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By J. P. Heller, H. B. Bradley, A. S. Odeh

It is an accepted procedure to represent oil field displacement problems in which the pressure is relatively constant by a potentiometric model. Variations in reservoir permeability thickness product are represented in the model by proportional variations in electrolyte depth. It is shown that significant errors are present wherever these variations are of such magnitude that the consequent differences in the electrolyte depth in the model or any regions therein are appreciable in comparison with their respective horizontal dimensions. To demonstrate the order of magnitude of this error, a hypothetical linear oil field in which permeability varies linearly with distance was treated both analytic.ally and by potentiometric model. The results obtained from the model are compared with the exact solution for various configurations of linear geometry. Deviations in flow times up to 11 per cent were observed. It is confirmed that these discrepancies can be reduced by increasing the areal scale and/or decreasing the vertical scale of the model. It is the purpose of this work to assist in the design of potentiometric models by indicating the relationship between this error and the chosen scale factors. INTRODUCTION The fundamental geometrical criterion which determines whether the pressure distribution in an oil or gas reservoir may be simulated in a conventional potentiometric model is the requirement that all reservoir parameters be constant along any vertical line between its upper and lower boundaries. This situation never obtains exactly; nevertheless, it is usually assumed that there is no permeability stratification within the section of interest, that all wells completely penetrate the sand, that there are no gravitational effects, and that variations in thickness of the sand are small compared to the horizontal extent of the field. In these ways the reservoir problem is reduced to two dimensions in which there is no variation of pressure in the vertical direction within the limits of the sand. Variations in sand thickness and/or horizontal pesmeability may be taken into account as described by Muskat, by considering the fluid conductivity of the reservoir in its horizontal plane to be proportional to the product of permeability and sand thickness. If the variations in sand thickness are small compared to the horizontal dimensions of the reservoir, then it is a good approximation to consider the reservoir problem to be essentially two dimensional. The same approximation, however, is made in the simulation of the assumed two-dimensional reservoir by the electrolytic model. The model, if it is to take into account variations of permeability-thickness product, must of necessity be made in three dimensions, that is, with variable depth. Most potentiometric model studies and theoretical treatments reported in the literature to date2,3,4,5,6,7,8 are those in which either an average permeability was used or a constant permeability was assumed. This is understandable since detailed permeability data are not usually available for the majority of reservoirs. Many investigators have recognized that the failure to incorporate permeability variations within a reservoir in model studies leads to serious error in predictions made

Jan 1, 1957

By J. D. Cooner

SINCE my working life of 32 yr has been spent in and about the anthracite mines of the Hudson Coal Co., and the previous 4 yr in a college school of mines, I can write best about the safety program of a coal mining company. However, most of the suggestions, statements and practices mentioned herein are applicable to the members of a safety organization and program of almost any industry. It is realized that industrial officials actually interested in real safety work are fully acquainted with the requirements of a practical safety program. Therefore, for such persons there may be nothing new in this paper. The Hudson Coal Co. of Scranton, Pa., employs 7,000 men and produces 5,000,000 tons of anthracite annually at nine collieries scattered for a distance of 40 miles throughout the Lackawanna and Wyoming valleys of northeastern Pennsylvania. For the past 17 yr of the above mentioned 32, I have been engaged in safety work as a safety inspector, assistant mine superintendent, and at present the safety engineer. I have also had the privilege of visiting coal and metal mines in other parts of the United States and Canada. We Americans are the most careless people in the world. If any one doubts this statement why are 100,000 of our people killed accidentally annually? Or why during the almost four years we were engaged in World War II were more of our people killed accidentally at home than were killed in our army, navy, marine corps, coast guard, and other services during the same period? We are careless everywhere in our homes, on the highway, at work and at play. The purpose of this paper is to outline the requisites of a safety department and its program to stop the accidents occurring to employees at work in mines or industrial plants. The first requisite for a safety program is that the management must be convinced of the need and value of a real safety program. By "management" is meant each department head from the president down. Otherwise a good safety department with a good safety program will not succeed because it will not have the proper personnel and equipment to work with, its rules and regulations will not be enforced, and the members of the safety department will be belittled in the eyes of most of the workmen and supervisors. Next, a safety engineer and his inspectors should have worked in the production end of the mines as workmen and also in an official capacity. They are then in a position to have practical and first hand knowledge of the accident hazards of the industry, how to prevent them, and in general the problems of both the workmen and officials. Some men are appointed as safety inspectors when they are physically unable to carry on as mine officials. Such men may know the safety end of the industry and even be safety-conscious, but if they are physically unable to be mine officials they are also physically unable to be safety inspectors, as a safety inspector in our mines must walk from 2 to 4 miles on each daily inspection-and visit each working

Jan 1, 1948

By A. T. Robinson, J. E. Dorn

The electrical resistivities of aluminum alloys containing CU, Ge, Zn, Ag, Cd, and Mg were found to increase linearly with the atomic percentage of the solute atoms. Application of Linde's rule to these data suggests that each aluminum atom contributes 2.5 electrons to the metallic bond. ALTHOUGH aluminum invariably exhibits a Jt\. valence of three in ionic solids, it does not follow necessarily that its valence in the metallic state is also three. As a matter of record, many properties suggest that the number of bonding electrons in metallic aluminum is less than three. For example, as shown in Fig. 1, the atomic radii1 of the metallic elements in the solid state decrease with increasing atomic number at the beginning of any one period. The atomic radius of aluminum, however, is greater than that which would result from a regular decrease in atomic radius with increasing atomic number, suggesting that the number of bonding electrons in aluminum is somewhat less than three. Correlated with the anomalously large atomic radius of aluminum is its abnormally low melting temperature. As the atomic numbers increase in any one period, the melting temperatures of the metallic elements increase.' As shown in Fig. 2, however, the melting temperature of aluminum (13) is only slightly greater than that of magnesium (12). Again the number of bonding electrons in metallic aluminum appears to be nearer two than the expected value of three. In addition Ageev and Ageeva3 alculated the electron density distribution in the aluminum lattice. A comparison of such electron density curves for various assumed valence states of aluminum with experimentally determined curves suggests that the actual number of bonding electrons in metallic aluminum is between two and three. Hume-Rothery and Raynor', " have suggested that the above-mentioned abnormalities are associated with the overlapping of the Brillouin zones of metallic aluminum when it is in the usual face-centered cubic structure. The importance of the number of bonding electrons in metals has been extended recently into the field of mechanical properties. While formerly it was thought that the plastic properties of alpha solid solutions were primarily dependent upon the lattice strain induced in the solvent by the solute, it is now known that the difference in the number of bonding electrons of the solute and solvent also has its influence on the plastic properties."1' In order to achieve a satisfactory correlation of the effect of alloying elements on the plastic properties of aluminum alloys,"'T however, it was necessary to assume that the number of bonding electrons contributed by aluminum was about two rather than the expected value of three. It appeared to be desirable, therefore, to seek other criteria for evaluating the number of bonding electrons contributed by aluminum to its alpha solid solutions, especially in view of the practical as well as the theoretical importance of the effect of valency on the plastic properties. Norbury' was perhaps the first to illustrate that the increase in resistance of alpha solid solutions is associated with the differences in valence of the solute and solvent metals. In a series of illuminating investigations Linden-'' has shown that the electrical

Jan 1, 1952

By John T. Galey

The outstanding developments of the year in southwestern Pennsylvania were the establishment of the Summit Fayette County gas pool and the gas pool in Nicholson township, Fayette County, and Monongahela township, Greene County, as major producing areas, and the indication of four new shallow gas pools. Curtailment of drilling for shallow gas is expected to follow order M68 of the Office of Production Management. Gas completions were approximately 70 per cent higher, oil completions nearly 25 per cent lower, dry holes were unchanged and drilling wells as of Dec. 31, 1941, nearly loo per cent higher than last year. Shallow Development Oil.—Outside Butler County, only 11 producers were drilled, with a total initial of 221 bbl. The best of these was in a portion of Gilmore township, Greene County, which ordinarily produces gas. This well flowed 77 bbl. in 11 hr., along with about one million cubic feet of gas from the Fourth (U.Dev.) sand. Washington County had a 10.20 and a 25-bbl. well in Morris township and a 20-bbl. well in South Franklin township. These were all in the Fifth Sand. The price of oil to Jan. 27 was $1.80 per barrel, when a 15¢ increase was made. This was followed by a raise of 20¢ on Apr. 23, 15¢ on May 21, 20¢ on June 18 and 25¢ on Aug. 14. The last increase was canceled on Aug. 23 by the Office of Price Administration, which pegged southwestern Pennsylvania crude at $2.40 per barrel. Gas.—An almost doubled initial production of natural gas is the result of the large increase in number of wells drilled. The outstanding discovery of the year was in the vicinity of Armbrust, Hempfield township, Westmoreland County, where a well drilled to what at first was considered the Bayard sand, but what is now known to be the Fifth (U.Dev.) sand, at 2100 ft. found nearly 5 million cu. ft. of gas. Since this completion 14 wells have been finished, only one of which was dry, giving a combined total open flow of approximately 15 million cu. ft. The sand is 35 to 40 ft. thick and the saturation extends through most of that thickness. Rock pressure, which is 1040 lb. per sq. in., is abnormally high. An area of only about one square mile has been proven but some of the 24 new wells drilling as of Dec. 31 will no doubt extend it considerably. This development has taken place in an area heretofore considered to have had little prospect. There were three good wells in other parts of Westmoreland County. One well in Franklin township, which had 12 million cu. ft, of gas in the Fifth sand, was entirely surrounded by dry holes but is still pro- . ducing at a high rate. In Bell township a 1.6 million cu. ft. well was found in the Speechley (U.Dev.) sand and in Washington township the same sand produced 2.7 million cu. ft. with shut-in pressure of 970 Ib. at 2820 ft. This well is offset by two dry holes and one well with a capacity of only 10 M cubic feet.

Jan 1, 1942

By R. P. Thomas

Secondary fertilizer minerals are the mineral materials used to supply directly and indirectly the secondary and trace plant food nutrient needs of a fertilizer. Since few soils contain sufficient availability of all plant nutrients for their proper growth, man has prepared mixtures of plant food materials to correct these nutrient deficiencies. These mixtures or fertilizers, when added correctly to a soil, make it possible for abundant and economic crop growth. Many kinds of materials are used as sources of these needed nutrients. They come from natural and synthetic materials and minerals including many beneficiated byproduct compounds. A fertilizer consists largely of carriers of one or more of the three major plant foods, namely nitrogen (N), phosphorus-phosphorus pentoxide (P2O5) and potassium-potash (K2O). Many other nutrients are just as essential for plant growth as the three major plant foods. In fact, the efficient use of fertilizers today depends upon an adequate supply of all these other nutrients. Since these additional materials are usually removed from the soil by plants and supplied in fertilizer in less quantities than the major nutrients, they are called secondary and minor nutrients. In the early days these special nutrients were contained as impurities in the primary nutrient carriers. Today, fertilizers are made primarily from concentrated and synthetic materials which carry very few of these other essential nutrients. Consequently, many secondary and trace nutrient carriers, as salts, byproduct compounds and even minerals have to be added to fertilizers. Secondary Nutrient Carriers The secondary plant foods in fertilizer are next to the major nutrients in abundance. They are calcium, magnesium, sulfur, chlorine, silicon and sodium. Although many of these elements are added to a fertilizer as part of the major nutrient carriers, they are also added in special carriers. The large tonnage of these secondary nutrient carriers used in fertilizers represents only a small percentage of the total production of these materials. A fertilizer producer thinks in terms of materials which supply nutrients instead of minerals. Therefore, these materials will be discussed by elements. CALCIUM Soils need calcium to supply the nutrient needs of plants and maintain the desired physical and biological conditions in the soil. The available calcium is usually 40 to 80 pct of the exchangeable bases. (These bases are ones which can be displaced by other cations and determined quantitatively. They are then expressed as milliequivalents per hundred grams of soil-me.) Direct applications of lime materials such as burnt, ground or hydrated limes are the important sources of calcium for the soil. Most crops, especially legumes, have a high requirement for calcium. The average farmer does not use enough lime to maintain the proper level of available calcium. Hence, it is necessary for many fertilizers to contain soluble calcium materials for efficient use of the major nutrients. The following major nutrient carriers supply some calcium: calcium nitrate, ammonium nitrate mixtures and cyanamid, and many of the phosphates. Both synthetic and natural gypsum are used in fertilizer production. Some crops such as peanuts require a large amount of soluble calcium. Gypsum is the important supplier of this soluble calcium. It is not applied with the fertilizer

Jan 1, 1960

By Joseph L. Gillson

Bentonite, designating a distinct type of clay, is a young name in mineral nomenclature in the light of the age-old names of most other useful nonmetallics. The earliest references in literature are to "soap clay" (1873) "taylorite" (1888) and finally "bentonite" in 1897, from its occurrence in the Fort Benton series of rocks near Rock Creek, Albany County, Wyoming. Bentonite is a rock term and consists largely of montmorillonite clay. The latter name was proposed in 1847 for a plastic clay found at Montmorillon, France. A clay of apparently identical properties was described by Cronstedt of Sweden in 1788 and a number of other similar clays found in France were given other names in publications from 1853 to 1856. The mineral name montmorillonite was recognized by Dana in 1892. The recognition of "clay mineral" distinctions which led to the present-day classifications of clays by their chief mineral content, dawned in the early part of the twentieth century. Grim6 has aptly said: About 1924, Ross10 and some colleagues of the U. S. Geological Survey began a study of the mineral composition of clays that led to a series of monumental papers on the subject. By the early 1930's what has come to be known as the clay-mineral concept became firmly established in the minds of a great many people actively studying clay materials. The clay mineral concept designates the major clays as kaolins, montmorillonites and illites and by this concept bentonites are now defined as "fine-grained clays containing not less than 85 pct montmorillonite" and a wide variety of clays found all over the world are included in that classification. They could all properly be called "montmorillonite clays" but the common commercial name is bentonite. For a period of over forty years from the time of the earlier discoveries, bentonite was thought to be only the sodium type highswelling clay produced principally in Wyoming. By the clay mineral concept, non-swelling montmorillonite clays also became known as bentonite. In the trade there are two broad divisions-sodium bentonite, often called Wyoming or "western," which expands in water and carries sodium as its predominant exchangeable ion, and calcium bentonite often called "southern," which has negligible swelling and carries calcium as its principal exchangeable ion. There are many intermediate gradations. Properties The mineralogy and chemistry of the clays are so complex that the subject cannot be summarized briefly. The reader is referred to Chapter 12 of this volume in which the subject is treated at some length. Grim6 gave the formula for montmorillonite as (OH)4Si8AL4020.nH2O. He wrote: Montmorillonite is composed of units made up of two silica tetrahedral sheets with a central alumina octahedral sheet. . . . Exchangeable rations occur between the silicate layers. . . . The words "tetrahedral" and "octahedral" refer to the coordination number of the cations in the unit cell in the crystallographic lattice. Carroll5a stated: That the montmorillonite structure is the same as that of mica, but the layers are not held together by K+ ions; and water and other polar molecules, such as organic molecules, can enter between the unit layers and cause expansion. Ex-

Jan 1, 1960

By A. Andreas

New Mexico established an annual record by producing 38,897,741 bbl. of oil during 1940. This was approximately 6 per cent greater than the 1939 production of 36,746,840 bbl. The daily average produc-tion was 106,569 bbl. New Mexico retained its position as the seventh oil-producing state. The recommendations of the United States Bureau of Mines were followed by the Oil Conservation Commission in setting the monthly state allowable. At the beginning of the year the average top allowable for each qc-acre unit was 40 bbl. and at the close of the year it was 36 bbl. Remedial work by the operators has been extremely beneficial and satisfactory in reducing the gas-oil ratios in various fields. Gas formerly blown into the air is now being processed by numerous casinghead plants. The Oil Conservation Commission, with the full cooperation of the Proration Office and operators, has taken bottom-hole pressure surveys and has done considerable remedial work in various fields. Two new oil fields and one gas field were discovered in New Mexico during 1940. Numerous extensions to the existing fields were made. Some of these were definitely wildcats in the same townships designated as fields and some, although called extensions, were more than 3 miles from production. Lea County continued to be the largest oil-producing county in the state, with a production of 33,976,394 bbl. It had the largest number of completions during 1940, with 303 oil wells, 9 gas wells and 13 dry holes—a total of 325 wells. Eddy County was the next most active county, with 239 completions, of which 163 were oil wells, 8 gas wells and 68 dry holes. It produced 4,405,158 bbl. of oil during the year. The increased activity in Eddy County and the completion of a large number of producing oil wells have created a transportation problem that can be solved only by additional pipe-line facilities. During the year Eddy County was unable to produce 1,500,000 bbl. of its allowable oil, because there was no pipe-line outlet. There were 601 wells completed in New Mexico in 1940, of which 478 were oil wells, 22 gas wells and IOI dry holes. This was a decline of approximately 9.5 per cent in the number of completions compared with 1939, when 659 wells were drilled. Southeastern New Mexico Lea County.—The largest producing field in Lea County was the Monument field, with 6,894,475 bbl.; followed by Eunice with 6,559,348 bbl. and Vacuum with 4,743,065 bbl. The Hobbs pool, which for years was the largest producing field in the state of New Mexico, was fourth with 3,790,477 bbl. The Vacuum pool was the most active area, having 68 completions, of which 67 were oil wells and one was a dry hole. Only one new field was discovered in Lea County during 1940; the discovery well was in the Caprock area, the Livermore State No. I, in the SE. 1/4 SE. 1/4 sec. 30, T. 12 S, R. 32 E. This well was drilled to a

Jan 1, 1941

By Irving Cadoff, Richard Nolder

An analysis oj a series of samples of single -crystal silicon grown on sapphire shows that ,four distinct orientation relations exist. There are at least thirteen crystallographic planes which serve as substrates ,for epitaxial growth The model which assumes that silicon substitutes for aluminium and bonds with the oxygen atoms of the sapphire to form the first later for subsequent growth can account for the epitaxial geometry in all four cases. Multiplici-ties 01 specific orientations are found which are explained by the symmetry of both the sapphire and silicon crystal structures. It was reported in the previous paper' that single-crystal silicon films can be deposited on single-crystal a A1,03 (sapphire) with a wide variety of orientations. The silicon films, however, were found to deposit in only four different orientation relationships with respect to the sapphire substrate. The X-ray data have been analyzed to determine the plane and direction of atomic fit and an atomic model to account for the epitaxial relationships at the silicon-sapphire interface has been developed. These results are described in the present paper. EXPERIMENTAL The Laue X-ray data described in the previous paper were reduced to stereographic projections in a standard manner. These data were supplemented with X-ray reflection data obtained with -& E and A Full-Circle Goniometer (Electronics and Alloys, Inc.) mounted on a Phillips diffractometer unit. The silicon films were thin enough to result in characteristic reflections from the substrate as well as the silicon. The superimposed stereographic projections were analyzed to determine the orientation relationships. Ambiguities were resolved by referring to constructed models of various lattice planes for both silicon and sapphire. These lattice models were also used to develop the model for atom fit at the interface. DATA AND ANALYSIS 1) Crystal Structures. The crystallography of silico-n, which is of the diamond cubic class with a. = 5.4~, is straightforward. The sapphire structure is more complex and generally difficult to represent in pictorial form. It is of the rhombohedra1 class but usually referred to hexagonal axes. The transformation of indices between these two systems can lead to ambiguities which will have bearing on the analysis presented herein. Therefore, the basis used in this paper is described in the appendix. Referred to the hexagonal system, the parameters of sapphire are co = 12.95.&, a, = 4.75~, c/a = 2.73. All parameters are for room temperature. Figs. 1 and 2 illustrate schematically the hexagonal unit cell model of sapphire used for this analysis. The oxygen atoms are assumed to occupy positions in an idealized hexagonal array on basal planes. Their actual positions are in a slightly distorted hexagonal array. The aluminum-atom positions are scaled to their actual positions in the lattice with respect to the basal layers of oxygen atoms. It was found that an idealized model where the aluminum atoms are assumed to lie exactly at the octahedral interstices of the oxygen lattice, similar to that used by ~ronberg,' was not adequate for this study.

Jan 1, 1965

By C. A. Bruch, J. F. Duffey

On the basis of metallographic and cooling-rate studies of 15 U-Zr alloys, a new version of the 6 phase region of the U-Zr phase diagram is proposed. IN several published diagrams of U-Zr alloy system:' there is good agreement that at elevated temperatures complete solid solubility exists between y uranium and ß zirconium. Similarly, there is reasonably good agreement concerning the uranium-rich and zirconium-rich ends of the diagram. However, there is no agreement concerning the nature of the diagram at intermediate compositions and at temperatures below about 650°C. The early work of Saller et al.8 hows an intermediate phase, 6. In a later diagram by Saller and Rough' shown in Fig. 1, the d phase field is drawn with dotted lines, indicating doubt that this phase exists. The diagram of Summers-Smith2 does not show the d phase. More recently Holden and Seymour' have shown that in the composition range 40 to 60 wt pet Zr, the high-temperature ? phase, which is body-cen-tered-cubic, transforms to an ordered structure, 8. They found that the order-disorder transformation occurs between 595° and 610°C, and presented a diagram based on the study of four different alloy compositions. Most recently Saller et a1.5 presented a new diagram which differs with respect to the composition limits of the 8 field from the others proposed by these authors. The purpose of the present investigation was to determine the boundaries of the d phase field. Experimental Procedures and Results Alloys—Buttons, weighing 80 g of 15 different alloy compositions were prepared by arc melting Mal-linckrodt uranium and iodide-process zirconium in a water-cooled crucible. A controlled atmosphere of argon and helium was maintained in the furnace. Prior to making each button, a sacrificial button of zirconium was melted to increase the purity of the furnace atmosphere. Each alloy was then melted six times to improve its homogeneity. Subsequently the alloy buttons were jacketed in copper and hot rolled to slabs at 775°C. From these slabs, specimens were machined for chemical, thermal, and metallographic analyses, Table I gives both the estimated chemical composition of the alloys, and the values which were obtained by analysis. The oxygen contents varied from 0.013 to 0.032 pet, nitrogen from 0.0014 to 0.014 pet, and carbon from 0.0013 to 0.011 pet. The purity of the alloys ranged from 99.947 to 99.975 pet. Thermal Analysis—The specimens for thermal analysis were blocks 11/4 x 1/4 x % in. The bead of a calibrated thermocouple was placed between two of these blocks and molybdenum wire was wrapped around the assembly. Each assembly was sealed in a quartz capsule having an argon atmosphere. The capsule was placed inside a refractory crucible which was heated in a furnace. Using a method described by Smith,' the emf of a differential thermocouple, with junctions inside and outside of the refractory crucible, was used to activate the

Jan 1, 1959

By D. Havlena, A. S. Odeh

The use of the straight-line method of solving the material balance equation is illustrated by means of six field cases. Also, the application of statistical criteria to arrive at the most probable answer is shown. The theory underlying the straight-line method of solution and the applicability of the statistical criteria was presented in a previous paper.' The field cases include saturated and undersaturated oil reservoirs with and without water drive. The aquifers discussed are: limited radial, infinite radial, very small aquifer and infinite linear. The field cases also include a gas reservoir producing under water drive. INTRODUCTION In a previous paper,' the authors presented the theory underlying the solution of the material balance as an equation of a straight line. The appropriate equations for various material balance cases as well as the methods of analysis and interpretation with comments and discussion were also included. To illustrate the various theoretical cases treated previously, five field cases are analyzed in this paper by employing the straight-line method of solving the material balance equation (MBE) and one example previously published is referred to. The use of statistical criteria to arrive at the most probable answer is also shown. All the field examples presented, except Case 2, are excerpts from complete reservoir studies. To illustrate the method, only sections specifically dealing with the material balance principles are included. Additional geologic information and basic data are reported to better acquire an understanding of the cases and thus to better follow the reasoning that suggested the successful application of the straight-line method of solving the MBE. The six cases are: (1) saturated reservoir, small gas cap, limited aquifer; (2) saturated reservoir, very small gas cap, infinite aquifer; (3) undersaturated-saturated reservoir, very small aquifer; (4) highly undersaturated reservoir, no water drive; (5) high undersaturated one-well reservoir, limited aquifer; and (6) gas reservoir, infinite linear aquifer. THE D4 SAND, GUICO FIELD, VENEZUELA The D, sand, which was discovered in 1943, is presently in a depleted state. Since its discovery it has produced under water drive, gas-cap-gas expansion, and solution gas drive. In Nov., 1947, water injection was initiated to arrest further pressure decline. When discovered, the D, sand was a saturated reservoir with a gas cap /oil zone volume ratio m estimated volu-metrically at 0.0731, an average permeability of 500 md, a porosity value of 25 per cent, and an oil viscosity at reservoir conditions of 0.3 cp. The volumetrically determined stock-tank oil initially in place was 23.1 million bbl. The volumetrically weighted physical data and production data available until Nov., 1953 are reported in Table 1. In Ref. 1, the effects on the straight-line plot of various values of ro/r for a constant ?to, or of various dimen-sionless times for a constant r8/r10 were theorized and were illustrated in Fig. 3A of that reference. In this field case, the previously theoretically predicted effects are established. Thus, the MBE calculations using Eq. 3c of Ref. 1 were performed for various r6/r10 and dimension-less time values. Eq. 3c of Ref. 1 is:

Jan 1, 1965

By B. S. Gottfried

A generalized mathematical model is presented, which describes the thermal recovery of oil in linear systems with convective external heat loss. Three-phase fluid flow, conduction-convection heat transfer, chemical reaction between oxygen and oil and aqueous phase change are included, making the model applicable to a variety of thermal recovery processes. The complexity of the model requires that numerical solutions be obtained with a digital computer. The numerical approximations of the partial differential equations are presented and the algorithm is discussed in detail. The analysis is applied to the detailed simulation of a forward-combustion laboratory tube experiment. The results of the simulation exhibit with reasonable accuracy all of the principal thermal and bydrodynamic characteristics observed in the laboratory (i.e., the propagation of a combustion zone, a steam plateau, and oil and water banks). Numerical variations in the parameters appearing in the external heat-loss term, the aqueous phase-change term, and the Arrhenius combustion term are examined, and their effects on the predicted temperature profiles, oil and water production histories, and the air-oil ratio are presented. In spite of an oversimplification in the chemical reaction mechanism and the considerable computer time required to obtain solutions, the model represents a major advance in the ability to simulate the phenomena observed in thermal recovery experiments. INTRODUCTION Thermal oil recovery refers to a class of recovery processes where heat is supplied to a reservoir to provide the necessary expulsive energy. This thermal energy can be supplied externally as steam or hot water, or it can be generated in situ by forward or reverse combustion. In either case, however, thermal recovery processes are charac- terized by the simultaneous flow of two or three fluid phases in a variable - temperature field, accompanied by possible chemical reaction or phase-change effects.2-5, 7- 10, 14,16-18,20-22 Although a physical understanding of the thermal recovery processes is far from complete, it is possible to construct mathematical models which describe approximately all of the principal physical and chemical phenomena. However, attempts to solve such models, even with high-speed computers, involve formidable mathematical difficulties. Consequently, theoretical solutions have been obtained only for idealized cases in which important physical phenomena are neglected. For example, consider the process of forward in situ combustion. All such theories which have been developed consider only certain aspects of the process, such as heat transfer, 2-4,8,9,l6,l8 heat transfer with phase change,10 heat transfer with chemical reaction,7 or the hydrodynamics of three-phase flow.21 A general theory including all of the above phenomena has not been developed to date. This paper presents a unified theory of thermal recovery processes in linear systems. A mathematical model is developed which explicitly includes conduction-convection heat transfer with convective external heat loss, chemical reaction between air and oil, aqueous phase change, and the hydrodynamics of three-phase flow. A system of equations is developed which can be solved numerically on a high-speed digital computer, resulting in predicted temperature, pressure, and saturation histories in space and time. The model allows a more detailed simulation of thermal recovery tube experiments than had previously been possible. THEORETICAL DEVELOPMENT Consider the linear flow of gas, water and oil in a homogeneous porous medium. Assume that the oil will react with gaseous oxygen, and that mass is transferred between the water and gas phase by evaporation or condensation. In the absence of hydrocarbon phase change, intraphase diffusion,

Jan 1, 1966

By M. Semchyshen, A. P. Coldren, W. G. Scholz

A survey of the Fe-Mo-B system was made to determine the extent to which boron might affect the microstructure and strength properties of iron-rich Fe-Mo alloys. Seventeen vacuum-induc tion melted ingots were prepared with approximate mo-lybednum contents 01 2, 4, 9, and 19 wt pct and approximate boron contents of 5, 14,50, and 630 ppm by weight. Phases extracted from annealed specimens and identified by X-ray diffraction analysis included E Fe3MO2, Mo2FeB2, and an oxide hazling a diffraction pattern practically identical to that of MnFez04. Three types of alloy strengthening were observed: a) Fe-2 pct Mo-B alloys were hardenable by a bainitic-type transformtion of austenite to ferrile; b) Fe-4 pct Mo-B alloys were hardened by the solid-solution mechanism; and C) Fe-9 pct Mo-B and Fe-19 pct Mo-B alloys were hardened by precipitation of the E Fe3Moz phase. Boron was observed to have a very strong hardening effect in the Fe-2 pct Mo alloys and a mild strengthening effect on the 1200°F properties of the Fe-4 pct Mo alloys. In the Fe-9 pct Mo alloys there was no consistent effect of boron on strength at either room temperature or 1200° F. The Fe-19 pct Mo alloys were so brittle that meaningful tensile or creep-rupture data could not he obtained. No dispersion hardening from borides was recognized in any of the alloys. THE high-temperature properties of iron-rich Fe-Mo alloys were studied by Reiter and Hibbard.' They found that the strength of the alloys increased markedly as the molybdenum content was raised from 0 to 15.9 pct by weight. The authors explained the various degrees of strengthening in terms of a) solid-solution strengthening, b) strengthening from a martensitic-type transformation, and C) precipitation strengthening. The objective of the present investigation was to conduct a survey of the iron-rich portion of the Fe-Mo-B system to determine whether the beneficial effects of molybdenum on the strength of iron can be enhanced by the presence of boron. It was thought that perhaps fine dispersions of molybdenum- rich borides would be found which could improve the high-temperature strength of ferritic alloys beyond the strengths attainable by molybdenum additions alone. Also, it was considered worthwhile to study the effects of boron in alloys which are essentially free of carbon. Most, if not all, of our present knowledge about boron in high-temperature alloys pertains to alloys containing carbon and carbides. EXPERIMENTAL PROCEDURES Alloy Preparation. Seventeen 8-lb ingots were prepared from electrolytic Plastiron, unalloyed molybdenum chips, and boron powder by a vacuum-induction melting procedure employing hydrogen as the main deoxidizer. The alloys were melted in alumina crucibles using 35-lb melts, with each melt being split four ways to achieve varying boron contents within four Fe-Mo base compositions. The results of chemical analyses conducted on chips machined from the chilled ends of the ingots are presented in Table I. The boron analyses were performed by a spectrographic method utilizing primary standards prepared from boric acid. They indicated that in ingots to which no boron was

Jan 1, 1964

By Frederic L. Kadey

Diatomite is a siliceous, sedimentary rock consisting principally of the fossilized skeletal remains of the diatom, a unicellular aquatic plant related to the algae. Thus, it has been formed by the induration of diatomaceous ooze, and consists mainly of diatomaceous silica, a form or variety of opal which is first formed in the cell walls of the living diatom. Diatomaceous silica is not generally regarded as a synonym or the equivalent for diatomite, although it has been so used at various times. Accurately, diatomaceous silica is the preferred name for the principal mineral component of which the rock, diatomite, is composed. The terms diatomaceous earth and kieselguhr are used as synonymous with diatomite. The designations tripoli, tripolite, infusorial earth, etc., were used at one time but are now obsolete. With the changing nomenclature, these terms that were at one time correct when proposed and used for generations would be considered incorrect if used today in the light of current knowledge. The designation diatomite is reserved for those accumulations of diatomaceous silica that are of sufficient quality, size, and minability to be considered of potential commercial value. Processed diatomite possesses an unusual particulate structure and chemical stability that lends itself to applications not filled by any other form of silica. Foremost among these applications is its use as a filter aid, which accounts for over half of its current consumption. Its unique diatom structure, low bulk density, high absorptive capacity, high surface area, and relatively low abrasion are attributes responsible for its utility as a functional filler and as an extender in paint, paper, rubber, and in plastics; and as an anti-caking agent; thermal insulating material; catalyst carrier; and chromatographic support; polish, abrasive, and pesticide extender to name a few representative applications. The United States is the principal producing country, although diatomite is found in numerous other locations. Geology Composition and Morphology Diatomaceous silica qualifies as a. mineral of organic origin in much the same way that aragonite and collophane do. The silica of the fossilized diatom skeleton closely resembles opal or hydrous silica in composition (SiO2 • nH2O) .4, 12, 203 The silica is of acute biological significance, not only for the cell wall component, but also for the basic life process.45, 51 Without silica, cell development ceases .31 In addition to bound water, varying between 3.5 and 8%, the siliceous skeleton may also contain, in solid solution, or as part of the Si02 complex, small amounts of associated inorganic components-alumina, principally-and lesser amounts of iron, 46, 49, 55 alkaline earths, alkali metals, and other minor constituents.59, 63, 67 Boron is reported to be an essential element for diatom growth .52, 58 Since diatomaceous silica is not pure hydrous silica but contains other intimately associated elements, there is good reason to consider it a distinct type or variety.4 Associated with the diatomaceous silica, and integrated as part of the diatomite, may be variable amounts of organic matter, soluble salts, and particles of rock-forming minerals that were syngenetically deposited or precipitated with the diatom frustules. Sand, clay, carbonate, and volcanic ash are typical common contaminants. Other contaminating minerals may be present, such as feldspar, mica, amphiboles, pyroxenes, rutile, zircon-the result of weathering, then transporting, and subsequent redeposition of surrounding land masses. Commercial diatomite may also contain fragments and particles of

Jan 1, 1983

By John H. Schemel

Large Zircaloy-2 hammer or press forged bars did not exhibit the uniform excellent corrosion resistance to steam normally expected of the alloy in wrought form. Weight gains of coupons cut from forged bars were 40 to 60 mg per sq dm compared to the 28 mg per sq dm obtained on hot rolled sheet and strip. The mechanism of this corrosion and its relation to microstructure is discussed. After these observations, a solution heat treatment followed by rapid cooling was tried on coupons from eight heats of forged bars. The basket-weave structure resulting from the quench did not show agglomeration of intermetallic compounds. These coupons showed uniformly good corrosion resistance with weight gains very close to the 28 mg per sq dm expected of Zircaloy-2 after the 14-day steam test. A large forging was solution heat-treated and tested for structure, mechanical properties, and corrosion resistance. Corrosion resistance was excellent and uniform throughout the section. The normally anisotropic mechanical properties were changed to completely iso-tropic. Strength levels were raised while there was a small loss in ductility at the service temperature. Tempering of the quenched structure below the ß transus did not improve the ductility at the test temperature of 600°F. ZIRCALOY-2 end caps for nuclear fuel elements Zircaloy-2 is an alloy of 1.5 pct Sn, 0.1 pct Fe, 0.1 pct Cr, and 0.05 pct Ni, balance hafnium-free zirconium patented by Westing-house Electric Co. used in pressurized water reactors are machined from large hammer-finished forged bars. The bars forged for this application range from 3 1/2 in. to 7 1/2 in. squares. One of the tests used to evaluate Zircaloy-2 for this service is a 14-day exposure to very high-purity steam at 75oF and 1500 psi pressure. Normally wrought products will exhibit a black lustrous film of zirconium oxide after the test and show a weight gain of approximately 28 mg per sq dm. Coupons representing the forged bars exhibited a wide variety of corrosion results ranging from acceptable black coupons to some covered with white crystals of zirconium oxide that had weight gains of nearly 100 mg per sq dm. One of the most common effects was a white corrosion product that looked like a stain to some observers and the outline of massive metal grains to others. Very careful specimen preparation prior to the corrosion test did not affect the result and metallographic examination did not reveal a structural feature of a size and shape that would correlate with the corrosion product. In addition to the relatively poor corrosion resistance, the forged product was not as ductile as desired. The problem of obtaining uniform and more acceptable properties in these heavy-forged sections seemed to be a function of the microstructure of the metal and, in particular, the distribution of the intermetallic compounds. None of the four alloying elements however are appreciably soluble in a zirconium and are present as compounds which usually appear scattered randomly throughout the structure. Moudryl showed that the distribution of these intermetallic compounds in Zircaloy could be related to a ostringero corrosion failure. Grozier et al. discussed another structural defect that causes a similar corrosion effect. In this case, an elongated gas-void was determined to be the cause. M. L. Picklesimer held in his discussion of the Grozier paper that at least a part of the observed =stringersn were caused by the distribution of the intermetallic compounds. He proposed a

Jan 1, 1962

By L. R. Duncan, O. M. Wicken

Magnesium, the eighth most abundant element in the earth's crust, is found widely distributed in a variety of minerals. Among the more commercially important ones are magnesite (MgCO3), brucite (Mg[OH]2), dolomite (CaMg[C03]2), and the salts magnesium sulfate and chloride often found in natural brines. Among other commercially important magnesium-containing minerals are olivine ([MgFe]2Si04), talc (H2Mg3[Si03]4), and serpentine (H4Mg3Si2O9). These are valuable because of desirable characteristics given them by the magnesium content and its placement in the particular crystal structure. These minerals are the raw materials for a host of products including magnesium metal and several grades of magnesia or magnesia-containing materials for refractories, fluxes, fillers, insulation, cements, decolorants, fertilizers, and chemicals. Considering only those minerals valued for their magnesia or magnesium content, over 85% of the material tonnages are processed to be used as refractories. Dolomite, which is used in enormous tonnages for its physical properties in construction, has an important use as a refractory raw material in its own right and, after calcination, as a precipitant for magnesium hydroxide, which is an intermediate for the production of magnesia or magnesium metal. Magnesia from the reaction of calcined dolomite (or limestone) with seawater or magnesium-containing brines has supplanted much of the production of magnesia from mined magnesite, particularly in the United States. The best known of the minerals directly and widely exploited for magnesia content is magnesite, one of the calcite group of rhombohedral carbonates which includes calcite (CaC03), siderite (FeCO3), and rhodochrosite (MnCO3) among others. The members of this group enter into a wide range of substitutional solid solutions when the positive ions have similar radii. The radii of magnesium and iron ions are within 6% of each other; hence, magnesite and siderite form a complete series of which breunnerite (ferroan magnesite) is a well-known end member. However, the radius of calcium ion is 36% larger than that of magnesium ion, and only limited substitution exists at each end of the MgCO3-CaCO3 series. Dolomite is not a member of the calcite group, but results when calcium and magnesium ions alternate in equal number in an ordered structure among carbonate ions. The result of these relationships is that calcite and dolomite, often found intermixed with magnesite, occur commonly as identifiable crystal entities which can often be separated to a varying degree from the magnesite by various beneficiation techniques. Magnesite, when pure, contains 47.8% MgO and 52.2% CO.. The pure mineral is sometimes, but rarely, found as transparent crystals resembling calcite, but, preponderantly, magnesite contains variable amounts of the carbonates, oxides, and silicates of iron, calcium, manganese, and aluminum. Magnesite may be either crystalline or amorphous (cryptocrystalline). The crystalline form has a hardness of 3.5 to 4.0. The color may range from white to black with shades of yellow, blue, red, or gray. The color is not a fundamentally significant indicator of purity, but in a given deposit, an experienced person can often roughly grade magnesite by assessing color and crystallinity. The crystalline form of magnesite occurs in

Jan 1, 1983

By Robert B. Hoy

If the reader finds that the basic information in a commodity chapter is insufficient, he can consult the appropriate sources in this chapter to find more detailed or more up-to-date information. In these days, technology develops so rapidly that this 5th edition will be somewhat out of date even by the time it is distributed. A comparison of this edition with the 4th edition (1975) of Industrial Minerals and Rocks will clearly demonstate how rapidly the scene changes. One of the best sources of new information, of course, is attendance at technical meetings. For example, the papers presented at the national and sectional meetings of AIME usually discuss new developments in the respective divisions of the society. Frequently this information is available in Preprints. In addition some are printed in Mining Engineering and/or the Transactions of the Society of Mining Engineers of AIME. Furthermore, other professional and trade journals contain articles pertinent to the field. A journal introduced in 1967, Industrial Minerals, published by the Metal Bulletin, Ltd., London, is an excellent source of information. The Mining Journal, Ltd., also in London, publishes a weekly journal, a Mining Magazine (monthly), and a Mining Annual Review. The latter covers the field from three aspects: (1) by commodities, (2) through technical developments, and (3) geographically. The Industrial Minerals Directory 1977, 1st ed., Metal Bulletin Books, Ltd., London, provides addresses of organizations in the field. Other useful magazines and periodicals include Engineering and Mining Journal, Pit and Quarry, Rock Products, and World Mining, all published in the United States. In addition many new books related to industrial minerals have been published since the 4th edition of Industrial Minerals and Rocks. Most of these are included in the bibliography of each chapter in this volume. Another excellent information source is the proceedings of the Forum on Geology of Industrial Minerals. This group, which held its 18th annual meeting in 1982, is sponsored by a state geological survey or another mineral agency on a rotational basis. The proceedings have been published by the various sponsors and are available as indicated in Table 1. Two major sources of basic industrial mineral and rock data in the United States, and also a good source for many foreign countries, are the US Geological Survey and the US Bureau of Mines. The two agencies publish many reports and maps on a variety of geological and mining subjects. In addition, each agency has an indexed list of all their publications with a free service announcing new publications: New Publications of the Geological Survey, US Geological Survey, 329 National Center, Reston, VA 22092 and New Publications-Bureau of Mines, Publications Distribution Branch, US Bureau of Mines, 4800 Forbes Ave., Pittsburgh, PA 15213. The US Bureau of Mines (USBM) publishes annually Minerals Yearbooks which provide statistical data on mineral products including production, consumption, imports and exports, as well as information on new developments. Another very useful USBM series is called Mineral Facts and Problems. Editions were published in 1960, 1965, 1970, and 1975. Four major series of publications by the Bureau are Information Circulars, Reports of Investigations, Mineral Trade Notes, and Minerals and Materials. The last two are particularly good for news of foreign developments. The Bureau of Mines Employee Directory, available at all USBM offices, lists addresses and telephone numbers for all offices as well as same for all commodity and area specialists.

Jan 1, 1983

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick's First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood's analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner's diffusion-controlled kinetics is based upon the same form of mass balance using Fick's First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By Langtry E. Lynd

The predominant tonnage use of titanium is as a white pigment, in the form of rutile or anatase, which are allotropic modifications of titanium dioxide. Because of its whiteness, high refractive index and resulting light scattering ability, titanium dioxide is unequaled as a white pigment for paints, paper, rubber, and a wide variety of other materials. Consumption of titanium dioxide pigments for these uses has been rising steadily for many years, United States consumption in 1956 amounting to about 486,000 tons, worth $250,000,000. Production was off a little in 1957 and 1958. An outstanding development in the titanium field in recent years is the expansion of titanium metal production. Virtually nonexistent before 1948, United States production of pure titanium metal sponge reached a high in 1957 of about 17,200 tons, worth about $77,000,000. United States titanium sponge metal production in 1958 was cut back to about 4,600 tons because of reductions in military requirements. Another major use of titanium, in the form of the mineral, rutile, is for welding rod coatings. United States consumption of rutile for this purpose in 1958 amounted to about 11,000 tons, worth $1,100,000. Titanium-Bearing Minerals Although several minerals contain titanium as a major constituent, only a few of these occur in sufficient quantities and concentrations to be of commercial importance. These are ilmenite (FeTiO3), rutile (TiO2), and alteration products of ilmenite which have been referred to as weathered ilmenite, leucoxene, or arizonite. The other polymorphs of titanium dioxide, brookite and anatase, occur in a few deposits, of which only one has been of even minor importance. Considerable concentrations of titanite or sphene (CaTiSiO5) and perovskite (CaTiO3) are known, but do not compete with ilmenite and rutile deposits in grade or size. Rutile is very widely distributed as an accessory mineral in most rocks, but large deposits of commercial importance are rare. A few rock deposits have been worked for rutile but only one, in Virginia, is in operation (1959). Development of one in Mexico was discontinued recently. At present, the main sources of rutile are the beach and dune sands of Australia and Florida. A major use of rutile is for the manufacture of titanium tetrachloride, which is the intermediate compound universally used in titanium metal manufacture. Another main use of rutile is for welding rod coatings. Although the whiteness and brightness of titanium dioxide pigment is due to the high refractive index of rutile or anatase, natural rutile is too impure to be used directly as a white pigment, is too expensive to use for manufacturing pure oxide pigment, and is too scarce to provide the required tonnages. Instead, the cheaper, more abundant, mixed oxide of iron and titanium, ilmenite, which is readily decomposed by sulfuric acid, is used for manufacture of rutile and anatase pigments. Ilmenite is mined from both rock and sand deposits. Rock deposits contain ilmenite in massive or heavily disseminated form along with magnetite or hematite and are almost invariably associated with anorthositic and gabbroic rocks. Ilmenite also occurs as an accessory mineral in a great many igneous and metamorphic rock types. Concentrations of

Jan 1, 1960

By J. F. Breedis

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

Jan 1, 1964

By F. D. Wright

Production of a coal preparation plant is governed by many restrictions, such as the tonnage of different products and blends that can be sold within a given period, capacities and output proportions of the cleaning and sizing units, blending proportions, quality specifications, and costs and prices for the various products. Determination of the tonnage of each product and blend that should be made in order to obtain the maximum profit can be difficult unless a systematic method such as linear programming is used. In this paper the basic method of linear programming is described briefly. The Old Ben No. 9 preparation plant is used as an example to illustrate in detail how eqwations can be written to form a linear programming model of a coal preparation plant. Three sample problems, each requiring 56 or more equations and 63 structural variables, were solved with an IBM 650 computer. Linear programming is one of several mathematical tools used for operations research. It has been applied to many fields and has been used by a number of industries either to maximize the profits of certain operations or to minimize costs. P. B. Nalle and L. W. weeks' have described the use of the method by the Riverside Cement Co. to minimize the cost of blending raw materials to make portland cement. Their problem is to obtain at minimum cost a mix with certain specifications from a number of possible materials which have various costs and various amounts of CaO, SiO2, Fe2O3, and other constituents. In a paper on the use of linear programming by the National Coal Board in England, K. B. Williams and K. B. Halley2 describe how the transportation method, a variation of linear programming, is used to minimize the cost of sending 37 grades of coal from 28 mines to seven central washing plants which produce coal for furnace coke and foundry coke. The various coals have different percentages of volatile matter, moisture, sulfur, ash, and phosphorous, so there is considerable choice in how they can be blended to meet the specifications of the two products. The purpose of this paper is to show how linear programming can be used to maximize the profits of a coal washing plant which produces individual final products as well as blends. The Old Ben Corp. furnished assumed sample data from their Old Ben Mine No. 9 preparation plant for this investigation. However, the data that have been used are entirely the author's responsibility. METHOD OF LINEAR PROGRAMMING Numerous articles and books have been written on the theory and applications of linear programming.3-5 However, since the method has not been widely applied by the mining industry, a brief, nontheo-retical discussion of its basic method seems to be in order. Linear programming (Table I) is used to determine the best possible solution to a number of interdependent activities. It is essentially a method for making systematic selections from a number of possible solutions to determine positively the optimum solution. There may be other equally good solutions but no better ones. Each activity must have linear coefficients and there must be a criterion to judge how good the solution actually is. Linear programming is different from the solution

Jan 1, 1961