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By F. M. Perkins, R. H. Jamison

Publications concerning scaling laws for laboratory flow models of oil reservoirs indicate that the relative permeability and capillary pressure relations must be the same functions of saturation in the model and its prototype. In this paper, the relative permeabilities and saturations are redefined in a way which permits one to have diflerent relative permeability and capillary pressure relations in the model and prototype. The development of the new scaling criteria is demonstrated by deriving scaling laws for one simple flow problem. INTRODUCTION The successful application of information gathered through bench-scale model studies to the prediction of multi-phase fluid flow behavior in petroleum reservoirs requires careful consideration of the scaling criteria. The requirements which must be met for a small-scale model to duplicate the behavior of a much larger reservoir prototype have been discussed by Leverett, et al,' Rapoport,2 and Geertsma, et al.3 According to these authors, the relative permeabilities to water, oil and gas and the dimensionless capillary pressures must be the must have the same values in the model and prototype. Furthermore, they point out that the viscosity ratios must have the same values in the model and prototype. In addition to these requirements, other scaling criteria are given which, when considered, usually dictate a much higher permeability in the model than exists in the reservoir. Since the more permeable model sands may have connate-water and residual oil saturations quite different from those in the prototype, the scaling requirements pertaining to the dependence of relative permeabilities and dimension l ess capillary pressures on saturation usually are not met. Also, if the model fluids are selected to give equal viscosity ratios in the model and prototype, one may find greatly different mobility ratios* in the two cases and, therefore, may expect grossly different flow patterns. For this reason, Craig, et al,' correlated the results of their model studies with mo- bility ratio rather than with viscosity ratio. As yet, however, no satisfactory method has been advanced which permits use of anything other than the scaling requirements outlined in the previously mentioned papers. The purpose of this paper is to present a method of developing a set of scaling criteria which permits different relationships between saturation and relative permeability or capillary pressure in the model and prototype. Rather than attempt to report scaling criteria for a variety of practical situations, this paper demonstrates by use of one simple example how the modified scaling criteria are derived.

By S. Vela, R. M. McKinley, L. A. Carlton

Johnson et al. have described a new well-testing technique that measures formation flow properties between wells.' The technique, called pulse-testing, requires a sequence of rate changes in the flow at one well and measzcrement of the re.rulting pressure changes at an adjacent well with a very sensitive differential pressure gauge. This paper describes an extensive application of the technique in a producing oil field. Pulse-tests on 28 of 45 possible well pairs in the field provided a picture of the areal distribution of reservoir hydraulic diffusivity, trans-missibility and storage. The primary objective in presenting these data is to demonstrate the potential of the methcid for reservoir description. A second objective is to show in three ways the qualitative and quantitative accuracy of reservoir parameters determined from pulse-tests: (I) pulse-test data show a nonuniformity in the field, closely correlating with the oil-water distribution as given by production data: (2) pulse-test values for permeability are comparable with core va1ue.s; and (3) perhaps most important, the field responds to a conventional interference test in the manner in which pulse-test data predict it should. The pulse-testing technique by Johnson et al.' is an ideal source of data for purposes of reservoir description, for it provides a measurement of formation storage S = +ch, hydraulic diffusivity 91 = k/+cp and transmissibility T — This paper describes an application of this method in a producing oil field. Results were analyzed to give numerical values for the parameters 7, T and S. These values were compared with oil-water production data (for the effect of fluid saturation), with core data and with data from an interference test. The reservoir in which the pulse-test survey was run is the result of a structural trap formed by a fault along the east side of a north-south trending anticline. A down-structure aquifer providcs a natural flank water drive for the pool. The producing formation is a dolomitic lime- stone having mainly vugular permeability; the formation oil has a gravity of 29" API with negligible dissolved gas. The field contains 19 wells, all on pump, arranged on 40-acre spacing along the top of the anticline. Fig. 1 shows the location of all these wells except two at the south end of the field. The dashed line on the right-hand side of the figure represents the approximate location of the fault with respect to well positions. Pulse-Test Survey and Analysis of Data A pulse-test requires a pulsing well and a responding well. In the field, changes were made in the rate of flow at the pulsing well by stopping and starting the pump periodically and measuring the corresponding pressure

Jan 1, 1969

By A. S. Emanuel

A correlation has been developed for calculating the phase behavior of, gas-condensate systems at reservoir conditions. The correlation is based on the principle of corresponding states and has been coded for an IBM 7094. Experimental K-values were determined for several gas-condensate systems at reservoir conditions to evaluate various semi-empirical parameters of the correlation. The approximate range of application of the correlation is 150 to 300F and 1,500 to 6,000 psi. INTRODUCTION The rapid development of digital computers during the past several years has made feasible the calculation of hydrocarbon phase behavior by methods based on rigorous thermodynamic principles. Good correlationsl have been developed for low to moderate pressures, but these techniques have not yet been extended successfully to reservoir fluids at high pressures. Consequently, the determination of phase behavior of oil and gas systems at reservoir conditions is still based almost entirely on generalized data correlations or on experimental studies of the fluid in question. While these methods have been used successfully many times, they do have inherent limitations that restrict their applicability. Generalized correlations, such as the NGShlA K-charts, are limited to the range of pressure, temperature and components for which the data were determined. The accuracy of these correlations is often questionable because the effect of total system composition is not well defined. Experimental studies offer a reliable method for determining phase behavior, but usually the studies are costly and time consuming. Recently, Leland and co-workers presented a new approach to calculating phase behavior from the principles of corresponding states.6-8 Corresponding states methods determine the thermodynamics properties of a given system by comparison with a reference substance whose properties are known. The accuracy of this approach depends on close chemical and structural similarity between the reference substance and the system in question and between components within the system itself. For high accuracy, it is usually necessary to correct for chemical and structural dissimilarities. In principle, however, the corresponding states method should be no less accurate at high pressures than at low pressures, provided reference substance properties are known. This paper describes an empirical modification of the basic correlation proposed by Leland, et al.6 for the specific purpose of calculating the phase behavior of gas-condensate fluids at reservoir conditions. The modified correlation, which has been programmed for an IBM 7094, may be used for either approximate or precise determination of fluid behavior depending on the amount of analytical and, experimental data available for the system. BASIC THEORY The basic theory of the corresponding states phase equilibria correlation was first published by Leland, Chappelear and Gamson.6 Subsequently, Leland, Chappelear and Leach published methods for improving the accuracy of the original theory.7-9 The aim of the correlation is to calculate the K-value of each component of a given system as a function of pressure, temperature, and over-all composition, where Once the K-values are known, the phase behavior may be determined directly by an appropriate flash calculation. The basic equation for calculating component K-values was taken from the work of Joffe. 4 For any component i of a mixture, the K-value is given by

Jan 1, 1969

By H. S. Price, J. C. Cavendish, R. S. Varga

This paper presents a new technique for solving some of the partial differential equations that are commonly used in simulating reservoir performance. The results of applying this technique to a simple problem show that one obtains accurate pressure values near wells, as well as accurate pressure pdients, which can be explicitly calculated. The method is completely rigorous in that convergence of the discrete numerical solution to the continuous solution for both pressure and pressure gradient is established. High-order, piecewise-polynomial approximations are used near the wells where pressure gradients are steep, while low-order, piecewise-polynomial approximations are used elsewhere to reduce greatly the calculation time. This combination is shown to give a uniformly good approximation to the solution. These approximations, obtained by using a Galerkin process with suitable Hermite subspaces, are shown to be theoretically and numerically superior to the usual approximations obtained from standard finite-difference techniques. Not only are much greater accuracies obtained, but computer times are also greatly reduced. The application of this technique to multiphase flow problems (e.g., single well coning problems) would have considerable practical interest, but such extensions of this technique with full mathematical rigor have not been made as yet. However, the numerical methods presented here are general, and in principle extend to multidimensional, multiphase flow. Moreover, the preliminary results given in this paper are sufficiently encouraging that we feel the effort in attempting these extensions is justified. INTRODUCTION The problem of obtaining accurate pressure distributions and pressure gradients around wells is of considerable importance in the numerical simulation of reservoir performance. The most common approach to solving this problem is to use finite difference techniques (see McCarty and Barfield9 or Peaceman and Rachfordl0). This approach, however, has many disadvantages, the major one being that many grid points are generally necessary for accurately describing the pressure distribution and the pressure gradient around wells. This need for a fine grid results in large computer times and often in prohibitively high costs. Besides investigating the method of finite differences, some authors, such as Welge and weber17 and Roper, Merchant and Duvall,13 have considered a combination of analytical and numerical techniques with some success. These approaches, however, are all nonrigorous and quite often cannot even be applied. In this paper, we present a numerical formulation of high-order accuracy, based on the Galerkin method, for solving this problem. We treat here only the partial differential equation that describes steady-state, single-phase flow. However, the methods presented are general and in principle extend to multidimensional, multiphase flow. Specifically we treat special cases of the problem in two dimensions described by: where G is a rectangle (with sides parallel to the coordinate axis) with boundary ?G, ?/?n denotes the outward normal, and y and B are non-negative constants such that y + B > 0.

Jan 1, 1970

By E. DeGolyer

The only known direct method of discovering oil deposits is by the drilling of test wells. Such exploration is always hazardous and generally very costly. The problem of the prospector, therefore, is to select test sites that are favorably located and so to reduce the odds against his venture. Early in the history of the oil industry, it was realized that oil and gas deposits, other conditions being favorable, were usually found in anticlinal types of structure. This very undestandable and rational habit of occurrence furnished the first substantial clue to the prospector. Oil occurs in sedimentary rocks, and beds of such rocks are deposited originally in approximately parallel layers. An anticline at the surface, therefore, could be accepted as an indication of an anticline in lower beds. Structural geology became the tool of the prospector, and by its use in the past two decades the majority of the known important oil deposits of the world have been discovered. This is but a partial, and the simplest, statement of the problem, Nine-tenths and more of the important oil pools of the world belong to the great class of accumulations controlled by structural traps—anti-clines, faulted structures, salt domes, etc.—but by no means all of these structures are clearly or adequately expressed at the surface. As the more obvious anticlines were explored and the search for new deposits led to the testing of progressively deeper beds, it became more and more apparent that marked favorable structures involving petroliferous rocks can, and do, exist without any marked surface expression. There are great areas where the surface, covered by some masking material such as water, alluvium, glacial deposits, or sand dunes, affords no clue to structural conditions in the subsurface, and there are also regions where the surface formations are unconformable with the oil-bearing formations. The structure in which the prospector is fundamentally interested is that of the oil-bearing formation itself, together with roof and floor beds. No other geologic information is of interest or importance to him except as it affords clues to the stratigraphy and structure of the supposed oil-bearing formations.

Jan 1, 1932

Due to the advanced date of publication of this Bulletin, the lists of new members, changes of address, etc., for the month of July will be printed in the September number of the Bulletin. CANDIDATES FOR MEMBERSHIP. The following persons have been proposed during the period July 1-20, 1913, for election as members of the Institute. Their names are published for the information of members and associates, from whom the Committee on Membership earnestly invites confidential communications, favorable or unfavorable, concerning these candidates. A sufficient period (varying in the discretion of the Committee, according to the residence of the candidate) will be allowed for the reception of such communications, before any action upon these names by the Committee. After the lapse of this period, the Committee will recommend action by the Council, which has the power of final election.

Jan 8, 1913

Optimism over the continued growth of coal ex- ports received a significant shot in the arm September 18 at Norfolk, Va., when huge, new ship coal-loading facilities of the Norfolk & Western Railway were formally dedicated before a large audience of American and foreign dignitaries. Guest of Honor at the occasion was Christian A. Herter, Special Representative for Trade Negotiations, who, in a speech, stated, "The prospects for the expansion of our coal exports are excellent. The competitive pricing and high quality of our coals, whether for the production of coke for steel mills or for the generation of electric power, have won the respect of consumers everywhere in the world. Last year, the United States coal industry exported over 40 million net tons. . . . There are excellent reasons to believe that by 1970 we shall be exporting at double this rate."

Jan 10, 1963

By O. J. Neslage, R. W. Jenkins

MINE operators today are paying increased attention to the mechanization of drilling operations as an important factor in increasing efficiency and decreasing costs. Recent progress in the design of drill jibs for mounting on drill carriages, or jumbos, has done much to advance the mechanization of mining methods. This progress has introduced new opportunities in the application of "jib jumbos" that are worth serious consideration. An attempt will be made here to classify the various types of jumbos and drill mountings available for level development and flat stope work, t6 indicate applications, and to measure their effectiveness in relation to their cost. The data here are based on a wide variety of field usage, and are offered only to point up, in a general way, the relative efficiency in proportion to cost. It should be remembered that any contemplated jumbo installation must be studied to determine what type of installation is most suitable, considering ground conditions, loading, timbering and haulage equipment, service available, and attitude of manpower. Early Drill Carriages: The advantages of some sort of a drill carriage were recognized at the time rock drills were introduced. In drift or heading operations where a fairly standard drill round and cross section were anticipated, as well as in flat bedded deposits where standard slabbing rounds were used, track and crawler-mounted drills found an early application. These first drill jumbos were little more than drill carriers, designed locally and manufactured with materials at hand. Of comparatively simple construction, function, and low capital cost, they usually consisted of a hinged column which supported one or more drills on arms or universal bars. When the column was pivoted vertically, the drills were moved into position. Screw jack extensions reached from the column to the roof and floor to hold the drill rigid. In some cases, particularly in tunnel jumbos, enough weight was carried that rail clamps or roof jacks were sufficient. Many of these column and arm-type jumbos, usually equipped with air and water manifolds, steel racks, and staging for drillers, are still in use today. Some have employed air or hydraulic extensions for securing the columns. They offer the equip-saving advantage of having all the necessary out, ment together, and they un be moved i and t. set up and torn down as a unit. Boom-type Jumbos: When the advantages of to column-type jumbo were seen, operators could to realize the further gains possible. More time could be saved with mechanical assistance to position api drill vertically. A rack on the column and a pinion on the arm for raising and lowering the drill in the manner of a quarry bar were tried with some success. The most outstanding solution to the vertical handling problem was reached with the boom-type of jumbo. Here two or more machines were mounted on a cross arm at the end of a boom that was pivoted at the rear of the track. This was raised and lowered by various mechanical aids. Occasionally air or hydraulic power was used. Nearly all of today's wagon drills use this boom-type principle. Boom jumbos represent a savings in time and physical effort expended in raising and lowering the drills. The boom must be balanced by the roof of the truck which is secured by rail clamps or type jacks. The most successful application of areawhere this of jumbo has been in the Tri-State area where multiple long-feed machines are used on caterpillar-mounted, boom-type jumbos for slabbing

Jan 1, 1951

By R. W. Jenkins, O. J. Neslage

MINE operators today are paying increased attention to the mechanization of drilling operations as an important factor in increasing efficiency and decreasing costs. Recent progress in the design of drill jibs for mounting on drill carriages, or jumbos, has done much to advance the mechanization of mining methods. This progress has introduced new opportunities in the application of "jib jumbos" that are worth serious consideration. An attempt will be made here to classify the various types of jumbos and drill mountings available for level development and flat stope work, t6 indicate applications, and to measure their effectiveness in relation to their cost. The data here are based on a wide variety of field usage, and are offered only to point up, in a general way, the relative efficiency in proportion to cost. It should be remembered that any contemplated jumbo installation must be studied to determine what type of installation is most suitable, considering ground conditions, loading, timbering and haulage equipment, service available, and attitude of manpower. Early Drill Carriages: The advantages of some sort of a drill carriage were recognized at the time rock drills were introduced. In drift or heading operations where a fairly standard drill round and cross section were anticipated, as well as in flat bedded deposits where standard slabbing rounds were used, track and crawler-mounted drills found an early application. These first drill jumbos were little more than drill carriers, designed locally and manufactured with materials at hand. Of comparatively simple construction, function, and low capital cost, they usually consisted of a hinged column which supported one or more drills on arms or universal bars. When the column was pivoted vertically, the drills were moved into position. Screw jack extensions reached from the column to the roof and floor to hold the drill rigid. In some cases, particularly in tunnel jumbos, enough weight was carried that rail clamps or roof jacks were sufficient. Many of these column and arm-type jumbos, usually equipped with air and water manifolds, steel racks, and staging for drillers, are still in use today. Some have employed air or hydraulic extensions for securing the columns. They offer the equip-saving advantage of having all the necessary out, ment together, and they un be moved i and t. set up and torn down as a unit. Boom-type Jumbos: When the advantages of to column-type jumbo were seen, operators could to realize the further gains possible. More time could be saved with mechanical assistance to position api drill vertically. A rack on the column and a pinion on the arm for raising and lowering the drill in the manner of a quarry bar were tried with some success. The most outstanding solution to the vertical handling problem was reached with the boom-type of jumbo. Here two or more machines were mounted on a cross arm at the end of a boom that was pivoted at the rear of the track. This was raised and lowered by various mechanical aids. Occasionally air or hydraulic power was used. Nearly all of today's wagon drills use this boom-type principle. Boom jumbos represent a savings in time and physical effort expended in raising and lowering the drills. The boom must be balanced by the roof of the truck which is secured by rail clamps or type jacks. The most successful application of areawhere this of jumbo has been in the Tri-State area where multiple long-feed machines are used on caterpillar-mounted, boom-type jumbos for slabbing

Jan 1, 1951

By Ralph Monaghan, Arthur Youmans

General principles of scintillation counter-type instruments for radioactivity logging are discussed and the various possible causes for instability are examined. It is shown how instrumentation problems are solved. Means are discussed for minimizing drift and instability due to "fatigue" of the photomultiplier tube and neutron activation of the crystals. INTRODUCTION Neutron and gamma-ray logs made with logging instruments employing scintillation counters are now routinely available from most of the logging service companies. The superior characteristics of scintillation counters by comparison with older types of detectors promises to bring about important improvements in quantitative interpretation of radioactivity logs. Moreover, new types of logs can be made with scintillation counters which are not possible with other detectors. But in spite of the obvious superiority of these counters with respect to efficiency, speed, and versatility, they suffer from a number of inherent difficulties and weak- nesses. Unless these inherent diffi-culties are fully recognized and satisfactorily overcome by sound engineering of the associated instrumentation, scintillation counter logs are particularly likely to exhibit drift and instability of sensitivity. This defect in logs when they are intended for quantitative interpretation is intolerable and more than outweighs any advantages over the older type of instrumentation when the latter is operating correctly. SCINTILLATION COUNTER OPERATION In general all radioactivity logging instruments consist of a detector sensitive to gamma radiation or to neutron radiation coming from the strata. This radioactivity is either due to naturally decaying radioactive elements in the rock, radioactivity induced in the rock by a neutron source in the instrument, or scattering by the rock of neutrons or gamma rays coming from a source in the instrument. In the scintillation counter the gamma radiation or neutron radiation reacts with the scintillation phosphor to produce light pulses. These light pulses are then converted to amplified electrical pulses by the multiplier phototube. Basically the problem of making a good scintillation counter logging instrument is to make the radiation sensitivity of the system as nearly constant as possible. The size of each scintillation counter pulse is dependent on the energy of the individual quantum of radiation being detected. In normal radiation logging, gamma rays of all energies, up to some maximum value, reach the detector. If a suitable scintillator is used, such as a sodium iodide crystal, each gamma ray produces a number of photons proportional to the energy absorbed by the crystal from the impinging radiation. The light flashes are detected by means of a photo-multiplier tube which contains not only a photo-sensitive cathode from which photoelectrons are collected, but also an amplifier, called an electron multiplier, built inside the photomultiplier tube; the electron multiplier usually has about 10 stages, having an over-all gain of perhaps 500,000. In an ordinary gamma-ray log one wishes to detect all gamma rays down to the lowest possible energy; therefore, one wishes only to reject the "noise" pulses which are invariably present due to thermal emission of electrons from the photo-cathode of the photomultiplier. In other radioactivity logs it may be desired to measure the radiation within a particular energy band, or above

Jan 1, 1958

By N. S. Keith

No one of the live subjects of the day, to which the attention of the mining engineer and metallurgist should be turned, is of greater practical interest to him than electricity in its applications to various mechanical, chemical, and metallurgical operations.. The object of this paper is to call the attention of my fellow-members and associates of the Institute to various new, as well as comparatively old, developments in the science and art of electricity which seem to promise results of advantage. Too many of the comparatively old applications have been neglected by the mining engineer, which, if he had given them a place among his appliances, would have assisted him greatly. The telegraph may be noticed as one. Its use is, however, confined to a person having skill in the manipulations of the key, the reading of the alphabet, and familiarity with the sounder. One of the simpler forms—the call-bell—has a range of application far greater as to distance and convenience than the old wire-pull, or the hoarse voice of the windlass-man or the bucket-dumper. A few Leclanche cells, two or more electric bells, and a mile or more of mire judiciously placed will put the superintendent, at his office, in communication with the foremen of his mills and mines, so that by the aid of a code of signals, great advantages may be gained without necessitating a knowledge of the Morse alphabet, or of the mechanical voice of the sounder. The telephone furnishes a means of communication be-

Jan 1, 1882

By J. B. Newsom

IN the September 1936 issue of MINING AND METALLURGY the pioneer work of boring a 5-ft. shaft to a depth of 1125 ft. at the Idaho Maryland mine in California was described. Later, a Bureau of Mines Information Circular (No. 6923) gave additional data. In re¬cent months still further progress has been made in this technique through the sinking of a 5 1/2-ft. shaft for Pickands, Mather & Co. at their Zenith mine, Ely, Minn. The present work was done with new carefully designed equipment and several experienced men so that progress, as shown below has been much better:

Jan 1, 1938

By John L. Walter

A sintered compact of iron containing 0.007 vol fraction of glass , prepared 6). powder rnetullurgtcal lechniques, was rolled lo foil, 0.001 in. /hick. The foil sullrples were anneuled a1 650° to 850°C in hydrogen. Pri,narj recryslullization prodtnced large grains which Lc3ere highly elongnled in the rolling direclion und which had an unusual prgferred orientation. The glass parlicles assumed a stringerlike dispersiorz on working; llie slrinyers were parallel lo the rolling direction and to the long axis of the grains. The same unusual grain structure, preferred orientation, and stringerlike dispersion of purticles are found in heal-ily rolled and annealed foil of tungsten which has heen doped wilh small amounts of aluminum, silicon, and polassiutvt. Both the proper dispersion of the particles and severe working (reductions in excess of 98 pct) are necessary to produce the elongzcted grain structure. RECENTLY, the author reported on the origin of the elongated or "nonsag" grain structure in tungsten foil which was doped with aluminum, silicon, and potassium.' It was observed that particles, identified as mullite (Al6Si2Ol3), were present in the doped ingot (as sintered) and at all stages of processing from ingot to sheet or wire. It was shown that the particles, being plastic at tungsten working temperatures (up to 1550"C), underwent a "stringing out" parallel to the working di-direction. It was concluded that these strings of particles were responsible for the formation of the highly elongated interlocking grains observed in doped tungsten wire or sheet. To give further credence to this explanation of a long-observed but not understood phenomenon, it was decided to design a new system, one which was analogous to the doped-tungsten system. Thus, a bcc metal, iron, was chosen to be doped with glass which would be plastic at reasonable working temperatures for iron. The glass chosen was a #0080 Corning lime glass which melts at about 810°C. This is approximately the same fraction of the melting point of iron (0.6) as the melting temperature of mullite is of tungsten. It will be shown that all the observed unusual features of the doped tungsten are duplicated in the glass. doped iron, even to the preferred orientation of the grains in the recrystallized sheet. In the tungsten sheet the preferred orientation consists of two components, (1i3)(691) and (013)(362), neither of which has been observed as a component in textures of primary recrystallized bcc metals. EXPERIMENTAL PROCEDURE The glass, in the form of fine powder, was added to high-purity electrolytic iron powder and mixed dry. The particular composition chosen was 0.007 vol fraction of glass. After mixing, the powder was mechanically pressed to a disk 0.5 in. diam and 0.15 in. thick at a pressure of 5000 psi. The pellet was sintered, in pure dry hydrogen, for 2 hr at 8 50°C. The sintered pellet was then heated to 750°C and rolled to 50 pct reduction of thickness in two passes, with reheating between passes. The rolling temperature was then reduced to 600°C and the slab was rolled to a thickness of 0.050 in. Rolling to 0.010 in. was accomplished in several passes at 300°C. Final reductions to 0.003 and 0.001 in. were taken at room temperature. This rolling temperature schedule was similar, in terms of the fraction of the melting point, to that used in the rolling of the doped tungsten. The total reduction of thickness was in excess of 99 pct. Samples of the rolled foil were lightly electro-polished and annealed for 1 to 6 hr at temperatures of 650" to 85O°C in hydrogen. Samples for transmission electron microscopy were thinned on a Disa Electropol using AC-1 electrolyte.

Jan 1, 1968

By J. S. Hegwer, P. M. Dunlap

An improved acid for the treatrrzent of sulfate-con-raining limestones and dolomites is described. The acid is designed to reduce he reprecipitation of dissolved calcium sulfate and the possibility of plugging permeable flow channels. In addition, this improved acid has a much lower reaction rate than that of regular acid; the advantages of a "retarded" acid are obtainable. Field testing of the acid has shown it suitable for use in sulfate-containing formations. Substantial improvements in productivity generally resulted. INTRODUCTION Acid treatments of limestones, dolomites and other formations bearing carbonate deposits are frequently unsuccessful when the calcareous formation contains sulfate, either as anhydrite (CaSO,) or gypsum (CaSO4. 2H2O). Preliminary dissolution in acid followed by redeposition of calcium sulfate appears to be a major factor contributing to poor well performance after acidizing. The precipitate is usually the gypsum form of calcium sulfate, but in higher temperature formations it may be anhydrite. The freshly precipitated crystals are nearly always very small and needle-like. They may occupy a gross volume many times that of the original anhydrite crystals and will obviously constitute an impediment to flow through newly enlarged flow channels. It is believed that the redeposition problem is most severe when anhydrite lines the fracture systems and large pores which supply the effective permeability of a formation. Microscopic inclusions of calcium sulfate also present large sulfate surface areas for dissolution in acid. In either case, great amounts of calcium sulfate may dissolve before the acid can be spent on formation carbonates. For regular spent acid (originally 15 per cent hydrochloric acid) the precipitate could be as much as 270 Ib gypsum/1000 gal acid. Two techniques have been applied by the industry for reducing sulfate plugging during acidizing. The method'.' commonly employed in the field is the attempted removal of a quantity of regular treating acid before it has reacted completely with the formation. This is practiced because the solubility of calcium sulfate is greater in a solution that is still acidic than in one which has been largely spent on the formation rock. The chance of precipitative plugging is therefore reduced if the withdrawal is successful. However, it is often impossible to get the acid out of the formation before precipitation occurs. A second possible method, which at first glance appears practical, involves addition to the acid of sequestering agents which form strong soluble complexes with calcium ions. These chemicals do increase the "solubility" of calcium sulfate in fresh acid, but to a lesser extent in spent acid. The sequestering agents have, therefore, proved unsatisfactory because the amount of sulfate eventually deposited from the spent acid may be greater than that from regular acid. Another logical approach to the problem of calcium sulfate reprecipitation is the prevention of the initial dissolution of calcium sulfate by the common ion effect. This may be accomplished by adding a soluble calcium salt to the fresh acid. The use of calcium salts in treating acids is not entirely new. An earlier suggested use of a soluble calcium salt in hydrochloric acid apparently failed to recognize the full extent to which the solubility of calcium sulfate could be suppressed. The present study extends this earlier work and adds certain improvements toward the development of a practical anti-anhydrite acid. LABORATORY DEVELOPMENT Calcium Sulfate Solubility Table 1 shows the results of a laboratory study performed to establish the effect of calcium chloride concentration on gypsum solubility. Because of the strong tendency of calcium sulfate to form supersaturated solutions, accurate solubilities are difficult to determine. These solubility data probably are reliable to within ± 15 per cent. The solubility of calcium sulfate in 15 weight per cent hydrochloric acid increases with increasing temperature. This trend is also followed in hydrochloric acid which cantains calcium chloride. This is contrary to the solubility behavior of calcium sulfate in water, wherein the solubility decreases with increasing temperature.

By E. Lifshin, R. E. Hanneman

QUANTITATIVE applications of the electron micro-beam probe frequently involve the evaluation of complex mathematical expressions and/or the analysis of large amounts of experimental data. The purpose of this communication is to describe briefly a versatile and useful computer program system that is applicable to analyze rapidly a wide variety of practical microprobe problems. This system consists of a group of ten FORTRAN programs that can be stored on tape, cards, or in the memory disc of the computer. These programs, or links, can be run individually or in any prespecified sequence without interrupting the operation of the computer or without destroying information which is being transfered from one link to another. For the program system described here a GE-235 computer with disc storage was used, so that the DCHAIN method of program linking was employed. Included in the library are programs to: 1) initiate analysis of a new set of data and transfer control between all other programs in any predetermined manner; 2) generate theoretical calibration curves of composition vs relative intensity; 3) generate empirical deviation parameters from least-square fits of experimental calibration data from standards of known composition; 4) convert raw X-ray data to corrected composition; 5) determine inter diffusion coefficients by Matano analysis of con centrat ion -distance data on a uniaxial diffusion couple; 6) determine activation energies and frequency factors of temperature-activated processes such as diffusion; and 7) generate calibration curves for determination of the thickness of thin films using microanalysis. A detailed description of these computer programs and their underlying principles is available on request from the authors."' The first program to generate theoretical calibration curves of corrected relative intensities vs composition uses the Poole and Thomas atomic number correction' and the Philibert absorption factor' with a voltage-dependent mass absorption coefficient for electrons in the alloy. A modified Castaing fluores- cence correction is also used which includes the effects of both Ka and KO radiation and over voltage.' Once the theoretical curves have been calculated in 1 wt pct intervals, these results are least-squares fit to obtain Ziebold deviation parameters' which are stored in COMMON in the computer memory. The net discrepancies between the original theoretical calibration curve and the regenerated curve using the Ziebold parameter are computed. Although this link is explicitly written for K-K fluorescent interactions, it can be applied to K-L, L-K, and L-L interactions as previously disc~ssed."~ Similar programs have also been written to utilize the Wittry fluorescence correction, Birks combined corrections, and various other corrections.' These modified programs have proved to be quite useful for quantitative comparisons of the results of the various theories. The program for conversion of raw X-ray data to corrected composition includes corrections for drift, backround, and instrumental dead time. The corrected intensities are converted to composition by use of the Ziebold equation"2 and parameter obtained from the program system. The results can be obtained for either atom or weight fractions. In addition to accurately computing interdiffusion coefficients the Matano analysis program calculates least-square smoothed values of concentration, concentration gradient, and curvature for each point on the raw input concentration profile. In order to obtain high accuracies a unique method of performing a least-square polynomial fit to incrementally advancing profile segments which overlap is used.' This program has been successfully modified for use in ternary diffusion problems3 and can readily be modified to handle analysis of diffusion profiles which include phase boundary discontinuities. This link is generally applicable to analysis of interdiffusion data obtained by other techniques as well as by the microprobe. The primary function of the next program is to least-squares fit experimental diffusion data to the normal Arrhenius function: D = Doexp(-Q/RT), to obtain values of Do and Q. In addition the probable error and one, two, and three u statistical confidence limits of DO, Q, and log D are evaluated. This program is also directly useful for analysis of any other simple temperature-activated processes including conductivity, and certain deformation and chemical processes. The program to generate calibration curves for film-thickness determination using the microprobe is based on a numerical integration of the equation derived by Cockett and ~avis.' Values of film thickness obtained by this program for copper on various substrates are in good agreement with measurements made by other techniques. Versions of the above program system have been prepared for use with or without a remote teletype connection to the computer for processing on either a real-time or time-share basis. The instrumentation coupling a microprobe to a teletype for automatic data collection and analysis by the presently described program system has been reported elsewhere by the authors.' If teletype equipment is not used to communicate with the computer, standard methods of card reading and tape reading can be used. In either

Jan 1, 1967

By AIME AIME

A new Index of the Transactions, Volumes I. to XXXV., is now being prepared, and will probably be ready for distribution during the coming summer. The Index will be about the size of the average volume of the Transactions, and will be bound in cloth and in half morocco. The price of the cloth-bound copy is $5, expressage prepaid. Half morocco binding will cost $1 extra. It is very desirable that all who wish to purchase this Index will notify the Secretary's office promptly, sending a check, money-order or draft, made payable to the American Institute of Mining Engineers.

May 1, 1907

By W. A. Griffith

Fractional replication of factorial design, a general method for planning experimentation and for analysis of data obtained, is described as applied to a flotation investigation. This method leads to determination of optimum process conditions with minimum experimental effort. Its advantages over simple factorial design are demonstrated. A METHOD for planning experimentation and for analyzing the data secured will be demonstrated. This method, termed fractional replication of factorial design, employs a relatively small number of individual experiments to determine which of a large number of process variables are controlling, to determine which combination of levels of these variables is most likely to produce optimum results, and also to predict what results will be obtained with a particular combination of conditions not already tested. Although the general method is not new, having been developed by Finney in 1945,' the extent to which it can improve the effectiveness of applied research generally has not been recognized by metallurgists. The fractional replication procedure is particularly useful in flotation experimentation and an example from such an investigation will be used in the paper. However, it has equal value in any investigation in which similar experimental difficulties are encountered. In developing a flotation process for a particular mineral separation, the investigator is inevitably confronted with the following difficulties: 1—There are a large number of potentially important process variables. 2—Results of individual experiments are not highly reproducible, due in part to the difficulty in precisely controlling all the variables. 3—Considerable effort is expended in conducting individual experiments. 4—There are practical limits on the number of individual experiments which can be made. In situations of just such a type, modern statistical methods of planning experimentation and analyzing data have their greatest value. Applications of one such technique, called factorial design, to problems of this type have been described by Dorenfeld and others.'-' The simple factorial design is an efficient procedure when the investigator hopes to provide a comprehensive understanding of the effects and interrelationships of a small number of variables over a limited range. In applied research, this is seldom the main objective. Rather, the investigator usually wishes to determine which of the many potentially important variables are in fact controlling, which levels of the controlling variables will provide opti- mum metallurgical results, and what these results will be at optimum conditions. Interest in detailed trends is limited to the controlling variables and to levels in the region of optimum conditions. Simple factorial design has serious deficiencies for such objectives and is not the most efficient method of experimental design. Deficiencies of Factorial Design In a simple factorial design, an experiment must be made at every possible combination of each level of every variable, once these have been chosen and the levels of each to be included have been decided upon. As the number of variables or levels of each increases, the experimental program quickly reaches prohibitive size. For example, an investigation of only four variables, each at four levels, requires 256 individual experiments. Often upon completion of such an extensive program, it is found that one or more of the variables has metallurgically unimportant effects or that a poor estimate has been made as to the appropriate range of levels to be investigated. The result is that only a small proportion of the data obtained falls in the range of real metallurgical interest. Indeed, it frequently can be anticipated that certain combinations of levels of variables will not produce results of interest, but they still must be included so that the essential balance, or orthogonality, of the design will be retained. It may be true that factorial design will provide the greatest amount of information from a given number of experiments, but it does not necessarily follow that it will lead to the desired information with a minimum number of experiments. Much of the information provided may be of little value. Advantages of Fractional Replication The disadvantages of simple factorial design are overcome to a great extent by a modification known as fractional replication. This is a technique for sampling systematically the potential data of a full factorial experiment, that is, the data which would have been obtained if the complete factorially designed program had been completed. Only a fraction of the total array of experiments is made, but the experiments are chosen in such a way that the important advantages of factorial design and the accompanying analysis of variance are retained. The data obtained from the first group of experiments are used to determine which of several variables are controlling and which levels of these variables are most likely to produce the desired result. Unimportant variables and levels of variables then may be

Jan 1, 1956

By R. E. Reed-Hill

A simple accurate graphical method for orienting fcc crystals using (111) slip traces on a single surface is described. Solutions placing the pole of the surface in a unit stereographic triangle are obtained using a Wulffnet, a (111) standard projection showing the four (111) planes, and a (111) standard projection ruled into unit stereogmphic triangles. The multiplicity of solutions is described in relation to this method. AN accurate, rapid single-surface technique for orienting fcc crystals, using (111) slip or twin traces, has been a matter of continuing interest, as evidenced by the periodic appearance of papers on this subject.'-4 This note presents a new method possessing some advantages over those previously reported. It is an analog to the technique for hcp metals5 where the solution is based upon a stereographic rotation of the specimen surface on a (0002) standard projection that contains the planes of the possible features that might account for the observed traces. In the hexagonal solution, the axis of rotation is the basal-plane trace in the surface. In the fcc case, the axis of rotation is one of the observed ( 111) slip or twin traces. It has been observed that the solution is greatly facilitated if the indicated movements of the (111) traces during the rotation of the surface are plotted directly on a paper copy of a Wulff net as shown schematically in Fig. 1. The trace selected to represent the axis of rotation is assumed to fall at the north-south poles of the Wulff net. The directions of the other traces are then plotted as points at the proper angles around one-half of the basic circle of the net. The loci of points corresponding to the movements of these traces (directions) during a 90-deg rotation of the surface, about the polar axis of the net, are then easily and accurately drawn by following the appropriate small circles on the Wulff net. The solutions to the problem are obtained with the aid of a (111) standard projection of the (111) planes, see Fig. 2. This is normally a Xerox copy of a carefully drawn master made on high-quality tracing paper. The (111) standard projection is superimposed over the Wulff net and rotated about its center until the points of intersection of the loci of surface traces, drawn on the Wulff net, and the great circles representing the (111) traces, all lie along a common meridian of the Wulff net as demonstrated in Fig. 3. This latter great circle represents a possible position of the surface. The pole of this plane is then plotted on the (111) standard projection. Its location in a unit stereographic triangle may be readily obtained by superimposing (over the standard projection) another tracing paper (111) standard projection subdivided into unit stereographic triangles. The result of this last operation is shown in Fig. 4. MULTIPLICITY OF THE SOLUTIONS The maximum possible number of (111) traces on a single grain surface is four. Any one may be selected as the axis about which the surface is rotated. Corresponding to each such choice are three possible surface-pole orientations, related to each other by a simple 120-deg rotation about the pole of the (111) basic circle. This is a direct result of the threefold symmetry of the (111) standard projection. Since each of the four rotations will normally give a different set of three-pole positions, there are, accordingly, twelve possible solutions. Each of these twelve solutions places the surface pole in the same relative position in a stereographic triangle so that all are crystallo-graphically equivalent. Accordingly, only a single solution is required to obtain a basic orientation of the crystal. It should be noted, however, that the orientations obtained by reflecting* any of these twelve orien- *The reflected orientations may be obtained by a 90-deg rotation of the opposite sense to that shown in Fig. 1. This rotation places the correspond-ing trace loci in the lower hemisphere of the Wulff net rather than in the upper hemisphere. tations through the surface are also possible orientations that could account for the surface traces. Thus, a given set of four traces always corresponds to a pair of basic orientations related by reflection through the specimen surface. This ambiguity can only be re-

Jan 1, 1967

By B. N. Thompson

Main industrial minerals produced in New Zealand are nonmetallic - clay, dolomite, limestone, pumice, salt, serpentine, and silica sand. Other minerals, some with minor production, include diatomite, feldspar, magnesite, sulfur, asbestos, and perlite. Energy and metallic minerals and aggregate are excluded from this account. These industrial minerals occur in a wide range of rock types and geological ages. For example, clays are known from the weathering products of Cretaceous rhyolite and leaching of Eocene coal measures; from Quaternary weathering of contemporary loess and shallow marine sediments, and of greywacke of Triassic-Jurassic age; and from the hydrothermal alteration of late Cenozoic acidic volcanic rocks.

Jan 1, 1984

By J. J. Gilvarry, B. H. Bergstorm

The first part of this paper describes a new approach to the problem of energy relationships in fracture and comminution. The basic theoretical method used (as contrasted to previous empirical or semi-empirical approaches) is an attempt to verify or disprove the hypothesis of von Rittinger, In the second part of the paper, theoretical conclusions for the three headings of single fracture, plural fracture, and comminution are tested. Agreement between theory and experimental results is demonstrated. The classical hypotheses on the energy relationship in brittle fracture are those of von Rittinger-that the energy required is proportional to the new surface formed— and the alternative one of Kick.' Over the years, repeated attempts have been made to discriminate experimentally between the two assumptions, or to replace both of them, as has been done by Bond? However, no semblance of agreement seems to exist among different investigators. This paper is the first in a series essaying a new approach to the entire problem of energy relationships in fracture and comminution. The purpose of this program of research is to verify (or disprove) the hypothesis of von Rittinger. In contrast to previous empirical or semi-empirical approaches to the problem, the basic method adopted is theoretical. The prime aim is to determine the distribution function for fragment size theoretically and to verify the predicted distribution experimentally. This approach should make possible determination of the total surface of the particles by integration over the corresponding distribution function; one may hope that this direct procedure will yield more definitive results than use of gas adsorption or other methods. The surface area so obtained can then be compared with experimental energies, as obtained by Bergstrom, Sollenberger, and Mitchell,4 for example. It is convenient to distinguish between single fratture, plural fracture, and comminution. Single fracture of a brittle solid is defined as fracture by an external stress system which is removed instantly and permanently when fracture is initiated. Plural fracture consists of single fracture of the original specimen, followed by a sequence of only a few secondary fractures; comminution differs in that the sequence of secondary fractures consists of a large number of repetitive steps. For single fracture, Gilvarrys has given a rigorous derivation of the proper distribution function for fragment size, based on a closely defined physical model and deduced strictly by the laws of probability. Gilvarry and Bergstrome have compared the predictions of the theory with experiment, and have found excellent agreement. The prior work of Gilvarry and of Gilvarry and Bergstrom considers only single and plural fracture. The purpose of the present paper is to extend the discussion to the case of comminution. For prefatory purposes, the theory of Gilvarry for single fracture will be outlined. The considerations will then be applied to the cases of plural fracture and comminution. SINGLE FRACTURE The derivation is based on the Poisson law.7 For Points distributed with mean density y over a domain, this law states that the probability p(t)dt of one point lying in the range t to t + dt with none in the interval 0 to Ms p(t)dt = ye-yt dt. For this distribution to be valid, it is necessary and sufficient that the points be distributed at random, individually and collectively in the sense of ~~~.7 The former qualification requires that the position of One Point be independent of another, and the latter implies that the probability of a region containing a

Jan 1, 1961