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[Executive J. V. W. REYNDERS, Chairman WILLIAM H. BASSETT E. DEGOLYER I-I. C. BELLINGER RICHARD PETERS, JR. Finance GEORGE OTIS SMITH, Chairman H. A. GUESS F. JULIUS FOHS Admissions GEORGE D. BARRON, Chairman DAVID LEVINGER P. A. MOSMAN H. K. MASTERS J. A, SINGMASTER Alternates F. G. BREYER C. W. HAMILTON F. E. PIERCE]

Jan 1, 1928

By FREDERICK MCAKCCOY

THE production of tin from Mexico has never reached the point of being considered a national industry, but the distribution of tin ores is so widespread that there are possibilities that one day it may become of importance. Of the twenty-seven states of the Republic, tin claims have been taken up in sixteen. In all there had been taken up to the end of 1926, two hundred and twenty-five claims, of a total area of about 7400 acres. The first historical mention of tin in the Americas is found in a letter of Cortez to the Emperor, Charles the Fifth, of Spain, which is as follows: Speaking of his manufacture of some small cannon, he says: "For these reasons I took considerable pains to get copper from some provinces of this country, and bought it at a high price in order to get it quicker.

Jan 1, 1929

By AIME AIME

WITH the recent increase in the price of gold, its economic recovery at depths formerly considered impractical has become a present possibility. Two important difficulties must be met: pressure bursts of the rock, and the reduced efficiency of human labor subjected to the higher temperatures and the increased humidity at the greater depths. In the following abstract of a paper by J. H. Dobson, presented before the South African Institution of Engineers on

Jan 1, 1935

By Frank G. Breyer

THE .following developments in the zinc field during 1935 are listed in the order of their importance. Each will he amplified in later paragraphs. In the field o f Metallic Zinc: (1) Construction of further continuous vertical retort smelting capacity in the United States and Germany. (2) Expansion of fractional distillation capacity in the United States. (3) Great expansion in the zinc-base die-casting industry in the United States and abroad. (4) Wide acceptance of heavy galvanizing by the steel industry. (5) Construction of the first commercial wire electroplating plant for putting on heavy coats of pure zinc. (6) Firm establishment and appreciable expansion of the practice of using zinc dust as a reducing agent in the organic chemical industry.

Jan 1, 1936

By W. V. Long, D. H. Reynolds, R. B. Bhappu

Equilibrium distribution coefficients were determined for some monovalent and polyvalent ions for several absorbing and exchanging media as functions of pH and initial ion concentration. Among ions studied were NH4 (I), K(I), Ni(II), Ce(III), Th(IV), and Mo(VI). Absorbents used were: ion exchange resins; a tertiary, and a quaternary amine in an inert solvent; and some activated carbons. The ions studied were in aqueous HCI, HNO3, H2SO4, or HC104 solutions. The classical mass action expression proved of little value in describing the variations observed. The data indicate that the determining factors in absorption and ion exchange may be the ionic species in the aqueous solution, which in turn depend upon pH, dilution, and perhaps other conditions. Three sorption processes have become prominent in recovering values from leach solutions. These are: 1) ion exchange, 2) solvent extraction (liquid ion exchange), and 3) physical adsorption by materials of high specific surface. In the first two of these processes the exchange reaction is considered chemical in nature, and is discussed in terms of the mass action principle. The third is considered a surface phenomenon and is discussed in terms of surface areas and various forms (Gouy, Stern, Grahame, etc.) of the Helmholtz double-layer theory. Generally speaking, we have found in chemical analysis and hydrometallurgical studies that there are close similarities between the three sorption processes, and also differences which are difficult to reconcile with any of the usual theoretical treatments. That others have experienced the same troubles is shown by the fact that usable processes, in chemical analysis as well as in hydrometallurgy, generally are discovered by empirical procedures. EXPERIMENTAL CONSlDERATlONS The gaps between theory and practice have allowed many conflicting statements to appear in the litera- ture. To learn, in particular, the behavior of some metallic ions on a cation exchange resin at a constant pH, equilibration studies were made over a wide range of concentrations.' Results are shown in Fig. 1 for four metals in hydrochloric acid solution on a strongly acidic cation exchange resin, AG 50W-X8 (Bio-Rad). The distribution coefficient, defined as D = amount of metal extracted per g of resin/amount of metal unextracted per ml of solution is seen to vary in a way to support all manner of reports about its behavior with changes in solution concentration. The metals used were chosen from those least likely to form stable chloro-complexes. The changes of slope in the various isotherms may reflect formation of unsuspected chloro-complexes of low stability (ion-pairing for example) whose concen-

Jan 1, 1967

By Fred H. Perfect

The thermite process, now approximately 80 years old, has heretofore been practiced in ceramic vessels. This paper outlines the successful production of several million pounds of alloy produced in zuater-cooled copper vessels. THE high temperatures necessary to produce fluid high-alumina slags have probably discouraged earlier workers from attempting to utilize water-cooled vessels. The following is a report of the successful application of this method, together with a report of the physical and chemical problems which had to be solved to make the process practical. About 1955, when Reading Alloys was more concerned with the production of ferrotungsten than with most other types of alloys, it was found to be exceedingly difficult to predict the reaction rate that one would experience from one tungsten ore to another . This difficulty was increased for two reasons: the physical state of the ore as received was seldom uniform, and the size of the mass to be reduced is a very important factor in developing the proper mix for the final reaction rate and temperature. For example, the reduction of ferric oxide with aluminum would theoretically produce temperatures of about 2600°C, and, in spite of the losses due to radiation, the energy is quite sufficient to produce a very fluid slag and iron effecting a very clean separation. On the other hand, the reduction of ferrous oxide with aluminum, while it is not as energetic as the first reaction, nevertheless should give temperatures above 2000"C, which should cause separation of alumina and iron, but, in practice, this is not the case and good fluid slag is not obtained. The heat of reaction, calculated from the thermo-dynamic heats of formation of the constituents of the reaction, offers a convenient guide to the feasibility of a thermite reaction. Thus, the values listed in Table I can be used as an approximate guide for estimating the results which may be expected in the reduction of various oxides and combinations of oxides using aluminum as the reducing agent. As a generalization, those reactions releasing approximately 600 cal per g of total mass represent the lower limit at which to expect separation of slag and metal. On the other hand, those reactions which release 1100 to 1200 cal per g are too violent to be used successfully without the addition of considerable inert material, such as lime, fluorspar, and so forth. Reaction rate is also a very important factor. This, of course, is governed very largely by the sizing and intermingling of the oxidant and reductant and by the starting temperature of the reactants. This is why those figures shown in Table I can only be a general guide. Further, it must be understood, that by adding powerful oxidizing agents, such as nitrates, chlorates or metallic oxides, such as molybdenum trioxide or chromium trioxide, certain problems respecting low temperatures are not necessarily solved. This is true in the addition of oxidants, such as sodium chlorate. By adding too high a concentration of sodium chlorate as a booster for a particular reduction, explosions are generated. Generally, they are of an intermittent type so as to give a Roman Candle effect to the reduction itself; with each surge resulting from a minor explosion more and more material is thrown

Jan 1, 1968

By R. Schuhmann

Jan 1, 1965

By AIME AIME

THE John Fritz Gold Medal for 1929 was presented to Herbert Hoover at the Executive Mansion on April 25, at a luncheon given by Mr. Hoover to present and past members of the Board of Award, preceding medalists, and presidents and secretaries of the American societies of Civil, Mining and Metallurgical, Mechanical, and Electrical Engineers. The presentation party of forty engineers which gathered at the White House, from all parts of the United States, was made up of past presidents of the four senior national engineering societies that established the John Fritz Medal and included five men who had received the medal in previous years. These former medalists were Edward Dean Adams, J. J. Carty, J. Waldo Smith, Elmer A. Sperry and Ambrose Swasey. This medal is the highest honor bestowed by these four national engineering societies, having a membership of 60,000. It is awarded not oftener than annually for "notable scientific or industrial achievement, without restriction on account of nationality or sex." In accordance with custom, the award to Mr. Hoover was made tentatively and without announcement in October, 1927, and was formally con- firmed and announced one year later.

Jan 1, 1929

By L. Obert, D. E. Stephenson

The objectives of this investigation were to develop a laboratory procedure in which core discing could be produced under known (and variable) stress conditions, and to study the discing characteristics of several fypes of rock. Discing of rock cores refers to the formation of discs or wafers of relatively uniform thickness which fracture or rupture on surfaces approximately *Fracture is a type of failure in which there is a complete loss of cohesion and fresh surfaces are created. Rupture is a type of failure in which there Is only a partial loss of cohesion. normal to the axis to the core (see Fig. 1). Usually the surfaces of the discs are concave-convex with the concave side toward the collar of the hole. The surface of the fractured discs are like those created by a tension failure (or possibly a shear failure with virtually no normal compressive stress). This phenomenon has been observed by a number of investigators1-5 in the course of diamond drilling in underground mines, especially in areas suspected of being under high stress. The state of stress in the core required to produce discing is not exactly known. Tranter and craggs6 theoretically investigated the stress distribution in an infinite cylinder, subjected to hydrostatic pressure, minus p, from z = 0 to z = 8 and unloaded from z = 0 to z = 8, Fig. 2. The exact solution to this problem shows that a tensile stress develops in the loaded region near z = 0 with the greatest tensile stress on the axis of the cylinder. A tensile stress also developed on the surface of the cylinder at a point just outside of the loaded zone. Jaeger and Cook3 experimentally investigated the discing mechanism by biaxially loading cores in a pressure jacket sealed at the ends by O-rings. According to the Tranter and Craggs theory it would be expected that failure should occur at the pressure discontinuity at the O-rings. The experimental results showed that if the specimen was unjacketed it broke at random points within the pressurized zone and at a pressure somewhat greater than the tensile strength of the specimen, presumably due to the development of a

Jan 1, 1965

By C. L. Dake

AN insistent and steadily growing demand is evident for the broadening of undergraduate curricula in engineering. Among suggested additions are training in public speaking, report writing, business law and contracts, accounting, finance, money and banking, scientific management, economics, social and labor problems, psychology, and ethics. The demand for these subjects comes from the older engineers and from the industries that employ our graduates. Of course, many of the men who suggest such changes are influenced largely by their personal needs and contacts, but the demand is sufficiently widespread to merit serious study by educators. In fact, many educators themselves concur in the proposals for broader training. These matters were examined intensively a few years ago in an exhaustive study of engineering education. Opinion at that time was rather strongly against any profound change. Since then, however, the whole economic system has undergone violent disruption. Even if recommendations made a few years ago were appropriate to the conditions then- obtaining, the enormously changed conditions of the present make advisable a further careful study of this problem. In recent years, mergers, to reduce costs, have sharply limited the number of engineers employed and have thereby intensified the struggle to secure positions. In this stiffer competition, engineers with the most adequate training undoubtedly fare the best.

Jan 1, 1934

By S. F. Emmons

Jan 1, 1899

By Edward H. Williams

IN the middle of the eighteenth century John Frazier and wife, Sarah Ingraham, removed from Boston, Mass., to Philadelphia, Pa., where he was held in such esteem that we find him one of the Committee which arranged the ball at Washington's inauguration. Their son John. Nalbro Frazier, was prosperous in his mercantile career and fortunate in his wife, .Anne West; who was an important personage in the early life of Professor Frazier. This cultured lady brought into the family an atmosphere of religious enthusiasm, of thoroughness and: of unity of purpose. Her son, Benjamin West Frazier, inherited her traits and displayed them during a. short and active life. Like his father, he engaged in mercantile pursuits, and was a member of the firm of Zimmerman, Frazier & Co. In their interests he lived for a short- time in Montevideo, and on his return married Isabella Zimmerman, a daughter of the head of the firm. Their happy married life was cut short by the death of Mrs. Frazier shortly after the birth of the subject of this sketch which, occurred October 3, 1841. Mr. Frazier did not long survive her, and left his orphaned sons to, the care of his mother, from whom he had inherited a lovable and deeply religious nature, an : artistic temperament and a capacity for thorough work. Whatever of these traits fell by inheritance to these children were strengthened by the influence of their grandmother, and. the purity of mind, the delicacy of sentiment, the refinement of honor, which characterized. Professor Frazier, are due to Anne West Frazier, and are generally present in the characters of all of gentle blood who have been under the sole and immediate influence of a mature and refined woman. Professor Frazier was educated at the Episcopal Academy in Philadelphia, and passed thence through the University of

Sep 1, 1905

By Martin G. Castro, Renato G. Bautista, Morton Smutz

During the last 25 years, multistage mixer-settlers have been used extensively for liquid ion exchange work. The mixer-settler has the advantage of being a compact device in which a large number of stages can be assembled in a relatively small area. They are particularly advantageous for the separation of rare earths. Most of the adjacent rare earths have separation factors which are near one, which means that a large number of stages are needed to produce a good separation. When two elements (m, n) are extracted simultaneously, the separation factor (ßm, n) is defined as: [ ] where Ym, Yn are the molarities of the respective elements in the organic phase and Xm, Xn, are their molarities in the aqueous phase at equilibrium. The industrial consumption of rare earth oxides rose to over 6800 tons in 1968, an increase of 33% over 1967.1 The increased production and demand for rare earth and lanthanum chlorides for petroleum cracking catalysts was one of the principal factors in this increased consumption of rare earths. In 1968 approximately 59% of the rare earth oxides produced were used for gasoline cracking catalysts in the form of rare earth and lanthanum chlorides. There was also an increase in the sales of lanthanum oxides for use in optical lenses and in fiber optics. The future looks good for the rare earth industry. The rare earths can be expected to be used in many new products which are being developed. Until the late 1950's tributyl phosphate (TBP) was the principal solvent used in rare earth liquid ion exchange. In 1957 Peppard3 reported the use of di (2-ethyl-hexyl) phosphoric acid (D2EHPA) as a solvent for separating the rare earths. Rare earth separation factors of up to 2.5 were obtained in nitrate and chloride systems while the maximum separation factor using the

Jan 1, 1972

By Arthur L. Hall

The purpose of this symposium is to challenge industry to better air classification, and as a first step toward fulfillment, to spotlight three fairly recent, aerodynamically designed, highly efficient air classifiers. This discussion does not intend to imply that present practice is bad. Actually, when present air separators are used for the jobs for which they were originally designed, they give high production and uniform operation, with a minimum of maintenance. The customers of nonmetallic mineral pigment producers, however, are making increasing demands for finer products, such as 99.9 pct -20µ, which appears to be beyond the economic capabilities of standard air separators industrially used over the last 10 to 30 years. Here is an actual example. A 10-ft diam pebble mill is in closed circuit with a conventional 12-ft diam centrifugal air separator, grinding 20-mesh wollastonite to a series of fine grades up to 99.97 pct - U.S. No. 325 mesh (44µ). Fig. 1 shows variations in fineness of mill discharge (or air separator feed), recycle for regrinding (or air separator tails), and product as measured by a wet rotating sieve test. For example, when the mill is turning out a product 80 pct -325, the mill discharge or separator feed is 30 pct -325, and the coarse tailings or recycle is only 5 pct -325. Hence 25 pct of the 30 pct available is accepted as product. This is efficient separation, and the ratio of recycle to feed is only about 2: 1. How- ever, to make a product testing 99.97 pct -325 the separator feed is 62 pct -325 and the coarse tailing 60 pct -325. In this case the recycle ratio is about 13: 1 and the economic limit to produce fineness has been substantially reached with this given equipment and process arrangement.

Jan 10, 1957

By Percy A. Robbins

I. INTRODUCTION. THE central power-station. of the De Beers Consolidated Mines, Ltd., was designed and built under my supervision about five years ago. Since no detailed description of this plant has ever appeared, it may possess sufficient interest to warrant its publication, even at this late date. Although some additions may have been Blade to the plant, the following account, prepared from my notes, and accurate up to May, 1905 (at which time I severed my connection with the De Beers Com¬pany), will, I think, be found substantially correct. Certain local conditions governing the design of this plant should be stated first. If. GENERAL CONSIDERATIONS. The climate is hot and dry. The .region around Kimberley is arid and water is very scarce. The supply obtained from the mines contains so much material in solution that it is unfit for use in boilers or condensers (although tests recently made with a water-softening plant, built by Hans Reisert, of Germany, would indicate that water thus treated is suitable for boilers). And the amount of water required for concentrating about 30,000 tons of ore per day is so large that the question of adequate water-supply for this power-station had to be carefully considered. The rainy season extends from December to April, and the rainfall averages about 15 in. per year. Droughts are frequent; and in some years there is scarcely any rain at all. The water-supply for the town of Kimberley is brought from the Vaal river, 16 miles distant, and pumped into town by a private water company. The charge made for water, which is

Mar 1, 1908

By C. A. Stiles, J. W. Nyhus

Erie Mining Co. is a 10.3-million-tpy pellet producer on the east end of the Mesabi Range 60 miles north of Duluth. Its complex includes facilities for mining, crushing, grinding and beneficiation in addition to a pellet plant and power plant. A 74-mile railroad links the mine and plant to Taconite Harbor on the shore of Lake Superior. The concentrate recovery ratio at Erie is about 1: 3, and this, along with stripping activity, makes it necessary for the company to mine nearly a million tons of material a week. At the outset, all crude ore mined at Erie was hauled entirely by rail, but with expansion into additional mining areas, the company made a gradual transition towards truck-to-rail haulage. Today, in Erie's 11th year of operation, over 50% of all crude taconite mined is transported by truck to loading pockets where it is transferred to rail cars. Future years will see more taconite moved in this manner. Thus, the company has an increasing interest in tire performance.

Jan 6, 1969

By R. W. Heins, N. Street

An investigation was made of the Rehbinder-Kuznetsov pendulum as an instrument to aid in the study of rock drillability and of the effect of surface active agents on rock drillability. The "critical weight", i.e., the pendulum weight at greatest sensitivity, was determined for several solids and it was shown that a change in surface environment changed the maximum value of the apparent hardness but not the critical weight, and the critical weight increased with increase of hardness of the solid used. Using silver halides as the solid material, and solutions of either silver nitrate or the appropriate alkali halide, it was shown that there is a hardness maximum at the zero point of charge of the particular silver halide. INTRODUCTION The development of relative hardness measurement by the method of damped oscillations, or what has been called the pendulum sclerometer, is due largely to the Russian workers P. A. Rehbinder and V. D. Kuznetsov and their co-workers.1,2 The apparent simplicity of the method has led to its use in a number of fields, particularly those where relative hardness has to be determined on a brittle solid. As will be shown, the simplicity of the method belies its complexities. THEORY OF THE PENDULUM SCLEROMETER The operation of the pendulum is quite simple. Make a sharp point such as a diamond, hardened steel or tungsten carbide, as the fulcrum of a pendulum, with the center of gravity of the system below the point of support. The attenuation of this pendulum is a function only of air friction, provided no fragmentation, breakage or other work is performed by the point. However, when the solid surface breaks or disintegrates under the point, and the latter penetrates the solid, part of the energy of oscillation is absorbed in the work of creating new surface, and the rate of attenuation increases. In the case of brittle solids, the point of the pendulum produces fragmentary particles, whereas the point produces plastic deformation in a plastic solid; but in both cases damping occurs. This pendulum damping is a function of the hardness or strength of the solid. Whereas a pendulum oscillating on a hard material attenuates primarily by air friction, in the case of a soft material, the points penetrate the surface of the solid, producing new surface, and the pendulum damps much faster. Thus the attenuation rate is a function of the hardness or strength of a material in both plastic and brittle substances. Russian workers initially used a single support for the pendulum, but this created many problems because of oscillation of the pendulum in more than one plane. A revised version used two points, or sometimes a prism as support, successfully confining oscillation to one plane. The version using two points was constructed and used throughout this investigation, making the recording of the attenuation as a function of time relatively easy. That both points should be in contact with the solid during the damping is implied. Rehbinder (c.f. Kuznetsov2) proposed that the hardness H as measured by this method could be expressed by a quantity which is inversely proportional to the relative initial rate of attenuation of amplitude. where H = hardness parameter (arbitrary units) a, = initial amplitude da/dt = rate of attenuation of amplitude with time. In the simplest case of damping with a constant logarithmic decrement, H can be regarded as a constant for the duration of the whole damped oscillation process. That is

Jan 1, 1966

CONTENTS PAGE ANDERSON, ARVID E., and CAMERON, FRANK K.-Recovery of Copper by Leaching, Ohio Copper Co. of Utah. Discussed by Thomas B. Brighton, H. C. Goodrich, Arvid E. Anderson, Thos. P. Billings, Frank K. Cameron 2 BEESON, J. J.-Mining Districts and Their Relation to Structural Geology. Discussed by Charles Keyes, Chas. A. Porter 4 DOBBEL, CHAS. A.-Deep-hole Prospecting at the Chief Consolidated Mines. Discussed by G. W. Crane 10 CRANE, G. W.-Notes on the Geology of East Tintic. Discussed by G. W. Crane, H. E. Havernor, N. O. Lawton 11 SACKETT, B. L., BARDWELL, CARLOS, JACOBSON, SIMON, and JENSEN, N. H. Lead Smelting in Utah. Discussed by D. W. Jessup, B. L. Sackett, E. H. Laws 13 BARDWELL, E. S., and MILLER, Roy H.-Pulverized Coal as Fuel for Copper Refining Furnaces. Discussed by L. D. Anderson, E. S. Bardwell, C. P. Crawford 15 WIGTON, G. H.-The Chief Consolidated Volatilization Process and Mill. Discussed by Thomas Varley, S. G. Olmstead, V. O. Lawton, O. C. Ralston.... 16 JESSUP, D. W.-Evolution in the Preparation of Ores for Lead Blast Furnaces. Discussed by W. Spencer Reid, D. W. Jessup, Carlos Bardwell 19 ALLEN, H. P., and MADGE, WM. C.-Chloridizing Mill of the Standard Reduction Co. Discussed by Thomas Varley, H. R. Hanley, H. P. Allen, George H. Dern 20 TUCKER, E. L., and HEAD, R. E.-Effect of Cyanogen Compounds on Floatability of Pure Sulfide Minerals. Discussed by Blarney Stevens 24 Mix, B. E., and BARKER, L. M.-Method of Unloading Ores and Coarse-crushing Practice at Magna Plant of Utah Copper Co. Discussed by W. C. Madge,B. E. Mix 25 KEIGLEY, C. T.-The New Byproduct Coke Plant of the Columbia Steel Corporation. Discussed by W. M. Grant, C. T. Keigley, A. C. Feilder 25 JACKSON, P. W.-Blast Furnace Plant of the Columbia Steel Corporation. Discussed by W. R. Phibbs, H. M. Henton 26 OLDRIGHT, G. L., KEYES, H. E., and WARTMAN, F. S.-Production of Ferric Sulfate and Sulfuric Acid from Roaster Gas. Discussed by G. D. Van Arsdale William E. Greenawalt, G. L. Oldright 27 MAZANY, M. S.-Braden Copper Company Caletones Smelter. Discussed by A. B. Young, G. L. Oldright 36 HARRINGTON, D.-Safety Methods in Utah Coal Mines. Discussed by Edward K. Judd, Otto Herres, Benedict Shubart, A. C. Watts, D. Harrington 36

Jan 12, 1925

By John C. Calhoun, Frank T. Bethel

The application of a method for analyzing pressure build-up curves to determine the effective permeability in the Spraberry is presented. Sixteen upper Spraberry wells of the Driver area arc analyzed and show variations in the in-place effective permeability of 2 to 183 md. Since these value- are much larger than the .5 md. or less reported for the matrix rock. a large part of the vertical fractures noted in Spraberry cores- must be considered native to the formation. The effectiveness of the well fracture treatment in connecting the well bore to the native fracture system is analyzed by comparison of the effective permeability as determined from the PI test to that obtained from a pressure build-up curve. These results show that the fracture treatment is sufficiently effective in connecting tile well bore to the native fractrure system to yield a flow capacity within about 50 per cent of that dictated by the native fracture system About two-thirds of the wells show some degree of local blockage. INTRODUCTION Fractured reservoirs have been known in the past.' However, during the past two years the Spraberry formation has directed the attention of the petroleum industry to a study of the performance of a fractured reservoir. The large variation in the number of fractures noted in Spraberry cores rile large variation in the producing ability of offset well.. the dramatic effect of well treatment on well ,productivity. the unknown quantity of oil stored in the fractures and matrix rock. and the unknown oil to be recovered were part of the initial Spraberry puzzle. In this type reservoir where the well treatment is an important factor in determining the productivity. it i- particularly desirable to determine the in-place flow capacity of the drainage area at distance* far removed from the well bore. This value. when compared to the flow capacity obtained from a PI measurement, will show the effectiveness of the well treatment (completion. fracture treatment, acidization. etc. in establishing a flow capacity in the vicinity of the well bore equal to that in the more remote region. The object of this paper i.; to show the application of a method of pressure build-up analysis for this purpose in studying the Upper Spraberry formation in the Driver area. STATEMENT OF THEORY The theoretical basis for the application of a pressure buildup curve to show the effective permeability of the rock at distances far removed from the well bore has been presented in detail in earlier publications.', in the previous development it was shown that pressure build-up behavior of all wells could be reduced to the same dimensionless build-up curve of Fig. 1. This mean.; that the bottom hole pressure of a well after hut-in will rise in such a manner that a plot of pressure against the logaritllm of time yields a straight line. The slope of this linp can be rlzed to calculate the effective permeability as expressed by the following equation: where: effective oil permeability md oil production rate prior to shnt in. STB/I) In practice the flow which occurs into the well bore after shut in and the variation in flow capacity in the immediate vicinity of the well bore usually cause the early part of the build-up curve to be unsatisfactory in the determination of permeability. In general the effect of these factors on the straight line section will become negligible after a time when the of the following equation is equal to 0.1. and the preferred section Of the curve for use in defining the slope lie-

Jan 1, 1953

By H. K. VAN POOLLEEN, W. Hurst, H. C. Bixel

In an earlier publication* I showed the development of the instantaneous point source solution for a well producing at a constant rate at the center of a system of two radial, adjoining sands of different permeabilities. I also showed how a wellbore radius could be incorporated if this were the development required. For the purpose of that paper and the point I wished to make, this solution served. It yielded a simplifying solution of sands in series identified by Eqs. VI-26 and VI-27. (These equations are reproduced in part by Bixel and van Poollen as their Eq. 3, Page 302.) I am well aware that the simplified solutions are approximations. The facts that these Ei-functions satisfy the diffusivity equation and meet the boundary conditions both at the well and at the interface between sands, and that the earliest time considerations yield zero pressure drop, are evidence that the solutions are good approximations. This was the purpose for these formulas, which I interpret that where the permeabilities are of finite order of magnitudes in the respective media, the relations give satisfactory answers. However, from the authors' point of view there are reservations, which leads me to consider their entire generalization as illustrated in their Figs. 1 through 14. What I understand from their storage capacity, relationship Fs, which is the ratio of the product of porosity and compressibility of Sand II to Sand I, that is employed here by the authors as a correlative means of identifying one figure from another, there is nothing in the exact mathematics that supports such a term as a means of correlation. This is taken out of context, unsustained that this applies. Here the mathematics are known, where the true correlation is the diffusivity term of one sand to another. This entails permeability that refers back again to the term M in their paper for the transmis-sibility of fluid from one sand to the other that should have also been a part of this storage capacity. In Figs. 8 through 14, which purported to show the simplified equation following this correlation, there are apparent discontinuities for M equal to or less than 0.1000 that differ from the trends for greater values of M. In this connection there is no reference radius given for this cumulative pressure drop in the paper that would permit me to make these calculations. However, what is clear for M equal to 0.1000 or less we are treated to almost a closed barrier at the interface; a condition entered by the writers without qualification. This across-the-board treatment of these simplified formulas, whatever the motive of the authors, enters into a range of permeabilities that even I as the contributor would have reservations that such could apply. Under comparable conditions I would be looking at a closed reservoir or some facsimile for such. The extent to which the approximation or the exact equations pertain is not evident in the generality offered by Bixel and van Poollen in their paper. Only when they or other writers show the comparison of the pressure distributions within the formations can one be able to judge the rational limits to subscribe to the simplified formulas.

Jan 1, 1969