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By H. A. Deans

A three-parameter mathematical model for one-dimensional flow in porous media is developed. The objective of the model is to predict accurately the longitudinal dispersion associated with the flow of either gases or liquids over a wide range of Reynolds number. A qualitative analysis of the model parameters is given. Published experimental pulse-response curves are compared with results predicted by the model. Several general types of problems are given for which the model can be used. INTRODUCTION The problem of multicomponent single-phase flow through porous media is encountered in the study of petroleum reservoirs, gas chromatographic and ion-exchange columns, industrial fixed-bed con-tacters and elsewhere. These particular examples span the wide range of flow conditions possible; Reynolds numbers of less than l0-4 are not unusual in oil-production problems, while values in excess of 103 are common in large fixed-bed operations. The study of flow-dependent transport phenomena is complicated both by the changes in the character of the flow over this range, and by the irregularity of the flow boundaries inherent to porous media. Dispersion is one of the important phenomena known to depend fundamentally on flow conditions as well as on fluid and medium properties. As used in this paper, the term "dispersion" refers to the observed mixing of fluid elements of different composition which occurs in flow systems. The actual mechanism may be one or more of a number listed below. Only dispersion in the direction of the mean flow (referred to as axial or longitudinal dispersion, or mixing) is considered here, although lateral dispersion arises as part of certain coupled mechanisms. MECHANISMS FOR LONGITUDINAL DISPERSION A number of distinct mechanisms are known3,5,7,8 to contribute to the phenomenon of longitudinal dispersion. The more important of these are as follows. 1. Molecular diffusion in the flow direction. 2. Turbulent (cell) mixing. 3. Lateral transport processes coupled with velocity and/or residence time distributions, including: (a) "Taylor" diffusion caused by the interaction of velocity profiles in individual voids with lateral molecular diffusion; (b) separation and remixing or interdiffusion of streams having different velocities around particles; and (c) the couplipg of gross velocity profiles, caused by viscous instability or inhomogeneous porosity, with lateral dispersion. 4. Finite mass-transfer rate between a porous matrix and the flowing phase, and finite diffusion rate inside elements of the porous matrix. It is a well documented fact that these mechanisms, whether acting individually or in combinations, produce essentially similar integral effects. The observed dispersion can be described approximately by solutions of the diffusion equation with a properly chosen dispersion coefficient. Necessary conditions for equivalence between dispersion and diffusion are discussed by Klinkenberg and Sjenitzer.7 Apparently these conditions are not satisfied exactly in many real systems. "Best fit" solutions of the diffusion equation often depart appreciably from measured breakthrough curves for the usual pulse- or step-forced experimental systems. In particular, pulse response curves usually show some degree of asymmetry and "tailing" which cannot be reproduced by the one-parameter diffusion model. The three-parameter model proposed herein attempts to produce these effects in a realistic manner. Asymmetry and tailing are predicted for certain sets of parameter values, while for other sets the new model agrees with the diffusion model. VELOCITY DEPENDENCE OF DISPERSION Molecular diffusion apparently controls at sufficiently low Reynolds number in both gas and liquid systems.*l3 At Re > 20, turbulent cell mixing is dominant for gases flowing at low pressure; the data of McHenry and Wilhelm8 show that the mixing cell is approximately 1 particle diameter long in random sphere packs. on the other hand, the data

By T. R. Armstrong

During the year 1939, Mexican production totaled 42,479,000 bbl.; a daily average of 116,381 bbl. or a little over 2 per cent of the estimated world production. The Mexican Government operates 100 per cent of the refining branch of the industry, 100 per cent of the domestic distribution, 96 per cent of the crude production and 92 per cent of the total exports. No discussion of the Mexican petroleum industry in 1939 is adequate without reference to the "expropriation" of the foreign-owned oil properties in Mexico by executive fiat on March 18, 1938. The forcible seizing of the properties culminated a long series of efforts on the part of the Mexican Government to obtain control of the oil properties developed through foreign initiative and with foreign capital in Mexico. The heart of the issue is whether the Mexican nation or any nation may with impunity confiscate the legally acquired properties of American citizens. The Department of State of our Government has in its communications to Mexico emphasized the fact that its "expropriation" of American properties was confiscatory because Mexico had failed to make "adequate, effective and prompt compensation"; that the taking was no less confiscatory "because there may be an expressed intent to pay at some time in the future," and that, consequently, "Mexico has assumed and continues to assume to exercise a right without compliance with the condition necessary to give such exercise a recognizable status of legality." Mexico has professed its willingness to pay for the oil properties but at the same time through its Supreme Court it has declared that the owners or lessees do not have the exclusive right to extract and dispose of the oil in the subsoil. This is a reversal of the Mexican position with respect to oil as set forth in the Mexican mining laws, affirmed by Mexican Supreme Court decisions, and as clarified in the Warren-Paync and the Morrow-Calles agreements, as well as in diplomatic correspondence. Efforts to Settle the Controversy Responding to suggestions from the State Department, representatives of the principal oil companies undertook in 1939 to effect a direct

Jan 1, 1940

By Joseph Jensen

When the legal holders of Government permits in the Middle dome of Kettleman Hills entered into an agreement on May 27, 1929, to suspend all drilling activities on five permits, covering portions of the Kettleman Hills Middle dome, until Jan. 1, 1931, and the owners of fee lands contiguous thereto assured Secretary Ray Lyman Wilbur, of the Department of the Interior, that they too would respect a drilling suspension for a period of a little more than 19 months, none of these interested parties realized that this was the first step in a chain of events that would culminate, more than four years later, in the formation of the Middle Dome Corporation for the development of the Middle dome area in a unit plan that would be the first unit plan to be approved by the California Regional Producers Committee and recommended to the President as a satisfactory unit plan, under Section 7 of Article III of the Oil Code, approved Aug. 17, 1933. Neither did they realize that more than two million dollars would be spent before oil or gas would be successfully and continuously produced from wells drilled on that Middle dome area. On Oct. 1, 1933, under the terms of the Middle Dome Agreement, the Middle Dome Corporation assumes control of activities and is responsible for the division of all product's produced from the Middle dome area to members of the Middle Dome Corporation. This Middle dome plan is the second successful unit plan developed in California in the past three years, the first being the Kettleman North Dome Associationll formed under the agreement, of Jan. 31, 1931, for the unified operation and development of more than 12,000 acres of land on the North dome of the Kettleman Hills. All other unit plans discussed in the past four years in the state have not yet been completed, for one reason or another, but under Section 7 of Article 111 of the new Oil Code numerous plans of development, some of which may be unit plans, will be forthcoming within the next few months. There is much

Jan 1, 1934

By T. R. Armstrong

During the year 1939, Mexican production totaled 42,479,000 bbl.; a daily average of 116,381 bbl. or a little over 2 per cent of the estimated world production. The Mexican Government operates 100 per cent of the refining branch of the industry, 100 per cent of the domestic distribution, 96 per cent of the crude production and 92 per cent of the total exports. No discussion of the Mexican petroleum industry in 1939 is adequate without reference to the "expropriation" of the foreign-owned oil properties in Mexico by executive fiat on March 18, 1938. The forcible seizing of the properties culminated a long series of efforts on the part of the Mexican Government to obtain control of the oil properties developed through foreign initiative and with foreign capital in Mexico. The heart of the issue is whether the Mexican nation or any nation may with impunity confiscate the legally acquired properties of American citizens. The Department of State of our Government has in its communications to Mexico emphasized the fact that its "expropriation" of American properties was confiscatory because Mexico had failed to make "adequate, effective and prompt compensation"; that the taking was no less confiscatory "because there may be an expressed intent to pay at some time in the future," and that, consequently, "Mexico has assumed and continues to assume to exercise a right without compliance with the condition necessary to give such exercise a recognizable status of legality." Mexico has professed its willingness to pay for the oil properties but at the same time through its Supreme Court it has declared that the owners or lessees do not have the exclusive right to extract and dispose of the oil in the subsoil. This is a reversal of the Mexican position with respect to oil as set forth in the Mexican mining laws, affirmed by Mexican Supreme Court decisions, and as clarified in the Warren-Paync and the Morrow-Calles agreements, as well as in diplomatic correspondence. Efforts to Settle the Controversy Responding to suggestions from the State Department, representatives of the principal oil companies undertook in 1939 to effect a direct

Jan 1, 1940

By B. Blumenthal

THE present investigation was planned as a survey of the lead-rich portion of the ternary lead-antimony-silver system by thermal analysis. Since, however, a rigorous application of the conventional thermal analytical method is time consuming, an attempt was made to speed up the investigation by reducing the time required for a single thermal analysis. This was done by increasing the rate of cooling to 12° to 18°C. per minute. Since such a rate does not permit even an approach to equilibrium conditions, the melt was stirred vigorously by a stirrer operating at the high rate of 665 r.p.m. This proved to be effective in obtaining cooling curves with distinct points of arrest and of excellent reproducibility, which satisfactorily compare with those obtained at a rate of 1° to 2°C. per min. with or without slow stirring (Fig. 1). By this method the lead-rich end of the lead-antimony system and a series of ternary alloys in sections parallel to the lead-antimony side of the ternary system were investigated and it was observed that the two branches of the' liquidus curve of the .binary alloys did not intersect at the eutectic temperature. An equivalent effect was observed in the ternary system. The eutectic temperature of the binary lead-antimony system was found to be 252.0°C., which confirms the recent investigation by Pellini and Rhines,1 who determined the eutectic temperature to be 251.5°C. The observation that the curves of primary crystallization of the lead-antimony system do not intersect at the eutectic temperature was previously made by Dean.2 Dean explains the phenomenon by assuming the existence of a compound Sb4Pb. He felt that super-cooling was not the cause of the phenomena because he was unable to influence them by inoculation. The X-ray investigation by Solomon and Morris-Jones,3. the metallographic investigations by Stead,4 Charpy,5 Gontermann,6 and Dean, Zickrick and Nix,7 and the numerous investigations of physical properties, definitely disprove the occurrence of any compound. The work of Dean was not confirmed by Broniewski and Sliwoski,8 whose experiments did not show any irregularity and who report a eutectic composition of 13 per cent antimony and a eutectic temperature of 250° to 252°C. at a rate of cooling of about 6°C. per min. Abel, Redlich and Adler9 then report a eutectic composition of 12.1 per cent upon reviewing the previous, publications and adding a few of their own cooling curves. In 1934 Quadrat and Jiriste10 found from careful analyses of the bottom portion of slowly cooled hypereutectic melts that the eutectic contains only 11,4 to 11.5 per cent antimony. (Previous analyses by Stead4 in 1881 gave 13 per cent:) Weaver," however, reported in 1935 that cooling curves indi-

Jan 1, 1943

By R. M. Briney

A RETURN to nonwar conditions characterized the year 1946. The acquisition and forced use, under Government auspices, of low-grade and uneconomic ores, both foreign and domestic, ceased in 1945, but there was some carry-over into the early months of 1946. The world shipping situation delayed the procurement of some foreign ores, but conditions were improving by the end of the year. No actual shortage of any important alloy was experienced, hence the industry was able to make prompt shipment of orders placed. Price levels of ferroalloys, which had remained virtually constant through the war years, were forced upward, with increases on specific products as conditions necessitated. Standard ferroman-ganese and low-carbon ferrochrome were notable exceptions in that their price did not change. No new ferroalloy smelting plants were constructed. The Defense Plant Corp.. sold the works at Ashtabula, Ohio, to the Electro Metallurgical Co. A new type of ferroalloy furnace was described at the Birmingham meeting of the Electrochemical Society. Known as the "Elkem Rotary Furnace" it is distinguished by a rotating shell. The whole furnace, including shell, refrac-

Jan 1, 1947

By W. H. Justice

Cycling operations have been successfully conducted in the La Gloria Zone for eight years. The cycling of this zone is now virtually completed. It is proposed that this report shall review the cycling operations of this reservoir so that the industry can more accurately evaluate the cycling process as a production method. The La Gloria project is one of the largest cycling operations in the State of Texas. The gas rights in the field are unitized in three operating units. By mutual agreement Magnolia Petroleum is the designated operator of the project for the 12 operators owning the gas rights. The La Gloria Corp, is the owner and operator of the cycling plant. The development and operation of the field are under the direction of an Operators Committee comprised of a representative of each operator. The Operators Committee is assisted by an Engineering and Geological Sub-Committee. The La Gloria gas field is situated approximately three miles north of Fal-furrias, Tex., and lies principally in the extreme south end of Jim Wells County, with its outer limits extending into the north end of Brookes County, Tex. It is a simple elliptically-shaped dome which has a closure of 350 ft. The field encompasses a surface area of 5,500 acres. The gas reserves are found in 20

Jan 1, 1950

By C. Harries

The mechanism of blasting and the effect that blasting has on rock properties including the generation of new cracks and the opening of existing joints is discussed and compared with changes in seismic velocities. .Knowing the extent of blast induced damage and the overall stable slope angle it is shown that it is possible to design blasting so as not to induce any damage behind the toe of the blast area. Practical methods of blasting to meet this criterion and the results of these blasts are then discussed.

Jan 1, 1983

By Harry H. Power

While the attention of all engineering branches is focused today on changes and improvements in the several curricula, we are concerned here with the many questions arising in industry and college concerning the preparation for the petroleum engineering profession. The succession of problems confronting the petroleum engineer demands a degree of versatility not ordinarily encountered in other professions. As a consequence, the student cannot acquire mastery of all the several engineering branches represented in field practice, and as an alternative, he has learned to appreciate the value of thorough training in the basic or fundamental sciences as a Preliminary foundation for professional work. While our attention is directed primarily to the training of engineers in educational institutions, it is necessary that the ultimate education of the professional engineer be kept in mind. It is apparent that his success as an engineer is limited not only by his educational and job experience, but by his native endowments: mentality, Personality and health. The engineer's lack of job experiences often proves as much a handicap as the lack of adequate college training. If the final product proves to be satisfactory, both industry and technical institutions are to be congratulated. However, if the Product is found wanting, the one most responsible should For the most part, students of engineering colleges have had their interests in applied science awakened at a relatively early age. Manyof them entered college as a convenient means of acquiring a technical education, but undoubtedly would have had better prospects in a shorter program offered by institutions of non-college grade. The activating motive of practical interest is also strong in students suitable for college training, but in many cases an intellectual interest must be awakened in order that it may survive graduation. Numerous engineers believe that this progressive process of selection and determination of career aims is one of the essential services rendered by the engineering colleges. Industrialists, who are more inter. ested in quality than quantity of petroleum engineering graduates, have pointed out the good that should result if more emphasis were given to the work of eliminating the misfits. They also point out the protective measures that have been taken by other professions for the betterment of professional standards. Mention has been ,de of the beneficial results to be obtdned by collective determination of the market for the products of engineering schools, particularly in that the students unsuited to the profession would have an opportunity to prepare themselves for employment more suited to their personalities and other qualifications. In the event that such a system of coordinated personnel direction is developed by the

Jan 1, 1941

By Harry H. Power

While the attention of all engineering branches is focused today on changes and improvements in the several curricula, we are concerned here with the many questions arising in industry and college concerning the preparation for the petroleum engineering profession. The succession of problems confronting the petroleum engineer demands a degree of versatility not ordinarily encountered in other professions. As a consequence, the student cannot acquire mastery of all the several engineering branches represented in field practice, and as an alternative, he has learned to appreciate the value of thorough training in the basic or fundamental sciences as a Preliminary foundation for professional work. While our attention is directed primarily to the training of engineers in educational institutions, it is necessary that the ultimate education of the professional engineer be kept in mind. It is apparent that his success as an engineer is limited not only by his educational and job experience, but by his native endowments: mentality, Personality and health. The engineer's lack of job experiences often proves as much a handicap as the lack of adequate college training. If the final product proves to be satisfactory, both industry and technical institutions are to be congratulated. However, if the Product is found wanting, the one most responsible should For the most part, students of engineering colleges have had their interests in applied science awakened at a relatively early age. Manyof them entered college as a convenient means of acquiring a technical education, but undoubtedly would have had better prospects in a shorter program offered by institutions of non-college grade. The activating motive of practical interest is also strong in students suitable for college training, but in many cases an intellectual interest must be awakened in order that it may survive graduation. Numerous engineers believe that this progressive process of selection and determination of career aims is one of the essential services rendered by the engineering colleges. Industrialists, who are more inter. ested in quality than quantity of petroleum engineering graduates, have pointed out the good that should result if more emphasis were given to the work of eliminating the misfits. They also point out the protective measures that have been taken by other professions for the betterment of professional standards. Mention has been ,de of the beneficial results to be obtdned by collective determination of the market for the products of engineering schools, particularly in that the students unsuited to the profession would have an opportunity to prepare themselves for employment more suited to their personalities and other qualifications. In the event that such a system of coordinated personnel direction is developed by the

Jan 1, 1941

By P. Lindstrom

Retreat mining, using yielding steel friction props, over a 7-year period has been successful at a uranium mine operated by Hecla Mining Co. in southeast Utah. The support system allows good roof control, maximum profit, complete extraction, and good ventilation. Unusual subsidence observations were made in that some of the surface was raised rather than lowered. Longwall mining, commonly practiced in European coal mines, has a potential of broader application because of mechanization possibilities and better roof control and ventilation at greater depths. The Radon mine was one of the first American metal mines to use yielding steel props for supporting the relaxed core of the pressure arch which is induced by retreating longwall mining. Full caving was induced. After more than 7 years of stoping experience, the method has proved very satisfactory for the conditions encountered. The mine and method have been described in references listed in the bibliography. U.S. Bureau of Mines Information Circular 8004 by Wilbert Dare and Philip Lindstrom gives the most information. Stoping experience at this mine indicates that there are many advantages to be gained by using yielding supports; such as in safety, timber cost, roof control, ventilation, ore dilution, and low cost per pound of metal produced. Subsidence measurements show that the surface will rise rather than slump in some areas over the mine. This appears to be an unusual observation and is presented as a new development in subsidence studies. The Radon mine is located 35 miles southeast of Moab, Utah in the north end of the Big Indian mining district in San Juan County. Hecla Mining Co. operated the mine from early 1955 to early 1964 through an operating agreement with Federal Resources, Inc. Development consisted of a 3-compartment, 690-ft shaft, 4 main levels driven on the ore horizon and a haulage level below the ore. Evaluation of physical and economic factors showed that this flat-dipping ore occurrence could be mined by a low-cost coal mining method. The value of the deposit was high and unusual premiums were possible by clean mining. Complete extraction without loss of ore pillars, minimum ore dilution and high production per man were obtained by longwall mining. The principle of working under the relaxed core of

Jan 1, 1964

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

By N. S. Stoloff, R. G. Davies

A study has been made of the efject oj different dislocation-precipitate interactions upon the temperature dependence of the flow stress of aged Ni-14 at. pct A1 alloy. It is observed that when the dislocations bow between widely spaced (-20004 coherent Ni3Al particles the flow stress decreases with increasing temperature in the normal way. However, when the dislocations cut closely spaced (-5004 particles the flow stress is independent of temperature from -100 to 600°C, due to a balance between softening of the matrix and an increase in strength of the particles with increasing temperature. The retention of strength at high tempera-tures of commercial nickel-base alloys, which are strengthened by the precipitation of a phase based upon Ni3Al, is thought to be due to the unusual strength properties of Ni3Al. The flow stress of Ni3Al increases continuous1y from -196"C to a maximum at -600"C. It is concluded from a series of thermal-mechanical tests that the sevenfold increase in flow stress over this temperature interval is due to a lattice effect and is not diffusion-controlled. The flow stress of precipitation- or dispersion-hardened materials depends on the resistance to dislocation motion within the matrix and the extra energy required for dislocations to bow between or to cut particles. If the dislocations bow between the particles or if the strength of the cut particles is constant with temperature, then the flow stress of the precipitation-hardened alloy must decrease with increasing temperature due at least to the decrease in elastic modulus of the material. There will be softening also from thermally activated cross-slip or climb, offering an additional degree of freedom for dislocations to avoid particles. For example, in the case of nickel containing a dispersion of thoria,' which most probably deforms by dislocations bowing between particles, the flow stress decreases by about 50 pct between 25" and 650°C. In A1-Cu alloys2 aged to produce the 8" precipitate, dislocations cut the particles, and the flow stress decreases by about 20 pct between -269" and 25°C. However, many commercial high-temperature nickel-base alloys, for example Inconel-X and Udimet-700, exhibit little or no decrease in flow stress with increasing temperature up to about 700°C. A characteristic feature of these alloys is that they are strengthened by the precipitation of a phase based upon Ni3A1. Guard and westbrook4 and flinn' have shown that Ni3Al (and alloys in which a third element such as molybdenum or iron is substituted for part of the aluminum) is unusual in that the hardness and flow stress increase with temperature to a maximum at about 600°C. For the flow stress of a precipitation-hardened alloy to be independent of temperature we propose that the particles must be cut by dislocations moving through the matrix and that the strength of the particle must increase with increasing temperature. Theories of precipitation hardening do not take into account the flow stress of the dispersed particles that are cut during deformation; the only dissipative process usually considered7 is the creation of interface within the particle and between the precipitate and matrix. The purpose of the present investigation has been to study in detail the temperature dependence of the flow stress of a nickel-base alloy strengthened by the precipitation of Ni3Al in two structural conditions such that when deformation occurs it does so by dislocations a) bowing between the particles and b) cutting the particles, respectively. A simple binary Ni-14 at. pct A1 alloy was chosen because considerable information is already available for this system concerning phase equilibria and precipitation reactions and rates.' Dislocation-precipitate interactions in the binary alloy should be similar to those in the more complex commercial alloys. In addition, the mechanical and physical properties of NisAl were studied in detail in the hope of elucidating the mechanism by which the strength increases with increasing temperature up to 600°C. EXPERIMENTAL PROCEDURE For the study of the effect of precipitation of Ni3A1 upon the temperature dependence of the flow stress, an alloy containing 14 at. pct A1 was utilized; a Ni-8 at. pct A1 solid-solution alloy was employed as a comparison material. Vacuum-cast ingots were hot-rolled at 1000°C and cylindrical compression samples, 0.20 in. diam by 0.40 in. high, were prepared from the 1/4-in.-diam rod. Specimens were recrystallized and solution-treated at 1000°C for 1/2 hr and then water-quenched. A preliminary study revealed that, when the Ni-14 at. pct A1 alloy was aged for 1 hr at 700°C, significant precipitation hardening was obtained, and that the structure was free from grain boundary discontinuous precipitation; an overaged condition was produced by annealing the aged specimens at 850°C for 1 hr. To circumvent the difficulties involved in the hot rolling and swaging of Ni3A1, compression samples,

Jan 1, 1965

By E. R. Brownscombe, Francis Collins

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

By E. R. Buchanan, R. E. Reed-Hill

A transmission electron microscope study was made of magnesium single crystals deformed in torsion using the basal pole as the forsional axis. While this type of deformation is predicted to result in the formation of hexagonal networks of screw dislocations, these networks were not observed. The basic dislocation arrangement consisted of arrays of nearly parallel and approximately equally spaced dislocations. The average dislocation density was over an order of magnitude higher than that required to account for the torsional deformation. The observed high rate of work hardening in these crystals is consistent with both their high dislocation densities and the arrangement of dislocations in pile-ups. The experimental observations are also in agreement with the assumption that dislocation sources are activated not only at the surface but at interior locations as well. In considering torsional deformation, Amelinckx and Dekeyser1 postulated that when a torque is applied to a crystal oriented with a glide plane normal to the specimen axis, deformation occurs by the following steps: 1) Nucleation of dislocation sources at or near the specimen surface in areas where the shear stress, resolved along a slip Burgers vector, is a maximum; 2) the screw orientations of the dislocations accommodating the twist move inwards towards the specimen center. If two glide directions lie on the glide plane, the geometry shown in Fig. 1 should result; 3) the screw dislocations that pile up in the central part of the specimen cross-slip to form a grid. At the same time, screws of opposite sign and most edges leave the specimen. Tinder,2 using zinc crystals twisted about the basal pole, independently reached essentially the same conclusions. He suggested a mechanism involving nucleation of ?(1120) screw dislocations at the six points of highest resolved shear stress that lie on the cross-section near the surface. Under the applied shear stress these dislocations were assumed to move inward and interact so as to form a hexagonal network of screw dislocations. Today it is often accepted that rotational slip occurs by a mechanism of the above type, but to our understanding this has never been experimentally proved. This paper reports an experimental study of rotational slip, using magnesium single crystals, that indicates that in this metal rotational slip does not conform well to this mechanism. EXPERIMENTAL PROCEDURES Mechanical Testing. Specimens with a (0002) axis were prepared from magnesium crystals of 99.95 pct purity grown by Jillson's3 modified Bridgman technique. The crystals were acid machined into cylindri-

Jan 1, 1970

By W. C. Meyer, R. R. Klimpel

A physical model of flotation, derived from viewing froth as a kinetic species since it constitutes the carrier of ore particles, not only agrees with and is simulated by engineering mathematical models, but is statistically verified by actual laboratory flotation data. The model couples the mechanical removal of froth using paddles with the more rapid interactions taking place in the bath. It clearly shows that the kinetics of mass removal is dictated by flotation cell dimensions, paddle speed, and, more importantly, froth characteristics. Some conclusions and model predictions are presented.

Jan 1, 1984

By J. H. Collier

The mother lode, or mineralized belt, at Angels, in Calaveras county, California, is 3 miles wide. At least, a region of that width has been, and is being, prospected which has shown considerable mineralization. The lode proper divides into three lodes, or groups of veins, at this point. On all of these branches, mines have been operated with more or less success.

Jan 1, 1900

By William A. Johnson

THE fundamental role of diffusion in many reactions occurring in solid metals has long been recognized, and there have been careful measurements of rates of diffusion in numerous alloy systems, but our understanding of the atomic mechanism by which diffusion occurs is scarcely in an advanced state 1-3 It is doubtful that this mechanism can ever he directly ascertained, rather, all imaginable mechanisms must be examined and the one that is in best accord with such data as can be obtained from suitably chosen experiments should be selected Because of its relative simplicity, diffusion in a system containing only one kind of atomic species-commonly called self-diffusion-is of considerable theoretical interest It may be expected that diffusion theory will not be advanced appreciably until a wide variety of diffusion experiments-of which diffusion in a chemical concentration gradient and self-diffusion are two important types-are carefully performed and inter-compared Aside from the purely theoretical interest in self-diffusion measurements, such studies will be of considerable engineering importance The rate of any process in a pure metal requiring the movement of atoms, of which recrystallization and creep are two familiar examples, will be understood more readily with the aid of self-diffusion data † Self-diffusion implies the diffusion of something into its exact counterpart, the detection of such a process is patently impossible, and it is-necessary to substitute for it the diffusion of one isotope (in this case radioactive) into another isotope (in this case stable) of the same chemical element There is, however, no reason to suppose that a radioactive atom will not diffuse at the same rate as its stable isotope, for all of the isotopes of the same element have exactly the same chemical properties, neither the difference in nuclear energy nor the difference in mass would be expected to exercise an important influence in this phenomenon In this sense, self-diffusion may be thought of as the diffusion of radioactive atoms down a radioactivity concentration gradient, just as usual diffusion is the diffusion of one kind of atone down its chemical concentration gradient The first measurements of self-diffusion ii ere made by von Hevesy4-6 using the radioactive lead isotope thorium B in ordinary lead The recent development of means for producing artificial radioactive elements has made possible similar measurements on gold,7,8 copper,2,9 and zinc 10 11 Many of the data that have been obtained are rather poor, and no adequate reason has been given for their poorness, it appears, however, that the unsatisfactory results are characteristic of the particular experimental procedure employed, and not of self-diffusion measurements in themselves The experimental technique that has yielded the poorer results is the deposition of a thin layer of radioactive atoms on the surface of a specimen and the determination of the rate of inward diffusion

Jan 1, 1941

By B. Stimpson, D. M. Ross-Brown

Borehole information is often the only source of information on rock conditions at depth during the stage of feasibility studies of a project, and from this data the rock mechanics engineer would like to make some quantitative estimates of rock mass cohesive strength. While judgement and experience will usually play a paramount role at this stage, simple tools for estimating rock mass cohesive strength would be an asset. In this paper, an approximate technique is suggested for assessing the cohesive strength of a randomly jointed rock mass from borehole data on fracture intensity and intact rock strength.

Jan 2, 1979

Jan 1, 1934