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By J. M. Smith, D. Kunii

Effective thermal conductivities of sandstones filled with stagnant fluids were measured using a steady-state technique. Data were obtained for seven sandstone samples, taken from four different locations and ranging in permeability from 18 to 590 md. The measurements with gases (helium, nitrogen, air and carbon dioxide) covered a pressure range from 0.039 psia to 400 psig. Data were taken for four liquids — n-heptane, methyl alcohol, 79.8 weight per cent glycerol-water solution and pure water at atmospheric pressure. The experimental results were used to evaluate the theoretical equations for predicting stagnant conductivities developed earlier 4 The low-pressure measurements permitted evaluation of the consolidation parameter bpDp/ks (necessary to utilize the theory) for the various types of sandstones. Using these characteristic values, the tbeoretical equations correlated well with the experimental conductivity data for the several fluids and rock samples. INTRODUCTION An aspect of heat transfer in solid-fluid systems of considerable current interest is the effective thermal conductivity of porous media. The stimulus for study of the subject arises from the need for sound procedures for designing thermal methods of petroleum production. The general system occurs when there exists a flow of fluid through the pores of the solid material. However, a logical starting point in developing a theory for predicting the effective thermal conductivity in the general system is to attack the special case when the porous solid is filled with stagnant fluid. Since the flow rates anticipated in thermal production processes are very low, such stagnant conductivities k,O are also of practical significance. Kunii and Smith4 recently reviewed the existing data for stagnant conductivities and proposed a theory for heat transfer in porous rocks. This leads to equations for predicting the stagnant conductivity as a function of the properties of the fluid and solid phases. The existing experimental information1-3,5,7,8 covered a range of porosities and agreed well with the theory. However, the available data were insufficient to examine critically the effects of two important properties on koe, — the thermal conductivity of the fluid and the pressure. The objectives of the present study are twofold: (1) to measure the effect on koe of (a) the pressure for gases, and (L) the thermal conductivity of the fluid kg for bloth gases and liquids; and (2) to determine for rocks of different porosities and permeabilities the apparent solid conductivity ks and the consolidation parameter bpDp/ks required in applying the theoletical equations. Measurements extrapolated to zero pressure are helpful in evaluating ks and the consolidation parameter. However, the extrapolations must be based upon data obtained at low pressures because in small pores the molecular conductivity of the fluid may be unusually depressed. This occurs when the mean free path of the molecules is of the same order of magnitude as the pore diameter, that is, in small-diameter pores at low pressures. The phenomenon has been studied recently by Schotte6in beds of unconsolidated fine particles. With particles in the size range of 45 to 200 microns, a significant reduction of kg with pressure was found even at absolute pressures greater than 1 atm. In the sandstones employed in the present investigation, pore diameters lower than those experienced by Schotte are likely, so that the effect would presumably be greater. SCOPE OF MEASUREMENTS Stagnant conductivities were measured for four types of sandstones using a total of seven samples. The characteristics of the samples, including porosity and permeability values, are given in Table

By W. T. Turrall, M. J. Cook

A discussion of modern developments in beneficiation of fine sizes of anthracite, this paper includes a description of the plant flowsheet, an analysis of operating results, and a summary of fundamentals of mineral separation relative to plant operation. DURING the past several years Lehigh Naviga-tion Coal Co. has installed equipment at Tamaqua and Lansford collieries for cleaning and sizing No. 4 buckwheat —3/32 + 3/64 in. and for recovering and cleaning flotation coal —20 + 200 mesh at Tamaqua colliery. Papers describing some of these installations have been presented to AIME. At Coaldale colliery, however, methods used to clean fine coal were inadequate and inefficient. Management decided upon a thorough investigation of all existing processes before building a plant to treat the combined three sizes mentioned. Investigation, carried out on company property and at other plants, entailed a study of hydrotators, hydroclassifiers, tables, spirals, flotation machines, methods of screening, and methods of dewatering. On the basis of this investigation a flowsheet was designed which necessarily excluded many processes in use, and the writers wish to emphasize that no criticism is implied by omission of processes or machines. A determining factor in selection of many machines was the policy of standardizing equipment wherever possible. Flowsheet and Operational Data The first principle to be considered in designing of any plant is efficiency of cleaning as related to laws of classification. Beneficiation of coal may be described as separation of two materials having different specific gravities. Although there is an inherent ash content even in the purest coal which slightly affects its specific gravity, it is recognized that many particles are true middlings. The percentage of these particles allowable in the final product depends upon the ultimate ash, or specifications of the consumer. Richards in his study of free settling and hindered settling classification' determined that particles of equal size and different specific gravities had unequal settling velocities. He also determined a definite size relationship for equal settling velocities with free settling and hindered settling conditions. Considering the design of machines used to clean No. 4 and No. 5 buckwheat, it may be assumed that both free settling and hindered settling conditions exist and that ratio of size for practical operations is between the established values. The essential factor is that the more efficiently and closely sized the feed is maintained, the more nearly perfect the resulting separation. Flowsheet design was governed primarily by factors related to the 1200 to 1500 tons per hr feed to the main plant. It should be stressed that because of the many sources of supply from mine and stripping, the physical characteristics of this feed varied considerably. The most significant influence was varying percentage of fines, necessitating that all machines be capable of operating under maximum peak load during periods of surge. Since cleaning practice is a wet process, about 9000 gal per min containing 14 to 15 pct solids, or 350 tons per hr, must be treated. This slurry contained all the fines, or —3/32 in., but also percentages of oversize, up to 1 % in., dependent on spills or breaks in screen jackets, a not uncommon occurrence in preparation plant practice. The flowsheet developed is shown in Fig. 1. Circled numbers represent points of sampling. Table I gives operational data including size, ash by size, composite ash, rate of flow in gallons per minute, percent solids dry weight, and average tons of solids per hour. It should be noted that these results are subject to human error in sampling practice. Detailed information reported is a representative evaluation of plant operation.

Jan 1, 1954

By Henry A. Stiff, and Lawrence E. Davis

The authors previously presented a method for predicting the tendency of oil field waters to deposit calcium sulfate. The present paper gives a similar method for calcium carbonate. Methods for predicting calcium carbonate scaling tendencies in fresh waters have been available for some time, but these could not be used for brines. By experimentally deriving the value of the K term in the Langelier equation, a method has been developed which applies to waters of high salt content. A statistical study is included which shows that the experimentally derived values of K are in good agreement with actual conditions. Several applications of the final equation to production practice are given. INTRODUCTION The authors previously presented a method for predicting the formation of calcium sulfate scale in oil field waters.' Although calcium sulfate deposition is important in production operations, the majority of scale problems involve calcium carbonate. The present communication discusses a method by which the formation of this type of scale in oil field waters can be predicted. Calcium carbonate precipitation is caused by a shift toward carbonate in the carbonate-bicarbonate-carbon dioxide equilibrium. When equilibrium shifts in the other direction, the precipitate goes back into solution. Since there is usually considerable delay between the establishment of an equilibrium and the precipitation or solution of calcium carbonate, unstable conditions exist in which a water will precipitate or dissolve calcium carbonate on standing. Tillmans? who did a major part of the early work on carbonate scaling, pointed out that the condition of equilibrium not only indicates the tendency of a water to scale but also is an indication of its corrosive properties. Previously precipitated calcium carbonate combines with iron to form a dense crust which inhibits corrosion. If the water tends to dissolve carbonate, the scale becomes porous, and electrolytic corrosion takes place. Tillmans1 work was extended by several investigators until in 1934 Langeliers developed an equation setting forth the conditions of carbonate equilibrium. By the use of this equation the pH of a water at equilibrium can be calculated. If the actual pH is higher than the calculated pH, the water has a tendency to form scale. If it is lower. the water has a tendency to be corrosive. Langelier's equation can be expressed in a simple form as follows: SI = pH-pCa-pA lk-K where: SI is the stability index. A positive index indicates scale formation. A negative index indicates corrosion. pH is the pH of the water sample, as actually determined. pCa is the negative logarithm of the calcium concentration. pAlk is the negative logarithm of the total alkalinity. K is a constant, the value of which depends on the total salt concentration and the temperature. This equation has been shown to apply to waters with totaI solid concentrations as high as 4.000 ppm. In fact, control of fresh water treatment by means of this equation has been standard text-book practice for a number of years. Nomographs have been worked out so that the stability index of a fresh water sample can be determined in a matter of minutes. Most oil field waters, however, contain well over 4,000 ppm of salts and for this reason the usual application of Langelier's equation can not be made. By an empirical method we have extended the application of the Langelier equation to waters of high salt concentration. By the use of this equation the tendency of oil field waters to deposit calcium carbonate can be predicted.

Jan 1, 1952

By W. I. Duvall

A brief review of the resonant frequency and ultrasonic pulse methods for obtaining elastic constants of rock samples shows that the equations for an iso-tropic elastic solid commonly used to calculate Young's modulus, modulus of rigidity and Poisson's ratio can result in appreciable error if the rock is even slightly anisotropic. Consideration of the equations that relate bar velocities and free medium velocities to elastic constants for orthotropic, transversely isotropic and isotropic solids shows that a combination of the two methods can be used to determine average elastic constants for a single sample of rock. The determination of elastic constants in different directions requires a large number of tests on oriented samples. The use of both the resonant frequency and ultrasonic pulse methods is recommended so that the determination of both Young's modulus and modulus of rigidity is independent of the determination of Poisson's ratio. The dynamic elastic constants of rock can be determined in the laboratory from measurements on small samples which may be in the form of right circular cylinders (diamond drill core). Either the resonant frequency6 or ultrasonic pulse method1 can be used to determine the longitudinal and shear velocities in the same specimen. The resonant frequency method provides a measure of the longitudinal bar velocity, V,, and the torsional bar velocity Vt; whereas the ultrasonic pulse method provides a measure of the free medium longitudinal velocity, Vp, and the free medium shear velocity, V, . The elastic constants (Young's modulus E, modulus of rigidity G, and Poisson's ratio v) are calculated from the density of the specimen, p, and one of the pairs of velocities by means of equations from isotropic elastic theory. For the resonant frequency method the equations are: It should be noted that Eq. 5 is derived from Eq. 4 and 6 and the relation between the elastic constants for an isotropic solid as given by the first part of Eq. 3. The in situ determination of dynamic elastic constants is accomplished by generating a complex seismic pulse in the rock and measuring the arrival times for the longitudinal and shear phases of the pulse at two distant points.5 From these travel times and the distance of the travel path both Vp and Vs are determined. The density of the rock is determined from samples in the laboratory, and Eq. 4 to 6 are used to calculate the elastic constants. These three methods involve the assumption of isotropy and perfect elasticity, and require the use of the relation v = (E/2G) - 1, which holds only if the elastic constants are the same in at least two directions. The calculation of v by means of Eq. 3 introduces considerable error, as a 1% error in V, and V, results in a 20% error in v. If frequencies for samples with a length-to-diameter ratio greater than four and a length greater than 8 in. are measured carefully, the experimental error can be kept to 1%. However, it is not unreasonable to expect that the variation in Vb and Vt with direction may exceed 1%. Thus, for even a small percentage of anisotropy the use of Eq. 3 can result in considerable error in v. The calculation of v by Eq. 5 also involves some uncertainty as a 1% error in Vs and Vp can result in a 6% error in v. By means of the pulse method both

Jan 1, 1965

By D. J. DeLazaro, W. Rostoker, R. E. Riley, M. Hansen

KNOWLEDGE of the isothermal transformation behavior and the TTT chart method of graphically summarizing such information has been of invaluable aid to the ferrous metallurgist in understanding and developing heat treatments intended to provide specific mechanical properties. It is to be expected that similar lines of study directed to titanium-base alloys will be as profitable. This paper summarizes, on conventional TTT charts, the isothermal transformation products and pertinent reaction rate data for binary alloys of titanium containing 1, 3, 5, 7, 9, and 11 pct Mo, respectively. The results so presented were derived from metal-lographic examination. Some X-ray diffraction work was done to clarify certain points of question. Ti-Mo System To the authors' k.nowledge, TTT charts have only been used to describe the reaction rates of eutectoidal decompositions. It would seem that the kinetics of decomposition of any unstable solid solution might be conveniently described in this manner. The equilibrium diagram of the Ti-Mo system' is shown in Fig. 1. The similarity with the Fe-Ni system will be recognized. Additions of molybdenum serve to stabilize the /3 phase to increasingly lower temperatures. The solubility of molybdenum in the a phase is restricted to less than 1 pct at 600°C. Under normal conditions. a homogeneous ,8 structure quenched to a, temperature in the a f & field will reject a of invariant composition. The rate at which this occurs depends on the degree of undercooling and the degree of supersaturation of /3. The structural character of the rejected phase may also be expected to be related to the undercooling. Materials and Experimental Methods A sponge titanium was used which has a nominal impurity content as reported in Table I. The nominal composition of the molybdenum used is also included. The alloys were prepared in 150 g melts by arc melting in an evacuated water-cooled copper crucible of the type reported in an earlier paper.' The pancake-type ingots were forged to 1/4x1/4 in. bars and homogenized for 24 hr at 1000°C in evacuated Vycor bulbs. Specimens Vi in. thick were cut from these bars for heat treatment. The heat treatment cycles followed an invariant procedure. The specimens were soaked at 1000°C for 20 min under a helium protective atmosphere prior to quenching into a lead bath held at a temperature corresponding to a chosen degree of undercooling. After a prescribed period of time at this temperature, the specimen was removed and water quenched. A series of specimens so treated for progressively longer periods served to establish the times for initiation and completion of the decomposition of the /3 phase at a particular temperature. Although heat treatment of unprotected specimens in a lead bath does permit surface contamination by lead diffusion, this method is necessary to insure sufficiently rapid quenching rates. As long as the bath treatments were of less than 1 hr duration. the contaminated surface was not unduly deep and could be removed without excessive grinding. Metal-lographically, the contaminated zone could be readily distinguished from the pure binary alloy. Transformation Characteristics of Ti-Mo Alloys Metallographic examination showed that a supersaturated p phase may decompose by one of two processes. Alloys containing 1 to 9 pct Mo, when quenched in water from the homogeneous /3 field,

Jan 1, 1953

By F. G. Stone

A strain anneal process has been developed for the production of iron tensile test specimens, the gauge length consisting substantially of a single crystal. Since the method has been quite successful and the results of general interest, the process will be described in detail. The essential feature of the method is the continuous, slow increase of furnace temperature during the grain growth annealing treatment. Briefly, the procedure is as follows: I. Heat machined bars to 950°C in vacuum, hold I hr, furnace cool. 2. Strain to 3.5-3.8 pct elongation (axial loading). 3. Anneal, continuously raising furnace temperature from 450 to goo°C at a rate of so0 per day. 4. Hold at 900°C for 100 hr, furnace cool. Tensile test bars with a 1/4- X I-in. gauge section have been machined from 35 in. Armco iron plate and from 3/8 in. rounds of Puron, a high purity laboratory iron. The axes of the test bars were parallel to the rolling direction. During the machining operation the bars were polished in the lathe with No. 600 emery paper, and this polished surface proved satisfactory for subsequent macrographic examination. A micrographic examination of the materials showed that both were high in FeO inclusions, those of the Puron being smaller but much more numerous. An initial vacuum anneal of I hr at 950°C followed by furnace cooling resulted in a ferritic grain size of ASTM No. 3 for Armco and No. I for Puron. Special heat treatments which reversed these initial grain sizes produced no marked improvement in single crystal production after subsequent treatments. The strain for subsequent grain growth was determined by measuring the decrease in diameter of the tensile bar during elongation. The change in diameter could be measured with a micrometer to +0.0001 in., corresponding to an accuracy of 0.08 pct for the elongation. The accuracy of the diameter measurement is also dependent on grain size because of surface roughening during elongation, and for this reason, a No. 3 grain size is preferable. Optimum grain growth was obtained for strains between 3.5 and 3.8 pct elongation. Once this critical range had been cstablished, all tests were held within it, and thus only meager data were obtained on grain growth following strains outside this range. In general, grain size decreased with increasing strain to about 5.5 pct elongation. Grain growth was occasionally ohserved with less than 3.5 pct elongation although this may have been the result of error in measurement. The program control device for the grain growth anneal consisted of a I rpm motor and worm gear drive, operating the dial shaft of a pyrometer controller through a pulley. Dial speeds of 33 and 50°C per day were tried, but the results at the slower speed were not sufficiently better to warrant the increased furnace time. The furnace tube was evacuated at intervals during the run and kept sealed the remainder of the time. When the controller reached 900°C, it was stopped and the temperature held for 100 hr. This eliminated most of the numerous minute crystallites of about 0.5 mm dimension usually visible on the etched surface of the single crystal. Since recrystallization occurs at the A3 point, the top temperature of 900°C provided a 10"

Jan 1, 1949

By G. Y. Chin, A. R. Von Neida

The relationship between crystalline texture and magnetic anisotropy in a Co-10 pct Fe alloy has been investigated by means of X-ray pole .figures, hysteresis-loop tracings, and magnetic-torque measurements. The cold-rolled texture of a sample after 95 pct thickness reduction is of the "brass-type", that is, (110)[112/. At 500°C the cold-rolled material recrystallizes fo a (311)[112] orientation, plus a minor (210) [001] component. This texture persists up to 1400°C, at which point it is replaced by a secondary recrystallization texture, (111)[112]. Magnetic-torque measurements show that the easy axis of magnetization lies along the transverse direction in the cold-rolled material and changes to the rolling direction after primary recrystallization. This change is also reflected in the hysteresis characteristic; whereas the B-H loop along the rolling direction is nonsqunre with a low value of residual induction (750 vs 19,000 gauss at saturation) for the cold-rolled material, the annealed sample exhibits a very square loop with a large value of residual induction (16,000 gauss). Theoretical torque curves calculated from the texture data on the basis of magnetocystalline anisotropy energy compare favorably with the observed torque curves. Values of the crystal anisotropy constant, K1, obbained from these comparisons are in good quantitative agreement with single-crystal data. Furthermore, both the torque amplitude of the poly crystalline material and the magnitude of K1 obtained with a single crystal show an identical temperature dependence over the range from —195° 10 +220°C. It is thus conclzided that the magnetocrystalline anisotrpopy erlergy is chiefly I-esponsible. for the nzagnetic allisotropy of textured Co-10 pct Fe alloy. THE results of a study on the relationship between crystalline texture and magnetic anisotropy of an alloy containing 90 pct Co and 10 pct Fe by weight are reported in this paper. The alloy has an fcc structure: a saturation magnetization of about 19,000 gauss,2 and a nearly zero value of magnetoatriction.3 puzey4 has reported a large crystalline anisotropy constant of -7.4 X 105 ergs per cu cm, indicating the (111) directions as the easy axes of magnetization. Hence, texture variations resulting from cold work and annealing are expected to introduce a magnetic anisotropy in the polycrystalline material through the alignment of these (111) easy directions. In the present study, magnetic anisotropy of both rolled and annealed strips was determined by magnetic-torque measurements and hysteresis-loop tracings The results were correlated quantitatively with calculations based on texture data obtained by the X-ray pole-figure technique. It is established that the magnetocrystalline anisotropy energy is indeed chiefly responsible for the magnetic anisotropy of textured Co-10 pct Fe alloy. EXPERIMENTAL Material Preparation. The alloy nominally contained 90 pct Co, 9.5 pct Fe, and 0.5 pct Mn by weight, the chief impurities being nickel, carbon, and silicon (less than 0.5 pct total). The cast ingot was rolled to strips 10 mils thick and slit to 1 in. in width. After strand annealing at 900°C in a hydrogen atmosphere, these strips were further cold-rolled to various thicknesses down to 0.25 mil (97.5 pct reduction), with samples collected for study of the development of texture and magnetic anisotropy as a function of thickness reduction. subsequently, samples cold-rolled from 100 mils to 0.25 mil were obtained, thus extending the thickness reduction range to 99.75 pct. In addition, 0.5-mil samples cold-rolled from 10 mils were selected

Jan 1, 1965

By S. L. Couling, D. J-P. Adenis

i2) twinning in poly crystalline magnesium does not usually occur homogeneously but is concentrated in localized regions or bands inclined at about 45 deg to the stress axis. These bands of twinning are in many ways similar to the Luders bands seen in mild steel alzd Al-Mg alloys. Within a hand the percentage of the volume twinned may approach 100 with no twinning outside the band. Bands are not produced in specimens of grain size a3 x 10-= in. or in samples deformed at temperatures 300°F. Annealing of heavily twinned regions leads to re crystallization textures markedly different from those found in the starting material. The exact preferred orientation appears to depend on the starting grain size, the amount of compres-sive strain and the manner in which it is introduced. MAGNESIUM, with its hexagonal crystal structure, deforms plastically at room temperature by a variety of deformation mechanisms, one of the most important of which is (1012) twinning. In single crystals such twinning occurs on compression parallel to the basal plane or tension perpendicular to it. In wrought polycrystalline magnesium, such as rolled sheet, the preferred orientation is such that almost all the grains have their basal planes nearly parallel to the sheet surface. Therefore, if sheet material is deformed by cold rolling or by tension in the plane of the sheet, deformation of the grains by (1012) twinning is not favored. On the other hand, twins form readily on compression parallel to the plane of the sheet as in a compression test, on the compression side of a bent sample, or at the outer rim of a drawn cup. The first part of this paper deals with the morphology of (1012) twinning in polycrystalline magnesium. Some aspects of this subject were covered by Barrett and ~aller.' Of direct bearing on the work to be reported here are the comments of Jetter' in discussion to Ref. 1. He shows that Mg + 1.5 pct Mn alloy sheet when bent about a transverse axis develops a pattern of transverse bands on the surface of compression. A longitudinal section through the sheet shows that the bands are wedge-shaped and inclined to the rolling direction. The bands were identified as "outcrops of regions in which deformation is localized as the result of the reorientation brought about by (1012) twinning". The second part of the paper treats the recrys-tallization texture of the specimens twinned by compression. Magnesium deformed and then annealed generally recrystallizes with no change in orientation.1'3'4 This statement is true provided that the amount of (1012) twinning occurring during deformation is small. In an isolated observation, Anse15 has shown that, when deformation produces much (1072) twinning, annealing causes new maxima to appear in the pole figure. The second part of the paper elaborates on this point. I) MATERIALS AND PROCEDURES All of the experimental work to be reported was done using the commercial sheet and plate alloy AZ31B (nominal composition: 3 pct Al, 1 pct Zn, 0.4 pct Mn, balance magnesium). This alloy is available commercially in two tempers, -0 (fully annealed) and -H24 (partially annealed), and specimens of both tempers were used in various experiments. The average grain. diameter (AGD) for -0 temper 0.125-in. sheet is about 0.5 x 10- in.; where material of larger grain size was desired, anneals at elevated temperature were used to grow the grains. compression tests were made on a screw-driven "hard" machine. The specimens were clamped in a

Jan 1, 1964

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'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'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 J. L. Zakin, G. K. Patterson, J. M. Rodriguez

Correlation has been obtained between drag-reducing characteristics for turbulent flow in a pipe and measurable properties of several polymer solutions. Several concentrations of high molecular weight polymethyl methacrylate in toluene, high molecular weight polyisobutylene in both toluene and cyclohexane, medium molecular weight polyisobutylene in cyclohexane and benzene and low molecular weight polystyrene in toluene were studied. Data obtained in these nonpolar solvents and literature data for more polar solvents were successfully correlated as the ratio of measured friction factor to purely viscous friction factor vs the modified Deborah number vrl/D0.2 where 71 is the first-mode relaxation time of the solution estimated by the Zimm theory. A shift factor which is a function of intrinsic viscosity 1/(4[?] - 1) allowed all the data obtained with nonpolar solvents to be correlated as a single function. For these systems, most of the data fit a single curve to within + 5 percent of the average friction factor ratio. The shift factor did not give a unique function of the data for the more polar systems. INTRODUCTION The phenomenon of drag reduction in polymer solutions was first studied by Toms1 in dilute solutions of polymethyl methacrylate in mono-chlorobenzene. The drag ratio for flow through circular tubes has been defined2 as the ratio of the pressure. drop of the solution to the pressure drop of the solvent at the same flow rate. The drag ratio is less than 1.0 for a drag-reducing fluid. Practical use of drag reduction is being made in fracturing operations in the petroleum industry.3 A more fundamental quantity is the friction factor ratio, defined as the ratio of the observed pressure drop to that predicted for a solution of the same viscosity characteristics and density at equal flow rates using the Dodge-Metzner friction factor equation4 Viscous solutions with drag ratios greater than 1.0 can have friction factor ratios less than 1.0. For practical applications, it is drag reduction which is of interest. However, for correlation the fundamental ratio is the friction factor ratio. In recent years, drag reduction has been studied extensively. Recent studies have shown that reasonable predictions of the incipience of drag reduction in polymer solutions can be made from the properties of the solutions and the flow Variables.5 However, it has not been possible to predict accurately the amount of drag reduction to be expected for a given polymer solution without any drag-reducing turbulent flow data on the same solution.6 For flow through circular tubes it is well established that there is a concentration effect and a diameter effect on drag reduction. Toms1 observed that drag reduction increases with an increase in the concentration of the solution up to an optimum concentration beyond which, due to the increased viscosity of the solutions, the drag ratio increased with an increase in concentration. Hershey 7 observed that for dilute Newtonian polymer solutions in nonpolar hydrocarbon solvents, a normal transition region may be obtained followed by a departure from the von Karman equation (on a friction factor-generalized Reynolds number chart). The point of departure is a function of diameter: the smaller tubes depart at the lower Reynolds numbers. Concentrated solutions may show no abrupt transition region, but merely an

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'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'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 E. S. Bumps

A series of macrographs are presented for the purpose of graphically recording the strain phenomenon that accompanies the energy transition in the Charpy impact testing of a mild steel that is susceptible to strain aging. STRAIN patterns in mild steel Charpy impact specimens were obtained in order to determine whether, on the first appearance of plastic strain during deformation, the initial fracture cracks appear in the region of plastic strain or in the elasti-cally deformed regions between. Although this attempt to locate the initiation of cleavage was not successful, the observed strain patterns illustrating various stress conditions in partially deformed Charpy specimens are presented along with a discussion of the possible dependence of transition energy on the yield phenomenon. Earlier work on the development of strain patterns in mild steel have been reported by Fry1 and later by Jevon.2 Harris, Rinebolt, and Raring3 observed characteristic strain markings on the surface of Charpy V-notch impact specimens fractured above and below the transition temperature which they presented schematically. It is intended that the strain figures presented here will add to the literature a graphic correlation of strain with transition energy in impact specimens. Samples of % in. round hot rolled, 0.20 pct C steel were machined to standard 0.394 in. sq, V-notch Charpy impact specimens. Preliminary testing involved determination of transition temperature, Fig. 1, using a Sontagg impact tester. These data were subsequently used to select temperatures above, within, and below the transition range at which specimens were partially deformed. Partial deformation was obtained by either varying the energy or the testing temperature, see Table I. Macroscopic strain figures shown in Figs. 2 to 19 were produced by several metallographic repolish-ing and etching steps. The macroetchant used was as follows:4 120 g HCl, concentrated; 100 ml water; and 90 g cupric chloride. Strain figures were obtained on the outer surface and on sections through the central portion of the impact specimens in order to determine an approximation of the volumetric strain pattern. In the tensile strain figures reported by Jevon, it was found that strain etching would not work immediately following strain unless the material was heated to 200°C. The impact strain patterns presented here were obtained without this heating, but the specimens were not etched until ten months after straining. This confirms a discussion of Jevon's paper, in which it was pointed out that strain figures can also be developed after aging for long periods of time at room temperature. Hardness of the strained and unstrained portions, revealed by the etched pattern, was explored using R, impressions converted to R, hardness values. Discussion of Results In the impact test, as in the tensile test, some parts of the specimen yield and deform plastically, while other regions are deformed only elastically. The plastic deformation bears a relation to the imposed stress pattern. In the strain figures presented here, the plastically deformed regions are the dark etching ones. The strain figures are always symmetrical because the stress state in the Charpy-type specimen under impact loading is symmetrical. The difficulties encountered to produce initial cracks are intimated in Figs. 2 and 4. At a temperature of —75ºF, the stress was not sufficient to pro-

Jan 1, 1953

By J. J. Fischer

COMPOSITES containing cold-drawn, high-strength steel wires have shown promise for normal and slightly elevated temperature applications, particularly where strength-to-weight ratios or corrosion resistance are important.'-3 Although tensile strengths up to 500,000 psi may be obtained by cold drawing these wires, processing the composite at elevated temperatures will result in a rapid decrease of the wires' strength. In wrought maraging steels, high-strength levels can be obtained by aging at 900' . Because these alloys do not rely on heavy cold working to achieve their strength, and because they do not overage readily, they are of potential interest for use in composites. In view of this, the tensile strengths of composites containing The total heat effect thus represents the heat of formation, AHf of the compound at 273' . Since the heat of solution of tin in the tin solvent bath is zero, AHz = 3( - H273)Sn and Hf is given by: For LaSn3, AH3 had a measured value of 11,285 i 380 cal per g-atom while for La2Sn, the corresponding value was 33,658 870 cal per g-atom. Using the measured data for the compounds and pure lanthanum, a value of -15,150 200 cal per g-atom was calculated for the heat of formation of LaSn, at 273°K, while Hf for La2Sn3 was found to be -28,090 400 cal per g-i&om. The authors would like to acknowledge the financial support of the Army Research Office, Durham, North Carolina. under contract No. DA-31-124-ARO-D-384.

Jan 1, 1969

R. W. Balluffi (Atomic Energy Div., Sylvania Electric Products Inc., Bayside, N. Y.)—Since porosity is known to form in the copper side of Cu-Ni couples during diffusion24,25 it is of importance to consider this factor in interpreting the large variations of chemical diffusivity with copper concentration reported for this system. The presence of porosity may affect the measurement of D in two ways: 1—density changes in the couple invalidate the usual solutions of the diffusion equation, and 2—the pores may act as short-circuiting paths when transport through the vapor or along internal surfaces is appreciable or else as open circuits when these effects are small. The error produced by the first effect may be estimated by a graphical analysis. Fig. 8 shows the porosity generated in the copper side of the Kirkendall interface of a pure nickel vs pure copper couple after diffusion for 350 hr at 1040°C in hydrogen. In Fig. 9 the actual diffusion curve which would be obtained by the usual slicing technique is shown as a solid line drawn to the same scale (from the data of da Silva and Mehl"). The amounts of porosity (obtained by lineal analysis) and of nickel are graphically represented by the hatched areas. The standard solutions of the diffusion equation are valid only when all volume elements of unit length and unit cross section contain equal numbers of atoms." It is possible to correct the experimental curve to satisfy this condition by shrinking the couple in the direction of diffusion in such a way as to eliminate the porosity.* The corrected diffusion curve obtained after

Jan 1, 1954

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 A. P. Young, F. C. Holden

IN many of the early investigations of the aging of titanium alloys, it was observed that the retained beta phase could be aged to a high hardness without an apparent change in microstructure; moreover, in some alloys it was found that even a very rapid quench produced beta having an anomalously high hardness. What appeared to be hard beta phase was designated as "beta prime," to distinguish it from the softer normal retained beta phase. Frost and co-workers'.' demonstrated that the increased hardness is caused by the formation of a metastable phase, omega, which can be identified from its X-ray diffraction pattern. This reaction also has been studied by Brotzen, et a1.,3 and the structure of the omega phase has been published by Silcock, et al.," and by Austin and Doig.3 The X-ray diffraction analysis by Austin and Doig indicated that omega is low in alloy content, approaching the composition of the stable alpha. The aging process proceeds by the path Thus, overaging results in the formation of alpha and the ultimate disappearance of omega. This is accompanied by a decrease in hardness and a recovery of ductility. The present work represents a study of the aging process in a high-purity Ti-6.4 Mn alloy, in which optical and electron microscopy, X-ray diffraction, and hardness data were correlated. The specimens, 1/8-in. sections cut from 1/4-in.-diam rod, were heated in argon to a temperature just into the beta field (810°C), held for 1 hr, and water-quenched. The aging samples were heated in air for 1 hr at 300 to 500°C. The specimens were ground and mechanically polished, finishing with alternate etching and polishing on a slow-speed wheel to remove disturbed metal from the surface. The surface finally was swab-etched, rinsed with tap water, and air-dried. The etchant used was an aqueous solution containing 1 1/2 pct HF and 3 1/2 pct HNO3. This procedure is identical with that used for preparing metallographic specimens, except that the optimum degree of final etching required for electron microscopy may vary from that used for light microscopy. Metal replicas, backed with silica, were prepared from plastic strip-pings for examination with the electron microscope. Complete details of the procedures used for preparing these replicas are available elsewhere." Fig. 1 shows a comparison between the structures revealed by the electron microscope and those obtained by conventional light microscopy. Hardness and X-ray diffraction data are listed in Table I. No evidence of a second phase is apparent in the optical micrographs for the as-quenched sample, or for the specimens aged at 300 or 400°C; fine alpha particles can be seen in the specimen aged at 500°C. In the electron micrographs, visible equiaxed pocks appear in the as-quenched specimen, and, with increasing density, in the samples aged at 300 and 400°C. After aging at 500°C, the structure becomes markedly coarser and develops an oriented appearance of a second phase, coincident with the appearance of visible alpha particles in the light micrographs. These observations are confirmed by X-ray diffraction and hardness data. In these specimens, aged for 1 hr, the intensity of the omega pattern increases to a maximum at the 400°C aging temperature, corresponding to maximum hardness and the maximum density of pocks in the electron micrographs. At this point the beta phase shows a definite enrichment in Mn. At 500°C, little or no omega re-

Jan 1, 1959

By D. G. Westlake

Polycrystalline tensile specimens of various Zr-0-H alloys have been tested at 298°, 178°, and 77°K. Solute oxygen and hydride precipitates in quenched alloys made individual contributions to the yield strength at 0.2 pct strain which combined to produce a resultant strength increment, a,., Ductility changes which were ohserved can he interpreted in terms of the various oxygen and hydrogen concentrations, testing tem -peratures, and dispositions of the hydride. ADDITIONS of oxygen in solid solution were known to increase the yield and tensile strengths of polycrystalline zirconium as early as 1951.' More recently, the critical resolved shear stress (CRSS) for prism slip in zirconium single crystals was also shown to be affected by the solute oxygen impurity.' This latter work also demonstrated that large increments of strength could be contributed by the finely dispersed zirconium hydride precipitates that are present in quenched Zr-H alloys.3 It was concluded that the combined strengthening due to alloying could be expressed by where to is the increase in the CRSS due to solute oxygen alone and TH is the increase due to finely dispersed hydride precipitates. Eq. [I] is analogous to one used to express the combined strengthening effects of work hardening and neutron radiation damage.4 Eq. [1] was verified only indirectly and for only small amounts of the impurities—up to 0.14 at. pct 0 and 0.63 at. pct H. The present investigation was undertaken to obtain a more direct verification of the validity of the form of Eq. [1] for this system and also to determine the combined effects of oxygen and finely dispersed hydride precipitates on the tensile strength and ductility of polycrystalline zirconium. EXPERIMENTAL PROCEDURE Tensile specimens were machined from the same rolled billet of Kroll zirconium used in the earlier study.' These measured 38 by 4.7 by 0.5 mm and had 10-mm gage lengths which were 2.8 by 0.5 mm. Each specimen was ß-annealed in vacuo at 1173°K for 15.5 hr and a-annealed at 1073°K for 4 hr to D. G. WESTLAKE, Member AIME, is Associate Metal l ur-gist, Metallurgy Division, Argonne National Laboratory, Argonne, III. Manuscript submitted July 17, 1964. IMD______________ give an equiaxed structure with grain diameters averaging 0.06 mm. Oxygen was added by allowing the metal to react with a known quantity of oxygen during the 0 anneal and known quantities of hydrogen were added during the a anneal. Each alloy was encapsulated in Pyrex under vacuum, annealed at 873°K for 4 hr, quenched into ice water, and polished by immersion in a solution of 46.75 vol pct H2O, 46.75 vol pct concentrated HNO3, and 6.5 vol pct HF (49 pct) at 298°K. Special heat treatments given to a few specimens are described in the results below. Tensile tests were done on an Instron machine and were begun within 20 min after the quench, except where specified otherwise. Tests at 298°K were in air, at 178°K in acetone, and at 77°K in liquid nitrogen. All tests were at a strain rate of 8x sec-1. RESULTS AND DISCUSSION Yield Stress at 298°K. The compositions of alloys and the corresponding yield stresses (0.2 pct strain) are given in Table I. A plot of the yield stresses of the oxygen alloys, A, B, C, and D, indicates that varies linearly with CO1/2, where Co is the oxygen concentration, Fig. 1. This is in accord with Fleischer's6 theory for solution strengthening if the oxygen atoms do not cluster, or the cluster size remains constant with increasing oxygen concentration. In Fig. 1, it appears that if one could prepare some oxygen-free zirconium its yield stress would be very low. Therefore, we shall assume that for the oxygen alloys is equivalent to O0, the strength increment contributed by the presence of oxygen. The relationship between0.2and Co is expressed by 0.2 = 31.3 CO1/2, when the yield stress is in kg per sq mm and the concentration is in at. pct. Each of the hydrogen alloys, Al, A2, A3, and A4, contained 0.081 at. pct 0 as an impurity. In Fig. 1, it appears that this small amount of oxygen makes a significant contribution to the strength which cannot be ignored when we evaluate the contribution of the finely dispersed hydride. Let us assume the validity of the following equation: a0.2 = (a2o+a2R)1/2 [2] which is analogous to Eq. [I] for single crystals, and calculate values of UH for the hydrogen alloys by using the experimental values of 0.2 and o (0.081 at. pct) = 8.9 kg per sq mm. For 0.36 at. pct H, oH = 6.47; for 0.72 at. pct H, OH = 11.30; for 2.16 at. pct H, OH = 19.4; and for 3.60 at. pct H,

Jan 1, 1965

By N. H. MacMillan, W. M. Mularie, R. E. Jackson, A. R. C. Westwood

The initial results of a study of the environment-sensitive microhardness and diamond rotary drilling behavior of granite and its constituent minerals quartz and feldspar (microcline)1 have established that many similarities exist between the environment-sensitive mechanical (chemomechanical) behavior of these materials and that of the simpler solids such as periclase, soda-lime glass, and alumina4 studied previously, at least as far as n-alcohol (straight-chain alcohol) environments are concerned. The results of this study (hereafter designated study I) also suggested that the rate of drilling of granite in these environments is controlled by the chemomechanical behavior of its quartz constituent, and is greatest in those environments which impart a zero l-potential to this phase, thereby maximizing its hardness. Now, cationic surface-active species strongly influence the l-potentials of silicate minerals. For this reason they are widely used in mineral separation operations. In particular, dodecyl trimethyl ammonium bromide (DTAB) was found in study I to produce f 0 for quartz at a concentration in water of 107 to 10-4 moles per 1. Accordingly, the influence of dilute aqueous solutions of this surfactant on the drilling behavior of granite also was examined in study I. This revealed that granite could be drilled three to four times faster in 10-° molar aqueous DTAB than in water, and confirmed by experiment the suggestion that granite is most effectively drilled with a diamond core bit in environments which impart a zero l-potential to quartz. According to O'Connor and Buchanan' however, the isoelectric point for quartz in aqueous DTAB solutions occurs at a concentration of .•.•2 x 10-° moles per 1, rather than [101 to 10-1] moles per 1. To confirm the results of study I, therefore, a more comprehensive investigation of the [ ]-potentials of quartz, microcline, and Westerly granite in aqueous DTAB environments has now been undertaken. At the same time an examination has been made of one of the basic assumptions of the current conceptual understanding of chemomechanical effects. In this view, although hardness changes occur essentially instantaneously following wetting of the solid, they are confined to a surface layer at most a few micrometers (µm) deep. Hence, to maximize the influence of chemomechanical effects on bit penetration rate only shallow cuts should be taken. Practical penetration rates are then obtained by increasing bit rotation speed. Experimental l-potentials were determined by the streaming potential technique using an automated rapid-cycling apparatus recently developed by Martin Marietta Laboratory from a design by Somasundaran and Kulkarni. The drilling studies employed 3.2-mm-OD 120-grit diamond-loaded core bits with a wall thickness of ~0.7 mm, and bit rotation speeds of 2200 and 25,000 rpm. The load applied to the bit was independent of the depth drilled in both cases. The 2200 rpm measurements employed the same drill press and puddle drilling technique as used in study I. The higher rotation speed was obtained using a water-driven dental turbine drill. In the case, the surface active fluid was pumped down the axis of the bit to ensure efficient wetting and flushing of the drilling debris from the hole. In both cases drilling rate was measured by the parameter D(200), defined as the average rate of bit penetration during the interval from 150 to 250 sec after drilling commenced.

Jan 1, 1976

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

By J. W. Eckerd, P. S. Lewis, N. H. Coates

USBM designed, constructed, and operated an 18-in.-diam fluidized-bed combustor for highly caking coals to evaluate the method for possible application to power generation. In initial tests, combustion was carried on successfully, with carbon losses as low as 0.8%+ Coal ash was not satisfactory as a bed material, but mullite proved to be acceptable. Overall heat-transfer coeffients from the bed (-20 t 50 mesh mullite) to a water-cooled tube were about 75 Btuper hr-sq ft. Fluidized-bed combustion is being investigated by the U. S. Bureau of Mines (USBM) as a potentially cheaper method of firing power plant boilers. Lower combustion temperatures in fluidized beds—only 1400" to 1800°F-—should reduce fireside deposition and corrosion and nitrogen oxides production. Fluidized-bed combustion also offers possible advantages in the use of additives to control SO, emissions and amenability to processing of high-ash, high-moisture coals without special preparation. This paper describes development of a fluidized-bed combustor and the results of preliminary tests. Equipment and Procedure Fig. 1 shows the 8-ft-high combustor. A cone-shaped plate perforated by I/8-in.-diam holes supports the fuel bed and admits the fluidizing air; water passing through the 3/4-in. pipe extracts heat from the combustion bed. Fig. 2 is a flow diagram of the system. Coal is fed pneumatically to the base of the fuel bed. Combustion products are passed through two centrifugal separators to remove most of the entrained solids, then to a water

Jan 1, 1971