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By D. M. James, J. C. Martin

The results are presented of a study of the application of analytical methods to the solution of two-phase flow into single wells. Approximate analytical expressions for the pressure distribution in two-phase flow are found ;;; a number of conditions. The results obtained from the analytical solutions me found to be in good agreement with results obtained by finite difference techniques using a high speed digital computer. Mathematical solutions for four sets of boundary conditions are presented. All of these solutions are composed of a short-term transient plus a steady or quasi-steady state. The rates of decay of the short-lived transients are analyzed. It is found that the durations of the short-term transients may be characterized by a parameter defined as the time constant which can be determined from simple relations. It is shown also that if the outer radius is much greater than the radius of the well. the short term transients decay at rates which are proportional to the square of the exterior radius, and the rates of decay are only slightly dependent upon the radius ratio. Numerical solutions based on finite difference techniques are presented for a number of conditions. The numerical solutions are in good agreement with the predictions based on the theoretical analysis for small and moderate drawdowns. Examples involving large drawdowns indicate that the nonlinearities in the equations of flow do not appreciably alter the longevity of the short-term transients. In all cases the time required for the short-tern transients to disappear is predicted satisfactorily. INTRODUCTION The mechanism by which oil and gas flow into a single well is of vital interest to the petroleum industry. The fundamental equations of two-phase flow which describe this mechanism are nonlinear partial differential equations. Numerical solutions of these equations describing pressure transients have been obtained with the aid of electronic computers. Although solutions obtained in this manner take into account a large number of effects, the reduction of this information to useful generalities is difficult. One method of obtaining generalities is the use of linearized approximations of the nonlinear equations. Since it is possible to obtain explicit solutions of the linearized equation, general properties of the role of pressure in the flow mechanism may be ascertained. Results obtained from this approach are limited to some extent by the linearizing assumptions. The severity of these limitations may be evaluated by comparing solutions of the linear equation with numerical solutions of the more exact nonlinear equations of two-phase flow. In the past considerable amount of work has been devoted to studying pressure build-up using the single-phase flow theory. Unfortunate1y, most prep sure build-up tests involve multiphase flow. A small amount of work has been done studying pressure build-up where the flow is two-phase. The encouraging results of these studies suggest that useful results may be found from additional studies of not only pressure build-up, but also the rapid transients associated with placing a well on production. This paper presents the basic theory of the pressure transients associated with placing a well on production and with closing it in. The paper is concerned chiefly with two-phase compressible flow; however, the results also apply to single-phase flow. The results are based on analytical solutions of the flow equations, and they are verified by numerical solutions using finite difference techniques. Much of the previous work on compressible flow into wells has been confined to single-phase flow. Some work has been done on compressible two-phase steady state flow, and solutions of the equations of flow have been found by finite difference techniques using high-speed computers. Muskat1 presents some rather general solutions to the equations of single-phase compressible flow into wells. Much work has been done on pressure build-up in wells (see, for example, Refs. 2-6). Almost all of the work on pressure build-up concerns single-phase flow with the exception of Ref. 5 and part of Ref. 2. Some work has been done on pressure fall-off in injection wells.718 Muskat9 presents the solution of the equations for radial steady state two-phase compressible flow. Handyl0 extends Muskat's solution to obtain

By William F. Boericke

THE Christy Creek clay mine of the General Refractories Co., in the Olive Hill District, ranks with the most important producers in the north-eastern Kentucky fire clay field, both from production of high-grade flint clay, as well as unusual extent and thickness of deposit. The property is but one of a number controlled by the General Refractories Co. in this district, but is given first consideration among them by the operating staff. Its total area is over 5000 acres, owned in fee or by lease of clay mining rights, and although mining operations have been in progress for over five years, scarcely one per cent of the ground has been worked as yet. The mine is near the southwestern end of the clay field, which extends in a belt 12 miles wide and 55 miles long, in a southwestern direction from Kenova, W. Va., which, as the name indicates, is at the junction of Kentucky, Ohio, and West Virginia. Olive Hill, where there is one of the l1Ulin plants of the General Refractories Co., and to which the clay from the mine is shipped, is about 26 miles distant from the mine. Connection is made with the Chesapeake & Ohio R. R. by a spur line . 8 miles in length, owned and operated by the company.

Jan 1, 1929

By J. B. Wagner, p. Hembree

The iron tracer diffusion coefficient of umstite has been measured at 110(fC across the phase field and at a single composition at 800°C. Assuming a simple cation vacancy model the tracer diffusion coefficient was found to be a linear function of the cation vacancy concentration at 1100°C. The equation is D = 3 x 20 29 where denotes the concentration of vacancies in numbers per cc. The tracer work at 800°C was carried out to investigate the reported "pinning" of tracer to the wustite surface at low temperatures. No evidence for the "pinning" of the tracer was found at 800°C in COz-CO gas mixtures. HIMMEL, Mehl, and Birchenall,&apos; Carter and Richardson,2 and Desmarescaux and La combe3 have measured the diffusion of iron tracer in wustite at several temperatures and compositions. The present work was undertaken to extend the measurements over a large composition range at 1100°C and to resolve certain apparent discrepancies in the data, expecially at lower temperatures. EXPERIMENTAL Wustite was prepared by oxidizing rectangular iron plates* in C02-CO mixtures. The samples were •The iron was supplied by the Battelle Memorial Institute courtesy of the American Iron and Steel Institute. The analysis is presented in Table I. quenched. Due to the inward flow of cation vacancies during oxidation, the center of the sample contained a thin void. The edges of the wustite slab were sanded until the sample could be split into two parts. Each part was then sanded on the front and back flat area until a smooth surface was obtained. The specimens were then replaced in the furnace and equilibrated at llOO°C in a predetermined COa-CO mixture by methods described elsewhere.4"6 The specimens were again quenched and the surfaces were lightly sanded to remove any roughness following the first equilibration. The specimens were then reequi lib rated in the same C02-CO mixture for thirty minutes in order to relieve any mechanical damage on the surface due to the polishing. The specimens were then quenched and the tracer was applied by an electroplating technique. The work of Carter and ~ichardson&apos; demonstrated that there was no systematic difference in the iron tracer diffusion coefficient in wustite if the tracer was plated, dried, or evaporated on the specimen. In the present study a piece of filter paper was saturated with an iron chloride solution of pH <* 3 that contained the tracer FeS5. The wustite was placed on the filter paper and made the cathode. A current density of 0.4 to 0.6 ma per sq cm was passed for about five to ten minutes. The thickness of the tracer layer was estimated to be about 7 x lom6 cm. This estimate was made by considering the area plated, the current flow, and time for plating and the activity of the iron in the plating solution. Different areas of the specimen were counted using a collimator to determine the uniformity of the tracer. Any specimen which exhibited a variation from the initial count rate (about 1500 cpm) by more than 15 pct was rejected. An estimate of the time necessary to convert the thin layer of iron tracer to wustite was made using the data of Pettit and wagner." he estimated time was 1 sec at 1100°C assuming linear oxidation kinetics. The shortest diffusion anneals were 1800 sec. The samples were suspended in the hot zone of a furnace by two platinum wires. Two separate specimens were run at the same time. Only the edges of each sample were in contact with the wires. The C02-CO gas of the same composition as that used in the pre-diffusion anneals flowed freely around the samples at a linear velocity of 0.9 cm per sec. To initiate a run, the specimens were lowered from the cold zone of a furnace to the hot zone by a magnetic lowering device." bout 60 sec were required for lowering. To terminate a run, the sample was withdrawn from the hot zone to the cold zone. Time zero for the beginning of the experiment was taken when the sample blended into the red glow of the furnace and conversely for the end of the experiment. The surface decrease method of measuring the tracer diffusion coefficient was used to collect the data. This method requires that counting geometry be reproducible because the specimen is counted before the diffusion anneal and after the anneal. A special jig was constructed for each specimen so the specimen could be removed from the jig and returned to the jig such that the well geometry was reproducible.

Jan 1, 1970

Jan 1, 1923

Jan 1, 1923

Edward Halse, Puerto Berrio, Colombia, So. Amer. (communication to the Secretary*): The Taviche mining-district is generally known as " Taviches," being named from the two villages called respectively San Pedro Taviche and San Jero-nimo Taviche. It is so called by Jose G. Aguilera, in his paper on the Geographical and Geological Distribution of the Mineral Deposits of Mexico;&apos; and in published reports by the late N. W. Rudston Read ;2 and by Juan de Dios Villarello3 The region is a large one, measuring about 24 miles long and 7 miles wide. Dr. Chance, in his interesting paper, tells us very little about the nature of the ores, and, with regard to the geology of the district, contents himself with observing that " the country, as a rule, consists of eruptive rocks; and no evidences of sedimentary strata appear near the mines." The latter part of the above statement is hardly correct. The formation is mainly

Jan 1, 1906

By R. M. S. B. Horta, W. T. Roberts, D. V. Wilson

Evaluation of results obtained by the Harris method for inverse pole figures is discussed. Two existing analyses and a new approach are compared. In the most frequently used analysis, different reflections are accorded equal weight. A second method involves area-weighting of reflections, mainly to take account of nonuniformity of Pole distribution. In the new method, reflections are weighted according to their multiplicity factors. Intensity ratios obtained from a sample of steel sheet by the three methods are compared. INVERSE pole figures offer a convenient method of depicting the proportions of material with various orientations referred to a unique specimen axis. The technique was first applied to fiber textures, but it is now frequently used as a description of texture in sheet metal, the unique axis in this case usually being the sheet normal. The Harris method&apos; for the determination of inverse pole figures has the great merit of simplicity. It suffers certain intrinsic limitations, but provided that these are borne in mind, the results allow useful conclusions to be drawn regarding the effects of texture components on certain mechanical properties. Much thought has been given to alternative methods of texture description, aimed at eliminating the ambiguity in the simpler methods.2"6 Refinements in the method of description are obtained at the price of increasing complexity, and it seems clear that a simple method, such as that of Harris, will continue to find application. The original derivation by Harris1 has been corrected by Morris7 and later by Mueller, Chernock, and Beck.2 Since the latter reference is more accessible, it is referred to more frequently than the work of Morris. Most users of the inverse pole figure method present their results on the basis of the treatment by Mueller et al., and it is the purpose of the present communication to comment on this treatment and to suggest a simple modification to the method of presentation which enhances the meaningfulness of the results. It will be convenient first to summarize the Mueller analysis as follows: The intensity Ihkl of a hkl reflection from a textured specimen is: Ihkl=CI0AL\Fhkl\2NhklPhkl [1] where C is a constant for a given sample I, is the intensity of the incident beam A is an absorption factor. With usual diffrac-tometer geometry and a flat specimen, A is inversely proportional to the density of the specimen. L is the Lorenz polarization factor Fhkl is the structure factor for the hkl reflection Nhkl is the multiplicity factor phkl is the fraction of crystals in the polycrystal-line aggregate with any particular (nkl) plane parallel to the surface. The corresponding equation for a specimen with randomly oriented grains is lR,hkl=CRl°ARL\fnkl\2Nnklk [2] the subscripts R indicating the factors that are different for the random sample, which will, in general, have a density different from that of the textured one. The intensity ratio is hkl , c A Phkl [3] IR,hkl CR AR PR The constants are eliminated by summing over all the measured reflections ^iRMi °R AR PR ljPkkl and from Eqs. [3] and [4] T IR,hkl The only unknown in Eq. [5] is Yj phkl and before this can be evaluated, it is necessary to adopt some form of normalizing procedure. Mueller et al. assume that when a large number, n, of reflections is used, the average value of p as defined by Eq. [6] below will be unity ? = £j**l3l [6] and the final result of their analysis follows: hkl Pkkl = i I&Jf~ [7] ±y* Ihkl ^ in,hki The normalizing procedure used by Mueller et al. involves an unrealistic assumption since it gives equal weight to each of the hkl reflections. Other normalizing procedures can now be examined with a view to selecting a more appropriate one. For an infinite number of reflections, the function p can be averaged over a continuous range of orientations covering the complete solid angle 4p by the integral relation: p =1 jp(a)dQ = l [8] This is the only exact procedure, but in practice a

Jan 1, 1970

By Norman Goss

IT is generally agreed that cold-working mechanically refines the grains into smaller fragments and with continued working these are oriented with certain crystallographic directions bearing a relation to the direction in which the metal is worked. Some of the energy expended on the metal during plastic deformation appears in the form of heat, but a very small portion remains in the metal as stored energy. The entropy, specific heat capacity, temperature at which recrystallization will just begin, density, ductility, elasticity, tensile strength, and resistance to corrosion are affected. These properties have been studied extensively and some of the changes in the physical properties due to cold-working were attributed to lattice distortion.1-8 The broadening of the K. lines on the X-ray diffraction diagrams of plastically deformed metals is believed to indicate lattice distortion, and consequently the existence of internal stresses. The evidence supporting this theory rests solely upon the observed experimental fact that the dif-fraction lines are broadened and the K a doublets are completely diffused. Elam9 has reviewed the matter of lattice distortion in relationship to the hardening of metals by plastic deformation. The X-ray diagrams of plastically deformed metals differ in general from annealed metals. The hardening of a metal was believed due to lattice distortion.9 The resolu-tion of the doublet is lost when a metal is cold-worked and the Lane spots are elongated. At one time this elongation was thought to indicate the elastic bending of the crystal planes. However, more careful work showed that the asterism was due to new orientations developed within the fragmented grains during plastic deformation. Some theories attrib-uted the hardening to fragmentation of the grains into smaller units.

Jan 1, 1940

By Frederick T. Williams

THE purpose of this paper is to discuss the relative merits of the large 31/8 in. machine and the small 21/4-in. tappett machine in driving development-headings ; and although the . data here presented were obtained from cross-cut headings alone, experience has shown that the results are equally true in drifting, raising and winning. Recently we drove two parallel cross-cuts through the same formation, using a 3k-in. machine at the breast of one cross-cut., and a 2k-in. machine of the same make at the breast of the other. The results of this work afforded an ideal comparison, since in both cases the headings were advanced through rock practically of the same hardness and breaking-properties ; the amount of sludging was equal, and there was no difference in the condition of the steel or the machines, in the air-pressure or in the experience of the operating-crews. Some operators in the Cripple Creek district contend that there is ground which cannot be handled with the small machine, the holes being too small to contain enough powder to pull the ground, etc. The results obtained in working the property of the Portland Gold Mining Co., however, show that the ground worked by them does not fall in this class. During a period of two years there have been driven, with the small machine, 4 miles and 308 ft. of development-headings, through a diversity of ground, including Pike&apos;s Peak granite (a coarsely porphyritic type of granite), highly indurated, andesitic or phonolytic breccia, true massive andesite, trachytic phonolyte, tuffas, and along dikes of decomposed basalt and hard phonolyte; in every instance a satisfactory record was made. The headings here described were driven through highly indurated, andesitic breccia, having a hardness of from 5.2 to 7.2

Mar 1, 1906

THOSE MARKED THUS * ARE MEMBERS, MARKED THUS ?ARE ASSOCIATES. THESE SIGNS DOUBLED INDICATE LIFE MEMBERS AND ASSOCIATES RESPECTIVELY. THE FIGURES AT THE END OF THE ADDRESS INDICATE THE YEAR OF ELECTION. HEAVY-FACED TYPE SIGNIFIES HONORARY MEMBERSHIP. *AARONS, J. BOYD, Vivian Gold Mining Co., Ltd., Harris, West. Australia. &apos;05 *ABADIE, EMILE R., Cons. and Min. Engr., 214 Union Savings Bank Bldg., Oakland, Cal. &apos;76 *ABBOTT, CHARLES W., Min. Engr. Pioche, Nev. ?08 *ABBOTT, JAMES W., Min. Engr: Ploche, Lincoln Co., Nev. &apos;94 *AOTT, ROBERT R., Met. Engr., Peerless Motor Car Co., Cleveland, Ohio. &apos;12 || ARAHAMS, ALEXANDER I., Student.. .67 E. 93rd St., New York, N. Y. &apos;13

Jan 1, 1917

By D. J. Blickwede

WHEN iron is dipped in molten zinc at temperatures in the range 840" to 930°F, the two metals react to form layers of Fe-Zn compounds which adhere to the iron. At the galvanizing tem- perature, the successive layers are:&apos; y (Fe5Zn21), 61 (FeZn;), and 5 (FeZn13), in conformity with the Fe-Zn constitution diagram. There is no quantitative information in the literature on the rates of growth of the individual alloy layers over the temperature range 840° to 930°F. Rather all the past experiments have studied the loss in weight of iron as a function of galvanizing

Jan 1, 1954

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of March, 1913 BAECHTOLD, CHARLES A., Engr 9G Liberty St., New York, N. Y. BRANTLY, JOHN E., Instructor in Geology Tuscaloosa, Ala. CADDY, JAMES P., Net., ,Lake View & Star, Ltd Fimiston, West. Australia. LONERGAN, PHILIP J., JR., Prof. of Mining, Government University, Peking, China. MCKANNA, EDWIN A., Min. Engr P. 0. Box 834, Oklahoma City, Okla. MACDONALD, ANGUS W., Supt. Labor Dept., Dominion Coal Co., Ltd., 21 Queen St., Sydney, N. S., Canada. TSUBOI, Yoshio, Min. and Met. Engr., Kosaka Mine, Fujita Co., Akita-ken, Japan.

Jan 4, 1913

By AIME AIME

PLANS for the Semi-centennial Meeting have almost reached completion, although in any undertaking of such magnitude a few changes are always to be expected at the last moment. As worked out up to the time of going to press, the program of the meeting is shown below. The headquarters will be the Irem Temple, in Wilkes-Barre.

Jan 1, 1921

On July 25, the first copper ore From American Smelting & Refining Co.&apos;s Mission open pit nine was sent into the new 15,000-tpd concentrator : three clays later, the first rail cars containing the Mission concentrate were sent north to the smelter at Hayden, Ariz. Thus two y,ears after stripping was started, Asarco&apos;s new mine, located south of Tucson. went on stream several months ahead of schedule. The plant, designed and constructed by Western Knapp Engineering Co., is expected to be operating at full capacity about September 1. with present plans calling for the copper concentrate from Mission to be shipped to Asarco&apos;s smelters at Hayden and El Paso.

Jan 9, 1961

Since its organization, in July, 1917, the War Minerals Committee of the Institute, of which William Y. Westervelt is chairman, has been studying important phases of the mineral industry and its relation to winning the war. From this has come a realization of the imperative need for more definite coordination than is possible without direction by some governmental agency. No privately controlled industry can have the detailed knowledge of war needs or the control of all its supplies and markets necessary to effect the adjustment of its activities for war purposes. Inevitable shortages of certain essential minerals confront us unless immediate steps are taken to stimulate and develop. the mining

Jan 2, 1918

By G. F. Swindle

This paper discusses a Personal Computer (PC) software package that reduces the time required to evaluate a mineral reserve. It provides for: •Entry of borehole data onto PC diskettes and the creation of a borehole database; •Capture of map data using an attached X-Y digitizer; •Calculation of uniform square grids for thickness, mineral qualities, overburden ratio, etc., •Compilation of multiple such grids into a digital model, and iterative evaluation of the model with the user applying constraints and cut-off values; and • Graphic display of grid cells (blocks) showing which cells failed, and on which constraint(s), and a complete reserve report showing tonnages, averages, histograms, and quality arrays.

Jan 1, 1985

By Paul Soros

Terminal facilities were recently completed at Conneaut, Ohio, on Lake Erie, for the Bessemer and Erie Railroad Co. (a wholly-owned subsidiary of U.S. Steel Corp.) which may become the blue- print for all future coal shipping terminals. Design and engineering of the new facility was by Soros Associates, New York, N. Y. Unlike terminals of conventional design, for example, those at Toledo and Newport News, which load coal directly from the railroad car to the vessel, the new installation passes the coal into temporary storage, loads the vessel from temporary storage and provides alternative reclaiming systems in case of major system failure.

Jan 1, 1966

Coal Division Industrial Minerals Division Minerals Beneficiation Division Mining, Geology and Geophysics Division Council Will Mitchell, Jr, Chairman (MBD), Kenneth L Cook, Vice-Chairman (MGGD). Edward L Clark (MGGD), Raymond B Ladoo (Ind Min Div), Sandford S Cole (Ind Mm Div), Norman L Weiss (MBD), C T Hayden (Coal), H F Yancey (Coal), Clayton G Ball (MED), P De Bruyn (MIED), Arnold Buzzalini, Secretary, AIME, 29 West 39th Street, New York 18, N Y Mining Branch Advisory Committee Will Mitchell, Jr, Chairman, Grover J Holt, J B Morrow, J L Gillson, Edward G Fox, S S Cole, Roger V Pierce, Norman L Weiss. H C Weed. J R Van Pelt

Jan 1, 1956

The American Gas Association, 420 Lexington Ave., New York, N. Y. The Proceedings and Reports of the American Gas Association are concerned with the technology and utilization of gas, and research along those lines. A list of publications will be sent upon request. Publications are classified under the general headings: Accident Prevention; Accounting; Commercial; General; Rates; Industrial; Publicity and Advertising; Technical; and Testing Laboratory. As&apos; illustrations of the type of paper presented, the following are cited from the Technical classification: Evaluation of gas oils (1930), 40 cents; Agglutinating value of American coals (1927), free; Composition of coal in relation to spontaneous combustion (1927), free; Physical and chemical

Jan 1, 1933

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the first half of March: James C. H. Ferguson, San Francisco, Cal. Capt. A. F. Lucas, Washington, D.C. Henry Adams, Stamford, Conn. Dexter P. Cooper, New York, N. Y. H. A. Wheeler, St. Louis, Mo. L. D. Moore, Chatham, N. J. John M. Sherrerd, Easton, Pa. Hennen Jennings, Washington, D. C. R. T. White, formerly General Manager of the Braden Copper Co., Chile, is to take charge of a copper company in Caucasus, South Russia.

Jan 4, 1914