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By J. E. Warren, J. H. Hartsock

An asymptotic solution to the equation that describes the flow of a slightly compressible fluid in an infinite porous medium has been used to estimate the interaction between two adjacent wells producing from a common reservoir. A direct method for approximating the interference time defined by Stevens and Thodosl has been suggested. An alternative definition for the time of interference, based on the minimum pressure change in the interference region, has been proposed; also, a direct method of determination has been prescribed. Examples have been employed to illustrate the use of both methods.

By J. C. Martin

Equations for three-phase, three-dimensional, compressible flow (including capillarity) are reduced to two-dimensional relations by a partial integration. This reduction allows three-dimensional flow problems to be treated with mathematics for only two spatial dimensions. The results can be used to formulate flow equations for two-dimensional reservoir simulators in which the effects of capillarity and fluid segregation in the third dimension are represented. Such reservoir simulators would retain many of the aduantages of two-dimensional simulators while simulating three-dimensional effects. The principal restriction of the method is that the thickness of the reservoir should be small, compared to the distance across the reservoir. INTRODUCTION In recent years, computers have been used to calculate the performances of many reservoirs. Most of the detailed calculations, however, are based on finite difference solutions of the flow equations, and present day computers are seldom able to handle a sufficient number of cells to produce entirely satisfactory solutions, even for reservoirs represented by two-dimensional arrays of cells. The situation becomes much worse when one wishes to approximate the reservoir by a three-dimensional array. A great saving in computation or a more detailed solution can be obtained for many reservoirs by using the partial integration of the equations of flow presented in this paper. The integration reduces the three-dimensional equations to two-dimensional relations; and, for studies of two-dimensional flows in vertical cross-sections, the equations are reduced to one-dimensional relations. Most reservoir performance calculations currently are based on one- or two-dimensional flow re1ations.l-3 In some cases flow in the third dimension is approximated by assuming a particular type of vertical saturation distribution, such as gravity segregation.l.2. The relations developed in this paper approach those for segregated flow as the capillary pressures approach zero, and they approach those for uniformly distributed saturations as the capillary pressures are increased. For this analysis, the ratio of the reservoir's thickness to the maximum distance across it must be small. The capillary pressures between the oil and water should also be small compared to the maximum pressure difference in the reservoir. This requirement is met by most reservoirs. It is assumed that the capillary-pressure curves are well defined, whether or not hysteresis effects are included. Also, the reservoir must have sufficient vertical permeability to allow the fluids to segregate. The results presented here provide a firm theoretical foundation to Coats' et aL5 assumption of vertical equilibrium and extend the relations to three-phase flow. Coats' assumption of vertical equilibrium, which he verified by calculations and experiment, is developed here mathematically from basic flow equations. DISCUSSION SATURATION AND PRESSURE DISTRIBUTIONS Appendix A presents a mathematical analysis of fluid flow in reservoirs where the ratio of thickness to maximum distance across the reservoir is small. The results indicate: (1) that the fluids along any line perpendicular to such a reservoir's upper surface are in static capillary equilibrium (vertical equilibrium); (2) that, to a first approximation, the fluid pressures and properties are functions of only areal position in the reservoir and time; and (3) that hydrostatic pressure gradients exist along any line perpendicular to the reservoir's upper surface. The results might be expected after studying several physical considerations. First, no flow is allowed normal to the upper and lower reservoir boundaries, which are relatively close together.

Jan 1, 1969

By V. J. Parks, Leonard Obert, A. J. Durelli

The state of stress in the region where core discing initiates has been investigated through the use of three-dimensional photoelastic models and the results of this study have been compared with those of a previous investigation of rock models. This comparison showed that discing initiates at a point of maximum shear stress, but that the magnitude of the shear stress, as determined photoelastically, is much larger than the shear strength of the rock as deter-mined from conventional triaxial testing. Moreover the shear stress required to produce discing is not constant, but depends on the applied stress field. Possible explanations for these effects are included in this article. In both exploration core drilling and overcore drilling to determine the stress in rock, occasional sections of the core obtained are broken into a series of discs.I* This discing phenomenon has been investigated in the laboratory to ascertain the state of stress required to produce it. The objective of the study was to obtain information that would make it possible to approximate the state of stress in subsurface rock from which disced cores are obtained. Referred to as the discing test, this laboratory study was conducted to determine the applied axial and radial loads required to produce discing in cylinders of rock from several sources. The dimensions of these cylinders are given in Fig. 1. Discing was produced by first applying an axial load to the cylinder and then diamond drilling the core along its axis. The radial load was then incrementally increased until discing initiated. The discs fractured or ruptured* on surfaces approximately normal to the axis of the core (planes A, B, C, D, E, Fig. 2). In many instances, the bottommost disc fractured before the drill had advanced past the points F and F', cre- ating a mush room-shaped fracture surface FEF'. Alternatively, it was also found that the same shaped fracture surface could be created by first drilling in an unloaded core to some point, say F and F', and then triaxially loading the core until fracture occurred on the plane FEF'. Jaeger and cook4 produced similar fracture surfaces in specimens subjected only to a radial biaxial load. From these laboratory studies and observations made in the field, it can be inferred that fracture or rupture initiates in the proximity of the lowest point in the kerf area, (at F and F', Fig. 2) and that the fracture or rupture surface progresses inward from this point. The experiments described above, however, do not provide any information as to the state of stress at the point at which fracture or rupture initiates. In the investigation discussed in the following sections, a three-dimensional photoelastic analysis was conducted to determine the stress distribution in the proximity of the kerf area of a triaxially loaded plastic (epoxy) cylinder containing a short section of core.

Jan 1, 1969

The following record of the important responsibilities already shouldered by Dr. Ricketts will give some indication of the trust and confidence reposed in him by his colleagues. The Institute is to be congratulated that a man who is already so much engaged should be willing to assume the further responsibility of guiding the Institute's Ship of state during the ensuing year. Louis Davidson Ricketts, who is brother of Professor Palmer or Chamberlaine Ricketts, President of Rensselaer Polytechnic Institute, was born at Elkton, Md., Dec. 19. 1859, was graduated from Princeton University in 1881 with the degree, Bachelor of Science, chosen a Fellow in Chemistry and W. S. Ward Fellow in Economic Geology, and after two years' study given the degree Doctor of Science. Following the completion of Iris work at Princeton, Dr. Ricketts went to Colorado and started to work as a mine surveyor. For the 15 years following, his time was chiefly occupied in reconnaissance work, geological work and mine examination. From 1887 to 1890 Dr. Ricketts was Geologist for Wyoming, and at, the end of that period transferred his operations to the Southwest. where he has since been steadily engaged in large mining projects. He was identified with the acquisition of the property now owned by the Moctezuma Copper Co., a , subsidiary of Phelps, Dodge & Co., at Nacozari, Sonora, Mex. From 1899 to 1901 he was General Manager of the property and during his administration the concentrator and reduction works were completed and the mines put on a dividend-paying basis

Jan 3, 1916

By R. N. Edmondson, L. Mair, M. Tenenbaum

It is the policy of The Metallurgical Society to provide, in the TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME, a prompt and accurate medium for publication of reports of significant new research in both the scientific and engineering aspects of metallurgy. Papers submitted to the Society are judged by competent reviewers according to established criteria for technical merit, accuracy, originality, and presentation. STAFF: Editor, Dr. Gerhord Derge; Editorial Assistant, M. A. Redmyrski; Staff Coordinator, James J. Burke. THE METALLURGICAL SOCIETY: W. R. Hibbard, Jr., President; J. C. Kinnear, Jr., Past-President; John Chipmon, Vice President; T. D. Jones, Treosurer; R. W. Shearman, Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: A. w. Thornton, Chairman; Dennis Carney, John Chipman, J. C. Fulton I. H. Hollomon H. H. Kellogg, A. E. Lee, R. Maddin, J. D. Sullivan, and D. Swan. Review and selection of manuscripts is under the supenision of the following Publications Committees: Extractive Metallurgy Division: T. 0. King Chairman; S. J. Dickenson, R. P. Hermsdorf R. Schuhmann. Jr.. and P. T. Stroup. Institute of Metals Division: Robert Maddin, Chairman F. Lincoln Vogel Jr., Vice-chairman, W. A. Baikofen, R. W. Boliuffi J. H. Bechtold M. B. Beyer. R S. Busk, C. G. Gaetzel, Paul Gordon C. D. Groham, Jr., Robert F. Hehe-mann,' R. I. Joffee, F. c. Joumot Jr lrving R. Kramer A. J. Lena Harold Morglin, C. J. McHargue, Russell A: Meussner, J. B. Newkirk H. W. Paxton, G. E. Pellissier, I. S, Servi, Alon U. Seybolt, A. J. Shaler, and Jack Washburn. Iron and Steel Division: J. C. Fulton, Chairman; T. B King, F. C. Langenberg, W. 0.. Philbrook, and T. 0. Winkler. Published bimonthly by the American Institute of Mining Metallurgical and Petroleum Engineers Inc., 29 West 39th Street, New York 18, N. Y. Telephon: pEnnsvlvanio 6-9220. Subscription 522 Per year for non-AIME members in United States and North South and Central America; $25 foreign;, $5 for AIME members. Single copies, 54.00, single copies foreign, $5.00. The AIME is not responsible for any statement made or opinion expressed In its publications . . . Copyright 1958 by the American lnstltute of Mining Metallurgical and Petroleum Engineers Inc. . . . Registered cable address AIME New York , . . lndexed in Engineering Index Industrial Arts Index and Chemical Abstrats . . . Application for second class mail privileges ii pending at New York, N. Y. Volume 212, Number 4.

Jan 1, 1959

By Charles E. Wait

It is said by some that the occurrence of a deposit of sulphide of antimony in Southwestern Arkansas has been known for fifteen or twenty years. Whether or not such is the case I am not prepared to say, but I am not able to find any record of such a discovery, or any analysis of antimony ore obtained from that section, published at so early a period. The present discoveries, that seem to be attracting some attention, date back to the winter of 1873-74. At that time a vein of ore was found by Mr. Robert Wolf, in honor of whom the vein was named, and still is called, "the Wolf lode." At the time of the discovery the ore was unknown to the prospector, and its composition was not thoroughly understood in that locality until samples were sent to several analytical chemists, who pronounced it sulphide of antimony—stibnite. Since the discovery of this ore there have been three mines opened, and a number of interesting minerals of the antimonial series have been found. I have had an unusually good opportunity to collect specimens from these mines; and it is owing to the constant inquiry concerning the character of these ores that I have collected for publication the results of quite a number of analyses, sufficient I trust to clearly point out their composition. This is one of the few localities in the United States where antimony ore is found in workable quantities ; I say workable quantities, because two different shipments of ore have been made to English reduction works, and in both cases excellent returns were made. The discovery of these deposits will, it is hoped, give rise to a prosperous and remunerative industry at no distant day, and when fully developed they may yield ore in sufficient quantity to supply the regulus for the home demand, thus adding wealth not only to those interested, but also to the State of Arkansas. The three mines are situated in the northern part of Sevier County, and may be reached by the St. Louis, Iron Mountain and Southern Railway to Fulton, thence by wagon-road to Columbus, Nashville, Centre Point, and to the mines. During most seasons of the year the

Jan 1, 1880

By G. E. Perry, R. D. Seba

The steam soak process is the most widely applied and most successful thermal supplemental recovery process in use today. This process, which consists of injection of steam in various quantities into a well that is subsequently used as a producer, can be repeatedly applied to the same well. The treatment, if successful, will increase the production rate of the well for a given period. For this reason, the steam soak process should be considered primarily as an acceleration method rather than as a method for producing oil that could not be recovered by primary means. However, application of this process to reservoirs containing viscous crude may produce oil that otherwise would have zero present value or would be produced at such low rates by primary methods that it would not be profitable. A major necessity for the successful application of the steam soak process is a source of natural energy. This source of energy may exist in one or more of the following forms: expansion of fluids, compaction, gravity drainage. This study was undertaken to determine the effect of gravity drainage on steam soak production and recovery and to develop a method for predicting production rates, ultimate recovery, and heat requirements when applying this process to a reservoir in which the primary driving mechanism is gravity drainage. (For additional discussion of some of the factors that affect recovery of viscous oils by the steam soak process, see Ref. 5.) Model The model developed for analyzing the performance of the steam soak process in gravity drainage reservoirs is a modified form of that developed by Matthews and Lefkovits.1,2 The model used in this study consists of two concentric cylindrical volumes of productive formation with cap and base rock of impermeable material. The inner cylinder, extending from the radius of the wellbore to some predetermined radius, is referred to as the hot zone; and the outer cylinder extending from the exterior boundary of the hot zone to the outer drainage boundary will be referred to as the partially heated zone. Fig. 1 is a schematic cross-section of the model, indicating its thermal properties. Horizontally the reservoir is divided into two regions, the upper region having a high gas saturation and residual liquid saturation, and the lower region containing a high liquid saturation. The boundary between these two regions is referred to as the free surface, which drops and changes shape as fluid is produced from the reservoir. The model was used to analyze the steam soak process by applying the following assumptions: 1. The horizontal formation is composed of one or more homogeneous noninterconnected layers containing incompressible fluids. Each layer is treated separately. 2. The hot zone is heated by the initial soak and is maintained at the steam temperature corresponding to atmospheric pressure by resoaking. 3. The height of the free surface at the producing well is at all times zero (producing well is pumped off). 4. The position of the free surface at the start of

Jan 1, 1970

By W. A. Burns

Vertical flow is an important mechanism in many petroleum reservoirs. Yet no adequate method has heretofore been proposed for determining the in-situ vertical permeability in a reasonable length of time. Core measurements of vertical permeability do not necessarily represent effective in-situ values. Cores may be representative of only localized pockets of high or low permeability, and total reliance on cores might cause one to overlook the presence of vertical fractures altogether. Conventional single-well tests, interference tests, and pulse tests commonly are used to determine horizontal transmissibility, khh/u, but generally are not designed to measure vertical trans-missibility or other groups containing vertical permeability, ku. A new well test described here provides a measure of in-situ vertical permeability as well as the previously measurable horizontal permeability. This "vertical test" determines the vertical diffusivity, kv/gcu, and horizontal transmissibility, khd1/u (where dl is the length of injection or production perforations). The test is basically a short-term interference or pulse test normally lasting less than a day. Conventional down-hole equipment is used between two isolated sets of perforations in the same well, as shown in Fig. 1. A "layer-cake" description of a reservoir can be obtained by running two or more vertical tests in the same well, each over different vertical intervals. Each test can be analyzed for the effective vertical and horizontal properties of the interval tested. In addition, a vertical well test can determine the effective- ness of a shale barrier or tight zone by testing across it. Field use to date of vertical testing has confirmed its utility in reservoir description. Mathematical Basis Interpretation of vertical tests for ku and kh is based on comparison of measured pressure response with computer-generated response. Pressure behavior during a vertical test in a homogeneous, anisotropic, infinite-acting reservoir (infinite in radial extent and bounded in both directions vertically) is given by the diffusion equation for slightly compressible fluids with negligible gravity effects.l A schematic diagram of the problem is presented in Fig. 2, and an analytic solution, based on the image

Jan 1, 1970

Jan 1, 1969

By J. C. Reed, J. M. Hansell

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

By J. C. Reed, J. M. Hansell

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

By J. C. Reed, J. M. Hansell

Cinnabar was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigell by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done considerable exploration work and has retorted the high-grade ore so obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district. In March, 1934, the United States Geological Survey began a study of the Arkansas quicksilver district, which was made possible by an allotment of funds from the Public Works Administration. Until

Jan 1, 1935

Discussion of "The Ordering Transformation in Titanium-Aluminum Alloys Containing up to 25 at. pct Aluminum" by F. A. Crossley, Trans, TMS-AIME, 1968, vol. 242, pp. 726-30. Dr. Blackburn, in his response, pointed out that the c/a ratio of the Ti-26 at. pct A1 alloy quenched from 900°C is 1.6006 and not 1.5965 as plotted in Fig. 19. An error in transcription was made in preparing Table V of Ref. 1 (F. A. Crossley, Trans. TMS-AIME, 1966, vol. 236, p. 1174). The corrected Fig. 19 strengthens rather than weakens the argument that a martensitic transformation occurs in alloys containing from 15 to 18 at. pct Al. A Study of the Factors Which Influence the Rate Minimum Phenomenon During Magnetite Reduction, by P. K. Strangway and H. U. Ross, Trans. TMS-AIME, 1968, vol. 242, pp. 1981-88. Page 1883 Reverse Figs. 5 and 6. Sigma—Its Occurrence, Effect, and Control in Nickel-Base Superalloys, by J. R. Mihalisin, C. G. Bieber, and R. T. Grant, Trans. TMS-AIME, 1968, vol. 242, pp. 2399-2414. Pages 2403, 2407, and 2414 Arrows should appear on Figs. 4 and 9; a sigma is missing from Table IV; line 2, page 2414, change "case" to "cast". These are published correctly in the bound volume. Index, December Issue There were a few omissions in the Author Index. These have been corrected and published properly in the bound volume.

Jan 1, 1970

By S. M. M. Safvi, A. Jowett

Small-scale continuous flotation tests are described in which the influence of 1) pulp density and 2) feed rate on the rate of flotation are investigated. The results provide further evidence of first-order kinetics for flotation and indicate that tests at different feed rates provide a particularly simple method of determining rate constants. Flotation kinetics are discussed in general terms. Over a period of many years numerous research workers have studied the rate of recovery of valuable materials from flotation pulps with a view to deter-mining the mechanism of the froth flotation process. Froth flo ation is fundamentally a collision process involviug at some stage collision and then mutual attachment between air bubbles and mineral particles. It is possible to draw analogies therefore between the flotation process involving mainly macroscopic particles and the ordinary processes of chemical reaction kinetics involving collisions between atoms, molecules and ions. By adopting this analogy we may postulate a general equation representing the kinetics of the flotation process: -dC/dt =K.CC ,Aa (1) The rate constant, K, will be a complex function involving reagent concentrations, particle and bubble sizes, induction times and no doubt flotation cell design. However, these are factors which can be kept constant in any series of experiments, permitting investigation of the exponents a and c, which determine the order of the reaction occurring in flotation. The various research investigations carried out so far have all aimed at evaluating a and c and in the majority of cases only since the concentration of air has usually been kept constant in a series of tests, so that a relationship of the following type has been investigated: -dC/dt = K1 Cc (2) The techniques of both batch testing and continuous testing have been used to investigate this relationship. The technique of continuous testing, in which steady-state conditions are established, permits direct investigation of the above equation. In the case of batch testing, C is decreasing continuously

Jan 1, 1961

By R. Greenwood

The advent of the space age and its promise of interplanetary flight has prompted new ideas for propulsion systems that will allow maximum energy with minimum fuel weight. The use of cesium as the source of energy for such rocket flights has been found desirable. Theoretical efficiency of a rocket fuel is measured in terms of specific impulse, defined as the number of pounds of thrust per pound of propellant consumed per second. Specific impulse is usually expressed in seconds (the number of seconds for which one pound of fuel would produce one pound of thrust) although it is really a measure of total energy, not of power. The most sophisticated chemical fuels have a specific impulse of 300 to 400 sec; liquid hydrogen heated by nuclear reactor has a specific impulse of 1000 to 1200 sec. Specific impulses as high as 20,000 sec, however, are theoretically attainable with the ion rocket, in which free cesium ions are accelerated across a voltage drop and ejected at high velocity.' Characteristics of the system have been sketched by Boden.2 The desirable properties of an ion propellant are: 1) low ionization potential, 2) low boiling point, and 3) high atomic weight. Alkali metals best fulfill these requirements, and Table I indicates the superiority of cesium. The use of heavy complex ions such as UCl3 is ruled out by their instability and other disadvantages.' Despite its enormous superiority in specific impulse, the ion rocket is inherently low-powered, capable of very small acceleration. Application of ion propulsion will be limited to large rockets and spaceships on missions requiring powered flight for weeks or months and employing a separate chemical propulsion system for escape from the earth's atmosphere where power requirements are large but of brief duration. For example, Kraemer and Larson3 considered the case of an unmanned 25,000-lb pay-load placed in a 300-mile orbit by chemical rockets, proceeding thence by ion propulsion to the vicinity of Mars, where it would go into orbit once again. Calculations provide for 8500 lb of cesium for such a voyage. The question of whether such quantities of cesium will be readily available to the space program does not appear to have been considered by geologists and mining engineers. Present Production and Uses Literature on industrial applications of cesium is scanty. The metal is used in scintillation counters, photocells, infra-red detection devices, and as a "getter" in low-voltage vacuum tubes. Production is sporadic and total figures are not published, but the annual consumption is measured in pounds rather than in tons. The few pollucite deposits known, small as they are, can easily supply the present limited demand for gram or pound lots of cesium. Until recently the price of cesium was $2 to $4 per gram, but according to Chemical Engineering, cesium salts are now available at $13 to $27.50 per lb. Geochemical Distribution As a large alkali ion, the cesium ion accompanies potassium in geological processes and tends to be concentrated in the latest crystallizing fractions of potassium minerals in much the same manner as rubidium. Most of the cesium in igneous rocks, therefore, is in the micas and potash feldspars of granites, and especially in granitic pegmatites. The cesium content rises markedly in the micas of the late by-drothermal replacement stage in complex pegmatite~.' Typically, cesium is only 0.5 to 0.01 times as abundant as rubidium in potassium minerals. Rb', with a radius of 1.47 A, is close enough in size to K' (1.33 A) so that rubidium forms no minerals of its own. Cs+ is so large (1.67 A) that only small concentrations can be taken up in potassium minerals; when cesium is present in solution in larger concentration it forms the mineral pollucite, Cs3-Na2A17Si17O48.3H2O, which is known only in pegmatites. In the weathering of igneous rocks, cesium is dissolved, carried to the ocean, and apparently in-

Jan 1, 1961

Since the comprehensive review of the Persian fields presented by Sir John Cadman last year, operations have proceeded normally. No developments of especial importance fall to be recorded and it remains only to bring up to date the full information given at the beginning of 1933. Controlled production from the Masjid-i-Sulaiman and Haft Kel fields has been maintained at slightly higher rates than during 1932. The figures for the past five years are as follows: These represent crude oil and products piped to the coast but exclude products reinjected into the reservoir, a process that has been in continuous operation at Masjid-i-Sulaiman during the period under review. The systematic delimitation of the Haft Kel field has been continued during the past year and results have been sufficiently encouraging to justify the inception of a wider scheme for distribution of production. Drilling has been resumed recently in the Persian sector of the Naft Khaneh field, and preliminary survey work is in progress for the selection of a site for a refinery at Kermanshah arid the construction of a connecting pipe line. Investigations in connection with the scientific control of reservoir were dealt with in considerable detail in last year's review. This work has been steadily pursued during 1933 and certain of the investigations have been the subject of papers presented to the World Petroleum Congress held in London in July of last year.

Jan 1, 1934

By H. C. H. Darley

The principal causes of unstable boreholes* have been known for many years. For example, in a paper published in 1938, Halbouty and Kaldenbachl listed nearly all the classes of troublesome shales that we know today. Much progress has been made since then, but we still have difficulty in identifying the cause of hole problems and consequently in selecting the right technique for combatting them. This subject was discussed at length by Kelly2 in a recent paper and much valuable information was provided. In the Shell Laboratory it was felt that there was a need for a better understanding of the basic mechanisms underlying the various forms of hole instability, and accordingly, a study was undertaken. This entailed reviewing the physics and chemistry of shales, developing tests for characterizing shales, and constructing a model to study borehole stability. Full simulation of underground conditions was not attempted; for example, we used reconstituted shale specimens, and often simple solutions or suspensions rather than practical drilling muds. Such procedures are necessary in order to establish mechanisms, but caution must be exercised in applying the results to the more complex conditions in the field. Part I — Compaction Swelling and Dispersion of Shales Compaction of Sediments Shales are formed by the compaction of sediments. Water is expressed as sediments are buried by subsequent layers, and the degree of compaction is proportional to the depth of burial, provided the water is able to escape easily to permeable formations. The younger sediments, when recovered at the surface, soften and disperse when mixed with water; the older shales have undergone diagenesis (alteration of the clay minerals, secondary cementation, etc.), and remain hard and unaffected by water. In this paper we shall apply the term "shale", as the drilling engineer does, to everything from clays, which are highly reactive to water, to completely lithified materials such as claystones and slates, which are completely inert. However, because these materials behave quite differently when encountered in the drilling well, it is desirable to develop a simple means of characterizing them. The feature that distinguishes the various shales is their dispersibility in water —soft clays disperse readily, harder shales disperse slowly when agitated, the lithified materials will not disperse at all unless milled. In the dispersibility test used in our study, a weighed amount of dry shale particles in the 12-to-100-mesh-size range was placed in a tube filled with distilled water and allowed to soak for 16 hours. The

Jan 1, 1970

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher' estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,' however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,' in his test of Cottrell's theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell's theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley's assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12'13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a', an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969

Jan 1, 1970