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By W. C. Winegard, A. Galibois, C. J. Beingessner

The effects of solutes on the distribution of two-dimensional configurations of grains in zone-refined tin have been studied. When solutes with partition coefficients (ko) greater than unity are added, three-sided pains become more prevalent and the growth law changes. It is shown by electron-Probe micro-analysis that a solute buildup occurs ahead of a moving grain boundary when ko > 1. It has been found recently1, 2 that solutes with partition coefficients greater than unity have a larger retarding effect on grain growth than solutes with k, less than unity. ko is defined as the ratio of the concentration of solute in the solid to the concentration of solute in the liquid with which the solid is in equilibrium. Niessen and winegard2 have suggested that this effect is probably due to the complex shape changes which occur during the process of grain growth and that no theory based on single boundary motion3-5 can explain the results. They suggested that the dissociation of the unstable fourfold junction was delayed in alloys where ko was greater than 1 because the boundaries at the junction had to move into a region of high solute concentration. If indeed this mechanism were correct, it was felt that not only would the dissociation of fourfold junctions be affected by the solute buildup ahead of the boundaries, but the collapse of three-sided grains would be impaired. These combined effects would naturally lead to a modification in the distribution of the number of sides per grain seen on a two-dimensional section. The present investigation was undertaken to test these hypotheses by examining the grain-growth process in detail. EXPERIMENTS The Distribution of Grain Configurations in Zone-Refined Tin as Seen on a Two-Dimensional Section. Following the method of Bolling and Winegard,6 zone-refined tin was cast into button-shaped specimens and, subsequently, plastically deformed under a drop hammer at room temperature. The resulting flat coin-shaped samples were annealed at 200°C, some for 50 sec and others for 100 sec. The specimens were then examined to determine the distribution of the number of sides per grain, i.e., the num- ber of crystals adjacent to any particular grain in the section. For simplicity, the grains were classified as three-sided, four-sided, and so forth; this concept is schematically illustrated in Fig. 1. As indicated by smith,' it was necessary to examine every grain within an enclosed area to obtain a proper distribution of the relative frequency of each type. The distributions for the two annealing times are illustrated in Fig. 2. The total number of grains examined is also indicated on the figure. It is evi-

Jan 1, 1965

By D. S. Pye, J. P. Gallus

Successful hydraulic pressure treatment of oil and gas wells that have long producing intervals, multiple pay zones, fluid thief zones, or natural or induced fractures has long been a serious problem plaguing the petroleum industry. High fluid-injection rates, straddle packers, ball sealers, and either liquid or solid additives to the treating fluids are being used to cope with this difficult and costly problem.l-6 The use of ball sealers and straddle packers is limited, in practice, to wells that have been completed with perforated cemented casings or liners. Well stimulation with ball sealers and straddle packers is usually successful as long as the cement remains competent. The other techniques of diverting are used with all types of completions. However, there are two significant disadvantages of the high rate method: excessive horsepower requirements, and the need of large treating-fluid volume. Consequently, most well stimulation techniques that involve diverting depend upon ball sealers or granular materials. Liquid diverting agents, and some of the solid ones in use today, frequently will cause formation damage. On the other hand, the most popular particulate diverting agents often are so soluble in the treating fluid that they become largely ineffective; their particle size is severely reduced as they dissolve while being transported through thousands of feet of pipe to the formation face down hole. In our attempts to deal with the shortcomings of these diverting agents, we experimented with a large variety of potentially suitable deformable materials the solubility of which could be controlled. Following are the criteria for the diverting agent sought: 1. The material must be effective in reducing fluid loss to thief zones, including existing fractures and very high permeability layers in the formation to be pressure treated. 2. The material must have enough strength to bridge under the treating pressure. 3. The material must be insoluble or slowly soluble in the treating fluids so that the particles retain sufficient size to be effective after they reach the formation face. 4. The material must be completely soluble in the produced oil or condensate liquid so that it can be removed readily; it must not cause formation damage. A number of products consisting of various polymers blended with waxes and other solid hydrocarbons were examined. All these materials satisfied the criteria for a diverting agent and also exhibited some degree of plastic deformability. On the basis of initial tests of strength and hardness, several blends of wax and polymer were selected for extensive testing in the laboratory and the field. These compounds have congealing temperatures ranging from 140 to 190F; they are insoluble in water and soluble in oil. They conformed, therefore, to the criteria specified for a theoretically superior diverting agent. Laboratory and field tests were conducted using these wax-polymer materials to demonstrate that the use of a deformable diverting agent can significantly improve fluid diverting performance. Data in this

Jan 1, 1970

By S. G. Gibbs, A. B. Neely

Jan 1, 1967

Jan 1, 1969

By Samuel M. Shallcross

The principal function of the Bell limestone mine, of the American Lime & Stone Co., at Bellefonte, Pa., is to supply raw material to the company's modern rotary kiln plant at Bellefonte. Because mining costs are naturally higher than many open quarries with more favorably lying strata, it cannot compete, except to a limited extent, in the markets for road material and fluxing stone. In the broad sense, mining does have an advantage over the average open quarry when the end products are designed for and controlled by process and final inspection for the exacting demands of the industrial and chemical markets. Approximately 80 per cent of the output of the Bell mine is sold in the industrial and chemical markets. And as higher standards are set each year for construction and agricultural work, the remainder of the mine output goes to these two classes. Mining produces more fines than open quarries, and these fines are difficult to market; on the other hand, owing to absence of contaminating clay and impure rock, a greater percentage of the output of a mine is marketable. Because of the great production of fines, rotary kilns for lime burning are necessary when the stone must be mined. In 1921 the American Lime & Stone Co. operated 19 quarries and 72 lime shaft kilns spread over an area of 40 miles between Bellefonte and Altoona, Pa. At that time the lime-production capacity of the 72 kilns amounted to approximately 700 tons per day. After 15 years the company operates three rotary kilns and six shaft kilns, with a combined output of approximately 500 tons of lime per day, concentrated in its single Bellefonte plant (Fig. 1). Its only stone-producing plants are now the limestone mine at Bellefonte and a construction-stone open quarry at Union Furnace, near Tyrone, Pennsylvania. Since the middle of 1922, the management of the American Lime R. Stone Co. has been under the direction and ownership of the Warner Company, of Philadelphia. To the Warner Company's experience, gained through successful operation of lime plants in eastern Pennsylvania for many years, and the successful solution of material-handling problems

Jan 1, 1937

By E. H. Jr. Dix

THE use of magnesium as an alloying element in aluminum alloys has been limited, in general, to comparatively small quantities. In duralumin-type, strong-aluminum alloys, magnesium is present to the extent of ½ to ¾ per cent. and various grades of Magnalite and the "Y" alloy of the National Physical Laboratory of England contain up to 1 1/2 per cent. In this country small quantities of aluminum alloy sheet containing 4 per cent. magnesium are produced commercially. All commercial aluminum contains sufficient silicon to convert a portion of the magnesium added to the compound Mg2Si. It is well known that the solubility of both magnesium and magnesium-silicide decrease with decrease in temperature. It is, therefore, impossible to separate the age-hardening effect of the magnesium-silicide from that of magnesium, except by the use of aluminum of such high purity that the silicon content is negligible. The present paper is the fifth1, 2,3,4 of a series from the laboratories of the Aluminum Co. of America reporting the results of investigations of the equilibrium relations in aluminum-rich alloys made from the high purity aluminum manufactured by this company .5

Jan 1, 1929

By W. W. Krech, T. E. Perkins

As fractures are propagated through rocks, energy is absorbed near the extending crack tip. Apparent surface energies for several rocks have been measured by cleavage under dynamic con-ditions. At nominal crack velocities from 0.5 to 500 in (min, measurements showed that fractures propagated in discrete jumps. Calculated surface energies and moduli were relatively insensitive to nominal rate of cleavage. in another set of experiments, rocks were cleaved under high confining stresses. The rocks were submerged in low leak-off fluids which formed a filter cake on the freshly cleaved surfaces (similar to the hydraulic lracturing process). Apparent surface energies were increased substantially as the surrounding fluid pressure was increased. Moduli in bending increased significantly upon application of the first 1,000 psi but were insensitive to stress level at greater pressures. INTRODUCTION For almost 20 years, hydraulic fracturing processes have been utilized effectively to stimulate oil and gas wells. During this period, some process improvements have resulted from studies of fracture orientation, mechanics of fracturing, areas generated, conductivities of cracks, etc. Yet many questions remain concerning the conditions and pressures needed during fracture propagation. In this paper we will report additional studies of the mechanics of fracture extension. It was shown previously3 that large rock samples could be cleaved under controlled conditions so as to measure the apparent surface energy (that amount of energy absorbed per unit area of new surface created). In this paper we consider the effects of two additional factors on surface energies, viz.: (1) effect of cleavage rate and (2) effect of confining stress level. THEORY Cleavage experiments were conducted on rock samples similar to that illustrated in Fig. 1. Blocks of rock several inches wide, 2- to 3-in. thick, and up to 3 ft in length were grooved longitudinally with shallow guide slots. A crack was initiated and allowed to extend along the web as the top of the rock specimen was pulled (or pushed) apart. Auxiliary equipment permits the measurement of (1) force applied at the top, (2) separation at the top and (3) crack length. (Further experimental details will be given in the next section.) The rock beams created by the crack are considered ton be cantilever beams. The deflection (or separation of the rock beams) at any point is calculated 4,5 by the beam Eq. 1.

Jan 1, 1967

By M. V. Mielke, R. E. Hagen, R. L. Bennett

FINE IRON ORES, and concentrates such as those produced from taconite, must be converted to lump form by some process of agglomeration before they can be used effectively in the blast furnace or open hearth. At the present time, four major processes for agglomerating these materials are being used on a commercial scale: sintering, nodulizing, pelletizing and briquetting. IN 1945 U. S. Steel Corp. through its subsidiary the Oliver Iron Mining Div., drew up tentative plans for an agglomerating plant on the Mesabi Range which would include a nodulizing kiln and a sintering machine. The purpose of the plant was two- fold: during its initial operation it would provide data on agglomeration of high grade ore fines, and would help relieve the shortage of ore for open hearth charging. Subsequently, it would be available for agglomerating taconite concentrates. While operating on fines screened from direct ore, it was planned to develop techniques and personnel so that a workable plant would be ready to handle taconite concentrates when the time came.

Jan 1, 1954

By A. C. Fieldner, W. A. Selvig

For purposes of coal classification it is desirable to know the composition and calorific value of the pure coal substance; that is, of the coal free from its ash-forming minerals. Two methods suggest themselves: (1) To free the coal from most of the ash-forming material previous to the analysis; and (2) to analyze the coal as received and calculate the analysis, with certain more or less arbitrary corrections, to the pure-coal basis. Calculation methods are obviously more apt to give correct results with low-ash than high-ash coals. With coals of unusually high ash it would appear preferable to remove, previous to the analysis, as much of the inorganic matter as possible, by float-and-sink or acid-treating methods. Effect of Ignition on Inorganic Constituents of Coal The need of corrections in calculating analysis to the pure-coal basis is due to the fact that the ash, as determined by ignition, is not the same, in either weight or composition, as the inorganic mineral matter in the coal. On ignition a number of changes occur in the coal such as loss of water of hydration of the shaly material, conversion of pyrite (FeS2) to ferric oxide (Fe203) with evolution of the sulfur as sulfur dioxide or possible fixation of more or less of the sulfur in the ash as calcium sulfate (CaSO4), and decomposition of calcite (CaC03) to calcium oxide (CaO). The amount of sulfur from pyrite which remains in the ash as calcium sulfate depends on the amount of calcite and pyrite in the coal. Certain coals high in both calcite and pyrite show relatively large amounts of sulfate sulfur in the coal ash. The determination of total carbon and hydrogen in coal includes, besides the organic carbon and hydrogen, the carbon of inorganic carbonates such as calcite, and the hydrogen of the water of composition of some of the ash-forming minerals. For detailed discussion of corrections proposed for calculations of coal analyses to the " pure "

Jan 1, 1930

By R. L. Whiting, H. J. Ramey

The basic study from which this paper was prepared was started as the result of the growing need throughout the world for increasing quantities of energy in all forms. Quite obviously, natural forms of energy that are readily available at low development cost are those in greatest demand. The underdeveloped countries — and particularly those having little or no petroleum resources — are the countries in which the most interest is being shown in the newer energy sources. One of the least expensive energy sources is natural geothermal steam.'-* Although this form of energy has been recognized for centuries, it has been only during the past 20 years that serious efforts have been made to harness it. Natural geothermal steam energy in Italy, New Zealand, Mexico, Japan, and California is now being produced through wells to drive turbines and generate electricity. Further, active exploration for natural geothermal steam is being conducted in Hawaii, Fiji, Taiwan, Chile, Russia, Greece, and Katanga. It is surprising to find that most geothermal steam exploration is in the "steam seep" stage. That is, surface studies are made and exploratory wells are drilled in the general area of steam seeps. However, in the larger geothermal steam areas, there have been efforts to apply the most modern geological and reservoir engineering principles in order to define the reservoir parameters, particularly those relating to estimates of reserves and future productivity. This paper is concerned with the development of appropriate equations and techniques to facilitate these estimates. Production of natural steam or hot water presents problems different from those experienced in the production of oil and gas. For example, steam or hot water systems may be essentially single-component systems, while hydrocarbon systems are most frequently multicomponent fluid systems. Heat effects are much larger for water than for hydrocarbon systems; and the natural steam production may or may not be isothermal, while production of petroleum reservoirs is considered normally to be isothermal. Petroleum reservoir engineering principles may be applied to natural steam or hot water reservoirs if the inherent differences in the systems are considered. The basic considerations involved in geothermal steam reservoir engineering are: thermodynamics, physical and thermal properties of water, materials and energy balances, fluid influx, and performance matching and predicting. Thermodynamics Fig. 1 is a pressure-temperature diagram for the liquid-vapor region for pure water, showing the critical point and five other points representing possible initial conditions for a geothermal steam reservoir. To generate a physical appreciation for the mechanics of natural steam production, it is helpful to consider

Jan 1, 1970

By R. E. Morgan, D. L. Douglass

The determination of phase relationships and solid-solubility limits can be performed by quantitative metallography in addition to the usual X-ray and metallographic techniques. For example, Beck and smith1 redetermined the ß/ß + ?, ß + ?/?, a/a + ß and a + ß/ß boundaries in the Cu-Zn system by measuring the volume fraction of second phase of several alloys and extrapolating the volume fraction-composition curves to 0 and 100 pct. A modification of this technique is suggested for certain alloy systems, in which it is not necessary to use several alloy compositions but merely one. A single two-phase alloy may be used to determine terminal solubilities in the following manner. The method consists of equilibrating samples of the alloy in a two-phase region adjacent to the desired solid solution, at three or more temperatures, quenching, measuring the volume fraction of second phase present, and applying an analytical treatment to calculate the unknown solid solution. However, two restrictions are inherent in this technique. They are: 1) only certain types of alloy systems are amenable to it, and 2) the general features of the system must be known. The first drawback to the new technique, i.e., that only certain types of systems may be studied, necessitates that the composition at one end of the tieline must either be constant with temperature or well established as a function of temperature. Either a pure metal or some intermetallic compounds fulfill the former. If it is assumed that the volume per gram-atom of a dilute solution is unchanged by the addition of element B to element A, the composition of the solid solution in equilibrium with the second phase may be determined by a material balance and is given by where X, = volume fraction of B in a solid solution Xc = volume fraction of B in compound c X = volume fraction of B in alloy f = volume fraction of second phase The composition by weight may then be determined by the use of tables in the Metals Handbook2 when the density ratio of the solid solution constituents is known. A possible alternative treatment involving the use of the lever rule is less precise than the above tech- nique. This may be used when the density of the solid solution is either known or may be calculated from X-ray data for several compositions. The following analysis is then made. The ratio of compound to solid solution (by weight) may be expressed as follows: x0 - x wc = xr-x = x0 - x r2i Xc -X where Wc = weight of compound w = weight of solid solution x, - alloy composition, weight percent x = unknown composition Xe = compound composition but where V, = volume of compound VA = volume of solid solution pc = density of compound p, = density of solid solution fc = volume fraction of compound fB = volume fraction of solid solution and fs = l -fc then If pc and xc are known, and f, is measured, then pB is the only unknown on the right side of Eq. [4]. The known densities of the solid solution can be plotted for various compositions and can then be expressed mathematically as a function of composition. The use of an expression of pB = f(x)reduces the equation to one unknown—the desired solubility. In the event that the densities are unknown, they may be calculated for various compositions from Vegard&apos;s law. The calculated values are then plotted and expressed analytically. The most accurate results are obtained for Eq. [4] when fc<< 1, i.c., when (x, -x,) - 0, &/l-f, - m; but as fc/l -fc - 0, (xl-x,)- (x, - x), and x - x,,. However, the accuracy with which fc can be measured decreases as f, decreases.3 Alloys for investigation must be selected by a compromise, which is based upon an error analysis of Eq. [4] and knowledge of the accuracy of volume fraction measurements. An examination of phase diagrams in the literature showed many which were amenable to the technique described here. The zirconium-copper system was selected in order to determine the solubility of copper in beta zirconium. Pieces of an alloy which was arc-melted three times were wrapped in tantalum foil and sealed under an argon atmosphere in Vycor tubes. The sealed samples were equilibrated at temperatures from 850" to 960°C for 3 weeks and quenched to room temperature by smashing the capsule in water. Several planes of polish were examined, and

Jan 1, 1960

By O. E. Palasvirta

Several drum-type, low-intensity dry magnetic separators have recently been described 1,2,3,4 all of which share at least two generic similarities. The magnet consists of a multiplicity of poles of alternating polarity and, the speed of the drum shell, relatiw to the magnet, is such that the magnetics are agitated through rotation of the magnetic particles around their individual axes. The speed of the drum relative to the magnet (differential speed) determines the frequency of the field reversals. For effective agitation this frequency generally has to be above a specific value, which varies according to the mean particle size of the magnetics. With separators of small diameter, say less than 11/2 ft., a sufficient differential speed for treatment of fine magnetite can be attained only by rotating both the magnet and the drum separately; separators of large diameter may attain sufficiently high differential speeds with stationary magnets. Separators of large diameter thus have the advantage of simplicity of design. The capacity of a separator of this type is directly proportional to the speed of the shell. As the centrifugal force opposing the magnetic force increases at a slower rate than the peripheral speed of the shell when drum diameter is increased, large drums can be operated with higher peripheral speeds. Thus they have a higher capacity than smaller drums. Separation is also a statistical phenomenon, i.e. the grade of concentrate improves as the number of agitations or rotations of the magnetic particles per separation increases. As separators of large diameter have space for a large number of magnets they are best suited for production of optimum grade concentrate. The statements above are general clues For separator design. In the following an expression IS derived showing a more exact relationship between the pertinent separator variables. As both magnetic attraction and centrifugal forces are directly proportional to the volume of the affected bodies, complications in mathematical analysis, arising from variable particle size, are avoided by considering the force per unit volume of affected material. For the magnetic force per unit volume Runolinna (3) gives the following equation: V " 1 + N(ur, - 1) uo dr (1) where ur and uo stand for the relative permeability and the permeability of vacuum, respectively, N is the demagnetization factor, B the intensity of the magnetic field, and r the distance from the face of the magnetic pole. The permeability of a specific magnetite ore can generally be considered as a constant. For ground, liberated material N can also be treated as a constant, and the first simplification can be made by writing ur-1 1=k1. 1 + N(ur - 1) uD k1. Fig. 1 shows the field intensity curves for two U-magnets of different size, but of roughly similar geometry of cross-section as plotted against the distance from the plane of the pole faces. The curves

Jan 1, 1961

By R. J. Charles

F. C. Bond: This is an outstanding paper on comminution theory and represents a considerable advance in mathematical formulation. It clears the way for a discussion that should ultimately decide whether the work index should be considered as a parameter according to the Third Theory or as a constant. In the empirical differential equation dE = —Cdx/x [1] either Corn must be treated as a variable to satisfy known crushing and grinding conditions. The author has chosen the exponent n as the variable, with C as a constant. According to the Third Theory, in the general case n is a constant equal to 3/2, and C is a variable related to the work index Wi. If x is placed equal to P (the size in microns which 80 pct of the product passes) and F is the size 80 pct of the feed passes, then C equals 5 W1, and dE = 5 -5 Widx/x = 10 Wi 10 Wi w = vP vF which is the basic equation of the Third Theory. It is apparent that this integration involves the error of treating the parameter Wi as a constant, just as the author&apos;s treatment involves the error of integrating his variable n as a constant. These errors are probably relatively unimportant, considering the small range of the variables. When more is known about the factors contained in the work index, Eq. 1 can be revised as a partial differential equation. The Third Theory exponent of 1/2, or n = 3/2 in the Charles&apos; differential equation (Eq. l), was not chosen primarily because it is the average between the Kick and Rittinger exponents; this may be merely fortuitous, since it is illogical to define truth as the average between two errors. It was first discovered from the study of a large mass of crushing and grinding data and confirmed by laboratory testing. The general correspondence of the Third Theory equation to actual crushing and grinding results over the entire size reduction range argues strongly that a fundamental phenomenon is involved. The a posteriori theoretical explanation of the constant Third Theory exponent is that the work done in breaking rock is proportional to the length of the crack tips formed. Compressive force applied to the rock results in deformation and strain energy. When this locally exceeds the breaking strength a crack tip forms, the surrounding strain energy flows to the crack tip and extends it to split the rock, with release of the energy as heat. Under rapid impact the crack tip may form before the strain has reached equilibrium, resulting in less energy expenditure and probably a coarser product. In any case, the elastic limit of a brittle material is practically the same as its breaking strength, and the work necessary to form the crack tip is the work required to break. The crack length of a ton of broken rock cannot be measured directly. However, the particle shapes of feed and product are similar, and the crack length is considered equal to the square root of one half of the new surface area formed. It is, therefore, proportional to 1/vD, where D is the equivalent product particle diameter. This is the basis of the Third Theory equation. Many secondary factors can be imposed upon the crack length breakage. These may cause the Third Theory work index to increase or decrease somewhat as the product size becomes finer. The work index is properly a parameter rather than a constant, making it an increasingly valuable practical criterion of the work input required in crushing and grinding.

Jan 1, 1959

By T. Price, H. A. Holl, A. P. Greenough, A

UdIN, Shaler, and ulff&apos; first used wires for the determination of the surface energy of a solid metal. A gage length was marked by tying knots in the wires, which were then suspended in a cylinder of the same metal, heated in an inert atmosphere for the appropriate time, cooled to room temperature, and finally removed from the furnace so that the lengths of the wires could be measured. With iron wires, difficulties associated with deformation during the phase changeszp3 made it necessary to measure the gage lengths at the tem-

Jan 1, 1964

By H. Foster Bain

I. INTRODUCTION. By H. FOSTER BAIN.+ THE recently aroused public interest in the conservation of our natural resources has peculiar importance to mining-men, since they deal with resources which are stored products. Within certain limits, the fertility of a worn-out soil may be restored, deforested areas can be replanted, one year&apos;s wasted water-supply is followed by another; but coal and ores, once taken out, cannot be mined again, and should therefore be conserved with especial care. This means, however, not that mining should be restricted, but that it should be done most economically and with the minimum of waste.

Nov 1, 1908

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K&apos; curve is equal to unity.

Jan 1, 1949

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K&apos; curve is equal to unity.

Jan 1, 1949

By Charles S. Barrett

NUMEROUS determinations1-7 of the tex-ture of cold-rolled polycrystalline iron, steel, and ferritic alloys have been made with good agreement among the various observers as to the principal features of the texture common to all, but there has been no adequate explanation of the texture in terms of the behavior of individual grains. This study presents an explanation of the texture based on the observed rotation of single crystals when deformed in a manner similar to a grain in the aggregate, a method we have found useful in leading to a better understanding of compression and tension textures;8,9,10 in particular, the aim has been to determine experimentally the end orientations of rolled single crystals of iron. These are discussed in connection with the point of view of Wever1 and of Boas and Schmid2 that the rolling texture is a simple compression texture (compression normal to the rolling plane) superimposed on a simple tension texture (tension in the roll-ing direction), and the point of view of Kurdjumow and Sachs3 that three ideal end orientations exist.

Jan 1, 1940

By R. E. Ray, J. W. Stevenson, J. A. Berry

Conventional concrete block plastered with a cementitious coating is the most common material used in the construction of permanent stoppings to direct airflow in underground mines in the US. All mines experience various degrees of strata convergence depending on depth of overburden, geological conditions, and type of roof support employed. Strata convergence will cause cracks and joint openings in masonry stoppings, resulting insignificant air leakage losses. Where strata convergence is severe, complete structural failure of the stopping can ultimately occur. Reconstruction of damaged or destroyed stoppings adds expensive overhead to mining operations, and even greater expenses are incurred from the additional fan horsepower required to overcome leakage losses. Ideally, a stopping should maintain high resistance to airflow while yielding to strata convergence. By properly incorporating a polyisocyanurate rigid foam material within the masonry block structure, stopping service life can be increased in mines experiencing strata convergence problems such as floor heave, roof loading, and lateral rib movement.

Jan 1, 1986

By B. P. Nutter, M. Lebourg, J. A. McAlister

The Multi-Flow Evaluator (MFE) is a new system of tools providing an original approach in drill-stem testing. It improves control during the testing operation and gives a more accurate evaluation of the fluid recovered while providing additional pressure information for reservoir analysis. The tools are operated entirely by up and down motion of the drill stem. This up and down operation provides a positive means of control and offers easily observed surface indications of tool operating position. An unlimited number of shut-in and flow periods may be taken with this tool while in the hole. The key to the success of the MFE system of tools is the safety seal packer. Until this development, operation of the tools by up and down motion only had proven unreliable. The success ratio of the MFE now exceeds the ratio achieved by conventional tools. The equipment includes a 2,750-cc chamber in which a representative sample of the flowing formation fluid is trapped at the end of the last flow period and brought to the surface under pressure. The sample can be evaluated at the wellsite or transferred under pressure for laboratory analysis. The sampling feature of the tool allows a sample to be obtained from a reservoir which has suffered minimum influence from production. A representative sample can be obtained for laboratory or empirical analysis by employing a testing technique to minimize drawdown during flow periods. Interpretation methods to take advantage of this additional information are presented and supported by actual field examples. INTRODUCTlON The Multi-Flow Evaluator (MFE) represents the most recent technical advance in formation testing. Drill-stem testing techniques prior to the MFE have been limited in three areas—(1) operaiion, (2) recovery analysis, and (3) reservoir analysis. The tools in the MFE system allow maximum control during testing and provide test information superior to that obtainable with conventional tools. The system of tools and the operation procedures are described to illustrate the mechanical advantages over present tools. Methods of pressure build-up and fluid

Jan 1, 1966