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By J. N. Ong, J. P. Ratledge, J. H. Boyce

Since German operators opened the Tsumeb mine in the early 1900's, continuous operation has been interrupted only by enforced shutdowns during two world wars and the depression of the 1930's. Original metallurgical practice was blast furnace smelting. This was applicable only to low zinc ore, leaving large tonnages of high zinc ore to be stockpiled on the surface. A gravity concentrator using tables, buddles, and jigs operated for several years, but differential flotation of the ore did not get beyond the experimental stage. When the property was put up for sale by the South African Custodian of Enemy Property there was an estimated 434,000 tons of ore on surface dumps. The dump material, assaying 4.48 pct Cu, 15.8 pct Pb, and 10.9 pct Zn, had become highly oxidized during a stay of many years on the surface. But these dump ores had to be used in evaluating possible metallurgy because the shaft became flooded after the 1940 shutdown and underground ore was unavailable. Many companies examined Tsumeb but quickly lost enthusiasm because of the formidable metallurgical problems presented by the dump ore. However, on the basis of extensive test work, the present company decided that differential flotation would be successful and purchased the property after competitive bidding.

Jan 4, 1955

By Alberto J. Terrones L.

THE classical papers on contact metasomatic deposits by Lindgren on the Clifton-Morenci district,1 by Barrel1 on Marysville, Mont.,2 and by Goldschmitt on the Oslo district, Norway,3 laid the foundation for understanding of the importance of separating the metamorphic process from the subsequent metasomatic stage. Knopf4 made a big step forward by recognizing that sulfide ore minerals are invariably younger than silicates and by further stressing the importance of structural control5 ore finding. Some years later Harrison Schmitt6 fought the idea that contact metasomatic deposits are erratic, irregular, bunchy, economically marginal, and of small size, concluding that these descriptions have little factual basis. He emphasized the importance of detail mapping and careful geological study as fundamental requirements for a better understanding of these deposits. This article presents a comparative description of the structural features at the Magistral, Antamina, Morococha, Vilca, Ferrobamba, Katanga (Quibio), Tintaya, and Huarca contact deposits (Fig. 1). Further, it will describe how these structural features controlled the emplacement of the intrusives, their shape, distribution of metamorphic and metasomatic halos, and sulfide deposition in post-skarn structural channelways. Finally, the modifications introduced by a superimposed hydrothermal stage recognized at some localities will be discussed.

Jan 3, 1958

By A. J. Fenn

Long experience with underground mining inspired the unusual idea of using an underground crusher-conveyor system as a substitute for surface haulage at the Cananea open-pit copper mine in Sonora, Mexico. Now implemented and working well, the system has born out the expectations of its originator, Cia. Minera de Cananea S.A. de C.V., that it would effect substantial cuts in the high cost of haulage. The Cananea deposit is a large, low-grade orebody above the mined-out Colorada pipe which was once one of the largest high-grade underground deposits in the district. Present facilities at the pit consist of: (1) A large open-pit mine capable of moving 80,000 tons of material per day with a shovel-truck, underground crusher and belt conveyor haulage system. (2) A 25,000-tpd concentrator equipped for four stages of crushing, rod mill-ball mill grinding with cyclone classification, and flotation in conventional machines. (3) A dump leaching process producing 1 million lb of copper per month in a tin-can scrap precipitation plant. (4) A two-reverberatory, six-converter smelter which can make 140 tons of blister copper per day. (5) A well-integrated contingent of supporting departments running the gauntlet from housing to power generation.

Jan 3, 1969

By S. Katz, M. E. Nicholson, J. J. Kelly, D. R. Curran

A series of wedges of 1020 steel (2 1/2 by 6 by 8 in.) were explosively loaded, as shown in Fig. 1. A slab of explosive on the surface of the steel wedge was initiated simultaneously along one edge, producing an essentially two-dimensional oblique shock in the metal. Pressure and density in the metal were measured as a function of distance from the explosive-metal interface by a method described elsewhere.' While for pressures below 130 .kbars the technique produces accurate results, for greater pressures the presence of two shock waves in the metalzy3 makes interpretation of the data uncertain. However, the location of the transition in pressure at 130 kbars can be readily identified from the data. The assumption of a single shock in the region above 130 kbars overestimates the pressure computed on a multiple-shock model. After firing, the wedges were sectioned, lapped, and etched with 2 pct Nital. A photograph of an etched specimen is shown in Fig. 2. The specimens were examined metallographically. The dark region, at the top of the specimen, was heavily banded, Fig. 3, while the lighter area was comparatively free from banding, Fig. 4, the boundary between the two regions being quite abrupt. The very light regions at an angle of about 45 deg to the explosive-metal interface show virtually no banding. The origin of these light regions, which are not Luder's bands, is not yet explained. The thickness of the heavily banded area was measured and compared with the pressure at the boundary between the heavily and lightly banded regions. The results of these measurements and calculations are given in Table I. For all shots, the pressure at the boundary is approximately the same

Jan 1, 1960

By W. H. McFarland

The mechanical properties have been determined for a large number of alloy-free martensitic steels with carbon contents ranging from 0.08 to 0.20 pct and with manganese contents of about 0.4 to 0.5 pet. These steels were tested 1) as water-quenched, 2) after quenching, temper rolling, and tinning, and 3) after tempering treatments which involved temperatures from 400o to 1300oF and times from 1 min to 8 hr. The majority of these tests represent steel from commercial-size coils, i.e., strip 32 in. wide, coil weights up to 20,000 16, and steel thicknesses from 0.0055 to 0.024 in. As a result of these treatments, it has been shown that as-quenched low-carbon alloy-free steels can be produced with tensile strengths ranging from 140,000 to 220,000 psi and tensile elongations from 3.0 to 4.0 pet in 2 in. The tensile strength of the as-quenched martensites can be represented by the equation, tensile strength (ksi) = 119 + 560 (wt pet C). The response to tempering of these steels is related to previous work by Muir, Averbach, and Cohen and by Grange and Baughman. Strain aging of low-carbon martensite has also been investigated. If low-carbon steels are defined as those steels with a maximum carbon content of 0.2 pet, it is found that the literature on low-carbon, alloy-free martensites contains little data on the mechanical properties of these steels. However, the following facts concerning low-carbon alloy-free martensites seem firmly established:'-' 1) The major factors in controlling the strength of the martensite appear to be a) fine structure, b) the internal strain resulting from the transformation, and, particularly, c) the amount of carbon in solid solution. 2) In low-carbon steels, the martensite is auto-tempered and is in the form of needles with only minor amounts of internal twinning, whereas the martensite in high-carbon steels forms as plates which are internally twinned on a fine scale. 3) Care must be taken in comparing the results of work that has been done on low-carbon steels with varying amounts of alloying elements to data on plain carbon steels. As has been noted by Irvine, Pickering, and Garstone,6 alloying elements generally lower the martensite start temperature and, thereby, decrease the amount of auto tempering obtained during the quench. This makes it difficult to

Jan 1, 1965

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before break-age, which appears as heat. An empirical equation is presented which covers the entire comminution range. The new strain-energy theory considers comminution from the known principles of mechanics and the reduction ratio. Energy requirements according to the different theories are compared.

Jan 8, 1950

By Frank Firmstone

THE indicator cards shown herewith were taken by the writer in June, 1877, from the water-pressure blowing engine of the Longdale Iron Co., at Lucy Selina Furnace, Longdale, Virginia. A description of this engine with figures, and some indicator cards, was published by Washington Jones, Esq., Superintendent of the I. P. Morris Co.,* in the Journal of the Franklin Institute for May, 1877, to which those desiring a full account are referred, but for convenience the principal dimensions, etc., are given below. The machine consists of a pair of horizontal directacting blowing engines, connected at right angles to a common fly-wheel shaft. The blowing cylinders are 4 ft. diameter by 5 ft. stroke; the water cylinders were 18 in. diameter by 5 ft. stroke as built. Both water and blowing cylinders are double acting. The water valves are balanced piston valves, 18 in. diameter, moved directly by eccentrics on the fly-wheel- shaft. Great care was taken to have the areas of the ports and passages at least equal to the area of the working piston. The engine is set about 14 ft. above the tail-race, and the * The engine was built by the I. P. Morris Go., from drawings made by Messrs. Tuws and Hartman.

Jan 1, 1879

By Benjamin Smith Lyman

The question of the original extent of the anthracite-beds of Pennsylvania has often been raised; and even discussed with reference to the probability of their present existence under the New Red, a matter of immense practical importance. So high an authority as my revered master, J. P. Lesley, Honorary

Jan 1, 1903

By A. Gatti

Studies were made on the system iron plus alumina. Various methods of dispersing and various amounts of alumina were used. Powder metallurgy techniques were used to produce the final product. Microstructures and some mechanical properties are presented. Alloys containing up to 16 pct alumina by weight are ductile at all temperatures tested. The ivon-alumina materials have a higher yield stress and improved creep resistance over that of pure iron. SINCE the development of SAP' an A1- Al2O3 powder metallurgy product, great interest has been shown in the development of a SAP-like structure in metals and alloys other than aluminum. The outstanding properties of this class of materials are: 1) Good creep resistance at high temperature. 2) High yield strengths and high hardness at high temperatures. 3) High recrystallization temperature. However, the lack of ductility and formability has thus far limited the applications of SAP-like materials. The following report deals with methods of dispersing A12O3 in Fe, processing of powders into rod, structures produced after processing, and mechanical properties of the iron-alumina material produced. Methods of dispersing the alumina and also the volume fraction of alumina added were varied. MATERIAL Powder Processing— Four methods of obtaining dispersions of alumina in iron were studied. 1) Oxidation-reduction of a Fe + 8 pct Al alloy. .2) Coprecipitation of Fe(OH)3 + Al(OH)3 from aqueous solution. 3) Colloidal mixing of Fe,O3 and Al2O3. 4) Colloidal mixing of Fe powder and A1,O3. Fig. 1 is a processing flowsheet which outlines the processing steps taken to produce a final extruded bar 1/4 in. in diameter and about 30 in. long. The - 100 mesh iron-aluminum alloy was oxidized by placing a thin layer of powder on an alumina plaque. The reduction step was modified to include 1/2 hr at 1000°C since the powders tended to become pyro-phoric unless sintered slightly after low-temperature reduction. Compacting was done in a 1-1/8-in.-diam pressing die. The slugs produced averaged 1 in. in length. The billets were encased in low-carbon steel cans shown schematically in Fig. 2. The blank is included for structure and property comparison purposes. TESTING PROCEDURE All tests were made on as-extruded material.

Jan 1, 1960

By R. C. Mahon

THE importance of ground water control in glacial drift overlying mines is widely recognized. Adequate handling of the problem results in considerable saving in overall pumping costs, as the cost of pumping the larger quantity of water under low heads from surface wells is more than offset by the decrease in the quantity of water to be pumped from the mine under high heads. Eliminating or partly reducing seepage of water through the ledge reduces moisture content of the ore, a factor especially important in iron ore mines, where a reduction of 1 pct in moisture effects a very material saving. An important though indeterminate saving is also brought about by the elimination of water in the working places underground. The Homer and Wauseca mines of Hanna Coal & Iron Co. at Iron River, Mich., cover 480 acres. When these mines were started it was possible to operate on only one 40-acre tract, as the depth of water over the remainder of the property was too great to permit operation. Although the average depth of the ground water over the area being mined at that time was less than 50 ft it was necessary to pump 1200 gpm from the mine, the greater part from a depth of 750 ft. The slate footwall and graywacke hanging wall are almost impervious, and it was apparent that seepage into the mine was mainly through the iron formation in which the orebodies were located. Analysis of the water in the iron formation showed it to be of the same character as that in the glacial drift, while the water in both walls was heavily mineralized, also indicating that the water passed much more freely through the iron formation. The first attempt to take off the water above the ledge was by means of drainage drifts driven 15 to 20 ft below the ledge, Fig. 1. Various schemes were used to get the water into these drifts: 1—Holes 15 to 20 ft long were drilled from the back of the drifts to the ledge, but these were difficult to drill and blocked easily. 2—Sections of the drifts were blasted down. This gave a large flow for a time but eventually almost total blockup occurred. 3—Raises 4x4 ft were driven above the drifts to within 8 ft of the

Jan 1, 1955

By Alfred Weiss

When I first received the announcement of this meeting I was pleased to see that this 14th APCOM Symposium had expanded its range of interest. One new topic to be considered this year is long range or strategic planning--the continuous process by which current risk taking decisions are made systematically, and with the greatest knowledge of future impact. Long range planning should receive our attention. It is the first step in the management process and the foundation of many--if not all --key managerial decisions. Improvements made at this stage of managing are almost certain to be of benefit in later stages of decision making. It is obvious to many of us that in a physical process such as mineral beneficiation, one does not concentrate all of one's attention on the flotation design without also considering the grinding, cycloning, and desliming stages of the process. Taking this a step further it would be equally erroneous to find a mineral engineer designing a mill without due consideration for mine, smelter and refinery and beyond that the sales goals, growth and profit objectives of the firm itself. And yet, how many times have we seen organizations staff and reorganize without consideration of an overall plan; without adherence to the management process which by its definition, calls for a plan first, followed by the appropriate organization and staff. The computer applications traditionally discussed at APCOM meetings have concentrated on areas dealing with things and people-- the implementation of the plan, rather than with concepts and ideas, the formulation of the plan.

Jan 1, 1977

By C. Ernest Birchenall, Gerd M. Rosenblatt

The pressure and molecular weight of the antimony vapor over solid solutions of tin in antimony, containing 97.4, 94.9, 93.0, and 90.7 at. pct Sb, have been measured from 445° to 545°C by the torsion-effision method. The vapor is all Sb, within experimental error. A solidus curve which differs somewhat from the accepted curve has been calculated using the measured antimony activities. Metallographic examination of additional annealed alloys substantiates the accepted solidus. The solid solutions, which show negative deviations from ideality, probably do not deviate greatly from regular solution behavior. HANSEN' considers the Sb-Sn phase diagram to be well established with the exception of the boundary of the (Sb) phase.* Although there have been no pre- Their data can be combined with data for the solid alloys to calculate the solidus curve of the (Sb) phase. This paper presents measurements of the pressure ant1 molecular weight of antimony over Sb-Sn solid solutions containing 97.4, 94.9, 93.0, and 90.7 at. pct sb. Measurements were made by simultaneous use of the volmer3 torsion and Knudsen, effusion methods. The results of these measurements have been combined with the vapor pressure of pure antimony5 to obtain the activity of antimony in the primary solid solutions. The solidus curve calculated from these data differs somewhat from the accepted curve and is rather uncertain. Metallographic examination of Sb-Sn alloys was carried out to clarify the position of the solidus of the (Sb) phase. EXPERIMENTAL The apparatus and technique have been described previously.5 The measurements were made with the same effusion cells and torsion wire used in the measurements on pure antimony. The torsion measurements were calibrated with mercury at 30" using a mercury vapor pressure of 2.96 x 10-3 mm Hg determined by concurrent, absolute, weight-loss experiments. As in the measurements on pure antimony, an extraneous vapor was observed to distill off during the first run after the cell had been loaded with A fresh sample of alloy and during the first minute or two of every run. The change in composition after a series of runs with one sample was of the order of 0.1 at. pct and thus completely negligible in the calculation of the thermodynamic properties. The alloys were prepared from pieces of Merck antimony and Matheson, Coleman, and Bell reagent-

Jan 1, 1962

By R. H. Brown

EARLY workers attempted to study the structure of alloys by measurement of equilibrium electrode potentials in aqueous solutions containing ions of the metals from which the alloy was made.1 The method was subject to such limitations (e.g., the difficulty in attaining electro-chemical equilibrium at low temperatures) that it has not been widely used by metallurgists. Recently, Seltz and co-workers have introduced a greatly improved method for studying alloys by measurement of equilib-rium electrode potentials in molten salts.2-4 The mathematical treatment is the same, of course, as for equilibrium potentials of amalgams in aqueous solutions.5 This method will probably find extensive use, since it makes possible not only the deter-mination of phase fields of equilibrium diagrams but also the determination of certain thermodynamic quantities which can be used advantageously in metal-lurgical calculations. However, the method presents difficulties. With many metallic and alloy electrodes, reversibility is not readily obtainable. Also, the difficulty of obtaining suitable material from which to make the cells is increased as the temper-ature is increased. Moreover, the necessity of carrying out measurements in a vacuum requires additional apparatus and intro-duces considerable difficulty, especially at the higher temperatures.

Jan 1, 1940

Meeting of June 4, 1915.-The President announced the appointment of the following Committee on National Reserve Corps of Engineers: Dr. Henry S. Drinker, Chairman; Arthur S. Dwight, and Warren A. Wilbur; also, the appointment of Arthur F. L. Bell as Chairman of the Committee on Petroleum and Gas, and of James F. hemp as Chairman of the Committee on Mining Geology. All of these appointments were approved. It was voted that the following minute be, placed on record and a copy sent, by order of the Board of Directors, to the family of John Birkinbine: "The Board of Directors of the American Institute of Mining Engineers hereby records its sense of sorrow and loss in the death of John Birkinbine, a former President, and for many years an active member of the Institute, and contributor to its Transactions. "Mr. Birkinbine's eminence as an engineer, author and editor, intimately connected with the industrial progress of the United States, brought him into contact With the leaders of science and the captains of industry, among whom his genial and estimable personal character won for him many friends; and his departure in the prime of Strength and usefulness is mourned by a wide circle."

Jan 7, 1915

By W. O. Crosby

INTRODUCTION. THE crystalline belt of the Atlantic Seaboard, south of New York, attains its maximum breadth of 220 miles on the northern border of North Carolina; and in this State it is most widely characterized by the occurrence of gold in workable deposits. Half a dozen auriferous belts have been recognized by Nitze and Hanna.1 These are, in the main, coincident in position and trend with the NE.-SW. zones of metamorphic slates and schists, which, more than any other feature, give character to the geological map of North Carolina. The central gold-belts, accompanying the main zone of slates and associated igneous rocks, are much the more important and persistent, and may be regarded as continuous northward across Virginia and southward into South Carolina. Tile eastern belt, on the other band, is the shortest and, economically, one of the least important. Its extreme length does not exceed 25 miles, the narrow band of slaty rocks to which it belongs passing, both NE. and SW., beneath the coastal-plain formations. But, although limited in area and production, this belt is, perhaps, comparable with the central belts or any part of the sea-board crystallines in the variety of conditions under which the gold occurs. It lies chiefly in the NE. part of Franklin county and the NW. part of Nash county, on the watershed of Fishing creek and other tributaries of Tar river. The elevation is between 400 and 500 ft. ; and the Tertiary peneplain has here an exceptionally perfect development, the reliefs separating the slightly incised stream-courses consisting of broad, flat-topped peneplain remnants, bounded by gentle lateral slopes.

Mar 1, 1908

By J. C. Coughlin, M. C. Flemings, T. Z. Kattamis

Experiments on Al-4.5 pct Cu alloy shou the dendrite arnz spacing increases with time during isothermal holding in the liquid-solid region. This coarsening of the dendrite structure is then shown to occur at roughly the same rate during solidification as during isothermal holding. Final dendrite arm spacing in both types of experiments depends primarily on coarsening kinetics. It is concluded that driving force for the coarsening is reduction of liquid-solid sur/ace area. Calculations based on two simple models show qualitative apreement with experinzent. 1 HERE has been considerable interest in recent years in determining effects of solidification variables on dendrite arm spacing in cast alloys. The interest has resulted primarily from the clear evidence that 1) the degree of homogeneity which can be obtained in a cast alloy with commercially practical homogeni- zation treatments depends on dendrite arm spacing, and 2) mechanical properties of the heat-treated casting depend on the homogeneity obtained.'-' In wrought alloys, microsegregation from the original ingot is carried to some extent into the final wrought product, and affects mechanical properties in similar fashion Experimental evidence available indicates that dendrite arm spacing in cast aluminum alloys is influenced only by cooling rate (or "local solidification timev*) and alloy content.Fig. 1, for example,

Jan 1, 1968

By I. N. Zavarine

The observations presented in this paper were recorded during a study of the spheroidizing process. Spheroidization of cementite in steel is either brought about to develop a set of desirable mechanical properties or is an incidental result of mechanical and heat-treating manipulations. Physical properties of steel are materially influenced by the state of the cementite. Conversion of cementite from the lamellar to the spheroidal state is usually accompanied by a decrease of hardness and of strength and by an increase in ductility. The spheroidized structure is usually considered as an ultimate step in the process of the softening of steel. The unorthodox hardening of a 3.5 per cent Ni steel (SAE No. 2330) after a heat-treatment that previously proved entirely suitable for a complete spheroidization of cementite in carbon steels led to the observations that constitute the subject of the present paper. Experimental Procedure The steels used for the experiments described were bought on the market. All were in the form of 3/4-in. round bars. Their chemical compositions are given in Table 1. The spheroidization of cementite in steels can be obtained in several ways. The method used in the present work is, perhaps, the least known. It consists of cyclic heating and cooling of steel, the temperature being

Jan 1, 1939

By I. N. Zavarine

The observations presented in this paper were recorded during a study of the spheroidizing process. Spheroidization of cementite in steel is either brought about to develop a set of desirable mechanical properties or is an incidental result of mechanical and heat-treating manipulations. Physical properties of steel are materially influenced by the state of the cementite. Conversion of cementite from the lamellar to the spheroidal state is usually accompanied by a decrease of hardness and of strength and by an increase in ductility. The spheroidized structure is usually considered as an ultimate step in the process of the softening of steel. The unorthodox hardening of a 3.5 per cent Ni steel (SAE No. 2330) after a heat-treatment that previously proved entirely suitable for a complete spheroidization of cementite in carbon steels led to the observations that constitute the subject of the present paper. Experimental Procedure The steels used for the experiments described were bought on the market. All were in the form of 3/4-in. round bars. Their chemical compositions are given in Table 1. The spheroidization of cementite in steels can be obtained in several ways. The method used in the present work is, perhaps, the least known. It consists of cyclic heating and cooling of steel, the temperature being

Jan 1, 1939

By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

D. N. Williams(BatteZle Memorial Institute)-The authors have presented an extensive collection of arguments pertaining to the role of stress in hydrogen embrittlement. The basic assumption of these arguments is that stress is essential as a driving force for diffusion of hydrogen. However, in view of the rapid diffusion rate of hydrogen in steel at low temperatures as evidenced by the ability to alloy with hydrogen by electrolytic charging, it seems unlikely to me that stress acts in this manner. Instead, I would like to suggest that stress may be essential for the nucleation of hydrogen in steel. I believe that such an assumption would equally well satisfy the experimental data presented by the authors. I should also like to comment on the interpretation of the data presented in Figs. 5 and 6. Fig. 5 shows the effect of hydrogen content on ductility in a rupture test. The curve as drawn by the authors indicates an abrupt transition from ductile to brittle behavior at about 0.001 amp per sq in. (5 ppm). The data points would equally well support a gradual transition from ductile to brittle behavior extending over the range from 0.0008 to 0.02 amp per sq in. (4 to 8 ppm). A gradual transition would be the ex-

Jan 1, 1962

By Francis Collins, E. R. Brownscombe

A study has been made of the material balance-fluid flow method of estimating reserves and degree of water drive from pressure and production history data. By considering the effect of random pressure errors it is shown that in a particular example a standard deviation of three and one-half pounds in each of ten pressure survey? permits the determination of the reserves with a standard deviation of 8 per cent and the water drive with a standard deviation of 15 per cent, assuming that certain basic geologic data are correct. It is believed that this method of estimating reserves and water drive is useful and reliable in a number of cases. The method is particularly valuable when reservoir pressure data are accurate within a very few pounds, but may also be applied with less accurate pressure data if a relatively large reservoir pressure decline occurs early in the life of the field, as for example in an under-saturated oil field. INTRODUCTION A knowledge of the magnitude of reserves and degree of water drive present in any newly discovered petroleum reservoir is necessary to early application of proper production practices. A number of investigators have contributed to methods of relating reserves, degree of water drive, and production and pressure history. 1-8 Three types of problems of increasing complexity may be mentioned. If a reservoir is known to have no water drive. and if the ratio of the volume of the reservoir occupied by gas to the volume of the reservoir occupied by oil (which ratio permits fixing the overall compressibility of the reservoir) is known, then only one further extensive reservoir property remains to be determined, namely the magnitude of the reserves. A straightforward application of material balance considerations will permit this determination. The problem becomes very much more difficult if we wish to determine not only the magnitude of the reserves but also the magnitude of water drive, if any, which is present. In principle, a combination of material balance and fluid flow considerations will permit this evaluation. Finally, if neither the magnitude of reserves, the degree of water drive, nor the ratio of oil to gas present in the reservoir is known and it is desired to determine all three of these variables, the problem could in principle be solved by a fluid flow-material balance analysis which determines the overall compressibility of the reservoir at various points in its history. The change in compressibility with pressure would provide a means of determining the ratio of gas to liquid present, since the compressibilities of gas and liquid vary differently with pressure variation. However, in practice this problem is probably so difficult as to defy solution in terms of basic data precision apt to be available.' It is the purpose of this discussion to illustrate the second case, which involves the determination of two unknown variables, single phase reserves and degree of water drive, from pressure and production history and fluid property data, and to study the precision with which these unknowns can be determined in this manner in a particular case. Although an electric analyzer developed by Bruce as used in making the calculations to be described, numerical methods necessary in carrying out the process have been devised and have been applied for this purpose. Schilthuis,' for example, developed a comprehensive equation for the material balance in a reservoir. He combined this with a simplified water drive equation, assuming that the ratio of free gas to oil was fixed by geological data and that a period of constant pressure operation at constant rate of production was available to determine the constant for his water drive equation. On this basis he was able to compute the reserves and predict the future pressure history of the reservoir. Hurst developed a generalized equation permitting the calculation of the water drive by unsteady state expansion from a finite aquifer. He showed in a specific case how the water influx calculated by his equation, using basic geologic and reservoir data to fix the constants, matched the water influx required by material balance considerations. Old3 illustrated the simultaneous use of Schilthuis' material balance equation and Hurst's fluid flow equation for the determination of the magnitude of reserves and a water drive parameter from pressure and production history. He used this method to calculate the future pressure history of the reservoir under assumed operating conditions. As a basis for determining reserves, Old assumed a value for his water drive parameter and calculated a set of values for the reserves, using the initial reservoir pressure and each successive measured pressure. The sum of the absolute values of the deviations of the resulting reserve numbers from their mean value was taken as a criterion of the closeness of fit to the experimental data possible with the water drive parameter assumed. New values of the water drive parameter were then assumed and new sets of the reserves calculated until a set of reserves numbers having a minimum deviation from the average was established. The average value of- the re-

Jan 1, 1949