under the respective heads of engineering, law, and economics are separate, they are dependent and interrelated. The present study will deal with the economic phases of production control and only incidentally with the legal phases as they affect the economics of the problem. No one of these forms of control is more important than the others. The engineers have performed their service well, and although there are many problems of engineering control yet to be solved, they are not pressing. Legal control is a problem for the legislatures and the courts to solve. The petroleum industry is such a comparatively young industry and the legal problems are of such recent origin that the courts have not yet been called on to settle all the issues and the legislatures still have before them bills concerned with the regulation of the industry. Economic control of production in the petroleum industry is a highly desirable goal but it has not yet been completely achieved. Since the first commercial well was drilled in 1859, there have been recurring periods of overproduction. (Over- production will be used here to describe a condition wherein so much crude oil is available that a satisfactory and reasonable price is not received for the product.) The production of oil in 1859 approximated only 2000 barrels. In the following year production jumped to 500,000 barrels, thus bringing into

Jan 1, 1932

NORTH AMERICA Number Members Alaska 31 Canada 302 Mexico 175 Newfoundland 3 United States Alabama 52 Arizona 131 Arkansas 9 California 723 Colorado 184 Connecticut 98 Delaware 19 District of Columbia 133 Florida 16 Georgia 6 Idaho 61 Illinois 241 Indiana 57 Iowa 7 Kansas 32 Kentucky 33

Jan 1, 1932

By V. H. Wilhelm

The trend initiated in January 1936, of stabilized gasoline prices, increased demand and extraordinary drilling activity, continued in California during the year 1937. Crude prices were maintained during the year at the highest level since September 1930. Wildcat activity with resultant new discoveries and development of proven acreage were greater than in any year since 1928. Many fields in California in former years have been produced at full capacity, with consequent loss of reservoir energy, but at the present time continued activity is maintained to develop adequate reserves, so that production in these fields can be taken at a rate to correspond with good operating practice. Naturally, this good operating practice will be influenced to some degree by gas outlets and, in certain instances perhaps, by oil outlets. In any event, these last two controlling features will result in favorable rather than detrimental operation. In fields producing from great depths, ultimate production will be practically limited to the flowing and compressor life of the well, since there is as yet no economical method for pumping wells below depths of approximately 7000 ft. Experience has shown, however, that such pumping difficulties will be overcome and that production secured by pumping will add some to reserves established on the flowing life of the wells. California continued to operate under voluntary curtailment, but with unlimited transfers of allowable between various fields. Even though there was at all times considerable production above the Umpire's established quota, a constantly increasing demand reduced storage during the year. This increasing demand was due mainly to the rapid rise in Pacific foreign shipments from May to September. It is questionable, however, whether this favorable condition will be maintained over a prolonged period. (See Fig. 1.) Field Discoveries The great drilling activity during the year resulted in the discovery of three new fields in the San Joaquin Valley, as well as many extensions

Jan 1, 1938

NEW MEMBERS The following list comprises the names of those persons who became members during the period Dec. 10, 1915 to Jan. 10, 1916. ANDERSON, FRANK BASIL, Min. Engr., Sampler, Copper Queen Cons. Min. Co., Bisbee, Ariz. BAILEY, LEWIS NEWTON, Min. -Engr 4227 St. James Place, Sail Diego, Cal. BELL, JAMES E., Min. Engr., Care Chile Exploration Co., Chuquicamata, Chile, South America. BONILLAS, YGNACIO SAFFORD, Min. Geol., Copper Queen Cons. Min. Co., Bisbee, Ariz. BRADLEY, GEORGE OLIVER, Mech. Engr Hobart Bldg., San Francisco, Cal. CLARK, GEORGE L., Min. Engr Vipond Mine, Schumacher, Ont., Canada. CONKLING, RICHARD A., Geol., Roxana Petroleum Co. of Oklahoma, Tulsa, Okla. GOHRING, W. B.. Geol., Supt. of Mines, Calumet and Arizona Min. Co., Warren, Ariz.

Jan 2, 1916

By Harry K. Ihrig

Jan 1, 1947

By Harry K. Ihrig

Jan 1, 1947

By Robert H. Hafner, Irvin R. Kramer, Stewart L. Toleman

IN his paper on the calculation of hardenability from chemical composition, Grossmann1 discussed the effect of most of the alloying elements used commercially. The purpose of the work reported in this paper was to determine the effect of several other elements on hardenability-arsenic, antimony, beryllium, cobalt, columbium, germanium, tellurium, tin, aluminum, and titanium-and to extend the range of composition of some of the elements studied by , Grossmann-chromium, copper, manganese, molybdenum, nickel and silicon. EXPERIMENTAL METHODS To determine the effect on hardenability, suitable amounts of the alloying elements were added to experimental heats and the hardenability determined by means of end-quenched hardenability specimens. The steels were melted in a high-frequency induction furnace with a basic crucible, using ingot iron as a base for some of the heats and S.A.E. 1015 for others. The alloying additions were made as ferroalloys or as metal, depending on the ' alloying element. Hundred-pound heats were split and poured into square, tapered, cast-iron ingot molds with hot tops. Aluminum was not used as a deoxidizer in most of the heats. The ingots were homogenized for 12 hr. at 1260°C. (2300°F.) , and forged into rounds of 1 ½ in. diameter. These bars were normalized twice from 840°C. (1550°F.) before machining into Jominy bars. The composition of the steels was deter- [ ] mined in most cases by samples taken from the end-quench hardenability specimen. As suggested by crafts,2acid-soluble

Jan 1, 1943

By D. J. MacKinnon, J. M. Brannen

Smooth, compact, dendrite free 24-h zinc deposits have been electrowon from zinc chloride electrolyte using a diaphragm cell. The cell consisted of sealed anode compartments containing DSA anodes separated from an open cathode compartment by Dynel cloth membranes. Fresh electrolyte was fed to the cathode compartment where zinc deposition onto an aluminum cathode was aided by air sparging. The catholyte passed through the diaphragms into the anode compartments from which chlorine gas and spent anolyte were withdrawn. Standard electrolysis conditions were: 15 g/L Zn, 0.12 M HCI, I5 mg/L tetrabutylammonium chloride (TBACI) as the addition agent, 35°C, and 323 A/m2 (30 ASF) current density. The effect of variations in these conditions on the morpohology orientation, current efficiency, and energy requirement for 24-h zinc deposits was determined. The effect of total chloride ion concentration on the zinc deposit was studied by adding various amounts of NaCl to the electrolyte.

Jan 1, 1983

By M. E. Wadsworth, J. R. Lewis, J. M. Quets

Samples of snythetic magnetite were reduced in hydrogen at various partial pressures and temperatures. The reaction mas found to be surface controlled and directly proportional to hydrogen partial pressure over the temperature range studied (400° to 1000°C). A transition in the mechanism occurred at approxirnately 590°C. This has been attributed to a change in the slow step of the reduction reaction resulting from the presence of stable wüstite at higher temperatures. Below 590°C the heat of activation for the reduction was found to be 14,700 cal per mole and it was 3,200 cal per mole above 590°C. THE reduction of the oxides of iron has been a subject of study and interest for many years. Edstrom1 has reviewed the work up to 1953 and his findings provide much basic information concerning details of the reduction of hematite (Fe2O3 ) and magnetite (Fe3O4) with both H2 and CO. He concluded that below 600°C the reduction of both hematite and magnetite was essentially identical, since the rate was controlled by a surface reaction at a magnetite gas interface and the iron formed was very porous. The decrease in the reduction rate for both hematite and magnetite immediately above 600°C was attributed to the formation of a stable wüstite phase across which diffusion was very slow. The wide difference in reduction kinetics for hematite and magnetite above 600°C was explained in terms of the character of the wüstite formed. The rate of magnetite reduction increased slowly with temperature beyond the minimum immediately above 600°C and rates equivalent to those observed at 550°C were not obtained until the temperature was increased beyond 850oC. Edstrom and Bitsianes2 studied the solid-state reduction of magnetite, the reaction of which can be written (4x-3)Fe + Fe3O4—4 FexO [1] where x is between 0.83 and 0.95. The rate was found to be controlled by the kinetics of transport of iron ions through the wüstite phase. Bogdandy and Riecke3 studied the kinetics of reduction of small grains of iron oxide in hydrogen and qualitatively attributed the slow step in the reduction process to the diffusion of hydrogen and water vapor through pores. McKewan4 has analysed the data of Joseph,5 Stalhane and Malmburg,6 and Lewis7 and has demonstrated that the kinetics of reduction of both hematite and magnetite are controlled by surface reactions and also that the variation in surface area during reduction must be accounted for. McKewan was able to correlate the reduction data by the equation rodo[1-(1-R)1/3] = Kt [2] where ro is the initial particle radius, do is the density of the iron oxide, R is the fraction reduced at time t, and K is a rate constant. The applicability of Eq. [2] for temperatures above 600°C where a stable wüstite phase is present, indicates the slow step in the over-all kinetics does not result from diffusion unless diffusion occurs laterally along the oxide metal interface or through a wüstite layer of constant thickness. Diffusional control through a layer of wüstite is unlikely, however, in view of the pressure effects demonstrated by Tenenbaum and Joseph,' Diepschlag,9 McKewan,10 and the results of the present study. McKewan has demonstrated a linear rate dependence on the hydrogen partial pressure over the temperature range 400" to 1050°C for the reduction of hematite.

Jan 1, 1961

By H. R. Brannon, F. M. Perkins, Weldon O. Winsauer

Both the abnormal resistivity exhibited by shaly reservoir materials and their potential are due to adsorption of ions. Interrelationships between the two have been derived and verified by laboratory results. These relations which have resulted from this work may be used in a qualitative manner to estimate whether or not a particular shaly reservoir contains hydrocarbons, and also to estimate the porosity of shaly sands. INTRODUCTION In spite of the progress which has been made in the last decade toward a better understanding and utilization of the electric log, there remain a number of problems in the interpretation of the log. One of these which is often troublesome is that of divining the nature of the fluids in sandstones or carbonate rocks which contain appreciable amounts of shale. It was shown by Patnode and Wylliel in 1949 that shaly rocks exhibit an abnormally low resistivity when saturated with solutions of low ionic concentrations. This phenomenon has been demonstrated to be due to the adsorptive properties of shale or clay in the rock.' In estimating the fluid content of shaly sands or carbonates from the electric log, it is desirable and sometimes necessary to correct for the abnormally low resistivity. A similar correction is likewise often necessary if attempts are made to estimate the porosity of a stratum from resistivity measurements. The correction may be made from data obtained on core samples and from information on salinity of interstitial water. Cores, however, are not always available. Moreover, even if cores are at hand, their examination is time-consuming. It would be most desirable, therefore, to make corrections of this nature from the log itself. Since both the abnormal resistivity and the potential' are consequences of the adsorption of ions on shale, it should be possible to utilize the potential curve to give better interpretation of resistivity data obtained in logging shaly materials. The work described in following sections was directed toward this end. THEORY Relation of Resistivity of Shaly Reservoir Rock to Adsorpttve Properties In discussing the effect which the presence of shale or clay exerts on the resistivity of a reservoir rock, it is convenient to make use of the resistivity factor.4,5 This quantity has been defined as the ratio of the resistivity of the rock when it is completely saturated with an electrolyte to the resistivity of the electrolyte itself. When the rock, such as a clean sand or carbonate, is free of shale the resistivity factor is virtually independent of the ionic concentration of the electrolyte used to saturate the sample, so that F = R0/Rw = constant for a clean rock . . (1) where F is the resistivity factor, R0 is the resistivity of the rock saturated with electrolyte, and Rw is the resistivity of the electrolyte. When the rock contains argillaceous material, the resistivity factor as defined above is no longer independent of the concentration of the electrolyte used to saturate the rock, but decreases as the ionic concentration of the electrolyte decreases. In explanation of this behavior, it is instructive to consider a sample of shaly porous rock placed in contact with a large volume of a dilute electrolyte. The sample is considered to become saturated with the electrolyte, and to attain equilibrium with it. As a result of adsorption by the shale surfaces within the rock, there is a greater concentration of ions in the solution adjacent to the shale particles in the interstices of the sample than there is in the external solution with which the

Jan 1, 1955

By W. T. Cardwell

Physically absurd, triple-valued saturations appear in the straight-forward solution of the Buckley-Leverell equations for the displacement of oil by water or gas. From an engineering viewpoint, the triple value causen no difficulty. It is well known how it may be compensnted in order to obtain physically meaningful, numerical results. From a scientific viewpoint, the question still arises: What did the triple value mean? This paper explains how and why the triple value arose in non-capillary Buckley-Leverett theory. The discussion should serve as a background for the understanding and use of the modern method of characteristics in di.~pkzc(>ment theory. INTRODUCTION Displacement theory was introduced to petroleum technologists in 1 941 by Buckley and Leverett.' Their first equation, which they wrote down without derivation, was equivalent to the following: ?s/?t= - qr/F ?f/?r (1) where S = saturation of displacing fluid (a fraction) r = time q,. = total volumetric velocity of both the displacing phase and the phase being displaced (usually, but not necessarily, assumed to be a constant) F = porosity (a fraction) f - fraction of the total volumetric velocity that is the volumetric velocity of the displacing phase (assumed to he a function of S only x = distance. Buckley and Leverett called Eq. I "a material balance equation". Actually it is derived from both a continuity equation, or material balance equation, and Darcy's law. Buckley and Leverett jumped from their Eq. 1 immediately to their Eq. 2, which was the equivalent of the following: (?x/?t)x = qr/F df/ds = qr/F f'(s) (2) The jump from Eq. 1 to Eq. 2 involves apparently simple mathematics, but in that apparently simple mathematics lies a subtle point that is part of the key to the meaning of the triple value to be discussed here. Eq. 2 may be readily interpreted as saying that a point of constant saturation (on a saturation-vs-dis-tance curve) moves with a constant velocity that is proportional to the total volumetric rate, inversely proportional to the porosity, and is otherwise a function of the saturation itself. So that if one knows the derivativc with respect to saturation of the fractional flow function, f(S), for each saturation, one knows the velocity of each point of the moving saturation-vs-distance curve. The function f(S) can he determined experimentally and its derivative f'(S) can be calculated. It turns out that the experimentally derived f'(S) is not a monotonic function of S, but instead it has a definite maximum and declines away at both high and low saturations. This in turn means, in accordance with Eq. 2, that on a moving saturation-vs-distance curve, ccrtain intermediate saturations will travel faster than the saturations either higher or lower. The result is indicated in Fig. 1. In Fig. 1, the abscissas represent distances along a column of porous medium, which column is assumed to be uniform in cross-section perpendicular to the ab-scissal direction. The ordinates represent fractions of pore space occupied by the displacing phase, which may be either water or gas. It is assumed that the saturation is uniform over all planes perpendicular to the abscissal direction. The saturation is a function only of time and one space variable. Time variation of the saturation is represented by change in shape of a curve such as curve AGJ, which represents the initial saturation-vs-

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick's First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood's analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner's diffusion-controlled kinetics is based upon the same form of mass balance using Fick's First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By William E. Galloway, Gary E. Smith, Christopher D. Henry

INTRODUCTION Studies relating to the Oakville aquifer as presented in this report and by Henry et al. (this volume), are part of a larger , comprehensive examination of regional and local stratigraphic, hydro- geologic, and geochemical parameters within the Oakville Formation recently completed by the Bureau of Economic Geology. The Oakville serves both as a major Gulf Coast aquifer and an important uranium host (Fig. 1). Regional and local controls on hydrodynamics and hydrochemistry have important implications for hydrochemical exploration, the establishment of premining baseline parameters, and the design of post mining restoration procedures. Investigations of the Oakville Formation were de- signed for the purpose of determining the response of the aquifer to uranium extraction and were funded by the U.S. Environmental Protection Agency under grant numbers R-805357-01 and R-805357-02. Physical Stratigraphy Physical stratigraphic analysis shows that the Oakville Sandstone, a lithostratigraphic unit deposited by a major coastal-plain f luvial system, consists of five mappable, component depositional elements (Figs. 2 and 3). Each major component element is the product of one or more rivers traversing the Miocene coastal plain. In turn, each river possessed a unique sediment load, discharge characteristics, and source terrane. Consequently, each element exhibits distinguishing geometric and compositional parameters that potentially influence the flux and hydrochemical evolution of contained ground waters (Galloway, Henry, and Smith, in preparation). The Oakvil le Sandstone, as mapped and interpreted as a lithostratigraphic unit in the study area, corresponds closely to the Jasper aquifer system, an equally well-defined Gulf Coastal Plain hydrogeologic unit (Baker, 1978). Principal surrounding hydrogeologic units include the underlying Catahoula confining system, the Jasper aquifer system itself, and the overlying Burkeville confining system (lower Fleming mudstones). The Evangeline aquifer system includes much of the Fleming Formation. The Jasper aquifer system is bounded above and below by relatively less transmissive, finer grained confining systems, although absolute transmissivity varies greatly within both the Jasper and confining units. Lithostratigraphic and hydrogeologic boundaries coincide almost exactly within the Hebbronville flu- vial axis (Fig. 3). Correspondence of geologic and hydrostratigraphic boundaries is good within the George West axis; farther to the northeast the correlation of the Jasper aquifer with units mapped as Oakville Formation diverges to varying degrees. A complete analysis of these trends and a study of the depositional facies comprising the Oakvillle are included in Galloway, Henry, and Smith (in preparation). REGIONAL HYDROGEOLOGY The stratigraphic, compositional, and structural framework of the Oakville Formation and the mosaic of interrelated depositional facies that are combined in this framework play a key role in defining the hydrogeology of the Oakville. Furthermore, a combination of climate and hydrogeology, as well as past and present socioeconomic conditions, has determined water and land use patterns within the region of Oakville outcrop. Utilization of Oakville Ground Water Stratigraphic control for determining which wells produce ground water from the Oakville aquifer was established by preparing structural and isopach maps of the Oakville Formation using regional electric log cross sections. Surface elevation and screened interval data (or total well depth, if open-hole completion techniques were used) from each water well, combined with the stratigraphic data, allowed accurate assessment of the producing aquifer for individual wells. Information on well and screen depths, water levels, and usage of water from

Jan 1, 1980