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By J. B. Fletcher

The Miami mine first started operations in 1910. For convenience, the history of the orebody can be divided into the following categories (Fig. 1): 1) 1910 to 1925: 24.4 million tons of high grade ore, mined by top slicing, sublevel caving, etc. 2) 1926 to 1954: 102 million tons of low grade ore, mined by block caving.

Jan 1, 1961

By Ove Alm

Wet and dry specimens of three rocks of approximately granitic composition were deformed at different experimental conditions. These experiments were carried out in order to study the extent to which water, either added or released from mineral reactions, may affect the mechanical properties and the microstructure of these rocks. The experiments were conducted in a Griggs&apos; hot creep apparatus at temperatures and pressures up to 900ºC and 1000 MPa respectively; and most of them were performed in the constant strain rate mode [(1.10-6 < t < 1 • 10-4 s-1 )]. All three rocks were low porosity rocks, and the wet specimens never contained more than 0.9 wt % of added water. The experimental results are, however, quite unequivocal: They show that wet rocks are weaker than dry ones. A significant difference is even found for rocks tested in uniaxial compression at room temperature. A few experiments carried out on specimens obtained from larger prestressed rock cores indicated that the central parts of these cores were more likely to contain more microcracks than the ends. Optical microscope examinations revealed that extensive microcracking takes place even at the highest temperatures, where other mechanisms such as slip and dislocation creep also become important. Very little partial melting could be observed except for the specimens deformed at 900ºC.

Jan 1, 1982

By Edna A. Dancy, Gerhard J. Derge

Jan 1, 1963

By R. G. Vardiman, M. R. Achter

Observations of dislocation structure in niobium are presented using two techniques. Triangular pits developed by electroetching are confined to orientations in the stereographic triangle between the (111) pole and planes of the (1ll) zone and require the presence of carbon. Some unusual electroetching phenomena at other orientations are noted. A chemical etch of dislocations decorated by the addition of carbon to 50 ppm reveals the complete dislocation line structure in a surface layer up to 30 p deep, with a resolution of less than 1 p. This effect is independent of surface orientation. The structure of subboundary nets may be resolved for misorientations up to about 1&apos;. Dislocation structures found in strain anneal grown crystals, such as helices, prismatic loops, and high-density areas, are observed. The measurement of dislocation density is discussed and values obtained in different ways are compared. IN the course of some work on the response of refractory metals to thermal-mechanical treatments, it was desired to examine the defect structure of relatively low dislocation density crystals of niobium in bulk form. Surface and bulk methods for the observation of dislocations have been reviewed by ~melinckx,&apos; and include etch pitting, decoration, and various X-ray techniques. The dislocation line structure has been developed by decoration in a few metals, although observations were limited to certain orientations, or by the coarseness and nonselectivity of the precipitate. The most commonly used technique is etch pitting. In niobium, etch pits have been developed chemically&apos;0," in material of high impurity content and electrolyti-cally&apos;&apos; in relatively pure material. In this paper, etch pits developed electrolytically, and the dislocation line structure of a surface layer developed by decoration and chemical etching, are examined, and observations are presented from both techniques. EXPERIMENTAL METHODS Our starting material was electron-beam-melted niobium, swaged to 4 or -in.-diam rod. Chemical analysis is given in Table I. Single crystals were grown by a strain anneal technique using 1 to 2.5 pct of strain and growth temperatures of 1700" to 2300"~.&apos;~ Some crystals grown by zone melting were also examined. The desired surface orientation was exposed either by spark machining or by sectioning with a cut-off wheel and prepared for etching by electro-polishing.

Jan 1, 1969

By G. E. Perry, R. D. Seba

The steam soak process is the most widely applied and most successful thermal supplemental recovery process in use today. This process, which consists of injection of steam in various quantities into a well that is subsequently used as a producer, can be repeatedly applied to the same well. The treatment, if successful, will increase the production rate of the well for a given period. For this reason, the steam soak process should be considered primarily as an acceleration method rather than as a method for producing oil that could not be recovered by primary means. However, application of this process to reservoirs containing viscous crude may produce oil that otherwise would have zero present value or would be produced at such low rates by primary methods that it would not be profitable. A major necessity for the successful application of the steam soak process is a source of natural energy. This source of energy may exist in one or more of the following forms: expansion of fluids, compaction, gravity drainage. This study was undertaken to determine the effect of gravity drainage on steam soak production and recovery and to develop a method for predicting production rates, ultimate recovery, and heat requirements when applying this process to a reservoir in which the primary driving mechanism is gravity drainage. (For additional discussion of some of the factors that affect recovery of viscous oils by the steam soak process, see Ref. 5.) Model The model developed for analyzing the performance of the steam soak process in gravity drainage reservoirs is a modified form of that developed by Matthews and Lefkovits.1,2 The model used in this study consists of two concentric cylindrical volumes of productive formation with cap and base rock of impermeable material. The inner cylinder, extending from the radius of the wellbore to some predetermined radius, is referred to as the hot zone; and the outer cylinder extending from the exterior boundary of the hot zone to the outer drainage boundary will be referred to as the partially heated zone. Fig. 1 is a schematic cross-section of the model, indicating its thermal properties. Horizontally the reservoir is divided into two regions, the upper region having a high gas saturation and residual liquid saturation, and the lower region containing a high liquid saturation. The boundary between these two regions is referred to as the free surface, which drops and changes shape as fluid is produced from the reservoir. The model was used to analyze the steam soak process by applying the following assumptions: 1. The horizontal formation is composed of one or more homogeneous noninterconnected layers containing incompressible fluids. Each layer is treated separately. 2. The hot zone is heated by the initial soak and is maintained at the steam temperature corresponding to atmospheric pressure by resoaking. 3. The height of the free surface at the producing well is at all times zero (producing well is pumped off). 4. The position of the free surface at the start of

Jan 1, 1970

By Henry M. Howe

PART I. § 1. Introduction. After giving certain definitions, this paper gives the reasons which led to Roozeboom&apos;s form of the diagram of the freezing-point curves and general equilibrium of the iron-carbon compounds, steel and cast-iron ; and then those which led to replacing it with the present or double diagram, in which graphite is at all temperatures held to be the more stable and cementite the less stable (metastable) form of carbon. Next in § 10 the evidence supporting this greater stability of graphite is examined, then in § 17 that which seems to oppose it, and in § 22 a summary of the evidence is presented. The second part of the paper considers the topography of the graphite-iron diagram, rejecting summarily the solubility-lines based on the data of Charpy and Grenet and of Mannes-mann, on the ground that the data even on their face do not really point toward these lines, and that they are wholly incompetent to determine any solubility-lines whatsoever, because they report together with the dissolved carbon also an indeterminate quantity of cement-carbon, and because even such carbon as is actually dissolved, only in part represents the solubility of graphite, and in another and indeterminate part represents the solubility of cementite, or at least of carbon in presence of cementite as distinguished from graphite. It might be thought that graphite is but slightly soluble in iron, because of the absence of any suggestions of eutectoid graphite, corresponding to the eutectoid cementite of pearlite in very many cases in which the cast-iron seems to consist of ferrite and massive graphite only, and because of the micrographs of Goerens and Gutowsky. In these the primary austenite of cast-iron quenched but little below the eutectic freezing-

Jan 7, 1908

By Albert Zima

ACCORDING to recently published statistics, it is predicted that as much oil must be produced during the next 16 years as has been produced during the past 75, in order to satisfy the high rate of consumption of petroleum products. During 1934, over 17,000 oil wells were completed in the United States, and it is expected that over 20,000 additional wells will be drilled during the current year. Were it not for the remarkable progress made during recent years in the improvement of drilling technique and in the development of equipment used in the production phase of the oil industry, it is doubtful whether sufficient oil could be produced to meet present requirements. A few years ago, wells seldom were deeper than 3500 to 4000 ft., owing to the limitations of the drilling methods and equipment employed. Today, however, through the application of scientific drilling methods and the adaptation of modern equipment and improved materials, many wells range from 6000 to 8000 ft. in depth, and a few recent completions exceed 10,000 feet.

Jan 1, 1935

By W. T. Malone, J. R. Williams, R. L. Tiner, J. M. Tinsley

Hydraulic fracturing methods for production stimulation have become a common procedure in the oil and gas industry. Fracturing treatments are performed on wells of various potentials to help increase the production rate. In addition to the desire for increased production is the need to predict what increase might be expected. This knowledge is useful in economical treatment planning to accomplish the desired production goals for the well. Theoretical production increases due to horizontal radial fractures may be calculated using equations developed from mathematical analyses and electrical models.1,2,6 It also is possible to predict theoretical production increases due to vertical fractures using curves developed from electrical3 and mathematical models.8 However, these studies assumed that the vertical fracture height and the formation height were equal, which may not be true." In addition, the final fracture height through which fluid is produced may not be equal to the created height. The development of vertical fracture proppant transport relationships has made unrealistic the assumption that propped fracture height is equal to created fracture height. Through the use of published proppant transport equations,4&apos;12 it is possible to calculate the height of a bed of propping agent deposited in a fracture of a given height. Assuming that the fluid flowing in the fracture moves through only the propped portion of that fracture (i.e., that the un-propped part of the fracture heals) it becomes essential to know how production increase varies with the ratio of propped fracture height to formation height. It should be recognized that future investigation may determine that the fracture does not heal completely and that a highly permeable channel exists over the deposited bed of proppant. The effect of this channel was not considered for the present study. The following analysis of experimental data allowed development of curves to determine theoretical production increases considering fracture height as a variable. Discussion In designing a fracturing stimulation treatment a number of variables must be considered. The size of the treatment, type of proppant used, proppant concentration, treatment fluid properties and well conditions are all factors affecting the dimensions and permeability of the fracture. Production increase due to a vertical fracture is affected by propped length, height, width and permeability of the fracture for a given set of formation conditions. Production increase may be defined as the ratio of production rate after fracturing to the production rate before fracturing at the same pressure differential, pe — pw. The producing rate in an

Jan 1, 1970

By W. C. Peters, M. W. Pullen, C. A. Bays

During the past three and a half years considerable improvement in the techniques of solution extraction of salt has been made by the use of wells which are cross-connected by hydraulic fracture at the base of the salt. Fracture is initiated by the application of hydraulic pressure. Underreaming and perforating techniques are used to control initiation. The fracture is then extended by continuous pumping until a pressure communication is obtained. Pressure communication is followed by washing-through to obtain a low-pressure connection. Well construction using non-shrinking cements that will bond with the salt and with associated strata is essential to the process. The connecting procedure described permits solution to attack the salt deposit from its base upward, thereby permitting greater recovery, fewer well repairs, better saturation of brine, and overall economy of development and operation. The fracture method of cross-connection requires special pumping of the fluid and is limited by present experience to initial well spacings up to about 1200 feet. The method has been used in bedded salts and is applicable for wells in salt domes. Since spring of 1956, new developnents in salt extraction wells have followed procedures substantially different from those in prior use. Although multiple well systems, connected either by the natural consequence of the solution process or by undercutting under protective pads, have been used previously, the past three and a half years have brought about new designs and new operation procedures based on cross-connection of the wells using hydraulic fracture. To date these techniques have been applied largely in the bedded salt deposits of Michigan, Ontario, Ohio, West Virginia, and New York. To the writers&apos; knowledge they have not been used in salt dome wells. The methods have not yet been in use for a sufficient period to permit any statistical comparison with the older methods. It is evident from experience to date that the methods result in higher recoveries, lower capital and operating costs, better saturation of produced brine, reduced well maintenance and repair, and in considerably fewer production units to insure

Jan 1, 1961

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By R. F. Hinds

A pressurizing system was designed and built to apply a radial pressure of 5.000 psi to rock samples. Samples of the Bradford, Weir and Kirkwood sandstones were subjected to radial pressures parallel and perpendicular to the bedding in the system and the changes in conductivity, porosity and permeability were deter-mined. Asymptotic decreases in conductivity, porosity and Klinkenberg permeability were observed over the 0- to 3,500-psi range. From these data, the increase of formation factor over the same range was calculated. The cementation exponent expressed in the Archie equation was found to increase with pressu,re. The rate of change varied from formation to formation. Only small differences were observed for samples taken parallel to the bedding as comnared to those taken perpendicular to it except for the Bradford sand. Above 3,500 psi the data are not good enough to tell if the properties continue to fall-off asymptotically or in a different manner. A possible explanation for the probable litnit of the asymptotic rate around 3,500 to 4,500 psi is that this represents the maximum pressure which the formations have unrdergone during their geological life as a result of burial. INTRODUCTION For many years measurements have been made in the laboratory of the properties of oil-bearing sandstones with little consideration being given to whether these properties had been changed when the samples were moved from their original position in the ground to the laboratory. Relatively little has been reported in the literature on the effect of pressure on the properties of sandstones. The changes in permeability for eight typical consolidated oil-bearing sandstone samples with overburden pressure (0- to 15,000-psi range) was presented by Fatt and Davis&apos; in graphical form. In 1953 Fatt&apos; also reported the relationship between porosity and overburden pressure for four typical consolidated oil-bearing sandstone samples (0- to 5,000-psi range). Fatt later described the changes of formation factor and porosity of 20 typical oil-bearing sandstone samples with overburden pressure changes (0- to 5,000-psi range) giving the values of the coefficients and exponents in the Archie&apos; equation, and the more general Winsauer equation&apos;, where C, k and m are empirical constants, F is the formation factor, and + is the porosity. During the experiments of this investigation the core was contained in a neoprene rubber sleeve as shown in Fig. 1. It was held between two steel end members which were mounted in a steel cylinder. The unassembled pressure cylinder with its component parts is shown in Fig. 2. The core was insulated from the two steel end members by a Teflon sleeve with a small hole in the

By Ott F. Heizer

The mines and the mill of the Nevada-Massachusetts Co. are on the east slope of the Eugene Mountains, in Pershing County, Nevada, 8 miles northwest of Mill City, a station on the Southern Pacific R.R. and on the Victory Highway. Fig. 1. Supplies and, concentrate are transported by truck over an automobile road of easy grade. The property is at an average elevation of 5500 ft. and climatic conditions are generally favorable for continuous operation throughout the year. The ore treated is supplied by two adjoining mines, the Stank and the Humboldt. Physical and mineral characteristics of the ores produced by these two mines are substantially similar, although variations occur in hardness and mineral distribution.&apos; The economic mineral is scheelite (CaWO4), composed, when pure, of 80.6 per cent tungstic trioxide (WO3) and 19.4 per cent lime (CaO).

Jan 1, 1935

By R. N. Edmondson, L. Mair, M. Tenenbaum

It is the policy of The Metallurgical Society to provide, in the TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME, a prompt and accurate medium for publication of reports of significant new research in both the scientific and engineering aspects of metallurgy. Papers submitted to the Society are judged by competent reviewers according to established criteria for technical merit, accuracy, originality, and presentation. STAFF: Editor, Dr. Gerhord Derge; Editorial Assistant, M. A. Redmyrski; Staff Coordinator, James J. Burke. THE METALLURGICAL SOCIETY: W. R. Hibbard, Jr., President; J. C. Kinnear, Jr., Past-President; John Chipmon, Vice President; T. D. Jones, Treosurer; R. W. Shearman, Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: A. w. Thornton, Chairman; Dennis Carney, John Chipman, J. C. Fulton I. H. Hollomon H. H. Kellogg, A. E. Lee, R. Maddin, J. D. Sullivan, and D. Swan. Review and selection of manuscripts is under the supenision of the following Publications Committees: Extractive Metallurgy Division: T. 0. King Chairman; S. J. Dickenson, R. P. Hermsdorf R. Schuhmann. Jr.. and P. T. Stroup. Institute of Metals Division: Robert Maddin, Chairman F. Lincoln Vogel Jr., Vice-chairman, W. A. Baikofen, R. W. Boliuffi J. H. Bechtold M. B. Beyer. R S. Busk, C. G. Gaetzel, Paul Gordon C. D. Groham, Jr., Robert F. Hehe-mann,&apos; R. I. Joffee, F. c. Joumot Jr lrving R. Kramer A. J. Lena Harold Morglin, C. J. McHargue, Russell A: Meussner, J. B. Newkirk H. W. Paxton, G. E. Pellissier, I. S, Servi, Alon U. Seybolt, A. J. Shaler, and Jack Washburn. Iron and Steel Division: J. C. Fulton, Chairman; T. B King, F. C. Langenberg, W. 0.. Philbrook, and T. 0. Winkler. Published bimonthly by the American Institute of Mining Metallurgical and Petroleum Engineers Inc., 29 West 39th Street, New York 18, N. Y. Telephon: pEnnsvlvanio 6-9220. Subscription 522 Per year for non-AIME members in United States and North South and Central America; $25 foreign;, $5 for AIME members. Single copies, 54.00, single copies foreign, $5.00. The AIME is not responsible for any statement made or opinion expressed In its publications . . . Copyright 1958 by the American lnstltute of Mining Metallurgical and Petroleum Engineers Inc. . . . Registered cable address AIME New York , . . lndexed in Engineering Index Industrial Arts Index and Chemical Abstrats . . . Application for second class mail privileges ii pending at New York, N. Y. Volume 212, Number 4.

Jan 1, 1959

By J. E. House, C. J. Lewis

In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-pregnant sulfuric acid leach solution is contacted with an organic extractant dispersed in kerosene; the uranium enters the organic phase and associates itself with the organic extractants. Simultaneously an-ions or cations, as the case may be, leave the organic extractant phase and enter the aqueous phase. The two phases are then allowed to separate by virtue of their immiscibility. Based on the data available, a generalized procedure for the recovery of molybdenum from the sodium carbonate scrub liquor of acid leach uranium mills using secondary and tertiary amine extractants is presented, as is another generalized procedure for the recovery of molybdenum from the bleed stream of alkaline leach uranium mill circuits. Such economic appraisal as can be made at this stage of the development is also indicated. Molybdenum occurs in most uranium ores. Whether the uranium is solubilized by the acid leach route or by the alkaline leach process, some of the molybdenum present in the ore is solubilized along with the uranium. Molybdenum in uranium mill pregant solutions may cause processing difficulties, among which may be mentioned the poisoning of resins, the precipitation of organo-molybdenum complexes, or the build-up of molybdenum in recycle streams. While the uranium milling industry has been successful in applying measures to overcome the problems arising from the presence of molybdenum in the circuits, such measures nevertheless add to the cost of producing uranium yellow cake concentrate. Table I shows the analysis of typical uranium pregnant leach solutions. Uranium recovery by solvent extraction is presently practiced only in conjunction with acid leach circuits, and it may be noted that of about 16,000 tons of uranium ore daily processed by sulfuric acid leach, more than half of this tonnage follows the solvent extraction route. Uranium mills leaching ore with sodium carbonate-sodium bicarbonate solution (the so-called alkaline leach circuit) do not use solvent extraction. In this case the uranium pregnant solution is sufficiently pure to permit the direct precipitation of uranium concentrate with subsequent recycle of the alkaline leach solution. While solvent extraction procedures may be developed which are economically attractive for the alkaline leach uranium process, this has so far not been the case. The earlier uranium mill solvent extraction circuits used organo-phosphate extraction reagents, among which di-2-ethylhexyl phosphoric acid was popular. It should be borne in mind that uranium in its sulfuric acid leach solution exists in an equilibrium involving uranium in both anion and cation forms: uo + 2S0 = [uo2(so4)2] For this reason uranium may be extracted by either cation extractors or anion extractors and this is likewise true of molybdenum. However, the organo-phosphate extractants also load ferric iron which is usually present in the uranium acid leach solution. For this reason, it is necessary to reduce this solution substantially to the ferrous state ahead of solvent extraction using organo-phosphate reagents. The amines, being anion extractors, selectively reject iron and thus render the iron reduction step unnecessary. In the solvent extraction process, also referred to as liquid-liquid extraction, the clarified uranium-

Jan 1, 1961

By H. E. Criner, M. G. Driessen

THE cyclone thickener has two important applications in wet washing plants: (1) water clarification, and (2) fine coal recovery. The thickener consists of a conical chamber into which the fluid is injected through a tangential nozzle at the periphery of the large end. The solids of the slurry are concentrated and removed from the apex of the cone while the "thinner" portion is discharged from a central tube in a flat head at the large end, fig. 1. The advantages of the cyclone thickener are that large volumes of slurry may be treated with small space requirements and that the underflow concentration may be controlled easily and readily to meet varying feed conditions. Control of Washery Water Solids Concentration: The first requirement, in the process of controlling solids concentration, is that the solids be removed from the body of circulating water at the rate at which they are introduced. If this condition is satisfied the concentration will remain at a fixed value and will not increase to uncontrollable levels. The second requirement is that the solids concentration

Jan 1, 1951

By M. G. Driessen, H. E. Criner

THE cyclone thickener has two important applications in wet washing plants: (1) water clarification, and (2) fine coal recovery. The thickener consists of a conical chamber into which the fluid is injected through a tangential nozzle at the periphery of the large end. The solids of the slurry are concentrated and removed from the apex of the cone while the "thinner" portion is discharged from a central tube in a flat head at the large end, fig. 1. The advantages of the cyclone thickener are that large volumes of slurry may be treated with small space requirements and that the underflow concentration may be controlled easily and readily to meet varying feed conditions. Control of Washery Water Solids Concentration: The first requirement, in the process of controlling solids concentration, is that the solids be removed from the body of circulating water at the rate at which they are introduced. If this condition is satisfied the concentration will remain at a fixed value and will not increase to uncontrollable levels. The second requirement is that the solids concentration

Jan 1, 1951

By D. F. Malott

The Michigan Dept. of State Highways makes extensive use of geophysics for subsurface surveying which would be applicable for uses in other fields. Examples of resistivity surveys are given which include a proposed large-volume excavation with suggestions for land use after excavation, subsurface evaluation for engineering design, and a subsurface survey for land appraisal. An example of a combined refraction seismic and resistivity survey is shown where the resistivity is used for outlining the unconsolidated soils, while the seismic method is used to outline bedrock and to evaluate it for rippability. A refraction seismic survey at the bottom of bridge caissons for evaluation of bedrock uniformity and a rehtive aid in assessing rock strength is reported. These past several years have been a period of unprecendented construction and commercial expansion. Vast private manufacturing complexes and government road, power, and office projects are being built or are in planning stages. Nearly everywhere, municipalities are expanding outward and upward. Many towns are developing into cities and many cities are displaying new skylines, and the building boom shows little sign of slowing down.

Jan 1, 1970

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&apos; 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

Map

Jan 1, 1941