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(Under this heading will he published notes sent too the Secretary of the Institute by members or other persons introduced by members.) Management or superintendency desired by member, graduate mining engineer of large practical experience in the details of mining, milling, concentration and cyaniding. Experienced in the efficient mechanical equipment and operation, and in the general business management of a mining property. No. 444. Metallurgist and operator who has specialized in the hydrometallurgy of. gold and silver, particularly stamp milling and cyaniding, desires change from present position. Ten years' experience in Western U. S. Thirty-six years old, married, in best of health and will go. anywhere. Available in 30 days. No. 445.

Jan 4, 1918

By Immo H. Redeker

Abstract-North Carolina is the leading state in the US in lithium mineral production. Spodumene is mined in open Pits and concentrated by flotation by the two companies, Lithium Corp. of America and Foote Mineral Co. North Carolina State University has a mineral research laboratory in Asheville, N. C., with trained personnel, batch and pilot plant facilities to assist in the state's mineral development. The NCSU Minerals Research Laboratory assisted both lithium-producing companies with spodumene concentration problems and has lately worked closely with Lithium Corp. of America to develop the best flowsheet for spodumene and byproduct recovery. The concentration of North Carolina spodumene and byproducts from pegmatites is presented and illustrated with figures.

Jan 4, 1979

By J. Mark Gronseth

The instantaneous shut in pressure often times is not a well defined feature of pressure-time records from in situ stress determinations by hydraulic fracturing. As the applications of in situ stress data become more sophisticated, the grea5er the need for an unambiguous method with which to identify the instantaneous shut in pressure becomes. Controlled experiments suggest that the instantaneous shut in pressure should be equated with the pressure at the inflection point of the pressure-time record following shut in. A method for determining this value is presented. Often times the minimum instantaneous shut in pressure determined after several pressurization cycles is the best estimate of the stress acting perpendicular to the fracture plane.

Jan 1, 1982

By Paul G. Hoffman

A survey of the role of the United Nations Special Fund in the field of mining and metallurgy. An aircraft, manned by Canadians and crammed with modern scientific instruments, crisscrosses over the dense rainforests of tropical Surinam at Y4 kilometer intervals, prospecting for valuable mineral deposits. Mill head samples of Burmese lead and zinc ores arrive at a Colorado laboratory for analysis and experimentation to determine the best milling and ore-dressing techniques. At the new Institute for Applied Geology in Manila, Philippine mining engineers receive instructions from a Finnish petrologist. These scenes illuminate only a fraction of the exciting work in the mining and metallurgical fields being carried out by the United Nations Special Fund.

Jan 8, 1963

By Immo H. Redeker

North Carolina is the leading state in the US in lithium mineral production. Spodumene is mined in open pits and concentrated by flotation by the two companies, Lithium Corp. of America and Foote Mineral Co. North Carolina State University has a mineral research laboratoy in Asheville, N. C., with trained personnel, batch and pilot plant facilities to assist in the state's mineral development. The NCSU Minerals Research Laboratory assisted both lithium-producing companies with spodumene concentration problems and has lately worked closely with Lithium Corp. of America to develop the best flowsheet for spodumene and byproduct recovery. The concentration of North Carolina spodumene and byproducts from pegmatites is presented and illustrated with figures.

Jan 1, 1980

By John J. Reed

The mines of southeast Missouri's Lead Belt have been in operation since 1864, almost 100 years. During this period about 10 pct of the total ore available has been left in place as pillars, and this now represents the best ore reserve left to the older mines. St. Joseph Lead Co. has been investigating various plans of pillar recovery for several years. The example to be described is only one possible approach under a specific set of conditions. Conditions vary greatly in the different areas within the Lead Belt, and the same approach would be entirely in- adequate in certain other areas, but there are important sections where this system is clearly applicable.

Jan 7, 1959

By James R. Evans

Forecasting demand is an art as well as a science, and much personal judgment is required. National forecasts made for sand and gravel, crushed stone, and/or aggregate may be misleading or unhelpful locally. This is because of significant variation in demand within different geographic and/or political areas in the US, and/or the use of an inadequate data base and forecasting methodology. The best forecasts may be made for local or regional market areas, irrespective of geographic or political boundaries, provided a proper data base is available.1 The Bureau of Mines compiles detailed statistics on commodities sold or used in the construction industries and, therefore, is in an advantageous position to make national aggregate demand forecasts.

Jan 1, 1979

By Colin C. Harris, Nathaniel Arbiter

Current scale-up procedures are discussed critically, including: constant specific energy criterion; determination of mill size and power for a given ore, throughput and mesh of grind; specification of operating speed and loading. A major dynamic and kinetic factor now recognized is that the ratio of media rotational flow to ore axial flow, and the number of mill revolutions that ore is subjected to during residence, both diminish as mill diameter increases. These factors can lead to capacity limitations when mill diameters reach a critical range, especially regarding coarse sizes. Experience at the Bougainville and Pinto Valley operations is contrasted. Corrective measures suggested are to reduce loading and increase speed towards the Davis best operating speed.

Jan 1, 1982

By Thomas Robins

About six years ago the writer had occasion to visit a large magnetic iron-ore concentrating-plant, and then saw for the first time rubber belts employed for conveying-purposes. These belts were from 20 inches to 30 inches in width, and some of them were as long as 500 feet between centers. When I spoke of the enormous amount of material they handled with a small expenditure of power, the superintendent assented, but at the same time complained that although he bought the best quality of belts, the abrasion of the ore wore them out very rapidly, causing continually very large bills for repairs and renewals. On close examination several interesting points were discovered :

Jan 1, 1897

By Robert W. Bruhn

An investigation was made of ground response to pillar retreat mining in a 1.7 meter thick seam at 108 meter depth at a site in northern West Virginia. This paper describes mining-related stress changes and movements at mine level, displacements within the overburden, ground surface subsidence and groundwater level variations. Subsidence approached 40 per cent of the mine height and continued more than a year after mining. Water levels declined in certain deep-lying strata.

Jan 1, 1984

By J. H. McCarthy, J. M. Botbol, R. B. McCammon, G. H. Gott

Four areas have been identified as favorable drill site locations for determining whether a suspected porphyry copper deposit exists in Rowe Canyon, NV. Favorability is bated on the similarity to a deposit model constructed from geochemical data for the porphyry copper deposit near Ely. Favorability is defined as the coincident number of positive anomalies for zinc, silver, aresenic, antimony, and iron. The favorable areas coincide with an observed magnetic high and areas in proximity to major faults.

Jan 1, 1983

By J. G. Faller, L. P. Skolnick

The distribution of cobalt and vanadium over non-equivalent crystallographic sites in C14-type Zr(VCo), alloys has been investigated. An anomalous X-ray scattering technique developed by Skolnick, Kondo. and lavine7 by which the separation in the scattering factors of two similar atoms can be enhanced was employed. Six alloys spanning the pseudobinary section ZrV1.6Co0.4-ZrVO.6CO1.4 at 10pct steps showed a nonrandom compositionally dependent distribution. Specifically, at high vanadium content cobalt preferentially occupied sites of type (6h) and vanadium, sites of type (2a; at low vanadium content the reverse was observed. In addition to the distribution fraction the structural parameters x and z were obtained. There was no significant deviation of these parameters from those obtained in the ideal C14 structure. Certain suggestions are made to account for the observed nonrandomness in the distribution of atoms on the two types of sites. INTERMETALLIC compounds of formula AB2 iso-morphous with MgCu2, MgZn2, and MgNi2 are known as Laves phases. Because Laves phases exhibit high symmetry and coordination numbers, the highest possible for an AB2-type compound,1 they are among the most frequently observed compounds in nature. In recent years interest has centered about the purely transition metal Laves phases2-' in efforts to understand the function of atomic size and electronic structure in the formation of these compounds. It has been observed that pseudobinary Laves phase systems often show a variation of structure across the phase diagram. Such a system is the ZrV2-ZrCo2 in which the structure varies from cubic MgCu2 to hexagonal MgZn2 to cubic MgCu2.4 Some understanding about the conditions under which the second modification is stable can perhaps be gained by studying the distribution of cobalt and vanadium atoms on lattice sites in the MgZn2 modification of the system ZrV2-ZrCo2. In both the MgZn2 and MgNi2-types there exist nonequivalent positions open to occupancy by the B element, whereas in the MgCu2 prototype all sites are equivalent. Skolnick, Kondo, and La-vine7 have developed an anomalous scattering technique suitable for this type of investigation. Whereas the influence of size on the formation of a Laves phase is well recognized, no substantial evidence has been put forth in support of the size ratio dependence of a particular prototype. Berry and Raynor8 suggested that RA /RB ratio does indeed affect the type of structure that is chosen, MgZn2 compounds tending to cluster about 1.225 while MgCu2 compounds were found at larger deviations from this ratio. Dwight,3 however, from a study of 164 Laves phases does not believe this generalization to be justified. Electronic effects are certain to play a part in the stability of Laves phases in general and in the choice of a structure type in particular. For example, size along would favor the formation of Laves compounds of Ti, Zr, Hf, Ta, or Nb as the A element with nickel or copper as the B element. The absence of such is attributed to an unfavorable electron : atom ratio by Elliott and rostoker.4 Early experiments of Laves and witte9 with pseudobinary and pseudoternary systems of the three prototypes established the dependence of crystal structure upon electron: atom ratios. They observed that the MgCu2 structure dissolved elements of higher valency until the electron: atom ratio of =1.8 was reached; the MgZn2 likewise dissolved elements of lower valency replacing zinc. witte,6 from calculations of the electron : atom volumes of Brillouin Zones, obtained limits of stability for the prototypes MgCu2 and MgZn2. Elliott and Rostoker4 used these limits with considerable success in the all-transition element Laves phases they investigated. According to witte,6 compounds between the electron :atom ratios of 1.80 and 2.32 were of the MgZn2 type; those above and below exhibited the MgCu2-type structure. On the basis of these limits and an assumed valency of zirconium based upon the near tetra-valence of titanium, Elliott and Rostoker obtained valencies for the first transition series elements. For the Laves phases with which this investigation is concerned, ZrV2 and ZrCo2, the authors calculated electron :atom ratios of 2.54 and 1.56, respectively. These ratios are for the MgCu2-type structure and straddle the stability band of the MgZn2 modification. One could, therefore, predict that a pseudobinary system ZrV2-ZrCo2 should pass through the MgZn2 modification in traversing the composition diagram from one end to the other. Implicit in this assumption is a smooth change of the electron: atom ratio from 2'54 to 1.56. MOSS10 states that his finding the low temperature structure of ZrCr2 to be C15 instead of C14 alters greatly Elliott's valency of zirconium and hence the assumed valencies of the other metals. Such a quantitative correlation of structure with electron : atom

Jan 1, 1963

By Frank S. Shuri

INTRODUCTION The Calumet Pumping Station, located on the south side of the Greater Chicago area, is part of the Tunnel and Reservoir Plan to accomodate the city's wastewater. The Station consists of two parallel rock caverns, each 18 m high, 20 m wide, and 62 m long, located in Silurian dolomite approximately 91 m below the ground surface. The caverns are oriented N-S with a 24-m-wide pillar between them. Prior to construction, rock mechanics studies were conducted in an L-shaped test adit at the location of the west cavern. The purpo3e of the rock mechanic studies was to characterize the site, particularly the in situ stress field and deformation characteristics of the rock. This information, together with other physical properties of the rock and geologic data, was used to evaluate the stability of the preliminary cavern design, with particular emphasis on cavern orientation, rock reinforcement, and pillar stability. GEOLOGY OF THE SITE Stratigraphy The Chicago area is located on the Kankakee Arch, a broad, gently sloping arch of Paleozoic sediments. Rocks in the project area consist of Silurian dolomites unconformably overlain by Pleistocene glacial deposits. The formations of interest to this study are: - Racine Formation, inter-reef facies. This dolomite is gray- brown, silty, and compact. It contains occasional prominent bedding surfaces. The Racine Formation in the project area varies from 73 to 74 m in thickness.

Jan 1, 1984

By L. J. West, R. M. Perrry

This chapter describes the rock mechanics studies performed for a high cut at a nuclear power station in Pennsylvania. Two units presently are being constructed on the Susquehanna River. When these units are completed, they will generate approximately 2100 MW of electricity. It was necessary to excavate about 1 million cu yd of rock to prepare the site. This excavation resulted in a high cut on the west and north sides of the station area with a maximum height of about 200 ft. The location of the high cut with respect to the plant facilities is shown on Fig. 1. The recommended slope angles ranged from 1 ½ (horizontal) to 1 (vertical) for the upper residual soil to ½ to 1 for the deeper competent rock. Because of the significant height of this cut and the fact that the slope is immediately adjacent to the proposed nuclear facilities, extensive stability analyses were performed prior to, during, and after excavation to evaluate the steepest angle at which the slopes could be safely cut. The studies consisted of evaluating both qualitatively and quantitatively all apparent factors which could affect the stability of the slopes. These factors include the strength of the material, the zones of weak material which are present along the planes of schistosity, the prominent joint systems, the ground water, and postulated seismic effects. FIELD AND LABORATORY STUDIES A comprehensive program of field explorations was performed to evaluate the geologic characteristics of this site. This program consisted

Jan 1, 1970

By K. L. Ludeke, A. D. Day

For many reasons, it appears that deep rooted, perennial shrubs offer potential for improved stabilization and provide maintenance free vegetative cover to harsh sites where perennial grasses have not been successful. The major objective was to select various shrub species of arid plants for initial soil stabilization of disturbed mining areas. The very fact that a drought-adapted shrub has a massive root system that can use moisture from a greater volume of mineral waste soil materials suggests that arid environment disturbed soils may be vegetatively stabilized using desirable forage shrubs. A secondary effort is underway to assemble information and plant materials of promising species from many arid regions of the world for reclamation of mined lands. Surprisingly, many of the better plants for arid sites are quite high in protein content. With proper management, breeding, and selection, they may prove to be very desirable livestock feed when mined lands are used in range land areas. Advancements in arid land solid waste stabilization hold favorable promise for many industries that mine and mill in arid regions for effective reclamation of disturbed areas. Particularly exciting is the possibility of establishment of high density maintenance free vegetative cover of climax vegetation that reclaims the disturbed area back to its original land use. Due to high shrub productivity, stabilization potential, nutritional quality, and reclamation success, greater use should be made of shrubs in disturbed land reclamation associated with mining and milling operations in harsh aril environments.

Jan 1, 1986

By E. G. Leonardon

The object of this paper is to describe briefly the practical results obtained in several problems of civil engineering by resistivity measurements of the underground. It is intended for the mining engineer, as well as for the construction engineer; the stratigraphical problems discussed are general and frequently are encountered in mining exploration. Resistivity measurements have been used in mining and oil exploration for a number of years.' Their introduction in the field of civil engineering, on the contrary, is rather recent. It was applied for the first time in the spring of 1928 near Littleton, N. H., in the survey of two dam sites for the New England Power Assn.2 Since then, the geophysical firm with which the author is connected has had an opportunity to develop this field of activity, and more than 20 investigations at dam and tunnel sites have been carried out in the United States and Canada. A part of this work has been verified by underground or drilling exploration. This paper deals with but a few of the results, which we are permitted to make public now. The theoretical and technical sides of the processes employed will not be discussed; they have already been described in various technical publications. A few general points will be mentioned, to make clear the practical examples given. Resistivities OF the Rocks The surveys are based on the measurement of the specific resistance of the rocks. This resistivity is the electrical resistance of a cylinder of

Jan 1, 1932

By H. Kenyon Burch

INTRODUCTION THE Inspiration Consolidated Copper Co.'s plant at Miami, Ariz., was designed and built to make possible the profitable working of a low-grade, finely disseminated copper deposit containing 100,000,000 tons of ore averaging 1.64 per cent. in copper. From the-beginning it was evident that the-plant could not, be kept integral but that a break would have to be made somewhere in the flow-sheet, removing at least the concentrator to a site more suitable than any available near the mine. It was finally decided, after considering numerous arrangements, to do the coarse crushing at the mine, to store the crushed ore in a bin from which it could be loaded into railroad cars and to haul it to the concentrator, an excellent site for which was available about 1 ¾ miles from the mine. The original intention was to equip a plant to treat 7,500 tons of ore per clay, but through the acquisition and proving up of additional ore reserves, the introduction of the Ohio caving system, and the excellent results obtained in the test mill (which made it possible to treat a lower-grade ore than had been thought possible) it was evident that a plant of much greater capacity should be supplied. It was, therefore, decided to treat approximately 15,000 tons of ore per day, the duties of the four main divisions to be as follows:

Jan 9, 1916

By Richard L. Ashbrook, John F. Wallace

Several high-temperature eutectics of cobalt and nickel alloys were modified by small additions of selected elements. Thes-e alloys were compared to unmodified melts for microstructural variations. A few modified compositions were selected on the basis of structure and their tensile and stress-rupture behavior determined. The results of stress-rupture tests in air at 1800 F and room-temperature tensile tests of four high-temperature eutectics showed modification capable of producing substantial improvements in properties. The microstructures were altered and mechanical properties improved by: a.) dispersing a subordinate phase more uniformly throughout the matrix; b) replacing large continuous -network or platelike constituents with small equiaxed discontinuous phases; and c) by forming new, finely divided phases. tHE term "modification" is most commonly used to describe the refinement in microstructure of the Al-Si eutectic that occurs as a result of rapid cooling from the melt or on slow cooling after treatment with small amounts of sodium.1 "Modification" has also been used to describe the change from flake to spheroidal graphite in the austenite-graphite eutectic of cast iron.2 This change of graphite shape is accomplished by small additions of cerium or magnesium.3 Other systems have also been shown to be capable of modification, for example: Pb-Sn by copper;4 Al-Cu by sodium;5 Al-Mn by sodium;5 and Pb-Sb by aluminum.5 Although modification of Al-Si alloys and cast irons is usually accompanied by improved mechanical properties, a general definition of modification has been suggested to include the effect of small quantities of impurity elements on the microstructures of all eutectic alloys, regardless of the effect on the mechanical properties.6 In this paper, the term "modification" is employed in a broad sense to include the formation of third phases or even the supplanting of one of the binary eutectic phases by a third phase. The mechanism of modification, as for any solidification phenomenon, must be considered primarily in terms of nucleation and growth. Although both nuclea-tion and growth mechanisms are required to explain all the phenomena observed in connection with the solidification of modified eutectics, various investigators have usually favored one or the other.7"16 It has been shown that modification of a binary eutectic can be effected by addition of a solute element that has greatly different distribution coefficients or k values in the two phases of the eutectic. Under these conditions, differences in the temperatures at the solid-liquid interfaces of the two phases retard the growth of one phase with respect to the other.4 It has also been shown that increased undercooling favors a transition from a rodlike eutectic to a globular eutectic.17 A mechanism proposed for the transition from lamellar to rodlike eutectics depends on the concept of constitutional super cooling.18 The modification of eutectic alloys may be of interest for high-temperature service as well as at room temperature. Although "high-temperature eutectic alloys" may appear to be a contradiction in terms, many eutectic systems, including those studied in this work, have melting points in excess of 2400°F. One of the mechanisms by which high-temperature alloys are strengthened is dispersion of a relatively brittle phase such as an oxide, carbide, or an inter-metallic compound throughout a ductile matrix. For a given volume fraction of dispersed phase, strength is increased by decreasing the size and spacing of the dispersed particles.19'20 Furthermore, room-temperature ductility may also be increased by changing the shape of a brittle dispersed phase from platelike to equiaxed or spheroidal.8 Overaging and redissolving of the secondary phase limit the maximum temperature to which precipitation-hardened alloys can be used. However, in a binary eutectic system, both phases coexist up to the melting point. Although all eutectic structures are not completely stable,21 a dispersion-hardened cast high-temperature alloy might result if a fine distribution of one of the eutectic phases could be obtained during solidification. An additional reason for interest in eutectic alloys is their excellent castability.22 Since eutectic alloys, like pure metals, freeze at a single temperature rather than over a range of temperatures, their castability is superior to solid-solution alloys with long liquidus to solidus ranges. The purpose of this research was to study the effects of small solute additions on the microstructure and mechanical properties of a number of high-melting-point eutectic compositions.

Jan 1, 1967

By J. D. Meakin

J. D. Meakin (The Franklin Institute Laboratories)— In a recent paper Garofalo12 has shown that a number of experimental creep results can be represented by the empirical relation In this expression ? is the steady creep rate, s is the applied stress, and A is a constant at a given temperature; a and n are adjustable parameters. Garofalo has shown that Expression [6] approximates to a power function at low stresses and a simple exponential function at high stresses. Among the data used by Garofalo are the results we published for creep of copper." For these results we found that the best correlation was an exponential law with different parameters in the low-and high-stress region, respectively. That is, i = A exp qs where A and q have different values above and below a critical stress a,. In Ref. 13 are listed a variety of observations which support the proposal that different mechanisms are operative at stresses above and below a,, and it is not felt appropriate to repeat those observations here. The purpose of this note is to demonstrate that, although the representation used by Garofalo does fit the experimental data very well, this fit cannot be used to conclude that only one mechanism is rate-controlling. The argument is best made graphically and is illustrated in Fig. 9. The continuous curves 2 and 3 represent pairs of simple exponential functions which intersect at i = 10-5. The curve 2 closely resembles the copper results in that a change of slope of 2:1 occurs at i = 10-5; the two functions shown are in fact: e = 10-7 exp (1.150) and ? = 10-6&apos; exp (0.576s) For purposes of comparison, curve 3 represents two exponential functions with a change of exponent of 3:1 and curve 1 has the exponent 1.150 throughout. It is quite clear that a satisfactory straight-line fit is obtained on a Garofalo plot for all three curves. The curves represent processes which have either a single stress exponent or two ex- ponents in a ratio as high as 3:l. It must, therefore, be concluded that the ability to obtain a linear dependence between log i and log (sinh cyo) cannot be taken as evidence for a single activated process. In fact, to some extent the way the experimental points quoted by Garofalo lie about a best fit straight line on the log (sinh as) plot indicates that two processes are indeed occurring. This is seen in Figs. 7(c) and 8(c) of Ref. 12 where it is particularly evident that the experimental points deviate from the straight line in a manner similar to curves 2 and 3 of Fig. 9. It is, of course, recognized that the generally used exponential form is an approximation to the hyperbolic sine function which is not valid for exponents of less than 1.2, e.g., qs < 1.2. The only curve in Ref. 12 which is affected by this restriction is Fig. 6(b) where the deviation from a In ? vs s

Jan 1, 1964

By L. A. Rapport, J. R. McCord, W. P. Drews, K. H. Coats

Water movement about an oil or gas reservoir can be predicted provided an aquifer influence function is known. This function is generally determined from an electric analyzer study or by fitting an idealized mathematical model to field data. A prohlem arises in determining that influence function which best reproduces field data and satisfies certain smoothness requirements, without making any idealizations concerning aquifer geometry and heterogeneity. This study shows the problem to be solvable through the linear programming technique and presents applications to one oil reservoir and two gas storage reservoirs. In addition, a theorem is stated and proven which confirms influence junction smoothness requirements heretofore accepted on physical intuition and establishes additiotzal smoothness constraints formerly not recognized. INTRODUCTION The pressure decline accompanying production results in water encroachment into oil and gas reservoirs situated adjacent to aquifers. The importance of this water movement derives from the significant dependence of production rate upon reservoir pressure and of pressure, in turn, upon water encroachment. Pressure and rate of water movement are uniquely related through an "influence" function which may be in the form of reservoir pressure response to a unit water encroachment rate or of water movement caused by a unit reservoir pressure drop. This influence function reflects the heterogeneity and geometry of the aquifer and is therefore particular to each reservoir. If the influence function is known, then reservoir pressure may be predicted from a production rate schedule, or vice-versa, with the aid of the material balance equation which relates water influx to reservoir production and pressure. The problem of determining this influence function for a given reservoir has been approached in three different ways. Van Everdingen and Hurst calculated and tabulated certain influence functions pertinent to idealized mathematical models which satisfy simplifying assumptions such as aquifer homogeneity and elementary reservoir-aquifer geometries.&apos; Other studies developed additional tables for a variety of elementary reservoir-aquifer geometrical con- figurations and demonstrated their validity and utility.:&apos; Hicks, et al. described the use of an electrical network to determine an influence function giving "best" match of field history and allowing prediction of future performance.&apos; Finally, Hutchinson and Sikora5 and Katz, Tek and Jones attempted to develop a calculation method for deriving the influence function directly from field data with no idealizing assumptions concerning aquifer geometry and homogeneity. They encountered difficulties with inaccuracies in field data and with satisfaction of well-known smoothness requirements of the influence function. This study is concerned with the determination of influence functions from field data and, more specifically, treats the following problem: given field pressure-production data of arbitrary accuracy, how does one determine the influence function which, subject to satisfaction of known smoothness requirements, gives best agreement with field history? A rigorous solution to this problem is ohtained through linear programming as described below. Example applications to one oil and two gas storage reservoirs are presented. In addition, a theorem is proved which confirms influence function smoothness requirements heretofore accepted on physical intuition and establishes additional smoothness requirements formerly not recognized.

Jan 1, 1965