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By Philip R. Strand

Vermiculite is the name used for those micaceous minerals with a ferromagnesian aluminum silicate composition and the unique property of exfoliating to a low density material when heated. Commercially, the exfoliated products are also called vermiculite, or more exactly, expanded vermiculite. In its exfoliated state, vermiculite serves many markets, chief among them construction, agriculture, horticulture, and general industry. Composition and Properties Vermiculite, in a natural state, has the characteristic mica habit, splits readily into thin laminae, flexible but inelastic. In a mineralogical sense, vermiculite is a hydrated silicate with no exact chemical composition. The structural formula for a macroscopic, trioctahedral vermiculite may be written: [ ] The structure of vermiculite is basically that of a talc, and it could be regarded as a trioctahedral member of the smectite group. Macroscopically, vermiculite displays the prominent monoclinic crystal faces that are commonly marked by lines at 60° and 120°. Hardness varies from 1.5 to 2.8 or more; specific gravities are between 2.1 and 2.8; color is amber, bronze, brown, dark green, or black. When heated quickly to an elevated tempera¬ture, vermiculite expands by exfoliating at right angles to the cleavage, into wormlike pieces (the name vermiculite is derived from the Latin `vermiculare,' to breed worms). This characteristic of expansion, the basis for commercial use of the mineral, is the result of the mechanical separation of the layers by the rapid conversion of contained water to steam. The increase in bulk volume of commercial grades is 8 to 12 times, but individual flakes may expand as much as 30 times. All expansion occurs at right angles to the basal cleavage. Vermiculite may also be expanded by a number of chemical processes such as soaking in hydrogen peroxide, weak acids, and other electrolytes. There is a color change during expansion that is dependent upon the composition of the vermiculite and furnace atmospheres. Heating in an oxidizing atmosphere produces dull gray colors. The iron is generally not oxidized during chemical expansion. The exfoliation of the vermiculite crystal results in large pores being formed between groups of platelets. Thus exfoliation can make available a large increase in void volume without significantly changing the surface area of the platelets. This characteristic is important in the chemical carrier applications of vermiculite. Although there has been much research on the chemical and structural composition of vermiculite, an exact formula and composition cannot be described. This is to be expected since vermiculite derives from a number of different mineral sources. As has been proposed, vermiculite is not a single mineral species, but families of related minerals. Additionally, commercial interest in the end product has resulted in the name vermiculite being applied to the very voluminous, bloated products from calcination of baueritized (bleached) phlogopite. This has also resulted in many names for the specific vermiculite found in a particular deposit. All of this difficulty arises from the nature of its crystal chemistry. Consequently, vermiculite is now thought of as several related variable mineral series rather than a group of related species. The vermiculites have a common silica tetrahedral sheet structure with separating ions. It is now generally agreed that vermiculites must also be regarded as true clay minerals. The properties of the mineral, such as cation exchange capacity, organic complexing ability, and vari-

Jan 1, 1975

By E. L. Dougherty, J. W. Sheldon

Using the numerical techniques shown in this paper it is possible to compute the simultaneous dynamical behavior of multiple fluid-fluid interfaces in two dimensions. Hence, fluid-fluid inter face models of several oil recovery processes can be constructed which allow prediction of the effect of fluid flow in two dimensions on the behavior of these processes while taking into account various physical effects, such as saturation gradients, phase changes and thermal stimulation. Techniques for constructing fluid-fluid interface approximations for several oil recovery processes are reuiewed. The validity of these techniques is established by comparison to experimental results. The availability of a computer program for computing the behavior of multiple fluid-fluid interface problems makes the use of potentiometric models uneconomic. The results indicate the areal sweep efficiencies obtained from potentiometric model studies at high mobility ratios may be somewhat optimistic. The results also indicate that the areal sweep efficiency curves obtained at high viscosity ratios 2—4 using miscible fluids in porous media are misleading and that considerable care must be taken in defining the mobility ratio for a displacement process, especially for miscible fluids. INTRODUCTION Many of the methods used to estimate areal sweep efficiency assume that the oil recovery process can be represented by one or more fluid-fluid interfaces. When the mobilities of the displaced and displacing phases are assumed equal, this quantity can be computed using analytical mathematical methods.l.2 For non-unit mobility ratio, experimental methods based upon the fluid-fluid interface concept include potentiometric and electrolytic blotter models. Scaled models of porous media have also been used to study this problem. Fay and Prats3 and Aronofsky4 used numerical techniques to compute breakthrough sweep efficiency, but neither of these studies were extended beyond breakthrough. Numerical techniques which have been developed for solving a general fluid-fluid interface problem are presented in a companion paper.5 These techniques have been incorporated into a program for a large-scale digital computer which can treat simultaneously the dynamical behavior of as many as six fluid-fluid interfaces. Thus it is possible to simulate the behavior of several oil recovery processes taking into account such effects as saturation gradients. Techniques for representing several oil recovery processes by fluid-fluid interfaces are presented. Processes considered are conventional water flooding with and without a mobile gas phase, hot water flooding, miscible flooding and enriched gas drive. Other processes, whose effects could be studied by this technique, but are not considered in detail here, are underground combustion and steam injection processes and various slug processes such as gas-water injection and alcohol-solvent processes. Theoretical results obtained with single interfaces for mobility ratios of 0.25, 1, 2, 4, 8, 16, 32 and 64 in a repeated five-spot are compared to experimental results for this geometrical configuration obtained using miscible fluids and conductive analogs. Predicted recovery curves for water flooding in a repeated five-spot are compared to experimental results reported in the literature. Example calculations are shown for a conventional water flood in the presence of a free gas phase and for a hot-water flood. MATHEMATICAL PRELIMINARIES We assume that the rock matrix is homogeneous with constant thickness, absolute permeability and porosity. The fluids are incompressible. We also neglect the effects of gravity.

Jan 1, 1965

By E. Swartzman, G. C. Behnke

THE free-swelling index, a numerical value for the free-swelling properties of coal, is being used to an increasing extent in specifying coal for burning in various types of equipment. The empirical standard ASTM method for determining this index uses, as a source of heat, a gas burner which requires frequent calibration because gas pressures are not constant, relatively small changes in gas pressure resulting in rather wide variations in the temperature attained in a crucible and thus in the resultant size of the coke button. Furthermore, the quartz crucibles specified for the test are not standard equipment, and relatively small variations in dimension and wall thickness from those specified often result in rather wide variations in the resultant size of the button. A method of analysis to be satisfactory not only for a scientific laboratory but also for use in industrial control laboratories under varying conditions should employ equipment which is rugged, easily calibrated, and readily replaceable by standard materials. Gas is not universally available as is electricity, and it is generally easier to calibrate and control a simple electric furnace or heater than a gas burner, the voltage not usually fluctuating to the degree that gas pressure does. Quartz crucibles are fragile, and the size specified in the test is not normally used for any other purpose in the laboratory. Although more expensive, the 15-cc platinum crucible, available in all laboratories where volatile matter in coal is determined by the standard ASTM method, is sturdy and standard and easily replaced. Because of these considerations, a modification of the standard method has been developed which employs a standard laboratory 350-w cone heater and standard 15-cc platinum crucibles. The results of numerous tests conducted with such apparatus show conclusively that the free-swelling index values as judged by the buttons produced with this equipment are exactly the same as those obtained by the standard gas burner method. Thus it is suggested that this electric cone heater method employing standard 15-cc platinum crucibles be considered as an alternative to the ASTM method, Designation: D720-46. The free-swelling index of coal is determined by means of the ASTM method, D720-46. This method, which is an adaptation of the crucible swelling test for coal of the British Standards Institution, consists of heating 1 g of coal in a special covered quartz crucible in a regulated gas flame for a period of not less than 2.5 min in which time the temperature of the inner surface of the bottom of the crucible reaches a temperature of 82025°C. The residual coke button is then compared in size and shape with a series of standard profiles shown in Fig. 1 and designated by number from 1 to 9 in increasing order of size. As the method is empirical, it requires rigid standardization of the apparatus and repeated calibration of the gas burner. The dimensions of the low form quartz crucible recommended must be rigidly adhered to as small variations in diameter or wall thickness result in variations in the rate of heat transmission and thus in the resultant size and shape of the coke button. The gas burner must be calibrated almost every time a new set of determina-

Jan 1, 1952

By J. Gurland

The effects of variations of carbon content on the constitution and properties of sintered WC-Co alloys were studied. The grain growth of tungsten carbide during sintering was measured and it was shown that it takes place mainly by solution and reprecipitation of the carbide in and from the binder at the sintering temperature. It was found that the decomposition of W3C03C by carburization during sintering is responsible for the formation of very large grains. THE properties of sintered WC-Co alloys are critically dependent upon their final composition and structure. Slight changes of cobalt and carbon contents and small variations of grain size result in marked changes of mechanical properties and performance of products. Previous investigators have studied the microstructure as a function of composition' and have dealt with the influence of cobalt upon properties.' The present work is concerned with the effect of carbon content upon constitution, microstructure, and grain growth during sintering, as well as upon the physical properties of sintered compacts. Phase Boundaries at the Sintering Temperature The WC-Co section through the ternary diagram W-Co-C has been studied by Wyman and Kelley,' Takeda,V andford and Trent," and Rautala and Norton." Two phases, namely WC and a cobalt-rich solid solution (P), appear in the sintered structure if the carbon composition corresponds very nearly to the theoretical carbon content of WC (6.12 pct C). But small deviations from the ideal carbon content will bring about the occurrence of either graphite or the double carbide W,Co3C (7) . The 7 phase was long believed to be metastable, this conclusion being based mainly on the work of Takeda. More recent studies have shown that it is a stable phase of the ternary system,"5 but the actual phase boundaries have not been established and there has been some discussion as to whether or not the 7 phase occurs at some stage of sintering in the fully carburized alloys." In view of this uncertainty it was thought advisable to undertake an investigation of the phases present during the sintering of WC-Co alloys. Commercially available tungsten, cobalt, and carbon powders were used in the present study. A typical analysis of impurities in a sintered compact is reported in Table I. The desired carbon compositions were attained by varying the amount of carbon added to the tungsten during carburization and controlling the composition during sintering by packing the compacts into beds of mixed alundum-carbon powders of suitably selected ratios. The alloys were sintered in a hydrogen tube furnace at 1400°C, then brought to equilibrium at the temperature under investigation and quenched in water. The high temperature phases were identified by metallographic and X-ray diffraction techniques. The samples were etched with a 10 pct solution of alkaline potassium ferricyanide. The phase boundaries, established by metallo-graphic examination, are shown in Fig. 1, which is a vertical section through the ternary diagram at 16 pct Co. The temperatures of the invariant planes, at 1298" and 1357°C were established by Rautala and Norton. The vertical section shows that the three-phase field, WC + 7 + L, extends into the two-phase field, WC + L, but does not include the stoichiometric composition of WC. In practice this means that the 7

Jan 1, 1955

By M. A. Cook

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

Jan 1, 1961

By J. F. Havard

Gypsum is a useful industrial mineral found abundantly on the earth's crust. It is inexpensive to mine and process, and its calcined products have a wide range of readily controllable properties such as strength, density and setting time. It has proven to be such a useful material indeed, that ten American companies, operating some 57 calcining plants in 25 states in 1958, produced or imported in that year a total of 13,649,000 tons of the crude mineral valued at $39,361,000, which they then converted into manufactured products with a value of $329,070,000. Gypsum (CaSO4.2H2O) is calcium sulfate with two molecules of combined water, which are responsible for most of its useful properties. It is closely associated in most deposits with anhydrite (CaSO4), which contains no combined water and has limited commercial value in the United States. Man has long recognized the useful qualities of gypsum. It was utilized by the Egyptians in the construction of the pyramids and, later, by the Romans for important structures. Many of the ancient peoples prized gypsum for artistic and ornamental purposes, carving statuary from alabaster and making casts with plaster. The tabular variety, selenite, was used for windows, and the light transmitted through these windows reminded people of light from the moon (selene), hence the name selenite. The use of gypsum continued through the Middle Ages and into modem times. Benjamin Franklin was a famed exponent of gypsum because he applied ground gypsum to clover fields in the form of large letters which later read, in the more luxuriant growth, "land plaster used here." Gypsum is still used as an effective conditioner for some soils, but in recent decades, particularly in North America and Europe, it has become much more important as a major material for the building industry. Description Gypsum and anhydrite are closely associated minerals. Gypsum is found in a number of forms: massive rock gypsum, alabaster, selenite, satin spar, and gypsite. Anhydrite is found as massive rock or as smaller bodies or isolated crystals included in gypsum. Massive Rock Gypsum comprises most of the commercial gypsum and occurs as a sedimentary rock, interbedded in most places with shale, limestone or dolomite. This rock is soft and crystalline. Its color is white or shades of gray, pink, yellow, brown or other colors. Alabaster is a pure, compact and fine-grained variety suitable for use in sculpture or turning into artistic forms; it may be white or selected for attractive coloration. Selenite is gypsum crystallized in flat, transparent, flexible foliated plates, found in clays or in surface vugs in gypsum. Satin Spar is a fine silky fibrous variety with the axes of the crystalline fibers perpendicular to the vein or joint in which it has formed. Gypsite is an earthy mixture of gypsum with clay and sand in secondary formations; it is sometimes useful as a soil conditioner and has been used in making base-coat plasters. Pure gypsum contains 20.9 pct combined water, 46.6 pct sulfur trioxide (SO3) and 32.5 pct lime (CaO). Standard specifications (American Society for Testing Materials Designation C 22-50) read that minimum purity for material to be called gypsum is 70 pct CaSO4.2H20. Most of the commercial gypsum is 85 to 95 pct pure as produced. Impurities in

Jan 1, 1960

By J. S. Aronofsky

The results of polentiometric model studies and numerical computations are described. The purpose of these studies was to determine the influence of the mobility ratio on flooding efficiencies during water encroachment in petroleum reservoirs, in systems of regular well geometry. The direct line drive well pattern having relative spacing distances of one and one-half to one was investigated for water to oil mobility ratios of 10. 1. and 0.1. The results of these studies indicate that the pattern Sweep efficiency i.; very dependent upon the mobility ratio. INTRODUCTION The almost universal occurrence of water in the immediate neighborhood of oil-hearing sands lends considerable emphasis to the desirability of having a rational analysis of water encroachment into petroleum reservoirs. This problem has 1)become increasingly important with the accelerated use of water injection for secondary recovery operations. The water encroachment problem has been studied from both the theoretical and experimental viewpoints by Muskat.' He has formulated, in a precise manner, differential equations to express flow in a water encroachment system, and rigorous analytical solutions have been developed for the linear, radial, and spherical cases.' However, it becomes exceedingly difficult to solve the encroachment problem rigorously for any general two-dimensional system in which the shape of the two-fluid interface is not immediately evident from the geometry of the system. The difficulty lies in the fart that a rigorous analytical solution requires that the shape of the two-fluid interface be known simultaneously with its instantaneous posititon and with the pressure distribution on both sides of the interface. Although this paper concerns the study of the two-fluid system of oil and water. the methods described in the paper are generally applicable to other systems of incompressible and immiscible fluids in which the displacing fluid sweep-the displaced fluid down to a residual value. In each region it is assumed there is only one mobile fluid and its mobility is constant throughout the region. The Same procedure. with minor alteration, is applicable for gas injection systems provided the assumption can be made that both the displaced and displacing gases can be described by steady state formulas. For the particular two-fluid problem considered in this paper, there is a relative permeability. K, and a viscosity. p. associated with the water zone, and a different permeability and viscosity associated with the oil zone. The K/p (mobility value associated with a particular volume element of the porous medium. at any instant of time. will depend upon whether the element is ahead of. or behind the advancing interface. It is assumed that all volume elements ahead of the interface are characterized by the K/p value for oil, while all the elements behind the interface are characterized by the K/p value for water. That is. the K/p value in the oil zone is constant throughout the oil zone. and the K/p value in the water zone is also constant but different from the value in the oil zone. The symbols are defined at the end of the paper. The well pattern chosen for initial study is the direct line drive; the swept-out area at breakthrough was determined by two different methods which are described in the section on theory. These are: 1. Potentiometric analyzer 2. Numerical computation The use of the potentiometric analyzer for studying water flooding problems is adequately described in the literature, particularly for cases where the mobility in the water zone is assumed equal to the mobility in the oil zone." ' 5

Jan 1, 1952

By L. G. Jones

An approximate method of calculation is developed in this paper which allows duplication of radial unsteady-state gas flow computer results where Darcy's law applies, such as those reported by Aronofsky and Jenkins and Bruce, Peaceman, Rachford, and Rice. Moreover, the new calculation method can be used to obtain results for radial unsteady-state gas flow obeying the quadratic flow law proposed by Duwez and Green. Means are discussed for predicting well behavior at single or superimposed flow rates in finite or infinite reservoirs, determining reservoir rock properties from well-test data, reproducing and interpreting back-pressure test data, and determining the radial extent and reserves of gas reservoirs from well-test data. Example calculations are presented for gas flow following both Darcy's law and the quadratic flow law. INTRODUCTION Since the publishing of U. S. Bureau of Mines Monograph 7,1 most gas-well testing methods have been based on the equation q = y (pl2 - pw2)a, where q = production rate, pl and pw, are formation pressure and sandface pressure, respectively, and y and a are constants to be obtained from test data. These methods, used for predicting both deliverability and "open-flow" capacity of gas wells, have been useful and accurate in many cases but unsatisfactory in others. Even at best, however, they do not supply information about the formation or lead to an understanding of nonsteady-state gas flow in porous media. Many theoretically based studies2-4 of gas flow obeying Darcy's law have been made.' Since the partial differential equations which result from combining Darcy's flow law with the continuity equation are nonlinear, most of the published research consists of either numerical solutions or analytical solutions for linear approximating equations. Such solutions have been of limited value in field work due to their unhandy form and their failure to correlate most field data. There is evidence5,6 which indicates that Darcy's law is inadequate to describe gas flow at some flow rates of practical interest. A quadratic flow law: which reduces to Darcy's law at low rates, is more successful in accounting for experimentally observed behavior. This flow law has been applied successfully to a few hypothetical reservoir cases in work which has recently been published.10 However, these numerical solutions of the equations involved have been successful only on a special analog computer. Routine applications to field cases would be awkward and have not been attempted. The present paper describes an approximate method for computing nonsteady-state gas flow solutions which has been completely successful in predicting the results for both Darcy flow and quadratic flow obtained by elaborate numerical methods. The new calculation method allows determination of the observable variables in gas-well testing at constant rates. It is similar to the scheme of using a succession of steady states suggested by Muskat7 in that it makes use of steady-state and material-balance equations. It also is similar to the work of Aronofsky and Jenkins2 in that the new method includes Aronofsky and Jenkins' stabilized flow equation as a special case. It improves upon both of these calculation schemes in that it accurately describes all portions of reservoir history and suggests means of determining reservoir rock properties from well-test data. This paper deals only with production from a reservoir, in which case the rate is defined as being negative. The reservoir studied here is a homogeneous, disk-shaped porous body of uniform thickness, with all boundaries sealed except the inner radial boundary of the well.

By E. S. Machlin, Morris Cohen

GRENINGER and Troiano' were the first to establish the fact that the habit planes of mar-tensitic products are usually planes of high indices. In steels containing 0.55 to 1.4 pct C, the habit plane indices are {225}A.* In steels with more than 1.5 pct C and in Fe-Ni alloys, the indices are {259In. The presence of both habits in certain alloy steels has been reported recently." Several investigators"-" have subsequently attempted to provide an understanding of these complex habit relations. Bowles'6 work is the most recent and the most successful. Like Greninger and Troiano, Bowles concluded that the transformation occurs in two steps, the first, a strain (or displacement) that is homogeneous throughout the volume of the martensitic plate, while the second is a strain that is homogeneous only within relatively small portions of the martensitic plate. The first strain yields the measured tilt of the specimen surface, but does not produce the final martensitic structure. This and the correct lattice orientations are achieved by the second strain. Bowles also reasoned that each strain could be described by the motion of a plane of no rotation and no distortion (hereinafter called the invariant plane) in a direction not necessarily contained in the plane.** In applying these considerations to steels with {225}a habits, Bowles found that the habit plane coincided with the invariant plane of the first strain, a result which signified that the atoms move along certain paths during the transformation. Whether this correlation results from the existence of some sort of a plate nucleus6 lying along the invariant plane of the first strain, or whether the invariant plane primarily defines the preferred directions of propagation of the first strain, will be discussed in a later section. There are two obstacles to the general acceptance of Bowles' treatment: 1—it has not been shown that elements of his double-strain analysis are unique, and 2—it is not known whether his treatment applies to transformations yielding the {2591A habit. Unless these two questions are resolved, the correlation between the habit and invariant planes in the {225}A systems might be regarded as coincidental. Experimental Procedure Using a 70 pct Fe-30 pct Ni alloy as an example of a {2591A habit system, preliminary attempts were made to obtain a double-strain solution based on a Nishiyamax** set of orientation relations and on a Greninger-Troianot set, adopting the stereographic technique described by Bowles" who used the Kurd-jumow-Sachstt set in connection with the {225}A habit. These attempts were unsuccessful because the method is essentially one of trial and error and requires either exceedingly good luck or a prior knowledge of the results being sought. Consequently it was decided to measure independently the strain associated with the formation of a martensitic plate as well as the habit-plane indices of the particular plate. By means of matrix algebra, the measured strain was applied to the austenite lattice, whose orientation with respect to the strain was determined, in order to ascertain whether the resultant structure would have the lattice of martensite. This was not found to be the case, and hence it was assumed that the measured strain was the first of two Bowles-type strains, characterized by the motion of an invariant plane. A solution of this displacement was obtained in terms of the invariant-plane indices and the direction of motion of the atoms. Then the second strain

Jan 1, 1952

By B. H. Caudle, A. R. Khan

The oil production performance of thin-oil-column type reservoirs producing entirely by natural water drive are discussed in this paper. The dimensionless production histories were obtained in a series of scaled porous-medium laboratory-model tests under varying effects of rate of production, mobility ratio across moving boundary, ratio of oil- and water-sand thickness and mobility ratio across fixed boundary including the effects of different residual oil saturations in the water-invaded regions. This scaled-model study of thin oil columns indicated that greater recovery of oil results for lower values of the following: rate of production, mobility ratio across the moving boundary, water-sand thickness relative to the oil-sand thickness, and mobility ratio across the fixed boundary or residual oil saturation in the water-invaded region of oil sand The results of the study are given as dimensionless production history plots which may be used to predict the performance of the field they represent. INTRODUCTION Oil fields producing under natural water drive can be classified into two major groups: (1) an "edge-water drive" reservoir group in which the water is encroaching from the reservoir periphery, and (2) the group of reservoirs in which the oil-sand is entirely underlain by an aquifer. Reservoirs in the second group are further subclassified as "bottom-water drive" reservoirs and "thin-oil-column" reservoirs. The latter reservoirs are characterized by their relatively equal oil- and water-sand thicknesses and by having both the oil and water zone relatively thin. When oil is produced from a water-drive reservoir by a partially penetrating well, water breaks through sooner or later before all of the displace-able oil is recovered. Many analyses of this general situation have been made with varying degrees of realism in their approaches, both theoretical and experimental5.6 in nature. Pertaining to the scaled laboratory model studies of natural water drives using porous media, detailed investigations have been made by Henley, et al.7 on bottom-water drive and by Caudle8 on edge-water drive reservoirs. No laboratory model studies, however, have been made to investigate the performance characteristics of thin-oil-column reservoirs. This paper presents the results of a study on scaled models of thin-oil-column reservoirs, operated under varying conditions corresponding to the actual field practices. SCALING PARAMETERS The object of scaling is to produce a one-to-one relationship between physical and dynamic parameters of the model -and prototype. The most comprehensive treatment of scaling techniques for oil reservoirs is given by Geertsma, et a1.,9 which covers two methods for arriving at dimensionless groups for scaling. Table 1 lists the scaling parameters suitable for creating kinematic and dynamic similarities between the model and the prototype in the variables considered for the thin-oil-column reservoirs. In order to achieve similarity it is essential that the dimensionless groups listed in Table 1 have equal values in the model and the protorype simulated. Since it has been established that the role of interfacial forces is neglible in gross fluid movement in a reservoir no attempt was made to scale capillary forces- Although there are reports describing Scaling criteria for these forces,10,ll consideration of the necessary but restrictive conditions for

Jan 1, 1970

By C. R. Clark, G. Swift, D. S. Roberts

The purpose of this investigation was to measure PVT behavior of various types and combinations of heavy hydrocarbon components from the paraffinic, naphthenic and aromatic classes where the relative proportions Of the various components were selected to approximate those of natural gas or gas condensate systems. Synthetic mixtures were used so that the compositions Of the various components could be measured accurately. n-Heptane, methylcyclohexane and methylbenzene were used to represent the paraffinic, naphthenic and aromatic components of the heavy fraction. In the mixtures studied, the heavy fraction composition was held constant at O. O5-mole lraction, the balance being methane except for one mixture where 0.10-mo1e fraction of an intermediate component, propane, was added. The PVT data for the mixtures were determined in a variable-volume, constant-mass apparatus at psuedo-reducedtemperatures from 1.84 to 2.00, over a pseudo-reduced pressure range from 2.3 to 12.0. The experimental results showed that, regardless of the type of heavy material (paraffinic, naphthenic, aromatic, or combinations thereof) mixed with methane or methane and propane, the compressibility factors at equal values of pseudo-reduced temperature and pressure varied by less than 2.2 percent. INTRODUCTION PVT data is used for natural gas and gas condensate fluids in determining reserves of reservoirs and performance of wells, in metering produced fluids, and in recombining samples for laboratory studies. While there are vast amounts of PVT data reported for natural gas and gas condensate systems from which useful correlations have been developed, ' the compositional analyses for these systems and the resultant correlations typically were made with components analyzed through some arbitrary carbon number, usually C6, with the residue reported as a lumped "heavy" fraction. The heavy fraction was stoichiometrically recombined on the basis of an apparent molecular weight to give the final compositional analysis. It is virtually impossible to make a systematic analysis of the effect that variation of the relative amounts of paraffinic, naphthenic and aromatic constituents of the heavy fraction of natural systems might have on PVT behavior. Because there is considerable latitude in the relative amounts of these constituents, one speaks of crudes or condensate liquids as being "paraffin base", etc. It is of interest to determine if changes in the relative amounts of these three types of hydrocarbons in the heavy fraction cause significant changes in PVT behavior. If so, steps should be taken to describe better the nature of the heavy fraction in PVT correlations. If not, more confidence can be placed in the correlations presently employed. DESIGN OF THE EXPERIMENTAL INVESTIGATION We attempted to determine if changes in the base of the heavy fraction would cause significant changes in the PVT behavior of gas or gas condensate fluids. Synthetic mixtures were used to enable us to systematically vary the base of the heavy fraction and to analyze accurately the fluids. We found that the heavy fraction of naturally occurring condensate systems seldom exceeds 0.05-mole fraction. Thus, the mole fraction of the heavy fraction in the synthetic systems studied was set arbitrarily at 0.05, to maximize whatever deviations in PVT behavior that might occur. Further, we judged that since the C7 hydrocarbons normally are present in greater quantities than higher carbon number hydrocarbons in naturally occurring systems, the use of n-heptane, methyl cyclohexane, and methylbenzene to represent the paraffinic, naphthenic, and aromatic species in the heavy fraction would be most appropriate. Finally, to enable us to compare our

Jan 1, 1970

By P. K. Koh

Isothermal salt bath annealing of 0.014-in. thick 3 pct Si-Fe sheet was conducted at temperatures ranging from 927" to 1260°C in order to investigate the grain-growth behavior. Within the temperature range studied normal grain growth did not take place; instead nucleated grain growth prevailed. The nucleation frequency was found to increase with the annealing temperature, with corresponding decrease in grain diameter of ultimate secondaries after long-time annealing. Large secondaries grown by low-temperature isothermal annealing are essentially of (110)[001] orientation, and the (110)[001] texture is strong. The relatively small secondaries grown by high-temperature isothermal annealing also have orientations near (110)[001] as an average but widely scattered; thus the amount of (110)[001] texture is found to decxease with isothermal annealing temperature. Grain growth and texture development at various annealing temperatures can be described by families of sigmoidal curves with the time axis. ThE cube-on-edge (110)[001] texture and predominating large secondaries in fully annealed 3 pct Si-Fe are customarily produced by a 1100°C annealing of a primary recrystallized sheet. On annealing the primary recrystallized sheet above the temperature at which secondary recrystalliza-tion starts May and turnbull' have demonstrated that secondary grains decrease in size as the temperature is increased. The phenomenon was attributed to a decrease in the (G/N) ratio where G is the growth rate of secondary grains and N is their nucleation frequency. In addition, the growth of grains in orientations rather far from (110) [0011 occurred. The present investigation is devoted to detailed rate studies of the same phenomenon. Mi-crostructure, magnetic anisotropy, and texture data were obtained on strips of 3 pct Si-Fe isothermally annealed for various lengths of time in a BaC12 salt bath at temperatures ranging from 927' to 1260°C. The texture results are reported elsewhere.2 EXPERIMENTAL PROCEDURE Commercial 0.014-in. cold-rolled silicon-iron strip (3.16 pct Si), prepared by two stages of cold rolling with an intermediate short anneal, was given a decarburizing 3-min anneal at 800°C. Metallo- graphic studies indicated complete recrystallization. In order to provide a protective atmosphere and to obtain a rapid rise to an elevated temperature, a BaC12 and NaCl fused salt bath was used to heat samples isothermally at temperatures from 927" to 1260°C for various lengths of time. Torque magnetometer measurements were made on 1-in.-diam disc specimens before and after annealing, since magnetic torque curves supply information on textures and texture changes. Surface layers of the strip samples were polished and etched to reveal the grain structure. The diameters of grains were measured from micrographs at X100. The average value of diameters of matrix grains was established. Individual grains in the micrograph were cut out separately along grain boundaries. These grains were classified either as matrix grains or growth grains. The percent weight of growth grains in the cut-out patterns was reported as percent growth. Manv of the individual grains in the annealed samples were large enough to be X-rayed with a 5-mil beam for Lauegrams. Complete (110) pole figures were obtained for the primary recrystallized structure and short-time annealed structure with CoKa radiation at 30 kv in the back-reflection range, such as (220) for (110) poles, as described recently by Newkirk and ~ruce.~ Both the X-ray optics and the technique for pole figure differed slightly from those adapted previously.4

Jan 1, 1960

By Arthur B. Cummins

Diatomite is a siliceous rock of sedimentary origin, which may vary in degree of consolidation, but which consists mainly of the fossilized remains of diatoms. These are microscopic algae of the order Bacillaria. Diatomite is a unique form of silica, there being nothing else found in nature or produced by the manufacturing arts, that has its characteristic physical structure. There are numerous sediments which contain some diatom residues, admixed with a substantial amount of other materials-clay, carbonates or silica. While these are classified as diatomaceous silts, shales, or mudstones, they are not properly diatomite, a designation which is restricted to material of such qualities that it is suitable for commercial uses. The terms diatomaceous earth and kieselgur are synonymous with diatomite. The expressions infusorial earth and tripolite are obsolete. Diatomaceous silica is a definition best used to distinguish the basic component of diatomite, that is, the substance of the silica shell itself and is the major constituent of beneficiated diatomite or processed diatomaceous products. Some highly indurated materials, such as cherty shale, porcelanite, and opaline cherts which have resulted from diagenetic changes cannot be considered as diatomite although they may have been derived therefrom. On the other hand, diatomaceous oozes or loose sediments consisting mainly of diatom residues with or without much organic matter are source materials in process of becoming diatomite. Composition and Properties Pure diatomite is composed of opaline or hydrous silica, with small amounts of associated inorganic components-alumina, iron, alkaline earths, alkali metals, and minor constituents, all of which may occur in solid solution or as an essential part of the opal complex. Crude diatomite on the other hand may contain variable amounts of organic matter and soluble salts, and the usual contaminants of sedimentary formations-particles of rockforming minerals, sand, clay, or carbonates. As occurring in nature, diatomite contains an unusual amount of free water, which may vary from 10 to 60 pct or more. Diatomite, in the dry deposits which are characteristic of most of the important world deposits, occurs as a lightweight, comparatively light colored, "chalklike" material. The apparent density (dry basis) in situ varies from 20 to 40 lb per cu ft. The structure may be either massive or finely stratified. The earth is highly porous, usually soft and easily friable. It is nonreactive with acids and may be tentatively identified by the above characterizations. Confirmation is by microscopic examination which readily reveals the nature of the material. In deposits which contain organic matter the appearance of the material is totally different. The color may vary from light tan or gray to brown, greenish or nearly black. There is frequently difficulty in distinguishing it in the field from peatlike materials, but the difference is readily apparent after calcination. Powdered diatomite or diatomite products have an apparent density (loose weight) of 5 to 16 lb per cu ft, wet densities of 10 to 30 lb per cu ft, specific gravities 1.9 to 2.35, index of refraction 1.42 to 1.48. Diatomite is essentially micro-amorphous, but does show some tendency toward orientation in structure after a cristobalite pattern. Amorphous silica has been considered as a random association of cristobalite crystallites, the size of which are only slightly larger than a unit cell.20 The prop-

Jan 1, 1960

By Richard P. Hight

Abrasives include the substances, natural or artificial, that are used to grind, polish, abrade, scour, clean, or otherwise remove solid material, usually by rubbing action but also by impact (pressure blasting for example). They do not include abrasive tools, for instance, lathe tools and files--or polishing agents such as waxes, which act by filling pores. Detergents and cleaners whose action is chemical rather than physical are omitted al- though some chemical-action polishes and cleaners may also contain solid abrasives, for example, many automobile and metal polishes. General Considerations The most important physical properties of materials that qualify them for use as abrasives are hardness, toughness (or brittleness), grain shape and size, character of fracture or cleavage, purity or uniformity. For making bonded abrasive products such as grinding wheels, additional important factors are stability under high heat and bonding characteristics of grain surfaces. The economic factors of cost and availability are always important. No one single property is paramount for any use. For some uses extreme hardness and toughness are needed, as in diamonds for drill bits; for others, the factors of greatest importance are hardness and ability to break down slowly under use, to develop fresh cut- ting edges when grains become worn-for example: in garnet for sandpaper neither highly cleavable or friable grains nor extremely tough grains are wanted. For still other uses, great hardness is objectionable; for example, abrasives for dentifrices and for glass-cleaning soaps. For the most efficient use in the more critical applications, the different types of abrasives are rarely completely interchangeable; thus, while crushed quartz and garnet are both used in sandpaper, the papers are not at all interchangeable in their use applications. In the last analysis, the choice of a high grade abrasive depends upon the quality and quantity of work done by the abrasive per unit of cost. Initial cost of an artificial abrasive may be much greater than that of a natural abrasive but the artificial abrasive may do so much better work than the natural one, and do it so much faster that the ultimate cost will be less. It is for this reason that artificial abrasives have largely replaced natural abrasives. Abrasive Value Mineralogical hardness or "scratch" hardness as expressed in Mohs' scale is an important property in evaluating abrasive materials, but, as noted before, it is only one of several essential properties. The mineral hardness of pure crystal almandite garnet is about 7.5, but if the crystal is crossed by incipient fracture planes, or if it contains inclusions of other minerals, the apparent or useful hardness may be much lower. While the quartz grains in a sandstone have a hardness of 7, the bond holding the grains together may be so weak that the stone is valueless as a commercial abrasive. In artificially bonded wheels and stones, the hardness, strength, and character of the bond are fully as important as the hardness of the abrasive grains. Thus, in an overall consideration of abrasive hardness of loose abrasive grains, both "scratch" hardness and toughness must be considered. In naturally or artificially bonded abrasive stones, bond characteristics are a third factor, which is most important. The problem of abrasive hardness is further complicated by the inadequacies of methods of testing hardness and of expressing relative values. The Mohs' scale is inadequate both because the methods of testing are very crude and

Jan 1, 1975

By B. K. Larkin, H. R. Bailey

One of the most complicated and potentially one of the most promising secondary recovery methods is that of underground combustion. A number of field tests1,2,3 have been performed recently, apparently indicating that the underground combustion process is technically feasible. Relatively little has been published concerning laboratory or theoretical investigations of the underground combustion process. A few results of laboratory tube runs have been published4,5 and these data are valuable in understanding the process. The tube run data also emphasize the complexity of the thermal recovery process. Under various conditions, problems in heat transfer, multiphase fluid flow and combustion rates arise. For example, at low temperatures the combustion process proceeds so slowly that the front cannot be propagated. It is a problem in heat transfer to predict what injection rate of air is necessary to sustain combustion in a particular reservoir. Certain fluid flow aspects of underground combustion have been studied by Wilson, et a13. In the development of some of the flow equations, assumptions of adiabatic combustion were made. Vogel and Krueger1 have devised an analog model of the heat conduction process for a constant temperature cylindrical source moving radially outward in a homogeneous conducting medium. Jenkins and Ramey7, in a discussion of the Vogel and Krueger paper, present an analytical solution of a heat conduction problem related to problems considered by Vogel and Krueger. In the present paper an idealized model of the heat conduction problem is considered, which is more general than the model of Vogel and Krueger or Jenkins and Ramey. In particular, initial well heating, vertical heat losses and arbitrary frontal velocities are included. Equations for the temperature are obtained in terms of integrals. These integrals have been evaluated numerically for the case of frontal movement corresponding to a constant air injection rate and the case of constant frontal velocity. These results are presented graphically. From these graphs one may estimate conditions under which nearly adiabatic temperatures are obtained. The application of these results requires some knowledge of reservoir thermal properties, combustion rates and residual fuel content. Assuming no vertical losses it is possible to obtain explicit evaluations of these integrals in the linear con- stant velocity case and in the radial case corresponding to a constant air injection rate. PRESENTATION OF RESULTS The geometry of the radial system is illustrated in Fig. 1 where the reservoir is represented as a slab of thickness h. By making an energy balance for an infinitesimal volume, one obtains the following equation. T= x T+F(z.r).........(1) where F (z,r) =HWv1/pc (r-r1), if z h/2 = 0, if z >h/2 . In Eq. 1, V- represents the Laplacian operator and 8 is the Dirac delta function. Eq. 1 is the well-known diff-sion equation with a source term and may be applied to a linear system. For example, if the source is moving in the direction of the x axis, then the argument of the delta function is x - 1,. In deriving Eq. 1 the following approximations were made concerning the actual combustion process: (1) all heat transfer is by conduction in a homogeneous medium, (2) the formations bounding the reservoir have the same thermal properties as the reservoir, (3) the combustion fuel is consumed instantaneously as the front arrives, (4) there is a constant fuel concentration

By J. H. Reynolds

The possibility of using a semiconductor, metal, semiconductor structure as a light detector is discussed. A brief theoretical argument is presented which predicts that this structure should have pho-toresponse characteristics similur to those of a metal-semiconductor diode, but with the magnitude of the current increased by a transistor gain factor. Measurements made at low frequencies on a particulur S-M-S device agree u~th this prediction aizd shoul that significant gain factors are attainable. The current gain is substantially higher than that predicted for the metal base transistor. It is proposed that the operation of these units is more closely approxinzated by the metal-gate model which predicts higher current gains. A qualitative discussion of its high-frequency performance indicates that detection of light modulated at microwave frequencies by a S-M-S deuice is possible. ADVANCES in the technology of chemical vapor deposition'-4 have made it possible to form a S-M-S structure consisting of a thin metallic layer sandwiched between layers of single-crystal semiconductor. It has been proposed5-7 that, if the metal layer is made sufficiently thin, this structure could be used in an amplifier having several advantages over presently available transistors including higher-frequency performance. Calculations8 predict that the maximum gain-bandwidth product is nearly an order of magnitude higher than that of a bipolar transistor having the same geometry. Maximum oscillating frequencies in the microwave range are predicted. Electrical measurements made on S-M-S devices have shown that, although the theoretical frequency characteristics are not presently attainable, current and power gain is obtained. Another possible application of the S-M-S structure is its use in a light detector. This structure is a three-layer relative of the metal-semiconductor diode. Light detection using M-S diodes is the subject of considerable present interest. They are known to have a short response time and the ability to detect light having a photon energy below the semiconductor bandgap. In this paper, the mechanism by which S-M-S photocurrent is generated is discussed. An expression is derived which shows that the response characteristics are similar to those of a M-S diode, but that the magnitude of the current is increased due to the transistorlike behavior of the device. The results of low-frequency response measurements on a particular S-M-S structure are presented. These agree with the theoretical predictions and show that significant gain factors are attainable. A qualitative discussion of the high-frequency characteristics is presented which predicts that detection of light at microwave frequencies by a S-M-S device is possible. THEORY In this discussion, the photocurrent, iT, measured across terminals attached to the semiconductor emitter and collector layers is related to the current pho-toemitted from the metal base layer. The latter will be referred to as the primary photocurrent. The behavior of the primary photocurrent is determined by the characteristics of the two metal-semiconductor diodes. The diode photoemission is illustrated in Fig. 1, which shows the emitter and collector potential barriers. The metal thickness has been greatly exaggerated. As will be discussed later, the actual barrier shape can be much more complex, but this diagram illustrates the essential features of the photoemission process. An absorbed photon having an energy greater than the barrier height can emit an electron into the emitter or collector. Since this process is discussed

Jan 1, 1968

By L. A. Roe, John Jan

Iodine is a soft, lustrous, grayish-black nonmetallic element with a density of 4.9. It is the least active of the four members of the halogen family. The other members are, in order of increasing activity, bromine, chlorine, and fluorine. Iodine is a solid at ordinary temperatures, while bromine is a liquid and chlorine and fluorine are gases. Iodine melts at 113°C and volatilizes at 184.4°C to a blue-violet gas with an irritating odor. It occurs in nature only as iodates and iodides or other combined forms. It was discovered by Bernard Courtois in France in 1811, who noticed its presence as an unknown substance in crude soda ash obtained from burning seaweed. Gay-Lussac recognized it as a new element and named it iode, from the Greek word "ioeides or iodes" for violet color (MacMillan, 1970). The world production is not known with any great certainty, but it is probably between 25 and 35 million lb per year, of which about 30% is consumed in the United States. Geology and Mineralogy Iodine compounds occur as a minor constituent as a mineral in the Chilean nitrate deposits and in solution in brines and seawater. According to the US Geological Survey, it is the 47th most abundant element in the earth's crust. The minerals lautarite, Ca (I03)3 (calcium iodate), and dietzeite, Cat (103)2 (CrO4), (calcium iodate-chromate) are found in Chilean nitrate deposits which are located in Antofagasta and Tarapaca provinces on the eastern slope of the coast range in a desert area. Various brines contain iodine compounds. Seawater contains about 0.05 ppm of iodine and some seaweeds will extract and accumulate it up to 0.45% on a dry basis. Some coals in West Germany also contain iodine compounds. The known and potential sources of iodine reported in 1968 are given in Table 1. Table 2 lists estimated world iodine reserves. Iodine has been recovered from brines in Java, Indonesia, France, England, and the USSR. Iodine has also been recovered from seaweed in Ireland, Scotland, France, Japan, Norway, and the USSR. The indicated reserves and future resources of iodine are large but have never been adequately measured. Analysis Iodine as the free element can be detected by the characteristic blue color it gives to a starch solution. Quantitatively it is determined as the free element by titration with standard thiosulfate solutions using starch as an indicator. Colorimetric methods are also applicable. Markets and Prices Iodine and its compounds are generally marketed in the form of: iodine, crude; iodine, resublimed; calcium iodates; calcium iodide; potassium iodide, sodium iodide, and numerous organic compounds. Product Specifications Crude iodine, World market: 99-99.5% 12. Crude iodine, US produced, average: 99.8% 12. Crude iodine, USP XVII Specs: not less than 99.8% percent I2. Resublimed iodine is usually 99.9% and ACS specifications call for not over 0.005% total bromine and 0.020% nonvolatile materials (Anon., 1971). Prices, c.i.f. United States, for iodine have been steadily increasing from $1.18 per lb of crude in 1967 to $6.37-7.27 in January 1981 (Anon., 1981). In 1980 the price of iodine increased by 50%.

Jan 1, 1983

By C. L. T. Edwards

IN the preparation of this paper, the author has drawn upon experience with the operation of a blast furnace on 100 per cent scrap burden, which he believes was the first operation of its kind in the country. It is the writer's further belief that much of the controversy attending discussions of this subject may be obviated by the presentation of a group of facts that should be known by blast-furnace men and open-hearth men alike. The following question has been raised: "Is iron made with scrap in the blast-furnace charge as good iron as that made without scrap-made with straight ore?" This question may be answered in part by the fact that the open-hearth men of the Bethlehem Steel Co. who used pig iron from a blast furnace that operated on 100 per cent steel scrap found no difficulty in the processing of such iron other than that to be expected from the known analysis. OPERATION WITH 100 PER CENT STEEL SCRAP During World War I, there was accumulated at the Bethlehem plant of the Bethlehem Steel Co. some 22,000 tons of alloy-steel turnings and borings. This scrap material was highly corroded and, like alloy-steel turnings of that period, were as a drug on the market. There was also a small tonnage of scale, rich in valuable metal. If this scrap could be worked up into pig iron, it would become readily available for use in the open hearth. In order that the pig iron should contain the maximum percentage of nickel, permission was obtained from the Management to try a 100 per cent scrap operation. Accordingly, a blast furnace was swung over on July 25, 1919; the percentage of steel scrap increased more or less irregularly until July 29, when l00 per cent steel turnings were charged. Except for occasional charges of nickel scale as an "extra," the operation continued uninterruptedly until Aug. 27, when the furnace was swung back to the regular ore-ore and scrap-operation. During this period, the furnace production ranged from a low of 568.60 tons to a maximum of 766.07 tons. At the swing-over from i00 per cent scrap to the regular burden, the charge hung up rather severely. While the latter condition has nothing to do with the object of the paper, a brief discussion of the experience will appear later because of the interest it may have for blast-furnace operators. In Table I, results of the first and last days of the ore charge are shown, July 25 and July 29. The last column shows a summary for the period of maximum scrap charge. The furnace employed had a hearth 16 ft. 0 in., bosh 22 ft. 0 in., stock line 15 ft. 6 in., bell 11 ft. 6 in., batter ¾ in., bosh angle 73° 27' and a Baker-Neuman top, with gas-engine blowers. Analyses Range of Material Charged Gravel: Si02, 64.40 to .7o.54 per cent; A1203,3-52 to 4.58; CaO, 7.27 to 9.49; M90, 5.09 to 6.14; FeO, 1.67 to 3.34, ignition loss, 9.50 to 13.83.

Jan 1, 1941

* The greatest and richest iron ore body in the world was discovered by U. S. Steel in Venezuela in April 1947, and is disclosed for the first time in this issue (p. 178), One solid mountain of ore, Cerro Bolivar, will furnish more tonnage than the famous Hull Rust pit at Superior has, or can produce. Total resources are on the order of 2 billion tons plus. Big Steel is now moving with great speed on construction to bring out this ore, and 10 million tons are scheduled for shipment into Baltimore and Birmingham by late 1952. This ore will arrive at, Pittsburgh at a price lower than present natural ores from Superior. The Venezuelan properties will be completely mechanized. •U. S. Steel and independent companies are embarking on a taconite beneficiation program of tremendous proportions, which must be speeded to completion in the 1950's (see p. 185). By 1960 over $l.2 billion dollars will be spent on Venezuela, taconite, and Labrador to solve the United States iron ore crisis. In addition, U. S. Steel will spend another $300 million plus for a new steel mill at Trenton, N. J., before 1955. •The Deister Concentrator Co. gave $500 to the 1950 Coal Division Scholarship Fund. •Howard N. Eavenson, in analyzing the bituminous coal situation (see p. 193), suggests that anti-trust laws be extended to labor unions, disinterested trustees to administer pension funds, begin pension funds now and stop the collection of all "check-offs" for union dues or funds. •Minerals and metals worth 13.9 million dollars were produced in the United States in 1949, Secretary of the Interior Oscar L. Chapman announced. Although this value was 11 pct less than in 1948, it was the second greatest in history. Nonmetallics was the only major group that in 1949 equaled the 1948 production high. Mineral fuels decreased 12 pct and metals 15 pct. • Prospects for making gas from coal are seen to be unattractive by the Pittsburgh Consolidated Coal Co. because the success of operation depends on price and supply of coal which presently are not attractive. The company has shut down its gasification plant at Library, Pa. * Economic prospects for the immediate future in the United States are good and business probably will continue at its present high levels throughout at least the early part of 1950, Secretary of Commerce Charles Sawyer said in his year-end report to the White House based on his personal survey of business conditions. •A 467-ft well 34 miles north of Rock Springs, Southwestern Wyoming, is said to be flowing a 5 pct solution of nearly pure trona (sodium carbonate) at the rate of 10,000 barrels a day. Trona, natural soda ash, is mined for the chemical trade at Searles Lake, Calif., and from about 1500 ft underground near Green River, Wyo., and has been in short supply. •The AEC is "very much interested" in a discovery of radioactive material that has been made in Baraga County bordering Lake Superior in the Upper Peninsula of Michigan, reported F. G. Pardee, Michigan State mining engineer. The material has been identified as uranium oxide in the form of pitchblende or uraninite. The discovery, made by a geologist of the Jones & Laughlin Ore Co., is the only instance in which the commission has certified samples of Michigan rock.

Jan 2, 1950

By B. C. Wonsiewicz, G. Y. Chin

THE presence of deformation bands in cold-worked metals is known to influence the development of deformation textures1 but has not been considered in any theoretical treatments. At the present time the most rigorous theory of deformation textures appears to be based on Taylor's concept of homogeneous deformation of a crystal within a polycrystalline aggregate.' For each crystal the Taylor theory allows the operation of several equivalent combinations of five or more slip systems. Hence deformation bands can arise from the operation of a separate combination of slips in each of several portions within a crystal. On the other hand, a second type of band may occur as a consequence of slip on systems other than those selected on the basis on homogeneous deformation. This type appears to be associated with crystals of symmetrical orientations, such as the [loo] and [lll.] axial orientations in drawn wires of fcc single crystals studied by Ahlborn.3 In this note we propose a simple mechanism of deformation banding of the second type, and compare the theoretical results for wire drawing of [loo] and [Ill] with Ahlborn's observations. In outlini the model requires that the work to accomplish a given overall shape change by banding be less than or equal to the work to accomplish the same change by homogeneous deformation. While the work by homogeneous deformation, WH = ?T ;dri, can be calculated exactly by the equivalent methods of Taylor2 or of Bishop and Hill,4 the work by banding, WB, is less certain. The latter consists of 1) Wi, work by slip within a band, 2) Wb, work associated with formation of a boundary between bands, and 3) Wc, work to correct the difference in shape change arising from banding and homogeneous deformation. The Wi term can be evaluated explicitly for a band with an assumed set of slip systems, but a satisfactory analysis of Wb and Wc has not been obtained. Since WB = Wi + Wb + Wc WH, for banding to occur, however, a necessary condition is Wi = WH . Hence it seems reasonable to choose a band with the lowest value of Wi among competing bands consistent with Wi = WH, and then minimize Wb and Wc by arranging the physical configuration of the selected band. Wc is minimized by combining neighboring bands such that their net strain matches the macroscopic strain as closely as possible, and Wb is minimized by enforcing strain compatibility across the boundary between two neighboring bands, similar to the case of a grain boundary.5 It is realized that this procedure is not completely satisfactory, but it does seem to explain Ahlborn's observations reasonably well. The procedure is now outlined for the two corner orientations. a) [l00]. Fig. 1 shows a (100) stereographic projection. The results of the Taylor analysis for axi-symmetric flow by homogeneous deformation6 show that, while [loo] itself is unstable, the rotation of the tensile axis will nevertheless be confined to within about 15 deg from [loo]. Alternatively, less work may be expended by banding with slip on a pair of systems with primary-conjugate relationship, e.g., (ll1)[10l.I + (li1.)[110]. The latter represents minimum Wi for all possible bands.* Since there are four symmetrically

Jan 1, 1970