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By E. P. Whittemore

Experience with the ASC multipoint gas lift system was obtained in Colonia zone of the West Montalvo field near Oxnard, Calif. The wells in this pool produce from depths varying from 10,500 to 12,000 ft. Oil gravity is generally 14 to 15' API with a few extremes of 12 and 20" API. Some salt water is produced which causes some very viscous emulsions. Viscosities at 150F (which is the approximate wellhead temperature) vary from 5,000 to 100,000 SSU. Most of the production is by gas lift, although a few wells are produced by rod and hydraulic pump. About half of the gas-lift wells are on continuous flow and the remainder are on intermittent lift using large, ported, pilot-operated valves for single-point transfer of gas from casing to tubing. Gas-liquid ratios vary from about 6 to 10 Mcf/bbl of gross fluid lifted. Wells are produced to a 450-psi trap system. The following remarks will be confined to intermittent lift only, since this is the type of lift which has been achieved with the ASC valve system. The maximum gross fluid which has been produced by single-point intermittent lift is about 350 B/D in 3-in. tubing and 200 B/D in 21/2-in. tubing with gas-liquid ratios of approximately 7 to 9 Mcf/bbl. Some design changes could reduce this ratio. The ASC multipoint system has provided production as high as 480 BOPD in 21/2-in. tubing with gas-liquid ratios just under 4 Mcf/bbl. To be able to apply the multipoint system, it is recommended that a detailed explanation be obtained concerning transition-point pressure and stabilizer setting—what its significance is to the string design, how it may work for or against the operation of the well, how it is related to tubing sensitivity and how it affects the unloading operation. The unloading operation may only be of academic interest in a technical paper, but to the production foreman, unloading and setting the valves in operation is a very real problem and should be understood in detail. One item touched lightly in the paper was the unloading valve. This valve controls the maximum pressure at which the well can be operated. When lifting heavy viscous fluids, it is most important to set this valve for the maximum possible realistic operating pressure at the surface. If the well lifts easily, it is simple to set the ASC valves at a lower operating pressure and the unloading valve will remain closed; but if the well happens to be heavier to lift than anticipated, it may be desirable to operate on the unloading valve itself and use all the energy obtainable at the bottom of the hole. In the Colonia pool very heavy wet-gas gradients are experienced due to the viscosity of the liquid and the dense mist which is left behind a slug of fluid. There are many combination strings of 3- and 21/2-in. tubing. This aggravates the wet-gas gradient problem and provides wet-gas gradients of about 50 to 70 psi/1,000. An advantage which multipoint lift has provided is increased slug efficiency through better maintenance of pressure under the slug and decreased fall back as the slug passes up the tubing. By using multipoint injection, wet-gas gradients have been reduced to about 30 psi/1,000. This has reduced bottom-hole operating pressure and given a production increase. The ASC valve is not a simple device. It's operation is difficult to understand, and it must be understood to be used efficiently in gas-lift design. Operating problems are difficult to diagnose—whether they be caused by the fluid lifted, valve malfunction, lift gas rate, or operating pressure. Calculations and reasoning are required to find out what is causing the problem. Inherent in the ASC valve is the inability to create large pressure differentials across a slug. Large differentials may be required to overcome the inertia of very viscous fluid as it is being accelerated in the bottom of the hole. This is tied back to the design of the unloading valve and is one reason for the importance of setting the unloading valve for the highest possible operating pressure. ~u; to the narrow spread the ASC valves provide, it is impossible to cycle slower than about 24 cycles/day on choke control. If small production of 150 BOPD and less is expected, a surface time-cycle controller will be required if the most economical operation is to be achieved. To achieve a satisfactory operation, the operator must keep a record of any changes made in the operating pressure of the ASC valves. Anything which may cause changes in casing pressure in excess of the stabilizer setting will change the valve operating pressure, and if this is not noted from daily inspection of the well casing-tubing pressure recorder charts, the operator will lose control of the well. Significant results can be achieved using ASC valves; however, considerable knowledge is required to design with them, and attention to detail is required for satisfactory field operation.

Jan 1, 1965

By P. W. Bakarian, John C. McDonald

Three magnesium alloys were processed in various ways to exhibit a wide variation in the ratios of yield strength and tensile strength in the rolling direction compared to the cross-rolling direction. Basal-plane pole figures were prepared from several specimens. A fair correlation was observed between the property ratios and the ratio of percent of poles oriented in the cross-direction quadrants compared to the percent oriented in the rolling-direction quadrants of the pole figures. THE modes by which magnesium crystals deform are such as to lead to marked preferred orientations in all forms of wrought products. The effect of the active modes at room temperature, coupled with these orientations, is often to produce a lower compressive yield stress compared to the tensile yield stress. The phenomenon is due to easy twinning in compression, and has been well-related to the preferred orientations as described by basal-plane pole figures of the hcp magnesium single crystal. The literature contains some information on the variation with test direction of the tensile properties of sheet, but no quantitative relationship to the observed pole figures has been established. These effects have been reviewed in the few com- prehensive treatises in English which have been written on magnesium technology and metallurgy.1°3 Roberts presents several pole figures, but no tensile-property data in the plane of the sheet. Raynor has no pole figures, but quotes Frommer's4 results. The information in Beck's compendium more or less parallels the results of Jones and powell.5 In both a Mg + 1.5 Mn alloy and a Mg + 4.6 A1 alloy, cold rolling was found not to change the general situation of higher properties in the cross-rolling direction,* than in the rolling direction. Thomas'6 X-ray studies of Jones and Powell's specimens did not permit correlation of properties and preferred orientation. Ansel and Betterton7 report tensile and compressive properties on three other alloys as a function of degree of cold rolling, plus a recrystallizing anneal. As rolled, there was a change in anisotropy with degree of reduction, but all alloys were reasonably isotropic in tension when annealed. X-ray diffraction photograms illustrated the kinds of orientations present, but were not correlated with the properties. Bakarian8 has described a method of determining quantitatively a preferred orientation, and illustrated the method by applying it to pure magnesium and two of its alloys. This method was used in the present work as a basis for correlating the strength properties with the texture.

Jan 1, 1965

By R. G. Grieves, G. Thodos

A method is presented for the accurate calculation of the cricondentherm and cricondenbar pressures of multicomponent hydrocarbon mixtures of known composition. The mixtures may contain six and quite possibly any number of components including paraffins, isoparaffins, olefins, acetylenes, naphthenes and aromatics. The approach is similur to that used for calculating critical pressures and cricondentherm and cricondenbar temperatures. The critical pressure, the normal boiling point and the approximate vapor pressure behavior of each component are all that art required. A stepwise culculation procedure is necessary for mixtures containing more than two components. From an analysis of 22 binary systems and 118 mixtures, the average deviation of calculated cricondentherm pressures from reported values is 2.4 per cent. For nine multicomponent mixtures the average deviation is 1 per cent. Considering 19 binary systems and 108 mixtures, the average deviation of calculated cricondenbar pressures from reported values is 1.7 per cent. For 15 multi-component mixtures, the average deviation is 2.2 per cent. INTRODUCTION A knowledge of the phase behavior in the critical region of multicomponent hydrocarbon mixtures is of value both in industrial processing operations and for the optimum operation of gas condensate reservoirs. Accurate methods of calculating the critical temperatures and critical pressures4,6,7,8,9,23 and cricondentherm and cricondenbar temperatures6p10 of multicomponent hydrocarbon mixtures are available in the literature. If the cricondentherm and cricondenbar pressures could be calculated with equal accuracy, the entire phase diagram of a multicomponent hydrocarbon mixture could be well approximated. The work of Etter and Kay6 is limited to systems containing the normal paraffins and has not been tested on systems containing a heavier component than heptane. In addition, the development of their multicomponent equations is based upon a limited number of mixtures containing from three to six components. Silverman and Thodos have considered systems containing both paraffinic and non-paraffinic hydrocarbons, but their correlation is limited to binary systems and is highly inaccurate for methane systems. Eilerts has done extensive work on the cricondenbar pressure; he has produced an excellent correlation for binary systems. However, his procedure for multicomponent mixtures is chiefly useful for highly complex mixtures requiring a knowledge of the vapor-liquid equilibrium behavior of the mixtures; he has not considered the cricondentherm pressure. The objective of this study was the development of an accurate and rapid method for the calculation of the cricondentherm and cricondenbar pressures of multicomponent mixtures containing all types of hydrocarbons and having a wide volatility range. The approach that was adopted is similar to that used by Grieves and Thodos for cricondentherm and cricondenbar temperaturesl0 and for critical pressures.9 However, methane systems had to be considered separately and a modified stepwise calculation procedure was utilized for the cricondertherm pressure. The correlations were developed in a manner similar to those for critical pressures and cricondentherm and cricondenbar temperatures. Based upon binary data reported in the literature it was observed that the ratios of cricondentherm and cricondenbar pressure to the pseudocritical pressure (molar average), pt/ppc and pp/ppc, respectively, in two-component systems depended upon the mole fraction of the low-boiling component and upon the diversity in properties of the two components. A dimensionless boiling-point parameter Tb,/Tb was chosen to represent the diversity in properties of the components. For a binary system, Ti,'is the molar average of the normal boiling points of the two components involved. For a multicomponent system it is either the molar average of the normal boiling points of all of the components involved or the molar average of the normal boiling point of the pure low-boiling component and of the atmospheric boiling point of the low-boiling-free mixture of

Jan 1, 1965

By George C. Price

The Bureau of Mines conducted this study in the Roslyn No.5 coalbed in the State of Washington to determine the feasibility of mining hydraulically the portion of the coalbed that was steeply pitching. All of the experimental mining was done while advancing raises and rooms. A Bureau-developed hydraulic mining machine was used successfully in the pitching coalbed. It consisted of a remotely controlled monitor mounted on a self-advancing roof support unit of the type commonly used for roof support in longwall mining systems. The coal cutting rates averaged 0.73 and 0.54 ton per minute in raise and room mining, respectively, while using water volumes up to 230 gpm at a pressure of 4,000 psig. Productivity averaged 4.7 and 5.2 tons per man-shift for raise and room mining, respectively, compared with 7.5 and 8.5 tons per man-shift, respectively, by conventional hand mining methods.

Jan 1, 1965

By Charles E. Whieldon

Data on the oilfields in Mahoning, Columbiana, Carroll, Jefferson, and Harrison Counties, Ohio, were collected from scattered sources and compiled to make the information readily available to operators who may be interested in conducting secondary-recovery operations in the area. General geology, oil production, oil-productive acreage, core data, reservoir calculations by townships, and miscellaneous data and reference material are presented.

Jan 1, 1965

By R. A. Pasternak, B. Evans

In an ultrahigh-vacuum study of the sorption of nitrogen by niobium* resistivity data for this metal have been obtained as function of temperature and of low nitrogen concentrations. The ultrahigh-vacuum system in which base pressures of about 5 x l0-10

Jan 1, 1965

By J. D. Grozier, W. W. Mullins, H. W. Paxton

The morphology of the nucleation and growth of austenite into high-purity iron in NH3-H2, gas mixtzires has been studied. The growth rate of an austenitic rim (planar interface) from scratched surfaces of- polycrystalline iron specimens was determined as a function of temperature and percent NH3 and found to he in reasonahle agreement with growth-rate calculations based on a model which assumes the diffusion of nitrogen to he the rate-controlling step. Under certain conditions, austenite pew as platelets; growth rates of these along the surface of single crystals were found to he dependent on surface preparation, orientation, THE development of microstructures can conveniently be thought of in terms of nucleation and growth. The complex topic of nucleation in solid-solid transformations will not be discussed at length, although a few qualitative experiments were performed. Growth is determined by the mobility of the various possible interfaces under the available driving forces in a particular situation. In homophase transformations, it has been clearly demonstrated that the mobility is very sensitive to small amounts of impurities, to the kind of impurity, and to the orientation relations across the boundary.' A degree of quantitative knowledge has temperature and percent NH3. On electropolished surfaces with a (110) pole, the maximum growth rate of platelets was determined and found to be in agreement within a factor of 2 to 3 with theoretical calculations of the edgewise growth rate of a platelet. The calculations are based on a model which assumes that the diffusion of nitrogen in the ferrite in front of the moving curved attstenitic interface at the tip of the platelet is the rate-controlling step. The growth direction on the surface of the single crystal and resztlting habit plane of the platelets were determined and found not to he unique but to vary systematically with the pole of the surface. been obtained. In the case of heterophase transformations, which are significantly more complicated to treat, a comparison of theoretical and experimental studies often shows rather poor agreement.'-' The main purpose of the experiments discussed below was to obtain additional quantitative data on crystallographic effects on boundary mobility in a system which was otherwise as simple as possible, viz. the growth of iron-nitrogen austenite into fer-rite. In the course of the experiments, it became necessary to re-examine the theory for the growth of Widmanstatten plates, especially the influence of anisotropic interfacial free energy. Some other minor experiments in the Fe-N system were performed, and are described briefly. EXPERIMENTAL METHODS A) Material Preparation. The floating zone purified iron used for this investigation was supplied by Battelle Memorial Institute. The nominal composi-

Jan 1, 1965

By W. I. Duvall, L. D. Sadwin

Three explosives with different detonation characteristics were tested by studying their cratering ability in a granite-gneiss. The strain wave generating characteristics of these explosives were also studied in the same rock medium. Correlations between the relative performance of three explosives as evaluated by crater studies and other methods of evaluation are indicated. Numerous test methods have been employed to evaluate the output performance of explosives; for example, the underwater explosion method, the airblast method and the ballistic pendulum method.'*' For blasting applications, the study of explosion produced craters and explosion generated strain waves are the most meaningful. This laboratory has employed these techniques extensively for many years and has shown that the detonation properties of explosives and their ability to generate strain waves in rock are related and that the amplitude and shape of the strain wave is related to some of the crater parameters such as slab thickness and fly rock velocity.3'11 However, a good comparison between the relative performance of explosives as determined by the crater and strain wave methods had not been made. The purpose of this investigation was to determine if the relative performance of three explosives as determined by the crater method shows a correlation with the relative performance as determined by the strain wave method. If a good correlation exists between these two sets of relative performance, it should then be possible to relate the detonation properties of an explosive to its ability to break rock in a crater test. In most commercial blasting operations, the diameter of the blast hole remains constant even though the type of explosive may change. In general, it is the explosive volume rather than the weight which remains constant when two or more explosives of different density are compared. Therefore all tests in this investigation were conducted on a constant volume basis rather than on a constant weight basis. TEST SITE AND ROCK PROPERTIES The tests described in this paper were conducted at a granite quarry owned and operated by the Consolidated Quarries Div. of the Georgia Marble Co. at Lithonia, Ga. The tests were performed in an area where the exposed rock surface was nearly horizontal and where the general rock mass had few joints or faults. The rock has an apparent sp gr of 2.6 and a longitudinal propagation velocity of 18,000 fps. The characteristic impedance of Lithonia granite gneiss is 53(lb - sec/in3). EXPERIMENTAL PROCEDURE There are many parameters which must be considered in the study of explosion-produced craters. The role played by each variable in the explosive-rock-crater system can be determined by experimental techniques in which one parameter is varied while others are maintained constant. In this investigation, the crater geometry was studied as the depth was varied for each of three explosives. The explosive volume and rock-type were held constant for all crater tests. The experimental arrangement used in performing the crater tests is illustrated schematically in Fig. 1.

Jan 1, 1965

By E. T. Stephenson

Wert and Marx1 pointed out that a straight-line relationship exists between the activation energy of a relaxation process and the temperature at which the maximum relaxation occurs. The data available at the time indicated that this relationship held for a number of Snoek peaks, several grain boundary peaks, and pair relaxation in a brass. Theoretical justification for the observed relationship was found in the following equation, which Wert and Marx derived from the theory of interstitial atomic diffusion coefficients:' where AH is activation energy, R is the gas constant, T is the internal friction peak temperature, v is the interstitial atomic frequency, f is the frequency of the applied stress, S is entropy of activation. More accurate internal-friction data on interstitial diffusion in bcc metals have become available since Wert and Marx's paper. Table I gives activation energies calculated by several authors from a combination of elastic aftereffect data and the peak temperatures at several frequencies of measurement. (In the case of Fe-C and Fe-N, the referenced authors5'7'8'10 also used high-temperature diffusion data.) However, diffusion experiments at 150°C and above1'-13—rather than anelastic techniques—were used to determine the activation energy of hydrogen diffusion in Fe-H. In order to plot this recent data as a AH vs T graph we calculated the peak temperatures of the systems listed in Table I (with the exception of Fe-C, Fe-N, and Fe-H) by using published values3'' of AH and Do. These calculated peak temperatures varied by only a few degrees from experimentally determined peak temperatures. The calculated values were felt to represent the better average. A number of investigators have found the peak temperatures in Fe-C and Fe-N to be 38 to 40°C and 20° to 24°C, respectively. The values of 39" and 22°C (312° and 295°K in Table I) were determined by carefully executed experiments.6'8 The hydrogen peak temperature has been measured at 1 cps,12 20 cps,14 and 35,000 cps.15 All hydrogen peak temperatures were adjusted to 1 cps for Table I using AH = 3000 cal per mole. As Fig. 1 shows, the data of Table I fit a straight line at least as well as the earlier data used by Wert and Marx. Linear-regression analysis was applied to the data in Table I. The Fe-H data was omitted because the activation energy has not been experimentally determined in the temperature range of the peak. The analysis yields the equation: with a standard error of 860 cal per mole. The agreement of the data in Table I with the Wert-Marx equation is excellent. Strict application of Eq. [I] forces the linear regression analysis through the origin. In this case, the analysis gives a slope of 62.1 cal per mole per deg, and a standard error of *890 cal per mole. With this value, it follows from internal-friction theory that Hence, Do varies by only 30 pct among these bcc-interstitial systems. Thus, a concept suggested originally by Wert and Marx1 is confirmed by recently published data. The

Jan 1, 1965

By M. F. Corcoran

Rapid advances have been made in the past few years in the application of automatic controls and instrumentation to iron ore pelletizing plants. Present practice in applying instrumentation and control to the Grate-Kiln system of iron ore pelletizing is described. Major control points and loops are tabulated. Future trends in the application of digital control including computer data logging systems are described.

Jan 1, 1965

By Warren E. Morrison

The expansion of the United States economy in the postwar period has had a tremendous impact on the demand for energy. Not only has total energy consumption increased at an unprecedented rate, but there have been major shifts in the composition or mix of energy resources within the end-use sectors. Because of the numerous interrelationships between substitutable energy resources and their markets, the energy economy can only be analyzed in terms of the trends of its component parts. This problem takes on additional complexity when attempting to chart the nation's future energy requirements. Total energy consumption can be forecast with reasonable accuracy for periods up to 15 years by relating this to projections of economic indicators. However, forecasting the component parts of the energy economy constitutes a dilemma in that the sum of the projected parts frequently exceeds predictions for total energy. Areas of uncertainty in energy forecasting tend to mount rapidly when proceeding from total energy to the consideration of specific energy resources consumed as fuel, power, or raw materials.

Jan 1, 1965

Jan 1, 1965

By H. W. Weart, S. Sarian

The effect of temperature, impurities, and capillarity on the morphology of solid particles in a liquid matrix is investigated. For the NbC-liquid iron system, at least, it is found that those particles which are dissolving will assume a spherical shape; all others will take the equilibrium shape. An aniso-tropic-isotropic transition in the interfacial tension is observed at about 1725°C and is believed to be due to cooperative roughening of the interface on an atomic scale. The presence of boron as an impurity lowers the transition temperature. It is the purpose of this paper to present some observations on the shape of particles in a system consisting of solid particles of nonuniform size in a liquid matrix and to propose an explanation for these observations. Although qualitative only, these observations, which were made largely in the course of a study of particle-growth kinetics,' are presented separately to draw attention to them. They reveal the effect of particle size, temperature, and surface-active impurities on particle shape in the solid NbC-liquid iron system, and are unique in demonstrating for the first time the reversible effect of temperature and impurity concentration on the anisotropy of the energy of the solid-liquid interfaces involved. Some of the changes are readily demonstrated with the few particles whose shapes can be clearly shown in a single photomicrograph, but others are more subtle, and their recognition depends upon some experience and the study of a much larger sample. For this reason, a certain amount of judgment must be acknowledged to underlie their detection, but every effort was made to maintain proper scientific objectivity in evaluating the observations. The observations will be presented first, and then an explanation rationalizing them will be offered. Brief reminders of the relevant theories will be inserted into the discussion at the appropriate points. EXPERIMENTAL The observations were made of the shape of NbC particles dispersed in liquid iron. All specimens were prepared by pressing NbC powder and car- bony1 iron powder treated according to standard powder-metallurgical procedures. Except as noted, all specimens were heated to 1900°C for 1/2 hr. In investigating the effect of temperature, specimens were quenched from 1900°C to various lower temperatures, and held long enough (48 hr) to allow shape changes to be completed. Boron, in the form of amorphous powder, and oxygen, in the form of niobium oxide powder, were added as impurities to some specimens. Nitrogen was introduced into some specimens as an impurity by heat treating the samples under a partial pressure of nitrogen gas. Effect of Temperature. It was first observed that increasing temperature had a marked effect in rounding the corners and edges of the particles. At 1900°C the particles are all very nearly spherical and remain so even when the holding time is extended to 48 hr. As can be seen from Fig. 1, there is virtually no evidence of the presence of low-index planes. At 1300°C, however, most of the particles are prismatic with very slightly rounded edges and corners, Fig. 2. (In making these shape comparisons, attention should be focused on the larger particles, even though the smaller ones would be expected to be the first to change shape, owing to the shorter diffusion distances involved. The cause of the mixed particle shape will be explored later.) It was established that these structures are re-

Jan 1, 1965

By G. W. Toop

Jan 1, 1965

By T. Yoshioka, Paul A. Beck

SILICON, germanium, and tin occur with both the white tine-type structure and the diamond cubic structure. In the latter form these elements are semiconductors; in the former they are metallic. The metallic form of germanium and silicon is obtained only under high pressure.' For all three elements the transition from the semiconductor to the metallic state is accompanied by a decrease in the atomic volume of somewhat more than 20 pctily2 Table I. At such a large compression the widening of the s and p bands is sufficient to make the energy gap of 1.1 ev, or less, of the semiconductor disappear, giving rise to the metallic state.*

Jan 1, 1965

By J. L. Eakin

A method was developed by the Bureau of Mines in the laboratory and in the field to relieve capillary waterblocks in gas wells. Impaired gas permeability was improved by this inexpensive chemical treatment which lowers the surface tension of the water held in the capillaries of the formation. Effectiveness of the alcohol-surfactant treatment was tested with a variety of chemicals and with sandstone cores cut from rocks having relatively low permeability. Field tests on 20 gas-producing and storage wells demonstrated the effectiveness and limitations of the method. The productive capacity of some wells was doubled by the treatment. The final test was evaluated by the neutron logging technique for measuring changes in apparent liquid saturation. Maximum apparent liquid saturation was reduced by 52 percent; gas production rate increased from 2.3 to 3.5 MMcfd (million cubic feet per day).

Jan 1, 1965

By R. M. Hudson

Equilibrium constants have been determined for the jeaction C (in steel) + H2O = CO + H2 as a function of carbon content (0.013 to 0.74 ujt pct) and temperature (1200° to 1800°F) by using a flow system in which the water-vapor content of various gas mixtures containing hydrogen, carbon monoxide, and nitrogen was systematically controlled. The equilibrium partial-pressure ratio K1 = PcoPH2/PH2O was obtained for two low-carbon steels and four Fe-C binaries from a series of runs made at each temperature. By comparison of Ki with the analogous ratio for the reaction C (graphite) + H2O = CO + H2, the activity of carbon in steel (ac) was comDuted for each temperature and carbon content studied. From these data values of the equilibrium constants for two other carburization-decarburiza-tion reactions of importance were estimated. The chemical compositions of the two steels and four Fe-C binaries used are given in Table I. Specimens of Steel E were cut from a 0.035-in.-thick commercially box-annealed and temper-rolled lot of a low-carbon low-metalloid steel. Steel F was a commercially hot-rolled rimmed steel that was cold-reduced at the Laboratory to a 0.059-in. thickness. Fe-C binaries A, B, C, and D were vacuum-melted and poured, hot-rolled, pickled, and cold-reduced at the Laboratory to furnish specimens 0.035 in. thick. Sheet specimens were cut from all lots to approximately 3/4 by 3 in. by gage and were vapor-degreased with trichlo-roethylene and weighed before heat treatment. Heat treatments were carried out in a hinged-top Hevi-Duty electric furnace with a Vycor-glass tube. When the furnace was at the desired

Jan 1, 1965

By Thomas C. Wilder

Jan 1, 1965

By B. H. Caudle, R. E. Watson, I. H. Silberberg

The production history of an inverted nine-spot injection pattern was studied with a porous plate model similar to Habermann's. Colored fluids were used so the boundary movements could be photographed. By varying the production rates of the side and corner producing wells, the optimum pattern sweep efficiency can be obtained. Results of the laboratory tests indicate that interpolation of the pattern sweep and conductivity ratio data will permit application of the data to predicting fluid injection operations with mobility ratios between 0.1 and 10 and production rate ratios between I and the optimum values. INTRODUCTION The inverted nine-spot injection pattern in Fig. 1 has some unique advantages over other regular injection patterns (five spot, line drive, etc.) used in secondary recovery operations. It has three producing wells for each injection well, while the five-spot and line-drive patterns require an equal number of injectors and producers. Futher-more, of the eight producing wells surrounding each injection well, four are of the "side well" type which lie nearer the injection well than the remaining four "corner wells". This allows the production rates of these two types of wells to be adjusted independently of each other to obtain better pattern sweep efficiency. This latter advantage may well be the reason why the nine-spot patterns have not been studied as extensively as the patterns containing only one type of injection or producing well. The pattern sweep efficiency of the inverted nine spot is affected almost as much by operating with different producing rates of the comer and side wells as by differing mobility ratios. Possibly because of this added operating parameter, published studies of nine-spot systems have been limited in their coverage of the pertinent variables.'-' The model studies reported here covered the mobility-ratio range normally found in waterflood operations, as well as the variation in well production rates necessary to achieve optimum pattern sweep efficiency. Conductivity ratios — a measure of the change in total flow at constant pressure difference — were obtained during each model run. A porous-plate model with miscible fluids representing the in-place and injected fluids was used in this study. This model technique is the same as that used in both X-ray shadowgraph" and visual techniques4 described in the literature. Using miscible fluids eliminates residual oil in the model, and the permeability to the injected fluid is the same as to the in-place fluid. Thus the mobility ratio in the model is given by the ratio of the viscosity of the displaced fluid to the viscosity of the injected fluid. Because of the non-linear nature of the viscosity vs composition curve for two miscible liquids, the mobility change across the boundary between the two fluids is reasonably sharp. This technique thus represents the displacement of a region of one fluid mobility by a region of possibly different mobility in an isotropic system under steady-state flow conditions. Table 1 shows the dimensionless similarity groups used to scale the model conditions and results to

Jan 1, 1965

By R. M. Asimow

The magnetization curves for specimezs containing superparmagnetic particles are considered. It is shown that the curves may differ from a Langezlin function because of particle anisotropy, particle interactions , and the presence of a size distribution of particles. The various causes of particle anisotropy are considered, and magnetization curves for specimens with cubic and uniaxial anisotropy are presented. The magnetization curves depend on the In the particle-size below 100A it is quite difficult to obtain quantitative size and shape information on precipitate particles. All of the available techniques have their limitations; however, quantitative applications of superparmagnetism have not been developed as fully as possible due to a lack of analysis of the complete magnetization curve. With such an analysis it appears possible to obtain from a single magnetization curve of a specimen containing randomly oriented SPM (superparamagnetic) particles a quantitative volume distribution and a description of the particle shape.* sign of the anisotropy energy and in the case of a negative uniaxial anisotropy (prolate spheroids) the resulting curves may differ very considerbly from a Langevin function. A graphical technique is developed whereby it is possible to separate out the effects of the size distribution, the particle interaction, and the particle anisotropy. Thus it is possible to obtain quantitative values for both the particle shape and the size distribution. Langevin function2 I/Is = ctnh(HVIs/k T)-k T/HVIS [ 1 ] where I, is the saturation magnetization, V the particle volume, H the applied field, T the particle temperature, k the Boltzmann constant, and I the magnetization in the direction of the applied field. Such behavior is rarely if ever observed in actual systems. One explanation for this is that the SPM particles do possess a significant anisotropy and thus the magnetic energy associated with the particle depends on the direction of magnetization in a more complicated way than for the isotropic particle of Eq. [I]. In general the magnetic energy E of an isolated SPM particle embedded in a nonmagnetic matrix can be expressed as a sum of several contributions: E = Eh + Ed+Es+Ec [2] where Eh is the external field energy, Ed the energy resulting from the particle demagnetizing factor, E, the magnetostriction energy, and E, the crystalline anisotropy energy. In each term we consider only the part dependent on the orientation of the magnetization vector and the particle axes as the shape of the magnetization curve will be determined by these contributions. Following the same procedure used in deriving the Langevin function,

Jan 1, 1965