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By S. C. Sun

With the aid of emulsifiers, intense high-frequency sound waves are capable of emulsifying any collector in water. The data show also that ultrasonically emulsified collectors are more effective in floating minerals than the nonemulsified collectors. THE use of ultrasonics in forming emulsions is not new. As early as 1927 Wood and Loomis reported preparation of emulsions with ultrasonics. In 1935 Rschevkin and OstrawskyV escribed the use of great ultrasonic power in producing fine emulsions of various oils and paraffin in water. Recently Oyama and Tanaka3 employed ultra-emulsification to increase the effectiveness of sodium ethyl xanthate in flotation of chalcopyrite and galena. An emulsion is a two-phase system consisting of two incompletely miscible liquids, the one being dispersed as finite droplets In the other. The dispersed liquld is known as the internal or discontinuous phase, and the surrounding liquid is termed the external or continuous phase. There are two types of emulsions; one is oil-in-water (O/W) and the other water-in-oil (W/O). The word oil refers to the liquid other than water. Circumstances exist in which the emulsion type is not clearly defined, and the internal and external phases both contain portions of the opposite phase. This is said to be a dual emulsion. Among the many hypotheses, 5a, B proposed for the formation of emulsions, the Bancroft's adsorbed film or double interfacial tension theory is widely accepted. Bancroft 7, 8 deduced that in the process of emulsification the interfacial tension between oil and water is lowered by the formation of an emulsifying film, which contains the adsorbed molecules and/or ions from the emulsifying agent and the two liquids. This film has two interfacial tensions, one with the water and the other with the oil, which are not necessarily equal. The difference in interfacial tension between the two surfaces of the film is chiefly responsible for forming different types of emulsions. For example, if the interfacial tension between water and film is less than that between oil and film, the film will become convex on the water side, thereby tending to form an oil-in-water emulsion. On the other hand, if the interfacial tension between water and film is greater than that between oil and film, the film will become concave on the water side, thereby tending to make a water-in-oil emulsion. In line with this theory, emulsifying agents soluble in water have the tendency to form oil-in-water emulsions, while those soluble in oil form emulsions of the reverse type. Apparatus and Experimental Procedure: The ultrasonic apparatus shown in Fig. 1 consisted of a hypersonic generator (A), Brush Development Co. model Bu-204; a hypersonic transducer bowl (B) whose resonant frequency is 400 kc per sec; and a round-bottomed glass tube (C) of 2.2 cm ID and 21 cm in length. The acoustical output power of the hypersonic transducer bowl was standardized with a Hewlett Packard vacuum tube voltmeter, model 41 0B, across the hypersonic generator output. The glass tube, containing the materials to be emulsified, was placed 1 cm above the central surface of the transducer bowl, which was filled with water as shown in Fig. 2. Ultrasonic emulsification was performed in three steps, although a one-step method has been used: 1) emulsifying the predetermined amounts of col-

Jan 1, 1956

By H. Warlimont

Precipitation of cementite plates from carbon-rich austenite gives rise to localized formation of martensite in the matrix next to the precipitate upon quenching. The growth of this martensite is urmsually restricted. A distinct lattice relationship is found between this martensite and the cementite phase. It is concluded that the martensite is nacleated in the region of lowest carbon concentration at the austenite-cementite integace, with low-energy matching to the cementite lattice. The restriction of the growth of the martensite phase to the vicinity of the cementite plates can be explained by misfit in the austenite -martensite glissile interface and the uphill carbon gradient in the austenite. The investigation was carried out by light- and electron-microscopy and by electron-diffraction of thin foils. THE precipitation of cementite from carbon-rich austenite gives rise to a localized formation of martensite in the matrix next to the precipitate upon quenching. This behavior has been described previously by A. B. Greninger and A. R. Troiano1 for a 1.78 pct C steel ("pseudomorphic martensite"), and by A. Hultgren2 for a Fe-0.99 pct C—5.20 pct Mn steel. By measuring the axial ratio of the martensite phase,' it was found that the carbon content of this martensite was lower than that of the martensite which formed without prior partial transformation to cementite. Therefore, it was concluded that lowering of the carbon concentration in the matrix next to the precipitate raised the M, temperature locally and thus led to nucleation of martensite at the ce-mentite-austenite interface. However, the restriction of the growth of the martensite phase to the vicinity of the cementite plates cannot be explained by localized carbon impoverishment alone. Under ordinary conditions a martensite plate which has been nucleated in a favorable site can continue to grow until it encounters a physical barrier, or until it encounters a compositional barrier in the matrix, where the total free-energy change for the reaction is not negative, since it has been shown by numerous experiments that the activation energy for growth of ordinary martensite is virtually zero.' An investigation was conducted by transmission electron microscopy and electron diffraction to study this extraordinary martensite. It was expected that crystallographic in addition to compo- sitional conditions caused this abnormal mode of martensite formation. MATERIAL AND PROCEDURE An Fe-C-Mn alloy containing 1.15 pct C and 5.1 pct Mn was used for most of the experiments. For metallographic work, specimens 15 by 15 by 3 mm were used. For preparation of thin films, the initial specimen size was 15 by 15 by 0.7 mm. The heat treatment of each specimen consisted of austenitizing for 1/2hr at 1100'~ in an argon atmosphere, subsequent isothermal holding in a lead bath at one of a series of different temperatures, and, finally, quenching into brine at room temperature. For metallographic examination, the specimens were mounted in bakelite (slight tempering effects resulted from the heat in the mounting press) ground, polished, and etched in nital. Thin films for transmission electron microscopy and electron diffraction were obtained by grinding the specimens to approximately 0.2 mm thickness and subsequent electrolytical thinning. The orientation relationships were evaluated from sets of electron micrographs and selected-area electron diffraction patterns of single units of the transformation products and the adjacent matrix. RESULTS In the alloy which was used for the experiments, proeutectoid carbide precipitates over a wide tem-

Jan 1, 1962

By E. F. Sumner, C. K. Eilerts

A partial differential equation was developed and programmed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious dimunition in delivery capacity. The pressure dilferential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. INTRODUCTION A computing program developed by the authors 1 to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, W(Po) = kD(p0)/M(p0)z0(Po).......(1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(pD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville 2 for computing multicom-ponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(pD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. BASIC EQUATIONS The partial differential equation for calculating

By R. DiBella, H. Biloni, G. F. Bolling

A study of the detailed relationship between solidification substructure and microsegregation in dilute tin alloys has been continued. New observations reveal that depressions form at the solid-liquid interface not only as an initial form of segregation but throughout the range of increasing constitutional supercooling. In order to show the importance of this node formation it proves convenient to make two simplifications. Although substructure changes continuously as constitutional- supercooling increases,&apos; the following discrete stages may be used for discussion: 1) the planar solid-liquid interface; 2) ordered nodes, or depressions at the interface;&apos; 3) two-dimensional or elongated cells;3 4) regular or hexagonal cells;4 5) distorted cells, or hexagonal cells with branches;4 6) dendrites. It is also convenient to ignore observations made near grain boundaries which interact with the cellular substructure.2-4 And, it should be clearly pointed out that all singular depressions at the solid-liquid interface will be called nodes. Heretofore, the term "node" has been used without clear justification to describe both the truly isolated depression and the junction of cell walls appearing in a later stage of segregation. This usage is continued because it seems proved by the observations. Standard systematic growth of tin crystals was undertaken over a broad range of constitutional supercooling using various added solutes. Except for one or two chance observations, this research failed to reveal any appreciable range of growth conditions over which a disordered array of isolated nodes exists. Even though &apos;some finite range of random instability must exist, it is now concluded that stage one passes very rapidly to stage two. Next, after confirming that stage two passes to stage three by the elongation of isolated nodes: a reexamina-tion of stages three, four, and five followed. Standard metallography showed that pockets of higher solute concentration (for ko < 1) became more numerous in cell walls the more severe the growth conditions. These high-concentration regions must arise from depressions; however, in stage three their segregation is not distinguishable from the segregation of the nodes which join cell walls together. It seems, therefore, that the presence of nodes is causal in the formation of new cell walls, and that the mechanism by which stage three passes to stage four is initiated by nodes. If a similar reasoning is followed, the separation of stage four from stage five appears to be just a convenience that has arisen from the decanted interface observations made in the past. The present observations again show that more severe growth conditions relate directly to an increase in the number of nodes in the hexagonal cell walls. These nodes apparently serve as the origin for lines of segregation extending within the body of a cell, and can thus be assumed to represent the earliest form of branching,* as shown here in Fig. 1. The examination of stage six involved decanted-interface structures as in Fig. 2, which are similar to those considered by Rutter and Chalmers,5 Plaskett and winegard,6 and Hellawell and Herbert,7 and where distinct protrusions are each surrounded by a depressed boundary. The corresponding microsegregation behind the interface, but not far enough behind to allow a smearing of the segregation because of diffusion,4 is shown in Fig. 3. Both the shape of the decanted interface and the segregation pattern behind it

Jan 1, 1968

By M. Bevis, A. G. Crocker

A. G. Crocker and M. Bevis (Battersea College of Technology)— Richman and Richman and conard17 have recently published the very interesting results of their studies on the plastic deformation of Fe-Ni-C martensites and of an Fe-5 wt pct Be alloy. Other work on the range of Fe-Be alloys containing between 16 and 27 at. pct Be has also been reported by Richman." One of the fascinating features of this work is that the materials investigated deform primarily by means of twinning and that several twinning modes are operative in addition to the well-established (112 ) mode of bcc materials The composition planes of these unusual twins were determined using a single-surface analysis and reported as (0131, "{045)" or "{089)", and "{2,3,10)" or "(127)". (It is now thought1&apos; that the "{0,1,13)" habit reported for the Fe-Ni-C alloys&apos;&apos; is more likely to be near "{127)". Although the full twinning elements of these unusual twinning modes could not be determined directly from the experimental results, the authors attempt to deduce the elements by considering twin intersectionslQ and by using the projection technique of Jaswon and Dove.&apos; The basic assumption of their approach is that the (013) habits are truly rational planes but that the other habits are irrational and merely approximated to by the indices quoted above. They thus deduce that the twinning mode describing the (013) habit is either Type I or compound and that the modes describing the other habits are Type 11. This deduction must however be false as all twinning modes in cubic structures obeying the classical orientation relationships of deformation twinning must be compound. Type-I and Type-I1 modes can occur in all of the other crystal systems (indeed in the triclinic system compound modes are not allowed), but in the cubic system only compound modes can arise. This fact, which does not appear to be well-known, fol- lows immediately from the relations between the four twinning elements defining a twinning mode. Thus for a Type-I mode which is uniquely defined by the rational twinning elements K1 = hi and tj2 = vi (i = 1, 2, 3), the Kz qd 771 elements are given by: where the summation convention of the tensor calculus has been adopted. For cubic materials the metrics cij Iand cij reduce to the unit tensors 6ij and 6ij so that we have It is clear from these equations that both ki and ui must take on integral values; i.e., Kz, and ql must be rational, if hi and vi are integers, i.e., if K1 and 77~ are rational. Thus for cubic materials a Type-I mode must degenerate into a compound mode and the same result also arises for Type-II modes. The apparently irrational habits observed by the authors can thus not be explained in terms of Type-I1 twinning if the classical laws of deformation twinning are to be obeyed. An alternative explanation of the irrational habits is that they may arise from twinning modes with four irrational twinning elements. These modes, which do not obey the classical orientation relationships associated with deformation twinning, have been shown to arise as the result of double twinning processes in magnesium,22 but may also describe a simple shear on an irrational plane in an irrational direction. Indeed double twinning processes in bcc

Jan 1, 1963

By Lawrence H. Van Vlack

The energy of the y-iron grain boundary was determined to be 850 ergs per cm2 at 1105°C. The a/a and the a/y boundaries possess somewhat less energy. The microstructures of several iron alloys are discussed in terms of the interfacial energy relationships. THE dependence of the shape of liquid interfaces upon their energies has been studied for some time.1"3 Recently, Smith&apos; concluded that many of the microstructures observed in metals may be attributed to the energies of the interfaces between the grains and phases. While the energies of liquid surfaces have been measured by numerous different methods: only two attempts have been made to determine experimentally the energy of surfaces involving crystalline solids. Udin, Shaler, and Wulff8 used a procedure introduced by Berggren7 to measure the surface tension of solid copper. It consisted of determining the load required on a thin copper wire so that the surface tension was counteracted, and no net strain resulted. Bailey and Watkins8 sed a different technique and were able to determine both the surface tension of copper and the tension of the copper grain boundary. They measured the contact angle which liquid lead makes against a copper surface. They then calculated the above energies from the surface energy of liquid lead by using the Pb vs. Cu/CuY dihedral angle and the surface groove angle formed during thermal etching. They obtained a value of 1800 dynes per cm for the surface tension of clean copper and approximately 640 dynes per cm for the tension of copper grain boundaries. The former value was somewhat higher than Udin&apos;s value of 1500 dynes per cm. This paper includes a determination of the energy of the y-iron grain boundary. In addition, the micro-structural relationships of several other metallic and nonmetallic phases with iron were examined and an attempt was made to interpret the observed structures in terms of interfacial energy relationships. Theoretical Considerations In a three-phase material containing a solid and two liquids, there may be two solid/liquid interfaces, one liquid/liquid interface and one inter- granular interface. Liquid/liquid interfacial energies can be measured directly. Therefore, by determining the energy of such an interface and by measuring the required interfacial angles: the energies of the interfaces involving solids may be obtained.10 They may be shown schematically as in Fig. 1. The above procedure requires the following assumptions: 1—The interfacial energies are, in general, unaffected by boundary orientation, and 2— the shapes of the interfaces are unaltered between annealing and sectioning for microscopic examination. The first assumption is good to a first approximation as shown by Dunn and Lionetti11 except for a few critically orientated boundaries. Two conditions may alter the shape of a boundary upon cooling: 1—Precipitation of dissolved material upon one side of the interface, and 2—a change in volume during the transition from one phase modification to another. The former must be detected by microscopic observation. The latter may become appreciable in systems containing an interface between two liquids which solidify after annealing. However, possible movement of the two-liquid interface may be checked in the system diagrammed in Fig. 1 by measuring 8, for example, and comparing it with its value as calculated from the other interfacial angles by: tan8, C11 05 COS- o- + cos 8, cos- The choice of a suitable pair of liquids is limited by several factors. The relative values of the several

Jan 1, 1952

By G. S. Upadhyaya, A. D. McQuillan

HERE would appear to be a simple relationship between the group number in the periodic table of the early transition metals and the maximum amount of hydrogen which they can absorb.&apos; Thus group IIIA metals (Sc, Y, and La) yield a trihydride in which the metal atoms are on a fcc lattice and the hydrogen atoms occupy both tetrahedral and octahedral interstices. Group IVA metals (Ti, Zr, Hf) form dihy-drides in which the metal atoms are on either a fct or cubic lattice, but in which only the tetrahedral interstices are occupied by hydrogen atoms. In group VA (V, Nb, Ta) the hydrogen-saturated metal attains a composition slightly below that of a monohydride under normal conditions. Finally the metals of group VIA (Cr, Mo, W) do not dissolve appreciable quantities of hydrogen. The manner in which hydrogen solubility disappears on alloying a group VA metal with one from group VIA has previously been investigated.2 It is necessary, in order to obtain a general picture of the reactions of alloys of the early transition metals with hydrogen, to examine a system containing metals from groups IVA and VA in which there must be a change from a fcc to a bee hydride phase. The system chosen for investigation was the pseudobinary system between titanium hydride and niobium hydride. Metallic alloys were prepared by melting iodide-prepared titanium with zone-refined niobium in an argon-atmosphere are-furnace. To ensure homogeneity each alloy was cold-swaged and then heated at 1250°C in a high-vacuum furnace until metallo-graphic examination confirmed its complete homogeneity. Small weighed specimens of the alloys were charged with hydrogen using gaseous hydrogen generated by heating titanium hydride. The apparatus has been described elsewhere.3 Throughout the charging process the hydrogen pressure was kept at about 1 atm while the specimen, initially at 800 °C, was slowly cooled to 150°C over a period of days. The total amount of hydrogen absorbed by each specimen and the room-temperature crystal structure of the hydride powders were determined. The X-ray investigation indicates that the fee hydride phase arises from alloys extending in composition from titanium to 67 at. pct Nb. After a two-phase field lying between 67 and 74 at. pct Nb in which the fee and bee hydrides coexist, all alloys richer in niobium yield a distorted bee hydride. Data derived from parameter measurements are presented in Fig. 1. The atomic volume per metal atom has been plotted against the composition of the initial metallic alloy in order to facilitate comparison of the effects of hydrogen addition in the two phases of different crystal structure. The amount of hydrogen absorbed by each alloy at saturation in terms of the hydrogen to metal ratio and alloy composition is given in Fig. 2. Over the whole range of the fee hydride phase the hydrogen content remains constant, while in the distorted body-centred hydride phase, the hydrogen content increases with increasing titanium content reaching a hydrogen/metal ratio of 1.4 at the boundary of the two-phase region. It seems likely, therefore, that the maximum hydrogen content of the fee hydrides is limited to a hydrogen/metal ratio of 2 because hydrogen atoms

Jan 1, 1962

By H. R. Stahl

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

Jan 1, 1947

By H. R. Stahl

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

Jan 1, 1947

By J. W. Whalen

The design, operation and evaluation of an instrumental method for the determination of fluid saturation in porous materials during multiphase flow studies is described. The presence of a magnetic tracer comprising approximately 20 per cent by weight of the aqueous phase is necessary in the utilization of this method. The results of two-phase relative permeability studies on two samples of porous media are presented. The realizable accuracy of the magnetic susceptibility apparatus in fluid saturation determination is estimated to be 2 saturation per cent. The response characteristics of the instrument, together with its simplicity of operation and maintenance are sufficient to recommend its use in routine laboratory studies. INTRODUCTION The problem of fluid saturation determination in laboratory multiphase flow studies characterizing oil recovery processes is one which has been given exhaustive study. Briefly the requirements which are considered essential for a method sewing this purpose are: (1) that the measurement be made external to the porous rock sample under study with no interruption of the fluid flow pattern, (2) the saturation indication must be independent of fluid distribution in the volume scanned by the measuring device, (3) the sensing element should have a small field of definition enabling several independent measurements to be made along the length of a core sample, and (4) the properties of the fluid phases should not be too greatly influenced by required tracer substances. Several methods of saturation determination have found acceptance as meeting most of the above requirements. These include resistivity,1 X-Ray absorption,2,3,4 radiotracers,5,6,7 and neutron8 diffraction The merits of these techniques have been discussed elsewhere in detail and will not be considered here. It may, however. be pointed out that the elaborate instrumentation required by the methods mentioned above, with the exception of the resistivity method (which is undesirable from other standpoints) encourages the development of methods of saturation determination which, while meeting the requirements listed, are simple to operate and maintain. It is the purpose of this paper to describe the instrumentation and evaluation of a technique for the determination of fluid saturation which combines relative simplicity with an accuracy and applicability comparable with methods now in practice. DESCRIPTION OF THE METHOD If the magnetic susceptibility of one of the fluid phases contained within a porous material is sufficiently greater than that of the remaining phases, the fluid content of the material with respect to that phase may be determined by an induction measurement. This may be accomplished by measuring the induced voltage in the secondary of a transformer which contains the porous sample and its interstitial fluids as a portion of the magnetic flux path. Since the fluids used in multiphase flow studies involving petroleum reservoir samples possess uniformly low magnetic susceptibilities, the use of a magnetic tracer in one of the fluid phases is required. In view of the relatively high paramagnetic susceptibility of salts of the transition elements, together with their high water solubility. these compounds become logical choices as tracer materials. Cobaltous chloride, having a specific magnetic susceptibility of 17.5 x 106 cgs electromagnetic units, was used as the tracer material throughout this work, in a concentration of approximately 20 per cent by weight in the aqueous phase. MAGNETIC SUSCEPTIBILITY APPARATUS Basically, the magnetic susceptibility apparatus consists of a transformer serving as the detecting head, a

Jan 1, 1955

By J. W. Downey, J. B. Darby, L. J. Norton

THE only previous investigation of the phase equilibria in the Ta-Pd system was reported by Greenfield and Beck.1 Their work (actually a portion of a much broader survey) was limited to the composition range 50 to 75 at. pct Ta and to a single temperature, 1000°C. The results indicated that no intermediate phases were present at this temperature. They pointed out that this was an unexpected result in view of the fact that niobium, which belongs to the same group in the periodic table as tantalum and has essentially the same atomic size, forms a o phase with palladium.&apos; Also, tantalum in combination with rhodium,&apos; iridium,&apos; or platinum&apos; stabilizes the s phase. By analogy, the Ta-Pd system would also be expected to contain a s phase. The present investigation was therefore undertaken to explore more fully the phase relationships in this system. Alloys were prepared by arc melting on a water-cooled copper hearth in an argon-helium atmosphere. The purity of the starting materials was greater than 99.9 pct. The weight losses on melting were less than 1 pct and therefore the alloys were not analyzed chemically. Specimens were wrapped in molybdenum foil, encapsulated in quartz capsules under a vacuum of at least 1 x 10-5 mm of Hg, annealed as indicated in Table I, and water quenched. Optical and X-ray metallography were used for identifying the phases present in the annealed and quenched alloys. The alloys were resistant to attack by several acids; however, a sodium cyanide electroetch and an immersion etch containing 1 part HF, 1 part HNO3, 2 parts H2SO4, and 5 parts H2O by volume were found satisfactory. The X-ray diffraction patterns were taken with a Straumanis-type Debye-Scherrer camera and filtered copper or chromium radiation. A summary of the phases found in this investigation is presented in Table I. No attempt was made to determine the composition limits of the various phases. The present results indicate that this system consists of two terminal solid solutions separated by at least four intermediate phases at the approximate compositions Ta3Pd, -TaPd, TaPd,, and TaPd3. The Ta-rich solid solution, containing less than 10 at. pct Pd at 1150°C, is in equilibrium with a o phase which is stable in the vicinity of 25 at. pct Pd. The latter phase is also in equilibrium with a bct phase at the equiatomic composition. At high temperatures it appears that the Pd-rich solid solution extends to at least 66.6 at. pct Pd and is in equilibrium with the bct phase. When annealed at 900°C, a sample containing 66.6 at. pct Pd transformed to an unidentified phase designated as X. An X-ray diffraction pattern of this phase contained sharp low-angle lines while the high-angle lines were characteristically diffuse. The observed d-spacings and relative intensities for lines in the low-angle region are presented in Table 11. In the vicinity of 70 at. pct Pd an intermediate phase having the TiA13-type structure is formed. It is stable to at least 1100°C, and presumably dissolves congruently into the ter-

Jan 1, 1963

By J. L. Thompson

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

By M. A. Cook

Sutherland used an ion-pair adsorption model to derive the author&apos;s hy-drolytic pee-acid) adsorption equation for the contact bubble curves of Wark and Cox. To do so it was necessary to postulate that the sum of coverages of surface anion sites by the collector and depressant anions is practically unity. It is here shown that the free energy of Sutherland&apos;s postulated collector ion (x-)-depressant ion (OH-) exchange reaction (for no other than the OH- to compete with X-), namely EX + (OH-) Z SOH- + X-, is in some cases positive and X- should not even adsorb. Also, in many cases the (OH-) adsorption must be quite negligible even though the collector covers only about a sixth of the mineral surface at the threshold of air bubble contact. This, however, contradicts the postulate that permits one to derive the correct bubble contact eqwztion for the ion-pair model. Furthermore, the requirement for charge neutrality leads in the ion-pair model to the (impossible) constancy of the ratio @+)/(OH-) along a contact bubble curve in which pH may change by more than seven units. HYDROLYTIC ADSORPTION EQUATION Hydrolytic (free-acid or free-base) and ion-pair (H&apos;, X-, or R&apos;, OH-) adsorption models of the collector in metal sulfide and similar flotation systems are superficially alike and somewhat difficult to differentiate. This is because they yield, under seemingly valid assumptions, equivalent forms of the equations describing the distribution of the collector between the aqueous solution and the mineral surface. This has been discussed by the author and associates1-4 and more recently by Sutherland,&apos; both for simple collector-mineral and for more complicated collector-depressant-mineral systems. In the hydrolytic adsorption model the equations describing the contact bubble curves of Wark and coxeJ7 are as follows :2 Here X is the collector anion, D- the depressant anion, 9, and On are the fractions of the free-acid sites S on the surface of the mineral covered by collector and depressant free acids, respectively, and @ is the fraction of uncovered sites. Kx is the free-acid collector dissociation equilibrium con- stant, K1 that for the free-acid collector adsorption, KD that for the free-acid depressant dissociation, and K2 the equilibrium constant for the free-acid depressant adsorption. Eqs. 1 to 5 yield upon simultaneous solution the result is the critical free-acid concentration for bubble contact in the absence of depressant-free acid. Eq. 8 expresses the conditions along a simple collector-mineral contact bubble curve for the case HD = 0, or V = 0. Last and Cook showed that Eq. 6 applies generally and with good accuracy in the collector-depressant-metal sulfide mineral systems. Inci-dentally, it has been shown by infrared absorption studies that in some cases the free-acid adsorption process splits out water.&apos; In this case, Eq. 2 might be written SHOH + HX Z SHX + H20, with a similar equation replacing Eq. 4 for depressant-free acid-water exchange. This possibility does not change, however, the basic equations or considerations of the hydrolytic adsorption model. Indeed, this type of free acid-water exchange reaction was predicted for fluorite and iron ore flotation by oleic acid in the dry grinding and boiling processes.410

Jan 1, 1961

By O. J. C. Runnalls, L. M. Pidgeon

Some observations on the kinetics of the iodide process are reported. The deposition rate is geometry-sensitive in a system containing a finely divided titanium charge. Further, results indicate that the iodine diffusion rate influences the velocity of the process. The nonvolatile iodide, Til,, forms in the hot filament zone, thus removing iodine from the cycle. TITANIUM metal of 99.9 pct purity may be prepared using a refining technique originated by Van Arkel and de Boer.&apos; The purity of this metal, commonly called iodide titanium, exceeds that produced by any known process. In a recent application, the method was employed by Gonser et al.² to prepare titanium rods up to 2 to 3 cm in diam. In the Van Arkel-de Boer system, the relative influence of the fundamental mechanisms: l—production of titanium iodides, 2—gaseous countercurrent diffusion, and 3—decomposition, on the deposition rate have not been clearly established. Blocher and Campbell" have indicated that the controlling step in the process under practical conditions of operation may be the reaction rate of iodine with the crude metal. Fast&apos; reported that crude titanium metal reacted with iodine rapidly, even at room temperature, in his apparatus. Little has been reported on the effect of gaseous diffusion or decomposition on the deposition rate. It is these aspects of the process about which this investigation is centered. An attempt has been made to separate these latter effects from those due to the formation of the iodides at the crude metal surface by a division of the experimental program. Reaction of Iodine with Titanium Apparatus: In the investigation of gas-metal reactions of this type, the chemical reactivity of the halogen and halide vapors dictates the use of all-glass apparatus. In such a system standard techniques for measuring reaction rates are difficult to employ. Here, a simple apparatus was devised (Fig. 1) so that some indication of the reactivity of titanium powder with iodine vapor could be obtained. A stream of iodine gas was evolved from a bulb of controlled temperature and passed over a sample of titanium powder heated in a horizontal tube furnace. The product of the reaction, TiI4, volatilized and was condensed outside the furnace in a series of four glass bulbs, each cooled to room temperature in turn. Preliminary experiments indicated that distillation was retarded in a sealed evacuated system due to a pressure build-up in the condensing end of the apparatus. Hence, the system was pumped continuously using a mechanical pump and two oil diffusion pumps in series, through a liquid air trap. The iodine bulb was made large and a capillary restriction was inserted between the titanium bulb and the condensers so that the iodine pressure over the metal would approach the equilibrium pressure over solid iodine crystals. The effect of this restriction on the evaporation rate of TiI4, was determined separately. The iodine bulb was heated in an oil bath controlled to ±2°C. The titanium bulb temperature was automatically controlled to ±5°C. Procedure: About 200 mg of —30 mesh titanium powder, weighed to 0.1 mg, was placed in the reaction bulb after part B had been joined to part A. The powder was tapped into a long (5 cm) shallow mass along the bottom of the tube. Two chromel-alumel thermocouples were inserted into the magnesium radiator which was clamped to the reaction

Jan 1, 1953

S. Tandanand, Twin Cities Mining Research Center, U. S. Bureau of Mines As an addition to the fine reviews on drilling presented in the foregoing papers, we feel it would be appropriate to mention briefly some work in this area by the U. S. Bureau of Mines. The Bureau has had under way for several years at its Twin Cities Mining Research Center studies directed toward a better understanding of basic drilling mechanisms. The work includes drillability investigations with diamond rotary, and with percussive drilling systems, as well as fundamental studies of rock behavior under drill bit types of loading. Results of our work to date have contributed the following to the state of the art. MECHANISM OF ROCK FAILURE-Rock fragmentation through use of mechanical energy systems, including drilling systems, consists of two major components-machine and rock. The two components are related to each other by their functional behavior and their resultant motion which the components mutually influence. Forces in the systems are transmitted directly to the bit which in turn induces stresses in the rock. When the induced stresses exceed the strength of the rock, the rock fails resulting in penetration. Rock strength is a function of the forces applied to the rock. Stresses under a drill bit, regardless of bit configurations, are essentially compressive, resulting in a condition where the rock has the highest resistance to failure. The ratio of principal stresses induced under drill bits is an indication of the mode of failure in the rocks. Initially, compressive stresses under the drill bit cause rock to undergo inelastic deformation. The impression observed at the first stage of crater formation under the drill bit shows that rock is no longer elastic. Associated subsurface failure at this stage precedes total rupture which subsequently appears at the rock surface. Thus, explanation of crater formation, by applying theory of elasticity alone, is likely to be over-simplified. ENERGY VERSUS VOLUME OF ROCK REMOVED-Experimental results show that energy per unit volume of rock removed is constant for a particular rock and bit type. Rock offers a definite resistance to penetration, depending on the method of the energy application; this may be defined as the drilling strength of a rock. Energy consumption in a drilling system may be divided into two components: 1) Energy required to move the machine parts; and 2) energy consumption in breaking rock. Component 1 is dependent on the type of the machine. Component 2 is dependent on the strength properties of rock and the efficiency of the bit in rock cutting. The sum of the energy required in both components determines the total energy required in breaking rock. Our work in this area has included consideration of both diamond and percussive drilling systems. PENETRATION RATE-For a drilling rate expression to be useful in predicting field performance, it should include the operating characteristics of the drilling machine. Eq. 37, for example, is simply a statement of the fact that the drilling rate is determined by the power output of the machine (2pNT) and the power requirements to break the rock in the hole (AER). In order to predict the performance of a particular drill and the effect, for example, of the rotary speed, on the drilling rate, R, Eq. 37 must be modified to include the

Jan 1, 1967

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation&apos;s supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation&apos;s need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By H. A. Wahl

This paper presents methods of designing hydraulic fracture treatments in formations saturated with slightly compressible liquids. Howard and Fast describe the fluid-loss control resulting from the viscosity and compressibility effects of the reservoir fluid in terms of a fracturing fluid coefficient. However, for horizontal fractures, this coefficient is applicable to infinitely thick reservoirs. These methods of evaluating fluid loss from horizontal fractures during treatment differ from previous methods in that: (I) formation thickness is incorporated in the velocity function describing the rate of fluid loss to the formation; and (2) for a given thickness the relative position of the fracture to the horizontal boundaries of the reservoir or any interrnediate permeability barrier is incorporated in the design procedure. This theory is applied to several actual and hypothetical field cases. The results of these calculations demonstrate that the eflect of formation thickness on fluid loss from horizontal fractures may result in fractures several times larger than predicted by other methods. INTRODUCTION Hydraulic fracturing has been the dominating well-stimulation technique during the last decade. From the time it was commercially available, fracturing has had a very favorable success ratio compared to other stimulation methods. However, numerous wells that were successfully stimulated remained economic failures. Only in the last few years has the oil industry recognized the importance of designing treatments for each well which will yield the maximum profit. This implies that for a given set of treatment conditions the size and general physical characteristics of the fracture can be determined. One of the outstanding contributions in the field of fracture design was presented by Howard and Fast.&apos; In their paper, three flow mechanisms that control fluid loss from the fracture to the formation are defined: (1) viscosity effects of the fracturing fluid, (2) viscosity and compressibility effects of the reservoir fluid, and (3) wall-building effects of a treated fracturing fluid. The rate of fluid loss to the formation adjacent to a fracture is shown to be a function of time. For each flow mechanism the velocity function v(t) is expressed as a constant or fracturing fluid coefficient divided by the square root of time. This form of v(t) can be used in the Carter equation, as developed in the Howard and Fasc paper, to estimate the areal extent of fractures. This equation may be written as In the following sections the effect of formation thickness on fluid loss from horizontal fractures is evaluated when the controlling flow mechanism is the viscosity and compressibility of the reservoir fluids. The major assumptions inherent in the Carter equation are brought out in subsequent mathematical developments. THE EFFECT OF RESERVOIR FLUIDS ON FRACTURE EXTENSION When a fracture treatment is performed using a fracturing fluid identical to the reservoir fluid, the only flow mechanism controlling fluid loss is the viscosity and compressibility effects of the reservoir fluids. In developing a fracturing fluid coefficient for this mechanism, Howard and Fast considered a segment of the formation bounded by a unit area on the fracture face and extending to infinity in the direction of leak-off as shown in Fig. 1(a). The direction of leak-off z is normal to the fracture face. The equation governing the linear isothermal flow of fluid into this segment is where a = Eq. 2 is a form of the diffusivity equation. It is derived from the equation of continuity, Darcy&apos;s law and Eq. 3

By G. Thodos, R. J. Smialek

A method has been developed that permits the correlations of Mehra and Thodos8 and Dastur and thodos2 for binary systems to be used for the prediction of the vapor-liquid equilibrium constants of the light and heavy constituents, Kland Kh, of a ternary hydrocarbon mixture. Furthermore, the unique relationship observed in this study, i.e., a plot of log Ke/Ki vs log Kp/K h is linear and passes through the origin, permits the calculation of the K-value for the intermediate component. This approach has been used to establish K-values for the constituents of the three ternary hydrocarbon systems used to develop this method and has also been applied to two additional ternary hydrocarbon systems to yield an average deviation of 7.7 per cent resulting from a total of 294 points for the five ternary systems considered. INTRODUCTION The rigorous calculation of vapor-liquid equilibrium constants for systems containing two or more components is a difficult problem and becomes extremely complex at elevated pressures and for conditions approaching the critical point. Although thermodynamic relationships can be developed to account for the vapor-liquid equilibrium behavior of simple systems, their use is limited because the necessary PVT data for these systems are not generally available. To establish a method for calculating K constants directly, without any recourse to the PVT behavior of a system, Mehra and Thodos8 applied the principle of corresponding states to the vapor-liquid equilibrium constants of binary hydrocarbon systems. They developed a series of charts which made possible the prediction of K-values for all binary hydrocarbon systems not containing methane. This work has been extended by Dastur and Thodos2 to include binary hydrocarbon systems containing methane. The charts developed in these two studies cover the high-pressure region and are applicable to conditions in the vicinity of the critical point. The ability of this approach to predict vapor-liquid equilibrium constants of binary hydrocarbon systems suggests that this method may be extended to the prediction of the K-values of the components of ternary hydrocarbon systems. In this investigation, the charts developed for both the methane and non - methane binary systems,2,8 together with mixture rules developed in this study, have been used to predict the K-values of the light and heavy components of a ternary hydrocarbon system. These calculated values are then used to establish the K-value of the intermediate component through the use of a novel relationship developed in the present study. DEVELOPMENT OF METHOD FOR PREDICTING K-VALUES OF TERNARY SYSTEMS The application of the corresponding state charts developed for binary hydrocarbon systems is restricted to those systems containing two components. The extension of these correlations to three-component systems requires that the ternary system be reduced to an equivalent binary, which can be treated in a manner consistent with the corresponding state development. To establish such an approach, the vapor-liquid equilibrium constant of the light component K is first calculated by assuming that the ternary mixture consists of the light component and a pseudo-heavy component of the intermediate and heavy constituents of the original ternary. To establish the vapor-liquid equilibrium constant of the heavy component Kh, the light and intermediate constituents of the ternary are combined to form a pseudo-light component of another equivalent binary system. The calculated values Kl and Kb are then utilized to calculate the vapor-liquid equilibrium constant of the intermediate component EQUILIBRIUM CONSTANT FOR LIGHT COMPONENT K To calculate the K value of the light (most

Jan 1, 1965

By E. P. Miesch, P. B. Crawford

A study was made of the effect of permeable and impermeable lenses in a reservoir on the production capacity of a well. Both steady-state and unsteady-state data were obtained. An electrical resistivity model was used to obtain the steady-state data and thermal models. were constructed to obtain the unsteady-state data. The productivity of a well is affected very greatly only when the lenses are close to the well. The effect of circular lenses on the productivity ratio can be correlated with the distance from the center of the lens to the center of the well divided by the radius of the lens. When this dimensionless distance is equal to six or greater, the effect of the lenses on production capacity will be negligible. The pseudo steady-state productivity of a heterogeneous reservoir can be predicted using steady-state data. INTRODUCTION Many analytical solutions of reservoir behavior assume that reservoir rock is uniform and homogeneous. Although this assumption is used, all of the data from core analyses and well logging indicate that the reservoirs are heterogeneous. Very little work has been done on the performance of heterogeneous reservoirs. The work of Landrum,l et al. showed that transient phenomena in oil reservoirs could be studied with thermal models. Pickering and Cotman2 used thermal models to study flow in stratified reservoirs and investigated the effect of inhomo-geneities in oil reservoirs on transient flow performance. Loucks3 made a mathematical study of the pressure build-up in a system composed of two concentric regions of different permeability. Root, Silberberg and Pirson4 studied the effect of the growth of the flooded region on water influx predictions using a thermal model consisting of three concentric cylindrical regions of different thermal properties which simulated the aquifer, the flooded region and the unflooded portion of the original hydrocarbon region. Tomme, et a1.5 made a mathematical study of vertical fractures. The object of this investigation was to study the effect of highly permeable and impermeable lenses in the vicinity of the wellbore on the pressure depletion history of the well. Steady-state data were obtained for both conductive and nonconductive lenses that completely penetrated the formation. The lenses were symmetrically located at various distances from the wellbore. The unsteady-state data were obtained on seven thermal models. EXPERIMENTAL EQUIPMENT AND PROCEDURE STEADY-STATE DATA The steady-state data were obtained from an electrical resistivity model 30 in. in diameter and approximately 11/2 in. deep. The outside of the model was lined with a 30-in. diameter copper strip, which served as the outer boundary of the reservoir. The bottom was covered with a sheet of plexiglass so that it would be nonconductive. The model was filled with a slightly saline solution. The well size was varied from an 0.064-in. diameter copper wire to a 10-in. diameter copper cylinder. Readings were taken with an impedance bridge using AC current to prevent polarization at the contacts. Copper and wax lenses were used to represent infinitely conductive and nonconductive lenses, respectively. The resistance was first measured for each well diameter with no lenses in the reservoir. Then the conductive and nonconductive lenses were spaced symmetrically at various distances from the well and the resistance read from each lens location. The diameters of the conductive lenses were 3, 1.022 and 0.624 in., and those of the nonconductive lenses were 3, 2.25 and 1.563 in. The ratio of each resistance reading to the resistance reading with no lenses in the reservoir

Jan 1, 1965

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation&apos;s supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation&apos;s need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951