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By Pol Duwez, Paul Pietrokowsky

Titanium and vanadium form a complete series of solid solutions at temperatures above 885°C. Below 885°C, vanadium is slightly soluble in a titanium (about 1.5 pct V at 650°C) and a two-phase a plus ß region extends to 18.5 pct V at 650°C. The alloys up to 15.0 pct V transform into a supersaturated a solid solution upon rapid cooling from the ß phase. Above 15 pct V the ß phase may be retained. The temperature at which the ß to a' martensite-type transformation takes place decreases steadily from 850°C for 0.5 pct V to 325°C for 12.7 pct V. IN the transition series of the periodic table, the six elements that have a body-centered cubic structure at all temperatures, namely chromium, vanadium, molybdenum, columbium, tungsten, and tantalum, fulfill the conditions required for the existence of complete series of solid solutions with the high temperature (ß) form of titanium. Up to the present time, complete solubility at temperatures above the a to ß transformation of titanium has been observed in the systems Ti-MO,1,2 Ti-Cb,2 Ti-W,³ and Ti-Ta.³ The two remaining elements, vanadium and chromium, have atomic diameters which are not as near that of titanium as the atomic diameters of the four other elements. Both are smaller than titanium and the difference, expressed in percentage of the titanium atomic diameter, is 12.3 pct for chromium and 8.2 pct for vanadium. On this basis, the least favorable conditions for solid-solution formation are therefore encountered in the Ti-Cr system. The early work on the Ti-Cr system4 revealed that up to about 1100°C the solubility of chromium in ß titanium is limited, and an intermetallic phase exists near the stoichiometric composition TiCr2. It was found later' that a continuous series of solid solutions extends across the diagram at higher temperatures, and TiCr2 forms by solid state reaction. It became apparent therefore that complete solubility would also be present in the Ti-V system. The present investigation confirms this possibility. The iodide-refined titanium used in this investigation was purchased from the New Jersey Zinc Co., New York. According to the manufacturer, a typical analysis of this product is 0.0065 pct Mn, 0.0022 pct Fe, 0.0015 pct Cu, and 0.0042 pct Pb. The Vickers hardness number (10 kg load) of the crystalline bar varies between 55 and 80. The vanadium metal was purchased from the Westinghouse Electric Corp., Lamp Div., Bloomfield, N. J. The purity of this metal is probably above 99 pct V. The oxygen content must have been quite low, since a bar about 1/4 in. square could be cold rolled into a ribbon 0.020 in. thick. To prepare the various alloys on the titanium-rich side of the diagram, the titanium rod was machined into cups 1 cm in diam and about 1.5 cm high. Pieces of vanadium, of the proper weight, were cut from the square bars and placed within the cups prior to melting. On the vanadium-rich end of the diagram, single pieces of the metals, in the proper weight pro-

Jan 1, 1953

By Raymond D. Sloan

Dropping from third position among the oil-producing states of the nation in 1942, Oklahoma ranked fourth in 1943 with a total output of 121,431,ooo bbl., a decline of 11.9 per cent from the previous year's total of 137,792,000 bbl. Production ranged from a maximum of 346,900 bbl. daily in February to a low of 322,800 bbl. daily in October, and at the close of the year was averaging 330,000 bbl. daily from 52,096 wells, or an average of 6.3 bbl. per well. The state's well, average at the close of 1942 amounted to 6.7 bbl. At the turn of the year, it appeared reasonable to assume that Oklahoma's producing rate would continue its downward trend during 1944 unless reversed by greater than normal discoveries. To Jan. I, 1944, Oklahoma has produced 5,188,466,-ooo bbl. of crude oil. Development and Exploration A total of 1287 wells was drilled in 1943, representing an increase of 77 wells, or 6.4 per cent over the preceding year's total of 1210. Of the wells completed, 587 (45.6 per cent) were oil wells with an average initial production of 319 bbl.; 127 (9.9 per cent) were gas wells with an average initial of 8,639,000 cu. ft.; and 573 (44.5 per cent) were dry. A total of 333 wildcats was drilled (25.9 per cent of all wells), an increase of 13 (4.1 per cent) over the 1942 total of 320. Of the*wildcats drilled, 46 (13.8 per cent) were oil wells with an average initial production of 235 bbl.; 27 (8.1 per cent) were gas wells with an average initial of 8,249,-ooo cu. ft.; and 260 (78.1 per cent) were recorded as failures. Reconditioning of wells throughout the state led to a total recompletion of 230 wells. Of these, 131 were oil wells with a combined initial production of 8360 bbl., 31 were gas wells with a total initial of 211,950,000 cu. ft., and 68 were abandoned. The 46 successful wildcats opened 33 new producing areas, one of which produced from three separate horizons, and led to the development of production in new horizons in 11 old pools. While none of the 1943 discoveries have as yet developed into what might be termed major pools, the West Moore pool, in Cleveland County, and the West Edmond pool, in Oklahoma County, are the two outstanding new areas opened to production. The West Moore pool, sec. 29, 10 N., 3 W., discovered in December 1943, was completed for an initial production of 248 bbl. of oil in 3 hr. through small tubing chokes in the second Wilcox sand from 8787 to 8800 ft. One well was drilling in this area at the close of the year. The West Edmond pool, an April discovery in sec. 32, 14 N 4 W., is producing from the Hunton lime at a depth of approximately 6950 ft., the world's deepest Hunton lime pool. To the end of the year, 15 oil wells had been completed, with no gas wells and no failures. Accumulated production to Jan. I, 1944, amounted to 474,300 bbl. of 41" gravity oil. There were 29 active operations in the field at the end of the year. The West Edmond and West Moore pool discoveries established the first commercial production west of the Granite Ridge,

Jan 1, 1944

By Raymond D. Sloan

Dropping from third position among the oil-producing states of the nation in 1942, Oklahoma ranked fourth in 1943 with a total output of 121,431,ooo bbl., a decline of 11.9 per cent from the previous year's total of 137,792,000 bbl. Production ranged from a maximum of 346,900 bbl. daily in February to a low of 322,800 bbl. daily in October, and at the close of the year was averaging 330,000 bbl. daily from 52,096 wells, or an average of 6.3 bbl. per well. The state's well, average at the close of 1942 amounted to 6.7 bbl. At the turn of the year, it appeared reasonable to assume that Oklahoma's producing rate would continue its downward trend during 1944 unless reversed by greater than normal discoveries. To Jan. I, 1944, Oklahoma has produced 5,188,466,-ooo bbl. of crude oil. Development and Exploration A total of 1287 wells was drilled in 1943, representing an increase of 77 wells, or 6.4 per cent over the preceding year's total of 1210. Of the wells completed, 587 (45.6 per cent) were oil wells with an average initial production of 319 bbl.; 127 (9.9 per cent) were gas wells with an average initial of 8,639,000 cu. ft.; and 573 (44.5 per cent) were dry. A total of 333 wildcats was drilled (25.9 per cent of all wells), an increase of 13 (4.1 per cent) over the 1942 total of 320. Of the*wildcats drilled, 46 (13.8 per cent) were oil wells with an average initial production of 235 bbl.; 27 (8.1 per cent) were gas wells with an average initial of 8,249,-ooo cu. ft.; and 260 (78.1 per cent) were recorded as failures. Reconditioning of wells throughout the state led to a total recompletion of 230 wells. Of these, 131 were oil wells with a combined initial production of 8360 bbl., 31 were gas wells with a total initial of 211,950,000 cu. ft., and 68 were abandoned. The 46 successful wildcats opened 33 new producing areas, one of which produced from three separate horizons, and led to the development of production in new horizons in 11 old pools. While none of the 1943 discoveries have as yet developed into what might be termed major pools, the West Moore pool, in Cleveland County, and the West Edmond pool, in Oklahoma County, are the two outstanding new areas opened to production. The West Moore pool, sec. 29, 10 N., 3 W., discovered in December 1943, was completed for an initial production of 248 bbl. of oil in 3 hr. through small tubing chokes in the second Wilcox sand from 8787 to 8800 ft. One well was drilling in this area at the close of the year. The West Edmond pool, an April discovery in sec. 32, 14 N 4 W., is producing from the Hunton lime at a depth of approximately 6950 ft., the world's deepest Hunton lime pool. To the end of the year, 15 oil wells had been completed, with no gas wells and no failures. Accumulated production to Jan. I, 1944, amounted to 474,300 bbl. of 41" gravity oil. There were 29 active operations in the field at the end of the year. The West Edmond and West Moore pool discoveries established the first commercial production west of the Granite Ridge,

Jan 1, 1944

By D. Turnbull, R. E. Cech

FISHER, Hollomon, and Turnbull have developed a theory for the nucleation of martensite. They first tested the theory on Fe-C alloys and low alloy steels. The major factor influencing nucleation of martensite was considered to be statistical composition fluctuations occurring in small regions at high temperature and frozen-in on quenching. These local regions of varying size and composition serve as nucleation centers. They become supercritical, one by one, as temperature is progressively lowered, resulting in temperature-dependent or athermal transformation. Fisher next applied nucleation theory to substi-tutional solid solution alloys. Detailed predictions were made for Fe-Ni alloys because of the availability of free energy data on this system. It was shown that composition fluctuations that were significant energy-wise did not occur, and nucleation frequencies could be calculated from average properties of the system. Nucleation was predicted to occur as time-dependent and having the functional relationship to give a C curve of nucleation frequency vs temperature. The analysis further predicted that the nucleation frequency was extremely sensitive to composition. Experimentally, it would be found that the transformation in some compositions is so slow that measurable amounts will not form in a reasonable length of time. With other compositions, only slightly different, the nucleation frequency becomes so great that the material becomes transformed while still distant in temperature from the maximum nucleation frequency. On quenching an alloy of such composition, the observed transformation kinetics would be similar to those found in Fe-C alloys. Cech and Hollomon repeated experiments of Kurdjumov n which the kinetics of transformation were similar to those predicted by Fisher for Fe-Ni alloys. The alloy studied in this investigation contained 73.3 pct Fe, 23.0 pct Ni, and 3.7 pct Mn. Fisher,' using an idealized model for the extent of transformation as a function of the number of martensite crystals per grain of parent phase, derived nucleation frequencies from the transformation curves of Cech and Hollomon. Complicating influences such as coupling effects between grains in the polycrystalline specimens were neglected. Nevertheless, excellent agreement was found between the theoretically and experimentally derived nucleation frequencies. These experiments, however, could not provide a critical test of the theory. Experimental nucleation frequencies could vary widely from those calculated, depending upon the extent of deviation from ideal partitioning and the extent of coupling effects. Further, since the compositions of material theoretically analyzed and experimentally determined were different, the free energy changes involved in the experimental work could only be estimated. Also, the effect of heterogeneities on the transformation kinetics was not considered. For these reasons, it was decided that experiments designed to test the validity of the Fisher analysis must be conducted on binary Fe-Ni alloys, which were the ones considered theoretically by Fisher. The martensite transformation in Fe-Ni alloys has been the subject of considerable study. Machlin and Cohen have shown that transformation proceeds in a manner quite unlike that in any other ferrous alloy system. They found that single crystals would transform to a large extent in a single burst. In large grain polycrystalline specimens, frequently more than one grain and sometimes the whole specimen would transform at the same instant in this manner. Results on filings indicated that different particles would undergo the burst transformation at widely different temperatures. These results support the conclusion that the transformation behavior could not be described by a single nucleation frequency as would be the case if the nucleation were homogeneous. It appeared that further work was necessary to define the factors responsible for burst-type transformation, so that the conditions could be altered to favor homogeneous nucleation of martensite if such could be accomplished. This report summarizes the results of some experiments conducted with powdered Fe-Ni alloys for this purpose and the re-

Jan 1, 1957

By K. C. Hong, R. B. Jensen

The problem of determining the optimum set of steam volumes and cycle lengths for a single well undergoing multicycle steam stimulation in order to maximize the cumulative discounted net income has been formulated mathematically and programmed for a digital computer. The mathematical fonnulation of the problem and the method for its solution are discussed in this paper. The oil production performance during each stimulation cycle was simulated by either a constant percentage or a harmonic decline. Using simple analytical expressions for production performance, the cumulative discounted net income and cumulative time of operation were related to the pertinent process and cost parameters and two principal process control variables (cycle length and steam injection volume). The discrete maximum principles was used to transform the equations for cumulative time of operation and cumulative discounted net income into a set of simultaneous equations. The simultaneous equations then were solved by trial and error on a digital computer to determine the set of cycle lengths and stem injection volumes that gives maximum cumulative discounted net income over the project life. INTRODUCTION Steam stimulation is a process for improving the oil recovery rate from wells producing high-viscosity crudes. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three phases: steam injection, soaking (steam condensation), and production. Significant increases in production rate following the stimulation operation result from heating the reservoir around the wellbore. As heat is removed with produced fluids and dissipated into nonproductive formations, the production rate declines, usually to near the prestimulation value. Typical production responses are given in case histories reported by Owens and Suter,l and are depicted in Fig. 1. Duration of the production phase is equal to the time for the oil production rate to decline to some specified value and is called the cycle length. (Cycle length is defined as the producing portion of the cycle and does not include the downtime required for steam injection and soaking operations.) Termination of the production phase coincides with the start of steaming for the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable. Models 2-4 have been developed to simulate behavior of a single well during one cycle of steam stimulation and have been used to investigate the effects of system and operating conditions on the production responses. However, these investigations have not shown how the models can be used to determine a most profitable set of operating conditions for a multicycle stimulation project. Perhaps these models are too complicated mathematically to be adapted readily to an optimization study. This paper presents a method for optimizing a multicycle steam stimulation project based on simple production performance models. First, the performance of a steam-stimulated well during each cycle was simulated by either a constant percentage or a harmonic decline model. Using these simple analytical expressions for production performance, the cumulative discounted net income (before tax) and cumulative time of operation for each cycle were related to the pertinent process and cost parameters and two process control variables—the cycle length and the steam injection volume. Finally, the profit function to be maximized was formed. The analogy between the above problem and problems of optimizing multistage decision processes that have been reported extensively in the chemical engineering literatures5-10 in recent years has led this investigation to the use of the discrete maximum principle.5-7 This principle was used to transform the equations for cumulative discounted net income and cumulative time of operation into a set of simultaneous equations characterizing the optimum operating conditions in terms of the two control variables. These equations

Jan 1, 1970

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

By W. N. Poundstone, G. R. Spindler

A comprehensive report on extensive experimentation in degasification of the Pittsburgh Coal seam is presented. Detailed accounts of the procedures and results are given for permeability tests, vertical bore hole tests, measurement of gas flow from sealed drainage areas, horizontal rib hole tests, and water infusion tests. The removal of methane gas from coal seams in advance of mining is not a new idea with mining men—much attention has been given to the possibility for many years. In other parts of the world, a principal concern has been in the recovery and utilization of the gas and a number of successful projects have been developed in Europe and elsewhere. In this country, the principal motivation has been related to the safety aspect with some possible side benefits concerning costs and efficiency in mining as secondary objectives. To date, experimental work in this country has been largely or entirely exploratory to determine bed characteristics with respect to the liberation of combustible gases to investigate or establish the possibility of degasification in advance of mining and as an aid in projecting mine ventilation systems to provide for safe, effective and economical handling of combustible gases liberated during mining. With these objectives in mind, the School of Mines and Engineering Experiment Station at West Virginia University, in cooperation with the Christopher Coal Co. of Osage, W. Va., initiated some experimental work in May 1952 and the project has been more or less continuous since that time. The work has been centered entirely in mines of the cooperating company in Monongalia County, W. Va., and Greene County, Pa. LOCATION AND GENERAL CONDITIONS OF THE AREA The principal mining in the area involved is in the Pittsburgh coal seam which lies at the bottom of the Monongahela series of the Pennsylvanian. The Pittsburgh coal in the area is generally uniform in its structure and physical characteristics. The bed thickness averages about 7 to 8 ft and the coal has a characteristic blocky structure as the result of pronounced face cleats and definite, but somewhat less pronounced, butt cleavage. It is a medium volatile coal, averaging about 37 pct, and is marketed principally as a steam fuel and for metallurgical purposes. The Pittsburgh coal outcrops along the Monongahela River and dips gradually, but not uniformly, slightly north of west (about N75°W). The westward extensions of the bed, from the areas contiguous to the Monongahela River which have been heavily mined, constitute the principal reserves and are all well below drainage with the depth of cover increasing with the distance from the river. In general, with deeper cover, it may be expected that methane liberation will be more of a problem in future mining as compared to areas mined previously; therein lies the interest in possible de-gasification in advance of mining. Fig. 1 shows the Pittsburgh coal area in the vicinity of Morgantown in Monongalia County, W. Va., and Greene County, Pa., in which the experimental work discussed is located. Fig. 2 shows the contours on the Pittsburgh coal in the test area. It will be noted that the first two bore holes for the experiments were at the edge of a bench or terrace with considerable change in the gradient in the immediate vicinity of the test holes and that the same general condition applies to later test areas. Mining is intensively mechanized in the area and in the mines involved in the experimental work with corresponding rapid advance of working faces a typical characteristic. In the areas now mined the total methane liberation ranges from moderate to relatively heavy, but the actual face liberation is extremely variable and may range from practically

Jan 1, 1961

By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By E. L. Claridge, K. S. Lee

Areal sweep efficiency of oil displacement by enhanced-viscosity water exhibiting pseudoplastic behavior was measured in a Hele-Shaw model representing one-quarter of a five-spot pattern. The pseudoplasticity of polymer solutions and the velocity distribution in the five-spot pattern produced a condition under which the mobility ratio between the displacing and the displaced fluid could not be assigned a single value. Instead, the movement of the displacement front is governed by local mobility ratios which are also time dependent. The areal sweep at breakthrough with polymer solutions was poorer than the sweep obtained with Newtonian fluids of comparable viscosity. However, the areal sweep at 1 PV throughput was greatly improved as compared to flood water without polymer. It was also demonstrated that, even after the oil-cut had declined to a low value during a regular waterflood, switching to polymer flood efficiently swept out the oil remaining in the model. INTRODUCTION The behavior of fluid displacements in isotropic porous media for various patterns of injection and production wells has been extensively investigated.1-7 These investigations all concerned Newtonian fluids, i.e., the viscosity of each fluid was constant regardless of flow rate. The generally unfavorable influence on areal sweep efficiency of higher mobility of the displacing fluid as compared to the mobility of the displaced fluid has been established for both miscible and immiscible fluids. The principle was also established that a close correspondence exists between miscible and immiscible flood front behavior,2, 3 although oil recovery in a waterflood at unfavorable mobility ratio may be less than that observed in a miscible displacement at the same mobility ratio. This is true even when oil recovery is expressed on the basis of movable oil. The reason is that oil saturation only slowly achieves its final value behind the water-flood front in accordance with the Buckley-Leverett8 simultaneous flow relations. It is convenient to use miscible displacements for laboratory simulation of waterflood frontal advance since the interfacial tension forces which are negligible in proportion to viscous forces on a reservoir scale9 are thus made nonoperative in the laboratory model. For miscible displacements, the Hele-Shaw type of model adequately represents a porous medium so long as the appropriate scaling rules5-10 are observed in its design and operation. During simulation of waterflood front behavior in the laboratory by using miscible displacements, the behavior of connate water may ordinarily be disregarded since it is usually indistinguishable from flood water in this process. However, when the flood water is deliberately thickened to improve the mobility ratio between water and oil. the effect on the sweep efficiency due to generation of a connate water bank during the process must be considered. In a uniform porous medium, such a bank is generated11 and efficiently displaced by injection of thickened water.l2 The oil originally in-place at the start of the waterflood is then displaced by connate water followed by thickened water. If the flood water must be thickened to obtain a favorable mobility ratio, the mobility of the oil phase is appreciably less than that of the connate water. Hence, the oil phase is inefficiently displaced by the connate water bank, and a considerable proportion of the oil comes in contact with and is displaced by the thickened waterflood front' A recent study 12 of five-spot displacements using miscible Newtonian fluids in which connate water banks of various sizes were simulated shows that, for connate water banks as large as 40 percent of 1 PV, major improvements in sweep efficiency resulted from use of a thickened

Jan 1, 1969

By O. K. Miniato, L. Massé, K. Nobe, J. S. Aronofsky, W. F. 213-000-000-016 Seyer

MUCH work has been done dealing with the effect of mechanical stress on electrode potential in an electrochemical system. The contradictory nature of the experimental results indicates the complexity of the problem although thermodynamic considerations show that a simple relationshir, should exist. In those systems where a gas was the electromotive active substance satisfactory agreement between theory and practice has been found. Des Coudres' found this to be so even when the active substance of the electrode, in this case mercury, was in the liquid state. In contrast, attempts to correlate theory and experiment for the solid state have met with a very limited success. The early workers in this field, Andrews,2 Walker and Dill3 used iron, certainly one of the most reactive of metals. Others have made use of less active metals such as copper and nickel. Recently Fryxell and Nachtrieb4 investigated the electrochemical behavior of gold and silver under both tensile and compressive stresses and concluded that it was doubtful whether true stress potentials could ever be measured. Much of the lack of success to measure the thermodynamic stress potential can be ascribed to the presence or formation of a complex film on the metal surface in contact with the electrolyte. Further, the theoretical stress potential is very small and therefore difficult to measure directly. Thus the calculated emf between a 24 B & S gage cold-drawn copper wire stressed with a weight of 1 kg and an unstressed portion of the same wire is only 2.60 X 10"7 volts. This is very small compared to that which can be produced by chemical reactions at the metal electrolyte interface which in turn can be so large as to mask completely the stress potential. Hence in this type of measurement all chemical side effects must be eliminated or reduced as much as possible. It was for this reason that the system copper-sodium chloride solution was selected for study. INSTRUMENTATION In the many preliminary experiments conducted, two major difficulties were encountered. The first was to measure the small electro-potentials to be expected and the second to obtain a suitable electrode surface. The conventional potentiometric method was found to be unsatisfactory for measuring the small emf expected. However, by using an L & N No. 2290 galvanometer having a resistance of 915 ohms consistent measurements were possible. The reference electrode was always the unstressed one made from the same sample of wire. The steady current flow was approximately 10-8 amp. Lewis and Randell5 have stated that for currents of the order of 10-8, if there is no sensible polarization, the measured emf may be taken as a reversible one. To check the galvanomenter readings an alternative method was devised to measure the potential difference between the wires. This involved a Liston-Falb d-c breaker amplifier model 10, an L & N k-2 potentiometer and a moving-coil galvanometer having a sensitivity greater than 0.1 µv (microvolt) per mm. To increase further the output voltage of the amplifier a d-c amplifier, model B. L.-932 was introduced into the circuit. This amplifier was in turn connected to a Brush recorder which had been calibrated previously by the test signals from the Liston-Falb instrument. These test voltages employed took into account the impedance of the input current. Unfortunately, this method had too low a sensitivity for measurement below 10 µv. Above this value the voltage agreed reasonably well with those obtained directly by the simple galvanometer method. The main advantage of the amplifier setup was that one did not have to wait until no deflection occurred on the galvanometer in the circuit when first exposing the wires to the solu-

Jan 1, 1959

By R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR's are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By Ralph W. M. Lai, D. W. Fuerstenau

This paper presents the results of a study of the principles which control the distribution of ultrafine particles between an oil phase and an aqueous phase. Alkyl sulfonates were used to control the wettability of fine alumina particles and to stabilize the water-isooctane emulsion system in the extraction process. The effects of sulfonate chain length, sulfonate adsorption, pH, and oil-water ratio on the recovery of solids in the oil phase were investigated. Higher extraction was found under conditions which yield higher hydrophobicity and large interfacial area of the oil-water emulsion. Today there is considerable interest in developing methods for the recovery of fine particles from disseminated ores. One such method might be the extraction of fine particulate solids from aqueous suspensions into an oil phase, and one example of a successful industrial process based on oil-water distribution phenomena is the emulsion flotation process used in concentrating manganese ore.' The oil agglomeration process of Farnand, Smith, and Puddington has been suggested for concentrating tin ore. Patents 3-4 for oil flotation processes extend back to that of William Haynes in 1860. The basis of all these processes is directly related to the stabilization of emulsions with solid particles. The first extensive study of oil-water emulsions stabilized by finely divided solids was made by Pickering. Later, Briggs,6 weston, 7 Chessman and King,8 and Leja and Schulman9 experimentally demonstrated how solid particles control water-oil and oil-water systems. Hildebrand10 suggested that fine particles can stabilize an emulsion because the fine particles are partially wettable by both oil and water, that is, that the contact angle must be finite. Takakuwa and Takamori 11 recently applied emulsion inversion to the study of collector adsorption in flotation systems. At the Royal School of Mines, Shergold and Mellgren12 are currently carrying out a comprehensive study of the extraction of fine particles into an organic liquid phase. In the present study of the liquid extraction or oil flotation of ultrafine particles, the recovery of hydro-philic alumina particles of 0.1-µ average diameter was determined after separating an isooctane-water mixture (emulsion) into its two phases. Alkyl sulfonates of different chain lengths were used to change the wettability of the alumina and to effect emulsifi-cation of the oil-water mixture. The effects of the oil-water volume ratio, sulfonate adsorption, and pH on the recovery of the fine particles were investigated. Since the surface charge on an oxide such as alumina is determined by the adsorption or interaction of H+ and OH- with the surface, pH control is extremely important. Furthermore, since the zero point of charge (zpc) of alumina13-14 occurs at pH 9 to 9.4, major adsorption effects with anionic collectors in these systems will occur below pH 9. The results of the foregoing investigation are discussed in terms of the recovery of the fine particles, the oil-water ratio, contact angles, surface tension, the adsorption of sulfonate onto the solid surface, and the emulsifica-tion of oil. MATERIALS AND EXPERIMENTAL METHODS Materials: The particulate solid used in all the experiments was Linde "A" alumina, a high-purity, readily available form of a-alumina. The surface area of the alumina, as evaluated from measurements of stearic acid adsorption from benzene, was 14.5 sq m per gm, based on a value of 20.5 sq Å for the cross-sectional area of stearic acid.13 All aqueous solutions were prepared from triply distilled conductivity water. Other materials included high-purity crystals of sodium alkyl sulfonates, isooctane, and, for pH adjustments, reagent grade hydrochloric acid and sodium hydroxide-Because sulfonic acids are strong acids, they are

Jan 1, 1969

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By Franklin J. Hill, Theodore D. Tiemann

Sized fractions of Wisconsin Gogebic taconite were reduced with hydrogen over the temperature range from 600° to 1000°C. In general, the degree and rate of reduction increase with temperature. Particle size has no observable effect except in the smaller fractions at 900°C and above, where reduction is impeded, possibly due to the siliceous nature of the ore. Gaseous diffusion appears to be significant as a rate controlling factor at certain stages. THE depletion of high grade iron ore reserves in the United States has established the need to utilize all available iron ore deposits, both in long range planning and from the viewpoint of national emergency. This has led to extensive research and development in this field. The beneficiation of Wisconsin Gogebic taconite ore has been previously studied by investigators at the University of Wiscconsin, 1 the United States Bureau of Mines,, Battelle Memorial Institute, 3 and others. Methods investigated have included concentration by flotation processes, magnetic and gravity separation, magnetic roasting and various combinations of them. The foregoing studies have been concerned with the production of an enriched ore suitable for blast furnace use. If the ore could first be reduced to metallic iron and then beneficiated, the product could be used directly in the open hearth or electric steel-making furnace. The by-passing of the blast furnace should enhance the economic feasibility of the beneficiating process. The work reported here,4 was undertaken to establish data on the hydrogen reduction of Wisconsin taconite that would eventually lead to the development of an economic direct reduction process for this and perhaps other low grade siliceous ores. The volume of work on direct reduction can be judged by the fact that 240 direct reduction processes were patented in the United States alone up to 1951, 5 and numerous additional processes have since been developed. Some of the factors contributing to direct reduction development are: 1) The increasing capital cost of the blast furnace and its accessory equipment. 2) The decreasing availability of high grade domestic ore. 3) The high cost of steel scrap for use in the open hearth and electric furnaces. In general, direct reduction processes can be divided into two types; those using a solid reductant (coal, peat, lignite) usually carried out in a kiln, and those using a gaseous reductant (H2, CO) in a shaft furnace or a fluidized bed retort. As there is no low cost coal readily available in northern Wisconsin but natural gas could be quite easily obtained, it is believed a gaseous reductant process would offer the greater feasibility for use on Wisconsin taconite. It is hoped that this preliminary work will beof interest to other investigators in this increasingly important field. TACONITE ORE The ore used in the investigation was obtained originally from the U. S. Bureau of Mines, and consisted of a representative composite made up from trench samples of the Norrie, Pabst, Plymouth, Pence, and Yale members of the Wisconsin Gogebic range iron formation. Chemically, the ore contains approximately 52 pct SiO, and 30 pct Fe. X-ray diffraction and other studies indicate the principal minerals to be quartz (SiO2), hematite (Fe2O3), and goethite (Fe2O3. H2O). Minor amounts of iron containing silicates, siderite (FecO3), and magnetite (FeO-Fe2O3) are present. The iron minerals and quartz are so finely disseminated that the ore requires grinding to less than 200 mesh (74 µ) for essential liberation.l,2 The iron content of each of the several size fractions studied is shown in Table I. EXPERIMENTAL METHOD The method used throughout the investigation was based on that developed by the U. S. Bureau of Mines in Minneaopolis6,7 in which the course of reduction is followed by the loss in weight of the ore sample. More specifically, a 100-g sample of the size frac-

Jan 1, 1962

By Paul A. Farrar, Harold Margolin

The Ti-Al-V system has been delineated from 50 to 100 wt pct Ti and front 600 to 1400°C by X-ray and ntetallographic techniques. Isothermal sections were delineated at 600, 700, 800, 900, 1000, 1100, 1200, 1300, and 1400°C. X-ray and metallographic evidence indicated the presence of two phases and in addition to those reported by previous investigators of the ternary system'-3. T HE titanium-rich region of the Ti-Al-V system as originally proposed by Rausch et UZ, and Jordan and Duwez3 was based on the binary Ti-Al diagram as proposed by Bumps et uZ. As additional phases have been shown to exist5-' in the region previously thought to be all a, the titanium-rich region of the Ti-Al-V system is open to serious question. Therefore, in order to determine the effect of the indicated changes in the Binary Ti-Al system on the ternary Ti-Al-V system the present investigation was initiated. EXPERIMENTAL PROCEDURE The experimental procedures in this investigation are the standard techniques used in the study of titanium-alloy systems which have been described in detail previously.1° Consequently, only details pertinent to the present work are discussed. The alloys employed for the delineation of this system were prepared from titanium obtained from the Bureau of Mines (73 BHN) 99.99 pct Al and 99.7 pct V, by the consumable arc-melting technique. The titanium was premelted into buttons of 25 g because spattering during the first melt caused uncontrollable loss of alloying constituents. Typical analyses of the material used have been reported elsewhere Attempts to hot roll the alloys prior to heat treatment were made on the first series of alloys prepared, but as the area of extensive hot workability was fairly restricted, see Table I, this practice was discontinued. The times of isothermal annealing are given in Table 11. A preliminary heat treatment of 96 hr at 1000°C was used prior to heat treatment at lower temperatures. The standard techniques used for polishing specimens involved belt-grinding, grinding on emery paper, polishing electrolytically, and etching with Remington "A" etch. In the low-alloy region it was found that the oRo etch, developed by Ence and Margolin,o gave better contrast between phases. Where this procedure did not differentiate between phases clearly, the method of stain etching developed by Ence and was used. It has been previously reported15 that filing of titanium alloys is not desirable for producing X-ray powders, since the powder becomes contaminated by the file material. Therefore, for those samples not brittle enough to Crush, the procedure described below was used. The specimen was wrapped in molybdenum sheet and placed in a vacuum system and evacuated to 0.03 p. Palladium-pur if ied hydrogen was then admitted to the system until a partial pressure of 5o Cm of H was reached. The specimen was heated in the system to the temperature of original heat treatment and was slowly cooled over a period of 3 hr to 400°C while the partial pressure of hydrogen was maintained. The sample was removed from the system after it had completely cooled and was crushed to a powder of 230 to 270 mesh. The powder, wrapped in molybdenum sheet, was dehydrogenated at the temperature of original heat treatment until a partial pressure of 0.03 p was maintained in the system for at least 1/2 hr. The tube containing the powders was quenched in iced brine while still connected to the vacuum system. After dehydrogenation, the powder, except for the

Jan 1, 1962

By L. V. Pirela, S. M. Farouq Ali

Some interest has been expressed recently in the application of solvents in conjunction with a thermal drive, such as a steamflood. At least one field project of this type has been reported. This paper makes the first attempt to provide some of the basic information necessary for choosing a solvent for such an application. Results of displacements conducted at elevated temperatures are also discussed. This paper shows that, in the case of alcohol-hydrocarbon-water or brine ternary systems, the system miscibility may increase, decrease, or both increase and decrease within the same system when the temperature increases. The distribution coefficient was consistently found to increase in favor of the oleic phase with an increase in temperature, which is advantageous from the standpoint of oil recovery. Results of solvent displacements in a sandstone core showed that even a relatively small temperature effect in the favorable direction (increase in miscibility and distribution coefficient) can lead to a 50 percent increase in oil recovery. On the other hand, if the system miscibility decreases with the temperature, even though the distribution coefficient increases, the oil recovery at the higher temperature may not increase. INTRODUCTION Miscible displacement has been the subject of many investigations. Miscible-phase solvent flooding, employing solvents such as alcohols that are miscible with both oil and water, has received considerable attention. Investigations conducted by Gatlin and Slobod,l Taber, Kamath and Reed,2 Holm and Csaszar,3 and Farouq Ali and Stah14 have helped in understanding the mechanism of solvent flooding. While the use of alcohols and similar solvents as oil recovery agents is economically unattractive, these solvents nevertheless provide a means of understanding the mechanistic aspects of important miscible-phase oil recovery processes such as the Maraflood process (discussed by Gogarty5). As shown by Taber et a1.,2 the phase behavior of a solvent-oil-water system is of .utmost importance in determining the efficiency of the oil displacement. This paper makes the first attempt to obtain the ternary phase behavior data for nine alcohol-hydrocarbon-water/brine systems at elevated temperatures. Results of core tests at elevated temperatures are also presented which corroborate the effect of temperature on oil recovery, as judged on the basis of phase-behavior data. The use of solvents at elevated temperatures has been suggested earlier by Farouq Ali.6 At least one field test of this type has been reportedO7 With the widespread use of thermal recovery techniques, it is possible in some situations (especially in steamflooding) that the use of a suitable solvent in conjunction with the heat carrier may be economically feasible. This paper attempts to provide some of the basic information needed for judging such feasibility. LOCATION OF THE PLAIT POINT The phase behavior of a typical ternary system consisting of a solvent, hydrocarbon and brine (or water) can be represented by a triangular diagram such as the one shown in Fig. 1 (for temperature TI). Point Pon the binodal curve represents the plait point, being the limit of tie lines such as Y1 Y2 The compositions of the coexisting oleic and aqueous phases are given by points Y2 and Y1, respectively, for any mixture composition along Y1Y2. The characteristics of ternary diagrams have been discussed by Findlay8 and others. Taber et aL3 have shown that the position of the plait point in a particular ternary system plays the decisive role in determining whether or not theoleic phase would be displaced in a continuous manner during an alcohol displacement. The area above the binodal curve also is important, since it represents

Jan 1, 1969

By R. G. Garlick, H. B. Probst

Tungsten single-crystal specimens of various orientations were deformed in tension at room temperature. Slip traces indicated both (112)(111) and (110) (111) slip; however, about 10 pct plastic dejormation was required bejore these traces could he seen. Resolzled shear-stress considerations indicated that at least some of the particular systems observed were not those on which slip initiated hut were secondary systems. This is highly probable, considering the high plastic strains involved. Analysis of the stress data with respect to possible slip systems indicated that slip must have been initiated at stresses below the proportional-limit stresses measured. ALTHOUGH there is general agreement that slip deformation in fcc and hep metals takes place on the plane of close packing and in the direction of close packing, there is no such agreement for slip in bcc metals. It is generally agreed that the close-packed direction (111) is the slip direction, but investigations have led to conflicting descriptions of the slip plane. As Hoke and Maddin1 point out, there are essentially four points of view. 1) Deformation in bcc metals is composite shear on (112) and (110) planes or on nonparallel (110) planes, and any apparent slip on other planes can be accounted for completely by slip on these planes. Chen and Maddin have reported this to be the possible case for molybdenum." 2) Slip occurs in the (111) direction and is limited to {110), {112), and (123) planes (the three closest packed planes of the lattice). 3) Slip occurs in a (111) direction, but not necessarily on planes of close packing (banal slip). 4) Slip occurs in those directions and on those planes for which ß, the ratio of Burgers vector to interplanar spacing, is a minimum. The slip systems of the bcc metal tungsten have never been fully determined, although several investigators have reported pertinent results.3"7 The present work was initiated to determine the active slip systems in tungsten at room temperature, the critical resolved shear stresses associ- ated with these systems, and the orientation dependency of operative systems. These features of tungsten deformation at room temperature have never been reported in the literature. The authors find this somewhat surprising, particularly in view of the availability of tungsten single crystals since the advent of electron-beam zone-melting techniques and the widespread interest in refractory metals. It would seem apparent that such work has been attempted but the results have not been reported, possibly due to the conflict with deformation theory. The results of the present work conflict with any straightforward description of deformation based on the proposed explanations of slip in bcc metals. Although these conflicts have not been resolved, a presentation of the problem seems in order and should be of value to others working in this field. MATERIALS AND PROCEDURE Single-crystal tungsten rods of 1/8-in. diameter were grown from undoped commercial rod by one-pass electron-beam zone melting in apparatus previously described by witzke.8 Representative analyses of the rod before and after melting are given in Table I. There was no detectable zoning of impurities during melting. Buttonhead tensile specimens, as shown in Fig. 1, were machined from single crystals. Two flats 90 deg apart were ground in the gage length of each specimen. These flat surfaces facilitated the analysis of slip traces. No attempt was made to position these flats with respect to the crystal orientation. The worked surface layer of the machined specimens was removed by electrolytic polishing in a NaOH solution. Tensile-axis orientations were determined by standard Laue back-reflection techniques. The sharpness of the Laue spots indicated that the crystals were free of strain.

Jan 1, 1964

By M. E. Nicholson

The effect of boron on the austenitic transformation rate of iron is smaller than on low carbon steels. The influence of austenitizing temperature on B-Fe is the reverse of its influence on steels. THERE have been many studies made of the influence of boron on the hardenability of steel, but apparently none has been made of its influence on the y-a transformation of pure iron. There are several facts suggesting that boron should have a pronounced effect on the transformation rate of iron. First, Simcoe et a1.l indicated that boron reduces the nucleation rate of ferrite and bainite. Second, they showed, along with others,', " that the lower the carbon content of steel the greater the influence of boron on hardenability. If this trend extends to pure iron, the influence on rate of ferrite formation should be considerably greater for iron than for medium carbon steels. According to Rahrer and Armstrong," the multiplying factor for boron in pure iron should be about 2.40, compared with 1.50 in a 0.35 pet C steel. According to an extrapolation made by Grange and Mitchell,' the effect should be even greater, and the multiplying factor should be about 3.5 in iron. Many investigations of the boron influence'.7, 2, 5 indicated that boron is effective only when in solid solution. On the other hand, Chandler and Bredig" suggested that boron increases hardenability by combining with nitrogen, thereby preventing formation of AlN, which catalyzes the decomposition of austenite. If their hypothesis is valid, boron should have no effect on an alloy free from nitrogen. Digges et al." showed that so far as low nitrogen high purity Fe-C alloys are concerned this is not the case. No experiments, however, have been made on low nitrogen iron. To determine whether or not boron has an effect on low nitrogen iron and, if an effect exists, to determine whether it is as large as predicted from the investigations of boron treated steels, the following work was performed. Because of the rapidity with which iron transforms from austenite to ferrite at even a moderate degree of supercooling, it was decided to study the influence of boron on the transformation rate of iron by determining the effect of quenching rate on the temperature of the beginning of transformation. The technique, essentially that used by Greninger' and Duwez,H consisted of heating small specimens, 0.1 in. sq and 0.010 in. thick, in an atmosphere of purified helium with a resistance heater coil, and then quenching the sample in a jet of helium gas. At the time the jet was applied, the heating coil was removed from around the sample. The sample was suspended in the furnace on 30 gage chrome1 and alumel wires, one welded to each side of the specimen, which also served as a thermocouple for measuring the specimen temperature. Specimens were prepared from vacuum-melted iron obtained from the National Research Corp. which was rolled to a thickness of 0.060 in. and then decarburized in wet hydrogen for 51/2 hr at 700°C. This treatment also removed any boron present in the iron. The resulting iron contained 0.001 pet C. 0.0002 pet N, and 0.005 pet 0. One half of the piece was then boronized by surrounding it with 325 mesh boron powder and heating it for about 2 hr at 900°C in H,. The boronized iron was then homogenized at 1100°C for 24 hr. The iron boride case formed by boronizing was removed by grinding 0.010 in. from each side of the plate, and the piece was finally rolled to a thickness of 0.010 in. The resulting alloy contained

Jan 1, 1957

By G. C. Bernard, L. W. Bernard, L. W. Holm, W. L. Jacobs

The effect of loam on the permeability of porous media to water was studied as a {unction of foaming agent concentration, specific permeability, pressure gradient, length of a porous medium and its oil saturation. At a given fluid saturation in a porous medium, the permeability to water was found to be the same whether loam was present or not. Foam decreases the permeability to water by developing a higher trapped gas saturation than that obtained by water flooding without loam present, increasing the concentration of foaming agent increased the trapped gas saturation and thereby decreased the permeability to water. The presence of oil reduced the capability of most foaming agents to decrease the permeability of a porous medium to water. A few surfactants were found to be effective loaming agents even in the presence of oil. These results are similar to those reported in a previous paper on the effect of loam on the permeability of porous media to gas. The effect of loam was found to persist in long porous media at moderately high reservoir temperatures and during the passage of many pore volumes of surfactant-free water. INTRODUCTION This paper describes part of a study on a novel approach in the use of surfactants for oil recovery; the use of foam rather than water to displace oil. Previously it was found that foam can displace oil which normally is not displaced by water.4 The foam is formed by successively injecting a suitable surfactant solution and gas into a porous medium. Foam appears to have at least two uses in the field: (1) it shows promise as a superior oil recovery agent, and (2) it shows promise as a selective permeability reducing agent. Foam may be very useful in water floods, or in other oil recovery processes, where highly permeable streaks or unfavorable mobility ratios are a problem. A previous paper reported the effect of foam on the permeability of porous media to gas.1 In the present study the effect of foam on the permeability of porous media to water is reported. The specific objectives of the study were to determine: (1) the effect of foam on the permeability to water in porous media of various specific permeabilities, (2) the effect of foam on the permeability to water in the presence of oil, (3) the effect of foam and crude oil on the trapped gas saturation, (4) the effect of foam on permeability to water at trapped gas saturation, (5) the effect of pressure gradient on the permeability to water under foaming conditions, (6) the persistence of foam during the passage of surfactant-free water through the porous medium, and (7) the effect of various foaming agents, length of the porous medium and temperature on the permeability reduction caused by foam. EXPERIMENTAL PROCEDURES EQUIPMENT AND MATERIALS The experimental apparatus consisted of consolidated and unco n soli dated porous media, wet test meters and constant delivery pumps. The porous media consisted of consolidated sandstone cores (6 to 36 in. long), and unconsolidated sand packs (3 to 30 ft long). The consolidated cores had permeabilities of 32 and 1,000 md and porosities of about 20 per cent. The sand packs had permeabilities of 3,500 to 211,000 md and porosities of about 40 per cent. (Throughout this report a term such as 100 md sand" is used. This term means that the porous medium had a dry, nitrogen permeability of 100 md.) Fluids used in the experiments were distilled water, 1 per cent NaCl solution, aqueous solutions of foaming agents, nitrogen gas, air and crude oil.

Jan 1, 1966