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By F. J. Deadrick, A. L. Ramirez, R. J. Lytle

This article describes the evaluation of a new geophysical technique used to map fractures between boreholes: electromagnetic geotomography used in conjunction with salt water tracers. An experiment has been performed in a granitic rock mass. Geotomographic images have been generated and compared with borehole geophysical data: neutron logs, acoustic velocity logs, caliper logs and acoustic televiewer records. Comparisons between the images and the geophysical logs indicate that clusters of fractures were detected but single fractures were not.

Jan 1, 1982

By S. C. Sun

With the aid of emulsifiers, intense high-frequency sound waves are capable of emulsifying any collector in water. The data show also that ultrasonically emulsified collectors are more effective in floating minerals than the nonemulsified collectors. THE use of ultrasonics in forming emulsions is not new. As early as 1927 Wood and Loomis reported preparation of emulsions with ultrasonics. In 1935 Rschevkin and OstrawskyV escribed the use of great ultrasonic power in producing fine emulsions of various oils and paraffin in water. Recently Oyama and Tanaka3 employed ultra-emulsification to increase the effectiveness of sodium ethyl xanthate in flotation of chalcopyrite and galena. An emulsion is a two-phase system consisting of two incompletely miscible liquids, the one being dispersed as finite droplets In the other. The dispersed liquld is known as the internal or discontinuous phase, and the surrounding liquid is termed the external or continuous phase. There are two types of emulsions; one is oil-in-water (O/W) and the other water-in-oil (W/O). The word oil refers to the liquid other than water. Circumstances exist in which the emulsion type is not clearly defined, and the internal and external phases both contain portions of the opposite phase. This is said to be a dual emulsion. Among the many hypotheses, 5a, B proposed for the formation of emulsions, the Bancroft's adsorbed film or double interfacial tension theory is widely accepted. Bancroft 7, 8 deduced that in the process of emulsification the interfacial tension between oil and water is lowered by the formation of an emulsifying film, which contains the adsorbed molecules and/or ions from the emulsifying agent and the two liquids. This film has two interfacial tensions, one with the water and the other with the oil, which are not necessarily equal. The difference in interfacial tension between the two surfaces of the film is chiefly responsible for forming different types of emulsions. For example, if the interfacial tension between water and film is less than that between oil and film, the film will become convex on the water side, thereby tending to form an oil-in-water emulsion. On the other hand, if the interfacial tension between water and film is greater than that between oil and film, the film will become concave on the water side, thereby tending to make a water-in-oil emulsion. In line with this theory, emulsifying agents soluble in water have the tendency to form oil-in-water emulsions, while those soluble in oil form emulsions of the reverse type. Apparatus and Experimental Procedure: The ultrasonic apparatus shown in Fig. 1 consisted of a hypersonic generator (A), Brush Development Co. model Bu-204; a hypersonic transducer bowl (B) whose resonant frequency is 400 kc per sec; and a round-bottomed glass tube (C) of 2.2 cm ID and 21 cm in length. The acoustical output power of the hypersonic transducer bowl was standardized with a Hewlett Packard vacuum tube voltmeter, model 41 0B, across the hypersonic generator output. The glass tube, containing the materials to be emulsified, was placed 1 cm above the central surface of the transducer bowl, which was filled with water as shown in Fig. 2. Ultrasonic emulsification was performed in three steps, although a one-step method has been used: 1) emulsifying the predetermined amounts of col-

Jan 1, 1956

By E. T. Turkdogan, L. S. Darken

Using the quadratic formalism, thermodynamic equations are derived for the composition dependence of the heat and entropy of mixing. The applicability of these equations is confirmed by available experimental data on the activities and heats of mixing for binary metallic systems of Group ZZB elements. In a recent paper arkeen' introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. That is, in the terminal region, which may extend to as much as 60 at. pct, the logarithm of the activity coefficient, log y,, of component 2 is a linear function of (1 - N,)' where N2 is the atom fraction of component 2. Similarly, for the other component, log yl is a linear function of (1 - N,)'. A number of iron-base binary liquid alloys were shown to obey this quadratic formalism. arkeen' extended this formalism also to any corner of a ternary system and showed that the activity coefficients of the components 1, 2 and 3 (1 is taken as the solvent) can be represented by quadratic terms involving five parameters, four of the binaries and one for the ternary system. Numerous examples given by arkeen' demonstrated the general applicability of the quadratic formalism to iron-base systems over a wide composition range. In this paper further examples are given of binary liquid systems (Group IIB elements, Zn, Cd, and Hg) and of several solid solutions, again demonstrating the appropriateness of this concept. A further purpose of this paper is to extend the quadratic formalism to the enthalpy and excess entropy of binary metallic solutions and to test the equations so found using available experimental data. QUADRATIC FORMALISM FOR HEATS AND ENTROPIES OF MIXING OF BINARY METALLIC SOLUTIONS The following equations, reproduced from Darken's paper, are for the two terminal regions of binary systems. at infinite dilution and a's are temperature dependent parameters to be determined from the experimental data. Although the quadratic formalism is an assumed representation of the data, Eqs. [I] to [4] are thermo-dynamically consistent with the Gibbs-Duhem relation and satisfy Raoult's and Henry's laws as limiting cases. As pointed out previously,' the following form of the Gibbs-Duhem equation facilitates the integration in general but particularly in regions I and 11, where each of the derivatives is constant. The partial molar enthalpy of solution i, (and i; the value of i, at infinite dilution) are related to the activity coefficients y, and y," by the thermodynamic relation Differentiating Eq. [l ] with respect to 1/T and substituting the above thermodynamic relation gives for region (I) It is reasonable to assume that over a temperature range of experimental interest, the enthalpy of mixing is essentially independent of temperature, implying from Eq. [7] that the derivative da,,/d(l/) is also independent of temperature. On the basis of this argument, the temperature dependence of a has the form where £ and S have the units of enthalpy and entropy respectively; they are characteristic parameters for a terminal region of a binary system, e.g. for region (I), C12, S12 and for region (II), d:,,, S2,. Using this equation gives for dff ,/ d(l/), From Eqs. [7] and [9] an expre_ssion is obtained for the composition dependence of L,. Similar calculations are made for El and the results are summarized below for the two terminal regions. For region (I), The corresponding expressions for the molar heat of solution, AHM, are readily obtained from the above equations for the two terminal regions: For region (I),

Jan 1, 1969

By E. I. Organick, B. H. Golding

A simple correlation is presented for the prediction of saturation pressures in condensate-gas and volatile-oil mixtures. Saturation pressure is related directly to the composition of the mixture with the aid of two generalized composition characteristics, B, the molal average boiling point, and W, the modified weight average equivalent molecular weight. The need for hydrocarbon equilibrium constants is entirely eliminated. Only the values of the two conlposition parameters need be obtained, and these are calculated in a simple and reproducible manner from the stream analysis of the mixture and the ASTM distillation for the heavy ends. The correlation is given .in the form of a set of 14 working charts in which saturation pressures, either retrograde dew points or bubble points, are plotted cs temperature, forming partial phase envelopes for mixtures having discrete values of the composition parameters, B and Wul. A locus of critical states on each chart intersects the partial phase envelopes, distinguishing retrograde dew point pressures from bubble pressures. A comparison Between experimental and predicted saturation pressures reveals that: the probable error of the predicted values, when considering the data as a whole (214 experimental points), is five per cent; for high gasjoil ratio condensate fluids (approximately 40.000 or more cu ft/bbl) the probable error is about 8 per cent. In either case, however, the probable error is comparable with the overall uncertainty of the data from which the correlation is derived. INTRODUCTION There is a present need for a simplified, yet reasonably accurate method for predicting upper phase boundaries of reservoir fluids. In the case of high gas/oil ratio fluids, namely the so-called highly volatile oils and the condensate gases, no simple method, accurate within 5 to 10 per cent, is now available by which bubble point and retrograde dew point pressures may be predicted. In order to calculate the upper phase boundary of a volatile reservoir fluid, using correlations now available, it is necessary to find and employ the proper K-values (equilibrium volatility ratios of the hydrocarbons in that fluid). This process of finding the Proper K-values usually involves a double trial and error computation. Since the K-values are in themselves dependent upon the composition of the fluid, their use in the calculation of a saturation pressure actually represents an unnecessary complication. The correlation described in this paper relates saturation pressure directly to the stream composition, entirely eliminating the need for K-values. The only data required to calculate the Stream composition are obtained from the customary low temperature fractional analyses of separator gas and liquidt and from the ASTM distillation of the c,+ fraction of the separator liquid. A considerable simplification in the procedure for predicting saturation pressures is thereby effected without significant loss in accuracy. BASIS FOR A CORRELATION Empirical relationships between the saturation pressure and the composition of the fluid in question have already been partially explored by one of the authors.V n particular, a relationship between the critical pressure for a hydrocarbon mixture and its composition was developed. The critical pressure is in reality a saturation pressure, as it repregents a limiting case either of a dew point or of a buhhle point pressure for any given mixture. It was found that the critical pressure may be correlated as a function of two generalized composition characteristics or variables. One characteristic expressed a molal average prop-erty, the other a weight average property of the mixture. Specifically, the molal average boiling point (MABP, or B as it

Jan 1, 1952

By M. C. Flemings, T. S. Piwonka

Pore formation is examined analytically in cellu-larly solidified single crystals, in cylindrical castings of pure metals and alloys, and in unidirectionally solidified castings. Effects are considered of fluid flow. dissolved gas, and surface tension. Experimental results show that flow through a partially solid "mushy" aluminum alloy obeys relations similar to those applicable for flow through other types of porous beds. Flow rate is proportional to the square of the fraction liquid (fL) for fL less than 0.3. Results indicate models chosen for mathematical description of pore formation in alloy solidification are valid. ONE of the solidification variables which is influential in determining mechanical properties of castings and of wrought material produced from cast ingots is porosity. This porosity may result from shrinkage, dissolved gases, or a combination of both, and may take the form of either macroscopic pores in localized areas of the casting or microporosity evenly distributed throughout large areas of the casting. In alloys which freeze over a range of temperatures some microporosity is generally found after solidification. There has been much discussion as to whether the micropores are caused primarily by shrinkage, by gas, or by a combination of both.'-3 There has, however, been little experimental or analytical work performed to delineate the relative contributions of shrinkage and gas in causing microporosity or to quantitatively describe the influence of processing variables on microporosity. Porosity other than microporosity (e.g., center line shrinkage) has also received only limited quantitative treatment.495 The aim of this work is to examine analytically the general problem of pore formation in solidification and to perform limited confirmatory experiments. Consideration is first given to shrinkage porosity in pure and nearly pure metals (shrinkage in cellular growth, centerline shrinkage in cylinders). Next, a discussion is given of formation of shrinkage-caused microporosity in unidirectional solidification and in "mushy" solidification. Finally, influences of dissolved gas and surface tension on microporosity are examined. Numerical results are given for aluminum and an aluminum alloy. Typical examples of microporosity are shown in Figs. 1 to 3, for 1) cellularly solidified aluminum, 2) sand-cast aluminum alloy, and 3) low alloy steel. SHRINKAGE POROSITY IN PURE AND NEARLY PURE METALS 1) Cellular Growth. In cellular freezing of an impure liquid, liquid grooves may exist over a considerable length of the growing crystal.6 The cross-sectional area of the grooves decreases with increasing distance from the cell tips; the root of the groove is blunt if the liquid at this point reaches eutectic composition. As a result of volume contraction during solidification, flow occurs down the groove, parallel to the growth direction; hence, there must be a pressure drop from the groove entrance to points within the groove. The geometry of the groove is simplified to that of a circular cylinder of radius r and length L, Fig. 4, L » r, and a simple and useful limiting case is obtained. This is that, in the circular cylinder freezing at constant velocity, the pressure at the root of the groove is lower than that pressure at radius r in grooves of other geometries where r decreases continuously to a lower limit at L. As discussed below, a pore resulting from a given pressure difference

Jan 1, 1967

By Frederic L. Kadey

Diatomite is a siliceous, sedimentary rock consisting principally of the fossilized skeletal remains of the diatom, a unicellular aquatic plant related to the algae. Thus, it has been formed by the induration of diatomaceous ooze, and consists mainly of diatomaceous silica, a form or variety of opal which is first formed in the cell walls of the living diatom. Diatomaceous silica is not generally regarded as a synonym or the equivalent for diatomite, although it has been so used at various times. Accurately, diatomaceous silica is the preferred name for the principal mineral component of which the rock, diatomite, is composed. The terms diatomaceous earth and kieselguhr are used as synonymous with diatomite. The designations tripoli, tripolite, infusorial earth, etc., were used at one time but are now obsolete. With the changing nomenclature, these terms that were at one time correct when proposed and used for generations would be considered incorrect if used today in the light of current knowledge. The designation diatomite is reserved for those accumulations of diatomaceous silica that are of sufficient quality, size, and minability to be considered of potential commercial value. Processed diatomite possesses an unusual particulate structure and chemical stability that lends itself to applications not filled by any other form of silica. Foremost among these applications is its use as a filter aid, which accounts for over half of its current consumption. Its unique diatom structure, low bulk density, high absorptive capacity, high surface area, and relatively low abrasion are attributes responsible for its utility as a functional filler and as an extender in paint, paper, rubber, and in plastics; and as an anti-caking agent; thermal insulating material; catalyst carrier; and chromatographic support; polish, abrasive, and pesticide extender to name a few representative applications. The United States is the principal producing country, although diatomite is found in numerous other locations. Geology Composition and Morphology Diatomaceous silica qualifies as a. mineral of organic origin in much the same way that aragonite and collophane do. The silica of the fossilized diatom skeleton closely resembles opal or hydrous silica in composition (SiO2 • nH2O) .4, 12, 203 The silica is of acute biological significance, not only for the cell wall component, but also for the basic life process.45, 51 Without silica, cell development ceases .31 In addition to bound water, varying between 3.5 and 8%, the siliceous skeleton may also contain, in solid solution, or as part of the Si02 complex, small amounts of associated inorganic components-alumina, principally-and lesser amounts of iron, 46, 49, 55 alkaline earths, alkali metals, and other minor constituents.59, 63, 67 Boron is reported to be an essential element for diatom growth .52, 58 Since diatomaceous silica is not pure hydrous silica but contains other intimately associated elements, there is good reason to consider it a distinct type or variety.4 Associated with the diatomaceous silica, and integrated as part of the diatomite, may be variable amounts of organic matter, soluble salts, and particles of rock-forming minerals that were syngenetically deposited or precipitated with the diatom frustules. Sand, clay, carbonate, and volcanic ash are typical common contaminants. Other contaminating minerals may be present, such as feldspar, mica, amphiboles, pyroxenes, rutile, zircon-the result of weathering, then transporting, and subsequent redeposition of surrounding land masses. Commercial diatomite may also contain fragments and particles of

Jan 1, 1983

Jan 1, 1967

The One Hundred Eighteenth Meeting of the. Institute was held at the Milwaukee Auditorium, on Tuesday,. Oct. 8, to Thursday, Oct. 10, inclusive, 1918, under the joint auspices of the Committee on Iron and Steel (Chairman, Prof. J. W. Richards), and the Institute of Metals Division (Chairman, William M. Corse), and simultaneously with sessions of the American Foundrymen's Association and of the. American Malleable Castings Association. It was preeminently a war meeting. It was attended by 104 members of the Institute. The social features, so far as the members of this Institute were concerned, were slight, but generous and appropriate entertainment was offered to the ladies, consisting of automobile sight-seeing trips, reception, concert and dance on Tuesday evening, a theatre party Wednesday evening, and -a banquet in-the Auditorium Thursday evening, at which the speakers were Charles M. Schwab, Director General of the United States Shipping Board Emergency Fleet Corporation, Major A. Radclyffe Dugmore, and W. H. Blood, Jr., Assistant to the President of the American International Shipbuilding Corporation. A joint session was held on Tuesday morning, at which an address of welcome was delivered by Hon. Emanuel L. Phillipp, Governor of Wisconsin, with a response by Benjamin D. Fuller, President of the American Foundrymen's Association, and the following addresses: Activities of the Army Ordnance Department, Especially as Applied to Foundry Matters. By C. S. Koch, Cannon Section, Production Division, Ordnance Department. Washington. D. C.

Jan 11, 1918

By Julius Albert Krug

IN the field of mineral resources, today's problems and those we can reasonably expect in the future are so vast that nothing less than world-wide thinking and world-wide planning will suffice. I can imagine nothing more useful for the Institute to do in celebration of its seventy-fifth anniversary than to hold this conference on world mineral resources. Mineral resources are the basis of any nation's industrial production. Without expanding industrial production, the high standard of living found in the United States could not exist. Without such a standard of living it would be most unlikely that we should have a high level of culture. The hope of the world, as I see it, depends very largely on a general rise in living standards everywhere, and in the general increase of the levels of culture including a sympathetic understanding of the problems of other nations. For this reason, the proper use of the world's remaining mineral resources must be taken into account in any plans to safeguard the peace of the world. Being as exasperatingly human as human beings always seem to be,. we usually wait until almost too late to begin our plans to stave off an impending disaster. We do this as individuals, as components of particular States or Governments, and as citizens of the world. We waited, if not too late, certainly a very long time in getting started on the job of world-wide con-

Jan 1, 1947

By J. O. Lewis, Carl H. Beal

Introduction ............................... 492 Theories Relating to the Recovery of Oil.................. 493 Methods Commonly Employed for the Estimation of Future Production..... 495 Saturation Method........................... 495 Production Curve Method....................... 496 Production per Acre Method.....................: 496 Appraisal Curves.............................. 498 Derivation and Construction...................... 498 Comparison of Appraisal Curves of the Osage and Nowata Fields...... 505 Use of Appraisal Curves........................ 506 Accuracy of the Apprais?l Curves and Their Sources of Error........ 508 Relation Between Future Productions of Wells of Equal Output....... 510 Use of Appraisal Curves for the Derivation of Generalized Future Decline Curves. 513 Theory of Generalized Curves Showing the Decline in Production...... 513 Suggested Methods for Making Closer Estimates.............. 517 Use of Logarithmic Coordinate Paper.................... 518 Summary................................ 520 Introduction Oil wells usually reach their maximum daily output shortly after they are completed. From that time they decline in production, the rapidity of decline depending on the output of the wells and on other factork governing their productivity. The production curve of a well shows the amount of oil produced per unit of time for several consecutive periods; if the conditions affecting the rate of production are not changed by outside influences, the curve will be fairly regular, and, if projected, will furnish useful knowledge as to the future production of the well. By the aid of this knowledge the value of a property maybe judged, and proper depletion and depreciation charges may be made on' the books of the

Jan 1, 1918

By Irving Fatt, Robert J. S. Brown

INTRODUCTION The wettability of reservoir rocks is recognized as one of the major factors that determines their multiphase flow properties. Multiphase flow properties in turn govern reservoir performance. For this reason, the reservoir engineer is vitally interested in the wettability of reservoir rock. The production research scientist is interested in wettability because the solution of the problem of improving waterflood recovery by use of surface-active additives may hinge on a detailed understanding of the wettability of reservoir rock. Early workers believed that all reservoir rocks were preferentially water wet. Continued study soon uncovered certain rocks which had flow properties that indicated that they were preferentially oil wet. Recent studies show that there is a spectrum of wettability. Some reservoir rocks have multiphase flow properties which indicate that they have an intermediate wettability. The differences in recovery observed among different reservoirs may, in part be the result of small differences in wettability. Differences in wettability amcng reservoir rocks may be the result of differences in the fraction of the total surface area that is preferentially oil wet and preferentially water wet. Nuclear magnetic relaxation measurements may provide a method for determining the fraction of preferentially oil wet and preferentially water wet area in porous media. Measurements to be reported here were made on water-saturated unconsolidated sand packs which were mixtures of preferentially oil wet and preferentially water wet sands. The resulting data show definitely that the fraction of each wettability in these sand packs can be determined by this nondestructive method of measurement. THEORY OF NUCLEAR MAGNETIC RELAXATION The details of the theory of nuclear magnetic relaxation have been presented previously1. In this paper, only a very brief review of the theory will be given to show its application to the measurement of fractional wettability. Nuclear magnetic relaxation is a process of adjustment undergone by certain atomic nuclei when their magnetic environment is changed. They adjust, or relax, to be in equilibrium with a new magnetic field. The reason that some atomic nuclei are affected by a magnetic field is that they themselves behave in some respects like tiny magnets. In particular the proton, the nucleus of the hydrogen atom, behaves as a magnet. The proton spins, somewhat as the earth spins on its axis. The spinning charge produces a magnetic field just as current traveling in a loop of wire produces a magnetic field. No net charge is required, however; for instance, the neutron has spin and magnetic moment. When the spinning proton is subjected to an externally applied magnetic field, its axis tends to line up with the magnetic field, somewhat as a compass needle tends to line up, but the spinning proton cannot do this as easily as the needle can. The proton also has mass, and its spinning mass makes the proton behave somewhat like a gyroscope. As is well known, a force which tends to change the axial direction of a gyroscope merely causes the gyroscope to precess: lhat is, the axis begins to trace out a conical surface. The gyroscope cannot actually assume the position suggested

Jan 1, 1957

By J. Geertsma

In order to obtain a better insight into the pressure-volume relationship of reservoir rocks a theory of pore and rock bulk volume variations is presented. The theory is independent of the shape of the pores but is restricted to isotropic porous media built up of continuous homogeneous matrix material. The main conclusion obtained from this theory is that only three elastic constants and three viscous constants are required for describing pore and rock bulk volume variations if the porosity is explicitly introduced into the treatment. In addition, reasonable approximations are introduced for various types of reservoir rock, e.g., sandstones, limestones, and shales, which lead to further simplifications of the basic formulas. In consequence there is then a further reduction in the number of deformation constants which have to be determined experimentally. It is shown how measurements of these remaining deformation constants can be performed most conveniently. Finally the application of the theory to reservoir studies is discussed and the translation of experimental results obtained in the laboratory into reservoir behavior is considered. INTRODUCTION The decline of fluid pressure in connection with the withdrawal of fluid from an underground reservoir gives rise to a change in volume of both reservoir fluids and reservoir rock. The volume variation of the reservoir rock results in a decrease of both the pore volume and the total volume of the fluid-filled formation. Whereas the variation in volume of the reservoir fluids with pressure is usually known from PVT analysis, that in the volume of the porous medium is rarely measured, as it is considered of minor importance in reservoir engineering. Nevertheless, certain experimental results' suggest that in a number of cases the neglection of the variation in pore volume may introduce errors into material balance calculations of reservoirs producing above the bubble point. Only a few experimental results on the compressibility of porous rocks have been published. The compressibility of pure quartz and of calcite can be found in a paper by Adams and Williamson'. Botset and Reed' carried out some experiments on the compressibility of loose sands, while Carpenter and Spencer' measured the compressibility of a number of consolidated sandstones, which data were supplemented by Hughes and Cooke5. Hall' finally reported a number of experiments designed to study the influence of the porosity on the compressibility of oil-bearing formations, from which it appeared that, particularly in the low porosity range, the compressibility of the pore volume is important enough to be taken into account. Difficulties, however, arise in applying these experimental results to field cases. This is partly due to the fragmentary nature of the published data. Yet even if more complete data were available, the need for a theoretical background would be strongly felt. Such a background can be partially found in studies carried out by Biot,6,7 who published a theory of elastic deformations of porous materials and their influence on fluid displacement within the pores, by Lubinski8, who studied the stress distribution in an elastic porous medium neglecting pore compressibility, and by Gass-mann" who mathematically analysed the elasticity of packings of spheres. The contributions of Biot intro-duce a number of deformation constants which are impractical for reservoir rocks from an aspect of experi-mental determination. The theory developed by dass-mann is correct but difficult to read. It appeared, how-

Jan 1, 1958

By Walter J. Karplus

By means of a finite difference expansion a fluid flow field in cylindrical coordinates with axial symmetry, is simulated by a network of electrical resistors. A series of DC analog computing units, connected to the network bounrlary corresponding to the free surface effectively adjust the network parameterr to satisfy simultaneously Laplace's equation and the borrndary conditions. The system automatica1ly "re1axes" to the correct boundary shape in a fraction of a second. A detailed application of the method to the water coning problem in oil wells is presented. INTRODUCTION The water coning problem in petroleum production is a prime example of a class of problems known as free surface problems. A free surface arises in fluid flow regions when the shape of the boundary of a single phase flow region is affected in some manner by the pressure or potential gradients within the region. When there exists an interface of two fluids of different densities, the shape of this interface will be determined by the relative velocities of the two fluids and will therefore comprise a free surface. Other free surface problems of interest to petroleum engineers include the gas coning, water injection, and gravity drainage probIcms. In each case it is desired to predict the shape of the boundary of the oil zone as a function of the flow rate, the well penetration and the physical parameters and dimensions of the system. Such problems do not lend themselves to the classical analytical treatments of boundary value problems because in this case the boundary of the potential field and the potential distribution within the field are interdependent and must be calculated simultaneously. A further difficulty arises from geometric considerations. Since the fluid flow is of the radial type in most cases, such effective methods as conformal transformation and the hodograph are not applicable. It is the purpose of this paper to present a method whereby free surface problems of this type may be solved rapidly to the desired order of accuracy by means of a combination of a network of electrical resistors and conventional analog computer units. The water coning problem is treated in some detail. Then the procedure for extending the technique to other free surface problems is indicated. FORMULATION Most commercial oil reservoirs consist of an oil-saturated sand, bounded above by an impermeable strata and below by a water-saturated sand. Gravimetric separation results in a horizontal oil-water interface. When an oil well is drilled so that it partially penetrates the oil zone, and production is initiated at a constant rate, the oil-water interface will assume a new shape as a result of the pressure gradients in the oil zone. It should be emphasized that this is a steady phenomenon. After an initial transient period the water phase will be completely static and only the oil will be in motion. The new steady-state shape of the interface, as shown in Fig. 1, depends upon the depth of penetration, d, the thickness of the oil zone, I, the production rate, q, the hydraulic permeability zone of the sand, k, the viscosity of the oil, µ, and the densities of the oil and water, p.,. and pw.. The problem is to determine this relationship. Darcy's law + = - (P f g p z).....(1) it.

Jan 1, 1957

By B. W. Dyer

In 1924, the Crescent Eagle Oil Co., while drilling the salt section of the Paradox formation in Grand County, Utah, encountered a salt that did not appear to be sodium chloride. This salt was analyzed and showed the presence of potash minerals, both sylvite (KCl) and carnallite (KMgC12.6H2O). Because of the high potash content of the sample, there was considerable speculation: (I) as to whether the hole had been salted, and (2), if not, the extent, richness, and the depth at which the deposit occurred. The discovery caused a large amount of activity in the area. During the next few years, 68 potash prospecting permits were issued by the Government, 24 under the Act of 1917 and 44 under the Act of Feb. 7, 1927, each including about four sections of land. Several holes, all shallow, were drilled for potash. A number of holes were drilled for oil into the salt horizon and the cuttings collected at the oil wells were examined petrographically and chemically. The shallow test holes were not sufficiently deep to reach the potash horizon and revealed nothing of value, but several of the oil test holes gave some indication of where potash might be found. Location and Geology of Deposits The potassium and magnesium salts have been found in various places from the Denver and Rio Grande Western Railroad tracks about seven miles west of Thompsons, in eastern Utah, to Cane Creek, a tributary of the Colorado River— a distance north and south of about 35 miles. In this locality, there appear to be five separate deposits: the Crescent Eagle area, which is in T. 22 S., R. 19 E.; the Salt Valley area, in the vicinity of the north-south line of T. 23 S., between R. 20 E. and R. 21 E.; the Seven Mile area, in the eastern part of T. 25 S., R. 20 E.; the Cane Creek area, on the Colorado River, in T. 26 S. and T. 27 S., R. 20 E. and R. 21 E.; and the Salt Wash area, in T. 22 S. and T. 23 S., R. 16 E. and R. 17 E. (Fig. I.) The Crescent Eagle and Salt Valley areas are in the Salt Valley anticline, some of the wells being in the fault graben and others outside. Structurally, the Salt Valley anticline is very complex, and can be described in general terms as a northwesterly plunging collapsed anticline about 15 miles long. In the Crescent Eagle area, the valley graben is about 1 1/2 mile wide and the salt probably forms a plug, the apex of which is in the vicinity of the Crescent Eagle well. Owing to the complex structure, there has been every opportunity for flowage in the salt to cause local thinning or thickening of beds. The regular succession of formations in the general area* is: Cretaceous Mancos Dakota Jurassic Morrison Summerville Entrada Carmel

Jan 1, 1948

By B. W. Dyer

In 1924, the Crescent Eagle Oil Co., while drilling the salt section of the Paradox formation in Grand County, Utah, encountered a salt that did not appear to be sodium chloride. This salt was analyzed and showed the presence of potash minerals, both sylvite (KCl) and carnallite (KMgC12.6H2O). Because of the high potash content of the sample, there was considerable speculation: (I) as to whether the hole had been salted, and (2), if not, the extent, richness, and the depth at which the deposit occurred. The discovery caused a large amount of activity in the area. During the next few years, 68 potash prospecting permits were issued by the Government, 24 under the Act of 1917 and 44 under the Act of Feb. 7, 1927, each including about four sections of land. Several holes, all shallow, were drilled for potash. A number of holes were drilled for oil into the salt horizon and the cuttings collected at the oil wells were examined petrographically and chemically. The shallow test holes were not sufficiently deep to reach the potash horizon and revealed nothing of value, but several of the oil test holes gave some indication of where potash might be found. Location and Geology of Deposits The potassium and magnesium salts have been found in various places from the Denver and Rio Grande Western Railroad tracks about seven miles west of Thompsons, in eastern Utah, to Cane Creek, a tributary of the Colorado River— a distance north and south of about 35 miles. In this locality, there appear to be five separate deposits: the Crescent Eagle area, which is in T. 22 S., R. 19 E.; the Salt Valley area, in the vicinity of the north-south line of T. 23 S., between R. 20 E. and R. 21 E.; the Seven Mile area, in the eastern part of T. 25 S., R. 20 E.; the Cane Creek area, on the Colorado River, in T. 26 S. and T. 27 S., R. 20 E. and R. 21 E.; and the Salt Wash area, in T. 22 S. and T. 23 S., R. 16 E. and R. 17 E. (Fig. I.) The Crescent Eagle and Salt Valley areas are in the Salt Valley anticline, some of the wells being in the fault graben and others outside. Structurally, the Salt Valley anticline is very complex, and can be described in general terms as a northwesterly plunging collapsed anticline about 15 miles long. In the Crescent Eagle area, the valley graben is about 1 1/2 mile wide and the salt probably forms a plug, the apex of which is in the vicinity of the Crescent Eagle well. Owing to the complex structure, there has been every opportunity for flowage in the salt to cause local thinning or thickening of beds. The regular succession of formations in the general area* is: Cretaceous Mancos Dakota Jurassic Morrison Summerville Entrada Carmel

Jan 1, 1948

By B. W. Dyer

IN 1924, the Crescent Eagle Oil Co., while drilling the salt section of the Paradox formation in Grand County, Utah, encountered a salt that did not appear to be sodium chloride. This salt was analyzed and showed the presence of potash minerals, both sylvite (KC1) and carnallite (KMgC12.6H20). Because of the high potash content of the sample, there was considerable speculation: (I) as to whether the hole had been salted, and (2), if not, the extent, richness, and the depth at which the deposit occurred. The discovery caused a large amount of activity in the area. During the next few years, 68 potash prospecting permits were issued by the Government, 24 under the Act of 1917 and 44 under the Act of Feb. 7, 1927, each including about four sections of land. Several holes, all shallow, were drilled for potash. A number of holes were drilled for oil into the salt horizon and the cuttings collected at the oil wells were examined petrographically and chemically. The shallow test holes were not sufficiently deep to reach the potash horizon and revealed nothing of value, but several of the oil test holes gave some indication of where potash might be found. LOCATION AND GEOLOGY OF DEPOSITS The potassium and magnesium salts have been found in various places from the Denver and Rio Grande Western Railroad tracks about seven miles west of Thompsons, in eastern Utah, to Cane Creek, a tributary of the Colorado Rivera distance north and south of about 35 miles. In this locality, there appear to be five separate deposits: the Crescent Eagle area, which is in T. 22 S., R. 19 E.; the Salt Valley area, in the vicinity of the north-south line of T. 23 S., between R. 20 E. and R. 21 E.; the Seven Mile area, in the eastern part of T. 25 S., R. 2o E.; the Cane Creek area, on the Colorado River, in T. 26 S. and T. 27 S., R. 2o E. and R. 21 E.; and the Salt Wash area, in T. 22 S. and T. 23 S., R. 16 E. and R. 17 E. (Fig. I.) The Crescent Eagle and Salt Valley areas are in the Salt Valley anticline, some of the wells being in the fault graben and others outside. Structurally, the Salt Valley anticline is very complex, and can be described in general terms as a northwesterly plunging collapsed anticline about 15 miles long. In the Crescent Eagle area, the valley graben is about 1 mile wide and the salt probably forms a plug, the apex of which is in the vicinity of the Crescent Eagle well. Owing to the complex structure, there has been every opportunity for flowage in the salt to cause local thinning or thickening of beds. The regular succession of formations in the general area* is: [Cretaceous Mancos Dakota Jurassic Morrison Summerville Entrada Carmel]

Jan 1, 1945

By Nelson Severinghaus

Following the end of hostilities of World War 11, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, One near Camak, One near Lithonia and one at Stockbridge. All have had excess fines Or in in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling Of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed 'tone is generally sold with a a narrow margin Of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. By-products of Granite Dimension Stone It sometimes becomes difficult to differentiate between main product and byproduct. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of Uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I), They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1948

By Nelson Severinghaus

FOLLOWING the end of hostilities of World War II, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, one near Camak, one near Lithonia and one at Stockbridge. All have had excess fines or screenings in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed stone is generally sold with a relatively narrow margin of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. BY-PRODUCTS OF GRANITE DIMENSION STONE It sometimes becomes difficult to differentiate between main product and by-product. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I). They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1947

By Nelson Severinghaus

Following the end of hostilities of World War 11, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, One near Camak, One near Lithonia and one at Stockbridge. All have had excess fines Or in in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling Of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed 'tone is generally sold with a a narrow margin Of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. By-products of Granite Dimension Stone It sometimes becomes difficult to differentiate between main product and byproduct. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of Uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I), They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1948

By E. N. Mazza, H. S. Kalish

The effect of sintering types 302, 3028, and 430 stainless steel powder compacts in hydrogen and dissociated ammonia was investigated. It was found that sintering in dissociated ammonia resulted in as much as 0.5 wt pct increase in the nitrogen content of stainless steel even though the dissociation of the gas was complete. Sintering in hydrogen, on the other hand, reduced the nitrogen content of the stainless steel to less than 0.01 wt pct. In the case of the 302-type stainless steel, the low nitrogen content resulted in a material that was largely ferritic, whereas the high nitrogen content rendered the material fully austenitic. Sintering in dissociated ammonia resulted in lower density, generally lower tensile strength, less ductility, and higher hardness than sintering under equivalent conditions in hydrogen. The reduction of oxides on both stainless steel and iron particles was found to be effected by hydrogen partial pressure in the sintering atmosphere. Compacting pressure was found also to effect oxide reduction during sintering. DISSOCIATED ammonia often is used as a substitute'.' for hydrogen in sintering and in annealing, since economic advantages sometimes can be obtained by such a substitution. In addition, anhydrous ammonia contains very little impurity. Thus, dissociated ammonia gas is very dry whereas tank hydrogen often must be freed of oxygen and water vapor prior to use in many applications. The sintering of stainless steel powder compacts as well as bright annealing is well recognized as requiring a hydrogen atmosphere and for the foregoing reasons dissociated ammonia is frequently substituted. It has generally been overlooked, however, that the nitrogen in dissociated ammonia might have an important effect on the sintering process and on the properties of stainless steel compacts. Considered an inert gas in many applications, nitrogen, on the other hand, is very reactive with cer- tain metals. Dissociated ammonia could not be used for hydriding zirconium or titanium. Nitrogen reacts with columbium, tantalum, chromium, uranium, thorium, and many other active metals. Iron and iron-base alloys are, for the most part, inert in nitrogen but there are many borderline cases. It has been reported that stainless steel stabilized with columbium or titanium should not be sintered in dissociated ammonia.3 olybdenum has been reported as reacting with dissociated ammonia to a minor extent.' Although most of the reactions with iron-base alloys are attributed to the action of un-dissociated ammonia and the action of nascent nitrogen, Uhlig4 showed how readily pure molecular nitrogen reacts with and diffuses into 18-8 stainless steel at 1150°C. He also pointed out how readily nitrogen diffuses out of 18-8 stainless steel when heated in pure dry hydrogen, and these thorough investigations on the subject show that commercial stainless steels are nitrogen-bearing, since they are melted in air. The effects of nitrogen in stainless steel, particularly the 18-8 Cr-Ni type, previously have received considerable attention." In 1926, it was pointed out

Jan 1, 1956