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By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By I. A. Lesk

The various materials utilized in the construction of integrated circuits, and the resultant materials interfaces, are discussed with emphasis on a materials system that is compatible with all types of integrated circuits and minimizes the number of different interfaces. Problems with interfaces may originate in the silicon, on its surface, and between other materials within the integrated-circuit package independent of the silicon. ThE difference between integrated-circuit theory and practice may generally be spelled out in terms of the difficulties in fabricating a desired structure. There are, of course, problems in forming the requisite materials, of the necessary composition and geometry, where needed. A distinct class of problem, however, is associated with interfaces— generally between different materials, but occasionally between regions of the same material. We require that each interfacial system perform its proper electrical, mechanical, and thermal function, and do so in an unchanging manner with time under the most severe operating conditions. In a practical sense, we deal in nonideal systems, such that it is generally not possible to form an interface exactly the way it was intended, even if we allow for a knowledge of the practical limitations of the fabrication system. Another way of looking at this situation is to realize that, when we form a group of interfaces under apparently the same experimental conditions, there are often differences of important consequence between them. Very high-magnification pictures, such as are obtained by an electron microscope, reveal fine structure that often differs over the area of a given sample, as well as from sample to sample. Low-magnification pictures look better, but don't eliminate the problem. The trend towards integrated circuits, and away from circuits fabricated utilizing separate components, is very strong in many areas of electronics. A typical silicon monolithic integrated circuit, still in place in the wafer on which it was fabricated, is shown in Fig. 1. The increased reliability which is being experienced through the use of integrated circuits can, to a large extent, be credited to the reduced complexity of the interface system that is present in the electronic system. A glance at Fig. 1, however, with all of its epitaxial and diffused p-n junctions, and interconnect system, shows that interfaces have been far from eliminated. Fig. 2, depicting a schematic cross-sectional view of a (partial) typical integrated circuit, illustrates in detail the numerous interfaces that occur in this type of structure. Besides the individual circuit elements, there are interfaces for isolation, and, Fig. 3, even a crossover requires a series of interfaces. What has been accomplished, however, irrespective of whether or not the total number of interfaces in the circuit is increased or decreased, is that the variety of interfaces is very much reduced. This is because there are fewer materials involved. Since the expense incurred in an R & D program to improve reliability is pretty much directly proportional to the variety of interfaces involved, it is economically advisable to work with integrated circuits for highest reliability. That is not to say that circuits built using standard components could not be made as reliable as integrated circuits, but that the expense involved because of the more complex over-all interface system would be much greater. Although electronic performance utilizing integrated circuits with all silicon elements (i.e., transistors, diodes, resistors, capacitors) is adequate for many applications, there are numerous instances where thin-film passive elements must

Jan 1, 1965

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By J. E. 214-000-000-010 Warren, M. R. J. Wyllie, T. Meidav, L. Scharon, R. Uhley, A. J. deWitte

By considering the stoichiometry of the underground combustion process, an equrztion was derived relating the point velocity of the combustion front as a function of the air flux, fuel content, efficiency' of oxygen uitilization, hydrogen:carbon ratio, and ratio of carbon dioxide In carbon monoxide produced. In addition, an equation for cnlcrllating the amount of injected air necessary 10 produce the oil from I Cu. ft of reservoir space was derived. This equation has a direct bearing on evaluating compression costs for the process. Values calculated from these equations are in good agreement with experimentnlly obscrvcd values obtained from laborator) tube runs reported in the literature. The equations are also u\eful for atlcrlyzinf: experinlental data for inconsistencie.r.. I NTRODUCTION The injection of energy in the form of heat into an oil-bearing formation as a means of increasing the recovery of oil has been the subject of much discussion and experimentation as far back as 1920. The ideas have ranged from the injection of steam to the direct use of electricity as a means of getting thermal energy into a formation. However, most laboratory and field studies have been confined to the process whereby a portion of the crude in the reservoir is burned to generate the necessary heat to increase the mobility of the oil by reducing its viscosity. A recent paper by W. L. Martin, et al.', described the results of a number of laboratory experiments in which the combustion process was studied in a sandpack. Studies such as this indicate that with the temperatures involved, the oil is partially coked in this process and it is this coke which provides the fuel for combustion. The combustion of this residual coke can be analyzed theoretically by applying simple stoich-iometric principles to the combustion process. It is the purpose of this paper to compare the results reported in these experiments with those obtained from theoretical considerations. The variables studied by Martin, et al, among others, include combustion front velocity, air flux, oxygen utilization, fuel concentration, ratio of carbon dioxide and carbon monoxide in combustion gases, and the hydrogen:carbon ratio of the residual fuel. All these variables come into consideration when the stoichiometry of the combustion process is studied. The experimental conditions and results are tabulated in Tables 3 and 4 of Ref. 1. For purposes of comparison with calculated results, it was necessary to change the units of a number of the variables. UNDERGROUND COMBUSTION STOICHIOMETRY The combustion or oxidation of the carbonaceous residue or "coke" on the sand can be described in terms of the equation: where n is atomic ratio of hydrogen to carbon, m is ratio of moles of CO2 to CO produced, and CH. is taken as the unit molecular weight, realizing that actually the coke has a large range of high molecular weights. Assuming that all the fuel laid down in the sand is burned, the ratio of moles of oxygen consumed to moles of coke can be written as follows. Moles 0MolesMolescoke In terms of moles O2 per pound of coke, where 12 + n is the molecular weight in pounds per mole. If the 0, consumed is measured in standard cubic feet (60°F and 1 atm) and the coke in pounds per cubic foot of formation, 2, then:

By A. D. LeClaire

This paper claims to provide a description of diffusion processes in solids which is said to be a reformulation of Fick's Laws and therefore, presumably, is supposed to be as general as those laws. In fact, it appears to provide no more than an atomic model of a rather restricted type leading even to results in conflict with experiment. The restriction lies in the assumption, carried throughout the paper, that even in a chemical gradient the jump frequency i of an atom of species i is a function only of the composition on the plane from which it jumps, i.e., ?i = ?i(cl, c2 ...). This means that atom jumps in opposite directions from a site would occur with equal probability. There would then be no tendency for atoms to migrate preferentially in one direction along the gradient, so the model is incapable of accommodating the well established phenomenon of atom drift in a chemical gradient.10-" A more general model that does not suffer this difficulty was discussed in a paper13 I wrote in 1958, and the results therein already contain as a special case those given by Dr. DeHoff. The simplest sufficiently general assumption is to suppose that ?i is a function ?i(a1 a2,...; wl, w2, ..-) of the concentration aj and ? ?j at the site from which and to which, respectively, a jump is made. Any such function can always be expressed as a function of the sum and difference of its arguments. Thus d is the jump distance and g a geometrical constant. Obviously this is zero, i.e., no drift, if ??ri/??j = 0. X is written in this form, revealing two components of the total drift, because it can be shown that only the second component, depending on ??'i/???(?j -aj), actually contributes to the net diffusion flux Ji. This component can be shown,13 by a straightforward ther-modynamic transcription, to be responsible for the so called "thermodynamic factor" in the Darken approximation for a chemical diffusion coefficient is the activity coefficient of i. Because the jump rate ?i in DeHoff's approximation has no dependence on the concentration gradient it does not seem possible to derive the Darken equation from his Eq. [6] without the further rather arbitrary assumption that ?i = const ri. It is to be noted too that the author's derivation of Eq. [12] is only valid when ?i is in fact a function only of the cj at the plane from which the atom jumps—for only then is ci?i a unique function of position and therefore of A. Author's Reply R. T. DeHoff I am indebted to Dr. LeClaire for his penetrating discussion of my paper, "A Reformulation of Fick's First Law". I concede that it does appear initially that the relationship presented in my paper could be derived from the detail atomic model of random walk and atom drift presented in Dr. LeClaire's approach. However, there are some important differences in concept and viewpoint which deserve further amplification. Dr. LeClaire's description is penetrating, detailed, and fundamental. His approach describes an extremely complex phenomenon, the displacement of atoms in a multicomponent gradient, at a sophisticated level. For precisely these reasons, his analysis has not proved to be useful for experimental studies that have practical objectives. For example, in order to obtain the information required to complete the analysis of the jump frequency distribution in a ternary system, the following series of experiments would, I believe, be required: 1) chemical (gradient) experiments, covering the composition range;

Jan 1, 1970

By Ralph E. Esarey, Robert G. Reno

DriLLing activity and prospecting for oil and gas increascd in Indiana in 1941 over the previous year. The greater part of the drilling and development continued to centralize in the Indiana portion of the Interior Coal Basin, in the southwestern part of the state, but other parts of the state were not neglected. Many wildcat wells were drilled, including a series of core tests through the mantle of drift on the southern flank of the Michigan Basin. These core tests have been followed by several unsuccessful production tests. Production tests were made also along the axis of the Logansport-Kankakec branch of the Cincinnati Arch. In all, 411 field locations and 141 wildcat wells were completed in Indiana during 1941; that is, a total of 552 wells, an increase of 3 2 wells over the previous year. The field tests resulted in 260 oil wells, 57 gas wells, and 94 dry holes; wildcats included 16 oil wells, 3 gas wells and 122 dry holes. At the end of the year, 53 field wells and 34 wildcats were drilling. Gibson and Posey Counties led the state, with 154 and 155 wells drilled, respectively. However, 125 wells produced oil in Gibson County, while 98 produced oil in Posey County. Twenty-five per cent of all wells drilled were wildcat; II per cent of these produced oil and 5 per cent produced gas. Grifin field continued to lead in drilling activity, with 157 successful wells and 20 dry holes (including important wells defining the field). Production is found in five pay zones (Tar Springs, Waltersburg, Elwren, Aux Vases and McClosky). It produced a major part of Indiana's estimated 7,200,000 bbl. of oil during the year. Heusler field, Posey County, expanded with 11 oil ells and 4 dry holes in the Waltersburg and Tar Springs. Vienna field, Posey County, completed four oil producers in the Mansfield sandstone, between 1200 and 1250 ft. The College field, discovered late in 1940, received three oil producers and two dry holes in the Aux Vases. Two new fields were discovered in Posey County during the year: Lamott pool, in the Tar Springs, at 1950 ft., had initial production of 55 bbl. on discovery. One producer and one dry hole have been drilled since. Mt. Vernon pool found saturation in both the Waltersburg and Cypress formations. The discovery well tested about 1000 bbl. per day; it tested the McClosky at 2764 ft. Seven producers have been drilled since the October discovery. Welborne-Switch pool found oil in the Cypress sand at approximately 2500 ft., with an initial production of 33 bbl. One more well in the area proved a dry hole. Gibson County had the following discoveries in 1941: The Patoka field was opened by a McClosky producer of 300 bbl. Another producing well has been drilled. An attempt was made to extend the Illinois Mt. Carmel field into Gibson County, Ind., and one producer of 24 bbl, was completed on the Indiana side. A dry hole has since been drilled, one location south. One small well was completed in the Mans. field at 1105 ft. in sec. 31, T.2 S., R.12 W., Gibson County promising a new field

Jan 1, 1942

By Robert G. Reno, Ralph E. Esarey

DriLLing activity and prospecting for oil and gas increascd in Indiana in 1941 over the previous year. The greater part of the drilling and development continued to centralize in the Indiana portion of the Interior Coal Basin, in the southwestern part of the state, but other parts of the state were not neglected. Many wildcat wells were drilled, including a series of core tests through the mantle of drift on the southern flank of the Michigan Basin. These core tests have been followed by several unsuccessful production tests. Production tests were made also along the axis of the Logansport-Kankakec branch of the Cincinnati Arch. In all, 411 field locations and 141 wildcat wells were completed in Indiana during 1941; that is, a total of 552 wells, an increase of 3 2 wells over the previous year. The field tests resulted in 260 oil wells, 57 gas wells, and 94 dry holes; wildcats included 16 oil wells, 3 gas wells and 122 dry holes. At the end of the year, 53 field wells and 34 wildcats were drilling. Gibson and Posey Counties led the state, with 154 and 155 wells drilled, respectively. However, 125 wells produced oil in Gibson County, while 98 produced oil in Posey County. Twenty-five per cent of all wells drilled were wildcat; II per cent of these produced oil and 5 per cent produced gas. Grifin field continued to lead in drilling activity, with 157 successful wells and 20 dry holes (including important wells defining the field). Production is found in five pay zones (Tar Springs, Waltersburg, Elwren, Aux Vases and McClosky). It produced a major part of Indiana's estimated 7,200,000 bbl. of oil during the year. Heusler field, Posey County, expanded with 11 oil ells and 4 dry holes in the Waltersburg and Tar Springs. Vienna field, Posey County, completed four oil producers in the Mansfield sandstone, between 1200 and 1250 ft. The College field, discovered late in 1940, received three oil producers and two dry holes in the Aux Vases. Two new fields were discovered in Posey County during the year: Lamott pool, in the Tar Springs, at 1950 ft., had initial production of 55 bbl. on discovery. One producer and one dry hole have been drilled since. Mt. Vernon pool found saturation in both the Waltersburg and Cypress formations. The discovery well tested about 1000 bbl. per day; it tested the McClosky at 2764 ft. Seven producers have been drilled since the October discovery. Welborne-Switch pool found oil in the Cypress sand at approximately 2500 ft., with an initial production of 33 bbl. One more well in the area proved a dry hole. Gibson County had the following discoveries in 1941: The Patoka field was opened by a McClosky producer of 300 bbl. Another producing well has been drilled. An attempt was made to extend the Illinois Mt. Carmel field into Gibson County, Ind., and one producer of 24 bbl, was completed on the Indiana side. A dry hole has since been drilled, one location south. One small well was completed in the Mans. field at 1105 ft. in sec. 31, T.2 S., R.12 W., Gibson County promising a new field

Jan 1, 1942

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,' the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968

By C. Perez-Rosales

A simplified method for evaluating specific surface of porous media is described. The theory takes as its point of departure a previous statistical method. Due to its simplicity, it is considered that the proposed method has certain advantages over methods currently used. By making some simplifications, the procedure for estimating specific surface is reduced to superposing, on an enlarged reproduction of a section of the sample to be analyzed, an evenly spaced grid and counting the number of intersections of the grid lines with the perimeter of pores. An indirect test of the theory is presented and the advantages of the method are discussed. INTRODUCTION The specific surface of a porous medium, defined as the surface area of the pores per unit bulk volume, is an important parameter with regard to flow of fluids through porous materials. In particular, it has long been recognized that specific surface is closely related to permeability. Since the internal surface of any porous material is extremely complex, the measurement of specific surface can only be accomplished by indirect means. It is considered that the best method' in current use for determining specific surface is the statistical method of Chalkley, Cornfield and Parka who originally applied it for estimating volume-surface ratios of morphologic components, such as cells or nuclei. This method will be outlined later. A method which has been used extensively in determining specific surface is based on the adsorption of a vapor by the internal surface of porous media. However, this method does not yield the surface pertinent to fluid flow, since it includes the tiny molecular interstices which do not influence the permeability of the porous material.' This method has been employed by Brooks and Purcell measure internal surface area of sedimentary rocks. The Kozeny equation, which relates the specific surface to the permeability of a porous medium, has found wide use in determination of specific surface. However, the KOzeny equation is not strictly correct. Large discrepancies have been found between theory and experiments.' Consequently. the specific surface estimated by this method is subject to serious uncertainties. Finally, there are other methods for specific surface measurements which are based upon a variety of physical and chemical properties: the heat conduction by a gas, ionic adsorption phenomena and direct chemical reactions of the surface with other substances. This paper describes a simplified statistical method for determining specific surface of porous materials. It is considered that, due to its simplicity, it has certain advantages over the methods presently used. For its validity, it is required that the porous structure of the material under study be of a spatially random nature. This is not a serious limitation since the naturally occurring porous media have this characteristic. THEORY The method proposed in this paper takes as its point of departure the interesting result obtained by Chalkley et al The method shows that if a line of length r is dropped repeatedly at random over a section of a porous medium, and counts are made of the number of times the two end points fall within pore areas (denoted by h for "hits") and the number of times the line intersects the perimeter of pores (denoted by c for "cuts"), then in a very large number of throws where S is the internal surface of the sample (surface of pores) and V, the volume of the pores (Fig. 1). Since the specific surface S, and the porosity 4 are given, respectively, by S. = Sl V, and 4 = V,l V,, where V, is the total volume of the sample, it follows from Eq. 1

A Page Adam. H. F. and Ruggles! G. H., Results with Xanthate at Inspiration............. 337 Adnic proertiea of....................... 474 Africa; Gold Coast, manganese...........abs.474 191 mining districts......................... 254 Aid, H., biography........................ 154 Air compressors. In flotation................ 45 Air-gas lift: gae-oil ratios relation of......abs. 475 Gulf Coast. mechanical installations... .abs. 475 Seminole field........................abs. 476 Air-sand process. cleaning coal............abs. 89 Alabema, Birmingham district. drainage. . abs. 86 " Alclad." aluminum alloy................. 395 Alexander. W. Homer. biomaphy .......... 37 Allen. Andrews. Preparing Coal after Mechanical Loaders......:....T................. 181 Allison. F. H., Comparison of the Effect of Nickel and Cobalt in Steel.............aha. 151 Alloys: See Metals named. 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Jan 1, 1927

By D. Mills, G. B. Craig

The defortnaliotz of zirconicltt single crystals conlaining osygen in the range 740 to 6800 atom parts per nilllion was esanined oc7er the range 77" to 950°K. An anctlsis of the dqfarmaliotz parameters leads to the cotcllsiotr that the rale -cotzfrolling thermally activated dqivr,irrtion process oe-r /he range 77" to 560°K is oc.crco,ling osvgen alotns. A thermally actitaled defor,ilntion process is not found between 600" and 800", but does occur aboz%e 800°K. THE present investigation was undertaken to measure the effects of controlled amounts of oxygen on the deformation parameters of a zirconium single crystals over the temperature range 77" to 950°K and to determine the rate-controlling mechanisms. Although there is no doubt that the mechanical properties of the group IV metals, titanium, zirconium, and hafnium, are strongly influenced by the interstitial impurities oxygen, nitrogen, carbon, and hydrogen, there are many conflicting theories as to the role played by the interstitials during the deformation proess.'- There is general agreement that the mechanisms which control plastic flow in a metal impose characteristic values on such parameters as the flow stress and its temperature dependence, the activation volume, and the activation energies. These parameters will be used to analyze the deformation mechanisms. eltham,' Sargent,16 and ibbs' have shown that the stress relaxation technique allows the activation volume characteristic of the deformation process to be found during the course of a simple tension test. In many cases it is found that the relaxation of stress is logarithmic with time and obeys a relationship of the following form: T-T = AT =S logl0(qt + C) [I] where t, is the shear stress at the start of the relaxation test, t is the shear stress at time t, and S. q, and C are experimental constants, and S is the strain rate sensitivity of the stress t as shown in the appendix. The slope found from a semilogarithmic plot of At vs time is approximately equal to S. The activation volume u, association with the deformation process, is found from the following relationship: The theoretical treatment of thermally activated plastic flow due to schoeck18 shows that the activation volume when combined with the temperature dependence of the flow stress gives the activation energy for the process according to equations: seegerZ3 considers that the flow stress at lower temperatures ld is composed of two parts such that Tapplied = tinternal + Teffective , where Teffective 3 ff , is the stress necessary to overcome the local obstacles to deformation and Tinternal, ri, is the stress necessary to overcome the long-range elastic stress field of dislocations on other planes. ri is considered to be largely elastic in origin and can be estimated from the stress value at the temperature independent portion of the flow stress-temperature curve. EXPERIMENTAL The crystal bar zirconium used in this investigation was supplied by Wah Chang Corp. whose certified analysis gave the following impurity contents in parts per million by weight: oxygen, 150; nitrogen, 10; iron, 180. All others were less than 100 ppm. The oxygen and iron contents were confirmed by neutron activation and chemical analyses, respectively. Single crystals were grown in an electron beam furnace according to the method of Wilson and Pickle-simer'' and ills.'' The orientation of the crystals was such that the specimen axes were located in the lower third of the standard section of the basal plane stereographic projection for zirconium. This orienta-

Jan 1, 1969

R,. P. JaRvis,* El Oro, Estado de México, México.—The practical problem raised by Mr. Wisser—that is, the determination of the lower limit of ore deposition, below which it is useless to look for ore shoots—is one of the most important in economic geology. He asks: "Can we learn to determine the position of such a line?" For individual districts, yes; but its determination has always been by empirical methods; that is by actually exploring the veins to such depths that the values drop below the economic limits. Usually the signs are plain enough that values have been bottomed without confirmation by the chemist or assayer. Most veins, when approaching their limit, begin to split into branches or stringers; the vein matter itself undergoes a change from "lively looking" rock to one that is dull and unpromising, the quartz, instead of having segregated into clean vein matter, has simply spread itself into the country rock, rendering this more siliceous but no richer—these, together with inclusions of the country rock in the vein, are all positive indications of the limit. Mr. Wisser seems disposed not to accept the law of cause and effect, which he calls "empiricism." He says: "Empiricism embodies an assumption perhaps not evident at first glance. It is this: that like effects spring from like causes and therefore necessarily have a common meaning." There can be no doubt as to the validity of this law, since it is the foundation stone upon which are built all inductive sciences, including economic geology. When demonstrable, proved facts become confused with inferences, as they seem to be generally in the paper under examination, no sound conclusions can be reached. Mr. Wisser has failed to give sufficient data covering the two vein systems which he cites as examples. Presumably they are situated in the Pachuca District of Mexico, but not everybody is familiar with the vein systems there in spite of the fact that it is world famous as a silver producer. Are these two systems separated some distance horizontally from one another and how far? He has given no estimate of the amount and kind of rock that has been eroded from over the present veins. His description of the two systems appears on page 100, beginning: "1. East-west veins," and ends on page 101, "they would lack spaces there in which to deposit." On page 101, with the paragraph beginning "On the other hand," he gives a picture of what he believes takes place in class 2 veins. The sum of this seems to be, according to Mr. Wisser's observations, that, in the east-west veins, class 1, there has been an invasion of an "altering solution," which I judge has been responsible for the formation of extensive "alteration haloes"; that these alteration solutions have followed along pre-existing fractures or fissures; and that after these alteration solutions finished their work the mineralizing solutions deposited the vein matter and metallic values. Mr. Wisser does not specify clearly what the "alteration haloes" consist of; in other words, what change the original rock has suffered, whether oxidizing, carbonating, or sulphidizing. If they came from depth they could not be oxidizing or carbonating, and in this case it is a bit

Jan 1, 1941

R,. P. JaRvis,* El Oro, Estado de México, México.—The practical problem raised by Mr. Wisser—that is, the determination of the lower limit of ore deposition, below which it is useless to look for ore shoots—is one of the most important in economic geology. He asks: "Can we learn to determine the position of such a line?" For individual districts, yes; but its determination has always been by empirical methods; that is by actually exploring the veins to such depths that the values drop below the economic limits. Usually the signs are plain enough that values have been bottomed without confirmation by the chemist or assayer. Most veins, when approaching their limit, begin to split into branches or stringers; the vein matter itself undergoes a change from "lively looking" rock to one that is dull and unpromising, the quartz, instead of having segregated into clean vein matter, has simply spread itself into the country rock, rendering this more siliceous but no richer—these, together with inclusions of the country rock in the vein, are all positive indications of the limit. Mr. Wisser seems disposed not to accept the law of cause and effect, which he calls "empiricism." He says: "Empiricism embodies an assumption perhaps not evident at first glance. It is this: that like effects spring from like causes and therefore necessarily have a common meaning." There can be no doubt as to the validity of this law, since it is the foundation stone upon which are built all inductive sciences, including economic geology. When demonstrable, proved facts become confused with inferences, as they seem to be generally in the paper under examination, no sound conclusions can be reached. Mr. Wisser has failed to give sufficient data covering the two vein systems which he cites as examples. Presumably they are situated in the Pachuca District of Mexico, but not everybody is familiar with the vein systems there in spite of the fact that it is world famous as a silver producer. Are these two systems separated some distance horizontally from one another and how far? He has given no estimate of the amount and kind of rock that has been eroded from over the present veins. His description of the two systems appears on page 100, beginning: "1. East-west veins," and ends on page 101, "they would lack spaces there in which to deposit." On page 101, with the paragraph beginning "On the other hand," he gives a picture of what he believes takes place in class 2 veins. The sum of this seems to be, according to Mr. Wisser's observations, that, in the east-west veins, class 1, there has been an invasion of an "altering solution," which I judge has been responsible for the formation of extensive "alteration haloes"; that these alteration solutions have followed along pre-existing fractures or fissures; and that after these alteration solutions finished their work the mineralizing solutions deposited the vein matter and metallic values. Mr. Wisser does not specify clearly what the "alteration haloes" consist of; in other words, what change the original rock has suffered, whether oxidizing, carbonating, or sulphidizing. If they came from depth they could not be oxidizing or carbonating, and in this case it is a bit

Jan 1, 1941

The papers discussed in the following pages were presented during two sessions of the Geophysics Education Committee of the Mineral Industry Education Division on Feb. 17 and 18, 1941. At the first meeting, to consider the "Influence of Geophysics upon Geology Curricula," this Committee was joined by the Geophysics and Mining Geology Committees of the A.I.M.E., the Society of Economic Geologists, representatives of the American Geophysical Union, and delegates from the Committees on College Curricula and on Applications of Geology of the American Association of Petroleum Geologists. Quentin D. Singewald and Sherwin F. Kelly presided. At the ensuing session, especially emphasizing the integration of geology, physics and chemistry for the solution of earth problems, the joint participants with the Geophysics Education Committee were the Geophysics Committee, and representatives of the American Geophysical Union and of the Committee on College Curricula of the American Association of Petroleum Geologists. Richard M. Field and W. R. Chedsey presided. In the following summary of the discussion at the two meetings, written discussion submitted subsequently is not differentiated from that offered orally at the session. A provisional report of the Geophysics Education Committee was presented at the second session, and some of the following discussion refers to it. This report has not been printed (it is anticipated that a more comprehensive, final one will be rendered at the 1942 annual meeting), but a few mimeographed copies of this provisional report are at the A.I.M.E. headquarters and will be mailed on request. . Dr. W. P. HAYNES presented some notes prepared by Dr. F. H. LAHEE, Chairman of the American Association of Petroleum Geologists' Committee on College Curricula. This Committee's inquiries reveal the general opinion that a four-year academic preparation is inadequate, five or six being advisable. The fundamentals, mathematics, physics, chemistry, and English composition, should be stressed in the first three years, with specialization in the last two or three years. Some companies provide an apprenticeship period, and themselves give additional training.. During academic years more attention needs to be given to engineering training, to field mapping, and in geology to stratigraphy and sedimentation. The amount of mere memory work should be cut, and men trained to observe and reason. Dr. Lahee emphasized the need of more adequate preparation in English composition, because of the inability of many graduates to compose acceptable reports. SHERWIN F. KELLY pointed out that much time in university training, which ought to be devoted to technical subjects, was taken up with English courses. He emphasized that it is the part of the universities to demand of the high schools that the students they send to the university be properly trained to speak and write English. Prof. W. T. THOM protested against the crowding of high-school material into already overcrowded college curricula. C. E. DOBBIN, chairman of the Committee on Applications of Geology of the American Association of Petroleum Geologists, described briefly the work of his committee in publicizing geology, and said that it found a widespread popular interest in the subject but a lack of appreciation of its importance. He recommended that attempts to coordinate the works of geologists and geophysicists be expanded somewhat, toward the further developing and encouraging of a "species of geopolitician" capable of assisting the progress of geology and geophysics by more vigorous advertising of

Jan 1, 1941

By E. W. Davis

About a year ago several carloads of magnetite ore from New York state were sent to the Mines Experiment Station at the University of Minnesota for grinding and concentration tests. The flowsheet used minus ½-in. ore as feed to a 3 by 3-ft. overflow cylindrical ball mill operating at 37 r.p.m. in closed ciruit with a vibrating screen. The screen oversize was returned to the mill for further grinding and the screen undersize was concentrated magnetically. Several different screens, between 8 and 35 mesh, were used and it was desired to determine the capacity of the ball mill operating in closed circuit with each screen. From earlier tests using this flowsheet and equipment, it was known that when comparatively coarse screens were used it was necessary to increase the grinding dilution in the mill beyond that ordinarily used when grinding in closed circuit with classifiers. It was also known that after the circulating load had passed about 100 per cent of the original feed it tended to increase rapidly in amount, and grinding conditions appeared to become unstable. These conditions may be peculiar to this small ball mill but they were very marked in this series of tests. If conditions were not right, the mill would suddenly "go dead," and it was found desirable to operate so that the occasional rattle of balls against the lining of the mill could be detected. As the test proceeded, it was found that the cure for almost any difficulty that developed in the grinding circuit was to add more water to the mill feed. To begin with, the mill was operated at pulp densities of from 60 to 65 per cent solids but gradually it was found that with higher dilutions grinding conditions were more stable and the ball-mill power per ton of screen undersize decreased. Actually, the most satisfactory operating conditions were secured with a pulp density of about 40 per cent solids. The ore was hard but it was possible to grind ½-in. feed so that all would pass an 8-mesh screen with a power expenditure in the ball mill of less than 2½ kw-hr. per ton and with a circulating load of less than 50 per cent. With so high a dilution in the feed to the mill, it was feared that steel wear would be very high. However, the mill was not noisy, and in order to find exactly the grinding conditions, a special test was made at the end of the main series of tests. After the mill had been in operation for several hours and grinding conditions had become balanced, the power to all the equipment was shut off at a given signal. The ball mill made about one revolution after the power was turned off, and just as soon as the mill stopped, a spout was placed at the discharge trunnion and all of the pulp that flowed out of the mill was caught in tanks. The manhole in the mill was then opened and the whole mill charge dumped into other tanks. Both of these products were weighed, dried, and weighed again. The balls were screened out and weighed, and the dry solids were sized. In this way it was possible to determine the nature of the pulp and the ore within the mill under actual grinding conditions.

Jan 1, 1947

By Stephen Royce

[PAGE Ground Movement Adjacent to a Caving Block in the Climax Molybdenum Mine (TP 2000 by JOHN W. VANDERWILT, Min. Tech., May 1946. Discussion by STEPHEN ROYCE and the Studies of the Design of Shaped Explosive Charges and Their Effect in Breaking Concrete Blocks (TP 2157 by GEORGE B. CLARK, Min. Tech. May 1947. Discussion by PHILIP B. BUCKY, V. H. CLARK, E. D. GARDNER, M. H. HAWKINS, H. L. WALKER, and the author) 2 See TP 2377, Min. Tech., May 1948 for discussion of San Manuel ProsPect (TP 2255 by H. J. STEELE and G. R. RUBLY, Min. Tech., Sept. 1947. Discussion by L. KENNETH WILSON, ELDRED D. WILSON and the authors)] Ground Movement Adjacent to a Caving Block in the Climax Molybdenum Mine STEPHEN ROYCE•-It is interesting to note from B, Fig 2, how closely the subsidence limits approximate to the 60° angle of draw, which is so commonly found to rule in large scale rock subsidence. The tension cracks shown at B are commonly found in the initial stages of subsidence movement and spread like a halo about subsidence limits as movement extends. These tension cracks usually grow into escarpments later on. Apparently from the illustrations and description given, a system of vertical fractures is the predominating weakness in the wall rock at Climax, and therefore both tension cracks and escarpments are prevailingly vertical in attitude. The illustrations in Mr. Vanderwilt's article seem to conform to the general rule that yield by subsidence is heralded by tension cracks which foreshadow the appearance of the subsidence scarps which are both described in the paper and shown in Fig 2. The difference between the B side and the A side of Fig 2 is apparently caused mainly by the vertical fracturing which controls subsidence at Climax as compared to the relatively homogeneous rock formation at A upon which the original figure in Peele's Handbook was based. The draw at B is exactly 60°, while the draw at A is a little flatter. The influence of the vertical fractures explains the difference. The surprising feature is the relatively small deviation from the general 60° draw line, which is about the average of rock subsidence experience. The influence of local fracture systems, faults and bedding in controlling subsidence all the way from extremely low angles of draw to vertical is rather fully discussed in the Peele's Handbook article referred to. The more illustrations of subsidence there are published the better will be our knowledge. The general principles are pretty well established. The wide local differences reflect the effect of local conditions. This paper is a very valuable contribution to the subject, and for the benefit of the mining industry, it is to be hoped that there will be many more such clear and concise presentations. Particularly block caving is apt to be of greatly increasing importance in the future of a mining industry that must meet high labor costs. More examples of block caving from small scale to large scale operations like those at Climax will serve a vital need. JOHN W. VANDERWILT (author's reply)-I would like to thank Mr. Royce for his discussion; however, in his comments the meaning of subsidence, draw and tension cracks is not entirely clear. As used in my discussion of subsidence at Climax, subsidence refers to movements involving appreciable downward displacement. Tension cracks indicate only

Jan 1, 1947

By L. W. Saperstein, D. Yeung, L. B. Phelps

Introduction The success of preventive methods for the mitigation of coal mine drainage formation will require a marriage of the minimization of initial coal mine drainage formation, the minimization of toxic fluid formation after toxic material disposal, the minimization of the mobilization and transpor¬tation of formed toxic fluids, and the maximization of the rate of diultion and attenuation of the formed toxic fluids. This paper contributes to the understanding of factors af¬fecting mobilization and dilution and attenuation of formed toxic fluids. When water containing a salt content different from in situ pore water in the soil is passed through a body of soil, the concentration of salts in the outflow will gradually change composition in a manner that depends on the kinds of hydraulic processes that occur in the soil. These processes are molecular diffusion, lateral dispersion, longitudinal dispersion, chemical reactions or exchange, physical adsorp¬tion, and biological retardation. This note considers only the first three processes. These three microscopic processes can be analyzed statistically on a probability basis. Such results, confirmed experimentally, indicate that a tracer introduced instantaneously as a point source will tend to form a Gaussian normal distribution as it moves downstream (Todd, 1964). Dilution During Flow The closed-form soltuion for pulse or instantaneous injec¬tion of a tracer during confined flow in a homogeneous porous medium shows that the maximum tracer concen¬tration at a point in space, x, after the time interval, t*, is given by [ ] where Aa is the effective flow cross-sectional area; A is the column cross-sectional area; a is soil porosity; M is mass of the injected tracer; C is concentration of the tracer in the permeating fluid and is a function of x and t*; D is the longitudinal dispersion coefficient; and va is the interstitial fluid velocity (Klotz and Moser, 1974). Therefore, the following conclusion can be made: • For a medium with a constant longitudinal dispersion coefficient, D, a constant soil porosity, a, a constant cross¬sectional area, A, and a fixed mass of injected tracer, M, Cmax will decrease as the time of peak outflow concen¬tration t* increases. • For a medium with a constant longitudinal dispersion coefficient, D, a constant soil porosity, a, a constant cross¬sectional area, A, a fixed mass of injected tracer, M, and a constant interstitial fluid velocity, va Cmax will decrease as the distance of travel, x, increases. • For a medium of constant cross sectional area, A, con¬stant soil porosity, a, a constant mass of injected tracer, M, and a fixed distance of travel, x, Cmax will decrease as D/va increases. Klotz and Moser (1974) concluded that D is about proportional to no.3 where r) is the kinematic viscosity; D is about proportional to a-3 where a is soil porosity; D in¬creases with increasing grain size; D increases as grains become less spherical; D increases with greater grain rough¬ness and angularity; D increases with increasing uniformity coefficient; and D is significantly affected by grain size and uniformity coefficient. The remaining parameters are not significant. Numerical Simulation Studies Numerical simulation studies were used to investigate the nature of flow and the optimum length of a toxic package within a saturated porous medium of fixed dimensions and configuration (Fig. 1). The width and position of the package was maintained constant (Phelps et al., 1981). Results indicate that if the package extends throughout the length of the model, the flow is vertically downward and

Jan 1, 1984

By Wei-Kao Lu

A general rate equation is derived for gas -solid reactions in metallurgical processes by considering the contributions of chemical reaction at inter-phase boundaries and diffusion through the solid product layer simultaneously. This equation takes care of the whole range continuously from purely diffusion control to purely chemical reaction control. The parabolic law,' McKewan's equationa derived with the assumption of interface area control and the equation derived by Kawasaki et al. with the assumption of purely diffusion control are found as the limiting cases of the corresponding forms of the general rate equation. Many metallurgical processes involving gas-solid reactions have been extensively studied. The common examples of these processes include the reduction of oxides to metallic products, the roasting of sulfides to oxides or chlorides and the oxidation of metals. Gas-solid reactions consist of at least two kinds of steps; one involves the transport of reactant and product to and from the reaction zone and the other is the chemical reaction taking place at the interphase boundaries. In the limiting cases one or the other of the above mentioned steps will be much slower than the other and is then rate controlling. For example, the oxidation of metals is diffusion controlled and obeys the parabolic law.' On the other hand, if the diffusion rate is much larger than the chemical reaction rate then it will be controlled by the chemical reaction rate. This latter case occurs for the reduction of iron oxides studied by McKewan. If the rate of diffusion and of the chemical reaction have the same order of magnitude, a more detailed analysis is necessary. Thus at the beginning of the reaction when the solid and gaseous reactants are in direct contact, the reaction should be chemical reaction rate controlled as no diffusion process is involved. At the other extreme as the reaction zone moves further into the solid, the diffusion distance becomes greater and the diffusion rate continuously decreases. Eventually, therefore, for a sufficiently large sample the rate must become diffusion controlled. As the transition from one controlling step to the other must be continuous, we cannot describe this transition period by either of the two limiting cases. In this paper the author attempts to derive a general rate equation for gas-solid reaction systems. This is effected by considering the rates of diffusion and chemical reaction simultaneously from the state of pure diffusion control to pure chemical reaction control. I) DERIVATION The system under consideration is made of at least three phases, namely the gaseous one, the solid reactant, and the solid product as shown in Fig. 1. The notations are listed at the end of the paper. The mass transfer process involves the diffusion of reactants and products across the solid product layer. It is reasonable to consider that no chemical reaction will take place in the solid product layer with respect to both gaseous reactant and product. For the characteristics of local equilibrium of the system, the diffusion process is really in a quasi-steady-state. It will be proved in the following paragraphs. Then we can invoke the law of conservation of mass valid for all chemical species passing through the layer. The solid reactant sphere has an initial radius, ro, after a fraction of completeness of the reaction, the unreacted core has a radius ri, where r, is in the solid product region. Let Cg be the activity of gaseous reactant in the

Jan 1, 1963

By E. W. Davis

About a year ago several carloads of magnetite ore from New York state were sent to the Mines Experiment Station at the University of Minnesota for grinding and concentration tests. The flowsheet used minus ½-in. ore as feed to a 3 by 3-ft. overflow cylindrical ball mill operating at 37 r.p.m. in closed ciruit with a vibrating screen. The screen oversize was returned to the mill for further grinding and the screen undersize was concentrated magnetically. Several different screens, between 8 and 35 mesh, were used and it was desired to determine the capacity of the ball mill operating in closed circuit with each screen. From earlier tests using this flowsheet and equipment, it was known that when comparatively coarse screens were used it was necessary to increase the grinding dilution in the mill beyond that ordinarily used when grinding in closed circuit with classifiers. It was also known that after the circulating load had passed about 100 per cent of the original feed it tended to increase rapidly in amount, and grinding conditions appeared to become unstable. These conditions may be peculiar to this small ball mill but they were very marked in this series of tests. If conditions were not right, the mill would suddenly "go dead," and it was found desirable to operate so that the occasional rattle of balls against the lining of the mill could be detected. As the test proceeded, it was found that the cure for almost any difficulty that developed in the grinding circuit was to add more water to the mill feed. To begin with, the mill was operated at pulp densities of from 60 to 65 per cent solids but gradually it was found that with higher dilutions grinding conditions were more stable and the ball-mill power per ton of screen undersize decreased. Actually, the most satisfactory operating conditions were secured with a pulp density of about 40 per cent solids. The ore was hard but it was possible to grind ½-in. feed so that all would pass an 8-mesh screen with a power expenditure in the ball mill of less than 2½ kw-hr. per ton and with a circulating load of less than 50 per cent. With so high a dilution in the feed to the mill, it was feared that steel wear would be very high. However, the mill was not noisy, and in order to find exactly the grinding conditions, a special test was made at the end of the main series of tests. After the mill had been in operation for several hours and grinding conditions had become balanced, the power to all the equipment was shut off at a given signal. The ball mill made about one revolution after the power was turned off, and just as soon as the mill stopped, a spout was placed at the discharge trunnion and all of the pulp that flowed out of the mill was caught in tanks. The manhole in the mill was then opened and the whole mill charge dumped into other tanks. Both of these products were weighed, dried, and weighed again. The balls were screened out and weighed, and the dry solids were sized. In this way it was possible to determine the nature of the pulp and the ore within the mill under actual grinding conditions.

Jan 1, 1947

By Mary Barrett, Walter Rose

INTRODUCTION The conventional way to program reservoir problems* for solution on the electric analyzer1 is one which concentrates the block units towards the inner radius of the prototype system being represented by the analog model. This is achieved by the device of considering block units of equal value radial resistance, leading to the consequences: (1) the ratio of the external to the internal radius of each block unit is a constant (i.e. r1/ri-l = constant a); (2) the external radius of the nth block unit is equal to the innermost radius of the system times the constant a raised to the nth power: (3) the capacitance of the block units increase by a factor of a2 going out radially from the innermost to the outermost boundaries of the system; (4) given n block units in the radial direction, the capacitance ratio of the outermost to the innermost block unit is a (2n-2); and (5) the vertical resistance of the block units decrease by a factor of a going out radially from the innermost to the outermost boundaries of the system, such that the ratio of the maximum to minimum vertical resistance is also given by the factor a(2n-2) PRESENT PROGRAMMING METHOD While this conventional way of programming problems is quite adequate for routine uses of the electric analyzer, it leads to difficulties in those cases where the inner radius of the prototype system (e.g., the well-bore) is small compared to the external radius (e.g.. the external reservoir boundary). To handle such a case by the conventional method would require either that a large value be selected for the constant a or that a large number n, of radial block units be chosen. In consequence, the capacitance and vertical resistance ratios become impossibly large, as will be evident from the relations given above. In any event, the size of the smallest and largest capacitors will always be limited by the size of commercially available components, and the analyzer itself will determine how many mesh points are available for radial block units. For example, it can be shown that if the maximum capacitance ratio which can be electrically handled is a factor of l04, the maximum external radius of the system which can be considered (assuming an internal wellbore radius of 0.25 ft is: It is thus seen that in direct consequence of having the inner wellbore radius small compared to the external radius, models extending beyond 30 to 40 ft are not possible when the capacitance ratio is limited to l04. (NB. A value of 10-9 farads can perhaps be taken as the minimum electrical capacitance possible if corrections for the capacitance of the lead wires are to be avoided. Values greater than 10-5 farads would require the use of unstable and inaccurate electrolytic capacitors). On the other hand, models extending out to 500 to 5,000 ft may be desired in single-well problems, and hence the need for a revised method of problem programming. * REVISED PROGRAMMING METHOD The revised method of programming is one which attempts to retain the desirable features of the conventional method (viz. concentration of block units towards the inner boundary, simplicity in computation, etc.) without having as a consequence that impossible capacitance and vertical resistance ratios will be required. Other advantages will also be achieved by the revised

Jan 1, 1957