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By R. W. Gurry, L. S. Darken

The solubility of cementite in austenite is computed by thermodynamic methods from the observed solubility of graphite. It is found that the solubility of cementite is greater than that of graphite in the entire austenite temperature range. Thus the prior discrepancy between this portion of the phase diagram and the observed metastability of cementite is partially resolved. FOR several years it has been apparent that a serious discrepancy exists in certain observations pertaining to the Fe-C system. Direct experimental data indicate: 1-That the curve representing the solubility of graphite in austenite'" crosses that for cementite4 at about 945°C as shown in Fig. 1. 2— That graphite and austenite saturated therewith are stable1 relative to cementite at all temperatures between the eutectoid, about 723°C, and the eutectic, about 1153°C. These observations are mutually incompatible in view of a well-known consequence of the second law of thermodynamics, namely, that the stable phase (presumably graphite at all temperatures) has a lower solubility than the metastable phase (presumably cementite). Hence either 1 or 2 above must be in error; either the measured solubility of graphite or of cementite, or the observation as to the stability of graphite, is in error. Our present purposes are: 1—To collate the available data on cementite and prepare a table of HO — HO° and of (Fa— HO°)/T. This tabular method seems the best and most convenient way to represent the heat and free energy of formation. 2—To determine whether the measured solubilities of cementite and graphite in austenite are in accord with the above table and the measured thermodynamic properties of austenite, in order to resolve, if possible, the existing paradox of these two solubilities. Enthalpy of Cementite The enthalpy of cementite at 273 °K, H279 — HOcem, was computed by integration of the low temperature heat capacity as measured by Seltz, McDonald, and Wells" 68" to 298 °K) and as given by the Debye functions recommended by them (0" to 68°K); the result is included in Table I. At higher temperature HCem — H,,"" is given by Kelley who used the data of Naeser7 (298" to 1037°K) and of Umino8,9 (273° to 1923°K). We have recalculated Hcem — H273 cem from the data of UminoO in the following way. In the equilibrated alloy at temperature the weight fraction of cementite Pct c -Pct cr is PctC -PctCr designated f(C), and the

Jan 1, 1952

By J. Gordon Parr, D. H. Polonis

IN a previous study of hypereutectoid Ti-Ni alloys' a substructure was observed in quenched powder specimens when the constitution was 100 pet retained ß body-centered-cubic phase. The alloy powders were quenched from 1000°C by a blast of helium gas and precautions already described were observed throughout the work, to minimize contamination. Ogden et al.2 have previously observed subboundaries in the ß phase of a Ti-Mn-N alloy; but this structure was attributed to nitrogen-rich a precipitation. The nitrogen content of the Ti-Ni alloys does not exceed 0.02 pet and the quenching rate was sufficiently rapid to suppress precipitation reactions. Since X-ray diffraction results have confirmed the absence of any second phase which might account for this phenomenon, it seems unlikely that this substructure is explicable in terms of nitrogen content. Fig. 1 shows the substructure in adjacent grains of 100 pet ß phase in a quenched 6 atomic pet Ni alloy. Fig. 2 shows adjacent ß grains in a similarly treated alloy; one grain contains marked intracrys-talline boundaries and the other is completely free from any substructure. The suberystals appear to have fairly regular shapes, suggesting a regular orientation relationship among them. Tempering the retained ß structure at temperatures below the eutectoid eliminates the substructure at an early stage of ß decomposition. At the present time it is possible only to guess at an explanation for this subboundary phenomenon, since very little work has been reported on substructures resulting from phase changes. It is believed that the present phenomenon is due to poly-gonization resulting from unrelieved stresses set up

Jan 1, 1957

By A. H. Larson, L. G. Twidwell

DURING the roasting of zinc sulfide concentrates and by-product recovery from flue dusts, the zinc sul-fate phase may occur in various stages of the processes. In addition to zinc sulfide, other sulfide phases are usually present such as CdS, PbS, CuzS, and FeS. Consequently, the effect of these sulfides on the thermal decomposition of ZnS04 was investigated. Merck high-purity, anhydrous zinc sulfate was used as the starting material. The sulfate was heated under an argon atmosphere, at a rate of 10°C per min. With the first slight indication of decomposition as determined by gas analysis, the sample was removed from the furnace and allowed to cool. X-ray patterns showed no other phase present. It is estimated that less than 0.05 pct of the ZnS04 decomposed. The metal sulfides were also heated under an argon atmosphere to drive off any adsorbed water. The materials were then sized (-200 to +270 mesh), mixed in predetermined mole ratios, and pressed into pellets. The experimental measurement of the reaction rate consisted of purifying the argon carrier gas, continuous flushing of the heated reacting mixture with argon, and collection and analysis of the SOn product gas. The reaction system was heated to 600°C and al-

Jan 1, 1967

By E. Northcott, F. N. Oberg

By electrostatic separation, course Florida pebble phosphate, too lou-grade to find a ready market, can be upgraded to a satisfactory saleable product. Pebble running from 60 pct bone phosphate of time may be upgraded to 73 to 77 pct BPL depending on the mineralogical. structure of the pebble and the nature of the silica innpurity. High-grade concentrates from Florida pebble phosphate deposits have long been recovered by wet methods. When work was begun in the field, only the coarse pebble (generally +1 mm) was re- covered. In the 1920's a froth flotation process was developed to separate quartz from the finer phosphate fractions, but this method proved unsatisfactory for treating the intermediate fraction (—1 mm +35 mesh). Consequently various other processes were adapted, including agglomerate tabling and spiral separation of reagentized feed. Today the three processes are used—washing and screening for coarse pebble, tabling or spiraling for intermediate sizes, and flotation for —35 mesh material.

Jan 1, 1959

By N. R. MacMillan

INTRODUCTION The Bullmoose Coal Project is part of a major development in northeastern British Columbia which comprises a new rail line, a new townsite, powerline, highway, the upgrading of the Canadian National Railway's main line, a new coal port at Prince Rupert and two new coal mines, the Bullmoose mine and the Quintette mine. The total investment by all parties is estimated to be in excess of $2.6 billion and made up approximately as follows : [Table No. 1 $ Millions - Quintette Coal Limited 950 Teck-Bullmoose Coal Inc. 275 Canadian National Railway Company 800 6 British Columbia Railway Company Port at Prince Rupert 280 Townsite, Roads 6- Power ] The new infrastructure is intended to serve not only the Bullmoose and Quintette coal projects but also eventually a number of other coal properties in northeastern British Columbia. The Bullmoose project is structured on a joint venture basis as follows : [Table No. 2 Teck Corporation 51% Lornex Mining Corporation Ltd. 39% Nissho Iwai Coal Development 1 0% (Canada) Ltd. -- 100% ] The mine has a capacity of 2.3 million tonnes of clean coal per year. In the initial years 1.7 million tonnes will be metallurgical coal and 0.6 million tonnes thermal coal. After the first three years of operations the annual production of metallurgical coal will increase to an average of approximately 2.1 million tonnes and the production of thermal coal will decrease to an average of approximately 0.2 million tonnes. At this level of 2.3 million tonnes annual production, the Bullmoose mine has sufficient reserves for at least 26 years of production. History Brameda Resources Ltd. commenced coal exploration in the Bullmoose-Sukunka area in 1969. Teck obtained an option on the Bullmoose coal licences in 1970 and started surface exploration and diamond drilling in 1971. Teck earned a 50% interest in the property, and thereafter expenses were jointly financed by Teck and Brameda. In 1981 Brameda merged with Teck making Teck the sole owner. The initial phase of the exploration program, which was completed in 1975, included 7,200 meters of diamond drilling in 35 holes. During 1976 and 1977, detailed exploration and test work were carried out on the South Fork and West Fork areas where multiple seams close to surfaces indicated the potential for large tonnages of strippable coal. In those two years, work included road construction, detailed mapping and trenching to outline the coal seam traces at the surface, 6,300 meters of diamond drilling in 80 holes, and 300 meters of underground bulk sampling from seven adits. Washability tests and analysis work were carried out on the drill cores and adit samples, and pilot plant washability studies were undertaken. In 1978 and 1979 Teck engineers prepared open pit mining plans and production schedules and Kaiser Engineering was retained to prepare a layout of the plant preparation facility. A feasibility study prepared by Teck's engineering group in January 1982 was the base document used by the Lenders in assessing the technical and economic viability of the project. Property Location The property lies some 650 kilometers northeast of Vancouver, and 87 kilometers south by road from the village of Chetwynd. The Sukunka property (British Petroleum) adjoins to the north, the Mount Spieker property (Ranger Oil Option) adjoins to the east, and the Quintette property is located to the southeast.

Jan 1, 1985

By P. F. Allen

WITH capacity of 51,000 tpd, the Morenci concentrator produces approximately 49,000 tons of tailing for final deposition. Disposal involves distribution of thickened tailing to dams in such a manner that solids can be used for dam construction and water can be impounded for reclamation. During early operation, although tonnage treated was lower, it was necessary to use orthodox disposal practices in the areas available for tailing. Trestles mounted on a series of dams, constructed of borrow material, carried the pipelines from which tailing were spigoted behind the dams. When adequate disposal areas were finally established, it became desirable to look for more efficient methods. The idea of placing the distribution pipe or manifold directly on the crest of the dam was advanced in 1945. After a period of testing, that procedure in modified form replaced the older trestle arrangement. Marked economies resulted, and time required to prepare dams for succeeding storage cycles was greatly reduced. The tailing disposal area for the Morenci concentrator lies south and southwest of the concentrator building. Ample storage space is available. A wide valley contains three sharply defined ravines lying on an average slope of 4 pct. The more central of these ravines, and the largest of the three, is known as Morenci canyon, which provides substantially more tailing storage area than the other two. Stargo canyon lies to the west; the other is appropriately named East canyon. Total area of the tailing disposal site is nearly 31/4 sq miles, or about 2000 acres. The storage area in use was somewhat more than 850 acres at the end of 1954, or 16 acres per 1000 tons of tailing to be stored daily. At the present time none of the east side dams are in regular use but they are available in emergency. There are five dams on the west side (in Morenci and Stargo canyons) as well as two auxiliary dams adjacent to No. 4 West and No. 5 West. This has made it possible to concentrate men and equipment in a smaller area with consequent savings in both manpower and machinery. Tailing Thickening: Tailing from the flotation process reaches the thickeners with a solid content of about 18 pct. The launder carrying this pulp is subdivided at a central point into seven launders carrying a proportional share to each of seven tailing thickeners, which are located in Morenci canyon close to the concentrator. Five of these thickeners are 300 ft diam and two are 325 ft diam. Thickeners are of the peripheral traction type and rakes travel at the rate of one revolution in 37 to 39 min. The entire installation provides 500,000 sq ft of settling area, or approximately 101/2 sq ft per ton of tailing to be thickened daily.

Jan 1, 1957

A record $18.7 billion worth of metals, non- metals and fuels was produced in the U.S. during 1962, according to a year-end estimate from the USBM. The 1962 total value, based on preliminary statistics compiled by the Bureau, was nearly $600 million more than in 1961. Most minerals gained both in value and volume of production during 1962 according to information collected by the Bureau. All mineral fuels except anthracite showed increases. Among nonmetallic minerals- other than fuels-gains exceeded losses by two to one. Metal production held steady as gains and losses balanced.

Jan 2, 1963

By M. Mortada

Nonsteady-state flow of slightly compressible liquids in porous media of non-uniform properties has been the subject of a number of recent studies. Most of these studies considered one-dimensional flow in systems with cylindrical geometry and with the properties of the porous medium varying with radial distance only. A. Houpeurt' studied the problem in its general form by examining the solutions of the differential equation, In Eq. 1, the permeability k and the porosity + are arbitrary functions of radial distance. Houpeurt concluded that, except for special forms of the functions k and the problem is not well suited for mathematical treatment, but lends itself to high-speed digital computation. Carslaw and Jaeger' discussed the solution of Eq. 1 for the case in which the permeability varies as a power of the radial distance. P. Albert3 studied analytically the pseudo steady-state solutions in systems of finite radial extent and non-uniform properties. He also obtained some numerical solutions for nonsteady-state flow using a high-speed computer. William Hurst4 examined the interference pressure drop due to a point sink located in an infinite system consisting of two permeability regions in series. In this case, the permeability changed at a radial distance r from the point sink. INTERFERENCE BETWEEN OIL FIELDS IN A NON-UNIFORM AQUIFER The interference pressure drop for oil fields located in an extensive aquifer of uniform properties is discussed in a number of places in the literature. This work considers the interference pressure drop for oil fields located in a non-uniform extensive aquifer comprising two regions of different properties as shown in Fig. 1. Region I of the aquifer extends from which is the radius of Oil Field A, to ar,,, where a>1. It has permeability k,, porosity +, and effective compressibility c,. Oil Field B is located in Region II which extends from ar, to infinity and has different properties from those of Region I, but the same formation thickness h. Region II has permeability k2, porosity and effective compressibility c2. The choice of this type of aquifer should not imply that it is of frequent occurrence. It is chosen primarily to illustrate the effects of non-uniform aquifer properties on oilfield interference. It is of interest to point out that a non-uniform radial aquifer in which both the permeability and the porosity are inversely proportional to the radial distance can be treated in a manner similar to a linear aquifer of uniform properties. The situation where only the permeability varies as the inverse of the radial distance is also amenable to analytical treatment. Both aquifers behave quite differently from a radial aquifer with uniform properties so far as the water influx and the interference pressure drop are concerned. METHOD OF SOLUTION The expression for the interference pressure drop in Oil Field B due to a constant rate of water influx in Oil Field A is developed in the Appendix. This is accomplished by the simultaneous solution of two partial differential equations describing the pressure in Regions I and 11. The two differential equations are solved subject to the following conditions: (1) at r,, the pressure gradient is constant; (2) at ar the pressure and

By Richard J. Lund

Stock piling-and by that I mean well-organized stock piling on a substantial scale-is almost as old as the hills themselves. It was back in early Biblical times, as recounted in the Book of Genesis, that Joseph was charged by Pharaoh with the responsibility of stock piling food during the seven years of plenty to guard against the seven subsequent years of famine that were revealed by the Pharaoh's dream. And this same policy of storing up food or materials to provide for future anticipated emergencies can be traced repeatedly down through the ages. So our own efforts are anything but new. Our modern concept of stock piling-the purchase and storage of strategic materials to assure supplies needed in time of some future war- stems from our experience in World War I. In 1920, the War Department was charged by Congress with the responsibility of procuring all War Department supplies and mobilizing industry in the event of another war. During the two decades that followed there were many authoritative studies made of our deficient mineral problem, all of which pointed out the urgent necessity of stock piling certain strategic materials as a reserve against future war. One such study, made in 1925 through the combined efforts of the Mining and Metallurgical Society and the AIME, was done at the ex- press request of the War Department. Eight years later another more de-

Jan 1, 1949

By Milnor Roberts

WAR struck the mineral industry of Washington with cross currents that produced a peculiar result. The State's production of coal, industrial minerals, and metals for 1941, valued at $28,507,282, was increased in 1942 under war pressure to approximately $35.000,000. Meanwhile a tremendous demand had arisen for men to construct airfields and many other large projects for the Army and Navy in Washington and Alaska, and Government plants for the mineral industry costing $140,000,000 or more, as well as a call for employees in the U. S. Navy Yard at Bremerton, the sixty shipyards, the four Boeing airplane factories with many auxiliary shops, and hundreds of other plants turning out war materials. In spite of an influx of nearly 300,000 people, causing an increase of 17.1 percent in the population since 1940, according to the Census Bureau, the State clearly is still engaged in an unusual amount of war production in proportion to its population. A large proportion of the workers have been drawn from the mineral industry to the war plants, whether through motives of patriotism, high wages, or, in the Boeing plants at least, the glamour of the operation

Jan 1, 1944

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates (or sodium-free compounds) are required for certain end uses, but in general, nonsodium borates are used only where borax is not avail- able. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of about a million tons of B2O3. Leadership in supplying borates has shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates. In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, Calif., is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, Calif., the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "lo-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7- lOH2O. In addition to ship- ping all major refined borate products from Boron, the company ships semiprocessed ore concentrates to treatment plants elsewhere.

Jan 1, 1975

By Burk, Hugh A.

AT THE inception of the cyanide process and its adaptation to the practice of gold and silver metallurgy much difficulty was experienced in applying it to auro-cupriferous ores, both in economy of treatment and recovery of the gold from solution. The presence of copper in the ore effected a high chemical consumption of cyanide during treatment, and in the solvent solution, it retarded the precipitation of the gold on zinc shavings. The coating of the copper on the zinc shavings presented even worse difficulties than the increased cyanide consumption as most ores contain a small amount of copper. This interference of copper led to the use of other precipitating methods and attempts to recover the cyanide which was consumed during ore treatment. Of the other methods used, electrolytic precipitation was the most practical until a better understanding of the application of zinc shavings and zinc dust developed. In September, 1905, a patent entitled, "Method for Recovering Precious Metals from Solution," was granted to Isaac Anderson and Michael Scanton. This method is adaptable to precious metal ores containing a small percentage of copper but has never been extensively used or perfected. The process has

Jan 1, 1925

By David J. Dunn

At a time when mill availability is at a premium, production costs are rising, and lead time for mill liner casting is a year or more, mill liner design is an important factor in ore grinding. Testing and selection of the optimum liner profile for a given set of mill operating conditions can improve mill capacity, reduce liner wear rate, and lengthen liner life. The mill liner that grinds best, lasts the longest, and costs the least is a necessity for economic mill operation. After testing four mill liner profiles for 3.96 X 3.65-m (13 x 12-ft) overflow ball mills, Climax Molybdenum Co. found that an improved design increased mill tonnage by 2.72 t/h (3 stph) while reducing finish grind by 1.7% minus 100-mesh, reduced liner wear rate, and almost doubled liner life.

Jan 12, 1976

By V. Jares

DESPITE the fact that a combination of metals-aluminum-zinc-tin, and sometimes aluminum-zinc-cadmium-is extensively used for aluminum solders, as well as for die-castings, the constitution of these alloys has not yet been made clear. I. BINARY SYSTEMS The system aluminum-zinc is the basis of the ternary alloys under consideration. Their composition was made sufficiently clear by the investigations of Rosenhain and Archbutt,1 Bauer and Vogel,2 Sander and Meissner,3 Hanson and Gayler4 and Isihara.5 Only the temperature of decomposition of the crystals 0 seems still to be doubtful, whether it is considered as a compound of Al2Zn3 (according to Bauer and Vogel) or as an intermediate phase of variant composition (according to Hanson and Gayler). This temperature is given by most of the authors as in the neighborhood of 256° C., only Isihara giving 280° C. As its accurate determination is of special importance in the study of the ternary alloys under consideration it was experimentally controlled in the following manner: An alloy corresponding in composition to the formula Al2Zn3 was made, in which the temperature effect was found to be the greatest. This was drilled and a silver-constantan thermoelement inserted into the cavity so as to be in direct contact with the alloy. The whole was then very slowly heated and the heating and cooling curves determined. The transition temperature from the heating curve was found to be 281° C., whereas from the cooling curve it was 252° C.

Jan 1, 1927

By Paul H. Lu

Methods and results of measuring three basic parameters for ground stability control, ground pressure, strata movement, and geomechanical properties of mine rock are presented in this paper. It is found that these parameters can be measured in situ by simple and practical techniques with nonsophisticated and inexpensive instruments. Specifically, a drillhole dilation technique employing a cylindrical hydraulic borehole pressure cell (CPC) was used to determine the modulus of rigidity. Premining ground pressures were determined by pressure convergence tests with a combination of one CPC and two pre-encapsulated flat hydraulic borehole pressure cells (BPC) installed in a single drillhole. Abutment pressures and pillar loading were monitored with BPC's. Differential strata movements and bed separations were measured with self-recording 10-anchor-point extensometers. Roof-to-floor convergence was measured with self-recording convergence meters. Some applications of these in-situ-determined parameters to mine design and ground stability control are also discussed.

Jan 1, 1984

By A. G. Rozner

TRANSVERSE rupture tests have been commonly used in mechanical investigations of brittle materials. The specimens are simple, easy to prepare, and loading presents no difficulty. Owing to the complexity of stress distribution in bending1 one can determine stresses rigorously only for the elastic range. The bend-test results, however, are at times converted into tensile-strength data, determined as maximum fiber stress. The assumption is made that for small plastic deformations the linear stress-strain relation applies. This problem was experimentally investigated by Bach3 who tested cast iron in bending and in tension and found that the maximum fiber strength obtained in bending exceeded the experimental tensile strength by a factor depending on the geometry of the tested piece. The factor varied from 1.57 for a rectangular cross section to 2.12 for a circular cross section of the tested beam. Since this work was carried out 60 years ago, the cast iron used could be expected to have been highly brittle, thus the extent of plastic deformation prior to fracture very small. We have therefore carried out a number of tests on magnesium-modified cast iron with an average elongation of -5 pct. It was hoped that the data obtained from the tests would serve as a guideline for comparing data obtained in tension and bending for brittle materials. Mechanical properties were measured at room temperature on an Instron tensile machine at a crosshead speed of 0.05 in. per min. The three-point bend test employed cylindrical bars 0.20 in. in diameter with a 1.0-in. span. For the tensile test, cylindrical tensile specimens with a gage length of 0.85 in. and a diameter of 0.160 in. were used. Results are summarized in Table I. From Table I one can see that fracture strength

Jan 1, 1965

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By M. N. Brodie, John Chapman

INTRODUCTION - DEFINITION & HISTORICAL PERSPECTIVE While this symposium is concerned with comminution which, by definition, relates to all stages of size reduction of an ore body to a form suitable for mineral separation, the electrical drive aspect of the grinding section will receive most attention in contrast to the crushing, screening and materials handling elements of the process. The reason for this is that today's large mills, thirty feet diameter and upwards, present mechanical and electrical problems which require a degree of sophistication in their solution not previously required. The ability to satisfy these demands, so far as electrical technology is concerned, largely results from the development of semi-conductor devices. These can now handle typical electrical distribution power levels within remarkably s m all volumes and with high efficiency when compared with the motor-generator sets, mercury arc rectifiers, rotating amplifiers, magnetic amplifiers and vacuum tubes which were commonly used to provide speed and torque controls as recently as the early nineteen-sixties. The hardware available to the electrical engineer has changed dramatically whereby even the simplest control system formerly using hard-wired relays is now superseded by the program m able logic controller with its computer-like memory containing the sequence of operation, in other words, the software. Reverting now to the mineral process itself, it is assumed that the ore body has been mined using explosives and is delivered to the concentrating plant in its 'run of mine' form. The problem becomes one of reducing the material to a size which will permit an acceptable recovery of the mineral with the most economical use of energy. The size of 'run of mine' material will range from about minus five feet for high tonnage open pit operations to minus two feet for the smaller underground mine. The final reduction in size may range from minus ten mesh to minus two hundred mesh (exceptionally as fine as minus six hundred mesh) depending upon the concentration method and dissemination of the mineral values within the ore. There is no single circuit that satisfies all applications, but the pattern of metallurgical equipment use shown in Table 1 appears discernable from current practice, in general terms.

Jan 1, 1982

By D. P. Harris

This paper examines recent developments and work in progress on the application of quantitative methods and computers to the appraisal of the mineral resource potential of discrete areas by employing reconnaissance geological information and general economic relationships. The perspective of this paper might be that of a firm planning a regional exploration program or of a legislative body seeking to choose between several alternative actions on the basis of their impact upon the regional resources. In addition to this general survey and commentary, an example is presented of the use of geostatistical analysis and computer simulation to evaluate the economic mineral resources of the Seward Peninsula of Alaska.

Jan 1, 1969