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By Samuel Storchheim

IT was noted that variations existed in the magnetic properties, namely, coercive force, He, and rema-nence, Br, of 18/8 stainless steel wires of the same analysis when these wires were given the same percentage of reductiori of area at different rates of reduction. In order to determine the extent of these variations, a program was initiated whereby commercial 302 and 304 stainless steels were drawn with a wide variation of speeds. Ultimate tensile strengths and specific resistances, as well as the Hc-BT measurements, were determined. If variations of considerable magnitude were found, it was thought that the knowledge accrued from the investigation could probably aid in determining the particular drawing speed required to obtain desired properties for a given specification for a particular analysis of wire. Drawing Procedure Two specimens (set I, No. 302 and No. 304), the chemical analyses of which are given in Table I, were drawn at different speeds, namely, 45 to 3900 ft per min, directly from 0.016 in. diam wire to 0.004 in. diam wire, a 93.7 pct reduction of area. To obtain this high percentage of reduction, the wire at 0.016 in. was softened by annealing at 1150°C. It was then strung in a No. 16CF variable speed Vaughn drawing unit and passed through 13 B.&S. gage dies of successively smaller diameter, as shown in the accompanying table. Following this step, several hundred feet of the wire was drawn, at a particular speed, through the dies and wound upon a spool. Once the sample of wire was drawn at the desired speed, the spool with the finished sample was removed, tagged for later identification, and an empty spool was placed in the machine. Another wire sample was drawn at a different speed, after making the necessary adjustments upon the Vaughn unit. At the greater speeds, several thousand feet of sample were drawn to insure that the wire to be used for testing would be uniform. This was done because the desired speed was not reached instantly; the wire taking a short while to attain the required drawing rate. All speed measurements were made by placing a tachometer against one of the machine's pulleys during the actual drawing of the specimens. 84.4 pct reduction of area. The 0.072 in. diameter wire was also annealed at 1150°C. The process of obtaining samples was the same as described above. The only difference between the two was that the rates involved were not as extensive, set II covering a range of 625 to 1150 ft per min. Tensile tests were carried out for the 0.004 in. diam wires on a horizontal Scott Tensile Tester, while tensile tests for the 0.028 in. diam wires were made on a vertical Scott Tensile Tester. Each value listed in the tables represented the average of five samples with a maximum deviation of approximately 3 pct among the samples. Resistance per foot of the wires was determined by use of standard bridges accurate to the nearest hundreth of an ohm for the 0.004 in. wire, and to the nearest thousandth of an ohm for the 0.028 in. wire. The resistances per foot were then converted to resistivities by use of the following equation: P = RxCM where R is the resistance per ft in ohms per ft; CM, the area in circular mils; and P, the resistivity in ohms—CM. The values listed in the tables likewise

Jan 1, 1952

By B. N. Webber

During World War II the Pocos de Caldas bauxite deposits of Minas Gerais in Brazil yielded some 60,000 tons. Since then they have maintained a small but almost continuous production. Known for many years, the deposits have been reconnoitered by a number of geologists,1-4 but no dimensional study has been possible because there have not been enough exposures to show clearly the depth, bedrock, and habit of occurrence. The deposits are somewhat unorthodox in their occurrence mainly on steep slopes of mountainous terrain. Although the parent rocks are a sequence of alkalic intrusions that bauxitize readily under the proper conditions, bauxitization has not been the dominant weathering process in the area. It is limited to certain localities where important volumes of bauxite have formed by laterization of several rock types, each yielding a distinctive type of bauxite. Bauxitization may be observed in several stages and in both direct and indirect cycles of formation. The deposits are unique in being of demonstrably recent age, so that the conditions under which the bauxite formed are essentially those of the present time. The bauxitization sequence is postulated in Fig. 1. Pocos de Caldas district is situated at approximately 21" 50' south latitude and 46" 30' west longitude in southwestern Minas Gerais, near its boundary with the state of Sao Paulo. It lies within the Eastern Plateau physiographic province of Brazil, occupying a prominent highland area that rises some 2000 ft above the surrounding country. The central portion of the Pocos de Caldas highland is characterized by gently undulating topography, with generally sluggish drainage, and is surrounded by a rim of hills rising above 1000 ft above it. In cross section the highland resembles a truncated cone with a depressed central area. The rim has been sculptured into a more prominent and abrupt topographic pattern than the central area, and streams that are of low to moderate gradient in the central plateau plunge over the rim in a spectacular series of cascades and falls. GEOLOGIC SETTING The Pocos de Caldas highland owes its physiographic expression mainly to the differential erosion of a complex intrusion of alkalic rocks into gneiss and sandstone. Erosion was guided somewhat by faulting. The highland is almost circular, and its limits, except in one locality, coincide with the periphery of the intrusion. The alkalic intrusions largely control its shape and extent, aided by some subsidence through faulting of the central portion. The mountainous rim of chilled phase, the later intrusions, and the indurated intruded rocks have resisted erosion more effectively than the central portion of the intrusion, which is composed of more coarsely crystalline alkalic rocks that form a central basin in the highland. Gneiss and sandstone are found coincident in elevation with the topographically highest intrusions. BAUXITE TYPES Most of the bauxite, which varies in physical type, is on the top and steep slopes of the northern rim. The only alumina mineral is gibbsite, definitely crystalline but iron-stained unless of secondary origin. Clay particles occurring with the bauxite are kaolinite. Some types of bauxite are an index to their origin. There are four general physical types of bauxite or bauxite laterite: 1) Surface Rubble: This partly nodular and partly fragmented type, usually less than 3 ft thick, results from surface weathering of massive bauxite or may form by superficial enrichment of nodular bauxite with a clay matrix when the interstitial clay is removed by surface runoff.

Jan 1, 1960

By E. L. Dougherty, J. W. Sheldon

Using the numerical techniques shown in this paper it is possible to compute the simultaneous dynamical behavior of multiple fluid-fluid interfaces in two dimensions. Hence, fluid-fluid inter face models of several oil recovery processes can be constructed which allow prediction of the effect of fluid flow in two dimensions on the behavior of these processes while taking into account various physical effects, such as saturation gradients, phase changes and thermal stimulation. Techniques for constructing fluid-fluid interface approximations for several oil recovery processes are reuiewed. The validity of these techniques is established by comparison to experimental results. The availability of a computer program for computing the behavior of multiple fluid-fluid interface problems makes the use of potentiometric models uneconomic. The results indicate the areal sweep efficiencies obtained from potentiometric model studies at high mobility ratios may be somewhat optimistic. The results also indicate that the areal sweep efficiency curves obtained at high viscosity ratios 2—4 using miscible fluids in porous media are misleading and that considerable care must be taken in defining the mobility ratio for a displacement process, especially for miscible fluids. INTRODUCTION Many of the methods used to estimate areal sweep efficiency assume that the oil recovery process can be represented by one or more fluid-fluid interfaces. When the mobilities of the displaced and displacing phases are assumed equal, this quantity can be computed using analytical mathematical methods.l.2 For non-unit mobility ratio, experimental methods based upon the fluid-fluid interface concept include potentiometric and electrolytic blotter models. Scaled models of porous media have also been used to study this problem. Fay and Prats3 and Aronofsky4 used numerical techniques to compute breakthrough sweep efficiency, but neither of these studies were extended beyond breakthrough. Numerical techniques which have been developed for solving a general fluid-fluid interface problem are presented in a companion paper.5 These techniques have been incorporated into a program for a large-scale digital computer which can treat simultaneously the dynamical behavior of as many as six fluid-fluid interfaces. Thus it is possible to simulate the behavior of several oil recovery processes taking into account such effects as saturation gradients. Techniques for representing several oil recovery processes by fluid-fluid interfaces are presented. Processes considered are conventional water flooding with and without a mobile gas phase, hot water flooding, miscible flooding and enriched gas drive. Other processes, whose effects could be studied by this technique, but are not considered in detail here, are underground combustion and steam injection processes and various slug processes such as gas-water injection and alcohol-solvent processes. Theoretical results obtained with single interfaces for mobility ratios of 0.25, 1, 2, 4, 8, 16, 32 and 64 in a repeated five-spot are compared to experimental results for this geometrical configuration obtained using miscible fluids and conductive analogs. Predicted recovery curves for water flooding in a repeated five-spot are compared to experimental results reported in the literature. Example calculations are shown for a conventional water flood in the presence of a free gas phase and for a hot-water flood. MATHEMATICAL PRELIMINARIES We assume that the rock matrix is homogeneous with constant thickness, absolute permeability and porosity. The fluids are incompressible. We also neglect the effects of gravity.

Jan 1, 1965

DEVELOPMENT of a chemical process for the extraction of pure metals from mill concentrates or metal scrap has progressed beyond the pilot plant stage and may prove an important adjunct to present smelting and refining methods if initial commercial operations prove economically successful. Developed by the Chemical Construction Corp., the new process involves the treatment of oxide and sulphide ore concentrates by chemical methods, instead of the usual smelting and refining techniques. Several of the many applications are now scheduled for commercial use. Refiners using the new process will prepare ore concentrates by standard flotation methods, introduce the concentrate as a slurry into an autoclave along with water and an acid or ammonia. From the resulting leach solution, recovery of individual metals is made by use of suitable reducing agents. By varying conditions during treatment, different metals in the ore are produced separately as pure powders, which may be pressed into forms ready to market, or in the case of copper, extruded as rods or pipe. The reagents are generally recovered. By manipulating the variables during reduction, selective separation of nickel, and/or cobalt, and/or copper can be made simultaneously. The separation is a continuous operation. Low metal prices are not immediately in view because of the tremendous demand at this time. However, reduced metallurgical treatment costs will allow economical mining of orebodies with lower metal content, permitting increased production to meet demand. Although the practical horizon for use of the new process appears to be limitless, one factor may enter into its employment. Just how low grade a concentrate can be economically used is unknown. In addition, for present practical considerations, only metal below zinc in the electromotive series may be processed. Each commercial application requires specific technique adaptation and pilot-plant data for engineering design. A nickel-cobalt-copper process has been researched and piloted in collaboration with Sherritt Gordon Mines, Ltd., for the firm's Lynn Lake properties. In addition, processes were tailored for cobalt concentrates of Howe Sound Mining Co., and National Lead Co., in view of the urgent need for this specific metal. Major General William N. Porter, president of Chemical Construction, says of the new process, "piloting experience has shown that production cost, from ore concentrates to pure metals should be considerably below current costs." Other savings may be realized by cutting transportation and personnel costs, and by reducing the time lag between mining and pure metal from months to a matter of hours. First commercial use of the process will start sometime this summer. Chemico is slated to finish building a $2.5 million cobalt refinery for Howe Sound Mining near Salt Lake City. The plant is expected to raise world cobalt production by 40 pct. The plant will process 35 tons of 20 pct cobalt concentrates from Howe Sound's Blackbird mine near Cobalt, Idaho, daily. Yearly production is expected to reach 2000 tons of pure metal, about one half of U. S. consumption in 1950. Steps in the Howe Sound application of the process are: 1. Acid oxidation leach. 2. Filtration (residues thrown away are insoluble compounds-gangue, iron, arsenic). 3. Cementation (for Cu removal because Cu content is too low for recovery). 4. Reduction from ammoniacal solution. 5. Separation of Co and Ni as mixed metals (95 pct Co and 5 pct Ni). 6. Recovery of ammonium sulphate. Under construction at the Fredericktown, Mo., mine of National Lead is a $5 million refinery sched- [ ]

Jan 1, 1952

By A. M. Skov, L. F. Elkins

Inclusion of anisotropic permeability in mathematical analysis of pressure transients observed during development of the huge Spraberry field indicates a major fracture trend which is in good agreement with that observed by fluid-injection tests spread over a 12- by 17-mile area. Delineation of this trend is important in selecting a pattern of injection for the pending large-scale water flooding in this field. Determination of reservoir parameters yielding best agreement between calculated pressures and observed reservoir pressures in newly completed wells was made using an IBM 650 computer. INTRODUCTION The Spraberry field covering 400,000 acres is a tight sand of less than 1-md permeability cut by an extensive system of vertical fractures. Primary recovery dominated by capillary retention of oil in the fractured sand matrix blocks is less than 10 per cent of oil in place. Strong forces of capillary imbibition of water into the sand, coupled with water flow under dynamic pressure gradient, indicate considerable increase in oil recovery can be achieved through water flooding. Best results will occur if the pattern of water injection is selected to force the water flow across the grain of the major fracture system. Existence of an oriented vertical fracture system in the Spraberry, observed first in cores, was highlighted more recently by the 144-fold contrast in permeability along and at right angles to the major fracture trend required to match relative water breakthrough times in Humble Oil & Refining Co.'s waterflood test there. Spraberry operators since have conducted two gas-injection tracer tests for further areal confirmation of the fracture trend. Re-analysis of early reservoir pressure transients for evidence of anisotropic permeability has permitted many more local determinations of major fracture trend without resort to further field tests. This paper is limited to updating analysis of reservoir pressure transients to include anisotropic permeability as a test for orientation of the major fracture trend in the Spraberry. The reader is referred to Refs. 1 and 2 for information about general Spraberry reservoir performance and to Refs. 3 and 4 for information about significance of fracture orientation in selection of the injection-well pattern for water flooding the Spraberry. RESERVOIR PRESSURE DATA—DRIVER AREA During early development of the Spraberry Driver area, Sohio Petroleum Co. made the extra effort to measure the initial pressure in each of the 71 wells in a 5-mile-long area immediately after completion. Progressively greater reductions in pressure ranging up to 400 psi were observed throughout the six-month development period. Detailed data are presented in Ref. 1. Since the reservoir oil was undersaturated some 300 psi initially, early reservoir performance involving 55 new well pressures is subject to analysis as flow of a single compressible fluid in a porous media. Assumption of uniform permeability in all directions yielded good agreement between calculated pressures and observed pressures of these wells in the earlier study,' but subsequent, additional, mathematical development to include anisotropic permeability in the transient pressure considerations and present availability of electronic computers to perform the much more extensive arithmetical calculations now yield even better agreement. The previous analysis, assuming uniform permeability, consisted essentially of calculating pressure reduction expanding circularly around each producing well and summing these effects at the time and location of each newly completed well for comparison with the measured pressure reduction. Permeability, effective fluid and rock compressibility, and permeability X thickness were varied until the best match with measured pressures was obtained. The present analysis, assuming anisotropic

By R. E. Gilchrist, R. R. Harvey, M. R. Dean

A simple and rapid three-component analysis procedure has been developed for use in fluid-flow studies. The method is based on refractive index measurements, combined with refractive dispersion measured between the Ha and H wave lengths. The procedure requires. calibration curves for the three-fluid system. The only restriction on the fluids employed is that only one be an aromatzc or olefinic compound. Individual sample measurements require only a few minutes. Composition results within the limits of accuracy required for fluid-flow analog studies are obtained. INTRODUCTION The simultaneous analysis of three-component mixtures is a problem often encountered in fluid-flow analog systems. In petroleum production research, the problem is usually encountered in experiments on the displacement of fluid from a porous medium. In the case of immiscible displacement, simple volumetric measurements of the produced fluids are usually sufficient, the analog fluids often being the actual reservoir fluids themselves — oil, water and gas. However, modern secondary recovery of petroleum sometimes involves production under miscible conditions, in which the oil is displaced by liquefied petroleum gas which, in turn, is displaced by dry gas. Since this type of displacement is done under conditions of pressure and temperature that are not easily reproduced in the laboratory, studies are often performed with analog fluids at essentially atmospheric pressure. Since the number of samples taken during one of these experiments is usually quite large, the time required for analysis becomes an important factor. In the past, the difficulty of conventional analysis has been avoided by the addition of various tracers to one or more of the components, or by the use of a tracer fluid as one of the components. With these techniques, a relatively large amount of analytical time is still required. Moreover, in the case of added tracers, the tracer material may migrate in part to one of the other fluids, may be adsorbed on the solid surfaces of the model, or may introduce side effects not characteristic of the prototype fluid. The substitution of a tracer fluid for one of the components can severely limit the choice of analog fluids. Optical refractometry provides a rapid and economical method of analysis of two-fluid systems or of monitoring small changes in composition of an essentially one-component system. Refractometric methods are capable of high degrees of accuracy, require only very small samples and can easily be adapted to automatic methods. They are not generally applicable, however, where three or more fluids are present over wide ranges of concentration. The method of three-component analysis described here has three essential characteristics. 1. It is based on refractometric measurements and thus preserves all of these desirable properties. 2. It does not make any stringent demands on the choice of fluids that can be analyzed. 3. It is capable of accuracy sufficient for fluid-flow analog studies. THEORETICAL The difference in the refractive index of a substance at two different wave lengths of light is known as its dispersivity. When the difference is taken between the specific refractions at the two wave lengths, the quantity is referred to as the specific dispersivity. Specific refraction was defined empirically by Gladstone and Dale1 as r = n-1/d....[1] where n is the index of refraction and d is the density. The definition is given more correctly by the expression r =n2-1/n2+1 1/d..........(2) 1References given at end of paper. MICIFTV OF PETROLEUM ENGINEER JOURNAL.

By Mary Barrett, Walter Rose

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

Jan 1, 1957

By J. L. Thompson

There are two basic forms of the LPG-slug process: the gas driven and the water driven. The pressure required for miscibility between gas and LPG prohibits the use of the gas-driven LPG process in shallow reservoirs. The water-driven LPG slug process normally exhibits good sweep efficiency. However, displacement of the LPG by water is poor. An improvement in this process appears possible by injecting a slug of carbon dioxide between the LPG slug and the water drive. Laboratory experiments were conducted in homogeneous linear systems to determine the effect of pressure on the various displacement zones. In the carbon dioxide-LPG displacement zone, the effect of pressure on the displacement efficiency is negligible above the miscibility pressure. However, the displacement efficiency decreases linearly with decreasing pressure below the miscibility pressure. With water displacing carbon dioxide, it was found that the recovery of carbon dioxide after water breakthrough can be predicted from its solubility in water. A displacement test was conducted with LPG and carbon dioxide slugs large enough to avoid interference between the oil-LPG, LPG - carbon dioxide and carbon dioxide - water displacement zones. Under these conditions, essentially complete oil and LPG recovery was obtained. However, a substantial amount of carbon dioxide was left in the core at water breakthrough. INTRODUCTION It has been shown in homogeneous linear systems that essentially complete oil recovery can be obtained by displacement with a miscible fluid such as LPG. Economic considerations dictate that the valuable LPG also be recovered. Methods proposed for recovering the LPG include (1) displacement with natural gas at a pressure high enough to make the two fluids miscible1 (the disadvantage of this method is that the required pressure of about 1,500 psi is too high for shallow reservoirs) and (2) displacement of the LPG with water2 (principal disadvantage is that a large amount of LPG remains in the formation because of poor displacement efficiency). This paper treats an improvement in the water-driven LPG slug process3,4 where carbon dioxide is injected between the LPG and water. Carbon dioxide is completely or at least partially miscible with propane and soluble in water; thus, displacement efficiency is improved at both ends of the carbon dioxide slug. To minimize effects of other variables, all experiments were conducted in linear core systems. GENERAL PROCESS DESCRIPTION The displacements of propane by carbon dioxide and carbon dioxide by water are considered separately, assuming enough of each is injected to prevent mutual interference. Displacement descriptions are confined only to the part of the pore volume containing mobile fluids unless otherwise specified. The schematic representation is given in Fig. 1. Starting at the producing well, a zone containing only oil is followed by a zone containing a single-phase mixture of propane and oil. The concentration of propane increases in the direction of the injection well and ultimately grades to pure propane. Then follows a zone containing a mixture of propane and carbon dioxide in continuously varying proportions until 100 percent carbon dioxide is reached. In this zone, the concentration of carbon dioxide in the immobile water phase also varies from zero to full saturation. Whether the displacement of propane by carbon dioxide is of complete or partial miscibility depends on pressure and temperature (Fig. 2). If the horizontal line representing the prevailing pressure intercepts the boundary curves of the phase envelopes for the prevailing temperature (i.e., if the pressure is lower than the critical

By Dean Goodermote, Carla S. Stone

I Introduction Coal fuels China. Roughly 70 percent of all commercial energy demand is supplied by domestic coal production and with the recent Chinese opening to the West, the Chinese Coal Industry may figure prominently in the export market as well. Because of the importance of China's coal industry to the future of China and the Pacific Rim energy balance, this paper reviews the industry and offers some cautious projections for its outlook. II Energy's Position in the Current Political and Economic Climate Traditionally, Chinese society has been dominated by the policies of its most important government leaders. Deng Xiaoping, Vice Chairman of the Communist Party is the current leader of China. Deng and his proteges are pragmatists. Although China's government structure is based on Marxist/Leninist tradition, Deng and his followers are promoting experiments with market economics and expanded relationships with Western Countries, which have encouraged foreign investment in China. Energy companies represent just one type of industry that is interested in helping the Chinese to develop their abundant natural resources. Although China's leadership is committed to a program of economic modernization, that program currently is experiencing what the Chinese government terms "readjustment". Readjustment cuts back in imports due to deficient foreign exchange and deemphasizes heavy industry, while it encourages agricultural and consumer goods output and, most imporant, energy production. Increased Chinese coal and oil production is essential both to fuel industry and, equally important, to provide foreign exchange. If sufficient energy production is not forthcoming, then economic growth will be severely retarded. China's 1979 per capita GNP of $260 is only slightly better than the weighted average achieved by low income countries of $230. (1) Delays in growth could lead to social unrest, threatening the position of the current leadership. Since there is no institutionalized mechanism for leadership succession and policy continuation, it is reasonable to assume that leadership changes could result in energy policy changes. III Energy Consumption Energy production is important to China's future economic health as highlighted by the World Bank. If China's economy grows rapidly, 5 percent to 6 percent during this decade, the Bank noted, a significant energy shortfall could occur as early as 1985. This state of affairs contrasts sharply with China's current position as a net hydrocarbon exporter. (2) To assure a healthy economic future, China's leadership is attempting to reduce its rate of increase in energy demand through conservation as well as to boost energy output. A massive conservation promotion program has been underway since 1979 and there is much room for improvement. China's industrial sector is only about half as energy efficient as is U.S. industry. (3) During the last two decades, each percent of increase in GNP has been accompanied by a 1.8 percent of increase in energy consumption. (4) This compares rather poorly with the United States where a less than one-to-one relationship exists. IV Energy Supply The short term prospects for oil production are uncertain. Production increases were rapid in the 1960's and early 1970's, averaging 20 percent annually, but most of this increase came from one field, Daquing. Now that Daquing's production has peaked and the offshore potential has yet to be developed, petroleum production has maintained a plateau of 2.1 million b/d, at least temporarily, of which approximately 15 percent is exported. (5) Output

Jan 1, 1982

By Philip R. Strand, O. F. Stewart

Vermiculite is the name generally applied to the group of hydrated ferromagnesian aluminum silicates that are characterized by the ability to expand when heated. This process, called exfoliation, results in a lightweight product of commercial value. Most uses of vermiculite are for the expanded material. The chief markets are in construction, agriculture, and horticulture, with lesser uses in general industry. Composition and Properties Vermiculite, in its natural state, has the characteristic micaceous habit, a perfect basal cleavage which causes splitting into thin laminae that are soft, pliable, and inelastic. The structure of vermiculite is basically that of a talc. The prominent monoclinic crystal faces are often marked by lines at 60° and 120°. Hardness varies from 1.5 to 2 or more; specific gravities are between 2.1 and 2.8; color varies from almost clear to amber, bronze, brown, green, or black. Vermiculite feels like talc, especially when wet. Although much research has been performed on the chemical and structural composition, there is not yet complete agreement on the exact formula. This is to be expected when different workers have examined the many different varieties. Vermiculite is not considered to be a single mineral species but a family of related minerals. The structural formula for a trioctahedral vermiculite may be written: (H20)-(Mg,Ca,K)-(A12,Fe,Mg)-(Si,A1,Fe)4O10 (OH) 2 Hydrobiotite also occurs with vermiculite and is usually considered a vermiculite for commercial uses. When heated quickly to elevated temperatures, vermiculite expands by exfoliating at right angles to the cleavage into wormlike particles. The name vermiculite is derived from the Latin vermiculare, to breed worms. This characteristic of expansion is the result of the mechanical separation of the layers by the rapid conversion of contained water to steam. The decrease in bulk density of commercial grades is usually approximately 10 times, from 50 to 5 lb/ft3, but varies depending on the quality, size, and furnace efficiency. Individual flakes may expand up to 30 times. Vermiculite may also be expanded by soaking in chemicals such as hydrogen peroxide, weak acids, and other electrolytes. Color change during expansion is dependent upon the type of vermiculite and furnace conditions. Heating in an oxidizing atmosphere produces a dull gray or tan color, whereas a reducing atmosphere can produce a bronze or gold color. The expansion of the vermiculite crystal results in large pores being formed between the platelets. Thus, exfoliation makes available a large increase in void volume which is important in the application of vermiculite as a chemical carrier. Mathieson and Walker (1954) state vermiculite must be regarded as a true clay mineral. The characteristic properties of the mineral, such as high cation exchange capacity, organic complexing ability, and variable interlamellar distance are very similar to those of montmorillonite. The cation exchange capacity of vermiculite is one of the highest of all the clay minerals. The interplatelet space is accessible to penetration by some electrostatically neutral molecules. Water and glycerine are two common substances whose molecules may be so imbibed. In the natural state and under normal atmospheric conditions, water occupies the spaces between the silicate layers. The crystal d-spacing is near 14.2A. By differential thermal analysis, it has been determined that the water

Jan 1, 1983

By P. E. Baker

Approximate solutions are presented for the heat-flow equations in a loss-free linear system with a moving source and with heat transfer by convection and conduction, representing in situ combustion in an oil reservoir. The rate of heat generation and the velocity vf of the source (flame front) are assumed constant. A cold front or convection front caused by the cooling effect of in-jected air develops behind the flame front and moves with velocity vc, which is determined by the thermal properties of the air and rock. Because of thermal conduction the fronts are not sharp; i.e., they do not represent temperature discontinuities. The following solutions apply after a sufficiently long time. where Q is heat generated per unit volume of formation, k is thermal conductivity, CF is volumetric heat capacity, a is thermal diffusivity, and subscripts 1 and 2 refer to values behind and ahead of the flame front, respectively. The parameter CF2 is contained in v . Te is initial reservoir temper- . C2 e ature and air-injection temperature. Other mathematically possible solutions are presented. The different solutions result from the use of different values for various physical parameters. The solution just presented is thought to be most commonly applicable. INTRODUCTION In this paper, approximate analytical expressions are derived for the temperature profile developed in the underground combustion method of oil recovery. A qualitative description of the process may be found in a paper by Tadema.1 The flame front is regarded as a moving source with a constant rate of heat generation. Heat transfer is by conduction and convection. Previous publications, of which a few are cited here, 2-5 have also attacked this problem and have presented solutions pertaining to different methods of approximating or idealizing the process studied. The present paper also treats an idealized case: linear flow is assumed for heat and fluids, and vaporization and condensation effects are neglected. The results obtained are similar to those derived by Bailey and Larkin,3 but are obtained by an entirely different procedure. The method used here should give considerably greater insight into the physics of the in situ combustion process. Four types of cases are considered, distinguished by thermal and fluid-flow properties of the system. A constant rate of heat generation and constant rate of flame-front advance are assumed. Flame-front temperature is determined for each case using a heat balance which involves the entire temperature profile. The applicability of the different solutions to real systems is discussed after they are all presented. Again, this is done for the purpose of understanding better the physics of the process. Consideration of the nonapplicable solutions and of the reasons for their not applying is significant. In a paper by Cooperman,4 the only case solved is one considered here as not applicable. Fluid flow, as such (pressures, saturations, oil recovery, etc.), is not treated. This subject has been covered in a paper by Wilson, et al.6 Also, we are not concerned with requirements for continuance of the process; we only attempt to determine the temperature history for cases where the process has continued for some time. PHYSICAL SYSTEM AND APPROACH TO PROBLEM A linear flow (heat and fluid) system is assumed and the x-axis is taken parallel to the flow direction. The combustion zone (flame front) is vertical,

By Nick Holonyak

Halogen vapor-transport synthesis of Ga(As,-,Px) and its preparation into laser junctions are described. Electrical and optical properties of Ga(As,-,PX) laser junctions are discussed. The present limitations in these properties are related to material proble?vzs and the very early state of development of Ga(As,-,PX), and are discussed in this context. Inhonzogeneity problems, fluctuation of As :P ratio, and problems with deep-level contaminants are described and related to Ga(As,-,PX) junction performance. Laser junctions are demonstrated which operate to wavelengths as short as 6470 A (77°K). The prospect that Ga(As,-,P,) will operate to wavelengths perhaps 100A shorter is mentioned. IN this paper we wish to describe some of the more important features of almost 1 year of experience in the preparation and properties of Ga(As,-,P,) p-n junction lasers. Because much data so far available are far from complete, some of the results still must be considered tentative and subject to correction and revision as work on Ga(As,-,P,) crystal problems progresses. Although the electrical, optical, and device properties of Ga(As,-,P,) junction lasers are understandably of considerable interest, the work to date points out that by far the most serious problems extant and those deserving first attention are problems involving the growth, doping, and perfection of Ga(As,-,P,) crystals. One of the most formidable of these is to grow Ga(As,-,P,) sufficiently free of deep levels, either due to contaminants or to structural imperfections, to allow fabrication of laser p-n junctions which can be cooled and not suffer from "freeze-out" of carriers on deep levels (and consequent double-injection behavior). In addition to the problems of growing crystals adequately free of deep levels and generally of the highest perfection, so that the best possible laser junctions can be realized, the further goal remains of increasing the phosphorus content well beyond 40 pct in an attempt to determine the practical lower wavelength limits of laser action in the Ga(As,-,P,) system. Even though the laser junctions prepared in Ga(As,-,P,) are of importance in their own right, we have considered them at this point mainly a means to study the growth and crystal problems of the material. It can be concluded that the laser junctions now available are almost completely limited by the purity and structural deficiencies of Ga(As,-,P,) crystals, and cannot be fairly compared with, for example, GaAs p-n junction lasers until Ga(As,-,P,) crystal growth has been more extensively developed. The basis for the statements above will become evident in the following sections which describe Ga(As,-,P,) crystal and junction preparation, and laser-junction properties. G(As,-,P,) CRYSTAL GROWTH As previously reported,2 we have found it convenient to employ the halogen vapor-transport process3 for synthesizing Ga(As,-,P,) crystals for use in laser junctions. Commercially available GaAs and Gap, separately prepared by halogen vapor tranport, are sealed in the desired ratio in a quartz vessel with a quantity of column-VI donor and a small quantity of metal halide which supplies the halogen for transport. The sealed ampoule, as shown in Fig. 1, is heated at a temperature in the range from 1025" to 1100°C at the position of the source GaAs and Gap. The GaAs and Gap are simultaneously vapor-transported and deposited as Ga(As,-,P,) at one end of the ampoule

Jan 1, 1964

By D. H. Gray, G. Bergamini, I. Fatt

A method developed by soil scientists for measuring permeability anisotropy of soils has been adapted for use in studies of sandstone permeability aniso-tmpy. Studies on Berea and Bandera sandstone show that permeability of these materials decreases upon application of simulated overburden pressure. Permeability reduction of Berea and Grubb sandstone cores subjected to simulated overburden pressure is shown to be a function of the ratio of radial to axial stress. INTRODUCTION The effects of mechanical stress on reservoir rock parameters are now generally accepted as being important in reservoir engineering calculations. In several oil fields the unique behavior of the reservoir has been attributed to the influence of overburden pressure or internal fluid pressure on rock permeability or fluid content. l Although the gross effects of overburden pressure on permeability, porosity, waterflood efficiency, electrical resistance and sonic velocity have now been established,3-9 there are some very interesting, and perhaps important, details of rock behavior under stress that have not heretofore been studied. In this paper we will show that permeability anistropy of several sandstones is a function of overburden pressure. We will also show that permeability reduction of cylindrical samples of two sandstones, when subjected to mechanical stress, is a function of the ratio of radial to axial stress. Most studies of overburden pressure effects made in the past have attempted to duplicate reservoir conditions by applying hydrostatic external pressure on all surfaces of the sample. Assuming perfect elasticity, that is, no viscoelastic flow during geological time, reservoir rock in situ cannot be under hydrostatic stress as is apparent from the value of 0.25 for Poisson's ratio for most rock. In the absence of tectonic forces the horizontal stress component If there are directional permeability effects, as has been reported from field and laboratory studies, l0,11 then one would expect hydrostatic stress as used in the laboratory to give a different permeability reduction from that occurring under reservoir stress conditions. The influence of stress on directional permeability was measured by a modification of the method first described by Maasland and Kirkham for use on soil samples.12 Their method permits calculation of the permeabilities along each of the three mutually perpendicular axes of a cubic sample. The modification reported in this paper extends the method to observing these permeabilities when the sample is under hydrostatic stress. The Hassler sleeve type of core holder is satisfactory for studying overburden pressure effects on permeability if a known force is applied to the end plugs. Wyble6 used a sleeve core holder but did not load the end plugs. In this paper we combine sleeve pressure and axial force to give permeability changes which we believe are close to those occurring in reservoirs when reservoir pressure changes. The combination of sleeve pressure and axial force assumes, however, that the sleeve pressure simulates both vertical stress and horizontal stress in one direction. METHOD PERMEABILITY ANISOTROPY The Maasland and Kirkhaml2 method of measuring permeability anisotropy uses a cube of porous material which is Open On three faces and has discs with a Center hole for an air inlet cemented to the other three mutually perpendicular faces (Fig. 1). The rate at which air pressure falls in a bottle of known volume, and pressure slightly above atmospheric, when the bottle discharges through each disc, is

By L. A. Wilson, N. H. Harrison, R. R. Clay, R. L. Reed. D. W. Reed

Experiments have been performed in a linear near-adiabatic system for the purpose of extending data on reverse and forward combustion from atmospheric pressure to 1,000 psig. Results obtained from reverse combustion appear to conform qualitatively with the existing description of the process when reaction kinetics are suitably modified to account for the increase in pressure, i.e., increasing tbe pressure decreases the peak temperature and increases the combustion zone velocity. Forward combustion appears to be a fuel dominated process wherein peak temperature and combustion zone velocity are not very sensitive to changes in pressure. The moderate effects of pressure that do exist at low flux virtually disappear at high flux providing all oxygen is consumed. With this provision. increasing the pressure decreases the frontal velocity and increases the peak temperature. Results me shown graphicaIIy which demonstrate the effects of presswe on peak temperature, rate of advance, oil recovery, air/oil ratio, carbon oxides produced and temperature distributions. INTRODUCTION Numerous field tests of oil recovery using the technique of underground combustion are now in progress. Operating pressures used are always substantially in excess of atmospheric pressure. Nevertheless, the literature contains no laboratory data pertaining to the effects of pressure except for those of Martin, Alexander and Dew.1 Unfortunately, these data appear to reflect heat losses which may have obscured some of the effects of increased pressure. The underground combustion processes are exceedingly complex, and general concepts relating to them have necessarily been described in relatively simple terms. Particularly with regard to forward combustion, the interaction between multiphase fluid flow, heat transport and various rate mechanisms is so involved that to date a rigorous treatment is not available. In this paper a linear near-adiabatic system is described which was found capable of operating at pressures up to 1,000 psig and temperatures of at least 1,100 F. Using this equipment, experiments on both forward and reverse combustion were accomplished at elevated pressures and the data presented as a function of air flux or temperature. It will be assumed that the reader is familiar with the papers of Wilson, Wygal, Reed, Gergins and Henderson on forward combustion and that of Reed, Reed and Tracht3 on reverse combustion, so that it is not necessary to repeat the details of the two processes. EQUIPMENT AND PROCEDURE It was decided to study the effects of pressure over the interval 0-1,000 psig using a near-adiabatic system. Since satisfactory operation of such a system requires very thin tubing walls, it proved necessary to insert the entire combustion tube and heater assembly into a high pressure jacket in such a way that the internal tube pressure could be counterbalanced by pressurizing the annulus. This meant that the numerous heater and thermocouple wires had to pass through gas-tight seals that required considerable effort to maintain effective. An unexpected difficulty arose in connection with the nature of the annulus pressuring gas. It turned out that the composition of this gas critically affected the functioning of the adiabatic control system. Operation of the equipment at elevated pressures was not particularly difficult. The problems that did arise were a direct consequence of the large numbers of connections and seals involved. EQUIPMENT The equipment consisted of the combustion tube which fitted within the pressure jacket. This jacket was in turn mounted on a wheeled carriage which facilitated movement and provided for rotation of the

By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By H. Larson, J. Chipman

The ferrous and ferric oxide concentrations of slags, expressed as j = Fe+++/(Fe+++ + Fe++), have been established through gas-slag equilibrium at 1550°C in a range of oxygen pressure of 10-I to 10-9 equilibriumatm. The value of j is increased by basic additions (BaO, CaO, MgO, MnO) and decreased by acidic oxides (SiO2 and TiO2). Oxygen pressure is shown graphically as a function of composition for slags which are analogous to those at the slag-gas interface of the open hearth furnace. THE progress which has been made in recent years in understanding the chemistry of metallurgical slags has been based largely on studies of slag-metal and slag-gas equilibria. There is a considerable body of knowledge which is applicable to reactions occurring at the slag-metal interface in open hearth steelmaking. There is little information concerning reactions of the slag with the furnace atmosphere and hence little basis for an understanding of the transfer of oxygen, sulphur, or hydrogen between gas and slag. The oxygen pressure of the open hearth atmosphere is normally of the order of 10-1 to 10-3 atm which differs by several orders of magnitude from that of about 10" atm at the slag-metal interface. The chemical properties of the slag, for example, the ratio of ferric to ferrous iron and the ability of the slag to hold sulphur in solution, are greatly affected by changes in oxygen pressure. This investigation was undertaken to enlarge our knowledge of the effect of oxygen Pressure on steel-making slags. Using air or controlled mixtures of CO a CO2 a range of oxygen Pressures from 10.' to 10.' was covered. Review of the Literature There are only a few references in the literature which pertain directly to this investigation. The most important is that of Darken and Gurry1,2 on the system iron-oxygen. This work included the determination of the phase diagram of the system and also a study of the field of homogeneous melts and their oxygen pressures. Their apparatus and procedure were very similar to that used in this study. Iron oxide was melted in a platinum crucible under an atmosphere of CO2:CO, CO2:H2, H2O, CO2, air or O2 depending upon the partial pressure of oxygen desired. After equilibrium was reached, the sample was quenched and analyzed for ferrous and ferric oxide. By appropriate calculations these authors were able to determine the oxygen and iron activities in the various slags, heats of formation of the oxides of iron, and heats of solution of iron and oxygen in the liquid slags. In a subsequent paper' the same authors made a less thorough investigation of the effects of additions of lime and manganese oxide on the composition of iron oxide melts. Only a few experiments were made and those in a narrower range of temperature and oxygen pressure. Darken' has investigated the fusion temperature of iron oxide in contact with silica under various atmospheres. He found that the temperature changes from 1120° to 1447°C as the gas composition changes from CO2/CO equal to 20.8 to pure oxygen. A comprehensive paper by White" predates the work of Darken and Gurry. The decomposition of ferric oxide into oxygen and lower oxides of iron was studied from 1000° to 1650°C and under oxygen pressures from 2 to 76 cm of mercury. The effect of

Jan 1, 1954

By H. R. Stahl

The ore of the Southeast Missouri lead district consists essentially of galena in dolomitic limestone. The galena usually is in a very finely disseminated condition. The experience of recent years in the concentrating plants of the St. Joseph Lead Co. has shown that dry crushing carried to a point where about 90 per cent of the ore passes a 14-mesh screen liberates the larger portion of the galena, and minimizes further necessary reduction in rod or ball mills. Concentration practice has attempted to carry size reduction to a point where economic unlocking of the galena is obtained, without causing undue sliming of the very friable galena. While 60 per cent of the tonnage of the district is treated by the flotation process, only 40 per cent of the total concentrates is produced by that means, as efforts have always been made to keep the grade and tonnage of flotation feed as low as possible. The milling practice of the district for some years has recognized the generally accepted idea of better selective grinding in rod mills as compared with ball mills, with the attendant decrease in production of fines. The function of rod and ball mills in the various concentrating plants is the grinding of table middlings and coarse tailings that carry lead values too high to be discarded. The simplified flowsheet in Fig. I illustrates the place of grinding mills in the circuit. The arrangement of classi- fiers, tables and mills constitutes a closed circuit within somewhat flexible limits. In 1937 experiments were conducted in replacing the ball charge in a 6 by 4-ft. ball mill with rods 2 in. in diameter and 51 in. long. This step was taken with some hesitancy, as it was easy to picture a mass of tangled and crossed rods. However, no difficulties developed, and after a short trial period, six more ball mills were converted to rod mills. These mills are of the spur gear and pinion, belt-driven type, using in most cases a 75-hp. motor and having a 9½-in. open trunnion discharge. As ball mills, they carried a charge of 16,000 to 20,000 lb. of balls, 2 in. in original size. The feed to the mills was dewatered by dewatering wheels and introduced at 70 to 75 per cent solids, with a single scoop feeder. One change in mill design was found advisable when rods were introduced. The existing end liners had an outward flare of 3½ in. in 12 in. These were replaced by linings having vertical interior faces, in order to prevent undue end travel of the rods. This change gave an effective working length of 52¾ in. inside the mill. No alterations were made in the shell liners, which are of the smooth type, made of manganese steel 2 in. in original thickness. The rods at present in use are 51 in. long and 1¾ in. in diameter. The composition has been varied at times; at present they contain 0.70 per cent carbon and 0.70 per cent manganese. Some breakage and etching occurs as the rods become small, but this is considered preferable to using softer rods, which may kink and cause tangling of the charge. The mill charges

Jan 1, 1947

By H. R. Stahl

The ore of the Southeast Missouri lead district consists essentially of galena in dolomitic limestone. The galena usually is in a very finely disseminated condition. The experience of recent years in the concentrating plants of the St. Joseph Lead Co. has shown that dry crushing carried to a point where about 90 per cent of the ore passes a 14-mesh screen liberates the larger portion of the galena, and minimizes further necessary reduction in rod or ball mills. Concentration practice has attempted to carry size reduction to a point where economic unlocking of the galena is obtained, without causing undue sliming of the very friable galena. While 60 per cent of the tonnage of the district is treated by the flotation process, only 40 per cent of the total concentrates is produced by that means, as efforts have always been made to keep the grade and tonnage of flotation feed as low as possible. The milling practice of the district for some years has recognized the generally accepted idea of better selective grinding in rod mills as compared with ball mills, with the attendant decrease in production of fines. The function of rod and ball mills in the various concentrating plants is the grinding of table middlings and coarse tailings that carry lead values too high to be discarded. The simplified flowsheet in Fig. I illustrates the place of grinding mills in the circuit. The arrangement of classi- fiers, tables and mills constitutes a closed circuit within somewhat flexible limits. In 1937 experiments were conducted in replacing the ball charge in a 6 by 4-ft. ball mill with rods 2 in. in diameter and 51 in. long. This step was taken with some hesitancy, as it was easy to picture a mass of tangled and crossed rods. However, no difficulties developed, and after a short trial period, six more ball mills were converted to rod mills. These mills are of the spur gear and pinion, belt-driven type, using in most cases a 75-hp. motor and having a 9½-in. open trunnion discharge. As ball mills, they carried a charge of 16,000 to 20,000 lb. of balls, 2 in. in original size. The feed to the mills was dewatered by dewatering wheels and introduced at 70 to 75 per cent solids, with a single scoop feeder. One change in mill design was found advisable when rods were introduced. The existing end liners had an outward flare of 3½ in. in 12 in. These were replaced by linings having vertical interior faces, in order to prevent undue end travel of the rods. This change gave an effective working length of 52¾ in. inside the mill. No alterations were made in the shell liners, which are of the smooth type, made of manganese steel 2 in. in original thickness. The rods at present in use are 51 in. long and 1¾ in. in diameter. The composition has been varied at times; at present they contain 0.70 per cent carbon and 0.70 per cent manganese. Some breakage and etching occurs as the rods become small, but this is considered preferable to using softer rods, which may kink and cause tangling of the charge. The mill charges

Jan 1, 1947

By Caudle B. H., Cooper H. E. Jr., O. K. Kimbler

The results of studies of areal sweepout behavior in nine-spot injection patterns are presented in this paper. The ratio of the production rates of the two types of producing wells in a nine-spot pattern is considered in its effect on breakthrough. A model study was used to develop a method to predict the production histories of both side and corner wells and to develop the production history of the pattern or the field. INTRODUCTION The importance of areal sweepout behavior in injection operations has been recognized for a number of years. We now know that the fraction of a reservoir which will be reached by an injected fluid is a function of the geometric arrangement of the production and injection wells and of the mobility ratio of the fluids. Of these two, the mobility ratio (which is a measure of the relative ease with which the oil and the injected fluid can move through the reservoir) appears to have the greatest effect on recovery. The effect of mobility ratio on production history has been reported for most of the dispersed injection patterns (i. e., five-spot, staggered and straight-line drives).4-6 ere has been very little published on the nine-spot injection pattern. This may be because the two types of producing wells in the nine-spot pattern can—and sometimes should —be produced at different rates. This adds a second variable (the fist being mobility ratio) to be covered in a study of the nine-spot flooding network. Muskat1 has reported the sweep pattern efficiency at breakthrough for a mobility ratio of one at various ratios of producing rates for the two types of wells. For these conditions he found maximum oil production at breakthrough to occur when the corner well (the producing well farthest from the injection well) is produced 10.7 times as fast as the side well. Other investigatorsa2,3 have studied a few of the many possible operating conditions possible with this injection pattern. This paper presents the results of studies which are strictly applicable to a nine-spot injection pattern surrounded by other nine-spots in a homogeneous reservoir and which has no flowable gas present (no oil bank is formed). Although the full ranges of the variables mentioned above have not been covered, the results reported here should allow reasonable estimates of field operations to be made. EXPERIMENTAL The well spacing geometry of the nine-spot pattern is shown in Fig. 1. Here we see that each injection well is surrounded by eight production wells arranged in a square. Four of these producing wells are located at the corners of the square; the other four are in the midpoints of the four sides. These two types of producing wells are called "comer wells" and "side wells" respectively. It is the ratio of the producing rates of these two types of wells that affects the breakthrough recovery, as calculated by Muskat.' This ratio is defined as the total producing rate of a corner well divided by the total producing rate of a side well. The model used in this study represented one-eighth of a nine-spot pattern, as shown in Fig. 1. It contained the equivalent of one-fourth of a side well, one-eighth of a comer well, and one-eighth of an injection well. Because of these proportions, the actual producing rate ratios in the model were one-half of the ratios of producing rates as

Jan 1, 1965

By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy's law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965