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(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Mining Geologist. Age, 34; wide experience in all Lake Superior iron-ore districts and Arkansas bauxite district. Examinations, tonnage estimates, reports, direction of prospecting, geologic mapping, churn and diamond drilling. Excellent references. A-2681. Mine Superintendent or Manager. Graduate mining engineer, age 31, married, 10 years' experience, now in government employ as metal-lurgist, desires employment with reputable mining company. New York interview if desired. A-4219. Research Engineer, now in Chile on erection of 50-ton mill with modern machinery for treatment of Chilean nitrate, desires connection, from the first of next year, with firm operating in South or Central America. A-4915. Mining Engineer. Young graduate of Michigan College of Mines; capable of handling men, conscientious worker; desires a position that will lead to assistant superintendency. Any place in the United States. Initial salary relatively unimportant. A-5195. Metallurgist, married, age 25; technical graduate; 3 years' experience in blast and open-hearth furnaces, blooming mills, metallographic, and heat treatment work; desires position as sales engineer in the Pittsburgh district. A-5196.

Jan 12, 1919

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who called at Institute headquarters during the period Feb. 10, 1916 to Mar. 10, 1916: D. A. S. Bell, Ottawa, Can. E. B. Latham, Santa Maria, Cal.. John Cooper, Exeter, Devonshire, Eng. H. N. Lawrie, Portland, Ore. I. Dally, Seattle, `Wash. L. A. Levensaler, Tacoma, Wash. George W. Evans, Seattle, Wash. George J. Lyon, Schenectady N. Y. Alexander Fyfe, London, Eng. Fred MacCoy, Antofagasta, Chile. F. C. Greene, Seattle, «rash. J. Mitchell-Roberts, London, Eng. I. Ishikawa, Tokio, Japan. Chas. W. A. Sultan, Yonkers, N. Y. William Kelly, Vulcan, Mich. R. B. Tinsley, Big Stone Gap, Va. Paul S. King, Wilmington, Del. Walter E. Trent, Reno Nev. Oscar Lachmund, Greenwood, B. C. Alfred W. G. Wilson, Ottawa, Can. J. S. Lane, New York City. Nelson Dickerman has resigned as general Manager of the Pato Mines (Colombia), Ltd., and The Nechi Mines (Colombia), Ltd., and will return from Colombia to San Francisco, Cal., the latter part of April. W. A. Prichard has been appointed as his successor.

Jan 4, 1916

Solution mining got back in the news recently when Kalium Chemicals, Ltd., a joint subsidiary of Pittsburgh Plate Glass and Armour & Co. announced its plans to go full speed ahead in mining potash by the solution method in its vast holdings 30 miles west of Regina, Saskatchewan. The company is keeping the technical details of this mining technique under wraps for competitive reasons, but company officials insist that the major difficulties in solution mining of potash have been overcome and that the final product will have definite competitive advantages on the open market. Kalium's holdings in the Regina area total about 500 sq mi. The ore-primarily sylvite mixed with appreciable quantities of halite-occurs in the Prairie Evaporite formation at a depth of 5300 ft. The ore zone averages about 100 ft in thickness. Too deep to be economically mined by conventional underground methods, such as is being done at International Minerals & Chemical Corp.'s Esterhazy mine (depth about 3100 ft), Kalium gambled that it could develop a successful method of solution mining even though earlier attempts in Germany, the U.S., and Canada had failed.

Jan 6, 1964

By Ira N. Holli

A meeting of Engineering Council was held on Thursday, Jan. 22, 1918, at the Engineering Societies Building, New York. Present: Chairman Ira N. Hollis (A. S. M. E.); Dr. Charles Warren Hunt, Alex. C. Humphreys and F. H. Newell (A. S. C. E.); B. B. Lawrence and .J. Parke Charming (A. I. M. E.); Charles Whiting Baker, D. S. Jacobus, and George, J. Foran (A. S. M. E.) ; H. W. Buck, E. W. Rice, Jr., N. A. Carle, C. E. Skinner and Comfort A. Adams (A. I. E. E.) ; Clemens Herschel and Calvert Townley (United Engineering Society); also, by invitation, D. W. Brunton, Chairman, War Committee of Technical Societies of Engineering Council. Of the several actions taken at this meeting, the following are selected as being of most general interest. Chairman-Baker-presented a resolution on the conduct of the war, to which objections were made. It was referred to a special-committee; Charles Whiting Baker, Charles Warren Hunt, and Calvert Townley, for re-drafting and presentation later in the meeting. The revised resolution submitted by this committee led to further discussion and as no agreement could he reached, the matter was laid on the table.

Jan 3, 1918

By V 7. 0 / 300 dpi

DRILLING in the Oligocene potash basin of Alsace prior to 1927 had shown important differences of level in the salt beds thus encountered. To explain this a somewhat unsatisfactory hypothesis of faulting had been advanced. During the latter part of 1926 and the beginning of 1927- our firm was engaged by two organizations for the purpose of trying to supplement, by an electrical survey, the geological data thus far collected. As a re-sult of this exploration it was possible to affirm that salt dome structures were present in the Oligocene basin of the Upper Rhine, something heretofore absolutely unknown in that region. Two salt domes were actually outlined, one, near Meyenheim, was made the subject of a communication to the Academy of Sciences, by G. Friedel2; the other, near Hettenschlag, was briefly dis-cussed by C. and M. Schlumberger3 before the same academy. The purpose of this paper is to indicate the strati-graphic and structural conditions of the area where these salt domes were found; to discuss the results of the electrical survey which led to the location of the domes, and indicate the new geological outlook which such a discovery suggests.

Jan 9, 1928

By John F. Shaw

The Denver Mining Research Center headquartered at Denver, Colo., is typical of the new research units recently activated as a result of increased emphasis by the U. S. Bureau of Mines on research concerned with metal and nonmetal (except mineral fuels) ore extraction. The Denver Center, together with the recently established Minneapolis Research Center and the Offices of Mining Research at Reno and Spokane, and the older, well-known Applied Physics Research Laboratory at College Park, Md., share the responsibility for the comprehensive mining research program. The Denver Center specializes in two areas of research: (1) The development of engineering principles and mathematical techniques applicable to exploration, development and operational problems in mining, and (2) the study of rock mechanics as applied to ground control. The first area presently includes three categories: research on methods of ore sampling, mine-systems analysis, and applications of statistics to problems of mineral exploration. The second area emphasizes research in two main categories: laboratory investigations designed to develop a fuller understanding of how rock be- haves under the loads imposed by mining, and field investigations to evaluate stress-strength relation- ships in full-scale, operating mines.

Jan 3, 1962

By B. C. Scott, A. Baker

The Pitch mine of Pinnacle Exploration, Inc. is in the Marshall Pass district, thirty miles east of Gunnison, Colorado. This is a new mining district, having come into existence as recently as 1955, when uranium mineralization was discovered rather late in the days of the uranium boom. There have been three other mines in the district, all of them now inactive. Two of these produced a few hundred tons of very high-grade uranium ore, and the third, Pinnacle's Little Indian 36 mine, produced a few thou- sand tons of lower grade ore. Pinnacle was one of the first companies in the district, and was able to acquire a large acreage. The first two years of exploration were essentially wasted in looking for Plateau-type deposits in a mineralized sandstone bed, but this "wasted" work produced two specific items that paid off. One was an ore-grade outcrop that ultimately became the Little Indian 36 mine, and the other was a boulder of very high-grade uranium ore that eventually led to the discovery of the Pitch mine; however, the actual source of the boulder still has not been found.

Jan 5, 1961

On Feb. 16, 1948, the Board of Directors of AIME authorized the publishing of "Technical Notes" in METALS TECHNOLOGY. The purpose is to provide prompt publication of wry short items of the following general types: 1. Results of short investigations which do not warrant a paper. 2. The conclusions of extensive investigations of insufficient general interest to justify a regular paper. 3. Conclusions arising in the course of an investigation, which, because of interest to others in the field, the author wishes to present prior to completion of the investigation. 4. Pertinent factual comment (not mere argument) on the subject matter of previous "Notes." Such Notes will be subject to the approval of the Auxiliary and AIME Publications Committees, but can be handled more promptly than regular papers because they need not be referred to readers. The recommended maxi- mum length is 500 words; notes in excess of 1,000 words will not be considered for this type of publication. A graph or photograph may be included as part of the note when particularly illustrative. As with regular papers, contributions to the new section should be submitted to the Secretary of the AIME.

Jan 1, 1948

By R. A. Foos

During the radium boom in the early part of the twentieth century, the basic chemistry of uranium was fairly well defined. Uranium production has progressed from the status of a radium by-product to a very important industry. With the ever increasing need for more efficient and cheaper methods of processing uranium ores, new techniques are being developed. Since uranium and vanadium often occur together in nature, the latter element will also be considered. As production rates, costs, and certain aspects of uranium chemistry are still classified by the Atomic Energy Commission, these will not be discussed. Domestic uranium deposits, in general, are composed of the minerals carnotite, which contains hexavalent uranium, and to a lesser extent, pitchblende and uraninite, which contain tetravalent uranium. Carnotite also usually contains vanadium. The uranium and vanadium contents of these ores vary considerably. The ores currently processed on the Colorado Plateau assay from 0.2 to 0.4 pct U and from trace amounts to 5.0 pct V. On the other hand, the phosphate rock deposits of the southeastern U. S., from which uranium is also recovered, contain only about 0.01 to 0.02 pct; processing of the

Sep 1, 1956

By J. McD. Porter

In many of the old placer-mining districts are still to be found large tracts of gold-bearing gravel not suitable to be worked with a dredge, because the bed is too shallow or the gulch too narrow. Frequently there is not enough grade to handle the gravel successfully by ground-sluicing or a bedrock flume, or it contains too many boulders to be worked succeeefully with the ordinary hydraulic pipe or tube elevator. In southwestern Oregon, two practical placer-miners named Ruble, after working for years trying to make money out of placer-ground coutaining many large boulders, invented and patented a hydraulic elevator of an entirely new type, and one that has been found to work very successfully in flat ground and in gravel containing many large boulders. It is a very simple contrivance. A few years ago I acquired the property near Pierce City, Idaho, known as the American placer-mine. Various attempts had been made to work this ground. A bed-rock flume had been installed by one company, an Evans elevator by another, and still other methods were tried on a smaller scale. All were

Jan 1, 1910

By S. M. Matthews, D. J. Maconochie, L. G. Alexander, V. H. Tillmann

Case studies of the behaviour of large open stopes at the New Broken Hill Consolidated Mine, Broken Hill and the CSA Mine, Cobar, N.S.W. are considered. Deformations were measured by multipoint rod extensometers in sufficient detail to note the phases of rock behaviour, from intact through to rock-fall. In one case readings were obtained from a zone of stress failure in which two bumps, felt as ground tremors, occurred. In this case noise and stress were also monitored. Deformations were analysed in relation to previously measured in situ rock stress, and conclusions drawn about the degree of conformity to, and the areas of departure from, elastic model behaviour. Attempts to describe the growth of instability utilize reduction factors of the apparent modulus, a magnification factor for the apparent Poisson's ratio, and a correlation between progressive noise count and displacement. Monitoring itself is seen as an aid in determiing the final dimensions of stopes and pillars. One large stope, of intermediate dimension 80 m, was mined essentially without change of plan, whereas a change in mining plan was necessary in other stopes. Aspects of interest to mine planners, and areas where futher research is needed, are indicated.

Jan 1, 1981

By W. J. Keep

We have shown in former papers the influence which aluminum exerts when added to cast-iron, and we have presented in another paper, accompanying this one, the physical properties of the metal aluminum and of some of its alloys. The present paper continues the investigation. The reader will find, in our paper on "Aluminum and Other Metals Compared,"* explanations not here repeated, which will render the diagrams in this paper intelligible. The scale of stresses is laid off on the ordinate which rises from the zero-point of the diagram. The scale of deflections is laid off on the abscissa which runs horizontally through this zero-point. By applying a given amount of stress, then running back to zero, and again applying the same stress, we describe a spring-line, in which the deflections are proportional to the stresses. Generally the deflections exceed this proportion during the original application of stress; and the excess is the permanent set. By laying off from the zero-point a line parallel to the springline, we shall generally find that this new spring-line and the diagram coincide for some distance; that is, that the test-bar is

Jan 1, 1890

By Stanley Kesler

The first of two initial 650-mw units of the Paradise Steam Station, located on the banks of the Green River in the south-central portion of the western Kentucky coal basin, is scheduled for operation in late fall of 1962. This plant will be the eighth large-capacity, modern station built by TVA in a series starting with Johnsonville, operated first in 1951. During the subsequent ten years, unit sizes have increased from a capability of 125 mw to 650 mw at Paradise. This new unit will take its place in a power system that serves an area of about 80,000 sq miles with a present installed capacity of over 12,000 mw. Upon completion of the Paradise units and other additional hydro and steam units presently under construction, the system capacity will have reached over 15,000 mw. Projected load estimates indicate that this system will provide a margin of slightly under 10% of dependable capacity above peak demand at that time. One Paradise 650-mw unit at that time will represent approximately 4yc of the total system installed capacity.

Jan 10, 1962

By Robert Glass Cleland

THE BEGINNING of a large enterprise is often as in- significant as a lump of leaven hidden in a bowl of meal or a handful of mustard seed that the wind blows across a field. In 1950 the company known today as the Phelps Dodge Corporation had nearly thirty-two thousand stockholders, paid salaries and wages of about fifty million dollars to some thirteen thousand persons, produced nearly four hundred and ninety million pounds of copper, and possessed net current assets of approximately one hundred and six million dollars. For the origin of this great business, one must go back approximately a hundred and fifty years to an obscure saddle-making shop in the small town of Hart- ford, Connecticut. Anson Greene Phelps, proprietor of the shop and master saddler in his own right, was born in 1781-the year of the Battle of Yorktown, the surrender of Cornwallis, and the close of the Revolutionary War Anson's forebears had come to America in the great Puritan migration that left fields, shops, pulpits, and hearthstones in the reign of Charles the First to transplant the strong, tough roots of their race, culture, and institutions in the New World.

Jan 1, 1952

By F. H. Rhines, A. H. Grobe

The constitution of the indium-zinc alloy series has been investigated by Wilson and Peretti,1 who determined the liquidus and eutectic temperatures by the conven-tional method of cooling curves and the eutectic composition by analyzing eutectic exudations. Recent developments affecting the availability of indium and consequent increased interest in its applications make a more complete knowledge of the constitu- tion of its alloys desirable. As a part of a program far the reexamination of the constitution of indium alloys by precision methods, the indium-zinc phase diagram (Figs. I and 2) has been redetermined in its entirety. The eutectic temperature (I43. 5°C.) reported by Wilson and Peretti has been confirmed exactly, but their value of the zinc concentration at the eutectic, 4 per cent, was found to be high; the new value is 2.8 per cent of zinc. There is also a rather large difference between the forms of the liquidus curves of Wilson and Peretti and those found in the present studies. The solidus curves herein have been located for the first time and the limits of solid solubility have been tenta-

Jan 1, 1944

By Donald W. Scott

THE year just ended was the 50th anniversary of that first flight at Kittyhawk, N. C., in 1903. In this 50-year period the aviation industry made startling developments from flight distances of 120 ft-at snail's pace-to speeds of over 1300 mph and flights that circle the globe. And 1953 also was the 50th anniversary of the Utah Copper Co., the Father of our mass production porphyry copper ventures. How do developments in the mining industry stack up with the aviation industry? The mineral industry can be as proud of developments over the past 50 years as the aviation industry. Only for the developments of the mineral industry could aviation and other allied industries advance as they have. The year 1953 made its contribution to this progress, with the normal number of process and equipment developments and an abnormally high amount of activity in new plant capacity, particularly copper. Tonnages are on the increase and operating troubles are becoming more and more problems in materials handling and control. We're approaching molecular dissemination of ores with hydro and pyro methods coming to the front to take over where flotation leaves off.

Jan 2, 1954

By A. H. Grobe, F. H. Rhines

The constitution of the indium-zinc alloy series has been investigated by Wilson and Peretti,1 who determined the liquidus and eutectic temperatures by the conven-tional method of cooling curves and the eutectic composition by analyzing eutectic exudations. Recent developments affecting the availability of indium and consequent increased interest in its applications make a more complete knowledge of the constitu- tion of its alloys desirable. As a part of a program far the reexamination of the constitution of indium alloys by precision methods, the indium-zinc phase diagram (Figs. I and 2) has been redetermined in its entirety. The eutectic temperature (I43. 5°C.) reported by Wilson and Peretti has been confirmed exactly, but their value of the zinc concentration at the eutectic, 4 per cent, was found to be high; the new value is 2.8 per cent of zinc. There is also a rather large difference between the forms of the liquidus curves of Wilson and Peretti and those found in the present studies. The solidus curves herein have been located for the first time and the limits of solid solubility have been tenta-

Jan 1, 1944

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before breakage, 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 the romnnred. THE present status of the theory of comminution is extremely unsatisfactory. The amount of various ores and rock products crushed and ground annually approaches the staggering sum of perhaps one half billion tons. Yet the basic concepts underlying an operation of such magnitude are unknown, and actual knowledge of what takes place in comminution is almost entirely empirical. The responsibility for this situation cannot be charged to apathy or lack of appreciation of the importance of the problem. Many attempts have been made to evolve a workable hypothesis, but none has been completely successful. General Considerations In order to break rock, it must be subjected to a stress which strains the rock beyond its critical breaking point. The stress imparts energy to the rock, most of which is released in the form of heat when the stress and resulting strain are removed. If the strain induced exceeds the critical strain, the energy is released by breaking; if the induced strain does not reach the critical point, the energy is released with removal of the stress as energy of resilience. Rock is a brittle material and it is assumed that it breaks approximately at its yield point, so that no permanent deformation results from strains below the critical. When rock is broken the total energy input is accounted for by the heat liberated, and by the surface energy of the new surface produced. A small and probably negligible amount is released as noise. Rock is commonly broken under compression and the applied stress is ordinarily compressive. However, for breakage to occur, it is only necessary that the induced strain exceed the critical value, and this strain may represent the resultant of compressive, shearing, and tensile forces. The stress-strain diagram of rocks under compression, and the modulus of elasticity as determined therefrom, should be fundamental considerations in the development of any theories of rock breakage. Crushing in jaw or gyratory crushers results primarily from a squeezing action, and reduction in a hammer mill is the result of impact. The action in rod and ball mills is a combination of impacting, squeezing, and wearing away by attrition, or rubbing. In ordinary crushing and grinding, the forces are applied at protruding points and are not distributed evenly throughout the rock. This is one of the features of comminution which theoretical considerations have not covered adequately. Another feature is the effect of impact velocities, which may greatly influence the total energy required for breakage. Impact velocities may vary from 1 or 2 fps in crushers to 10 or 20 fps for ball mills, and as high as 100 or more for hammer mills. However, according to the findings of geophysicists, the velocity of sound and of compression waves in stone is many times greater; the primary longitudinal compression waves travel at perhaps 15,000 fps, and the secondary transverse waves, which may reach the surface and cause cracks to form thereon, travel at perhaps 5000 fps. When a crack tip forms, the total surrounding stresses are concentrated in this tip, which rapidly extends throughout the rock particle.1 It would seem that the energy required to deform the rock beyond its critical strain, resulting in the formation of a crack tip, represents practically all of the energy required. Most of the primary crack tips presumably form on the surface. A simple method of designating feed and product size is necessary for the evaluation of crushing and grinding results. Taggart's suggestion2 that the 80 pet passing size be used has been found very practical. In this paper, the square opening screen size which 80 pct of the feed passes is designated as the feed size F, and the size which 80 pct of the product passes, or the product size, is designated as P. The reduction ratio at the 80 pet passing size, or F/P is designated as n. The feed and prod-

Jan 1, 1951

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before breakage, 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 the romnnred. THE present status of the theory of comminution is extremely unsatisfactory. The amount of various ores and rock products crushed and ground annually approaches the staggering sum of perhaps one half billion tons. Yet the basic concepts underlying an operation of such magnitude are unknown, and actual knowledge of what takes place in comminution is almost entirely empirical. The responsibility for this situation cannot be charged to apathy or lack of appreciation of the importance of the problem. Many attempts have been made to evolve a workable hypothesis, but none has been completely successful. General Considerations In order to break rock, it must be subjected to a stress which strains the rock beyond its critical breaking point. The stress imparts energy to the rock, most of which is released in the form of heat when the stress and resulting strain are removed. If the strain induced exceeds the critical strain, the energy is released by breaking; if the induced strain does not reach the critical point, the energy is released with removal of the stress as energy of resilience. Rock is a brittle material and it is assumed that it breaks approximately at its yield point, so that no permanent deformation results from strains below the critical. When rock is broken the total energy input is accounted for by the heat liberated, and by the surface energy of the new surface produced. A small and probably negligible amount is released as noise. Rock is commonly broken under compression and the applied stress is ordinarily compressive. However, for breakage to occur, it is only necessary that the induced strain exceed the critical value, and this strain may represent the resultant of compressive, shearing, and tensile forces. The stress-strain diagram of rocks under compression, and the modulus of elasticity as determined therefrom, should be fundamental considerations in the development of any theories of rock breakage. Crushing in jaw or gyratory crushers results primarily from a squeezing action, and reduction in a hammer mill is the result of impact. The action in rod and ball mills is a combination of impacting, squeezing, and wearing away by attrition, or rubbing. In ordinary crushing and grinding, the forces are applied at protruding points and are not distributed evenly throughout the rock. This is one of the features of comminution which theoretical considerations have not covered adequately. Another feature is the effect of impact velocities, which may greatly influence the total energy required for breakage. Impact velocities may vary from 1 or 2 fps in crushers to 10 or 20 fps for ball mills, and as high as 100 or more for hammer mills. However, according to the findings of geophysicists, the velocity of sound and of compression waves in stone is many times greater; the primary longitudinal compression waves travel at perhaps 15,000 fps, and the secondary transverse waves, which may reach the surface and cause cracks to form thereon, travel at perhaps 5000 fps. When a crack tip forms, the total surrounding stresses are concentrated in this tip, which rapidly extends throughout the rock particle.1 It would seem that the energy required to deform the rock beyond its critical strain, resulting in the formation of a crack tip, represents practically all of the energy required. Most of the primary crack tips presumably form on the surface. A simple method of designating feed and product size is necessary for the evaluation of crushing and grinding results. Taggart's suggestion2 that the 80 pet passing size be used has been found very practical. In this paper, the square opening screen size which 80 pct of the feed passes is designated as the feed size F, and the size which 80 pct of the product passes, or the product size, is designated as P. The reduction ratio at the 80 pet passing size, or F/P is designated as n. The feed and prod-

Jan 1, 1951

By J. R. Kyte, R. L. Dalton, V. O. Naumann, R. L. Ridings, R. W. Greene

This paper presents a one-dimensional numerical method for calculating dissolved-gas-drive behavior for a single well or a linear reservoir. Pressure and saturation distributions can be calculated, including the effects of capillary and gravity forces. The analysis has been programmed for solution on the IBM 7090 digital computer. A comparison of experimental and calculated behavior for two linear models demonstrates that the method is suitable for calculating dissolved-gas-drive behavior under reservoir conditions of flow. Dissolved-gas-drive tests were run, at different production rates and with oils of different viscosities, on short (6.ft) and long (173ft) flow models. For tests approximating reservoir pressure gradients and flow rates, there was excellent agreement between experimental and calculated results. A series of calculations of well behavior for thin, horizontal, homogeneous, dissolved-gas-drive reservoirs shows that ultimate recovery is independent of production rate or well spacing in such cases. These calculations also show that Muskat's method and similar material-balance analyses are not applicable under some conditions particularly for high pressure drawdowns. INTRODUCTION The problem of calculating dissolved-gas-drive reservoir performance has received a great deal of attention throughout the oil-producing indusfry for many years. Really significant advances, however, have been made only in recent years. The rapid evolution of high-speed computing equipment and techniques has opened up new approaches to the problem and led to realistic, quantitative analyses free of many of the assumptions and limitations of earlier methods. The one-dimensional numerical method described in this paper includes the effects of both gravity and capillary forces. A number of test calculations, based on different rates, spacings, and rock and fluid properties, have shown that the method is adequate for systems that can be reasonably represented by a one-dimensional model (linear or radial) and in which fluid segregation perpendicular to the direction of flow is not important. Along with the development of mathematical methods, an experimental program was conducted and the data were used to test the validity of the theoretical basis of the mathematical method. Linear models were used and all experiments were run using 1,000-psig bubble-point oils. The use of long, high-pressure models enabled us to more closely approach reservoir gradients and flow rates. MATHEMATICAL FORMULATION DIFFERENTIAL EQUATIONS The differential equations describing dissolved-gas-drive behavior in one dimension dare summarized here. They include Darcy's law for flow of oil and gas (Eqs. 1 and 2) and the equations for conservation of mass for oil and gas (Eqs. 3 and 4). The oil and gas pressures are related by capillary pressure (Eq. 51.