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By Earl S. Greiner, Eric R. Jette

The constitution of the iron-rich iron-nickel-silicon alloys at 600ºC. has been determined by X-ray crystal structure methods. If the results are represented isothermally by a conventional equilateral triangular plot, the single-phase solid solution (body-centered cubic structure) of the iron-rich alloys at 600°C. is bounded by four two-phase areas. Three three-phase areas separate the respective two-phase areas. Three of the phases in the polyphase areas have the same structures as the corresponding phases in the binary iron-nickel or iron-silicon alloys. There are two phases, however, that have not been reported previously and whose structures have been tentatively identified in the present investigation. The solid solubility limit of the iron-rich solid solution at 600°C. was determined by comparing the lattice constants of this body-centered cubic phase in the single and polyphase areas. It has been shown that the lattice constants of ternary alloys may be represented by surfaces whose distances above the ternary plot (representing atomic composition) are proportional to the lattice constants of the respective alloys. Then the intersections of the surface for the single-phase alloys with those for the corresponding phase in the polyphase alloys, at the respective temperatures, are the solid solubility limits of the single-phase alloys at these temperatures. The data of the present investigation were evaluated by this method, although by a system of orthographic projection it was possible to represent the three-dimensional model in two-dimensional diagrams. This investigation has shown that the solid solubility of nickel in the body-centered cubic phase of the iron-rich iron-nickel-silicon alloys at 600°C. changes from 3.7 weight per cent (Owen and Sulley) in the binary iron-nickel alloys to 5.0 per cent in the ternary alloys containing 4.8 per cent silicon. Further additions of silicon increase the solid solubility limit of nickel to 16.0 per cent at 12.6 per cent silicon. From this point the limit decreases to 9.5 per cent nickel at 15.5 per cent silicon and is, of course, zero at 15.3 per cent silicon in the binary iron-silicon alloys.

Jan 1, 1943

By D. E. Baldwin

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

Jan 1, 1967

By George W. Sheary

Situated 45 miles west of Philadelphia and 50 miles southwest of Bethlehem Steel Company's Bethlehem plant, the integrated Grace mine facilities produce 4000 tpd of high-quality iron ore pellets. Startup of the Grace mill was in November 1958, and iron concentrates were shipped until March 1960, when the pellet plant went into operation. The underground mine, when fully developed, will hoist about 9000 tpd, including development rock. The crude ore, which has an iron content of approximately 42%, is magnetically cobbed and crushed in closed circuit with 3/4-in. slotted vibrating screens. The ore is washed and screened in the mill and the plus 1/4 in. screen product is again cobbed prior to feeding to the rod mills. Grinding is done in rod mills, and in ball mills that are in closed circuit with 30 in, cyclones, to 1% on 100 mesh and 65% minus 325 mesh. The ground ore is magnetically concentrated by three-drum permanent type finisher magnets to 67% Fe. The magnetite concentrate is pumped from the mill to a 50 ft thickener in the pellet plant. The thickened magnetite concentrate is relayed to the filters through a two-stage pump arrangement. The filter cake is fed by belt from filter concentrate bins to mixer-muller belts where it is intimately mixed with bentonite and a slight amount of water for moisture control. The fluffed concentrate then drops into balling cones. The green pellets from the balling cones are fed in a prescribed feed pattern to shaft furnaces through the use of shuttle car mechanisms. The green pellets are dried, heated to 2500°F and cooled to 1200°F as they descend through the furnace and into pellet coolers where the pellets are further reduced in temperature to 250°F. Heat is recovered in the cooling process through the use of air-to-air heat exchangers. The cooled pellets discharge on a rubber conveyor belt and are transferred to 6000-ton pellet railroad loading bin. The final pellet product consists of 90% plus 1/4 in. material (after tumble testing1) and contains 66% Fe plus 3% silica.

Jan 5, 1962

The information in Tables 1 and 2, on the operations in the Dutch East Indies and North Borneo, has been kindly furnished to the Institute through the courtesy of Mr. J. August Kessler by Mr. B. H. van der Linden. It affords a very good picture of the situation in that region for the year 1933.

Jan 1, 1934

By J. Campbell

Long freezing range casting alloys are particularly susceptible to a type of porosity which is observed to form in layers parallel to the supposed position of the isotherms in the solidifying casting. Under favorable conditions (which appear to be typified by low-temperature gradients in the casting giving rise to a wide and more or less uniform pasty zone, and which arise from several factors, particularly: a) wide freezing range alloy, b) high thermal conductivity of metal, c) low thermal conductivity of mold, and d) high mold temperature3) layer porosity has been observed in many different casting alloys: copper,' aluminum, magnesium,' steels, and high-temperature alloys.3 Baker4,5 and later cibula6 argue that layer porosity occurs because of thermal contraction, in a manner analogous to hot tearing. In outline, the theory consists of the establishment of a coherent dendrite network by the impinging of dendrite tips. Subsequent shrinkage imposes tensile stresses on the network which tears perpendicularly to the stress, i.e., parallel to the isotherms. If these tears are not filled by the inflow of residual liquid then layers of porosity result. Baker7 attempted to test whether the porosity was the result of thermal contraction by casting test pieces in a mold designed to accentuate hot tearing. However, no significant increase in porosity was observed. This negative result of Baker's critical experiment appears to be substantiated by numerous observations, particularly the experiments by Lagowski and Meier8 on Mg-Zn alloys covering the range of zinc contents up to 30 pct Zn. These clearly reveal that the maxima for the incidence of hot tearing and layer porosity are well-separated, occurring at 1 and 6 pct Zn, respectively. Furthermore, the thermal contraction maximum occurred at 1 pct Zn, indicating that hot tearing is associated with contraction in the solid state, and not with porosity. These observations are further substantiated by the elementary consideration that the thermal contraction of the casting is likely to produce (if anything, since the temperature difference across casting of high thermal conductivity, such as aluminum and copper, is likely to be negligible) a compressive stress on the

Jan 1, 1969

By D. F. Gibbons

THIS investigation was undertaken in order to gain further information on the mechanism of plastic deformation of iron at temperatures between room temperature and 77.2°K, and also to contribute to our understanding of the low temperature brittleness phenomenon that occurs in both the tensile and impact tests. It was decided to study as pure an iron as possible and to use the tensile test in order to simplify the problem as much as possible. Two series of iron were used throughout the investigation: iron A, obtained from the National Research Corp. and supplied as gas-free, high purity iron; and iron B, obtained from Fast' and produced by melting iron under purified hydrogen. Typical analyses of samples of both irons, after fabrication, are given in Table I. The main difference in composition of these irons is in their nickel and oxygen contents. Nickel has a very large solid solubility in iron. However, oxygen has an extremely small solid solubility. An attempt was made to reduce the oxygen content still further by remelting under purified hydrogen. This was successful in reducing the oxygen content to -0.0006 pct. However, no results on tests of this iron are included, since difficulty was encountered in fabricating the ingot. Wire specimens 1 mm in diameter were used for the investigation. The wires were produced from the ingots, as supplied, by cold rolling and swaging, with intermediate vacuum anneals at 700°C. Care was taken to reduce preferred orientation in the wires to a minimum by keeping the percentage of reduction in area between anneals of 30 to 40 pct. X-ray transmission photographs showed no indication of preferred orientation. The final grain size of iron A was 20 to 24 grains per linear mm and of iron B, 16 to 18 grains per linear mm. All specimens were tested in the decarburized and denitrided condition unless otherwise stated. The procedure was to pass hydrogen, saturated with water vapor at 26oC, over the specimens at 730°C for 2 hr. The specimens were quenched in iced water and then annealed in a vacuum of - 5x10-6 mm Hg for one day at 560°C to remove hydrogen. Higher temperatures were used for the vacuum anneal but this temperature was found to be quite satisfactory in removing hydrogen. The specimens were slow-cooled after the vacuum anneal. Where it is stated that the specimens were carburized, the specimens were given an identical decarburizing treatment and then carburized by passing hydrogen, saturated with pure n-heptane vapor at 0°C, over the specimens at 730°C. The specimens were then homogenized at 730°C for 2 hr in dry hydrogen. After the carburizing treatment the specimens were given the same vacuum anneal as for the decarburized specimens. The carbon content was determined from the maximum value of the internal friction carbon peak.2 Apparatus Fig. 1 shows a diagram of the tensile apparatus, with half the cooling coil removed. The cooling coil enabled temperatures from 200" to 77.2oK to be obtained. The apparatus was designed to fit a standard Tinius Olsen Universal tensile machine. The apparatus consisted of the rigid plate A which carried two carefully machined hooks H. These hooks attached the plate firmly to the moving crosshead of the tensile machine. The lower grip B was rigidly suspended from the plate A by three stainless steel rods. The upper grip C was joined to the upper grip of the tensile machine by the stainless steel rod E. The lower part of the apparatus was surrounded by a Dewar vessel, which was made a sliding fit inside the brass collar D. The specimen was held in a clamp which fitted into the grip, forming a ball and socket joint (see inset a). This was to attain as nearly pure

Jan 1, 1954

By R. Ehrlich, F. E. Crane

A consolidated porous medium is mathematically modeled by networks of irregularly shaped, interconnected pore channels. Mechanisms are described that form residual saturations during immiscible displacement both by entire pore channels being bypassed and by fluids being isolated by the movement of an interface within individual pore channels. This latter mechanism is shown to depend strongly on pore channel irregularity. Together, these mechanisms provide an explanation for the drainage-imbibition-hysteresis effect. The calculation of steady-state relative permeabilities, based on a pore-size distribution obtained from a Berea sandstone, is described. These relative permeability curves agree qualitatively with curves that are generally accepted to be typical for highly consolidated materials. In situations where interfacial effects predominate over viscous and gravitational effects, the following conclusions are reached. 1. Relative permeability at a given saturation is everywhere independent of flow rate. 2. Relative permeability is independent of viscosity ratio everywhere except at very low values of wetting-phase relative permeability. 3. Irreducible wetting-phase saturation following steady-state drainage decreases with increasing ratio of nonwetting- to wetting-phase viscosity. 4. lrreducible wetting-phase saturation following unsteady-state drainage is lower than fir steady-state drainage. 5. Irreducible nonwetting-phase saturation 101lowing imbibition is independent of viscosity ratio, whether or not the imbibition is carried out under steady- or unsteady-state conditions. Experiments qualithtiveIy verify the conclusions regarding unsteady-state residual wetting-phase saturation. Implications of these conclusions are discussed. INTRODUCTION Natural and artificial porous materials are generally composed of matrix substance brought together in a more or less random manner. This leads to the creation of a network of interconnected pore spaces of highly irregular shape. Since the geometry of such a network is impossible to describe, we can never obtain a complete description of its flow behavior. We can, however, abstract those properties of the porous medium pertinent to the type of flow under consideration, and thus obtain an adequate description of that flow. Thus, the Kozeny-Carmen equation, by considering a porous medium as a bundle of noninterconnecting capillary tubes, provides an adequate description of single-phase flow. With the addition of a saturation-dependent tortuosity parameter in two-phase flow to account for flow path elongation, the Kozeny-Carmen equation has been used to predict relative permeabilities for the displacement of a wetting liquid by a gas. 1-5 It has long been recognized that relative permeability depends not only on saturation but also on saturation history as we11.6,7 Naar and Henderson8 described a mathematical model in which differences between drainage and imbibition behavior are explained in terms of a bypassing mechanism by which oil is trapped during imbibition. Fatt9 proposed a model for a porous medium that consisted of regular networks of cylindrical tubes of randomly distributed radii. From this he calculated the drainage relative permeability curves. Moore and slobod,10 Rose and Witherspoon,11 and Rose and Cleary12 each considered flow in a pore doublet (a parallel arrangement of a small and large diameter cylindrical capillary tube). They concluded that, because of the different rates of flow in each tube, trapping would occur in one of the tubes; the extent of which would depend upon viscosity ratio and capillary pressure. They limited

Jan 1, 1970

By J. F. Breedis

The morphology and crystallography of marten -site formed during quenclzing were examined by transmission electron microscopy in alloys whose compositions lie between Fe-19 wt pct Cr-11 wt pet Ni and Fe-33 wt pet Ni. Depending upon composition, four types of transformation products were observed in this portion of the Fe-Cr-Ni system. Three of these products are denoted as lath, plate, and surface martensite. The hcp structure found in association with martensite it? certain higlz-clzromium stairzless steels does not influence the transformation crystallogyaphy and cannot he Considered to act as a transitional structure in the transformation from austenite to martensite. DISTINCT changes in the characteristics of mar-tensitic transformations are produced by the partial replacement of nickel by chromium in austenitic iron alloys. Large, discrete martensite plates form in Fe-30 pct Ni, while aggregates of small crystals form in sheets parallel with (111)A austenite planes in stainless steels containing in the vicinity of 18 pct Cr and 8 pct Ni. These transformation structures are termed plate and lath martensite, respectively. In addition, an hcp structure (E) has been observed in certain high-chromium stainless steels in association with martensite. It has been suggested that the E structure acts as an intermediate step in the nucleation of martensitel-' and influences the morphology and crystallography of the final transformation product. However, this structure may be the consequence of the deformation of austenite arising from the shape distortion accompanying the transformation to bcc martensite.' An hcp stacking of atoms is produced in an fcc lattice by the introduction of an intrinsic stacking fault on alternate (111)A planes. At present, the arguments behind each explanation for the E structure are based on circumstantial evidence. This investigation seeks to determine the importance of the hcp structure to the martensitic transformation, and to examine the crystallography and morphology of the structures produced in bulk samples by quenching in alloys whose compositions lie between Fe-19 wt pct Cr-11 wt pct Ni and Fe-33 wt pct Ni. These aspects of the martensitic transformations occurring in these alloys have been studied by electron metallography and selected-area diffraction of foils examined in transmission in the electron microscope. EXPERIMENTAL METHODS The alloys have been prepared from thoroughly mixed powders of pure iron (99.6+ pct, 0.06 max pct C, 0.15 max pct N), chromium (99.9+ pct), and nickel (99.9+ pct). After sintering in an Ar-H2 atmosphere, the mixtures were melted by induction heating in recrystallized alumina boats under purified argon. The ingots were cold-rolled to 0.4-mm sheets (100 pct reduction in thickness) after the removal of at least 1.5 mm from their surfaces by grinding. Three-millimeter discs were punched from the cold-rolled sheet and annealed at 1150°C for approximately 24 hr in evacuated quartz capsules. The average grain size was 40 µ Thin foils for examination in transmission in the electron microscope were prepared from discs quenched to liquid-nitrogen temperature. A depression was first jet-machined into the center of a disc and a thin area (less than approximately 3000A in thickness) was produced at the base of the depression by electropolishing. Electron-microscope studies utilized the RCA EMU-3 and the Philips EM-100B microscopes operating at 100 kv. X-ray examination of the polycrystalline alloys was performed either in a diffractometer or in a

Jan 1, 1964

By A. T. Chatas

A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as backgmund material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. INTRODUCTION A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs.l The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work.2 PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred, Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundaries of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary.3-5 UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied:

Jan 1, 1967

By M. E. V. Plummer, F. E. Beamish, J. C. Hole, J. M. Kavanagh

Prior researches have shown that the iron-copper-nickel content of platinum concentrates may be reduced by carbon to form a collecting alloy for the platinum metals in a manner exactly analogous to the formation of the lead fire assay button. The nature of the iron-copper-nickel alloys with the platinum metals has been investigated. Palladium and probably some of the other platinum metals form solid solutions with this alloy. ONE of the greatest known reserves of the platinum metals is to be found in the nickel, copper, iron sulphide deposits of Northern Ontario. The very large tonnage of copper-nickel ore processed makes the Sudbury district a significant world source of the platinum metals, the latter being recovered as byproducts in the electrolytic refining process for copper and nickel. Chalcopyrite, pentlandite, and pyrrhotite are carriers of the platinum metals;' these minerals contain from 0.03 to 2.0 ppm of the noble metals. The analysis of the above ores for the platinum metals necessitates an initial concentration of the minute quantities present in the ore. The method usually employed involves the extraction of the noble metals by molten lead with or without small proportions of silver. The lead is then separated from the precious metals by cupellation, a process which involves absorption by the cupel and volatilization of lead oxide, leaving the precious metals collected in a silver bead on the surface of the cupel. The collection by lead is probably achieved by a process of dissolution followed by some degree of segregation in the lead alloy since the cold button is seldom uniform in composition. With silver-lead alloys this process of liquation has been used to re- cover pure lead since, during the cooling period, crystals of pure lead separate and silver becomes concentrated toward the center of the solid.' Platinum and gold liquate in a manner similar to silver which may account for the successful recovery of platinum by fire assay even though it is considered insoluble in a solid lead medium. 3 In the case of iridium the liquation process may be a disadvantage in that the iridium may appear in the outer areas of the button and thus be lost mechanically during the handling processes. In any case the deficient alloying characteristics of lead for the platinum metals encouraged attempts to find an improved collecting alloy, and by analogy with aqueous extractions, preferably one in which solid solutions would be readily formed. Since, beyond a certain minimum solute to solvent ratio, the formation of a solid solution is accompanied by a lattice distortion, one would expect some relationship between the atomic diameters of any two metals and their tendency to form a solid solution. In one survey5 the hypothesis was put forward that when the atomic diameter of the solute differs by more than about 15 pct from the solvent, the "size factor" is unfavorable and the formation of a solid solution is restricted. On the other hand, when the atomic diameters are within this limit the size factor is favorable and solid solutions are readily formed, e.g. the transition metals of Group VIII having similar radii form solid solutions over wide ranges of composition.6 Even with a favorable size factor, elements having different crystal structures cannot form a continuous series of solid solutions. Cell dimensions alter as the concentration of the solute increases, causing a

Jan 1, 1962

By G. V. Jere, V. Krishnan, C. C. Patel

Standard free energy and standard enthalpy changes as a function of temperature have been calculated for the chlorination reactions of different oxides constituting columbite and tantalite. The tallies of standard lee-energy change (F) indicate the possibility of pvefeential chlorination of different oxides but the ease 0.f chlorination of columbium pentoxide at about 250°C and the chlorinating tendency of columbium pentachloride in promoting the chlorination of tantalum and other metal oxides, p7-evetzt the separation of columbiu?n and tantalum from other oxides and pom each othel.. It is likely that low temperatuves of chlorination and continuous 1err2oval of columbium pentachloride from the ..eaction zone may help partial separation of columbium from tantalum as well as from titanium. The standavd enthaply change (AH?) values shotr that 1ou.-temperature chlorination around 300" to 500°C is likely to sustain the chlorination , without external heating. COLUMBIUM (niobium) and tantalum metals, their alloys and interstitial compounds are finding extensive uses in nuclear reactors and high-temperature equipment.la-3 These metals also find uses in chemical process plants, electrical rectifiers and capacitors and as "getters" in electronic tubes.la With the development of Kroll process of reduction of volatilized titanium tetrachloride by magnesium for the production of titanium metal, chlorine metallurgy is receiving greater attention. Chlorine metallurgy has several advantages, the foremost amongst them are: the ease of chloride formation, separation of the different constituents of minerals by selective chlorination, and the reduction of the chlorides in vapor phase to the respective metals. Recently, Si-bert, Kolk, and Steinberg4 have considered a number of methods for the preparation of columbium metal and the most promising is found to be the halide reduction. Since the minerals columbite and tantalite are comparatively abundant in nature, the future of the metallurgical processes depends on the utilization of these minerals for the production of columbium and tantalum chlorides by chlorination. In this paper, an attempt has been made to interpret thermodynamically the chlorination of individual oxides constituting columbite and tantalite, with the help of the recent thermodynamic data.5-8 For this purpose, standard free energy and standard enthalpy changes of the chlorination reactions of the oxides with chlorine, both in absence and presence of carbon as the reductant, have been calculated as a function of temperature and represented graphically. Similar calculations for the reactions employing carbon tetrachloride and carbonyl chloride as chlorinating agents have also been incorporated in this paper. REPORTED WORK ON CHLORINATION Cuvelliezg has patented a process for the separation of columbium and tantalum from their concentrate, wherein 75 pct Cb05 is claimed to be chlorinated at 1050°C in the course of 7 hr using chlorine or chlorine containing nonreducing gases, the products of reaction being CbC1, or CbOC1,. At this temperature, Ta,05 is claimed to remain unaffected. It is further claimed1° that at higher temperatures, the proportion of Ta205 chlorinated increases while that of Cb205 diminishes. During the studies on the action of chlorine on individual metal oxides, Kangro and Jahn" have observed that Ta,05 is not chlorinated even at 1200" in the stream of chlorine, while 75 pct of Cb,05 is converted into CbOC1, around 900 to 1100°C. The chlorination of Cb205 by chlorine in the presence of carbon, investigated by Lind and Ingle,' and

Jan 1, 1962

By S. J. Burns, W. W. Webb

The dislocation arrangements formed during unsteady propagation of cleavage fractures on (010) planes in LiF have been investigated by high-resolution etch-pit techniques and by X-ray diffraction topogvaphy. In impurity-hardened crystals, cracks propagating in any direction on (010) planes at velocities of about 103 cm per sec are usually accompanied by light plastic deformation which is enhanced wherever the crack is allowed to hesitate. Dislocations with [011] type Burger's vectors are often formed looped around the crack tip. They are dragged along with the crack tips leaving edge dislocations lying nearly parallel with the clearage surface about 5µ from it. These dislocations are easily overlooked since they may initially intersect with the cleavage surface infrequently and later may disappear from the crystals due to image forces during aging at room temperature. Although the plastic work associated with these dislocations is only comparable with the reversible (010) surface energy, an instability in crack propagation appears due to a limit of the velocity with which dislocations can be dragged along with the crack. Transition to a fully brittle nonplastic fracture mode occurs when the crack velocity exceeds the velocity with which dislocations can be moved by the stress field of the crack. TRANSITIONS between brittle and ductile modes of fracture appear to be common processes in the behavior of materials in which the flow stress is close to the stress at which brittle cracks can propagate. High-strength engineering alloys fit into this category and the transition from ductile to brittle modes of crack propagation may be associated with catastrophic failures in these important materials. The methods of theoretical mechanics indicate the geometrical conditions in which these processes may occur but the detailed mechanisms controlling the generation of dislocations in the initiation of the plastic mode and the process by which the loss of plasticity occurs on transition to the brittle mode are not yet clear. Since these mechanisms are not amenable to direct observation in engineering alloys we have chosen a semi-ductile alkali halide LiF as a model system in which to observe transition mechanisms between plastic and brittle modes of crack propagation. Cleavage cracks in this system are known to undergo a plastic-elastic transition at velocities between 103 to 104 cm per secl and dislocation configurations in LiF are amenable to study by optical-microscopic observation of dislocation etch pits2 and by X-ray diffraction topography.3 We have been able to identify a dislocation mechanism responsible for the transition from brittle to slightly plastic modes of crack propagation in LiF. A model based on this mechanism permits calculation of the critical crack-propagation velocity for this transition and indicates the importance of the stress dependence of dislocation velocity in determining the critical crack velocity. Of course, this model cannot be carried directly over to more complex materials but it is quite possible that its qualitative features are generally applicable. Dislocations intersecting fresh cleavage surfaces in LiF were reported by Gilman,4 by Forty,5 and by Wash-burn et a1.6 Such dislocations were construed to have been nucleated where the cleavage crack hesitated or stopped, near stress concentrators, such as cleavage steps, on the crystal face. The loci of such dislocations deposited On the cleavage plane in bands were called "stop lines" or "deformation zones". Gilman, Knudsen, and walshl measured the velocity of cleavage cracks in lithium fluoride by evaporating thin resistive strips on the crystal side and recording

Jan 1, 1967

By J. Szekely, V. Stanek

Heat and gas flow interactions in nonisothermal packed beds were examined in the paper. A study was made of the response of the system to a step or pulse change in the inlet gas temperature, with a fixed value of the overall pressure drop across the bed. Under these conditions the heat flow and fluid flow transients are coupled because the convective heat transfer rate is alfected by the mass flow rate of the gas which, in turn, for a fixed pressure drop will depend on the temperature profile in the system. The Problem was stated in terms of differential equations, which were integrated numerically. The parameters used in the computation were so chosen to reflect the operation of the stack region of blast furnaces and sinterbeds. The computed results showed that the pressure drop-flou1 relationships and the rate of progress of the temperature fronts (waves) were strongly interrelated and were also markedly affected by variations in particle size and in void fraction. MANY metallurgical processes involve the contact of solid particles with a gas stream in a packed bed arrangement under nonisothermal conditions. Examples are shaft furnaces, regenerators, pebble heaters, and the sinter process. Although the heat and mass transfer aspects of packed bed processing have been extensively studied, the associated flow phenomena and in particular the effects of nonisothermality on the flow, have received little attention to date. :In fact, most of the previous workers considered the flow rate of the carrier gas time invariant and independent of the heat or mass transfer processSzekely and carr2 have shown that the pressure drop-flow relationships in nonisothermal packed beds may be strongly affected by the temperature profile within the system. These authors have devised a method for relating the pressure drop to flow for a given temperature profile. thus providing an extension of the Ergun equation to steady nonisothermal systems. Finally, in a recent paper willmot3 examined the response of regenerators to externally imposed changes in the gas flow rate. Both these investigations were somewhat specialized since, in general, neither the temperature distribution nor the gas flow rate may be regarded as truly independent variables, thus the heat transfer and the fluid flow problems have to be solved simultaneously. The work reported here is divided into two parts: in Part 1 the general formulation is given and a detailed discussion is presented of fixed bed systems. Part is devoted to systems in which a gas and particulate solids are contacted in a counter flow arrangement. FORMULATION Consider a nonisothermal fixed packed bed, extending from through which a gas is flowing. The problem is to develop a relationship between pressure drop and gas flow (with the gas flow being the dependent variable) and to evaluate the rate at which a change in the gas temperature, imposed at the inlet, travels through the system. Let us consider an infinitesimal section of the bed and establish differential heat, mass, and mechanical energy balances over this region. In addition, relationships are needed describing the temperature dependence of gas density (equation of state) and the temperature dependence of viscosity. These may be written as: where c, and are constants. It is noted that in this formulation we neglected any temperature gradients within the solid particles, thus assuming these to be either sufficiently small or of sufficiently high thermal conductivity to meet this condition. The justification and consequences of this assumption will be mentioned in the discussion.

Jan 1, 1970

By G. W. Binkley, R. E. Collins, G. K. Dumbauld

A mathematical analysis has shown that the primary factors affecting the deposition of cement in unfractured perforations during squeeze-cementing operations are: the properties of the cement slurry, the geometry of the perforations, and the filtration time. The validity of the analysis has been substantiated by laboratory investigations. The information presented in this paper makes possible the prediction of the rate of deposition of cement in and about unfractured perforations under given squeeze-cementing conditions, the proper filtration time to control the amount of deposition to any desired value, and the deposition properties needed in cement slurries to restrict to any desired degree the formation of nodes of cement .Solids inside the casing. INTRODUCTION The deposition of solids against a permeable medium by the process of filtration is an important property of a cement slurry. General recognition of the role of filtration in the use of cement in wells is evident in view of the fact that several patents on low-water-loss cements have been issued during the past few years. In the conventional, high-pressure squeeze-cementing technique, a large volume of cement slurry is usually displaced into the area surrounding the perforated interval after the formation has been fractured hydraulically.&apos; Near the end of the job, the pumping rate is slowed or stopped intermittently in an effort to obtain a high pressure in the wellbore. The way in which a high pressure is obtained is not understood thoroughly. but it is be- lieved to be caused by the deposition of a rigid mass of compacted cement particles either in the fractures of the formations or inside the casing opposite the perforated interval. In a method of squeeze-cementing introduced several years ago, a small amount of cement slurry is squeezed into the perforations at a low pressure to avoid fracturing the formation. The filling of the unfractured perforations with cement particles by the process of filtration is important to the success of this technique. Early in the development of this low-pressure squeeze-cementing technique, laboratory and field-size experiments showed that conventional, neat cement slurries were unsatisfactory if the tubing was extended into or through the perforated section of the casing. The extremely high filtration rate of neat cement slurries caused the deposition of a compacted mass of cement inside the casing and made it impossible to remove excess cement by reverse circulation and difficult to withdraw the tubing. Because the need for cements with a reduced filtration rate was obvioils and urgent, modified cements containing 12 per cent bentonite were used until research was completed on modified cements containing 25 per cent bentonite.< These modified cements were useful in the solution of the immediate problem, but the following questions remained unanswered: (I) what is the optimum filtration rate of cement slurries for this application, (2) how long should the squeeze pressure be applied. and (3) how great are the effects of squeeze pressure and well temperature on the rate of deposition? Furthermore, the relationship of the filtration properties of cement slurries to the dimensions of the perforations and the wellbore was unknown. In order to obtain information relative to these basic considerations, a systematic evaluation of all the factors involved in the deposition of Cement during low-pressure squeeze-cementing operations was initiated. Although the work was directed toward an evaluation of the factors influencing the deposition of Cement in the low-pressure squeeze-

By F. I. Stalkup

Vapor-liquid phase equilibrium experiments have been conducted in a static equilibrium cell on mixtures of a light, 45 API stock- tank gravity reservoir fluid and a rich hydrocarbon gas containing approximately 55 mole per cent of intermediate hydrocarbons. Both apressure-vs-composition study of the gas and a simulated reservoir fluid, and a multiple-batch contact simulation of the condensing-gas-drive oil recovery process were performed. In the latter experiments equilibrium gas and liquid compositions were analyzed. Also, conventional, "condensing-gas-drive", long-tube displacement experiments of the reservoir fluid and gases of various richness were performed. The results of these experiments could not be satisfactorily interpreted by the conventional pseudo-ternary-diagram representation of multicom-ponent phase behavior. The results seem to be explained better by considering a bubble-point surface and a dew - point surface joined in a plait-point locus. Portions of the plait-point locus cannot be "seen" directly by the rich hydrocarbon gas because of curvature of the dew-point surface. In such a system, continuous injection of the rich gas over stationary reservoir fluid might form a zone of contiguously miscible compositions from pure rich gas to pure reservoir fluid by: (1) saturating the reservoir fluid with injected gas to the bubble-point surface; (2) creating by mass transfer with fresh injected gas a path of contiguously miscible compositions along the bubble - point surface to the plait-point locus; and (3) creating by mass transfer with additional injected gas a path of gas compositions along the dew-point surface up to the point where direct miscibility results between dew-point fluid and the injected rich gas. INTRODUCTION The use of the pseudo-ternary-phase diagram to illustrate miscible displacement phase behavior has been discussed by several authors.5,7 Such a representation of phase behavior is not rigorous, but the ternary diagram nevertheless gives a qualitative picture of what actually occurs in a miscible displacement process. Fig. 1 is a typical illustration of miscible displacement phase behavior by a ternary diagram. The multicomponent hydrocarbon system is divided into three pseudo-components: a light fraction containing methane and nitrogen, an intermediate fraction containing ethane through hexanes plus carbon dioxide, and a heavy fraction containing heptane and heavier components. A two-phase region is bounded by a dew-point curve and a bubble-point curve, which are joined at the critical point. The concept deduced from such a representation for miscible displacement by a condensing-gas-drive process is as follows: a rich gas G, which lies to the right of the limiting tie line through the critical point C, is injected into the reservoir and contacts reservoir fluid L, saturating the reservoir fluid to give bubble-point fluid L1 and equilibrium dew-point gas GI. Continued injection of rich gas changes the composition of the saturated liquid L1 through a series of liquid compositions lying along the bubble-point curve, until the critical composition C is reached, at which point direct miscibility with the rich gas is achieved. Some equilibrium gas with compositions lying along the dew-point curve from G1 to C is also formed in this process. Thus, continuous injection of rich gas forms a

Jan 1, 1966

air-lift and equipped with tapered tubing of proper design, we would have a gas input consumption of about 2500 cu. ft. per bbl., which at 3 to 4c. per 1000 cu. ft. would be 7 1/2 to l0c, per bbl., and there would be very infrequent loss of production due to stoppages. It has been demonstrated that with efficient design of air-gas lift, the production of wells can be increased much beyond that obtained with the former type of air-lift employed; also that small wells can be operated by air-lift with tapered tubing at a cost that places this method in competition with beam pumps in many fields. The next step in conservation that the writer expects to have an opportunity to demonstrate is that of restoring the pressure in a pool and producing by air-gas lift all of the oil possible to lift economically. This combined operation is probably the method toward which we shall eventually be working in recovering the maximum quantity of oil from pools where the oil is recovered through bore holes. General Discussion on the Air-gas Lift H. P. Porter, Tulsa, 0kla.—The papers presented at this meeting contain a great amount of valuable information. Wonderful progress has been shown in the development of air and gas-lifts. There has been nearly everything brought out that touches upon the subject. The real point that is lacking is exact knowledge of the velocity with in the flow column which will produce the best effect—that is the thing we must know more about. Velocity in Gas-lift Flow In other lines of industry the matter of velocity of fluids in pipe lines has been well analyzed and there are known laws by which to calculate velocity of flow; for instance, in irrigation work large pumps are designed with intake pipos to employ an intake velocity of 4 ft. per scc. By reduced cross-sect&apos;ion the velocity is increased rapidly as it enters the pump and the discharge rate is at 12 ft. per src., which in turn is reduced in the discharge column to 4 ft. per sec. Crushed coal, grain and granular material is found to be best conveyed by air when a pneumatic conveyor is employed at 100 ft. per sec. As in the design of a pumping plant or a pneumatic conveyor, the velocity at the lower end of the column in the flowing well must be controlled within certain limits for best results. Mr. Griswold, I believe, stated that they had velocity as low as 15 it. per scc. and from that up to 78 ft. per sec. Mr. Pierce and Mr. Lewis showed an ideal flow column showing how the velocity increased as the fluid was carried up the column, hut did not give any figures as to the velocity. It would be well to take that sort of a diagram to establish an ideal velocity at the lower or intake end, and then calculate the velocity from expansion of the gas as it goes up. It may be that the, ideal intake velocity would vary, depending on the depth of the well, the quantity of liquid to be handled or the pressure which it may be desired to hold. The subject is one that might be worth much research.

Jan 1, 1928

By C. K. Eilerts

Finite difference equations were programmed and used to integrate the second-order, second-degree, partial differential equation with variable coefficients that represents the transient linear flow of gas-condensate fluids. Effect was given to the change with pressure of the compressibility factor, the viscosity, and the effective permeability and to change of the absolute permeability with distance. Integrations used as illustrations include recovery of fluid from a reservoir at a constant production rate followed by recovery at a declining rate calculated to maintain a constant pressure at the producing boundary. The time required to attain such a limiting pressure and the fraction of the reserve recovered in that time vary markedly with properties of the fluid represented by the coefficients. Fluid also is returned to the reservoir at a constant rate, until initial formation pressure is attained at the input boundary, and then at a calculated rate that will maintain but not exceed the limiting pressure. The computing programs were used to calculate the results that would be obtained in a series of back-pressure tests made at selected intervals of reservoir depletion. If effect is given to the variations in properties of the fluid that actually occur, then a series of back- pressure curves — one for each stage of reserve depletion — is required to indicate open-flow capacity and related flow characteristics dependably. The isochronal performnce method for determining flow characteristics of a well was simulated by computation. INTRODUCTION The back-pressure test procedurel is based on a derivation of the equation for steady-state radial flow of a gas, the properties of which are of necessity assumed to remain unchanged in applying the test results. The properties of most natural gases being recovered from reservoirs change as the reserve is depleted and pressures decline, and the results of an early back-pressure test may not be dependable for estimating the future delivery capacity of a well. The compressibility factor of a fluid under an initial pressure of 10,000 psia can change 45 per cent and the viscosity can change 70 per cent during the productive life of the reservoir. There are indications that the effective permeability to the flowing fluid can become 50 per cent of the original absolute permeability before enough liquid collects in the structure about a well as pressure declines to permit flow of liquid into the well. The advent of programmed electronic computing made practicable the integration of nonlinear, second-order, partial differentia1 equations2.3 pertaining to flow in reservoirs. Aronofsky and Porter4 represented the compressibility factor and the viscosity by a linear relationship, and integrated the equation for radial flow of gas for pressures up to 1,200 psi. Bruce, Peaceman, Rachford and Rice5 integrated the partial differential equations for both linear and radial unsteady-state flow of ideal gas in porous media. Their published results were a substantial guide in this study of integration of the partial differential equation of linear flow with coefficients of the equation variable. The computing program was developed to treat effective permeability as being both distance-dependent and pressure-dependent. In this study all examples of effective permeability are assumptions designed primarily to aid in developing programs for giving effect to this and other variable coefficients. The accumulation of data for expressing the pressure dependency of the effective permeability is the objective of a concurrent investigation. FUNDAMENTAL DIFFERENTIAL EQUATIONS DIFFERENTIAL EQUATION OF FLOW Linear transient fluid flow is represented by the partial differential equation,

Jan 1, 1965

By C. K. Ferguson, J. A. Klotz

This paper describes experimental investigations conducted at the California Research Corporation&apos;s model oil well. The first part describes filter loss from several drilling muds through bore hole walls during mud circulation and drill string rotation. The effect of mud properties and drill string rotation with mud circulation is described. Filtration from a bore hole full of drilling mud, not circulating, but under pressure for extended time periods, is also discussed. The second part describes filter loss to permeable formations from beneath a drilling bit where filter cuke has no opportunity to develop appreciable thickness. If potential flow theory is applied to predict filtrate invasion from this hole bottom, targe invasions arc calculated. But model well experimentation shows that filtrate invasion from the hole bottom is controlled by mud particles that penetrate the formation ahead of the bit. This experimentation provides data to estimate the effect of mud particle penetration on fluid loss to formation. The third part presents an estimate of mud filtration during drilling of a well. INTRODUCTION As oil wells are drilled by the rotary method, drilling mud circulates up the annulus between drill pine and well wall. Drillers adjust mud density so that the pressure at the bottom of the mud column is several hundred psi greater than the pressure of reservoir fluid. As a result of this pressure difference, the liquid part of the mud filters into the rock around the bore and mud solids deposit as a filter cake on the well wall. For many reasons the petrogleum industry, within the past 20 years, has spent much money and energy to determine the volume of mud filtrate that enters rock around the well bore and dedicated much research effort to reduce this volume. Among the reasons for attempts to determine the volume of mud filtrate and to reduce this volume are the following: 1. If filtrate damages the permeability of oil sand, the resultant damage to oil well productivity will depend on the distance that the filtrate invades the oil sand; reduction of filtrate volume may, therefore, increase well productivity. 2. Filtrate that penetrates shale sections may cause the shale to swell and to slough into the well bore. Uncontrolled sloughing may stick drill pipe. Reduction in filtrate volume may reduce drilling trouble. 3. Electric log resistivity curves are changed by invasion of a mud filtrate; the change depends on the depth to which filtrate invades. Knowledge of this depth is necessary before resistivity logs can be interpreted accurately. For these reasons, specifications the place an upper limit to drilling mud filter loss are now written into almost all drilling programs. These specifications are based on APT Recommended practice 29, Standard Field Procedure for Testing Drilling Fluids,&apos; which describes a static filtration test operated at 100 psi filtration pressure and at ambient temperature. Although this test is adequate for mud control, it cannot be used to compare filtration properties of different muds. Schremp and Johnson&apos; showed, for example, that mud with a low API filter loss does not necessarily have low filter loss at bottom hole temperature and pressure. Also, no information has been available about the effect of bottom hole mechanics (mild circulation, drill string rotation, and bit action) on mud filtration. This paper discusses filtration data measured in the California Research Corporation&apos;s model oil well, which models closely oil well bottom hole geometry and hydrodynamic conditions. The filtration processes that

Jan 1, 1955

By R. H. Doremus, E. F. Koch

The first carbide phase that precipitates at 120°C from a iron containing about 0.02 wt pct, C was studied with the electron microscope. In both strained and unstrained material the carbide particles appeared to form on the dislocations in the iron, in agreement with the results of the kinetic study in part II. The structure of the carbide was tentatively identified as an expanded a-iron lattice (body-centered tetragonal) with about 0.7 wt pct C. This phase appeared to be metastable and apparently transformed into cementite or epsilon carbide when the iron was over-aged. WhEN a iron containing less than about 0.025 wt pct C is quenched from 700°C to room temperature the carbon is retained in solid solution and precipitates out slowly with time. The morphology and structure of the precipitating phase are still in doubt, two different carbide phases, epsilon carbide and cementite, have been identified, but there is considerable disagreement about the time and temperature at which they appear.1-4 Epsilon carbide seems to form at lower temperatures than cementite, although one group of investigators4 found only the latter phase over a wide range of aging temperatures. Usually these two phases have been identified after aging times much longer than needed to drain the carbon from supersaturated solution, at least for aging temperatures below 200oC. The precipitated carbides have been observed with the electron microscope,&apos;-5 but again most results have come from samples aged much longer than necessary to reduce the carbon concentration in solution to a low value. In this study the carbide phases were observed in earlier stages of precipitation with the electron microscope, in order to learn more about the shape, size, and distribution of the carbide particles. Samples strained small amounts before aging, as well as unstrained samples, were studied, and the structure of the carbide phase was tentatively identified. EXPERIMENTAL "Ferrovac E" vacuum-melted iron, from which the wires for kinetic studies were also made (Refs. 6 and 7 and the following paper) was used for this work. An analysis of this material is given in Table I; it agrees well with the manufacturer&apos;s values. The number of inclusions in the iron was very small, as can be seen in the optical micrograph in the following paper. Pieces of iron about 1 mm thick and 5 to 10 mm in diam were used for all the studies except for those in which the sample was strained before aging; then the specimen was a rod 3 to 6 mm in diam and 20 cm long. The samples were held at about 700°C in wet hydrogen for at least an hour to remove residual carbon and nitrogen, after which they were heated to 950" (in the y region) and cooled to room temperature in the furnace. This treatment gave an average grain diam of more than 1 mm, so that the effect of grain boundaries on the precipitation process was negligible. The samples were carburized at 710°C for about 2 hr in hydrogen that had passed over toluene held at -30°C; then they were rapidly quenched into water. From chemical analysis this treatment gave a carbon concentration of from 0.012 to 0.016 wt pct, which is less than the solubility of carbon at this temperature. After quenching, the samples were aged at 120 "C in an oil bath for vari-

Jan 1, 1961

By N. T. Cotman, C. H. Pickering, P. B. Crawford

A beat-conduction model has been developed to study the flow of fluids in a stratified oil reservoir which is being subjected to unsteady-state depletion. To simulate stratification, plates of different metals were joined together so that cross flow could occur between strata. A description of the model, plate construction and necessary instruments is included. The data indicate that stratified oil reservoirs experiencing cross flow may be treated as a single, homogeneous, producing sand having properties intermediate between those of the layers making up the system. A technique for averaging core-analysis data to arrive at the proper average value of rock permeability and porosity is presented INTRODUCTION Although oil has been produced from reservoirs for 100 years and reservoir injection processes have been undertaken for 40 years, the industry is still inadequately informed on the problem of reservoir inhomogeneities. Stratification is perhaps the best-known type of reservoir heterogeneity. Urenl discussed the possible significance of this nonuniformity in his 1927 paper on the theoretical aspects of water flooding. Since this time the problem of vertical permeability variations has been the subject of much discussion and numerous papers. Levorsen2 simply describes the origin of layered beds in his Geology of Petroleum. Some beds are field-wide and may be traced from well to well, while others apparently pinch-out and become discontinuous. In addition, the physical characteristics of a layer may vary from place to place. For these reasons, a stratified system is not easily defined. In calculations involving oil reservoirs in which permeabi1ities vary, methods presently used contain many simplifying assumptions. The reservoir frequently is considered as consisting of permeable layers, each of uniform vertical and lateral permeability and each behaving as if separated from adjacent layers by thin impermeable layers. Other assumptions frequently made in reservoir calculations are steady-state flow conditions, unit mobility ratio, linear geometry, average or homogeneous porosity, and negligible capillary-pressure and gravity effects. Muskat3 has. developed solutions to the stratification problem for mobility ratios other than unity for both linear and exponential permeability distributions. He assumes lateral uniformity and continuity of all productive strata and does not consider porosity. This study will take into account transient effects, cross flow and varying porosity, as well as the variations in permeability, by means of a heat analogy. Muskat5 has shown the similarity of the equations which describe the flow of fluids in a porous medium to the flow of heat through a solid. Landrum, et al,6 made an analogy between the flow of fluid in an unsymmetrical reservoir and the conduction of heat in a similarly shaped metal plate. This analogy is summarized briefly as follows. If fluid is produced from an oil reservoir above the bubble point, the resulting pressure distribution will be identical to the temperature which would result in a metal or heat-conducting plate if heat were similarly removed. This means that a study of heat flow in stratified thermal models will behave like fluid flow in stratified oil reservoirs. For mathematical correspondencies, set- Ref. 6. The fluid mobility k/p is proportional to the thermal conductivity, and the porosity-times-compressibility product is proportional to the density times specific heat of the thermal plate. EXPERIMENTAL EQUIPMENT AND PROCEDURE The stratified reservoir model used in this study is illustrated schematically in Fig. 1. A Leeds and Northrup Speedomax Type G temperature recorder