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By H. A. Lesser, H. L. Stone, G. H. Bruce

ESSO PRODUCTION RESEARCH CO., HOUSTON, TEX. A mathematical model that represents the conduction heating of a rock formation of limited permeability is formulated. Heat is introduced by the injection of a hot condensing gas into horizontal fractures through the formation. The fractures are assumed to be equally spaced; the flow of fluid is linear. The model consists of three coupled partial differential equations and two functional relationships. Temperature histories for both fractures and formation are obtained by numerical procedures. Application of the model in predicting in situ heating of oil shale is illustrated with four sample cases. Influences of shale thermal diffusivity, fluid pressure in the fracture and fracture spacing upon heating rate are demonstrated. In all cases considered, several years were required to heat all the formation to 700F with 1,000F steam. Less than 32 per cent of the injected heat was utilized for heating the shale. To facilitate extensive calculations of this type, a set of seven dimension-less quantities are derived. With this dimensionless system, the effect of controllable parameters on economics can be explored. INTRODUCTION Vast deposits of hydrocarbons are contained in oil shale formations in the western United States and in other countries. These hydrocarbons, known as kerogen, are difficult to recover because they are immobile solids and because the rock formations in which they are found have very limited permeability. The kerogen can be converted through pyrolysis to recoverable liquids and gases if the formation temperature is elevated to the range 600 to 800F. To accomplish this heating, the formation might be artificially fractured and a hot fluid injected into the fractures. If the injection and production wells are vertical and the fractures horizontal, interwell communication will be established and the hot fluid will flow from an injection well to a production well. In this process, some of the heat in the fluid will be given up and conducted into the formation. Products of pyrolysis will flow from the heated rock matrix into the fractures and be produced, commingled with the injected fluid. The practicality of such a process is strongly influenced by the rate at which heat can be transferred from the hot fluids to the formation. An analysis of this heat conduction problem is the subject of this paper. Linear flow of a condensing gas through a set of horizontal, equally spaced fractures is considered. Temperature histories for both fractures and formation are obtained from numerical procedures. The analysis also applies to formations containing streaks of natural permeability instead of fractures. Heat flow problems similar to the one treated here have been studied by other workers. Thomas1 has solved a radial problem in which he considers the injection of a noncondensing gas into a single, horizontal fracture and approximates the temperature profile in the fracture by a step function. The solutions to other problems, which are less similar to the present problem than the one treated by Thomas, have been reviewed by Spillette.2 In addition to these mathematical studies, a field test of an in situ shale oil recovery process using hot natural gas as the injected fluid has been reported.3 The first part of this paper is concerned with the mathematical development of the problem. The differential equations, boundary conditions and functional relationships which describe the physical model are formulated and the equations are cast into finite difference form. The method of solution of the difference equations is discussed (Appendix B). The second part of this paper presents results computed for a typical oil shale formation for which steam at 1,000F is the injected fluid. Fracture spacing, horizontal and vertical thermal diffusivities

Jan 1, 1967

By George A. Colligan, John M. Lo

Electrical resistivity as a function of temperature was investigated in undercooled gallium and under-cooled Ga-In alloy of eutectic compositian to examine structural changes in undercooled melts. A continuous linear extension of the resistivity was determined for 99.999 pct pure gallium when undercooled below the stable Ga(l)-liquid, and the metastable Gafl)-liquid equilibria. In icndercooled Ga-In, a significant continuous negative departure from linear resistivity behavior was observed below the eutectic temperature. All resistivity measurements were made by the four-point probe technique. ThE temperature range for investigations into the physical properties of liquids before freezing has been greatly extended with the undercooling of massive melts of pure metals and alloys. Experimental determinations of thermal and transport properties and diffraction patterns in undercooled systems should throw further light on the structural behavior of liquids. Many measurements showing prefreezing anomalies in viscosity1'5 have been regarded677 as evidence for structural groupings in the liquid state. However, the majority of viscosity results,~)~-~~ conforming to the law 17 =A exp(~/RT), do not support theories of atomic aggregation. For the system Cd-Sb, which exhibits a metastable solid phase, Fisher and Phillipsg reported that, in undercooled alloys, the activation energies for viscous flow below the stable liquidus are much higher than those above it. Similarly, Miller et a1." observed a doubling of the activation energies for electrical conductivity in undercooled Cd-ib alloys. These effects were suggested as indicative of atomic association and clustering in the liquids at lower temperatures. With the recent establishment of metastable phases in pure gallium22 and its alloys,23 attempts were made during this investigation to undercool bulk samples and to determine the temperature dependence of electrical resistivitv. Pure gallium, when undercooled below -17°C at atmospheric pressure, can crystallize to either a stable Ga(1) phase (mp, 29.78"C) or a metastable phase identi-

Jan 1, 1967

By W. A. Backofen, D. Lee

Titanium of commercial purity (RC-70) and two all-a (hcp) alloys (4Al-1/4O2 and 5Al-2.5Sn) were tested in sheet form under conditions of combined-stress loading. Plane-strain compression and plane -strain tension together with uniaxial compression and tension provided information for constructing the tension-tension and compression-compression quadvants of the plane-stress yield locus. Coordinate values were obtained from yield-strength measurements; the slope at each point was based on a plastic-strain ratio. The materials represented a wide range of plastic anisotropy, which was reflected in correspondingly varied departures of the yield locus from that for iso-tropy. The tension-tension and compression-compression quadrants were not identical. If the uniaxial yield strength is insensitive to direction and the sign of the applied stress, the Mises or perhaps the Tresca criterion is adequate for predicting the onset of yielding under combined-stress loading. The prediction is not so straightforward in plastically anisotropic material. Depending upon details of texture, combined-stress yielding resistance may be substantially different from that indicated by the usual criteria.' However. a continuum theory of yielding under such conditions is available for reasonably direct application.2,3 Whether or not it can be used successfully must, of course, depend upon how closely the conditions of the theory are satisfied in the material in question. In its present form the theory contains no provision for Bauschinger-type effects, nor does it allow for the consequences that might grow out of deformation by more than one mechanism, e.g., by slip and twinning.4 With those limitations, more importance must be attached to experimental information about the yield surface for anisotropic materials. Studies of the yield surface have generally been confined to states of plane stress (tension-tension and tension-compression) established in thin-wall tubes by externally applied forces and internal pressure. That approach would be entirely suitable for anisotropic materials if they were available in tube form or in sufficient bulk to be machined into test specimens. 6-9 It would not serve for the textured and anisotropic sheets of much current engineering interest, unless sheet could be formed into high-pressure tubing without structural change. Since there would seem to be little chance of the latter, practical alternatives are needed. One such alternative is the subject of this paper. It involves the use of a few selected but relatively simple uniaxial loading tests on sheet specimens. The underlying idea is presented here with some details relating to application and a few results bearing on how well it has worked. THE BASIS OF TESTING Conventional Measurements. Yielding for a general case of anisotropy is described by the plane-stress locus in Fig. 1. Reference directions in the sheet specimen are related to the stress coordinates as shown with the insert: x is the rolling direction, y the transverse direction, and z the through-thickness direction. The four reference-direction yield strengths (t, tension; c, compression), Xt, Xc, Yt, and Yc, are all different. Nine paths that can be followed in uniaxial loading experiments are identified. Paths 1, 2, 3, and 4 represent conventional tension and compression testing to establish Xt, Yt,.Xc, and Yc. Useful information also comes from the ratio of the transverse plastic-strain components associated with yielding and flow in conventional tension or compression. A condition to be satisfied in locus construction is that the plastic-strain vector be everywhere normal to the locus.10 The projection of the vector which would

Jan 1, 1967

By A. Lubinski, J. E. Hansford

Rotating drill pipe passing through dog-legs suffers fatigue damage due to cyclic bending stresses. Curves of the cumulative fatigue damage incurred in either steel or aluminum drill pipe going through Such dog-legs are presented. These curves provide means for properly planning the rate of angle build-up in directionally drilled wells and allow discarding of drill pipe which has been fatigue-damaged in dog-legs. INTRODUCTION Drill pipe which is subjected to bending as it rotates, experiences a cyclically varying bending stress. If this bending stress is sufficiently large, the drill pipe is fatigue-damaged by each revolution, and ages as fatigue damage accumulates. Drill pipe can be bent intentionally, as in the case of directionally drilled holes, or unintentionally due to unde-sired changes in hole direction caused by variations in formation properties, weight on bit, etc. These changes in hole direction, whether intentional or unintentional, are called dog-legs. The theoretical limits of dog-legs which are permissible before the drill pipe begins to fatigue can be calculated.' However, in wells where the maximum permissible dogleg is exceeded, the concept of cumulative fatigue damage can be used to estimate damage suffered by the drill pipe. This concept has already been used to estimate the cumulative fatigue damage of drill pipe due to drilling vessel roll.' The purpose of this paper is to extend the usage of the cumulative fatigue damage concept to drill pipe in doglegs, and to draw conclusions which may be beneficial in preventing numerous frustrating and expensive drill pipe failures. FATIGUE OF STEEL DRILL PIPE IN IDEALIZED GRADUAL AND LONG DOG-LEGS It is taken for granted that, if necessary, the reader will become familiar with the definitions and concepts which follow by examining the reference cited in each case. For Ref. 1, it will suffce to read only through the section Abrupt Dog-Legs. 1. Concept of the two extreme kinds of idealized doglegs: gradual and long dog-legs and abrupt dog-legs,' 2. Concept of why the bending moment in drill pipe un- der tension is the largest in the vicinity of the tool joint,' 3. Concept of why dog-leg severity which drill pipe can withstand decreases with an increase in tension,' and 4. Definition of the rate of change of over-all hole angle (dog-leg severity)." Figs. 1 and 2 indicate the aging (fraction of life expended) of steel drill pipe passing through a gradual and long dog-leg. Both figures have a left-hand ordinate scale labled Length of Drill Pipe Below Dog-Legs. This scale can be used for cases in which the drill collar weight is applied to the bit and does not contribute to the tension in the drill pipe. It can be used for either 3 1/2-, 4 1/2- or 5-in. drill pipe. This is due to the fact that, if the drill collars do not contribute to the drill pipe tension, then the effect of pipe tension on bending due to a change in pipe size is nearly compensated for by a corresponding change in pipe rigidity. On the other hand, if drill pipe is rotated off bottom, then drill collars contribute to the tension in the drill pipe and this increase in tension is not compensated for. In this case, one of the three right-hand ordinates must be used (the one which corresponds to the correct drill pipe size). In the right-hand ordinates, tension should be understood as the weight in mud of the portion of the drilling string below the dog-leg, minus the weight on bit.

Jan 1, 1967

By D. H. Forbes, I. B. Cadoff, H. M. Manasevit

Single-crystal silicon films have been obtained on several natural crystal faces of BeO using the thermal decomposition of silane and the hydrogen reduction of silicon tetrachloride. From an analysis of X-ray diffraction data it was determined that the following film-substrate orientation relationships exist: (111) Si 11(0001) BeO, (111) Si 11(1011) BeO, (100) Si 11f1010) BeO. and (110) Si 11(1010) BeO. An analysis of the crystallographic relationships between the film and substrate indicates that a match occurs between the silicon atoms in the film and the berylliuni ion sites in the substrate. This correspondence is in agreement with previous work on the deposition of silicon on sapphire.1-3 silicon on spinel: and tungsten on sapphire. The high resistivity, thermal conductivity, and radiation resistance of beryllium oxide make it an important substrate material for the deposition of thin films of silicon or other semiconductors. The importance of semiconductor-insulator composites to the field of integrated microelectronics has been well-documented in the case of silicon on sapphire.'-' The successful growth of large-area single-crystal silicon on an insulator, sapphire, was first reported in 1963.1,2 Since that time studies have been made of the crystallographic relationships between the deposited film and the sapphire substrate. On the basis of the observed relationships, a model has been proposed relative to the crystallographic requirements for epitaxy between the semiconductor film and the metal oxide substrate.3 It is proposed in this model that epitaxy is the result of a match between atoms of the deposited film and the metal ion sites of the substrate plane. This match is not limited to a 1 to 1 correspondence between sites in the two lattices. Sub- sequent studies of the deposition of silicon on spinel4 and tungsten on sapphire5 have yielded data which support this model. On the basis of this previous work it was felt that silicon on BeO should also fit this model. In the present study, the choice of substrate orientation was limited to the natural faces of synthetic BeO crystals. Of the faces available, the (0001) plane seemed the most favorable for epitaxial growth. EXPERIMENTAL PROCEDURE Silicon films were deposited from silane and silicon tetrachloride in the apparatus shown in Fig. 1. The hydrogen ambient gas was purified by passage either through a DEOXO unit, molecular sieves, and a liquid nitrogen cold trap, or through a heated Pd-Ag thimble. The gas was then mixed with the silicon source materiai and passed over the substrate which lies on a spacer above an inductively heated silicon pedestal. The following deposition conditions were used: a hydrogen flow rate of 3 liters per min with silane and silicon tetrachloride concentrations of 0.2 mole pct and a pedestal temperature of 1175" * 5°C as observed with an optical pyrometer assuming an emissivity of 1.0. Deposition was preceded by a 15- to 30-min hydrogen-etch period conducted at a temperature of 1275°C (obs). Adherent silicon films from 2 to 10 u were grown on the various BeO faces. The substrates were synthetically grown beryllium oxide single crystals ranging from 5 to 10 mm in

Jan 1, 1967

By R. B. Gordon, D. A. Koss

Ultrasonic-atlenuation changes due to the formation of free dislocations have been observed during tensile tests of magnesium and LiF single crystals and samples of polycrystalline Results on the LiF and samples are similar: A preyield attenzration increase is observed which, however, be-corlzes smaller as the magnitude of the drop in load al yielding increases. This indicates that the yield point observed in these materials is due to dislovation rather than dislocation unpinning and that the initial density ' free dislocations must be low if the yield point is to be sharp,. Tests on the magnesium ere conducted at both 27" and 200C. Magnesium has the unusual property that the yield drop is larger at the higher test temperature and is accomplished by a decrease in attenuation. The latter is due principally to the temprovary pinning of detained dislocations by highly solute atoms. After strain aging., a stress as low as 0.3 bur suffices to unpin dislocations; microstrain measuements of sufficient sensitivity should. reveal plastic flow at stress levels this low IN another paper,' we describe the technique of simultaneously observing ultrasonic-attenuation changes and plastic microstrain during deformation of spher-oidized carbon steels. Changes of ultrasonic attenuation indicate damping effects caused by the oscillation of long, freely moving dislocation segments. Simultaneous microstrain measurements are used to indicate total dislocation motion. The dislocation-damping observations are most useful in the study of the early stages of deformation where the dislocation density is low and the plastic strain is small and relatively difficult to measure. Particularly interesting results are found in materials which display sharp yield points. Observations of these phenomena are reported here for three materials: single-crystal LiF and magnesium, and poly crystalline molybdenum. EXPERIMENTS Dislocation-damping effects were observed by measuring changes in acoustic attenuation with the ultrasonic-pulse method. The end faces of each of the specimens were ground flat and parallel and a quartz 10 Mc per sec, x-cut transducer was attached to one face. The bonding agents used were: a) "Nonaq" stopcock grease with magnesium, b) beeswax with LiF, and c) salol with molybdenum. With the LiF, the best acoustic signals were obtained at 45 and 50 Mc per sec; all other measurements reported are at 10 MC per sec. The Sperry Ultrasonic Attenuation Comparator2 was used to measure attenuation changes. In the

Jan 1, 1967

By Wei-Kao Lu, G. Bitsianes

An improved general rate equation for a one-ditnensional gas-solid system has been derived. Fov the veversihle interfacial chemical reaction, there are concentrations of gaseous reactant and product at the reacting zone to be considered. They have been calculated with the velations fuvnished by the constraints on the system, namely, quasi-steady state and equimolal counterdiffusion of the gases. The results of the diffusiori study of Evans, Watson, and ,Mason based on the "dusty gas" model have been applied here. The interfacial chemical reaction is taken as first-order with respect to the concentration of the gases involved. The equation has proper dependence on gas composition and on solid structure through the relative values of Knudsen and normal diffusivities. The existence of the total pressure gradient inside the specimen has been predicted and confirmed experimentally. In a previous communication' we introduced a general rate equation for gas-solid reactions by considering the contributions of chemical reaction at inter- phase boundaries and diffusion through the solid product layer simultaneously. These equations, for one-dimensional and spherical specimens, take care of the whole range continuously from purely diffusion control to purely chemical reaction control. In this paper we study only the one-dimensional system. The corresponding rate equation is reproduced here: Of the two terms on the right-hand side of Eq. [I], the first represents the contribution of interfacial chemical reaction and the second that of gaseous diffusion. The shortcomings of Eq. [I] are that in its derivation the interfacial chemical reaction was assumed to be irreversible and the diffusion rate of gaseous product was not considered. Any pressure effects building up within the porous media were also neglected. Evidently. these simplifying assumptions will limit the general applicability of these equations. The rate of reduction of iron oxide by hydrogen, for instance, is very sensitive to the concentration of water vapor in the main gas stream, as has been reported by cewan' and by Quets et a1.3 Furthermore, the gaseous phase at the reacting interface will contain an appreciable amount of the gaseous product of reaction. If this were not true, a sufficiently high concentration gradient for the outward diffusion of the gaseous product could not be maintained. With these shortcomings in mind, Eq. [1I cannot be rigorously ap-

Jan 1, 1967

By Thomas C. Wilder

The concentration and activity of oxygen in liquid copper has been measured by the reversible galvanic cell: at 1100°and 1200°C for the concentration range of oxygen of 3 to 5600 ppm Measurements for approximately thirly alloys at each temperature indicate that the activity of oxygen roughly follows Henry's law, the activity coefficients of oxygen being 0.12 and 0.205 at 1100° and 1200°C, respectively. These results compare javorably with the results of seven other electrochemical and gaseous equilibrium studies on this system, the free energy of the solution reaction 1/2 O2 = O (7 at. pct in Cu, liq) being -18.10 * 0.30 kcal per gfw at 1200°C. Estimates of the standard molar free energy of formation of CupO(S) are also made. Praclicul consideration of this cell as an oxygen sensor for liquid metals is discussed briefly. SOLID mixed-oxide electrolytes which have a defect structure in the anion sublattice have recently become a very popular means by which the chemical potential of oxygen is measured at high temperatures. Since the pioneering work of Kiukkola and Wagner1 such electrolytes have been used in numerous cell studies for determining the thermodynamic properties of metallic oxides and oxy compounds, the partial pressure of oxygen in vacuum systems and other atmospheres, and the properties of oxygen dissolved in metals and alloys. The use of a solid electrolyte in a cell for a fast reliable method of oxygen determination in liquid metals would be a very important tool to the process metallurgist. In copper, for example, the oxygen content of the molten metal in the cathode furnace is a prime factor in determining the "set" or solidification profile of cast wire bars. In this investigation the activity of oxygen in liquid copper was measured by an electrochemical cell employing the electrolyte ZrO2 + 7 1/2 wt pct CaO. The cell used at 1100° and 1200°C was

Jan 1, 1967

By W. B. Hickman, J. J. Pickell, B. F. Swanson

Many physical properties of the porous media-immiscible liquid system are dependent upon the distribution of fluids within the pores; this in turn, is primarily a function of pore structure, liquid-liquiri interfacial tcnsion and liquid-solid wetting conditions. The cnpillary pressure hysteresis process provides a means of investigating the influence of pore structure upon fluid distribution for consistent sur/acc conditions. Invcstigntiot2s indicate that residual non-wetting-phase saturations /ollozuir,g the imbibition process (i.e.,wetting phase displacing nor2-wctting phase) are dependent upon both pore structure and initial non-raetting phase saturation and suggest that residual fluid is distributed as Discontinuous ,globules, one to a few pore sizes in dimension, thrnugh the entire range 01 pore sizes originally occupied. It clppears that air-mercury capillary pressure dala adequntely rellect the distribution of fluiris in a water-oil system when strong wetting condition preliczil. An oil-air counter-current imbibition technique has also been found to provide a rapid rneans of obtaining residual-initial saturation data. In a majority of cnses, rcsidual saturations detf-rniinecl from the oil-air or air-mercury process reasonably approximate residual oil saturation following water drive of a strongly water-wet medium. INTRODUCTION A reliable estimate of recoverable reserves depends not only on the amount of original oil-in-place but also on pore geometry and distribution of fluids within the pores. A critical parameter determining the recovery from a reservoir under waterflood, for example, is the amount and distribution of residual oil within the various rock types present. The purpose of this paper is to investigate the mechanism of capillary trapping and assess its importance in laboratory measureqents of residual oil saturation. The degree of wettability of a reservoir rock is recognized as an important factor in waterflood or imbibition experiments. In this paper, however, only the water-wet case has been considered. Considerable experimental evidence1 suggests that for water-wet rocks, capillary forces predominate in tile distribution of fluids and that viscous forces in the range normallv of interest in the reservoir have a minimum influence on residual oil saturation. It follows that if the ultimate recovery is controlled by pore geometry, a unique residual non-wetting phase saturation should exist for a given set of initial conditions. Two laboratory procedures.found to be extremely useful in the study of pore structure and degree of fluid interconnection at various saturations are decribed. Although air-nercury capillary injection curves have been used2 previously to characterize the drainage case, the withdrawal or imbibition case can provide valuable supplementary data. The air-mercury process, however, has several disadvantages; it is difficult to run in a sufficiently accurate manner, mercury does not always act as a strongly non-wetting liquid and in the air-mercury process the sample is rendered unsuitable for future analyses. An alternative process is described in which air is the non-wetting phase and naptha, hentane, octane or toluene is the wetting phase. INTERFACIAL TENSION AND CAPILLARY PRESSURE Interfacial tension between immiscible fluids is due to the difference in attraction of like molecules as compared with their attraction to molecules of the neighbouring fluid. This net attraction results in a tension at the interface. To extend the interface; thus, interfacial tension s can also be thought of as free surface energy. Interfacial tension is normally expressed as dynes/cm, and interfacial energy is measured in ergs/cm2 hence, both have dimensions ml A 2 and are numerically equal.

Jan 1, 1967

By T. J. Smolik, Harman, D. W. Fuerstenau

By means of electrokinetic measurements, the surface properties of the aluminosilicate polymorphs (sillimanite, andalusite, and kyanite) and also mullite have been found to depend on the ratio of A10 bonds to SiO bonds in the surface. The Al-toSi ratio in the surface is dependent upon the crystal lographic properties of the mineral, which in turn determine coordination numbers of A1 and of Si, cleavage characteristics, and density of the various solids. Mullite with a greater bulk Al-toSi ratio has the highest zpc of the aluminosilicates. By treatment in dilute acids or by cycling between acidic and basic solutions, alumina is selectively dissolved from the surface of these orthosilicates. This shifts the apparent zpc to lower pH values as the fraction of SiO groups in the surface increases. Thus, surface properties can be altered by procedures that alter the A l-to-Si ratio in the surface. Flotation of these aluminosilicates results from electrostatic interaction of the collector ions with the mineral surfaces. As a result, flotation response shifts in accord with any shift in apparent zpc by pretreatment. Separation of minerals by flotation is based on differences in the physicochemical properties of their surfaces.'-3 For many minerals, adsorption of flotation collectors results from their functioning as counter ions in the electrical double layer at solid-water interface. In such systems, separation depends on differences in the zero point of charge (zpc) of the various minerals. The zpc is defined as the concentration of potential determining ions in solution at which the surface is uncharged. The potential determining ions for inorganic oxide-water interfaces are hydrogen and hydroxyl.4,5 This work is concerned with the effects of crystal structure, composition, and surface preparation on the surface properties and flotation behavior of aluminosilicates. Differences resulting from crystal structure were studied by measuring electrokinetic potentials and determining the flotation behavior of three different aluminosilicate materials having the same chemical composition (Al2O3 SiO2), namely andalusite, kyanite, and sillimanite. Furthermore, the effect of the Al2O3-to-SiO2 ratio on flotation behavior and surface properties was investigated by including synthetic mullite, 3A12O3 .2SiO2. Gaudin and co-workers 6,7 have clearly shown how crystal structure determines the native floatability of certain minerals. Those solids in which the surface is comprised mainly of broken residual bonds possess naturally hydrophobic surfaces. It was found by Bakakin8 that for a number of oxidized lead minerals, differences in floatability were due to the distance of Pb atom from the surface. Only limited work has been done on relating electrical properties of surfaces to crystal structure and composition. Healy et. a1.9 found that the zero points of charge of various manganese dioxides ranged from about pH 1.5 to pH 7.5, and these differences in the zpc's were interpreted in terms of the atomic packing in the various crystals. The research presented here clearly shows that crystal structure and chemical composition do affect the surface properties of aluminosilicates and, in addition, that these effects can be altered by changing conditions under which the surfaces are prepared. CRYSTAL STRUCTURE OF THE ALUMINOSILICATES Sillimanite, andalusite, and kyanite are composed of regionally metamorphosed rocks differing mainly in degree of metamorphism. All three minerals have the same chemical composition, Al2O3 - SiO2, of which sillimanite is the high temperature polymorph and kyanite and andalusite the lower temperature polymorphs. Andalusite and sillimanite crystallize in the orthorhombic system while kyanite crystallizes in the triclinic system. The structure of these three minerals is essentially chains of aluminum-oxygen octahedra linked laterally by silicon and aluminum. The arrangement of these chains in the three minerals is shown in Fig. 1.l4

Jan 1, 1967

By W. M. Yim

Experimental results are presented which indicate that transverse striations in horizontal zone-leveled Bi-Sb alloy crystals are due to irregular growth rate resulting from thermal fluctuations in the melt (Iring gowth. Thc thermal fluctutations arose from two different sources. The first type was brought about by periodic fluctuations in the furnace temperature. The second type can be attributed to turbulent therrrol conlcclion in the trzelt near the solid-liquid inteyace. Tile arrzplitlcde ond fvequency of the tetiperaticre fluctlrations vesultity from llle lhevnal con1,ecrrell. The striation spacings in Lhe crystals covvelale well with the periodicity 0.f the tempevature flueluatiors. Altliough the strialiors represenl corrlpositiozul inhoiHogeneity oh a rzicroscule, less than f.z cil. be1 S6 in Best's as deterrirzed by electron-pro be chalq'sis, the slriations roerre fbund to ILUL' no rrleusuanble effect on electical vesistirity rwr on weak field macgnetoresistance of. the Bi-Sb a1lu.y in the ternpevutue ),unge 4.Polo 300°K. DURING the course of an investigation on the horizontal growth of semimetals,' it was found that crystals of Bi-Sb alloys contained many closely spaced parallel arrays of striations. These striations occurred perpendicular to the growth direction and parallel to the solid-liquid interface. We shall refer to them as transverse striations, or just striations'', to distinguish them from lineage substructures or longitudinal striations which form parallel to the growth direction and have been known to be associated with cellular structures.' Similar transverse striations have been reported previously to occur in other materials prepared by horizontal growth: metals,4 semiconductors,5 as well as their alls. - Various methods of crystal preparation have apparently little effect on the occurrence of the transverse striations. They form whether the crystals were grown by the vertical Czochralski technique, withe1' or without'3- rotation, or by the horizontal zoning methd.- Thus, the transverse striations are not limited to any one class of materials, nor to any particular method of preparation. It is likely, therefore, that all of the observed transverse striations may have some common cause. Previously, workers agreed that periodic changes in the growth rate bring about the striations. However, no agreement exists as to the origin of the growth-rate fluctuations. Some attributed the discontinuous growth to a purely external cause, such as fluctuations in the furnace temperature, jerky motions in the crystal pulling mechanism, or a nonsymmetrical temperature distribution in the melt (in the case of crystals grown by the Czochralski technique with rtation). Others looked for the cause in some fundamental property of the growth process itself. For instance, a certain degree of supercooling is required to initiate growth from the melt. But, with further growth, the degree of supercooling decreases because of the liberation of the heat of solidification at the solid-liquid interface. Thus, crystal growth would be brought to a halt until sufficient supercooling is resotred and the cycle begins again.3'11 According to this model, periodic fluctuations in the melt temperature should exist at the solid-liquid interface. Since the periodic fluctuations in growth rate would result in changes in the segregation coefficient of solute atoms, crystals containing the transverse striations may, in some cases, show a periodic impurity fluctuation along the length, resulting in a degradation of electrical properties. The resistivity striations in doped germanium'9-10 or lnsbB are well-known examples of this microsegregation. The present work was undertaken to explain the exact origin of the transverse striations, and to assess the extent of their effect on chemical homogeneity as well as on electrical properties of Bi-Sb alloy crystals. Results from our previous study of the crystal growth of Bi-Sb alloys1 indicated that the transverse striations may arise from the temperature fluctuations in the melt during growth. This paper will show that the melt temperature fluctuations are indeed responsible for the occurrence of the transverse striations. I) EXPERIMENTAL Although the transverse striations have been observed in all slow-grown Bi-Sb alloys across the entire compositional range, we selected a composition, Big3Sbs, for the present study in view of the extensive data available on the crystal growth of this alloy from a previous study.' High-purity bismuth and antimony, both a 6-nine grade by the manufacturer's emission spectrographic analysis, were used throughout. Independent mass-spectrographic analysis showed, however, that the starting materials were more nearly a 5-nine grade. each containing metallic impurities of approximately 10 ppm atomic. In zone-leveled Big5Sb5 alloys, the total metallic-impurity content was slightly lower, about 7 ppm atomic, indicating that some degree of purification was achieved during the growth. None of the electrically active impurities, such as tin and lead (acceptors) and tellurium and selenium (donors), were present in significant quantity in undoped Bi95Sb5. Typical analysis of the undoped Bi95Sb5 alloy is shown in Table I. Nonmetallic impurities, such as carbon and oxygen, were detected, sometimes as much as 100 ppm, in both the starting materials and the zone-leveled alloys: but the data were only qualitative. Temperature fluctuations in the melt were monitored over 1 or more days by means of a 5-mil chromel-

Jan 1, 1967

By N. Mungan

Laboratory imbibition and displacement experiments were performed using crude oil and cores drilled with water and preserved under anaerobic conditions. The purpose of these tests was to determine reservoir rock wettability and to find out if more oil could be recovered by use of NaOH solution than by conventional waterflooding. The preserved cores were found to be oil-wet. Contrary to work in the literature, these cores changed to water-wet upon contact with air. After exposure to air for a week, the cores yielded more oil by waterflooding than when preserved under exclusion of air. At reservoir temperature of 160F, flooding the preserved cores with 0.5N NaOH solution recovered more oil than an ordinary wa-terflood, and additional oil when following a waterflood. When the caustic solution was used from the beginning, all the extra oil was obtained before breakthrough; when the caustic followed a conventional waterflood, the extra oil was produced in the form of an oil bank ahead of the injected caustic. The increase in oil recovery resulted from wettability reversal. Also, use of caustic reduced the volume of injection required to flood out the cores. At room temperature, however, the caustic solution did not reverse the wettability and gave no additional oil recovery. Cores which had become water-wet by air exposure or caustic flooding were restored to their original oil-wet state when saturated with crude oil and allowed to equcilibrate at reservoir temperature for two weeks. Therefore, in the absence of preserved cores, it may be possible to restore weathered cores to their original wettability for use in laboratory floods. INTRODUCTION Waterflooding has been in use since 1865, and is by far the simplest of secondary recovery methods. Unfortunately, most waterfloods are inefficient in recovering oil, often leaving half or more of the original oil in place un-recovered. The low oil recovery generally results from low sweep efficiency and low displacement efficiency. Consequently, to increase oil recovery by waterflooding, sweep and displacement efficiencies should be improved. Sweep efficiency is primarily affected by reservoir heterogeneities and mobility ratio, while displacement efficiency is affected by the capillary forces between fluids and rock surfaces. For petroleum reservoirs, the capillary forces are expressed in terms of interfacial tension and wettability. If oil recovery is to be improved significantly in water- flooding, the capillary forces holding the oil in the raervoir porous matrix must be reduced or eliminated. One way to reduce capillary forces is to inject commercial surfactants ahead of the injection water into the reservoir. Laboratory tests of this method have shown no promise of an economical process yet, and no increase in oil recovery was obtained in the field trials which have been reported. Work is continuing in many companies to find surface-active agents which, in workable concentrations, can yield substantial added oil recovery. Another way to change capillary forces operating in petroleum reservoirs is by changing the pH of the injected water. Wagner et al.' showed that change in the pH sometimes activates the surface-active materials natural to some crudes and brings about gross wettability change. Since pH alteration can be obtained with cheap chemicals, such as hydrochloric acid or sodium hydroxide, the process shows promise of being economical in a field application. Pan American Oil Corp. reported oil recovery by use of caustic solution from a flooded-out reservoir.' Their test, conducted at a small additional cost, yielded results which were so sufficiently favorable and encouraging that the wettability reversal flood was expanded to portions of the field not previously flooded.13 It is important to bear in mind that changes in the pH of the water not only can reverse wettability but also can lower the interfacial tension between water and crude oil. Reisberg and Doscher4 have studied the pH dependency of the interfacial tension of Venture crude using sodium hydroxide solutions of various concentrations. Their data show that the interfacial tension was lowered from 23.0 to 0.02 dynes/cm by increasing the NaOH concentration from 0.005 to 0.5 per cent by weight. Thus, the use of NaOH may lead to additional oil recovery due to both wettability reversal and lowering of interfacial tension. Whether alteration of pH results in wettability reversal from oil-wet to water-wet and increases oil recovery depends on wetting properties of the reservoir rock and the crude. This necessitates delicate laboratory experiments, with suitable core and fluid samples from a field. Although many investigators have studied wettability reversal floods in the laboratory,1,2,5,6 these studies have been carried out with synthetic porous media, refined laboratory fluids and surface-active chemicals to simulate the process. The study presented in this paper is the first time that wettability reversal by pH alteration has been accomolished in laboratory core floods using carefully preserved natural cores, live crude and with experiments performed at reservoir pressure and temperature.

Jan 1, 1967

By J. E. Hanlon, J. D. Wolf

The relaxation peaks observed in plastically deformed materials at low temperatures have been reviewed by sack1 and Niblett and wilks. 2 In particular, the dislocation-relaxation in columbium has received considerable study.3-6 The present work deals with the lower-temperature dislocation-relaxation peak (referred to by Chambers and Schultz as the a peak) in columbium and Cb-5 pct Zr. The columbium and Cb-5 pct Zr specimens were machined to 3/8-in.-diam by 7-in.-long rods from bars hot-extruded at 1200°C. The internal friction and resonant frequency of the samples were measured in torsion at kilocycle frequencies at a maximum strain amplitude of -10-6. The interstitial content of both materials was approximately 70 ppm N and 200 ppm 0. The dislocation-re laxation peaks were measured in the hot-extruded state and after successive anneals. Fig. 1 is a compilation of the data. The resonant frequencies for the columbium and Cb-5 pct Zr samples were, respectively, 5.5 and 6.5 kc. Other workers have noted that the dislocation-relaxation peaks in columbium are not characteristic of a single relaxation time. As can be seen in Fig. 1, the zirconium addition further broadens the spectrum of relaxation times. The magnitude of the modulus defect as computed from resonant-frequency data also reflects this extension. The occurrence of the low-temperature a peak at a position 20°K higher in Cb-5 pct Zr as compared to pure columbium, in the hot-swaged state, suggests a decrease in the average dislocation mobility for the alloy. The authors do not feel that these data are sufficient to permit an interpretation in terms of any detailed models.

Jan 1, 1967

By R. M. Lumley, J. D. Wood

In this investigation, polyethylene terephthalate (Mylar) was coated with various thicknesses of a vapor-deposited silvel- precoat followed by a uapor-deposited zinc using several orders of- magnitude variation in deposition rate of both the silver and zinc. The grain size and resistivity of the zinc film was primarily a function of the silver precoat thickness (in the range of 0.001 to 10 average Agprecoat thickness) and a secondary function of the zinc film thick-ness. The silver and zinc deposition rates were found to have a minor effect on the characteristics of- the zinc film. Electron and X-ray dilffraction results slwwed that all zinc films exhibited a fiber texture mith the (0001) axes essentially perpendiculav to the platze of the film When coating nonmetallic substrates such as paper or plastics with zinc metal vapors, it is found that the zinc will not condense unless extremely high evaporation rates or very low substrate temperatures are used. In 1931, Fraser' reported a procedure whereby zinc could be made to condense on nonmetallic substrates by depositing a very thin precoat of silver. Utilizing Fraser's method, the ermans' developed a commercial process of making "metallized film" capacitors during World War 11. The metallizing process, which was introduced in the United States shortly after the conclusion of World War 11, became one of the first large-scale commercial applications of vapor-deposited metal films and remains one of the larger applications in the electronics industry. The process, as developed by the Germans, consisted of depositing a thin precoat of silver on lacquered, kraft paper followed by a conducting layer of zinc. The resulting silver-zinc film was used as the capacitor The term silver-zinc will be used throughout thiz paper to mean a metal film formed by an extremely thi layer of silver, 10A or less in average thickness, and a zinc film IOOA or more in thickness deposited on the silver film. ---. electrode with the lacquered paper being the dielectric. When polyethylene terephthalate was marketed by E. I. Du Pont Co. in the early 1950's under the trade name Mylar it was substituted for the kraft paper in many capacitor applications. Even though manufacture of metallized paper and metallized Mylar capacitors has been a large commercial process for many years, little information has been published about the deposition parameters. Correlating the work of others to the various effects to be expected of deposition parameters on silver-zinc films deposited on Mylar, it is expected that the

Jan 1, 1967

Jan 1, 1967

By L. C. Brown, C. St. John, C. C. Sanderson

The diffusion rate in Cu-Te couples is very sensitive to compressive stress, with a load of 20 psi making a significant difference to the width of the diffusion zone. At zero stress, two phases appear in the diffusion zone (Cu4Te3 and CuTe). Under compressive loading the third stable phase (Cuz Te) also appears, and its thickness increases progressively with increasing stress. The results are explained on the basis of an incipient Kirkendall porosity which restricts the transfer of atoms from the copper into the diffusion zone. DURING a study of the Kirkendall effect in Cu-Te couples prepared by clamping together the two components, it was found that the diffusion-zone width and shape in the plane of contact were not reproducible. Although the stresses involved in clamping are not normally sufficiently high to affect diffusion rates, preliminary tests established that the Cu-Te system is particularly stress-sensitive. The phase diagram for the system Cu-Te given in Hanssen1 shows that there is practically no solid solubility at either end of the phase diagram. Many areas of the diagram are not fully substantiated, but there appear to be three intermediate phases: Cu,Te—hexagonal in structure, having a grey luster; Cu4Te3—a tetragonal defect structure, having a red-purple luster; CuTe—orthorhombic in structure and having a golden-green luster. The existence of a fourth phase, the X phase at 37 at. pct Te, is considered doubtful. The composition ranges of the three stable phases are small, and are not accurately known. The phase diagram changes little with temperature up to 305°C, at which temperature a polymorphic transformation takes place in Cu2Te. The nature of the Cu-Te phase diagram indicates that the diffusion zone in a Cu-Te couple would consist of a series of layers of intermediate phases. The relative thickness of any one phase will depend on its diffusion coefficient and composition range.' In this type of diffusion couple it is often found experimentally that some phases are not visible at all in the diffusion zone due either to a small diffusion coefficient or to a restricted composition range.3 Since the composition ranges of the phases in Cu-Te are not known, it is not possible to determine diffusion coefficients in this system from a knowledge of the phase thicknesses. Several investigations have been carried out to determine the effect of compressive stress on diffusion rates in multiphase systems. Diffusion couples of Ni-A1 have been investigated by Storchheim et al.4 and by Castleman and Seigle.5 Two phases (ß and ?) appear in the diffusion zone under zero stress and the thickness of both phases is progressively reduced with increasing stress. According to Storchheim et al.4 a stress of 25,000 psi reduces the thickness of the diffusion zone by 50 pct. In a-brass—?-brass couples the thickness of the 0 phase formed in the diffusion zone was reduced by 20 pct at a stress of 20,000 psi.6 In other investigations the compressive load has been observed to increase the width of the diffusion zone. In A1-U, several investigators3,8 have found the width of the whase UA13 to increase with stress. According to casileman,8 the rate of formation of UA13 at 520°C is 75 pct faster at a stress of 20,000 psi as compared with a stress of 2500 psi. In Cu-Sb the effect of stress is greater than in the other systems described. According to Heumann9,10 only one phase (y) appears in the diffusion zone at a stress of 500 psi, but at a stress of 850 psi two phases (y and k) are present. If a diffusion couple containing both y and k phases is annealed at a low stress level, the y phase grows at the expense of the k phase. EXPERIMENTAL The diffusion couples were prepared from electrolytic copper bar stock with a nominal purity of 99.92 pct and from tellurium of 99.7 pct purity. The tellurium proved difficult to machine because of its brittleness and a technique was developed for casting the tellurium into a graphite slab mold and spark-machining specimens from this slab. Both the copper and tellurium were produced in the form of discs 2 in. diam by approximately 1/4 in. thick with surfaces ground flat to 3/0 emery paper. The diffusion apparatus is shown in Fig. 1. Auni-axial compressive stress was applied to the system through a simple lever system. A stainless-steel rod actuated by the lever arm lay inside a stainless-steel tube. The diffusion couple lay on top of the steel rod, and pressure was applied to the couple between the rod and a plug welded into the center of the tube. To ensure a uniform stress across the couple, a hemispherical boss and cup were used to transmit the load to the diffusion couple. A 400-w tube furnace with a uniform hot zone 3 in. long slid around the stainless-steel tube and maintained the assembly at temperature. A thermocouple situated 3 in. from the specimen operated a proportional temperature controller which maintained the specimen temperature constant to ±2°C. Most diffusion runs were carried out at 250C although a few tests were made at other temperatures in the range 235° to 300°C. The specimens were inserted and removed with the furnace at operating temperature, and took only 2 min to reach diffusion temperature—a time small compared with the total diffusion time. All the diffusion experiments were carried out in a hydrogen atmosphere, since consistent results were obtained in hydrogen and nitrogen atmospheres and in

Jan 1, 1967

By A. Raja, C. C. Harris

Apparatus for maintaining constant — but adjustable — pulp level and rate of froth removal are described. The results of preliminary experiments into the effect of scraping speed on the rate of solid and liquid recovery with a semi-batch system are presented. Glass spheres restricted to a narrow size range is the solid under investigation. Graphical methods for estimating the mass of recoverable material and the zero error are given. The semi-batch procedure1 is extensively used in laboratory flotation testing, though the method is subject to variability of moderate severity. Raffinot2 concluded from a statistical study of the difference between replicate tests, that the ptincipal source of errot was the test itself and not sampling or chemical analysis. These differences can be ascribed principally to changes in pulp volume and reagent concentration, and uncontrolled rate and depth of scraping. Semi-batch testing has been criticized1 on these grounds as a means of investigating flotation kinetics. This paper discusses and describes modifications to laboratory flotation equipment which reduce the number of manual operations and lead to improved control. Kinetic studies were the primary reason for developing the apparatus described. It should, however be a useful aid in normal flotation testing. Some preliminary results of experiments are presented.

Jan 1, 1967

By E. R. Gilbert

Klopp et al. have reported data on tensile and creep properties of are-melted and electron-beam-melted tungsten. We would like to point out some similarities between their creep results and ours on are-melted and powder-metallurgy tungstenand offer some alternate interpretations of the data which lead to different rate-controlling mechanisms. Klopp et al. observed extensive transient creep in the 2250" to 3500°F temperature range where the acthetivation energy is 106,400 ± 3300 cal mole-1. They suggest cross slip as the possible rate-controlling mechanism since "cross slip may occur only by the movement of screw dislocations, and not edge dislocations, thus allowing only partial recovery of the strain hardening and resulting in a continuously decreasing creep rate, characteristic of transient creep.'' Our tests on are-melted tungsten and powder-metallurgy tungsten displayed an extensive transient creep stage in the same temperature range but they also displayed a steady-state creep stage. The stress levels and strain rates of the two investigations, 1.4 to 7 kg mm-2 and 10-7 to 10-4 sec-1 for that of Klopp et al. and 4.5 to 10 kg mm-2 and 10-8 to 10-4 sec-1 for those of Gilbert et al., are overlapping. The activation energy for creep of our powder-metallurgy tungsten is 105,000 cal mole-1. This close agreement with the value found by Klopp et al. suggests that the same mechanism may be common to both types of materials. It may be possible to gain some additional insight into the rate-controlling mechanism by applying the analysis made by conrad22 in terms of the activation volume. The value for the activation volume depends upon the dislocation mechanism and may be used to help differentiate between various dislocation mechanisms. The activation volume for cross slip is 10 to 100 b3. Values determined from our data were 130 to 220 b3 which are in better agreement with the range of 102 to 104 b3 for nonconservative motion of jogs. Values determined from data of Klopp et al. are 240 to 1040 b3. We suggest that the rate-controlling mechanism for creep in this temperature range may be nonconservative motion of jogs assisted by enhanced diffusion along grain boundaries or dislocations. This model requires an activation energy lower than that for self-diffusion as is observed. If this is the controlling mechanism, a higher activation energy which is closer to that for self-diffusion might be expected for tests conducted on specimens with reduced grain boundary area, i.e., larger grain size. In support of this premise we have conducted tests on speci- mens having one to three grains per cross section for which a higher activation energy of 130,000 cal mole-1 was observed. Also, in agreement with results of Klopp et al., a faster creep rate resulted from the increased grain size and probable decreased dislocation density. Further argument against the cross slip mechanism is based on the constant activation energy we obsserved over the range of 5.0 to 10 kg mm-2,21 whereas the activation energy for cross slip displays a significant stress dependence.23 In addition to this, the powe on the stress term for the strain-rate dependence appears too high for cross slip. The values for tungsten fall in the range of 4.5 to 7 (Klopp et al. and Ref. 21) whereas values of approximately 2 are observed in creep by cross slip for hep metals.24 At temperatures from 3300° to 4000°F, Klopp et al. observed an activation energy of 141,000 ± 4000 cal mole-' which is less than that for self-diffusion, 153,000 cal mole-1, 25 and less than that reported for high-temperature creep of powder-metallurgy tungsten by Green:' 160,000 cal mole-1. Klopp et al. suggested that recovery of strain hardening by dislocation climb is the rate-controlling mechanism in this temperature region. Actually an activation energy larger than that for self-diffusion is predicted by this model if the temperature dependence of the elastic modulus27 is taken into consideration. Klopp et al. attributed this lack of correlation to the compositional differences between powder-metallurgy tungsten used by Green and their own arc- and EB-melted tungsten. It is our position that the value of 141,000 ± 4000 cal mole-' represents a transitional value between the higher and lower activation energies and does not represent a discrete mechanism of deformation. If the tests had been extended to higher temperatures the higher value of activation energy would have been observed as has been demonstrated by both our analy sis'' of isothermal test data by GE-NMPO28 and differential temperature tests28 on are-melted tungsten. The activation energies determined (170,000 and 160,000 cal mole-1) were greater than that for self-diffusion and are in better agreement with the value found by Green. The model of dislocation climb is associated with ; activation volume of 1 b3 according to Conrad.22 The activation volume calculated for the creep data of fou independent investigators in the temperature range where the activation energy for creep is near that for self-diffusion (Klopp et al. and Refs. 26, 28, and 30) is 110 to 2800 b3 and is in the range suggested for nonconservative motion of jogs. In the case of tungsten this mechanism may be preferred over that of dislocation climb. Sincere appreciation is expressed to Messrs. J. E. Flinn and F. L. Yaggee for the helpful discussions and suggestions in the preparation of this communication.

Jan 1, 1967

By J. L. Huitt, B. B. McGlothlin

The introduction of new fracture propping agents that are brittle but much stronger than sand created the problem of what loading strength is required for a propping agent to be effective in a given formation. It is shown that the load at which the propping agent crushes should exceed the load at which total embedment in the fracture faces is possible. Simple laboratory tests to determine loading strength of the propping agent and embedment in the fracture faces, and use of these data in selecting a propping agent for a given formation, are discussed. INTRODUCTION One of the most important factors in the design of hydraulic fracturing treatments is the selection of a propping agent that can effectively provide the fracture flow capacity needed for stimulation of a well. Sand, once generally accepted as being synonymous with propping agent in hydraulic fracturing, is now recognized as having limited effectiveness in many formations because of its low resistance to crushing. Sand particles are brittle and have relatively low strength. Because of this property, sand particles are crushed in rocks that offer high resistance to the penetration of fracture faces by the proppant particles when the fracture attempts to close under the action of the overburden load. For rocks that offer a high resistance to penetration, deform able particles are more effective propping agents than sand. However, for this same type of rock, a propping agent that does not deform, yet does not crush, is often more effective. Thus, a rigid propping agent with sufficient strength to prevent crushing is desirable. A method for determining the strength required for a rigid propping agent to function effectively in given formations is discussed. BEHAVIOR OF RIGID PROPPANTS AND FRACTURE FACES RELATED STUDIES An early qualitative description of the reaction of propping sand in fractures was given by Hassebroek et al.' In discussing fracturing in deep wells, the authors mentioned that even though propping sand entered the fractures, a high flow capacity did not result due to crushing or embedding of the propping sand. Dehlinger et al.2 in discussing the reaction of propping sand surmised that, because of the hardness of sand particles, deformation occurred in the fracture faces contacting the propping sand. In later studies,3,4 methods of determining the embedment of propping sand in fracture faces of soft rock and the critical load at which propping sand is crushed by the fracture faces in hard rock were discussed. In working with de-formable proppants, Kern et al. considered proppant particles to be deformed into cylindrical disks by action of the overburden and then pressed slightly into the fracture faces by further action of the overburden. Rixie et al.'0 reported on embedment pressure and presented a method of selecting a propping agent for use in given formations. The propping agents included sand, walnut shells and aluminum pellets. All these studies have contributed materially to a better understanding of propping agent behavior; however, the strength of brittle proppants (sand, glass and ceramics) required to result in embedment rather than crushing has not been discussed. This topic will be covered in the ensuing discussion. PROPPANT PARTICLE CRUSHING—-EMBEDMENT For this discussion, a rigid propping agent is considered to be one that is brittle and fails under tensile stress when loaded to a critical value. In an earlier study4 it was shown that the Hertzian4 loading theory could be applied to a spherical brittle propping agent if the propping agent and fracture faces behaved elastically. At the failure of the proppant, the ratio of the load to the square of the diameter of the particle should be constant for a given material combination, or: Lc/dp2=C ............(1) A partial derivation of this equation from proppant and formation properties is included in the Appendix. Should a rigid particle not be crushed as a load is applied, it embeds in the fracture faces. A study3 of particle embedment in fracture surfaces has been published. The embedment can be described by an equation based on Meyer's metal penetration hardness relationships: d1/dp=B 1/2[L/dp2]m/2..........(2) In Eq. 2, B and m are constants that are characteristic of the rock; the significance of the other terms is shown in Fig. 1. A STANDARD DEFINITION FOR PROPPANT LOADING STRENGTH Eq. 1 is useful in appraising propping agent strength," but it is strictly applicable only when the area of contact between a particle and a fracture face (or loading plate)

Jan 1, 1967

By S. Leber, R. F. Hehemann

Diffusion coefficients for the Cb-W system were measured using couples prepared from poly crystalline, commercially pure metals. The diffusion coefficients, measured in the temperature range between 1700° and 2300°C, decreased exponentially as the tungsten concentration was increased from 0 to 50 at. pct, then decreased abruptly at higher concentrations. A decrease of two orders of magnitude was observed over the entin? compositional range. The diffusion coefficients were in the range defined by the self-difiusion coefficients of the individual elements, indicating their general validity. An activation energy of 60,500 cal per mole was measured for the 20 pct W composition. Such low values, when compared with energies over 100,000 cal per mole for the pure constituent elements, indicated that transport mechanisnzs more rapid than volume diffusion were contributing substantially to inter dijfusion. Difference should, therefore, be expected between these data and the intrinsic diffusion coefficients. These differences should be significant in the kinetics of 'transport phenomena in practical systems. CONSIDERABLE attention has been devoted in recent years to the mechanical behavior and other properties of the refractory metals and their alloys. The Cb-W system has been of special interest as a base for the development of more complex compositions of commercial interest. In spite of the importance of mass transport to all aspects of elevated-temperature behavior, and especially to the production of alloys by powder-metallurgy techniques, little attention has been paid to diffusion in the Cb-W system. Results from a previous study of this system1 appeared to be anomalously high. The present investigation is, therefore, an attempt to obtain more accurate diffusion coefficients in this system. Intrinsic diffusion coefficients, of primary importance from the theoretical viewpoint, can only be obtained accurately from studies utilizing compositional gradients approaching zero. However, many practical problems involve diffusion under significant concentration gradients. The diffusion coefficients determined in this investigation were, therefore, obtained from couples prepared from elemental metals. The data obtained should be of value in the analysis of problems such as homogenization during powder-metallurgy alloying or reactions between base and clad in coated structures. In this vein, the investigation was conducted on poly crystalline materials of commercial purity. PROCEDURE Diffusion couples were prepared by sandwiching a columbium sheet between two sheets of tungsten. The composite was welded around all edges, the tungsten forming a protective can for the columbium. The composite was soaked for 4 min at 1600°C in a hydrogen-atmosphere furnace, quickly forged to 40 pct reduction in thickness, and then rapidly cooled to room tempera-

Jan 1, 1967