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By William E. Hubbard

During the last decade the known reserves of petroleum in the United States have increased from about five billion to over thirteen billion barrels. From the standpoint of public welfare the existence of these known reserves presents an undeniably favorable picture, but viewed from the position of many a harassed operator the blessing has not always been considered an unmixed one. Along with this increase in excess reserves, curtailment of production has come into being as a matter of necessity and the principle of proration as a matter of equity. As a practical matter it has been considered necessary to curtail the production of old wells as well as that of new wells in a pool. The right of new pools to produce has been recognized, and the allowable for them has come partly from increased market demand and largely from the allowables already enjoyed by the developed pools. The natural result—a downward trend in daily per-well allowables—has been especially felt by Texas operators. This trend may be illustrated by Table 1, which comprises the five active areas in Texas, and from which may be noted the following: 1. The average daily allowable per well has decreased about 53 per cent in three years. 2. Of the 184,000-bbl. increase in total allowable for the five areas, 29,000 bbl. came from the increase in state demand and 165,000 from the combined allowables of the remaining pools in the state.

Jan 1, 1937

By M. A. Bryant, J. C. Goodwin, T. B. Faddies, L. D. Kornze

The Mercur Gold Mine is located 56 km (35 air miles) southwest of Salt Lake City in north central Utah; In July 1981 Getty Mining Company made the decision to put Mercur into production. The first gold bar was poured in April 1983. This paper provides details on: 1) the history of the camp, 2) past production, 3) geology of the deposit, 4) the exploration and development program, 5) ore reserve estimates, 6) detailed geologic pit mapping, 7) production blasthole sampling techniques and 8) the use of geostatistics (kriging) in handling assays and gold extractions to produce the required mill feed.

Jan 1, 1985

By John F. Lundeberg

CLAUSS1 observed that if isothermal creep data could be approximated as straight lines on a log stress-log time plot, a relationship existed that could be expressed as log t = m log s + b [ l] where t = time,

Jan 1, 1965

By John D. Morgan, Sylvain J. Pirson

AN instantaneous and continuous analysis of a mineral suspension should be of great value in controlling various mineral preparation processes. Described herein is a method of analysis based on the use of high-frequency alternating current, which, under certain restrictive conditions, could be of use. THEORETICAL CONSIDERATIONS In a suspension of conductive minerals, the electrical effect primarily responsible for the variations in electric conductivity is the capacitance. In Fig Ia, let an alternating voltage E be applied across two electrodes F and F', between which are two rows (S and T) of mineral particles, all of approximately the same size, immersed in a fluid. Let the number of rows of particles between the electrodes be R and the number of particles in each row be N. If A is the area of a particle, D is the distance separating two particles, and K is a constant depending on the fluid, the capacity, Co, of the particle system will be given by: [KRA C0 ND] Referring now to Fig Ib, let R, the number of rows, be held constant, but let N, the number of particles in each row (S and T), be increased X-fold. The capacity, C1, of [ ]

Jan 1, 1947

By E. J. Eisenach, W. E. Jones

SAFETY and industrial hygiene have always been recognized as highly important in company policy, and the co-operative support of the company officials and entire plant personnel has contributed largely to the present success of the Company's program in this field. Growth has necessarily been slow, and dependent, at times, on trial and error but the program in its present form combines the regulations, working methods, and equipment that have proved their value under actual operating conditions. Every effort is made to keep the program on a practical basis. Continuous experimental work is carried on in conjunction with the health and safety program, with resultant periodic changes for improvement. As a proof of accomplishment, in 1945 the frequency and severity rates for accidents were the lowest in the history of the operation. A full-time safety engineer was employed in 1933 and an assistant safety engineer in 1936. During the following year a stenographer was employed in the office and a safety inspector was added for the mine. During the gradual expansion of operations that was climaxed by

Jan 1, 1946

US 4,192,851-Recovery of elemental sulfur and the metal values from a complex sulfide ore containing two or more of the metals zinc, lead, copper, silver, gold and/or other metals. A mixture of ore and sulfuric acid and/or spent electrolyte is flowed at optimum temperature and pressure in a quiescent zone to dissolve selected metals and sulfur and coalesce the sulfur. The coalesced sulfur and unreacted sulfides are separated by flowing the leach slurry with an upward velocity component The separated materials are discharged and further processed by conventional methods as war- ranted. H.E. Hirsch, J F. Higginson, EG. Parker, and G M Swinkels, assigned to Sherritt Gordon Mines Ltd. Mar. 11, 1980. 6 pp. (423-28) Filed. 3-14-78 (886,368). Priority. United Kingdom, 3-15-77 (10800/77).

Jan 1, 1982

By Roman Y. Poderny, Vladimir V. Rjevskii

In the USSR, the Moscow Institute of Radio Electronics tronics and Mining Electro-Mechanics (MIRGEM) has started what it hopes will become a nationwide movement to educate mining students in the precise specialties that industry has come to require. Courses for mining engineers, the MIRGEM faculty proposes, should dovetail as exactly as possible with specific jobs available in the mining profession. Acting upon this thesis, MIRGEM revised its own curriculum in 1962 and has since presented an over-all plan for Soviet mining education before two mining school conferences as well as the Ministry of Higher Education and a number of major Soviet industrial ministries. The plan was universally approved with some suggested revisions. SOVIET MINING EDUCATION TODAY At present, mining education in the Soviet Union covers the exploitation of solid minerals and raw materials, including coal as well as ferrous and nonferrous metals. The extraction, storage, and refining of oil and gas is treated as a separate discipline. In all, there are 33 Soviet universities and institutes that train mining engineers for careers in the industrial, research and educational fields.

Jan 9, 1966

By Arthur E. Focke

IF a metallurgist employed in an industry producing mechanical parts or assemblies wishes to make the most of his opportunities he will be concerned with every use of metals in that industry. He will not only take part in the testing and treating of the metals used but will assist in their selection and study their behavior in processing and in service. In addition, he will attempt to develop an understanding of the problems involved in the use of the metals in all plant tools and equipment. Metallurgists that follow this course will soon recognize that frequently too little thought is given to the effect of the design of parts on the way the metal in them is expected to behave in service. He will come to realize that changes in the design of a part will often be much more useful than changes in the hardness, strength, composition, or structure of the metals used in them. Does this mean that a metallurgist is out of place in these industries and that he should leave the field to others or be content to fill only a minor role?

Jan 1, 1947

W. A. SCHLESINGER,* Denver, Colo.-Two problems are of great interest to the radium manufacturer at the present tine: The first is to perfect a process, more efficient and more economical, which is capable of treating a greater variety of ores. . Practically all the radium now manufactured in the United States is extracted from carnotite ores and these vary a great deal according to their location. The amount of sulfates contained in the ore is of particular importance, and any straight acid-leaching method, such as developed by the Bureau of Mines, becomes prohibitive when the ore contains more than 0.5 per cent. of sulfates, as the sulfates go into solution and naturally precipitate the radium as insoluble radium sulfate. Since the amount of ore obtained from any one claim is usually comparatively small, it is necessary to work a number of claims in different localities, and a process, in order to be commercially satisfactory, should handle all of these ores. In other words, it would be entirely unprofitable for radium manufacturers to employ any process which cannot treat any but sulfate-free ores. He must deal with carnotite containing appreciable amounts of sulfates, and must be able to work this in with the other ores. Carbonaceous ores from certain sections in Utah; which are known to contain as pinch as 1.0 per cent. and more of volatile matters, are prone to a, nitric acid-leaching process. The second problem relates to the treatment of concentrates. There is no doubt that a very large amount of low-grade ore, containing less than 0.75 per cent. uranium oxide, is available. It has been demonstrated that these ores can be concentrated, but there is still room for research

Jan 11, 1918

By John B. Goddard, David R. Brosnahan

Leaching of uranium in situ from sandstone deposits with ammonium carbonate solution containing dissolved oxygen occurs rapidly compared with the leaching of the bulk of the sulfur present as FeS2. However, because of their high reducing capacity and their relative abundance, the FeS2 minerals consume the bulk of the oxidant. A pressure leach apparatus was constructed that permitted measuring oxygen consumption by FeS2, best described by a first-order reaction. The experimental rate constants for various cores are roughly proportional to their FeS2 contents.

Jan 1, 1983

By C. H. Bowen

NDUSTRY needs a generally applicable means of defining average grain size and grain size distribution. Students of sediments hade explored this field, employing methods that might also prove useful in engineering problems. Before attempting to solve specific problems it is well to review the derivation of commonly used grade scales and the reasons for their selection. This aspect of the problem seems largely to have been lost, and a review of basic factors may suggest causes for failures in using size analysis data. Three facts are implicit in selection of a grade scale: 1) Most particulate mixtures are continuous distributions of sizes, and any grade scale that may be employed is an arbitrary means of visualizing that distribution. 2) For purely descriptive purposes, any grade scale, regardless of the rationality of the class intervals, will be satisfactory if it is accepted by a sufficient number of workers. 3) For analytical purposes, class intervals must be small enough to define the continuous distribution accurately. Further, where statistical studies are involved, a fixed relationship should exist between classes or grades. An argument in favor of geometrically related size grades lies in the fact that most particulate mixtures contain such a wide range of sizes that use of an arithmetic diameter scale is practically impossible. Udden, who recognized this fact in 1898,' proposed one of the first grade scales based on a regular geometrical interval. Udden used 1 mm as his basic diameter and a ratio of 2 (or 1/2) between classes. In 1922 Wentworth2 re-examined Udden's grade scale, retaining the same class interval and basic diameter, but extending the scale in both directions and renaming the classes. In 1930 (Ref. 3, p. 82) the American Society of Testing Materials proposed what is now known as the U.S. Standard fine sieve series, also based on the 1 mm diam, with a v2 ratio between sieves. This, then, is a one fourth Udden-Wentworth series in the sizes below the 4 mesh sieve. The U.S. Standard coarse sieve departs from the 1 mm base and uses inches; hence it is not a direct continuation of the fine series. The U.S. Standard series would thus seem to possess all the attributes of a good grade scale, which it is. It has a large number of classes (sieves). in fact too many for practical use in its entirety. This v2 subdivision of the Wentworth grades has led to the common use of two v2 sieve series, the half-Wentworth and the engineers' series. Geologists and sedimentologists favor the half Wentworth, or 18, 25, 35, 45 sieves, etc., whereas the engineers, preferring round numbers, utilize the other half of the U.S. Standard grade scale in the 16, 20, 30, 40 sieves, etc. The fixed geometrical ratio between classes is an advantage in statistical analysis, but the unequal classes cause some complications in calculations. This is especially true when moment measures are used. It was to simplify these calculations that Krumbein in 1934 devised the phi scale. Phi is defined as being equal to —log2 of the diameter in millimeters. Selection of logarithms to the base 2 relate the phi scale directly to the Wentworth grade scale in such a manner that the whole or fractional diameter values 2, 1, 1/2, 1/4 mm, etc., become rational whole numbers, —1, 0,1, 2, etc. Since this is an arithmetic rather than geometric series, calculations are facilitated. When the logarithm is multiplied by —1 the phi values below 1 mm become positive, those coarser than 1 mm negative. Because of its relationship to the Wentworth grade scale (and in turn to the U.S. Standard fine sieve series) it is not necessary to use the transformation equation to calculate the phi value for each individual sieve; this can be done graphically as shown in Fig. 1. It should be noted that this graph may be extended in either direction to include the range of sizes most commonly used by the individual worker. Application to Statistical Analysis Any attempt at systematically relating size analysis data to properties involves a statistical study whether it is recognized as such or not. Since this is true it would seem more logical to use measures and devices related to the general body of statistical theory. Several methods are available for studying particulate mixtures. One of the most commonly employed, and also the most often misused, is the histogram or block diagram. If its limitations are recognized and provided for, the histogram is a very useful tool. According to conventional practice, the bars of equal width are plotted and the values noted in terms of diameters, when in point of fact, log diameter is implied by such notation. Further, the histogram is sensitive to choice of grade scale and size of class interval, either of which may color the result. Grade scales whose classes are not related by fixed intervals are particularly difficult. Another basic weakness of the histogram is that it pictures a continuous distribution as a series of discrete grades.

Jan 1, 1957

By G. R. Fritterer

INVESTIGATORS in the field of temperature measurement have long sought a thermoelectric couple fulfilling the following requirements: 1. It should be useful up to and including high industrial tempera-tures; i. e., 1000° to 1800° C. 2. Its thermoelectric variation with temperature should be linear and be maintained after heating to high temperatures for long periods of time. 3. It should be reproducible; i. e., different couples of the same elements should have similar calibration curves. 4. Its thermoelectric power should be large so as to allow the industrial use of rugged recording instruments. 5. Chemical reactions with, and physical changes within the elements of the couple should not alter its calibration. No thermocouple proposed to date exhibits simultaneously all of these characteristics, whereas the couple about to be described fulfills all requirements to a satisfactory degree.

Jan 1, 1933

By W. J. West, T. D. Mueller, J. E. Warren

The authors have presented valuable information on the influence of the interfacial tension and the contact angle on the recovery efficiency of the waterdrive process. It is considered, however, that the following points deserve a closer examination. 1. As pointed out by Wyllie and Spangler1 the displacement pressure PD i.e. the pressure required to initiate the displacement of the wetting phase from the core, is a measure of the maximum pore diameter dmax. If the capillary pressure Pe as a function of the wetting

Jan 1, 1956

By D. Y. Geng, S. S. Peng

Surface subsidence of two longwall panels, one with a private residence and the other with an arch bridge, was monitored over a period of 1 to 1' ½ years. Surface subsidence data were analyzed in terms of zone of advance influence and delay angle of maximum subsidence velocity. The variational characteristics of both features coincide with the periodic weighting at the advancing longwall face. Surface heaving in the subsidence process can also be attributed to periodic weighting. It was found that residential damages occurred when subsidence velocity exceeded 4.5 mm/day (0.15 ft/day). The effects of locating structures on the panel center and near the gob edges are illustrated. The effect of mining on ground water was also discussed. Finally, methods of reducing structural damages are recommended.

Jan 1, 1984

By P. G. Shewmon, H. E. Collins

A study has been made to determine the sites at which sulfur adsorption occurs on copper surfaces. measurements were made of the relative torques, Ys, at the intersection of twin boundaries with surfaces near the three low-index orientations, i.e., (100), @lo), and 011), over a range of H2S/H2 ratios. HZS concerztvations j'ro~n 3 to 1500pp)n between 830" and 1050°C were used. It is concluded that sulfur adsorption occurved preferentially though not exclusively at edge sites near the (100) and (110) surfaces in the HzS range — 700 Ppm giving rise to negative torques near these orientations. Beyond this HzS range, adsorption occurred at all sites. Near the (111) surface, 7/y little with HzS concentration up to approxiwzately 75pptn. Above this range, the results indicate adsorption is occurring OH both terrace and edge sites. SCIENTIFIC interest in surfaces and their interactions with a gaseous environment dates back to the beginning of the 19th century. The scientific luminaries of that period—Faraday, Maxwell, Rayleigh, Dewar, and Gibbs—were already concerned about such processes. However, it has only been within the past several decades that adsorption on metal surfaces has been actively studied. This increased interest in adsorption has been brought about by the advent of new and improved experimental techniques and apparatus, e.g., ultrahigh vacuum, and field-emission and ion microscopes. However, most of the work done using these techniques has been carried out at low temperatures. When adsorption studies have been made at either low or high temperatures, they usually gave no indication of the particular surface orientations or type of sites on which adsorption was occurring. In the last few years, there have been a series of studies in which the surface tension, y,, and/or its derivative with respect to orientation, 7, have been studied as a function of orientation and atmosphere.'-7 Nearly all of the work on the relative torque,* ~/y, silver annealed in hydrogen and air.6 Recently Winterbottom and Gjostein" have used a modified and more accurate Mykurian method to determine the y plot of gold in hydrogen The only work in which T/~, has been measured over a range of chemical potentials for a given solute, p2, is that of Robertson and shewmon7 on the Cu-0 system. They measured T/Y, vs Po, (10"" to 10- l3 atm) at 1000°C in various mixtures of Hz0 and HZ. From this work they estimated the value of p2 at which one half of the surface sites are occupied with oxygen, pg, as being in the range 10- l6 to 10- l5 atm of oxygen. They also found that increasing Pa increased the magnitude of ~/y, near the (111) and (100) orientations. This indicates that oxygen is not adsorbed preferentially at step edges, but uniformly over all surface sites. In addition, they did one experiment on sulfur adsorption on copper surfaces, which indicated that sulfur adsorption decreases ~/y, near the (100) orientation, while not affecting ~/y, near the (111). This could be interpreted as indicating that sulfur adsorbs preferentially at step edges near the (100). In this paper the primary objective of the work has been to carry out a study of sulfur adsorption on copper surfaces over a range of temperatures and p,. In conjunction with this work, thermal grooving at grain boundaries has been examined as a method of determining the effect of sulfur adsorption on y,. METHODS Ideally, one would like to have information on the quantity of solute adsorbed on a surface and the types of sites at which it is absorbed as a function of p2. The total quantity adsorbed or the surface excess is given by the thermodynamic equation Thus data on the variation of y, with pz indicates the value of p2 at which adsorption becomes appreciable and the quantity adsorbed. The type of adsorption site is more difficult to deduce but information on this can be obtained from the variation of rz with 8, the angular deviation of the surface orientation. This is obtained from the thermodynamic equationlg Data on t and ys as functions of p2 have been obtained by the following methods. 1) Twin Boundary Grooving—By determining the effect of adsorption on the torque, 7, where T is the variation of surface energy, y,, with orientation, it is possible to obtain some indication as to the preferred sites of adsorption. Experimentally, the torque value measured is the relative torque, 7/ys The twin boundary grooving technique suggested by Mykura'' was used in this study to determine near the three low-index orientations— (loo), (110), and (111). Mykura's equation relates 7 /yS to measurements of the di-

Jan 1, 1967

By C. G. Dunn

The measurement of interfacial teusions or grain boundary energies in metals is an important metallurgical problem, especially since it bears on growth and nucleation processes. Statistical methods of measuring equilibrium grain boundary angles, which relate interfacial tensions, have been used by some investigators1'2 but more direct methods would be preferred. A direct way, based on a simple extension of a successful method of growing single crystals of silicon ferrite to predetermined orientations in flat specimens,3 is to produce three-grain specimens in such a way that the equilibrium common grain boundary will be perpendicular to the surface of the specimen. The angles to be measured then appear as the grain boundary angles in the surface of the specimen. The method of producing a single crystal specimen with a predetermined orientation is basically the same as that employed by Yoshida and Fuji-wara4 in their work on aluminum wires. The specimen, prior to any single crystal transformation, must have a matrix which will support the growth of a crystal of the desired orientation. Growth may occur through exaggerated grain growth or, if the matrix is strained a critical amount. by normal recrystallization. In either case the matrix must have stability at the temperature used to effect the transformation, this stability appearing as a long induction period for exaggerated grain growth or for the formation of recrystallization nuclei. Additional control is gained by using a high temperature gradient through which the specimen is moved at a suitable rate. To obtain the desired orientation, the specimen is fed a short way into the furnace producing one or more crystals in the hot end. After the specimen is removed from the furnace, the orientation of a crystal is determined, so that this crystal may be reoriented by properly deforming a narrow piece of the matrix between the end crystal and the rest of the specimen. This part of the specimen in the case of silicon ferrite is preferably held at red heat during the reorienting process. Fig 1 shows a specimen which is ready to be transformed into a single crystal through growth of a reoriented "seed" crystal. When the method just described is applied to the production of a three-grain specimen two crystals are grown first side by side in one end, the specimen is then reversed and the third grain grown from the opposite end. A suitable group of grains each of different orientation is one where all three grains have the same crystallo-graphic plane in the plane of the specimen. Fig 2 shows a photograph of a three-grain group prepared as described. The notches are introduced in the open ends of the grain boundaries to anchor them during the final annealing operations which ultimately should bring the grain boundaries to the lowest energy configuration. Two-grain groups with different crystallographic planes in the plane of the specimen can be similarly prepared and treated. If the two grains have different surface (gas to metal) energies per unit area, the equilibrium condition leads to a curved grain boundary.* * This feature of the problem was pointed out by J. c. Fisher. References 1. Cyril Stanley Smith: Grains. Phases and Interfaces: An Interpretation of Microstructure. Trans. AIME 175, 15. Met. Tech. TP 2387, June 1948. 2. D. Harker and E. Parker: Grain Shape and Grain Growth. Trans. A.S.M. (194,5) 34, 156-195. 3. C. G. Dunn, A. Seddon, and R. Wylie: Unpublished Work, 1946-1947. 4. Takeo Fujiwara: A Method of Producing A Long Single-Crystal Wire of Aluminum with any Desired Crystallographic Axis. Jnl. of Sci. Horoshima Univ. A, (1939) 9, No. 3, 227.

Jan 1, 1950

By E. P. Pfleider, W. G. Pariseau

Even as the rational selection of excavation equipment requires a matching of machine performance capabilities to rock response characteristics, the functional features of transportation systems must be matched to the characteristics of the materials handled in order to secure optimum, trouble-free operation. In particular, ore passes and chutes must be designed for flow in order to insure controlled draw whenever a chute is opened. The alternative to quantitative design is, of course, the well known ad hoc procedure of freeing plugged ore passes, cleaning up spillage from flooded chutes, etc., after installation of the system. Since the voluminous empirical work sporadically undertaken through the years evidently had not led to reliable design methodology, it seemed worthwhile to attempt a rational and complete description of the movement of material through ore passes. The concepts of de- formable body mechanics applicable to gravity-induced flows of granular media or "soils" were involved. Accordingly, the mathematical theory of soil plasticity was adopted as a working hypothesis, and a two-dimensional laboratory model of an ore pass constructed in order to investigate the appropriateness of the theory. The general experimental strategy consisted of formulating the movement of material in ore passes as a boundary value problem in soil plasticity, determining the required boundary values of stress and velocity experimentally, and then using these data for the initiation of a theoretical solution for stress and velocity throughout the moving mass of material. A comparison between the theoretical and experimental constituted the test of the original hypothesis.

Jan 6, 1968

By D. Turnbull, J. C. Fisher

ACCORDING to the "reaction-path" modell,2 of martensite nucleation, the shear angle of the embryonic martensite plate must be treated as a variable, and included in any calculation of nucleus critical size. Also, as can be deduced from this model, the interfacial free energy between austenite and martensite does not reach its final value until the shear is completed. It is zero for zero shear angle. However, in order to account for the kinetics of the martensite transformation, some sort of interfacial energy barrier appears to be necessary even with the reaction-path model, for otherwise the volume and the energy of formation of the critical size nucleus both collapse to zero.3 Cohen independently suggested that surface energy could be incorporated into the reaction-path model, with the overall free energy of a martensite embryo being a function of its volume and shear angle.' It is possible to estimate the energy associated with the formation of a critical-size martensite nucleus starting with the reaction-path model and including a surface free-energy barrier. As the dependence of interfacial free energy upon shear angle is unknown, a simple type of dependence will be assumed, with the belief that the true dependence would not lead to appreciably different results. Consider the work required to form a lenticular martensite plate with radius r, thickness t, and shear angle 8. There are three contributions; one being the interfacial free energy, one being the free energy change in the martensite plate, and one being the free energy increase in the surrounding austenite. The interfacial free energy u is assumed to depend upon the shear angle 0 according to the relationship s=s0(?/?0)n [1] where 8, is the equilibrium shear angle and n is an exponent that may lie in the range 0 n 2. The work required to form the interfaces of a martensite plate then is W. = 2pr² s0(?/?0)n [2] The free energy change per unit volume of martensite is composed of two parts, one the ordinary volume free energy ?f1. which is negative, and the other the elastic strain energy G?m²/2, where G is the shear modulus and 7, the shear strain relative to the martensite structure. This expression for the strain energy is valid only when the shear strain ym, is sufficiently small that the martensite is within its linear elastic range. There is no doubt that ym, lies beyond the linear elastic range for embryos that are considerably subcritical. However, for critical nuclei it will be shown that ym, is 1.5 pct or less, within the linear elastic range of martensite. For embryos of nearly critical size, then, the strain energy of the martensite is correctly given by G?m²/2. The shear strain in the martensite is ym, = 8, — 8, and the work required to form the strained martensite is Wm --= (pr²t/2) [?fv + G(?O - ?)²/2] [3] The free energy change in the austenite is entirely that due to elastic distortion. The elastic strain is not uniformly distributed in the austenite, being large near the martensite plate and small elsewhere. Approximately, however, the energy corresponds to a uniform shear strain ya= (?t/2)/r [4] throughout the volume 4pr³/3 surrounding the plate. The work required to strain the surrounding austenite then is Wa = (4pr³/3) (G?a²/2) = (G?²/6) prt² [51 For simplicity, the same shear modulus G is assumed for each structure. The total free energy for forming a plate then is W = W3 + Wm + Wa. = 2pr² s0 (?/p?0)n + (pr²t/2) [?fr+G(?0-?)²/2] + (G?²6) prt2 [6] This expression is correct for nuclei and for embryos of nearly critical size, where, as will be shown, the strain energy in the martensite is correctly given by the expression G (? — ?)². Having W as a function of r, t, and 8, as in Eq. 6, there is a saddle-point where W has a stationary value, W subsequently decreasing indefinitely as the nucleus volume increases along the reaction path. The stationary value of W is the energy of the critical nucleus. The critical nucleus has radius, thickness, and shear angle such that ?W/?r - awlat: = ?W/?p? = 0. Performing these differentiations and calculating the critical nucleus energy, W* = [8192p(G?/6)²;s/27 ?fv4] [7] where a= (?/?0)3n+1[l +G(8"-8)'/2af.]' [7a] and where 8 is to be determined from the equation (1 + 3n/4) + G8(6O - (9)/[Af. +G(6>o-6>)72] = 0 [8] For ?f, near —200 cal per mol or —10" ergs per cc, and 8, near 1/6, as for iron-base alloys, Eq. 8 gives ?0 - ? ~ - (4 + 3n) ?f1./4G0O [9] as the difference between the equilibrium shear angle and the actual shear angle for a critical nu-

Jan 1, 1954

By G. G. Biggar

A MATERIAL contribution to the success of our Armies in the field has been the portable pipe-line system. These are the words of Brigadier General R. F. Fowler, chief of the supply division of the War Department. The portable pipe line is one of the "secret weapons" the American forces employed in their swift advances through Tunisia, Sicily, and Italy. Constructed of a light steel so flexible it can be snaked around trees, it can be laid at a rate of ten to thirty miles daily right up to the fighting fronts. It has played a major role in supplying combat troops with products varying from petroleum to water.

Jan 1, 1943

By A. S. Odeh

This paper analyzes the effect of limited entry to flow at the wellbore on the steady-state productivity of a well. Wells that have been opened to flow along a fraction of their productive interval are termed wells with limited entry. Previous work treated the cases of a partially penetrating well, a well producing from the central portion of the productive interval and a well in which several intervals equally spaced were open to flow. In this paper the open interval can be located anywhere within the productive interval. Thus, in a sense, it generalizes previous work. The finite cosine transform was used to arrive at a solution for steady-state flow of a slightly compressible fluid. The solution was programmed for a CDC 1604 computer. Numerical vaIues for rd = 660 ft, r, = 1/4 ft, and range of sand thickness of 20 to 200 ft are presented in graphical form. The effect of rd and r, values on the result is shown in a table. The correct calculation of skin and damage ratio in the presence of limited entry to flow is explained and illustrated by examples. Moreover, the paper shows how to calculate the net decrease in productivity due to the combined effect of limited entry and perforations. INTRODUCTION In some wells only a fraction of the productive interval is open to flow. Location of this fraction is usually dictated by formation characteristics and reservoir behavior. For instance, if a gas cap exists, the open interval is located away from the gas-oil contact to prevent any possible gas coning. Wells that intentionally have been opened to flow along a fraction of their productive formation are tened wells with limited entry. Obviously, unintentional completions of this type also exist. Limited entry to flow decreases well productivity. Magnitude of the loss depends on the fraction of the formation open to flow, on the thickness of the sand, on the location of the open interval and on the ratio of rd /r, where r , is well radius and rd is the drainage radius of the well. The use of pressure buildup data on producing wells to calculate the condition of the formation around the wellbore is an accepted practice. van Everdingenl and Hurst2 introduced the concept of she skin factor s considered to be due to a thin layer of different permeability immediately around the wellbore. These authors dealt with the case of a well of complete radial geometry, i.e., a well with open-hole completion that completely penetrates the formation. The presence of a low-permeability skin results in a loss of productivity, as does limited entry. Therefore, if pressure buildup data obtained on a well with limited entry are used to establish the presence or absence of skin (i.e., formation damage), and a correction is not made for this loss of productivity, the calculations would result in an erroneous skin value. They might indicate the presence of formation damage when in reality there is none, or they might indicate a value larger than the true value. This could lead to an incorrect basis for planning remedial measures. Muskat3 studied the problem of partially penetrating wells for the case of incompressible flow. He presented equations and figures which allow estimation of loss in productivity. Brons and Marting,4 using equations based on Nisle's work,5 studied the loss of productivity for three cases. The first was for a partially penetrating well; the second was for a well producing from only the central portion of a productive interval; and the third was for a well in which several intervals equally spaced were open to flow. Their work was for steady-state depletion-type reservoirs wherein the well radius of drainage is established and the fluid is considered to be slightly compressible. Considered in this paper is the problem of wells with limited entry in which the open intervals are located anywhere within the productive sand. The finite cosine transform is used to arrive at a

Jan 1, 1969