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By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas'-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller's results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By H. A. Koch, R. L. Slobod

This paper discusses a new oil recovery process called the "miscible slug process." This process involves the injection of propane or LPG into the reservoir prior to gas injection. The operating conditions are maintained so that the slug is miscible with both the reservoir oil and the injected gas phase. Thus, a miscible phase displacement is achieved, and high recoveries are obtained from the area of the reservoir contacted. The most striking discovery of the laboratory study which included displacements from cores up to 123 ft in length was that relatively small slugs of LPG are effective over reservoir distances in the miscible displacement of oil. This makes possible the commercial application of the process. The important factors controlling the size of the slug are: (I) reservoir length, (2) reservoir fluid composition, and (3) reservoir pressure at the displacement front. Of lesser importance are the effects of injection rate and porous medium type. Questions which have not been completely answered deal with the effects of gravity and reservoir inhomogeneities on the process. INTRODUCTION One of the major problems facing the oil industry today is recovery of the large fraction of the discovered oil which will remain unrecovered unless some new processes are found. Water flooding has been one successful method used to increase recovery over natural depletion. But even successful water floods may leave 25 to 40 per cent of the pore space filled with residual oil. Recently a process which involves the use of thermal energy has been reported1,'*' which may prove useful in increasing recovery from shallow reservoirs containing highly viscous crudes. This paper deals with a new oil recovery process involving use of miscible phases to displace the oil from the reservoir. Miscible phase displacement oil has been an intriguing idea because the elimination of capillary effects in the reservoir leads to 100 per cent recovery in the areas contacted by the miscible displacing phase. The big deterrent in the past to the practice of miscible phase displacement has been the high cost involved in using large volumes of solvent in the process. The use of high pressure gas to achieve a miscible phase displacement of reservoir oil has been reported4,5 as one economically feasible method. However, this process calls for the maintenance of pressures above 3,000 psi at the dis-placement front. The process described in this paper is not restricted to high reservoir pressures; the only qualification being that the slug of material which is injected into the reservoir must be miscible with both the displaced oil 2nd the displacing phase. Two such cases are the use of an alcohol slug followed by water to achieve a mis-cable water flood, and the use of a low boiling hydrocarbon slug such as propane followed by gas to achieve a miscible gas drive. This paper will deal specifically with the propane dug process. This process will obtain a miscible phase displacement at pressures as low as about 1,200 psi at a reservoir temperature 01 150°F. The process is very simple. The propane displaces oil completely at one front because it is miscible with the oil, and gas displaces the propane completely at a second or trailing front because it is miscible with the propane. A small band of propane should thus remain wedged between the gas and oil phases. This idea has been called the "miscible slug process."6 Unfortunately, the propane slug will become diluted as it flows through the reservoir. This results from a mixing action since the fluids flow through a complex reservoir porous medium rather than simple capillaries. Fig. 1 diagrams a miscible slug displacement. The effects of some of

Jan 1, 1958

By H. Schwartzbart, J. R. Low

Annealed, .Poly crystalline, low carbon steel exhibits a phenomenon known as the "yield point." If such a steel is loaded in tension, the load increases steadily with elastic strain, drops suddenly, fluctuates about some constant load value for a time and then rises with further strain. The load at which the sudden drop occurs is called the "upper yield point"; the load at which deformation proceeds at constant load is known as the "lower yield point"; the amount of elongation at constant load is termed the "yield point elongation." Deformation which occurs during the yield point elongation is heterogeneous in nature, deformed metal existing next to undeformed metal. The drop in load from the upper yield point is concurrent with the formation of a band of deformed metal which usually appears at a stress concentration such as a fillet and at an angle of approximately 45" with the direction of pull. As deformation proceeds during the yield point elongation, the deformed region grows until the entire specimen has been strained an amount equal to the strain in the first band. A phenomenon very often associated with the yield point is that of strain aging. Aging in steels may be of two types: quench aging, or precipitation hardening, and strain-aging. Strain aging differs from precipitation hardening in that if the metal is merely strained instead of given a solution anneal and quenched, it then undergoes changes in properties similar to those observed in quench aging. The yield point effect and strain aging are most markedly exhibited by low carbon steel, but have been observed in other alloys. Numerous explanations for the mechanisms of both phenomena have been advanced, but the evidence for the acceptance of any of the hypotheses is incomplete. One of the explanations of the yield point phenomenon frequently proposed is that there exists a honeycomb of grain boundary material that supports the load above the yield strength of the ferrite and that when this network ruptures, the ferrite flows with no increase in load. This notion was first advanced by Dalbyl in 1913 and has been since put forward in more concrete form by many investigators. The testing of this hypothesis was, in part, the object of the present investigation. Similarly, the mechanism by which strain aging occurs remains to be explained. Presumably, it is a precipitation hardening phenomenon similar to quench aging, the precipitation being initiated by strain. However, it is not known whether the process is a solution and precipitation effect or a change in solubility due to strain. One obvious method of determining whether or not the yield point is a grain boundary phenomenon is to determine if single crystals exhibit a yield point. Low and Gensamer2 have shown that carbon and nitrogen are responsible for the yield point and aging in steel and that these effects can be eliminated by the removal of these elements through wet hydrogen purification. Single crystals that have been grown in wet hydrogen treated material must then be recarburized or re-nitrided in order to evaluate the effect of grain boundaries. In the present investigation, single crystals of iron which had been annealed in wet hydrogen to remove the carbon and nitrogen were cut into two specimens having the same orientation with respect to the tension axis. Of these, one specimen was pulled in tension in the wet hydrogen treated state and the other was carburized or nitrided and tested similarly. All the crystals were examined for a yield-point and strain aging. The grain boundary hypothesis for the explanation of the yield point in steel has been tested only indirectly previously. Arrowsmith,3 Andrew and Lee,4 Edwards and Pfeil,5 Fell,6 Ludwik and Scheu,7 Winlock and Leiter8 and others found a decrease in proportional limit and yield point effect with an in-

Jan 1, 1950

By C. W. Thompson

The two-way belt conveyor for coal mine service simultaneously carries coal from faces and transports men and supplies into the mine, largely eliminating the necessity for rubber-tired supply and man haulage equipment and the necessity of maintaining additional headings. SINCE 1920 use of belt conveyor transportation has increased steadily, and capacity in tons per hour per unit has increased at about the same ratio. Belt conveyor systems for simultaneous two-way material transportation have been widely discussed, but heretofore have proved impractical for specific operations. Studies of a proposed means of disposing of wash-ery waste on the return trip of a main haulage conveyor, as yet uninstalled, led to the application of two-way belt haulage to Weirton's underground supply and mantrip problems. Except for a single-tracked main haulage entry, Weirton mine is essentially a full-belt haulage operation with attendant problems of supply and man-trip haulage that could not be handled with conventional belt conveyors during the regular work shift. It was necessary, therefore, to maintain rubber-tired haulage equipment and haulageways serving multiple-shift continuous operations. The conventional underground belt conveyor is primarily intended to transport coal from working faces to surface. Belts are usually reversed to haul men to face areas at the start of the working shift or to transport supplies. The two-way belt conveyor for coal mine service is not yet offered for sale as a unit by any manufacturer and must be built on order. This conveyor, with return run traveling parallel but opposite in direction to the outgoing or coal haulage run, permits not only haulage of coal from faces, but simultaneously permits transportation of men and supplies into the mine at any time, see Figs. 1 and 2. This eliminates, to a great extent, the necessity for rubber-tired supply and man haulage equipment and the maintenance of additional headings. Unlike conventional installations the return belt is in the open for inspection and maintenance. It is less subject to edge wear, since it runs on regular troughing idlers, see Fig. 3. The only points where the edge of the belt can rub are at the drive unit and the tail units where improved design should eventually eliminate edge wear entirely. Individual conveyor sections are lighter, since all that is needed is a tubular stringer on each side to carry troughing idlers only, no cover plates being necessary. The return run is carried on an assembly identical to that carrying the coal haulage run. These assemblies are definitely easier to handle and are cheaper than installations for the same length of conventional belt conveyor. The four pipes required for the complete conveyor frame may serve only as supports, or, with proper couplings, may be used for mine water discharge line, pressure line for face spraying, telephone cable conduit, or any other purpose requiring a pipe line, see Fig. 4. Additional expense, if any, for the increased number of pulleys needed to turn the belt over for the return service is more than offset by reduced expense for rubber-tired supply and mantrip haulage. The two-way belt haulage system is confined to a single heading on intake air, isolated from all other headings by stoppings on each side, and open for air circulation only at the main haulage way and at the faces. One additional heading, also on intake air, is maintained as an emergency rubber-tired haulage way, all other headings being center-posted and used as airways only until retreat work begins. This method, of course, can and should be used with any belt conveyor, since it provides two independent intake airways for escape in case of fire on the belt or elsewhere. Belt heading is heavily timbered even under good top conditions and space between the two runs permits center posting for the full length

Jan 1, 1954

By D. E. Baldwin

A method has been devetoped for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial etements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritiated water as the tracer fluid. Effiuent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for stratification by use of a layer cake model. INTRODUCTION Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston." Only a few of these investigations, however, deal with non-lin-ear flow systems. Raimondi et al.9 have presented an approximate solution of the dispersion equation for radial, diverging flow. Lau et al. 7 and Bentsen 1 have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi's solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith' have applied Raimondi's solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the disperson equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the five-spot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of l° (making a total of 45 elements) and a radius r, such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte,' Dyes, Caudle and Erickson 5 and Fay and Prats. 4 The resulting curve is shown as a solid line in Fig. 2. To match this curve with the radial model it was

Jan 1, 1967

By David E. Nicholas

INTRODUCTION In this paper, a numerical process for selecting a mining method, with the emphasis on underground mass mining techniques, such as caving, induced caving, and stoping, is proposed. In the past, selection of a mining method for a new property was based primarily on operating experience at similar type deposits and on methods already in use in the district of the deposit. Then, the chosen method was modified during the early years of mining as ground conditions and ore character were bet- ter understood. Today, however, the large capital investment required to open a new mine or change an existing mining system make it imperative that the mining methods examined during the feasibility studies and the method actually selected have a high probability of attaining the projected production rates. Although experience and engineering judgment still provide major input into the selection of a mining method, subtle differences in the characteristics of each deposit, which may affect the method chosen or the mine design, can usually be perceived only through analysis of measured characteristics. The parameters that must be examined when choosing a mining method include: 1) geometry and grade distribution of the deposit; 2) rock mass strength for the ore zone, the hanging wall, and the footwall; 3) mining costs and capitalization requirements; 4) mining rate; 5) type and availability of labor; 6) environmental concerns; and 7) other site-specific considerations. This paper encompasses a detailed look at the first two parameters since they, plus mining costs, have the greatest impact on the selection of a mining method. The proposed method selection process is for a project where drilling has defined sufficient geologic reserves, but little or no underground development has been done. Since each deposit has its own characteristic geanetry/grade distribution, and rock mechanics properties, mining method selection should be at least a two-stage process. In Stage 1, the deposit is described in terms of geometry, grade distribution, and rock mechanics properties. Using these parameters, the mining methods can be ranked to determine which are most applicable; they can then be considered in general terms of mining and capitalization cost, mining rate, type and availability of personnel, environmental concerns, and other site-specific considerations. In Stage 2, the most likely mining methods are costed out, based on a general mine plan. Mining and capitalization costs are used to determine a cut-off grade fran which a minable reserve can be calculated; economic comparisons can then be made to determine the optimum mining method and economic feasibility. During the mine planning phase of Stage 2, rock mechanics information would be used to provide realistic estimates of underground opening size, amount of support, orientation of openings, and caving characteristics, and open pit slope angles. If ground control or operational problems should be encountered with the methods being considered, modifications could be made. Although planning on paper extends start-up time, it is cheaper to err on paper than to find the error after mining has begun. METHOD SELECTION - STAGE 1 The main purpose of Stage 1 is to select those mining methods which should be considered in greater detail. The simplest way to do this is by defining those characteristics required for each mining method and then determining whether the characteristics of the deposit are suitable. However, no one mining method is so restrictive that it can be used for only one set of characteristics, as indicated by the classification system proposed by Boshkov and Wright (1973). In the mining method selection proposed, geometry, grade distribution, and rock mechanics characteristics are ranked according to their acceptability for ten general mining methods.

Jan 1, 1981

By Nicholas J. Grant, Robert H. Kane, Bill C. Geissen

The platinum-rich section of the Ta-Pt Phase diagram was worked out by metallographic and X-ray techniques, using twenty alloys; solidus temperatures and solid solubilities were determined. Besides s phase, four intermediate stoi-chiometric phases were found: TaPt (high-temperatzrre phase, structure unknown); TaPt2 (ortho-rhomhic, new type); a TaPt3 (orthorhombic, TiCu3 type); ß TaPf3 (monoclinic, new type). TaPt2 and TaPt3 melt congmentlv; two eutectic, two beritec-tic, and one eutectoid reactions occur in the inuestigated range. THE Ta-Pt system was examined as part of a study of the phase diagrams and the intermediate phases of niobium and tantalum with Group VIII transition metals. Since the main scope of this work was the relation among the ordered close-packed phases occurring in the concentration range from AB to AB3 (A = Nb, Ta; B = Pd, Pt, and so forth), only the platinum-rich side of the diagram was worked out thoroughly, while spot checks were made to determine the approximate outline of the tantalum-rich portion. The system has not been thoroughly treated in the literature; Greenfield and Beck1 in their survey of refractory metal intermediate phases found a o phase between -18 and 37 at. pct Pt which coexists at higher platinum concentrations with an unidentified intermediate phase. Browning2 worked on the range between 55 and 100 at. pct Pt; however, this preliminary study did not cover temperatures >1500°C, and included no conclusive crystallo-graphic data. More recently, a study of the platinum-rich section of the Ta-Pt system has been carried out by Ray,3 while Hartley, Parsons, and steedly4 have studied the tantalum-rich section. The crystal structures of TaPt2, a TaPt3, ß TaPt3, and others have been reported in abstracted form by Giessen and Grant.5 EXPERIMENTAL METHODS The methods of alloy preparation and processing and of the metallographic and X-ray procedures follow very closely those described by Ritter, Giessen, and rant' for other refractory metal-noble metal systems, and will not be repeated except where significant differences exist. Starting materials were: tantalum rod of 99.95 pct purity, supplied by National Research Corp., and platinum sponge 99.9 pct, supplied by The International Nickel Co. An oxygen analysis of the tantalum rod showed 30 ppm O; other impurities were C, N, Si, Nb, Mo, none of these exceeding 50 ppm, and 100 ppm W. Homogeneous buttons were readily prepared as follows: ingots of 5 g were weighed and arc-melted under welding grade argon, followed by two remelts after inverting the button. Between 40 and 100 at. pct Pt, weight losses during the first melt rarely exceeded 0.1 pct, in which case the alloy was rejected, and were nil on subsequent remelts. Since the vapor pressure of platinum far exceeds that of tantalum, the small evaporation loss could be assumed to consist of platinum; therefore, a corresponding amount of platinum was added on the second melt. Since it was confirmed on pure tantalum samples that no weight gain through oxygen or impurity pickup occurs (see Ref. 71, it could be assumed that the uncertainty in the composition did not exceed ±0.1 at. pct for the range 40 to 100 at. pct Pt. For the four control melts from 0 to 40 at. pct Pt, an error of ±0.5 at. pct was calculated. Microscopic examination of the whole buttons after melting showed no inhomogeneity other than local coring. This was eliminated by a homogenization heat treatment. A total of twenty-three alloys were prepared. Heat treatments were carried out in a tantalum

Jan 1, 1965

By W. Chubb

By measuring the hardness of metals at temperatures just above and just below their allotropic change point, it has been established that crystal structure has a real effect upon the strength of metals. The DPH of cobalt, iron, titanium, uranium, and zirconium have been measured at temperatures up to 1000°C. It was found that the body-centered-cubic crystal structure is always the softer structure when it is involved in an allotropic transformation. The close-packed and more complex structures are inherently harder, and may be expected, therefore, to be better base materials for high strength alloys. IT has been observed that for metals with nearly the same melting point (i.e., tin and lead, magnesium and aluminum) the metal with the more complex crystal structure has a higher tensile strength and hardness. It might be asked whether this effect is really caused by the difference in crystal structure; and, if so, just what is the contribution of crystal structure to the strength of these metals. A qualitative answer to these questions can be obtained by measuring the change in hardness produced by the change in structure in metals exhibiting allotropic forms. The evidence for changes in mechanical properties during allotropic transformations is rather meager. In 1909, Rosenhain and Humfrey' observed that "ß" iron showed much less deformation at the transformation temperature than a iron. By means of a torsion test, Lee found that iron bars were "critically plastic" at the a-7 transformation temperature. Sauerwald and Knehans have shown that the dynamic hardness of iron increases between 900" and 1000°C. In 1930, Albert Sauveur' presented data on the hardness, tensile strength, and torsional strength of pui-e iron up to 1000°C. He concluded, "At 900°C, the a iron transforms into y iron, and this is accompanied by increased strength and stiffness and decreased ductility." The same year, Schischokin" obtained data on the hardness of thallium at temperatures above and below its transformation temperature. His data are replotted on semilogarithmic coordinates as Fig. 1. The fact that his data fall on straight lines in this type of plot is believed to attest to the purity of his metal and the accuracy of his results. In 1941, Nadai and Manjoine" obtained tensile data on pure iron with an indicated increase in strength at about 900°C. These experiments make it quite evident that changes in mechanical properties occur when a metal transforms from one crystal structure to another; but, except for Schischokin's data on thallium, none of the measurements seem accurate enough to determine the relative magnitude of the mechanical property change. Materials The metals that have been examined for changes in hardness during transformation include l—as- deposited commercial electrolytic cobalt about 99.7 pct pure, 2—Armco ingot iron, 3—are-melted iodide titanium of a purity in excess of 99.8 pct, 4—uranium of a purity in excess of 99.5 pct, 5—are-melted iodide zirconium of a purity in excess of 99.8 pct, 6—annealed, 0.08 pct C, rimmed steel, and 7—commercially pure RC55 titanium. While the purity of the first five of these materials leaves something to be desired, it will be noted that the observed hardness discontinuities occurred at the accepted transformation temperatures. (These temperatures are indicated by vertical arrows in Figs. 1 and 3 through 7.) The last two materials are commercial alloys introduced to show the effect of minor alloying elements upon the hot hardness curve. Apparatus Hardnesses at elevated temperatures were determined by means of a vacuum hot hardness machine. A diagram showing the basic features of this machine appears as Fig. 2. This machine is essentially a deadweight hardness .machine in a furnace within a vacuum chamber. The sapphire-tipped indentor

Jan 1, 1956

By J. J. Taber, W. K. Meyer

Experiments on consolidated sandstones have shown that a variety of conditions are responsible for the wide range of behavior observed when oil and water are displaced simultaneously by a solvent which is miscible with both. The type of displacement is influenced most strongly by the relation between the plait point of the ternary phase diagram and the composition path followed by the system as it achieves mis-cibility. Neglecting viscosity, the displacement becomes less efficient as the distance between the composition path and plait point is increased in either direction so that a very wide spectrum of displacements is possible with different alcohol, oil and brine systems. It is possible by choosing various composition paths as miscibility is achieved to exercise some control over the actual displacement mechanism. Control over the composition path is exercised by adding oil or water in specific amounts to the alcohol prior to its injection into the porous medium. This technique apparently makes it possible to obtain piston-like displacements with systems which are usually characterized by the efficient displacement of only one of the two phases i.e., either oil or water, while the other phase lags behind. However, the simultaneous displacement of oil and water is not as efficient as other miscible displacements at a similar mobility ratio. The evidence indicates that both oil and water "leak" into the alcohol "piston" in compensating amounts. With oils of low viscosities the displacement is inefficient because the low oil saturation in the stabilized bank causes oil to be trapped by water before miscibility is attained. INTRODUCTION The simultaneous displacement of oil and water by solvents such as alcohol has been investigated in the laboratory and in the field. The laboratorv workers investigating all-liquid miscible systems have recognized the great importance that the nature of the traingular phase diagram exerts on the efficiency of the miscible displacement. Gatlin and Slobod pointed out that displacement efficiency will be improved if miscibility can be retained for long periods and that this behavior tends to be followed if the applicable phase diagrams have very low binodal curves. In their unconsolidated sand tests the alcohol was considered an ideal miscible piston displacing both oil and water phases. Later workers have pointed out that an important feature of the phase diagram as far as oil recovery is concerned is the location of the plait point. This is particularly true in the case of consolidated Sandstone.3 Since the original discussion of this effect, the importance of plait-point location has been confirmed and discussed by other author The early workers394 recognized that the position of the plait point could be altered by changing the oil or the alcohol used in an experiment. In addition, recent work has demonstrated that the plait point can be shifted by altering the nature and concentration of dissolved salts in the aqueous phase. However, the entire scope of the relationship between displacement and plait point has not been discussed previously and a technique for changing the composition path as miscibility is achieved in a particular ternary system, i.e., oil, water and solvent, has not been demonstrated. * The importance of oil viscosity on the efficiency of oil displacement by alcohol has not previously been observed, probably because the range of viscosities used in earlier experiments was too restricted. It is the object of this paper to describe the relationships between the ternary phase diagram, fluid properties and the displacement achieved. A technique for controlling the nature of the displacement is also presented. THEORY AND DEFINITIONS PISTON-LIKE THEORY The theory of alcohol flooding has been discussed in some detail.2-4 The concept was advanced that

Jan 1, 1965

By C. R. McEwen

This paper presents a technique for calculating the original amount of hydrocarbon in place in a petroleum reservoir, and for determining the constants characterizing the aquifer performance, based on pressure-production data. A method for doing this based on a least-squares line-fitting computationwus proposed by vanEverdingen,Timmerman andMcMahon in 1953. We found that their method would not work when there is error in the reservoir pressure data — even moderate error. The technique presented here appears to give reasonable answers when pressure data are uncertain to the degree expected in reservoir pressure determinations. The major change introduced in the present analysis is to limit the least-squares line-fitting to yield only one constant— the amount of hydrocarbon in place. The water-influx constant is then taken as proportional to the oil (or gas) in place. The constant of proportionality can be computed from estimates of effective compressibility and reservoir water saturation. It is also pointed out that the commonly used least-squares analysis assumes all of the uncertainty to be in the dependent variable. The material balance should be arranged so that this condition is fulfilled if correct inferences are to be made from statistical calculations. Examples are shown of the application of the new technique to gas reservoirs—both hypothetical and real—and to the oil-reservoir example of van Ever-dingen, Timmerman and McMahon. INTRODUCTION The amount of hydrocarbon originally in place in a petroleum resenroir can be estimated by means of the material-balance calculation. Simultaneous observations of pressure and amounts of produced fluids are required, together with the PVT data applicable to the reservoir fluids. If water encroachment is occurring, it is desirable to try to infer the behavior of the aquifer, as well as the original hydrocarbon in place, from the pressure-production data. This imposes additional demands on the method of calculation, and uncertainty in the data can result in large uncertainty in the answer. In addition, if the size of a gas cap is to be established, the whole problem becomes indeterminate, as pointed out by Woods and Muskat.1 Brownscombe and Collins2 simulated a gas reservoir and its aquifer on a reservoir analyzer and derived quantitative information on the effect of uncertainty in pressure and aquifer permeability on computed gas in place. Among the various techniques of estimating the performance of an aquifer, the method of van Ever-dingen and Hurst? based on compressible flow theory, seems to have been the most generally successful (see Ref. 4, for example). In this paper we shall confine ourselves to their representation of the aquifer. In 1953,' van Everdingen, Timmerman and McMahon5 introduced a statistical technique for deriving the amount of oil originally in place and the parameters which describe the aquifer. (We shall refer to this technique as the "VTM method'', as suggested by Mueller.6) Their example reservoir had no gas cap. It has been our experience that the VTM method gives a reasonable answer when the data are very accurate, but that inaccuracy (particularly in pressure) can cause the method to break down. The effect was first observed in gas reservoirs, but has since been seen in oil reservoirs also. In this paper we present another statistical method which has been successful in achieving a reasonable answer where the VTM method has failed. In the new method, one less parameter is derived from material-balance computations. It is assumed that values can be established for effective compressibility in the aquifer and reservoir water saturation independently of the material-balance calculation. The water-influx constant can then be obtained from these data and the quantity of hydrocarbon in place.

By Milton F. Goodrich

The idea of using water-only cyclones to scalp clean coal from the feed to other devices has recently been gaining in popularity. 1,2,6 An indication of this popularity is that water-only cyclone scalping is already employed in a few commercial plants. Water-only cyclones scalp the feed to a heavy media vessel in the Warwick plant,3 to Deister tables in the Rowland plant,4 and to a heavy media cyclone circuit in the Amherst Coal Company's McGregor plant.5 Despite this trend, we found surprisingly little information in the literature on the performance of water-only cyclone scalping. Therefore, we undertook a study of its technical merits, limiting our investigation to a water-only cyclone scalper in conjunction with heavy-media cyclones. We felt this to be a reasonable combination of equipment, since both processes operate well on the same size coal. First, we developed simple mathematical relationships revealing general characteristics of the system. Next, we compared the clean coal yield and quality obtainable by the system on four different coals with that obtainable by heavymedia cyclone circuit alone and water-only cyclones middlings recirculation circuit alone. This was done by using computer program to simulate the operation of the three systems. Finally, we considered the effect that implementation of the system would have on a typical preparation plant circuit. The System The system chosen for study [(shown schematically in Fig. 1)] comprises two stages: a primary stage (PI) consisting of water-only cyclones, and a secondary stage (P2) consisting of heavy media cyclones. The water-only cyclones separate raw coal at a low specific gravity, producing a relatively small amount of high quality clean coal and a refuse containing much good coal. This refuse is then recleaned in the secondary stage, where the sharper separation of heavy media cyclones, operated at a higher specific gravity, reclaims additional clean coal. Finally, the clean coal from both stages is combined as the system's clean coal, while the refuse from the secondary stage becomes the system's refuse output. Theoretical Analysis Two assumptions lie behind the following theoretical analysis. The first assumption is that partition curves can represent not only the performance of each stage but also the performance of the system as a whole. These curves show partition number as a function of specific gravity, where partition number is either the percent or fraction of a raw coal with a given specific gravity reporting to clean coal. The second assumption is that these curves are independent of the raw coal characteristics. At any specific gravity the system's partition number is solely a function of the partition numbers of each stage. For convenience, we use the following variables in describing this relationship: g = specific gravity, PS(g) = the partition number of the system at specific gravity g, P1(g) = the partition number of the primary stage at specific gravity g, P2(g) = the partition number of the secondary stage at a specific gravity g. For this system, we can show algebraically that the relationship is: [Ps (g) = PI (g) + (1- P1(g)) P2 (9)(1)] With this equation the system's partition curve can be determined if the partition curves of each stage are known. By definition, the partition numbers P1(g) and P2(g) must each be less than, or equal to, one. Placing these constraints on Eq. (1), we arrive at the relations: [Ps(g) % P1(g) and Ps(g) % P2(g)(2)] Thus, at any specific gravity the system's partition number is always greater than that of both stages. [Figure 2] shows typical partition curves. Curve I represents the primary stage, which consists of water-only cyclones operating at a separating gravity of 1.3. (The separating gravity or the

Jan 1, 1979

By P. M. Blair, D. W. Peaceman

The shape and position of the gas-oil transition zone during downdip displacement of oil by gas has been calculated using flow equations which include the effects of gravity, relative permeability, capillary pressure and compressibility of the fluids. The calculations treat the problem in two space dimensions, and results are compared with data from a laboratory model tilted at 30° and 60° from the horizontal on displacements near and above the maximum rate at which gravity segregation prevents channeling of the gas along the top of the stratum. The good agreement between calculated and experimental results demonstrates the validity of the tecbnique as well as that of the flow equations. INTRODUCTION Knowledge of the fluid distribution and movement in an oil reservoir is important in producing operations and estimation of reserves. The history of the oil industry has included steady progress in improving the accuracy of calculations which provide the required knowledge. The earliest method of calculating reservoir performance consisted of material-balance equations based on the assumption that all properties were uniform throughout a reservoir.l For many reservoirs such a simple formulation is still the most useful. However, when large pressure and saturation gradients exist in a reservoir, the assumption of uniform values throughout may lead to significant error. To reduce these errors, Buckley and Leverett2 introduced a displacement eqation which considers pressure and saturation gradients. Methods available at that time permitted solutions to the Buckley-Leverett equation in one space dimension; these solutions have been very useful in solving many problems related to the production of oil. However, the one-dimensional methods are not adequate for systems in which saturations vary in directions other than the direction of flow. An example of such a system is the case of gas displacing oil down a dipping stratum in which the gas-oil contact becomes significantly tilted. Of course, the Buckley-Leverett displacement method cannot predict the tilt of the gas-oil contact. Recent improvements3,4 of the one-dimensional Buckley-Leverett method achieve some success in predicting the tilt of the gas-oil contact at sufficiently low flow rates. However, at rates high enough that the viscous pressye gradient nearly equals or exceeds the gravity gradient, even these improved one-dimen,sional methods incorrectly predict the shape and velocity of the contact. Further progress in estimating such fluid movements in a reservoir appears to require consideration of the problem in more than one space dimension. The recent two-dimensional method of Douglas, Peaceman and Rachford5 appears adaptable to calculate changes with time of the saturation distribution in a vertical cross-section of a reservoir. The movement of saturation contours should represent the moving fluid contacts and include the effects of crossflow due to gravity, as well as variations in the rock and fluid properties. The nonlinear nature of the equations used in the method has prevented proof of the validity of the solutions. Douglas, Peaceman and Rachford made some comparisons with experiment but did not include cases in which gravity was important nor cases involving displacement by the nonwetting phase.For these reasons, a test of the two-dimensional method for a case in which these factors are included would be very desirable. The test selected was a comparison of calculated results with those from a carefully controlled laboratory experiment on a model with measured physical properties. The model selected was one in which gas displaced oil down a tilted, rectangular sand pack. The model can be thought of as representing a vertical cross-section taken parallel to the dip of a reservoir. The displacement thus simulates gas displacing oil downdip that might result from gas-cap expansion or gas injection. This report outlines the calculation method used

By R. S. Kinasevich, D. D. Crabtree, D. W. Fuerstenau, T. P. Meloy, A. L. Mular

This paper presents details of the concept that size reduction in comminution machines takes place by three mechanisms; namely impact, abrasion, and chipping grinding. Experimental evidence is presented to show that each of these comminution mechanisms produces particles of a characteristic size distribution. The actual product from a comminution device has been postulated to be the result of a composite of these three types of mechanisms. Composite curves are demonstrated for a material following the Gaudin-Schuhmann, Gaudin-Meloy, and Rosin-Rammler size distributions. About forty years ago, Gaudin1 showed that grinding may be considered a combination of impact and attrition. Since that time, major efforts have been devoted to studies, both experimental and theoretical, of impact and compression fracture, while attrition has been almost wholly neglected, at least quantitatively. A significant attempt to distinguish between attrition and impact grinding is the work of Tanaka2 in Japan. By means of an instrumented abrasion grinder and a drop weight device, he determined coefficients relating the increase in surface area of various materials to the energy expended by the two methods of comminution. He showed that physical properties of a material determine its response to attrition and impact grinding. By extending his ideas to ball milling, he concluded that to a large extent the basic comminution process in a ball mill is due to the impact of falling media. Because Tanaka used a mass of particles in his drop weight device, however, he did not obtain pure impact size reduction. The purpose of this paper is to define basic mechanisms of size reduction, to verify that each has a characteristic and meaningful distribution curve, and to show how a combination of these mechanisms results in a size distribution very like that produced by grinding mills. DEFINITION OF COMMINUTION MECHANISMS The product from a grinding device will be considered to be the sum of the contributions resulting from the action of three basic mechanisms of size reduction which operate in a ball and rod mill. These are impact grinding and two forms of attrition, namely abrasion grinding and chipping grinding. Each is defined below. Impact Grinding: If a straight line is obtained when the cumulative weight fraction finer than a given size is plotted on log-log paper as a function of that size, the slope of the line is defined as the distribution modulus. A number of investigators 3,4,5 have shown that impact fracture of single specimens of different composition and shape results in a distribution of daughter particles that exhibit a distribution modulus of unity. This has also been true for materials broken in slow compression. Moreover, under slow compression or impact fracture conditions, theoretical distribution equations6*' which approximate the Gaudin-Schuhmann distribution when the distribution modulus is close to unity agree reasonably well with the experimentally obtained products. If one now considers a comminution process where many impact or compression fracture events are taking place, then any rational summation of the individual events yields, in the finer size range, a Gaudin-Schuhmann distribution whose distribution modulus is also unity. If the size distribution of the product from a mill has a distribution modulus of unity, it is implied that particles are fractured in a manner which results in a comminution event having a distribution like that obtained for the breakage of single specimens. These impact events would occur when a particle is smashed between balls or between a ball and the mill liner. Attrition, on the other hand, is that form of grinding which cannot be called impact grinding, and comprises both abrasion and chipping grinding. Abrasion Grinding: Abrasion is a form of surface wear resulting when particles rub against each other or against balls or the mill liner of a tumbling mill, somewhat like a piece of wood being rubbed over a piece of sandpaper. The surface wears at a more or

Jan 1, 1964

By J. Spreadborough, D. LaW. King, E. Anderson

Tmzsile tests were performed on Armco iron samples, at various ternpe.ralures and strain rates, ocer a wide range of grain sizes. Analysis of the data suggests that the plot of the lower yield stress, against d-1/2,where 2d is the acerage grain diameter, is not linear (as is often assumed) but is concave toward the d. axis over the range of d-from 7 to 53 . The different values of the parameters obtained by other workers can be explained, in part at least, by the observed curvature. This curvalure is shown to be consistent with a model of yielding based on dislocation pile-ups; however, the values of obtained by fitting our data to this model differ appreciably from the values generally reported. The equation proposed by Cottrell, viz.: is a plausible empirical fit to the experimental results. The purpose of this paper is to comment on the validity of the widely used linear relationship first proposed by all' and Petch and coworkers2"4 between ay, the lower yield stress, and 2d, the average grain diameter, for bcc metals, viz.: Many workers, see Refs. 2 to 7 and Table 11, have fitted this equation to their experimental results and have obtained acceptable fits over the relatively narrow range of grain sizes used by most of them. Indeed, in some cases, so few data points were available that any more sophisticated fit would have been irrational. In most of the interpretations,'-' oi is thought to be a measure of the friction stress accompanying dislocation movement, and ky was originally inter- preted as a measure of the dislocation locking but is now believed by Cottrell" to be a function of the dislocation creation rate. In the "unpinning" theories, k, is equated to where od is the unpinning stress and 1 is the average distance from the boundary of the grain where yielding is taking place to the nearest dislocation source in an unyielded grain. Other considerations (see, for example, Refs. 11 and 12) lead to equations with a similar form to [I] where different meanings may be attributed to the parameters. While there are doubts as to the physical significance of the parameters i and k, they continue to be used by many workers; interpretations of the variations in the behavior of ferrite materials following certain treatments, e.g., aging,'3 neutron irradiation,14 have been given frequently in terms of these parameters. Some theories of the mechanical behavior of bcc metals are based on this relationship. We have investigated experimentally the oy - d-'lZ relationship for Armco iron over a wider range of grain sizes and with more data points than those given in published results. The analysis of our data suggests that the oy—d-'" relationship is not linear but is in fact concave towards the d-'I2 axis. RESULTS AND DISCUSSION The experimental work was carried out on 3-mm-diam Armco iron rods which were prepared by wire drawing from 5-mm-diam rods. By annealing in vacuum at temperatures between 7000 and 1200°C for various times, grain sizes from 7 to 20,000 grains per sq mm were obtained, the grains in all cases being regularly shaped. Grain sizes were measured by lineal interceptand by area methods; only specimens with Amax/A values of 3 to 6 were used in the Petch-Hall plots (where A is the average area of a grain and Amax is the area of the largest grain observed). For all the specimens used, the number of grains in a cross section exceeded 50, which should be adequate to avoid grain size effects.'= Tensile tests were performed at 296", 219, and 17l°K, using

Jan 1, 1969

By A. Kenneth Schellinger

DURING the comminution of a brittle material in the presence of dry air, no known phase change or chemical reaction takes place. The energy changes associated with the comminution are those of the transformation of kinetic energy into heat energy and the energy absorption represented by the actual rupture of molecular and/or ionic bonds. The random nature of the actual grinding process in a tumbling-mill often precludes the effective application of a rupture force on each individual particle of brittle mineral present. The result must be a great deal of useless vibration on an atomic scale in both the brittle mineral and the grinding medium below the elastic limit, which vibration is eventually manifested as heat energy in the mill. The actual rupture of molecular, or ionic, bonds creates new surface on the brittle minerals; each square centimeter of this new surface then must possess a number of potential bonds, each of which could reform theoretically with the release of energy. The sum total of this potential energy of bonding per unit of new surface, minus bond satiation effects of the enclosing gas or liquid, must be the surface energy of the mineral. If the comminution of the brittle mineral were carried out within the chamber of a calorimeter, the energy released as heat could be determined rather accurately. Moreover, the total kinetic energy input to the comminuting mass (mineral and medium) conceivably could be derived by a suitable torquemeter and revolution counter if the whole calorimeter were revolved. The difference between these two energy figures should then represent the net energy (gross energy input—heat enerb output) used in creating new surface, gliding or slip on atomic planes, twinning, and possibly other lattice rearrangements within the mineral. If it be postulated further that with a hard, brittle crystalline material, such as quartz, the energy used to produce gliding, twinning, and other permanent lattice movements is a very small fraction of the total net energy absorbed, then this energy absorption within the grinding calorimeter can be ascribed to the creation of new surface energy alone. Such energy is, from the thermody-namic standpoint, the true effective work of the grinding device, in this case a tumbling-medium mill. The ratio of this effective work (in calories) to the total energy input (in calories) should express the thermodynamic efficiency of the comminution taking place under the conditions used in the grinding calorimeter. This approach to the measurement of the energetics of tumbling-mill grinding was suggested by some previous work by Fahrenwald and coworkers' with a laboratory ball mill and a thermometer. They measured the efficiency of grinding based on the formula: Pct Grinding Efficiency = Energy (calories) — Thermal Energy x 100 1npZ Output (calories) Energy input (calories) Efficiencies thus measured, while grinding quartz sand, ranged from 19.7 pct to 7.4 pct. Cook in 1915,' used this approach to the problem of grinding efficiencies in stamp batteries and obtained the energy input by stamp weights times drop distances and the energy output by means of thermometers and pulp flow rates. He calculated that 80 pct of the input energy to the stamp shoes was wasted as sensible heat in the ore pulp. No other studies of comminution by this method of energy differences came to the author's attention. Reasonable agreement as to the order-of-mag-nitude of comminution efficiencies in tumbling-media mills is lacking in the literature. There is a widespread impression among technical workers that the grinding efficiency of the industrial ball mill may be on the order of 1 pct, or even a fraction

Jan 1, 1952

By D. J. Carney, E. Richard Randolph, E. Van Meter, J. J. Oravec, Stanley H. Ward, Gerald J. Anderson, Rolland L. 203-000-000-005 Blake

DURING the last 30 years the inductive electromagnetic method has been used chiefly in the search for massive sulphide mineralization. This application has met with varying degrees of success and in recent years has resulted in discovery of several large orebodies. Little has been written concerning its use in exploration for soft iron ores, but one of the present authors has reported on experiments with massive magnetic deposits.' To augment the exploration tools available to geologists in delineating iron orebodies, Cleveland-Cliffs Iron Co. and McPhar Geophysics Ltd. undertook in 1953 to apply the inductive electromagnetic method to Cleveland-Cliffs properties in the Lake Superior region. As a result of this project, equipment has been developed that enables simultaneous transmission of two audio frequency waves, and the field technique and interpretative procedure involved have furthered exploration in the district significantly. Thus far, inductive electromagnetic application in the Lake Superior region has been only a development tool, that is, it is used to locate obscured contacts and faults as a part of property expansion and development. However, its application to primary reconnaissance of unexplored areas may be feasible in the future. The method has assisted in placing drillholes efficiently, and the elimination of excess drilling foot-ages and/or actual elimination of unnecessary holes has amply justified the expense of the geophysical survey. Cost of the field work involved is comparable on a per station basis to the cost of a magnetometer or superdip survey. Since observations require no reduction, i.e., are directly interpretable, overall expenditure is low, and the scope and detail of the survey can be adjusted in the field as geological- geophysical correlation becomes evident. To a great extent, this eliminates the second-guessing so commonly arising after office calculations are completed on data obtained with other types of geophysical surveys. This unique feature of field interpretation and its associated intimate feel of the project area, is, perhaps, one of the most valuable aspects of the inductive electromagnetic method as applied to iron ore exploration. Basis of Method Fundamentally, the method involves transmission of an alternating electromagnetic wave, of a chosen audio frequency, which permeates the ground materials in the vicinity of a transmitting, or primary, coil, see Fig. 1. This wave, or field, induces an electric current in any conductor on which it is incident. The flow of an alternating current in a conductor sets up its own, or secondary, radiating electromagnetic field. These two fields form a resultant whose configuration depends on the following characteristics of the subsurface conductors: 1) size, 2) shape, 3) electrical conductivity, 4) magnetic permeability, and 5) frequency of the transmitted wave. To a lesser extent the resultant is also dependent on material adjacent to the conductor, topography, and surface conductivity. For illustrative purposes, the primary, secondary, and resultant fields may be represented by vectors. In operation, the direction of the resultant vector is measured by a small receiving coil tuned to the frequency of the transmitted wave. Generally speaking, the method can be compared to the transmission and reception of the familiar radio broadcast, with special variations permitting measurement of the effect on reception of intervening materials. Field Technique Mechanics of field operation are simple. The mast is set up in a vertical position and is then guyed in place. The transmitting loop then is raised by means of a sheave at the top of the mast and the coil connected to the motor-generator. A special plane table is clamped into position on the mast and the loop is plumbed. The plane table is oriented according to a grid system established over the project area. By means of this plane table it is possible

Jan 1, 1956

By G. W. Doepel, W. P. Sibley

A three-dimensional, multilayer, mathematical model has been developed for predicting performance by mis-c.ible displacement. Areal and vertical coverage, total gas-oil ratio, propane-oil ratio and oil-recovery factor for the multilayer system are computed as functions of hydrocarbon pore volumes of solvent injected. The technique has been programed for use on the IBM-7090 digital computer and was used in calculating perfortnance for continuous miscible displacement of a five-spot, 50-layer .system. Results reported are based on the use of published laboratory data for a single, uniform five-spot layer. However, the technique is sufficiently generalized to calculate performance of any system of layers of any pattern configuration and mobility ratio, provided data are available to describe perfortilance of a single layer. The technique has also been adapted for predicting oil recovery resulting from various gas-driven slug sizes. The results presented for both continuous and slug-type injection show, that permeability variation has 0 significant effect on oil recovery but that solvent composition, within the range studied, has a lesser effect on oil recovery. INTRODUCTION Experience from many of the miscible-phase displacement projects currently in operation indicates that the injected solvent flows preferentially through the more permeable zones in the reservoir. This preferential solvent flow in the high-permeability streaks results in a reduction of vertical coverage (C,) and an attendant decrease in oil recovery. The multilayer technique presented in this paper uses areal coverage (C.,) data for a single layer from the literature and from laboratory measurements of displacement efficiency (herein referred to as microscopic coverage, C,,) to calculate areal coverage (C,) and vertical coverage (C,) for the multilayer system. Oil recovery for the multilayer system is obtained as the product of (Ca) (Cm) (Cv). It is assumed that C, in a single layer is 100 per cent; therefore, (C,) (Cm) is a measure of oil recovery from that layer. Data presented in the literature for a single layer generally deal only with areal coverage and/or microscopic coverage —but seldom specifically with oil recovery. Nevertheless, this technique is flexible in that either Ca and C,, of an individual layer or a direct measurement of oil recovery for the layer may be used. In developing this technique, the problem arose concerning a method of determining the relative amounts of solvent that will enter each layer during any increment of solvent injected. To solve the problem, a dimensionless equation was derived for expressing solvent injected into each layer as a fraction of total injection. A finite-difference method was applied in integrating the equation to determine oil recovery for the system of layers as a function of pore volumes injected. The technique subsequently was programed for solution on a digital computer. The method was applied to predict performance of a deep California reservoir under continuous miscible displacement and has been extended for calculating oil recovery as a function of slug size for gas-driven slug injection. The technique may be applied to any petroleum reservoir that can be adequately represented as a layered system, by considering permeability variation,1-3 permeability range and average permeability. Each layer is then assigned its appropriate permeability, porosity and hydrocarbon saturation. RESERVOIR VOLUME CONTACTED BY SOLVENT It has been recognized for some time that high microscopic coverage (C,) can be obtained by injecting a miscible agent, such as propane, into an oil reservoir. These high values of C,,, have been demonstrated in the laboratory and are normally between 80 and 100 per cent, depending on solvent and reservoir oil composition as well as on reservoir temperature and pressure. In miscible-phase displacement, because there is no interface between solvent and oil, effective permeability to solvent is the same as that to oil. (This assumes that oil saturation has not changed and that water is immobile.) Consequently, mobility ratio (M) simply reduces to that of viscosity ratio . Perrine4 and Habermann5 have shown that large

By H. F. Webster, C. G. Dunn

Rolling md annealing procedures are described for developing the (110) preferred orientation in tantalum for use as a thermionic-emission materinl where electrodes of a uniform high work function are needed. The development of a (110) [001] annealing texture is also reported. A preferential growth process due to low (110) gas-metal surface energy is considered in explanation of the observed growth of (110) grains. ThE growth of (110)-oriented grains in thin strips of rolled zone-refined tantalum, previously discussed briefly,' is reported together with more recent information on the formation of a (110)[001.] annealing texture, i.e., one where the [001] direction of each grain lies close to the rolling direction. The development of tantalum sheet with a (110) preferred orientation (position of [001 ] directions unspecified) is of importance as a thermionic-emission material in thermionic-energy converters. Since therm ionic-emission properties of cesium-coated crystals vary over a wide range depending on (hkl) a2-7 a single (hkl) preferred orientation is more useful than either several preferred orientations or none. Furthermore, the (110) preferred orientation yields the highest thermionic-emission density for a cesium coverage of less than a monolayer.5-7 A consideration of the stability of the grain structure needed at high operating temperatures suggests that the preferred orientation itself should be produced by annealing processes. Information on annealing textures in tantalum, however, is rather limited. Pugh and Hibbard 8 obtained (111)[112] and (lll)[112] components in a 1400°C recrystallization texture in 95 pct cold-rolled foil; these components were enhanced on annealing at 2500°C. Muller9 rolled 99.97 Ta to 90 pct reduction in thickness in the final stage and noted only a slight sharpening of the rolling texture, with some intensification of the (111)[112] component upon annealing at 1200°C. The experimental procedure followed in the present work stemmed from the idea of using possible differences in (hkl) surface energies to provide a small driving force for growth of grains having the lowest (hkl) surface energy.l0* This would mean using high-purity tantalum processed into thin sheet form and annealed at high temperatures either in a noncontaminating atmosphere or in one producing additional sample purification. EXPERIMENTAL Zone-Refined Tantalum. National Research Corp. tantalum in the form of 1/8-in.-diam rod and of 99.98 purity (53 ppm 0, 15 ppm N, and 8 ppm C) was zone-melted four times. The traversing speed was 4 mm per min. Such treatment increased the resistance ratio, R293k/R20K , where R293K is the resistance of the specimen at 20°C and R20K the re-resistance at liquid-hydrogen temperature, from a value of 25 for the initial rod to 175 for the zone-refined rod (the increase in the resistance ratio provides a measure of purification11,12). Part of a zone-refined rod was rolled unidirec-tionally to a strip 0.003 in. thick and 0.28 in. wide. Samples were given anneals in the range 1300" to 2100°C using ac conduction heating in an oil-free vacuum system. Recrystallization to small grains appeared to be complete at 1300°C. Large grains were formed at higher temperatures, but these were not entirely strain-free, some grains showing asterism in Laue X-ray patterns and some displaying a range in orientation. Part of the difficulty was caused by thermal expansion of the tantalum strip as it was held between fixed supports. However, in a different arrangement with the tantalum freely suspended in a tantalum can, high-frequency induction heating in vacuo at about l0-6 Torr produced

Jan 1, 1964

By J. Fageant, W. C. Ellis

All major regions in a progressively solidified germanium ingot were related through successive orders of octahedral twinning. The occurrence of lineage structure and the generation and survival of orientations are discussed. WHEN metals solidify in a temperature gradient a preferred orientation, or casting texture, usually develops. For example, in face-centered and body-centered cubic metals, most of the solidifying crystals have a cube axis, <loo>, aligned approximately in the freezing direction.&apos; In the solidification of diamond cubic metals this is not the case, since there is a natural tendency to form twin orientations.&apos; . In this paper, twinning relationships in cast germanium are described; some conclusions with respect to nucleation and survival of new orientations are discussed. In the first experiment, an ingot of high purity germanium, % in. in diameter and 1 % in. in length, was formed by progressive solidification4 from the bottom. The ingot was cut into 21 slices, each circular and about 0.030 in. thick. The top surface of each slice was polished and etched to reveal the regions of different orientations. Orientations were determined by the Laue X-ray back-reflection method. The uncertainty in the determined orientation relationships was l" or 2" when separate slices and films were involved. Frequently, however, advantage was taken of illuminating across a boundary when the patterns of the two orientations were recorded on the same film. The uncertainty then was less than 1". Often the twin relation was evident from common zones or individual reflections. Twin relationships were recognized through comparison of the values of the nine angles between cube poles of the two orientations with those calculated for successive orders of octahedral twinning. The birth and survival of each region can be reconstructed by visual examination of the etched slices shown in Fig. 1. In slice 21, where solidification began, many regions are present; these regions were found to be twin-related. Solidification appears to have started from one nucleus formed probably at the wall of the crucible.* Subsequent ori- entations were developed by nucleation on existing solid surfaces, and only in the twin relationship. This is an example of a general process of nucleation on a surface of existing solid and may be descriptively termed oriented nuc1eation.t In germanium, and other diamond cubic substances, the orienting habit is that of twinning on an octahedral plane.&apos; " The prevalence of straight traces in the polished surfaces of succeeding slices (Fig. 1) suggests that the twinning observed in the first slice persisted throughout solidification. This was confirmed by X-ray determinations. The schematic diagram of Fig. 2 shows the twinning relationships of the major regions throughout the ingot. Since all observed relationships are describable as twinning, it is reasonable to conclude that no random nucleation occurred in the freezing of the ingot. An alternative possibility would be that nucleation of a random nature occurred, but only those nuclei in twin orientations survived in subsequent growth. This is unlikely for there would be as good a reason for the growth of randomly oriented nuclei as for the growth of the many different orientations present after several orders of twinning. The many twin components contain a wide distribution of orientations, and did grow. In fact, they are the only ones found in the solid. The conditions of solidification of this ingot were such as to discourage nucleation of crystals wholly in the liquid. The rate of solidification was 0.125 in. per min. This slow rate of heat removal afforded but small opportunity for supercooling within the liquid —a condition needed to provide enough decrease in free energy for such nucleation. When nucleation occurs on an existing solid surface, the interfacial energy between the existing and forming regions is important in determining the new stable orientation. The new orientation is expected to be one which minimizes this energy. In the diamond cubic structure, the interface for the

Jan 1, 1955

By F. J. Fayers, J. W. Sheldon

A theoretical discussion is presented of the behavior of the interface between two fluids of different physical properties when displacement is occurring along a thin tilted bed. An approximate equation of motion is deduced for the motion of the interface, suitable boundary conditions are derived and the conditions necessary for the approximation to be valid are determined. Steady-state behavior and the circumstances under which a steady-state interface can develop are discussed. Finite-difference solutions of the equation of motion for two characteristic water-drive problems are presenled. The theory of displacement in a thin bed may be regarded as being the porous-medium-equivalent of the classical "shallow-water wave" theory of hydrodynamics. INTRODUCTION The solution of moving interface problems are important in predicting the behavior of oil reservoirs under various conditions of production. Kidder4,5 has obtained analytic solutions for the fingering problem and for another particular case of the motion of the interface between two immiscible fluids of unequal density in a porous medium. In the present analysis, we analyze the problem of the motion of an interface along a slightly dipping bed whose length is long compared with its thickness. The requirement of a thin bed is necessary in order to give a simple differential equation for the motion. The two fluids are of unequal density and mobility. In the derivation of the equation of motion, it is assumed that the lighter fluid is being injected at constant rate at the high end of the porous layer, while heavy fluid is produced at the low end of the layer. The analysis applies equally well, however, to the reverse procedure in which the heavier fluid is injected at the low end of the tilted layer. It will be shown that the behavior of the system is critically dependent on which fluid has the higher mobility and that the interface can in certain circumstances achieve a simple progressive steady-state shape. The fluids may be considered to be immiscible or miscible. It is assumed, however, that the thickness of the interface region is negligible in comparison with other dimensions of the system, and that the strength of the saturation or concentration discontinuity remains constant during the motion. In conjunction with Buckley-Leverett theory and areal sweep-out calculations, the tilted interface problem is one of the fundamental problems of reservoir engineering; it defines the very important underpassing and overpassing phenomena associated with water-drives, gas-drives and secondary recovery operations. The tilted interface problem has been dealt with previously by Dietz.2 In the present paper, we endeavor to derive the pertinent mathematical results more rigorously, and in doing so we obtain modifications in both the differential equation and boundary conditions for those given by Dietz. We also attempt to show the connection between these results and some of the recent work on the stability of interfaces. Finally, we attempt to demonstrate the practical importance of the thin bed theory by showing the difference in behavior of two characteristic waterflood problems. In the favorable mobility case recovery is improved by increasing production rate, while in the unfavorable case undercutting or overcutting is minimized by reducing the displacement rate. PROPERTIES OF THE EQUATION OF MOTION Fig. 1 illustrates a porous layer of constant thickness H and tilt 8 with Fluid 1 of mobility ?l and density pl below Fluid 2 of mobility ?2 and density p2. The fluids are incompressible and flowing with volumetric flux q along the layer. Both the slope a of the interface with respect to the bed and the curvature of the interface are assumed to be small. What is meant by "small" is indicated in the derivation given in Appendix A of an approximate equation of motion for the interface. Other symbols are defined in the "Nomen-