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The income of the Institute is derived from dues, subscriptions to MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization.

Jan 1, 1936

By J. Lohrenz, C. R. Clark, B. G. Bray

Procedures to calculate the viscosities of in situ reservoir gases and liquids from their composition have been developed and evaluated. Given a composition expressed in methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide together with the molecular weight and specific gravity of the heptanes-plus fraction, the procedures are capable of calculating the viscosity of the gas or liquid at the desired temperature and pressure. The procedure for reservoir liquids was developed using the residual viscosity concept and the theory of corresponding states, and was evaluated by comparing experimental and calculated results for 260 different reservoir oils ranging from black to highly volatile. The average absolute deviation was 16 per cent. This is the first known procedure for calculating the viscosity of reservoir liquids from their compositions as normally available, i.e., including the heptanes-plus fraction. The procedure for reservoir gases uses a sequence of previously published correlations. Evaluation of the procedure was accomplished by comparison of 300 calculated and experimental viscosities for high-pressure gar mixtures in the literature. The average absolute deviation was 4 per cent. The calculations are useful for (I) determining viscosities in compositional material balance computations and (2) predicting the viscosity decrease which occurs when gases, LPG, or carbon dioxide dissolve in reservoir oils. INTRODUCTION Methods to predict viscosities of reservoir fluids from the normally available field-measured variables have been presented. Beal,1 Standing,2 and Chew and Connally3 orrelated oil viscosities with temperature, pressure, oil gravity and gas-oil ratio. Carr, Kobayashi, and Burrows4 and Katz et al.5 have presented correlations for reservoir gas viscosities as a function of temperature, pressure and gas gravity. Lie all intensive physical properties, viscosity is completely described by the following function: Eq. 1 simply states that viscosity is a function of pressure, temperature and composition. These previous correlations1- hay be viewed as modifications of Eq. 1, wherein one assumes more simple functions may be used. The assumptions are practical, because the composition is frequently not known. Further, the assumptions are sufficiently valid so that these correlations are frequently used for reservoir engineering computations. In compositional material balance"' computations, the compositions of the reservoir gases and oils are known. The calculation of the viscosities of these fluids using this composition information is required for a true and complete compositional material balance. For reservoir gases, Carr, Kobayashi and Burrows4 have presented a suitable compositional correlation. For reservoir oils, no correlation is available, and data from reservoir fluid analyses have been used7-9 for compositional material balance calculations.* From a theoretical point of view, this is entirely invalid. The reservoir fluid analysis, whether flash, differential, or other process, does not duplicate the compositions which occur during the actual reservoir depletion process, therefore the viscosities measured during reservoir fluid analysis are not those which occur in the reservoir. From a practical point of view, the "error" of using viscosities from reservoir fluid analysis is of varying and unknown significance. One can say qualitatively that the error is greatest where compositional effects are greatest, i.e., for volatile oil and gas condensate reservoirs and pressure maintenance operations. The first requirement to obtain a quantitative estimate of the significance of the error is to develop a reliable compositional correlation for the viscmities of reservoir oils. No such correlation has been available. Consistent with this requirement, the objective of this study was to develop a procedure to predict the viscosity of reservoir fluids from their compositions. Normally, the compositions of reservoir fluids are available expressed as mole fractions of hydrogen sulfide, nitrogen, carbon dioxide and the hydrocarbons methane through the heptane-plus fraction, with the average molecular weight and specific gravity of the latter. The final correlation was to use the composition in this form. While the more challenging objective of the study was the development of a correlation for the viscosities of reservoir oils, the viscosities of reservoir gases were also studied. The end result of the study was a procedure to calculate the viscosities of reservoir gases and liquids suitable

Jan 1, 1965

By D. R. Parrish, K. W. Beaver, H. W. Wood, R. W. Rausch

A pilot test of forward combustion in the Shannon pool, Salt Creek field, Wyo., is described. The Shannon sand, 950-ft deep, contains a heavy (25" API), viscous (76 cp) oil. Natural reservoir energy is limited. Primary production, intermittent since 1889, recovered only about 2 per cent of the oil in place. The field is operated by Pan American Petroleum Corp. for the Midwest Oil Corp., the owner. The original pilot was a 1.32-acre five-spot. The expanded pilot has eight producing wells surrounding a roughly triangular area of about five acres with the injection well near the center. A control or comparison well was also recompleted in another part of the field. Operation of the pilot has been little different front an ordinary gas drive. Little special equipment was found to be absolutely necessary. Except for some use of a temperature-resistant cement, all wells were conventionally completed. In spite of poor oxygen consumption, the over-all performance of the pilot has been good. Total oil recovery to June 1, 1961, was 73,971 bbl. The wells of the original pilot alone had produced about 24,000 bbl, equivalent to 50 per cent of the oil in place, when fire breakthrough at the first well occurred. These wells have now produced oil equivalent to more than 74 per cent of the oil in place in the original pilot area and production is continuing. It appears that ultimate recovery will approach theoretical maximums before the wells must be abandoned. Performance of the pilot has been encouraging, and expansion to a fieldwide combustion operation is being investigated. INTRODUCTION The results of both laboratory investigations and field tests of underground combustion have been reported previously.' However, most of the field tests were primarily experimental. More information and experience are needed before forward-combustion operations can be engineered with confidence. The purpose of this paper is to present the results of a successful pilot test of forward combustion. These re- sults should increase confidence in forward combustion as a practical method for commercial oil recovery. HISTORY OF THE SHANNON POOL The Shannon pool is located on the north end of the Salt Creek field in Natrona County, Wyo. It is approximately 50-miles north of the city of Casper. The Shannon pool's3 discovery well was completed in 1889, making this one of the oldest oil fields in the Rocky Mountain region. Three more wells were drilled in 1890. First production was hauled in wooden barrels by horse and wagon to the railroad in Casper. In 1894 a small refinery, the first in Wyoming, was built in Casper to process the Shannon crude. In the following years the field changed hands several times. It appears that each new owner did some development drilling as several wells were completed in each of the years 1895, 1902, 1905 and 1912, with negligible development in the intervening years. Forty-eight wells were drilled in this period, but many were later abandoned. Discovery of the more prolific Salt Creek field proper ultimately forced suspension of operations at the Shannon pool. After 1915 there was only sporadic production, mostly to supply cheap boiler fuel to drilling rigs in the Salt Creek field. But even this was discontinued in 1931. Since then the pool had been dormant until the recent operations, which are the subject of this paper. The Shannon pool is now owned by the Midwest Oil Corp. Field operations are conducted for Midwest by Pan American Petroleum Corp. THE RESERVOIR Fig. 1 is a map showing subsurface contours of the Shannon pool. The reservoir is on a nose of the Salt Creek anticline dipping to the north at about 500 ft/mile. The trap is provided by a shallow fault on the updip side of the productive area. The downdip limits are bounded by water, but this water has not provided an effective source of reservoir energy. The Shannon sand outcrops at many places in the immediate vicinity, providing good surface indications of the Salt Creek anticline. At the Shannon pool the sand has been lowered by faulting and is overlain by about 900 ft of shale and other sands. The Shannon sand consists of two members. The upper, a water sand, is about 40-ft thick and is separated from the lower member by several feet of sandy shale. The oil pay occurs in the lower mem-

By J. C. Savins

The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid* and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn' proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation' (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian- fluid the pipe equation (Poiseuille's law) could not be converted to the Lamb equation escriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde' and by Mori and Ototakeq. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1. In order to reduce the amount of calculation time which would be involved in providing a complete tabular or graphical solution to the problem, a high-speed electronic digital computer has been utilized. For this purpose the two simultaneous equations were transformed into more compact expressions by introducing reduced variables. These expressions are given in the following theoretical section. A similar procedure in this problem has been developed by Fredrickson and Bird1" Their tabular results, however, are very incomplete in the range of practical interest for problems of wellbore hydrodynamics. We have furthermore been able to express our graphical results in terms of convenient and familiar dimensionless groups. THEORETICAL DEVELOPMENT Use of Reduced Variables In terms of reduced variables the two simultaneous equations just discussed take the following form, The reduced variables q, x, a and z are defined in terms of the various measured quantities, where Q is volumetric flow rate, AP/L is pressure gradient, Dl is OD of inner pipe, D, is ID of outer pipe, is plastic viscosity, and is yield point. Thus, we have a dimensionless volume flux, a dimensionless reciprocal pressure gradient, and the ratio of the pipe diameters Before introducing the fourth reduced variable, z, it is of interest to consider the physical significance of the parameter x. As may 'be seen from the velocity profile of Fig. 1 the Bingham plastic fluid has the interesting property that a portion of the stream flows at a uniform velocity without shearing action. This section of the stream is situated approximately in the center of the conduit and is known as the "plug flow" region. Its existence is due to the fact that the shearing stresses within the region do not exceed the yield point, which is one of the two flow properties characterizing the fluid. The parameter x then turns out to be the ratio of the

By M. Prats, D. G. Russell

The performance of a well in a bounded, layered reservoir with interlayer crossflow has been investigated mathematically. The system studied comprises a centrally located well in a bounded cylindrical reservoir composed of two layers of contrasting physical properties. The reservoir contains a single fluid of small and constant compressibility. In the case of a well producing at constant pressure, the production rate of the crossflow system declines exponentially after the early transient behavior dies out. For wells which produce with constant rate, the pressure-time relationship is linear following the transient. For very early production time, the production rate of the two-layer crossflow system behaves as that of the two-layer stratified system (the case in which the layers are in communication at the well only). Except for early time, in most practical cases the performance of a two-layer reservoir with cross-flow can be duplicated by that of a single-layer reservoir. The equivalent single-layer reservoir must have the same pore volume and the same drainage and wellbore radii as in the two-layer case. In addition, the equivalent reservoir must have a "kh" (permeability x thickness) product equal to the sum of the "kh" products of the respective layers in the crossflow system. If the porosity and permeability distributions are known, the production and pressure behavior of a well with and without crossflow can be predicted. From a comparison of the observed pressure or production performance of a well and the theoretical behavior, the occurrence of interlayer crossflow can be detected. INTRODUCTION When flow is possible across the bedding plane from a low-permeability layer into an adjacent layer of moderate or high permeability, the earlier depletion of the more permeable layer will cause such flow to occur. If this situation exists, the oil recovery from tight layers can be appreciable; thus, the economic ramifications of interlayer crossflow are apparent. The possible importance and extent of flow between adjacent and connected layers — whether resulting from capillary, gravitational, or viscous forces — have been the subject of considerable speculation for many years. Jacquard1 presented a rigorous analysis of the crossflow due to single-fluid expansion occurring between two adjacent and connected layers when the well produces at constant rate. His presentation was entirely mathematical, however, and no numerical results from evaluation of the mathematical solutions were presented. Our objectives in the preparation and presentation of the present paper are essentially twofold— (1) to analyze the behavior of a well which produces a single compressible fluid from a bounded, layered reservoir with interlayer crossflow, and (2) to present practical numerical results and simplified formulas to facilitate engineering analysis of reservoirs with crossflow. The constant-terminal-pressure case was analyzed rigorously, whereas the constant-terminal-rate case was treated only for semisteady-state conditions. DESCRIPTION OF THE IDEALIZED TWO-LAYER RESERVOIR The reservoir to be studied is assumed to be bounded and cylindrical in shape, with a completely penetrating well at its center. The reservoir is composed of two adjacent horizontal layers between which fluid is free to flow. Each layer is assumed to be homogeneous, isotropic and completely filled with a fluid of small and constant compressibility. The total thickness of the reservoir is small enough

By J. A. Fellows, Earnshaw Cook, Howard S. Avery

HEAT-RESISTANT alloys of the higher nickel and chromium ranges have been empirically developed through the practical experience of the past two decades to a position of significant industrial importance. Few quantitative metallurgical data have been published, however, that could be related directly to engineering specifications and design. Inadequate information led to the inauguration, in 1934, of a research directed toward a better understanding of the properties and performance of these steels at temperatures between 1400° and 2000°F. Investigation was concentrated upon the 26 per cent Cr:12 per cent Ni type, which owes its extensive application to an excellent combination of economy, strength and surface stability at elevated temperatures. The requirements of the oil-refining industry have been prominent in influencing the scope and evolution of the program. Creep strength at the maximum allowable deformation ranges has been employed to evaluate the merits of these alloys. Permissible elongation rates vary from 1.0 per cent in one million hours for turbine blades to 1.o per cent in ten thousand hours for tube supports and heating-furnace equipment. Throughout this paper, the limiting creep stress (L.C.S.) for a given temperature has been defined as the stress that will produce a uniform elongation rate (stage II) of one per cent in ten thousand hours as extrapolated from rates per hour or tests of less than two thousand hours duration. Certain current specifications require a minimum L.C.S. of 1600 lb. per sq. in. at 1800°F., of 3600 lb. per sq. in. at 1400°F., and include a tensile acceptance test at room temperature, after aging for 24 hr. at 1400°F., as a measure of embrittlement in service. An elongation of 4 per cent is considered satisfactory for general use, while a minimum of 9 per cent is prescribed on occasion. Many differences of opinion concerning the properties and performance of these alloys appear to result from their sensitivity to unappreciated variations of chemical analyses which, for example, may change their L.C.S. from 3500 to 350 lb. per sq. in. at 1800°F. Within broad chemical limits, it is possible to balance the six or more important elements present to attain desirable properties with a number of different combinations. One method for adjusting the composition has been described under the sponsorship of the Alloy Casting Institute,1 in which, by maintaining a substantially austenitic* alloy, optimum creep strength and minimum tendency to embrittle after aging are expected. Unless, however, the limits are undesirably dose, it has not been possible to ensure a moderate range of strength and of ductility by any chemical specification alone. There is a definite need

Jan 1, 1942

The State Mining Bureau of California under the direction of Fletcher Hamilton, State Mineralogist, is starting a field campaign to report on the economic minerals of California, which have an important industrial and military bearing on the present war situation. Particular interest and value attaches at the present moment to our available supplies of chrome, coal, iron, magnesite, manganese, molybdenum, quicksilver and tungsten. Trained geologists and engineers of the Bureau's staff are being sent, out to obtain information with relation to the latest developments. Advance notices will be sent to the local newspapers, from time to time, of the arrival of the engineers in the various districts. All persons interested in the minerals mentioned are earnestly urged to cooperate with the State Mining Bureau by meeting the field men while in their districts or by communicating direct with the State Mineralogist at his office in the Ferry Building, San Francisco. The State Mining Bureau has just issued Bulletin No. 72 on The Geologic Formations of California. It was written by Prof. James Perrin Smith of Stanford University, and contains a complete bibliography and resume of all of our present knowledge relative to the geological formations occurring in California. It also contains much previously unpublished data, and six tables showing geologic columns. It covers 41 pages.

Jan 6, 1917

By R. D. Carnahan, G. A. Stone, R. J. Arsenault

An experimental technique has been developed for carrying out a dynamic tensile stress-strain test in which plastic strain is measured continuously throughout the microstrain region extending through the macroflow region to total deformations of 5 pet. The tests were carried out on niobium, samples having interstitial impurity levels of 160 and -800 ppm at temperatures ranging from room temperature down to 100°K. A band spectrum of activation energies was obtained from calculations based on the measured activation volumes and temperature dependence of flow stress. The inability of a single rate-controlling process to predict such a phenomenon has led to the proposal that several sequential rate-controlling dislocation mechanisms are operative in the preyield micro-strain region. These are thought to be: the motion of geometrical kinks, the formation of double kinks in edges, and finally in the macrostrain region the formation of double kinks in screws. In less pure niobium the effect of interstitial impurities is shown to be dominant in the microstrain region, suggesting that a fourth probable mechanism is overcoming interstitial barriers instead of geometrical kink motion and the formation of double kinks in edge dislocations. THE principal fundamental aim of most mechanical properties studies of crystalline solids is to determine the dislocation mechanisms responsible for the plastic behavior. The extension of such studies to the region of preyield microstrain behavior has received renewed attention in the past few years as the details of macroscopic flow behavior have become better understood. For the most part, microstrain studies have been carried out using one of two variations of a single experimental technique.1 The first method involves loading the sample at a constant extension rate to a predetermined stress level (less than the macroscopic yield stress), instantaneously unloading, and then determining the extent of plastic deformation to a sensitivity of 10"6. The microscopic stress-strain curve is then constructed from the results of a repeated series of such individual measurements, each of which involves loading to an incrementally higher stress level, by relating the accumulated plastic microstrain for each step to the maximum applied stress in that step. The second variation, also carried out by step-wise increases in stress, measures the total strain to a sensitivity of ~10"6 and relates the maximum stress to the area of closed hysteresis loops that are generated under certain conditions (namely, prestrained samples). The foregoing methods have yielded interesting information about the nature of preyield deformation and plastic response to stresses below the yield stress, but they offer certain disadvantages for studying the dynamic behavior of dislocations. In the first method it is physically impossible to specify a plastic strain rate inasmuch as the test sample is reexposed, as it is loaded to its maximum stress in a particular step, to lower stresses at which flow will take place. The strain corresponding to a given stress level on the stress-microstrain curve thus generated will then always be greater than that at the corresponding stress level of a truly dynamic test carried out at the same extension rate. The second method has been used to obtain correlations with dynamic macroscopic flow parameters by applying dislocation damping theory to the hysteresis loop areas.2 The approach has had some success but suffers in that only samples that have been prestrained a few percent can be studied. Although the stresses

Jan 1, 1968

By G. M. Gay, R. L. Perrine

This paper describes a method of numerical computation for three-dimensional, unstable, miscible displacement behavior useful for heterogeneous systems, as well as for more ideal conditions. In the method, flow equations are first linearized by a perturbation approach. The basic flow process is separated and a solution for its behavior readily obtained. The remaining problem of deviations from the basic flow caused by non-ideal conditions is then subjected to numerical analysis. Results obtained from use of the method are also presented. Although conditions assumed in the test cal-culations were severe, results show the type of dispersing flow expected and appear quite satisfactory. The method has eliminated or reduced in importance problems of oscillating values near steep fronts, excessive computer smoothing, etc. A unique advantage of the method is that the source of variations from ideal behavior can be observed. ,The one serious drawback results from the algebraic complexity of the perturbation approach, and the need for second-order terms to be retained in calculations of interest. Fewer array points are available and more computer time is required than would be desired. However, these difficulties are also experienced with other approaches to the solution of three-dimensional dispIacement problems. INTRODUCTION Prediction of behavior of the miscible displacement process within a porous medium for any system of engineering importance is plagued by a number of difficulties. With typical fluid properties the displacing fluid has the lower viscosity, and there is a natural tendency toward flow instability. The problem of predicting instability is compounded by the fact that every real system is heterogeneous. Permeability will vary from point to point — not entirely systematically, and yet not in a random fashion leading to a readily defined average. Furthermore, permeability is unlikely to be isotropic. These permeability properties, which are characteristic of any real porous medium, accentuate the effects of flow instability. Another factor to be considered is that flow dispersion accompanies the displacement process in a porous medium. Mechanistically, dispersion is due to the fact that flow between any two points in the medium follows multiple tortuous paths, each characterized by slightly different flow properties. The fact that the coefficient characterizing dispersive properties of the real medium JS a tensor with variable elements complicates matters. Further difficulties arise because the parabolic influence, while not negligible, is small. Thus, there is a tendency toward steep and uneven displacement fronts along which dispersion smoothing must be represented accurately. Yet frequently used numerical analysis schemes may tend toward either instability, oscillation or excessive smoothing, none of which gives the desired accurate picture of flow behavior. Thus, while many experimental and analytical studies of the process have been made, predictions of actual performance are still subject to considerable uncertainty and possible improvement. This paper reports on part of a study which attempts to develop improved methods for solution of the flow equations describing the miscible displacement process. Of necessity, the calculations were performed on a large digital computer. A three-dimensional system is represented, and the coefficients defining dispersion and permeability can be varied in a manner representative of a real system. Because the differential equations are nonlinear, a first step is to linearize them using a perturbation approach. Objective of this approach has been to separate the basic flow which would occur in an ideal system and for which predictions are readily made. Then the numerical analysis, which is necessarily complex, is directed toward solution of the perturbation equations. These equations state how the basic flow is modified

Jan 1, 1967

By E. Gybbon Spilsbury

(Pittsburg meeting, March, 1910.) THE recovery of gold and silver from their ores by means of the cyanide process has been so successful in the last few years that any radical improvement would seem impossible; yet the appliance to which I wish to call attention in this paper is really a radical departure from the methods now in general use. The most modern and approved of these, known as the all-sliming method, depends for its success on the grinding of the. ore so fine that practically 90 per cent. of it will pass through a 200-mesh screen. The slimes thus produced are then agitated and aerated in tanks of various types. The main object of this treatment is to insure such a thorough admixture of the pulp and solution that every particle of the ore is surrounded by a volume of solution sufficient to insure the dissolving of the whole of the gold- and silver-content. In addition, in order to expedite the action of the cyanide, and to oxidize such elements as would, if left in their active state, become cyanicides, air is blown in under pressure. In the Pachuca tank, this air is the active and sole means of agitation. The chief objections to all the methods off agitation used heretofore are the expense of operating and maintaining the mechanical devices for keeping the pulp in suspension, and the length of time required to obtain a fairly complete extraction. of the values. These objections are inherent to any method of agitation effecting a circulation of the pulp and the solution together, by giving the whole mass a circular movement, as in the low-tank system, or a vertical circulation, as in the Pachuca-tank system. In both methods, the particles of ore are kept traveling in the same direction as the solution, and with very little difference of speed; so that, while the whole mass is in

May 1, 1910

WE the undersigned, being all persons of full age and citizens of the United States, and a majority residents of the State of New York, desiring to form a corporation pursuant to the provisions of the Membership Corporations Law for the purpose of incorporating, as provided in Section 6 of Article I. of said law, the existing unincorporated association known as American Institute of Mining Engineers, do hereby make, acknowledge and 6le this Certificate for that purpose, and do Certify as follows: I. That the American Institute of Mining Engineers is an unincorporated association organized and existing with the object of promoting the arts and sciences connected with the economic production of the useful minerals and metals and the welfare of those employed in these industries by means of meetings for social intercourse and the reading and discussion of professional papers, and to circulate by means of publications among its members and associates the information thus obtained. 11. That the persons duly appointed or designated to manage the affairs of said association are designated by the rules thereof Members of its Council; that the under- signed are all members of said Council as the same was constituted on the 29th day of December, 1904.

Jan 1, 1942

By R. Simon, L. Yarborough

This paper presents a correlation for predicting the critical pressures of gas-solvent-reservoir oil systems of the type encountered in gas and solvent injection processes. Experimental data from 14 systems were used to develop the correlation which expresses critical pressure as a function of composition, C7+ mol weight, and C7+ characterization factor. Critical pressures predicted by the correlation for the 14 gas-solvent-reservoir oil systems have an average deviation of 2.8 per cent of the experimental values. The correlation war used to study a wide variety of other hydrocarbon mixtures reported in the literature whose critical conditions are in the range of interest in oil recovery work (100 to 280F and 2,000 to 6,000 psia). Critical pressures predicted by the correlation had an average deviation, expressed as per cent of experimental value, of 5 per cent for 20 miscellaneous mixtures from the literature, and 6.4 per cent for I7 methane-butane-decane mixtures reported by Sage and Lucey. INTRODUCTION Predicting critical points of hydrocarbon mixtures is an important part of phase behavior calculations. If the critical point can be predicted for a specific mixture, the separation between the bubble-point and dew-point regions will be defined, and physical properties of the mixture can be calculated by using the principle of corresponding states. Numerous correlations for predicting critical points of hydrocarbon mixtures have been published. Six of these correlationsl-8 were for light hydrocarbons, and two correlations7,8 ere for high boiling-point petroleum distillates. Organick9 And Eilerts" presented correlations which combined the published data from both light and heavy mixtures, and these correlations became the only available methods for predicting critical pressures for wide boiling range mixtures. In the course of the authors' work on secondary recovery by gas and solvent injection, experimental data were obtained for 14 mixtures of dry gas, ethane-propane-butane solvents, and various reservoir oils. The critical pressures and critical temperatures of these gas-solvent-reservoir oil systems were in the range of 1,900 to 4,800 psia and 180 to 265F. The critical pressures predicted for the 14 mixtures by the correlations of Organick and Eilerts had an average deviation from the measured values of about 13 per cent. The authors felt that it was necessary to develop a better correlation for engineering calculations and the resultant correlation, which is presented on Figs. 1 and 2, predicts the critical pressures of the 14 mixtures with an average deviation of 2.8 per cent. The validity of the correlation was tested by applying the correlation to other hydrocarbon mixtures reported in the literature. This subject is discussed later in the paper. The authors feel that there is also a need for an improved critical temperature correlation for gas-solvent-reservoir oil systems. However, developing a critical temperature correlation is a significant study in itself and is not included in this paper. EXPERIMENTAL DATA The compositions and critical points obtained by the authors for 14 gas-solvent-reservoir oil mixtures are shown on Table 1. The methane concentrations in these mixtures varied from 20 to 63 mol per cent. The intermediate hydrocarbon group, consisting of ethane, propane, and butane, varied from 20 to 64 mol per cent, and the concentration of the C,, fraction from 10 to 20 mol per cent. The physical properties of the C,, fraction covered the range from light, paraffinic, nonasphaltic (Mixtures 5, 6, 7, 8, 9 and 10) to heavy, aromatic, and asphaltic (Mixtures 13 and 14).

The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-

Alexander Forsyth, Southport, Me. (communication to the Secretary): In Mr. Irving's able and interesting paper he describes minutely the appearance of the wolframite and its association with the refractory siliceous gold-ore. He also describes this gold-ore, but fails to mention the important pockets of metallic gold found in the Lead City occurrence of it. I use the term " metallic " in preference to the more usual " free," for it has been found that this gold is not easily amalgamated. Metallic gold is comparatively rare in the refractory siliceous gold-ores of the Black Hills; hence its occurrence in considerable amounts in the Lead City wolframite district deserves notice. I possess a beautiful specimen from the Harrison mine. It is a lump of drusy, granular ore, about 6 in. in diameter. The gold .is " shot" through it in large and small pin-heads; and in two specially oxidized areas, each about 11/2 in. in diameter, it is peppered full. The famous " Grantz strike," made in the Lead City wolframite locality, produced many beautiful gold specimens. This district affords an excellent example of the repeated discovery of new mineral values upon old ground. By reason of its proximity to the Homestake vein, this wolframite deposit was inevitably traversed many times by experienced geologists, mineralogists and mining engineers, who evidently must have thrown aside, with no thought of wolframite, the lumps of " black iron " lying about. I have the admission of an able geologist that, six months before the wolframite was discovered, he visited some of the very mines where it occurred, and passed it by as magnetic iron-ore. At the time of the discovery, the mineral was scattered over the gold-mine dumps in no small quantities, having been culled as worthless out of the gold-ore. It remained for

Jan 1, 1902

By P. B. Baxendell

The performance of a water-drive reservoir having a gas cap depends primarily on the movement of the gar-oil and oil-water contacts. The movement of the contacts during production depends in turn on fluid withdrawals and how the reservoir pressure changes as fluids are produced from the reservoir; that is, on how effectively the aquifer maintains pressure by replacing withdrawals. inasmuch as pressure changes, fluid withdrawals, contact positions, and produced gas-oil and oil-water ratios are interdependent, the analysis and prediction of the performance of a reservoir produced in a given way must take into account this interdependence throughout depletion. This paper presents an analysis which, within the limitations of the assumptions made, yields an engineering approach to predicting future performance based on reservoir pressure and production history. The most significant assumption is the method of extrapolation of future gas-oil and water-oil ratios. The extrapolation procedure smoothly increases both ratios to preselected values as the remaining oil column undergoes a specified decrease in thickness. This preselection is made on the busis of previous field experience in depletion of similar reservoirs under similar conditions. For computing future performance a vdumebic balance L combined with the differential equation defining pressure distribution in the aquifer to obtain positions of water-oil and gas-oil contacts. From these positions are extrapolated produced water-oil and gas-oil ratios. Reservoir performance can be investigated when oil production rates are dependent upon various factors including the performance of the reservoir itself. Examples of practical application of the procedure are included. INTRODUCTION To predict performance of water-drive reservoirs with gas caps and thin oil columns, it is necessary to describe the motions of the fluids within the reservoir during the entire production period to depletion. These motions depend on the pressure changes and on the withdrawal of oil, gas and water. Production of oil from the oil zone primarily causes water to move in to take its place; production of gas from the cap tends to cause oil to migrate into its place. In addition, the volumes of oil and gas remaining in the reservoir depend on changes in the pressure, since a decrease in pressure causes fluid expansion, gas liberation and oil shrinkage. A method of relating the future pressure to total withdrawals is used to describe the motions of fluids within the reservoir under conditions arising in possible modes of production. The analysis is based on two relationships and will reduce the problem to one amenable to digital computation. The first of these concerns the dependence of the pressure distribution in the entire aquifer furnishing the water drive upon the total reservoir withdrawals. This dependence is dictated by the permeability distribution and the extent of the aquifer; at present, such information is most readily obtained from the performance history by means of the resistancecapacitance reservoir analyzer. The second relation involves withdrawals, pressure in the reservoir, and movement of oil, gas, and water within the reservoir. The analysis is subject to certain simplifying assumptions that are necessary to permit solution of the problem. A comparison of the methods of this paper with those presently practiced is pertinent. One method of analysis is to use the reservoir analyzer to predict reservoir behavior based on aquifer characteristics determined from production history. Inasmuch as the total withdrawal rate depends upon the gas-oil and water-oil ratios, which depend in turn upon, among other things, the positions of the gas-oil and water-oil contacts, these ratios must be assumed in advance. In this paper these ratios are, instead, related to the computed positions of gas-oil and water-oil contacts. Thus, our method can be applied to problems in which the oil production rate is limited by produced gas-oil ratio, or to problems in which it is desired to determine the variable gas injection rate that will maintain the gas-oil or water-oil contact stationary. These problems cannot be worked satisfactorily on the analyzer. Another method presently used is based on a paper by Hurst.' Since his procedure is dependent upon using the solution of the heat flow equation, which requires constant permeability within the aquifer, and our procedure recognizes variations of permeability in

By Leo Behr

RECENT years have seen important practical advances in the construction of recording instruments for use with thermocouples. The difficulties of the problem will be appreciated when it is remembered that a 10° F. change in temperature of a base-metal couple at 1500° means a change in the electromotive force of about 0.00035 volt. In a circuit having a resistance of 350 ohms, this means a change in the current of 0.00000,1 amp.; and despite this requirement of great sensitivity the instruments must be sufficiently robust to withstand the rough usage which is so often their lot. Two methods are in common use for the measurement of the electromotive force produced by a thermocouple: 1. The milliammeter method, in which the current produced by the thermocouple in a circuit of known resistance is measured and from. this the electromotive force is deduced by Ohm's law. 2. The potentiometer method in which a known potential difference is opposed to the thermocouple electromotive force. The use of thermocouple and milliammeter for measuring temperature introduces some possible sources of error, for the reading depends on a number of factors, including the following: (1) Electromotive force set up at the hot junction, (2) electromotive force set up at the cold junction, (3) resistance of the circuit including thermocouple, lead wires, and meter, (4) field strength of magnets, (5) strength of controlling springs in meter, (6) friction at pivots, of pointer on paper, etc. It is obviously necessary to so design and maintain the installation that the reading is independent of all the factors except the first. The electromotive force set up at the cold junction can easily be taken care of provided it is constant. This has been approximately accomplished by burying the cold junction in the ground or actually secured by locating it in a container, the temperature of which is kept constant by means of a thermostat.

Jan 9, 1919

By Earnshaw Cook, J. A. Fellows, Howard S. Avery

Heat-resistant alloys of the higher nickel and chromium ranges have been empirically developed through the practical experience of the past two decades to a position of significant industrial importance. Few quantitative metallurgical data have been published, however, that could be related directly to engineering specifications and design. Inadequate information led to the inauguration, in 1934, of a research directed toward a better understanding of the properties and performance of these steels at temperatures between 1400° and 2000°F. Investigation was concentrated upon the 26 per cent Cr:I2 per cent Ni type, which owes its extensive application to an excellent combination of economy, strength and surface stability at elevated temperatures. The requirements of the oil-refining industry have been prominent in influencing the scope and evolution of the program. Creep strength at the maximum allowable deformation ranges has been employed to evaluate the merits of these alloys. Permissible elongation rates vary from 1.0 per cent in one million hours for turbine blades to I .o per cent in ten thousand hours for tube supports and heating-furnace equipment. Throughout this paper, the limiting creep stress (L.C.S.) for a given temperature has been defined as the stress that will produce a uniform elongation rate (stage 11) of one per cent in ten thousand hours as extrapolated from rates per hour for tests of less than two thousand hours duration. Certain current specifications require a minimum L.C.S. of 1600 lb. per sq. in. at I800°F., of 3600 lb. per sq. in. at 1400°F., and include a tensile acceptance test at room temperature, after aging for 24 hr. at 1400°F., as a measure of embrittlement in service. An elongation of 4 per cent is considered satisfactory for general use, while a minimum of 9 per cent is prescribed on occasion. Many differences of opinion concerning the properties and performance of these alloys appear to result from their sensitivity to unappreciated variations of chemical analyses which, for example, may change their L.C.S. from 3500 to 350 lb. per sq. in. at 1800°F. Within broad chemical limits, it is possible to balance the six or more important elements present to attain desirable properties with a number of different combinations. One method for adjusting the composition has been described under the sponsorship of the Alloy Casting Institute,' in which, by maintaining a substantially austenitic* alloy, optimum creep strength and minimum tendency to embrittle after aging are expected. Unless, however, the limits are undesirably close, it has not been possible to ensure a moderate range of strength and of ductility by any chemical specification alone. There is a definite need

Jan 1, 1942

By J. A. Fellows, Earnshaw Cook, Howard S. Avery

Heat-resistant alloys of the higher nickel and chromium ranges have been empirically developed through the practical experience of the past two decades to a position of significant industrial importance. Few quantitative metallurgical data have been published, however, that could be related directly to engineering specifications and design. Inadequate information led to the inauguration, in 1934, of a research directed toward a better understanding of the properties and performance of these steels at temperatures between 1400° and 2000°F. Investigation was concentrated upon the 26 per cent Cr:I2 per cent Ni type, which owes its extensive application to an excellent combination of economy, strength and surface stability at elevated temperatures. The requirements of the oil-refining industry have been prominent in influencing the scope and evolution of the program. Creep strength at the maximum allowable deformation ranges has been employed to evaluate the merits of these alloys. Permissible elongation rates vary from 1.0 per cent in one million hours for turbine blades to I .o per cent in ten thousand hours for tube supports and heating-furnace equipment. Throughout this paper, the limiting creep stress (L.C.S.) for a given temperature has been defined as the stress that will produce a uniform elongation rate (stage 11) of one per cent in ten thousand hours as extrapolated from rates per hour for tests of less than two thousand hours duration. Certain current specifications require a minimum L.C.S. of 1600 lb. per sq. in. at I800°F., of 3600 lb. per sq. in. at 1400°F., and include a tensile acceptance test at room temperature, after aging for 24 hr. at 1400°F., as a measure of embrittlement in service. An elongation of 4 per cent is considered satisfactory for general use, while a minimum of 9 per cent is prescribed on occasion. Many differences of opinion concerning the properties and performance of these alloys appear to result from their sensitivity to unappreciated variations of chemical analyses which, for example, may change their L.C.S. from 3500 to 350 lb. per sq. in. at 1800°F. Within broad chemical limits, it is possible to balance the six or more important elements present to attain desirable properties with a number of different combinations. One method for adjusting the composition has been described under the sponsorship of the Alloy Casting Institute,' in which, by maintaining a substantially austenitic* alloy, optimum creep strength and minimum tendency to embrittle after aging are expected. Unless, however, the limits are undesirably close, it has not been possible to ensure a moderate range of strength and of ductility by any chemical specification alone. There is a definite need

Jan 1, 1942

By Hollis Peacock

THE Bingham area in the West Mountain mining district on the eastern slope of the Oquirrh range, some 28 miles southwest of Salt Lake City, has been the most consistent producer for the United States Smelting Refining and Mining Company, production having been continuous, except for minor interruptions, since the organization of the United States Mining Co. in 1899. This production has come from fissures and mantos largely within limestone members aggregating something less than 10 per cent of a thick quartzite sequence of Pennsylvanian age which has been warped into an open syncline plunging northwesterly. Bedding on the easterly limb dips 10°-45° but steep-ens to 90° and even overturns on the westerly limb. Ore bodies cluster about the more northerly of two elongate interconnecting stocks of monzonite which have risen in an axial position within this syncline. Largely within the more northerly of these stocks is the low-grade copper ore body exploited in the Utah Copper open cut of the Kennecott Copper Corp. The values, in seams, minute fracture fillings, and disseminations of pyrite and silica, pervade not only the stock but adjacent sediments, and form a nebulous, sprawling mass which both mineralogically and geographically is the center of the district. The more southerly of the twin stocks appears to be comparatively inert and without obvious relation to mineralization. which

Jan 1, 1948

By Alexander N. Mitinsky

UP to a certain limit, the increase of pressure on the diamond-drill increases the rate of progress in drilling. That limit is set by the resistance of the diamonds to compression; and beyond it, the destruction of the stones will involve an. economic loss, both in time and in money. It is, therefore, important to all diamond-drillers to know what is the resistance mentioned. In Europe, operators usually follow an empirical rule, which directs the maintenance of a pressure, on the area-of the bottom of the drilling-tool, of 12 kg. per sq. 4m. For the tools in ordinary use, this is equivalent to 1 kg. per sq. mm. of the diamonds set in the tool So far as I know, American drillers are using pressures as high as 50 to 60 kg. per sq. cm. of the total area of the drill, and the consumption of diamonds (on Denny's authority, 0.2 carats per meter bored) is greater in America than in Europe. But the reason for this difference may be the comparatively larger size of the diamonds commonly used by American drillers. With the assistance of my friend, the late S. Woisslaw, who was the pioneer of diamond-drilling in Russia, I selected from his stock a number of black diamonds, which I subjected in my laboratory to compression-tests. To prepare regular cubes for such tests, as is generally done with other stones, would have been not only costly, but, what is more important, practically useless. I therefore determined, in order to assimilate as nearly as possible the conditions of actual use, to place each sample between a hard plate (corresponding to the rock) and a softer plate (corresponding to the bottom of the tool), into which it would be pressed during the test.

Jan 1, 1906