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By David B. Scott

When mining operations were first instituted in the mines of the Miami Copper Co., at Miami, Ariz., the relatively hard character of the ground in the western section of the property made it seem advisable to use a wide shrinkage stope and pillar system. The system as finally evolved was applied to the mining of 2,300,000 tons of ore by the use of stopes and pillars each 50 ft. in width. Development, mining and extraction of this reserve has been continuously in progress since 1910, and the final stages of extraction are now reached. A complete survey of all phases of this system can therefore be made. Modification in working methods was obviously necessary, and the system to be described is believed to be typical of the best features. Development The preliminary work had three main objectives: The opening of a haulage level, the construction of a drawing-off level, and the driving of sublevels for use in stoping. In addition to these, some extra sublevel drifting was necessary to determine exactly the boundaries of the orebody, the general outline having been determined by churn drilling. This development was based on the requirements of stopes 50 ft. wide, with pillars 50 ft. wide between each stope. The length of these units varied from 200 to 500 ft.. Haulage Level The tramming level was 50 ft. below the floor of the stopes, and the tramming lines were run parallel with the long axis of the stopes. These lines were also beneath the middle of the stopes and pillars. Each line therefore served one stope or one pillar, this arrangement making it possible to load along an entire stope without switching or uncoupling. This advantage is apparent principally during the process of stoping when rapid drawing of excess broken ore is desirable. Furthermore, the arrangement of the drawing-off level chutes at 25-ft. intervals, as shown

Jan 1, 1917

By G. Sherburne Rogers

Introduction. ONE of the features of oil-field work that puzzles operator, chemist and geologist alike, is variation in the gravity of the petroleum produced, on neighboring leases or even from adjoining wells. Few fields in the United States yield oil that is of uniform gravity throughout; in some, fields the different grades are produced from different sands, in a few from different formations, and in many from different areas in the same sand. In a few cases, perhaps, a common assumption-that the heavier oil is derived from the lighter through the escape of the more volatile constituents-is valid, but many cases can not be explained in this way. Although in the California fields the specific gravity of the oil generally decreases with depth, there are numerous exceptions to this rule; and, as in many other regions the light oil is found nearest the surface, it is evident that evaporation underground is generally an unimportant factor. It is generally recognized that the great differences between petroleum from widely separated fields are due largely to differences in age and degree of metamorphism and to variation in the composition of the original organic matter; but in the writer's opinion some of these broader differences, as well as most of the minor variations in the character of the oil from any one field, are clue to the local action of natural reagents such as sulphur or oxygen. This is particularly likely to be true if the oil has migrated from one formation to another, as in the California fields; and in some areas it appears that variation in sulphur content may even afford a rough index of the extent or distance of the migration. It is the purpose of this paper to call attention to the chemical action of sulphur and oxygen on petroleum, to show that the gravity of the oil from any one field is intimately related to its sulphur content, and to discuss the possi-

Jan 7, 1917

By E. I. Salkovitz, F. W. von Batchelder

DURING the last few years several papers1-' have been published in which internal friction measurements have been used to determine the quantity of carbon or nitrogen dissolved in a iron. This method is based on the fact that, in pure Fe-N and Fe-C alloys, nitrogen and carbon cause peaks in the internal friction vs. temperature curve; at a frequency of 1 cycle per sec (cps) these peaks appear at $-200 and +360C, respectively, and if internal friction is expressed as Q-1, which is equal to times the logarithmic decrement, this figure will, by coincidence, give the weight percentage of nitrogen or carbon in solid solution.' In most of the studies published, very pure iron (Puron) was used. In one case the influence of manganese on the behavior of nitrogen in a iron was mentioned.4 It would be of great value, especially for the study of aging and related phenomena, if this method could be applied to commercial mild steel with norrnal percentages of manganese, phosphorus, sulphur, etc. As a rule, in such steels carbon and nitrogen are present together, and the amounts of these elements in solid solution should preferably be determined separately. The fact that their internal friction peaks appear at different temperatures (+36° and + 20°C in pure iron) seems promising for such a selective determination. It is necessary, however, that the peaks are narrow enough not to interfere with one another, and further, that there is no effect from carbon on the behavior of nitrogen in stress induced diffusion, and vice versa. According to Fast,' however, in the presence of manganese the nitrogen peak gets wider and appears at a higher temperature nearer the carbon peak, and thus the prospects for selective determination are reduced. (The carbon peak was not affected by the presence of manganese.) But even if fully quantitative de- terminations of the two elements are not attained, some relative figures on the sum of them and an indication of which one is the predominant one, would be of value. Some results from experiments along these lines will be reported here. An internal friction measuring device was assembled mainly following a description by KG." The measurements were also carried out as reported in that paper. Table I gives the chemical compositions of the four different materials used in this investigation. All materials were drawn to wires with diameter about 0.8 mm, and the analyses refer to these final shapes. Determination of Nitrogen Peak Wires from steels A, B, and C were decarburized in wet hydrogen (about 30 pct H2O) at 700°C until no carbon or nitrogen could be found by chemical analysis. No peak was then found in the internal friction. The wires were further annealed at 580°C for 16 hr in hydrogen bubbled through a solution of 6.8 pct NH3 in distilled water. Chemical analyses gave 0.04 pct N in A and C, and 0.06 pct in B. After annealing at 580°C for 15 min in a lead bath and water quenching, the internal friction was immediately measured. The resulting curves are shown in Fig. 1. At these high values of the internal friction the accuracy is comparatively poor; at Q-1 - 0.030 it is estimated to be 0.002. In order to make possible a calculation of the activation energy for diffusion of nitrogen, measurements were made at two different frequencies. Steel A shows rather broad peaks, and their temperatures can hardly be expected to be very accurate. Steels B and especially C are better in this respect. The finding of Fast' that manganese broadens the nitrogen peak is con-

Jan 1, 1953

By J. M. Karpinski, R. O. Tervo

A method and equipment have been developed for measuring the impact strength of grains of brittle materials. It is shown that brittle materials develop a characteristic particle size distribution when fractured by impact. A simple mathematical model has been found to describe this distribution, and one of the parameters of the model has been designated the r value. The r value is directly proportional to impact energy and, for fixed impact energy, it becomes a useful criterion of grain strength. Data are presented on the variation of the r value as a function of sample history, initial size, energy input and number of impacts. The results are interpreted in terms of the flaw theory of brittle fracture. The view is now widely held that brittle materials comprise a strong matrix, throughout which flaws or points of weakness are scattered at random. Failure always starts at one or more of these imperfections, and planes of fracture are established by the geometry of the flaw distribution. This view has been developed extensively by Weibull 1,2 and experiments of a confirmatory nature have been reported.3,4 Thus the process of fracture or size reduction of brittle materials can be regarded as a process of elimination or creation of flaws, and the concept of strength is intimately connected with the size and history of the specimen tested. One consequence of the point of view described above is that brittle materials will fracture to yield similar size distributions, although the impact energy to produce a given amount of fracture may vary greatly from one material to another. Generally speaking, experimental investigations of brittle fracture in solids have been confined to two extreme experimental situations. On one hand, we have tests on single specimens of well-defined, but artificial, geometry and, on the other, empirical data have been obtained on the feed-product relation in a variety of mills. The first situation necessitates specimen preparation, which in the case of brittle materials is equivalent to a priori size reduction, while the second one suffers from the disadvantage that little knowledge is gained about individual fracture events. Also, the statistical significance of single specimen tests may be questioned. Our approach lies somewhere between these two extremes. We test a large population of sized specimens and yet subject each specimen to a single fracture event. In 1956 G.H. Fetterley of Norton Co., Chippawa, Ont., made the empirical observation that product size distributions obtained from impacting sized grits can be described by the following equation where R is the proportion by weight of the grain that remains on a screen having an opening x on a side, x, is a parameter having the dimensions of length, and r is a number. This equation has since been derived on a theoretical basis by Gaudin and Meloy.5 They identify x, with the initial size of the test piece and r with the number of flaws per unit length. As will be shown below, our experiments indicate that both x, and r are functions of energy and hence they should more properly be called the effective initial size and the effective number of flaws respectively. Also, our empirical data give us no basis for assuming that r represents the effective number of flaws per unit length, rather than per unit volume. METHOD AND MATERIALS The impact test machine has been designed to feed specimens, essentially one at a time, into an evacuated chamber, where they fall freely and are struck with random orientation by one or the other of a pair of flat steel vanes. The vanes are mounted at opposite ends of a steel bar, which rotates at a closely controlled angular velocity about a vertical axis. Fig. 1 shows the flat circular vacuum chamber with the cover removed, and the horizontal steel bar with the steel vanes at the ends. The cylindrical pot in which the grains are collected after impact appears at the left. Fig. 2 shows the equipment assembled for a test. The vacuum chamber occupies the central position with the variable speed drive below the table surface, the vacuum pump at the extreme left

Jan 1, 1964

By G. C. Wallick, W. R. Foster, J. G. Savins

A comprehensive review of the salient features of the differentiation method of rheological analysis in Poiseuille flow from its inception circa 1928 is presented. Here no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical parameters are required in the data-analysis process. In contrast, the integration method involves interpreting flow properties in terms of a particular ideal model. It is shown that, although both methods represent modes of solution of the same integral equation, being relatively bias-free, the differentiation method offers a more discriminating procedure for rheological analysis. The application to problems involving plane Poiseuille flow is also described. INTRODUCTION In most instances, the approach to the problem of interpreting the rheological properties of various compositions as they are affected by changes in chemical or physical environment, assaying the characteristics of a particular constituent of a suspension, analyzing flow behavior in terms of interactions between components in a system, to cite but a few examples, has been in terms of what Hersey1 terms the integration method. Briefly, it consists of interpreting flow properties in terms of a particular ideal model. The usual practice of the integration method is to choose a model with a minimum number of parameters because, other things being equal, it is desirable to use the simplest model which will describe the behavior of a real material and yet be mathematically tractable for the requirements of data analysis. This expression is then substituted into an equation which relates observed kinematical and dynamical quantities, such as volume flux Q and pressure gradient ], and angular velocity and torque T, in a capillary and concentric cylinder apparatus, respectively. The rheological parameters appear on integrating, in an expression relating the pairs of observable quantities such as those just given. In many instances a particular model provides a good representation of rheological behavior over a reasonable range of compositional and environmental changes. Just as often, however, it is obvious that the interpretation of rheological changes by the integration method is not providing realistic information about changes in flow behavior. A more general method of interpreting rheological data for a given material is to make no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical quantities, e.g., flow rate and pressure drop in capillary flow or angular velocity and torque in a rotational viscometer. This general method Hersey1 terms the differentia-ation method. Instead of integrating, one differentiates the integral equation with respect to one of the limits, i.e., one of the boundary conditions; the resulting expression contains the same observable quantities just given, their derivatives, and the rheological function evaluated at that boundary. By obtaining these derivatives from experimental data, graphically or by a computer routine, they can be substituted into the differential equation and a graphical form of the function derived. THEORY OF THE DIFFERENTIATION METHOD FOR POISEUILLE-TYPE FLOWS In this introductory paper, two flow cases which are important in viscometry are considered (one for the first time) from the differentiation method of analysis, flow in a cylindrical tube and flow between fixed parallel surfaces of infinite extent, the basic integral equations being formulated in a manner analogous to the way they originally appeared in the literature. In addition, the following ideal conditions will be assumed: (1) an absence of anomalous wall effects, (2) isotropic behavior everywhere, and (3) steady laminar flow conditions. Before proceeding it would seem appropriate to preface the analysis of these flow geometries with the comment that the basic philosophy of the differentiation method could be said to stem directly from the efforts of Herzog and weissenberg2 to indicate systematically the various ways of using

By A. F. Meger

Coal treatment by oil spraying receives special attention at the Georgetown plant for the dividends it pays in satisfying present customers and attracting new markets. Customer satisfaction requires care, quality control, and use of suitable oils. REPRESENTED here are the ideas and varied experiences of many people in the Hanna Coal CO. who have helped develop, over a number of years, an efficient and flexible method for spraying controlled amounts of oil on coal. Since the Georgetown preparation plant began operations early in 1951, oil treatment of coal has received special attention. It is believed that oil treating will satisfy present customers and also attract new markets. The first step in developing the new method of oil spraying was the construction of a dust cabinet for testing 50-lb samples of treated coal with the available oil sprays on the market. Tests results were tabulated for both indoor and outdoor storage. The graph, Fig. 1, shows results of the original tests made with a 700-sec residual blend and a 500-sec lubricating oil on Georgetown stoker coal of 1¼x3/8-in. size.* The advantages of better price, improperly blended can raise havoc. Some.,pale oils also, although odorless when delivered, give off a sweet sickening odor when atomized under pressure. It is recommended that all products be tested before they are used. There is a specific place for all spraying oils. For example, at a power plant a severe dust condition exists around the stockpile area and in parts of the plant. The cheapest spraying oil made, regardless of odor, will do an excellent job in this case and will save the company 3 to 5c per gal or more. Domestic trade, on the other hand, must be carefully handled to prevent complaints about odor, and the only way to do this is to stay with the proved products after the odor tests have been made. The preparation plant at Georgetown has facilities to handle either tank car or tank truck deliveries. Steam is available at the unloading point if the weather is severe, and there is an indicator at the unloading point to prevent overflowing the 20,000-gal underground storage tank. Systematic test samples are removed from each delivery and sent to the lubrication engineer to insure quality control. Fig. 3 illustrates the chutes in which smaller sizes of coal are treated. Fig. 4 shows the entire spraying system. Buried in the ground is a 20,000-gal tank with immersion heaters grouped around the feeder line to insure adequate gravity flow to the pump under all conditions of weather. Oil flows to a 500-gal preheating tank where the temperature is kept about 150°F by six 1½-kw immersion heaters thermostatically controlled. Hot oil is fed through a self-cleaning disc-type filter to the hydraulic pump. Valves and piping make it possible to transfer oil from one tank to another or to drain the lines for maintenance purposes. All this equipment is below ground level in a covered pump room,

Jan 1, 1955

By Harold W. Scott

Geological Engineering is now a recognized curriculum in most of the mining schools in United States. Graduates of these schools are scattered over the face of the earth, participating in exploration and mining enterprises of diverse character. They are engaged in the mapping of new mineral deposits, in the extension of old deposits, the estimation of reserves, microscopic analysis, and in the direction of exploitation and conservation of man's natural resources. The training of men qualified to carry out these technical phases of modern industry has fallen essentially to the mining schools. For the most part they have met the demand for technically trained men in the mineral industries. Schools Offering Geological Engineering Degree The mining schools have passed through the early stages of their development and at the present offer varied curricula covering the fields of geological engineering, mining engineering, and metallurgical engineering. Usually a B.S. degree is offered in any of these three fields. However, .there has been some tendency of recent date on the part of the Engineers Council for Professional Development to question the validity of a B.S. degree in Geological Engineering. The of this paper is to examine the curricula as offered in the mining schools, to evaluate their engineering content, and to propose minimum requirements for the degree of Geological Engineering in the mining industry. The curricula of eight institutions that offer the degree of B.S. in Geological Engineering or Mining Geology have been studied (Table 1). All except one of these schools are in or near mining districts and occur west of the Mississippi River. They are all state-supported institutions that have come into existence because of the state's need for technically trained men. A graduate from .a mining school is called upon to perform many duties of a technical nature. His initial task may be to make a geological map of a mine or the surface above, but before the map is finished he may be asked to take over the responsibility of getting the ore "on top." And finally, he might find it essential to know how to mill the ore. Certainly this requires technically trained men and the mining schools are essentially the organizations to do the job. The departments of geology in these schools are training geological engineers. Field Of Geology If we were to accept the opinions of some writers, we would be forced to conclude that all geology departments offer only a "dilettante" variety of subjects.

Jan 1, 1944

By B. F. Tillson

HAVING been asked to talk about recent devel-opments in mining equipment, I chose the sub-ject of small units of storage-battery locomo-tives which recently have been developed with the idea of motorizing transportation in the mines as far as possible, replacing the manual labor of hand-tramming. Metal mines are probably less advanced in this field than coal mines, where transportation of large ton-nages on any one level is quite common. Of course, metal mines, where large tonnages are handled on any one level, are as advanced as coal mines, and storage-battery locomotives for main haulages are used quite commonly in such metal mines, but the mines having levels at many intervals in the depth of the orebody, or a number of intermediate levels in which a consider-able amount of hand-tramming has to be done, and small metal mines in which the size of the orebody does not seem to warrant the initial capital expenditure for the driving of main haulage levels and installation of rock and ore chutes and raises for the delivery of the broken ore and rock to the cars have been at consider-able disadvantage in replacing manual labor by some mechanical means of transportation. Several years ago the field was canvassed among the manufacturers of electric-locomotive equipment and the conclusion was reached that the art had not been devel-oped to the advantage of metal miners who desire to replace small units of labor by locomotive equipment. The need for such small locomotives is all the more em-phasized by the development in the past few years of mechanical mucking-machines (loading equipment for filling the cars from muck piles on the level). Any me-chanical loader is a liability instead of an asset unless means are also provided for keeping the material away from the loading-machines. Therefore the transporta-tion system must be equal to the capacity of a loading-machine, otherwise the latter is idle such a large per-centage of its time as to prove an unprofitable invest-ment. So there is a need for portable, small haulage units to handle small mine cars in many metal mines, and, naturally, units are desired which can be so readily shifted from level to level as to facilitate their free use. Of course, in mines in which each level comes to the shaft it is not such a difficult problem, but many mines have a great many intermediate levels which must be approached through raises, timber slides or other small openings required to transfer ore and to get timber and other supplies to those levels.

Jan 5, 1927

By Louis E. Toth, Alan W. Searcy

A modification of Le Claire's microscopic model for self-diffusion is developed in a form suitable for prediction of activation energies for diffusion in disordered substitutional solutions as well as in pure metals Bonding is considered as a localized interaction, and the energy of bonding between atoms of different types is taken as the arithmetic mean of the energies in the pure elements. The activation energies for vacancy formation and migration in substitutional alloys are shown to depend on the empirical constants developed for self-diffusion when the equations are adjusted for the mole fractions of the two elements. The differences in activation energies between alloys and pure metals are calculated and compared with the experimental differences. MaNY different correlations have been proposed for use in predicting activation energies for self-diffusion or diffusion in dilute alloys. Usually theories for self-diffusion cannot be applied to alloys nor can theories for dilute alloys be satisfactorily adapted to self-diffusion. We present here a correlation scheme which can approximate activation energies for diffusion, vacancy formation, and atom migration in substitutional-alloy systems of any concentration. The activation energy for self-diffusion QD has been correlated to the melting temperature Tm,1, 2 the sublimation energy L,,l the heat of fusion Lf,3 crystal structure, and valence.4 Working with mechanical parameters Le claire5 proposed that the activation energy for vacancy migration Qm could be related to appropriate shear moduli. He also proposed that the activation energy for vacancy formation 62, is proportional to Ls. THEORY We consider that Le Claire's expression for 4, is satisfactory. But an alternate expression for Qm in terms of the bulk modulus is just as satisfactory from a theoretical point of view for the prediction of the energy of vacancy migration in pure metals and can more easily be used for alloys. In order for Qm to be a minimum, not only the moving atom but also adjacent and nearby atoms must undergo distortions. These distortions are neither isotropic as is implied by a correlation with the bulk modulus nor unidirectional as implied by a correlation with a shear modulus, but are complex and multidirectional. A complete analysis in terms of the bulk modulus and all the shear moduli is not yet available. In a first approximation in which only one parameter is used, there is no obvious theoretical reason to prefer the shear modulus over the bulk modulus. The bulk modulus is a much more convenient parameter for use in predicting Qm. Shear moduli are known for less than half of the metallic elements while bulk moduli are usually available. Furthermore, because of the directional dependence of shear moduli, their estimation for alloys appears inherently more difficult than is the estimation of bulk moduli. We assume that the bulk modulus Bs reflects an average value of the shear moduli such that the strain energy at the point of maximum distortion of the lattice during vacancy migration can be expressed as

Jan 1, 1964

By L. H. Wolfe, J. O. Thieme

The tensile and shear strengths of frozen soil and the compressive strengths of ice and frozen soil were measured These tests showed that the strength of ice and of frozen soil increased as the temperature was decreased. A method is presented for the measurement of thermal conductivity and specific heat of earth and ice. Using the parameters thermal conductivity, specific heat and density, the thermal diffusivity was calculated. Results of thermal property tests establish water as the major variable contributing to thermal property values. INTRODUCTION During the last few years, a considerable interest has developed in underground storage of cryogenic liquids such as liquid natural gas. Because of its economy and safety, underground storage is being used. Before underground caverns could be seriously considered, however, the strength and thermal characteristics of the soil had to be obtained. Methods are presented herein for measuring tensile, compressive and shear strengths, specific heats and thermal conductivities. The tests were performed on two soils at temperatures from ambient to -195C. Because it is difficult to find data in the literature that pertain to a particular soil, ice was used to evaluate some of the experimental procedures. Some of our ice data are compared to the published values. PHYSICAI, PROPERTIES SOIL SELECTION AND SAMPLE PREPARATIONS The physical and thermal tests were performed on recompacted samples of two typical soils that might be encountered in underground caverns: a gray, fire clay that had been pulverized and mixed with water into a pliable mud; and a brown, sandy silt that was dug from a dry river bank and subsequent1y mixed with tap water. The moisture content of the test specimens was 17 to 22 per cent (based on the wet weight of the soil). This amount of water nearly saturated the silt, but the clay was well below the saturation point. The soils are partially described by the sieve analyses (Fig. 1) which show the particle size distribution of the coarser than 44 micron portion of the soils. The curves also show that approximately 75 per cent of the clay and 20 per cent of the silt are finer than 44 microns. The particle size seems to affect some of the physical properties, and the finer than 44 micron portion is important in the thermal conductivity test. Physical specimens were cut with a bandsaw from frozen blocks of the soil. The specimens were then sanded and kept frozen until after they were tested. They were stored at the approximate test temperature for several hours. Then, to equilibrate the samples to the test temperature, they were stored at the temperature at least an hour before they were tested. TEST EQUIPMENT An Instron, which is a constant speed gear-driven instrument, applied force to the samples and drew stress-strain plots of the test. All of the samples were strained at 0.02 in./min. All of the physical tests were conducted in a temperature cabinet that controlled the temperature to 1C. TENSILE STRENGTH Briquette or "dog-bone" shaped tensile specimens were pulled with suitably shaped jaws. This shape of specimen, which is usually used for tensile tests of concrete, is satisfactory for testing frozen soils except that the samples tend to

Jan 1, 1965

By Michael A. Zappia

INTRODUCTION The San Manuel mine of Magmacopper Company is located approximately 72 km northeast of Tucson, Arizona. The mine, concentrator, smelter, electrolytic refinery and continuous rod casting are located on the west side of the San Pedro River valley. Ore Production: 58 1W mtpd Production To Date: Over 340 000 000 mt since 1956. Ore Grade: 0.70% net sulfide cu. As conceived at the present time, the San Manuel ore body is the lower half of what was originally an elliptical (In cross sect ion) cylinder same 2400 m long with major and minor cross sectional axes of 1500 m and 760 m. After emplacement, the cylinder was diagonally sliced along its long dimension by the San Manuel fault, which separated it into halves, moving the upper half same 2500 m down dip and bringing a wedge-shaped blanket of tertiary conglomerate into position over the lower segment of the cylinder. The lower segment is the San Manuel ore body. The upper part, moved down dip, is the Kalamazoo ore body. Originally, these were one ore body. The San Manuel ore body is a structurally weak and highly fractured quartz monzonite, the principal ore minerals being chalcopyrite, with small amounts of molybdenite. The present mining method is full gravity diagonal retreat panel caving by block. This is shown on Figure 2 , (Block Sequence 56, 57, 58, 59 --on the following page.) The ore mined is hoisted to the surface for transportation to the concentrator. BLOCK CAVING MINING SEQUENCE HISTORY The San Manuel mine was planned and developed as a full gravity block caving mine. It continues as a full gravity block caving mine. Since its initial start, the major changes in mining have been in the areas of ground support, rate of draw and undercut sequence. Ground weight resulting from block caving plays a dual role. It can cause extensive damage to ex- traction openings, yet it is necessary to break the ore into easily handled size. The ground- weight problem resolves itself into finding ways to make it manageable. The initial early ground support in the production areas consisted of timber sets and various combinations of steel and timber sets. This sup- port system proved unsatisfactory and a new support system utilizing concrete was developed. Concrete support, 30 cm to 45 cm thick, proved satisfactory. Rates of draw were experimented with. A draw rate of 45 cm to 61 cm (32 to 45 mt) per draw point per day was determined as optimum in con- trolling ground weight. Undercut sequence or mining sequence was recognized as a major contributing factor to ground weight. This is the most difficult factor to change. The lead time from primary development to undercut can be as much as two years. Initial Checkerboard Pattern The initial undercut sequence was in a checker- board pattern (Figure 2). Blocks Sequence 1, 2, 3, 4, 5, 6--next page.

Jan 1, 1981

By G. H. Kessler

ALTHOUGH considerable attention has been devoted to reaction mechanisms and equilibria of a number of endothermic reactions through which metals or their refractory compounds can be formed upon heated surfaces, only a comparatively small amount of work has been done to develop rate information for these systems. The interestin and very worthwhile work of Holden and Kopelman, Runnalls and Pidgeon,Dijring and Moliere, and Herrick and ICrieble4 is to be noted; however, their work was done under very specific conditions and the rate information which they have developed is not applicable to many systems which have been studied experimentally. That a more generalized approach is needed is shown by the diversity of these systems and of the experimental conditions which they require. These include the preparation of titanium, zirconium, tungsten, molybdenum, chromium, co-lumbium, aluminum, and silicon by decomposition or disproportionation of their halides, in some instances through hydrogen reduction; the preparation of nickel and iron by decomposition of their car-bonyls; and the preparation of copper by decomposition of the acetylacetonate. They may be carried out at temperatures ranging from 100" to over 2000°C and at pressures of from less than one mm Hg to superatmospheric. The physical mechanism of the overall process can be broken down into several steps, any one of which may be rate-determining; and the rate associated with each of these basic physical processes can be predicted. Consequently, by proper application of the present technology of rate processes, it is possible to arrive at a rate of metal deposition in the system of interest and to reach an understanding of the influence of' each major variable upon the deposition rate. It is the purpose of this paper to illustrate how this can be done and to present experimental results for a specific system for comparison with theory. The overall process of deposition of metal upon a heated surface which is immersed in vapors of a compound of the metal can be broken down into the following steps: 1) Transport of the reactant vapors to the surface. 2) Decomposition of the reactant in the immediate vicinity of the surface to a) establish chemical equilibrium if reaction rates are high; or to b) establish a dynamic equilibrium in accordance with the several reaction rates. 3) Diffusion of reaction products away from the vicinity of the surface, with or without simultaneous recombinations to form still other products. The overall process is said to be diffusion controlled if Step 1, or the equivalent Step 3, is slow; it is reaction-rate controlled if Step 2b is slow. When experimental evidence shows the reaction rate to be controlling, the well-known theories of Eyring' and others can be used as a basis for correlating and extrapolating the experimental data. Although these theories give only approximate estimates of reaction rates, they are of considerably greater value in correlating experimental data. Most deposition systems operate at surface temperatures sufficiently high that reaction rates near the surface are very high. Mass-transport rates then become controlling; and it is this regime of diffusion controlled rates which is most often of concern and Which will be considered here. When the system pressure is very low, i.e., in the micron range, then the transport processes are those of molecular movement, and the results of kinetic theory can be applied to specify a rate of arrival of reactant molecules at the heated surface. If the condensation coefficient can be estimated, then the deposition rate will be given by the product (rate of arrival) x (condensation coefficient), Conversely, experimental data can be used to determine a condensation coefficient, as was done by Holden and Kopelman' for the decomposition of zirconium tetraiodide upon a heated molybdenum surface, who found the coefficient for zirconium on molybdenum to be 1.0 at temperatures of 1382°C and above. In this pressure range, the geometry of the system. and in particular the distance between the source of reactant molecules and the heated surface, can exert a considerable effect upon the deposition rate;

Jan 1, 1961

By M. C. Leverett, S. E. Buckley

The production of oil is accomplished as a result of its displacement from the reservoir by either gas or water, and the amount of oil recovery is limited by the extent to which the displacing gas or water accumulates. This paper describes the mechanism by which the displacement is effected and the advantages of water over gas as a displacing agent. In the light of the results of experimental observations of the flow of mixtures of oil and/or gas and/or water through sands, certain conclusions are drawn relative to the changing character of the displacement as depletion proceeds, and on the effects of the properties of the fluids and of producing conditions on the ultimate oil recovery. Introduction Crude oil has no inherent ability to expel itself from the pores of the reservoir rocks in which it is found; rather, it must be forcibly ejected or displaced by the accumulation of other fluids. Accordingly, a knowledge of the mechanism by which one fluid is displaced by another is essential to an understanding of the fundamental process by which oil is recovered. The displacing fluids normally available are gas and water, either or both of which may exist originally associated with the oil in a potentially usable form or may be supplied to the reservoir from external sources. Gas is present in most oil reservoirs. If the quantity is relatively small, it may exist originally completely dissolved in the oil, but if the quantity exceeds that which may be held in solution by the oil at the prevailing pressure, the excess will be found in the free state. Most reservoir sands appear to contain some water,l and in the majority of fields the oil is trapped in the structure and held over water. In certain conditions the entrapping water may advance into the oil zone and displace the oil therefrom. This paper describes in a qualitative manner some of the characteristics of the displacement of oil by either gas or water, with an attempt to elucidate somewhat the mechanism by which such displacement is effected. Role of Dissolved Gas When the pressure on an oil containing dissolved gas is reduced to the saturation or bubble-point pressure, gas escapes from solution and expands, imparting to the oil-gas mixture a high degree of expansibility and causing it to flow in the direction of reduced pressure. This expansibility has frequently been attributed to the oil; closer analysis, however, reveals that as gas escapes from solution the oil phase actually. contracts. Hence, it is the accumulation and expansion of the liberated gas that supplies the propelling force for the oil. It has been shown experimentally2-5 that within certain limits a sand containing oil, gas and water will permit the simultaneous flow of all three; the readiness with which they may flow depends upon the characteristics of the sand, of each of the fluids, and upon the relative amounts of the fluids in the sand. Thus, in the initial stages of production by the mechanism of dissolved gas drive, the liberated gas is present in the sand in low concentration and is unable to

Jan 1, 1942

By T. K. Prentice

ABSTRACTED AND REVIEWED BY E. W. DAVIS,* MEMBER A.I.M.E. THE January-February number of the Journal of the Chemical Metallurgical and Mining Society of South Africa is made up entirely of a discussion of Ball Wear in Cylindrical Mills. Following the principal paper by T. K. Prentice are several remarkably pertinent and carefully prepared discussions. Few persons in this country would be likely to see this publication, and since the information presented is new and of current interest, it seems desirable to abstract and review this publication for the benefit of the members of the A.I.M.E. The purpose of the investigation is stated in the first two paragraphs of Prentice's paper, as follows: Early in 1941, The Chamber of Mines Steel Products, Limited, initiated a series of tests under semi-working scale conditions to determine, if possible, those physical and chemical properties of a ball which make it resistant to wear when used in a cylindrical mill as a grinding medium, with the primary object of incorporating those beneficial qualities in the balls being produced at their works. This paper describes the tests carried out and discusses the results obtained. From these results it was possible to formulate a new theory relating to ball wear in cylindrical mills. This theory is presented in the second portion of this paper. PRACTICAL BALL-MILL TESTS IN A CYLINDRICAL MILL Part I of the paper begins with a discussion of the methods used for the manufacture of grinding balls in South Africa. The following paragraph is of particular interest. The cast steel ingots, 4 ¼ - in. square by 3 ft. 6 in. long, are re-heated in a gas-fired sloping stationary-hearth furnace and then rolled in a six-pass continuous mill into 2 5/8 in. round billets. Some of these billets are then removed and cut into suitable lengths for forging into 4 in., 3 ½ in., 3 in. or 2 ½ in. balls by means of three Drop and two Beché hammers, but the greater number, whilst still at about 1,000 ºC., pass directly into a set of scroll rolls which produce, in an ingenious manner, finished 3 in. balls direct from the 2 5/8 in. billets. Except in special cases, all balls are allowed to cool in the atmosphere and are not water quenched. Details of the Tests In order to enable the reader to evaluate properly the results and conclusions in the rest of the paper and in the discussions following the paper, most of the information presented by the author under this heading is quoted: ….. The testing unit was a nominal 30 in. diameter and 18 in. long centre discharge Denver Ball Mill. The ore pulp to the ball mill comprised a small portion of the normal feed to one of the fourteen City Deep 5 ft. 6 in. X 22 ft. tube mills, and the grinding media consisted of the balls under test plus other balls to give the desired load. The running time of the test-mill was divided into approximately equal periods of five days 13 ½ hours each. The usual procedure was to examine and make up the load

Jan 1, 1944

By J. Wade Watkins, E. S. Mardock

The accurate evaluation of reservoir-performance characteristics in the secondary recovery of petroleum by water flooding requires use of a water tracer that may be injected into water-input wells and detected at oil-production wells to supplement data obtained from core analyses, wellhead tests, and subsurface measurements. Radioactive iodine has been used successfully as a water tracer in field tests to determine: (I) relative rates and patterns of flow of injected water between water-input and oil-production wells and (2) zones of excessive water entry into oil-production wells. Laboratory evaluations of potential water tracers, previous tracer studies, the value of using a radioactive tracer, general field procedures, and the use of surface and subsurface instruments for the detection of the emitted gamma radiation, are summarized. Data from the field tests are presented graphically and discussed in detail. It is concluded that the radioactive-tracer method, using radioactive iodine, may be used successfully to measure either the relative rates and patterns of flow or zones of excessive water entry into wells under conditions of comparatively rapid transit time between wells. INTRODUCTION Extensive use is made of data obtained from core analyses, wellhead tests, fluid characteristics, and subsurface measurements in evaluating the sweep efficiency of water injected into oil sands for the recovery of oil. Theoretical flow rates and patterns may be calculated from those data using radial-flow formulas, if it is assumed that the physical conditions in the productive formation are homogeneous. Unfortunately, homogeneous conditions rarely, if ever, exist in oil-productive formations. The use of a tracer that may be injected into an oil sand and detected quantitatively, or even qualitatively, at offsetting oil-production wells provides basic data that may be used in determining more accurately the subsurface rates and patterns of flow of injected water between wells than is possible by theoretical calculations based on assumed conditions. Consideration of the data obtained by using a water tracer assists in the application of remedial measures to water-input wells, such as plugging of channels, or selective plugging of highly permeable zones, thereby effecting a more uniform flood and a greater ultimate oil recovery. A water tracer should have the following characteristics: (1) low adsorption on solid reservoir material; (2) high solubility in water; (3) low or negligible solubility in crude petroleum; (4) a wide range of solubility of compounds that may be formed by chemical reactions with ions present in reservoir rocks or waters; (5) high detectability in low concentrations by portable apparatus; and (6) general availability at low cost. Additional desirable characteristics are that the tracer should be nonhazardous in nature under normal working conditions and quantitatively detectable in the well bore, as well as at the surface. Review of Previous Tracer Studies The need for a water tracer has been recognized for many years. As far back as 1906, Dole1 described the use of fluorescein in flow-rate studies made in France in 1901. In 1921, Ambrose" discussed in detail the use of organic and inorganic dyes, chlorides, nitrates, and other anions, lithium salts, and the Slichter electrical

Jan 1, 1955

By S. E. Buckley, M. C. Leverett

The production of oil is accomplished as a result of its displacement from the reservoir by either gas or water, and the amount of oil recovery is limited by the extent to which the displacing gas or water accumulates. This paper describes the mechanism by which the displacement is effected and the advantages of water over gas as a displacing agent. In the light of the results of experimental observations of the flow of mixtures of oil and/or gas and/or water through sands, certain conclusions are drawn relative to the changing character of the displacement as depletion proceeds, and on the effects of the properties of the fluids and of producing conditions on the ultimate oil recovery. Introduction Crude oil has no inherent ability to expel itself from the pores of the reservoir rocks in which it is found; rather, it must be forcibly ejected or displaced by the accumulation of other fluids. Accordingly, a knowledge of the mechanism by which one fluid is displaced by another is essential to an understanding of the fundamental process by which oil is recovered. The displacing fluids normally available are gas and water, either or both of which may exist originally associated with the oil in a potentially usable form or may be supplied to the reservoir from external sources. Gas is present in most oil reservoirs. If the quantity is relatively small, it may exist originally completely dissolved in the oil, but if the quantity exceeds that which may be held in solution by the oil at the prevailing pressure, the excess will be found in the free state. Most reservoir sands appear to contain some water,l and in the majority of fields the oil is trapped in the structure and held over water. In certain conditions the entrapping water may advance into the oil zone and displace the oil therefrom. This paper describes in a qualitative manner some of the characteristics of the displacement of oil by either gas or water, with an attempt to elucidate somewhat the mechanism by which such displacement is effected. Role of Dissolved Gas When the pressure on an oil containing dissolved gas is reduced to the saturation or bubble-point pressure, gas escapes from solution and expands, imparting to the oil-gas mixture a high degree of expansibility and causing it to flow in the direction of reduced pressure. This expansibility has frequently been attributed to the oil; closer analysis, however, reveals that as gas escapes from solution the oil phase actually. contracts. Hence, it is the accumulation and expansion of the liberated gas that supplies the propelling force for the oil. It has been shown experimentally2-5 that within certain limits a sand containing oil, gas and water will permit the simultaneous flow of all three; the readiness with which they may flow depends upon the characteristics of the sand, of each of the fluids, and upon the relative amounts of the fluids in the sand. Thus, in the initial stages of production by the mechanism of dissolved gas drive, the liberated gas is present in the sand in low concentration and is unable to

Jan 1, 1942

By J. E. Hilliard

AS is well-known, the length per unit volume, Lv, of any lineal feature (such as grain edges in a polycrys-talline specimen) can be estimated from a count of the number of point intersections with a random plane of polish. Specifically:' Lv = 2NA in which NA is the expected number of intersections per unit area of the plane. As with all other measurements in quantitative metallography, the estimation of Lv is subject to a sampling error, the magnitude of which will depend on the number of observations. The analysis is usually performed by counting the number of intersections falling within a closed test figure of known area applied to a succession of different areas on the plane of polish. The test figure can be drawn directly on the screen of a projection microscope or else superimposed on the image of the structure by means of a reticule in a focusing eyepiece of an ordinary microscope. The use of micrographs is very inefficient unless, as in the present study, these are also needed for some other purpose. Consider an analysis in which n applications are made of a test figure within which the expected number of intersections is N. The expected total number of intersections counted is then given by NT = nN If (N) is the standard deviation in N for one application of the figure and if the latter is applied to non-overlapping regions so that the N's are independent in the statistical sense, then the standard deviation in Nt is given by: a(NT) = a(N)vn Eliminating n from Eqs. [2] and [3] we obtain: Thus, k will be a constant for a given specimen and test figure. From Eqs. [ I] and [4] we find As is to be expected, therefore, the fractional error in the estimation of Lv is inversely proportional to the square root of the total number of intersections counted. It is very desirable to have at least a rough estimate of k before starting an analysis, since it will then be possible to decide in advance by use of Eq. [5J how many counts should be made in order to achieve the desired accuracy in Lv. Without such information the investigator, unless lucky, will either do needless (and tedious) work or else obtain a result with too large an error. It is very easy to calculate k for the limiting case of N — 0, i.e., when the test figure is vanishingly small. In this case there is a negligible probability of two or more intersections falling within the figure. There are therefore only two possible outcomes: a count of one with a probability of, say, p and a zero count with a probability of (I-p). Thus and Therefore: We might expect k to depend on N and therefore on the size of the test figure. Such a dependence was observed2 in the analogous case involving the estimation of grain-boundary area per unit volume by a count of the number of intersections of a test circle with traces of the boundaries on the plane of polish. In this case the theoretical value of k at the limit N — 0 was 1.41. It was also predicted that k would display an initial sharp decrease with increasing N. Experimentally, k was observed to decrease to a value of 0.62 at N - 6 and thereafter remain approximately constant. Furthermore, the value of k for N > 6 was found to be insensitive to the form of the structure provided no pronounced anisotropy or grain-size variation was present. In order to determinewhether k would exhibit a similar dependence on N in the estimation of grain-

Jan 1, 1967

By L. H. Robinson

Triaxial compression tests on Indiana limestone indicate that chemical additives in the pore fluids can increase or decrease the strength in plastic failure but not in brittle failure. Tests using a series of the sodium salts of dicarboxylic acids show that odd-number carbon-atom chains decrease the yield strength as much as 3.0 x 10 3 psi, and even-number carbon-atom chains increase the yield strength as much as 9.0 x 102 psi. ,The most effective chemical (sodium citrate) decreased the yield strength of Indiana limestone from 16.0 x 103 to 12.0 x 103 psi. The chemical additives investigated have no influence on microbit drilling rate when drilling with zero differential pressure. However, when drilling at a 2.0 x 103-psi pressure differeniial and using an odd-number carbon chain compound as the circulating fluid, the roller bit drilling rates were slower than with water whereas the drag bit drilling rates were faster. One even-number carbon chain compound added to the circulating fluid produces the opposite effect: the roller bit drilling rate is slightly faster than with water and the drag bit slower than with water. INTRODUCTION A Russian book by Rehbinderl published in 1944 generated much interest in the possibility of aiding and accelerating the destruction of solids by the action of a liquid in which the solids are deformed. This book describes a process in which microcracks are generated during elastic deformation. To describe this process, the rock is divided into three zones: (1) the zone in which the destruction takes place, (2) the predestruc-tion zone (an affected area immediately below the destroyed zone) and (3) the undisturbed specimen. Consider a load applied normally to a surface of an infinite slab of rock. Immediately below the point of application of the load, the rock is destroyed by compression or shear forces. Below this area of destruction, because of a great number of discontinuities ranging from defects to weak points in crystals of discontinuities in crystal latices, very small cracks are created in or between the crystals (often referred to as microcracks). Upon removing the load, the broken rock in the destroyed zone could be removed. In the lower predestruction zone, however, the microcracks in and between the crystals could disappear by the process of rehealing, i.e., the molecular attraction from one side of the crack to the other side being sufficient to completely eliminate the crack. Thus, a large number of these microcracks possibly exist only for a relatively short period of time. The concept of small cracks being generated within the crystals of a rock is not unreasonable. If the rock matrix is deformed below the yield point, some of the defects present within the crystalline structure could start small cracks through the interior of the grains. Upon removal of the load, these microcracks reheal (or the newly generated surfaces come back together) so that all evidence of cracks completely disappears. Under various types of loading, and in various types of fluids, the rehealing of these cracks would be time dependent. If a liquid adhered to the surface of a rock, it could penetrate into the microcracks and thus delay or prevent the rehealing process. This suggests that the prevention of healing of the microcracks may be dependent upon the wetting characteristics of the solid. Thus, rocks which are water-wet should be more easily destroyed in water than in nonpolar hydrocarbon liquid. Adsorption of a liquid could also reduce the free surface energy which could explain the decrease in strengths of materials under nonrepetitive-type loading. Rehbinder's work prompted Boozer, Hiller and Serdengecti 2 to examine the effects of pore fluids on the deformation of rocks subjected to triaxial compression over a range of confining pressures, temperatures and strain rates. Fluids which strongly adsorbed on the rock grain surfaces decreased the strength of sandstone and limestone, which deformed plastically. For certain strain

By F. X. Tartaron

The comparison of actual energy of comminution with theoretical surface energy presents a wide gap. On the other hand, Solid State Theory presents a viewpoint that places actual energy of breakage in understandable relationship with the theoretical strength of materials. Therefore the physical background of comminution theory favors Kick's Law. A11 discussions of comminution theory appear farfetched when comparison is made of the actual energy of crushing with the energy input called for by thermodynamic theory. Quoting Taggart:' "The work required to crush halite was of the general order of 0.10 kg cm per sq cm of new surface produced (based on air percolation) whereas the theoretical energy of this new surface, based on thermodynamic calculation by a number of investigators is 1 x 10'4 kg cm per sq cm or the work expended was 1000 times the new surface energy — an indicated crushing efficiency of 0.10 pct." It is frustrating to probe into comminution theory with the prospect that the energy one is measuring is 99.9 pct waste energy. Do the laws of comminution deal with energy consumed by mineral breakage or with waste heat energy? There seems to be something wrong. Solid State Theory may provide the answer. The following statement is particularly apt to the situation: "The fundamental fact about metals and indeed all materials, is that they are much weaker than they should be. By this, we mean that if the stress required to cause a given plane of atoms to slip past a neighboring plane is calculated from basic atomic and Solid State Theory, the resulting number is some 1000 times too large to be accounted for by errors in approximations or assumptions. We know now that this is due to dislocations, and we even have a fair understanding of the details of the process by which dislocations make a crystal weak. An intriguing possibility which suggests itself, results from the discovery of very minute metallic crystals which are apparently free of dislocations and which have a strength approaching the ideal value for a perfect crystal." Here we have an extraordinary reversal of the situation. The actual energy for breakage is only one-thousandth the theoretical instead of 1000 times as given by Taggart. But the theoretical energy presented by Solid State Theory is the binding energy between atoms (or ions) in a crystal lattice. This is the kind of energy envisaged by Kick's law. The surface energy or the other hand corresponds to Rittinger's law. Comparison of theoretical with actual, on the basis of surface or on the basis of Rittinger's law, seems to present an absurdity; yet Rittinger's law is confirmed by an impressive array of experimental evidence. Comparison of theoretical and actual on the basis of Solid State Theory or, in other words, on the basis of Kick's law seems reasonable; yet there is not a scrap of evidence to verify Kick's law. The situation appears paradoxical, but the developments in the next section of this paper show that the paradox is a hint to a strange turn of events. ENERGY-WEIGHT FRACTION FUNCTION charles3 has presented a final equation showing the relation of energy consumed in comminution to size of product n{-1) a-n + 1 E is energy, C is proportionality constant, a and n are constants and k is the coarsest size in the ground product (size modulus). In the course of study of a large amount of experimental evidence, Charles discovered that in the general case, a-n + 1 approximated zero. For some reason, a and n differed only by unity. But if a—n + 1 = 0 within experimental error, then it is obvious that Eq. 1 states that it requires an infinite amount of energy to grind any sample to any size. This is a case where nature gives an absurd answer to a man-made mathematical equation, hence something is wrong with the equation. An adjustment must be made to fit the equation with experience. TO reveal the nature of the adjustment, the differential equation preceding the second integration in Charles' group of equations is given When Charles integrated the quantity xa-n it was almost impossible for him to realize that he was dealing with a special case of integration and that

Jan 1, 1962

By R. E. Collins, Paul B. Crawford

Potentiometric model studies have been made of ertically fractured reservoirs. All fractures originated at he well and extended into the reservoir for various distances. Studies were made to determine the areal sweep efficiencies for line-drive patterns. The areal sweep efficiency for the unfractured system studied war 70.6 per cent. It was found that if the vertical fracture war paralIel with the direction of flood, the areal sweep efficiency may be considerably reduced, approaching zero in some instances. If the fracture was at right angles to the direction of flood, the areal sweep efficiency may be greater than that for the unfractured system. The sweep efficiency depends on the length and orientation of the fracture and direction of the flood. It is concluded that considerable effort should be made to determine the nature and direction of fractures before initiating a flooding program. Such information is required if the maximum sweep efficiency is to be obtained and channeling is to be reduced to a minimum. INTRODUCTION The recent development and application of fracturing techniques to petroleum reservoirs has served to focus considerable attention on the effect such fractures may have on secondary oil recoveries. The opinion has been expressed that fracturing may not alter appreciably the water flooding possibilities. Others have thought that channeling may occur and that the creation of fractures may serve to substantially reduce the possibilities of conducting a successful water flood in the reservoir The purpose of this study was to obtain quantitative estimates of the effect of vertical fractures on the areal sweep efficiencies of line-drive flooding patterns. In presenting this work on vertical fractures, it is not to be inferred that the present fracturing techniques result in producing a vertical fracture. The types of fracture which are created are not known with certainty in every case. Some are believed to be horizontal, others inclined along bedding planes, and some data indicate vertical fracturing. Each fracture will probably exert a different influence on the sweep efficiency of the secondary recovery program; consequently each fractured well should perhaps be considered as a separate problem, requiring a careful analysis. Preliminary work on the effect of fractures on producing capacity of a well indicated that for practical purposes many fractures may be treated as having a nearly infinite permeability This assumption appears to be valid in some instances where the permeability of the fracture is only 10 or 100 times greater than the permeability of the matrix. It is known to depend on the type, orientation and length of the fracture. In realization that fractures of only 0.01 in. width have calculated permeabilities near 5,000 darcys, it is believed that many fractures may be considered as of near infinite permeability without incurring serious error. Primarily for this reason this study was made with fracture analogs of very great permeability compared to the matrix. FRACTURED SYSTEM ANALOG The pattern sweep efficiencies reported here were obtained with the aid of a potentiometric model. The application of this type model for solving reservoir problems has been described in the literature.1,2,3 The electrolyte reservoir was 20 in. wide by 30 in. long by approximately % in. deep. The liquid depth was constant, which corresponded to a constant permeability-feet product from the injection to the production well. The electrolyte reservoir was built to correspond to a unit in the line-drive pattern shown in Fig. 1. This figure shows part of an infinite array of wells having alternate rows of fractured and unfractured wells. The area within the dashed rectangle shows the area generally studied in the model. In using the model to represent a fractured system, a thin strip of copper was soldered to the well or wells and the length and orientation of the strip was made to conform to the vertical fracture under consideration.

Jan 1, 1955