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By D. Turnbull, J. H. Hollomon, J. C. Fisher

UNDERSTANDING of the diffusion problem has recently been furthered by the analysis of Birchenall and Mehl.1 They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,2 Jost,3 Dehlinger,4 and Darken,' who assumed the net flux of dif¬fusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's' activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Hargreaves.7 The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinski10 in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitutional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitutional alloys were analyzed on the basis of the concepts of the chemical rate theory. CHEMICAL RATE THEORY According to the theory of absolute reaction rates8 the reaction [A,+A2+ ... +.A;->X,+X2 +...+X; EqI] is viewed as taking place in two steps. First the reactants A1, A2, . . . A[i] combine to form an activated complex M with which they are in equilibrium; [A, + A2 + .. . + Ai = M. Eq 2] Second the activated complex decomposes to give the products X1, X2. . .. X[j]; [M->X1+X2+ ... +.X;. Eq3] It has been shown8 that the number of activated complexes decomposing per unit volume per unit time is given by the expression† [kT]

Jan 1, 1948

By F. M. Perkins, R. H. Jamison

Publications concerning scaling laws for laboratory flow models of oil reservoirs indicate that the relative permeability and capillary pressure relations must be the same functions of saturation in the model and its prototype. In this paper, the relative permeabilities and saturations are redefined in a way which permits one to have diflerent relative permeability and capillary pressure relations in the model and prototype. The development of the new scaling criteria is demonstrated by deriving scaling laws for one simple flow problem. INTRODUCTION The successful application of information gathered through bench-scale model studies to the prediction of multi-phase fluid flow behavior in petroleum reservoirs requires careful consideration of the scaling criteria. The requirements which must be met for a small-scale model to duplicate the behavior of a much larger reservoir prototype have been discussed by Leverett, et al,' Rapoport,2 and Geertsma, et al.3 According to these authors, the relative permeabilities to water, oil and gas and the dimensionless capillary pressures must be the must have the same values in the model and prototype. Furthermore, they point out that the viscosity ratios must have the same values in the model and prototype. In addition to these requirements, other scaling criteria are given which, when considered, usually dictate a much higher permeability in the model than exists in the reservoir. Since the more permeable model sands may have connate-water and residual oil saturations quite different from those in the prototype, the scaling requirements pertaining to the dependence of relative permeabilities and dimension l ess capillary pressures on saturation usually are not met. Also, if the model fluids are selected to give equal viscosity ratios in the model and prototype, one may find greatly different mobility ratios* in the two cases and, therefore, may expect grossly different flow patterns. For this reason, Craig, et al,' correlated the results of their model studies with mo- bility ratio rather than with viscosity ratio. As yet, however, no satisfactory method has been advanced which permits use of anything other than the scaling requirements outlined in the previously mentioned papers. The purpose of this paper is to present a method of developing a set of scaling criteria which permits different relationships between saturation and relative permeability or capillary pressure in the model and prototype. Rather than attempt to report scaling criteria for a variety of practical situations, this paper demonstrates by use of one simple example how the modified scaling criteria are derived.

By J. C. Fisher, J. H. Hollomon, David Turnbull

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By David Turnbull, J. H. Hollomon, J. C. Fisher

Understanding of the diffusion problem has recently been furthered by the analysis of Birchenall and Meh1.l They pursued the problem of the variation of the diffusion coefficient with composition for non-ideal solid solutions. Their analysis follows the tradition of Wagner,l Jost, Dehlinger, and Darken & who assumed the net flux of diffusing material to be proportional to the gradient of a quantity related to free energy. The basic assumption in Birchenall and Mehl's formulation of the problem is that the net flux of diffusing material is proportional to a thermodynamic activity gradient. To estimate the applicability of the derived relations, they corrected the diffusion coefficients of carbon in austenite by utilizing Smith's6 activity data for carbon, and the diffusion coefficients for zinc in copper with activity data computed from the vapor pressure measurements of Har-greaves.' The corrected coefficients for carbon were virtually independent of carbon concentration. For the diffusion of zinc in copper a moderate variation of diffusion coefficient with concentration remained after the correction. The problem of diffusion can be formulated in another way than that used by Birchenall and Mehl. The method is that of chemical rate theory and has been used by Eyring and his coworkers8,9 as well as by Eyring and Zwolinskilo in a discussion to Birchenall and Mehl's paper. As yet the method has not been applied to substitu-tional solid solutions. On the basis of their assumptions, Eyring and Zwolinski derived a relation between the diffusion coefficient and activity that is identical with that of Dehlinger and Darken but which does not correct for the variation of the diffusion coefficient with concentration as well as does the relation derived by Birchenall and Mehl. It was thought that the theory of diffusion would be more complete if the inconsistency between the two analyses could be rationalized and if diffusion in substitu-tional alloys were analyzed on the basis of the concepts of the chemical rate theory. Chemical Rate Theory According to the theory of absolute reaction ratess the reaction +..... +X, Eq I is viewed as taking place in two steps. First the reactants A1, A², . . . A; combine to form an activated complex M with which they are in equilibrium: A1 + A1+ . . . + A=M. Eq 2 Second the activated complex decomposes to give the products XI, XZ, . . . Xi: M?X, + X²+ . . . +Xi Eq g It has been showns that the number of activated complexes decomposing per unit volume per unit time is given by the expressiont kT -h CM † The transmission coefficient has been taken as unity.

Jan 1, 1949

By F. V. Lenel, G. S. Ansell, J. A. Dromsky

The growth of aluminum oxide particles in a nickel matrix was studied eve?. the temperature vange of 2140° to 2470°F. The instability of the dispersed alumina was shown to be independent of the crystal structure of the alumina. The activation energy for the growth of the dispersed alumina was found to be 84.7 1 2.0 kcal. The particle radius increased as a function of time. These results indicate that the growth is not diffusion controlled. It is believed that the rate controlling mechanism is the dissolution of the aluminum and oxygen atoms into the nickel lattice. THE strength properties of alloys which consist of a finely dispersed second phase in a metallic matrix depend upon the spacing between the second phase particles. It is therefore desirable to achieve very fine dispersions in these alloys. Furthermore, to retain the properties these very fine dispersions must be stable during fabrication and service of the alloys. The best known of the dispersion strengthened materials, the SAP type alloys, which consist of a dispersion of aluminurn oxide in aluminum, have exceptionally good stability up to the melting point of aluminum. There is evidence, however, that other dispersion strengthened alloys, even those consisting of refractory oxides in a metal matrix, may be less stable. This investigation is concerned with the stability of Ni-Al2O3 alloys in the temperature range in which these alloys are usually fabricated. The mechanical properties of Ni-Al2O3 alloys at elevated temperatures have been previously investigated by Crelnens and rant,' and Gregory and Goetzel.2 The behavior of these alloys in stress rupture tests appears to indicate that at temperatures below 1800°F they are highly stable. There is some doubt, however, as to their stability at the higher temperatures used during the conventional fabrication. Cremens and Grant, in preparing their test alloys, cousolidated, by powder metallurgical techniques, nickel powders as fine as 0.13 µ diam and alumina powders as fine as 0.018 µ. Metallo- graphic examination of the alloys following fabrication revealed that none had interparticle spacings of less than 2 µ. Considering the size of the original component powder particles, it is likely that the dispersions coarsened during fabrication. Gregory and Goetzel, in their studies of extruded alloys of 80 pct Ni—-20 pct Cr matrixes with nonmetallic dispersion, observed a definite coarsening of the alumina dispersions in alloys sintered at 2280°F as cantrasted to those sintered at 2000oF. Similar observations on the spheroidization and growth of thoria particles finely dispersed in a nickel matrix were made by D. K. Worn and S. F. Marton.3 As a result of such coarsening, much of the effort expended in the preparation of very fine powder mixtures would be lost. The mechanical properties of the alloys which had experienced coarsening would be expected to be poorer than if the original dispersions had been retained. EXPERIMENTAL PROCEDURE Ni-Al2O3 alloys were produced from powder prepared by a coprecipitation technique. Aluminum hydroxide and nickel hydroxide were coprecipitated from chloride solutions of the metals. The mixed hydroxides were calcined to form metal oxides and the nickel oxide in the mixture was selectively reduced to nickel by treating it in hydrogen. Specimens were compacted from the resultant powder which consisted of a fine, uniform mixture of aluminum oxide and nickel particles. The compacts were sintered by resistance hot pressing4, a densification technique which requires exposure times of the order of only a second or less at elevated temperatures. A conventional sintering process was not used, since the temperature required for densification would have to be in the region in which the stability of the dispersion was to be studied. A series of hot pressed specimens were treated in hydrogen at temperatures from 2140o to 2470°F (1171o to 1355oC, for times up to 120 hr. Changes in the microstructures were studied by electron microscopy using the two-stage preshadowed carbon replica method.5 In performing a lineal analysis on a series of micrographs from each specimen it was found more convenient to determine the mean free path between alumina particles rather than particle radii as the parameter of growth. Although these quantities are directly proportional for only spherical particles, the alumina particles in these alloys

Jan 1, 1962

By William P. Blake

The adaptation of aluminum to the construction of portable instruments of precision, where lightness is important, is well illustrated by the double reflecting and repeating circle, the invention of Captain Charles Hervey Tomnshend, of New Haven. One of these instruments, now exhibited to the members, has just been completed by Stackpole & Bro., of New York, and is made of aluminum, with the exception of a few minor pieces and a portion of the handle. This instrument is intended for use in a boat, and to be held in one hand like a sextant; and as it is a complete circle, lightness of the material becomes more important. The whole instrument, as shown, exclusive of the eye-pieces and the handle, weighs only one pound, or about one-third of the weight of a sextant of the usual construction. The circle, about nine inches in diameter, was cast in one piece from metal furnished by the Pittsburgh Company.

Jan 1, 1890

By Stephen C. Blair

Laboratory permeability measurements at elevated pressure and at temperatures ranging from 20º to 150°C have been conducted on samples of Ironton-Galesville sandstone. The purpose of this testing was to identify and characterize important physicochemical processes occurring in association with the injection and withdrawal of heated ground water at the U.S. Department of Energy's Aquifer Thermal Energy Storage (ATES) field site in St. Paul, Minnesota. Results indicate that permeability decreased significantly as temperature was increased and that dissolution of the dolomite and silicate cementing agents and accompanying changes in mechanical properties may occur in the heat storage aquifer at St. Paul. Further, loss of permeability with temperature in laboratory samples may be caused by the change in the mechanical structure of the sample. Tests at ambient temperature to evaluate the effect of particle migration under conditions of reversed flow indicate that this process will not significantly impair formation permeability at the St. Paul site.

Jan 1, 1984

By J. H. Wernick

IN a study of the rate of decomposition of %-in. cubes of limestone, dolomitic limestone, and dolomite in a sweeping nitrogen atmosphere, Joseph, Beatty, and Bitsianes' found that the zone of calcination advanced at substantially a constant rate at a given temperature. The purpose of this paper is to show that their data indicate at least two processes occurring when the above carbonates decompose. It is suggested that there are two processes occurring consecutively, one the limiting process in a given temperature range and the other the limiting process over another temperature range. The data of Joseph and co-workers have been extended by use of the Arrhenius equation, Eq. 1, a relation beween the velocity constant k of a reaction and the absolute temperature T. d In k A ' dT Rr2 A is the activation energy in calories per mol (additional energy that must be added for an average molecule to react), and R is equal to 1.986 cal

Jan 1, 1955

By Jan M. Mutmansky, Y. J. Wang

Mine ventilation analysis is an engineering discipline that can be considered a branch of the body of science known as network analysis. Likewise, the group of engineering procedures known as the critical- path method (CPM) is considered a branch of network analysis. It is therefore not surprising that mine ventilation network analysis and CPM have many similarities. These similarities are useful in analyzing several types of mine ventilation problems and will be utilized in this paper. The analogy between the free split in a ventilation circuit and the critical path in a scheduling network has been recognized by Owili-Eger (1973). While this was recognized as a property of a general ventilation network, many important applications to controlled- splitting problems also exist. The mathematical procedures necessary to apply CPM and network methods have previously been presented (Wang, 1981; Wang, 1982). This paper will illustrate the implementation of these methods by application to mine ventilation networks.

Jan 1, 1982

By W. A. Bruce

THIS paper presents the essentials of a mathematical method of studying the pressure behavior of an oil reservoir as the fluids are withdrawn. Methods are shown whereby the behavior of a reservoir can be used to predict the future relationship between withdrawals and pressure. The oil reservoir is considered as a small part of a large porous continuum, which contains for the most part water. The expansion of this water resulting from a decrease of pressure in the oil zone causes a movement of water that is an important factor in the relationship between fluid withdrawals and reservoir pressure. Examples are given to illustrate the methods of pressure prediction for a circular reservoir containing undersaturated crude, the pressure distribution over a field that has a uniform production rate, the effect of a fault line near a field, the mutual interference of near-by fields, and the perturbing influence of a gas cap. Applications of the analysis to sell-spacing problems are shown.

Jan 1, 1942

By J. Grosso, D. J. Nagel

In many metallurgical studies, it is necessary to reveal the composition and structural properties of materials. Usually this is done by etching, but some substances do not etch well or easily. Anodizing is known to provide an alternate treatment in many cases. In general, this technique is simple, often more sensitive to composition differences than etching, has excellent resolution, and provides variable contrast in those elements and alloys which anodize. Here we report the use of anodizing in diffusion studies in the TiCb system. Fig. 1 shows a cross section of the diffusion zone in a TiCb couple. The anodizing has clearly revealed both composition and crystallographic features. The maximum bulk penetration of the titanium into the columbium is marked by a sharp line because of the steep concentration gradient. The titanium grain size and orientation differences are also evident. Variation in the grain size reflects the gradually decreasing columbium concentration.

Jan 1, 1967

By Dean W. Lynch

Arizona: The San Xavier Indian Reservation mine is located approximately 2 ½ miles northwest of Asarco's Mission Mine southwest of Tucson. The company plans to produce oxide and copper-bearing siliceous ore at this operation, construction of which is scheduled for completion in 12 months. Asarco also plans a copper leaching and iron precipitation plant at its mine. The plant will leach 4000 tpd of oxide ore using sulfuric acid produced at the company's acid plant now under construction at Hayden. Copper precipitates will go to the smelter at Hayden. A drilling program at the Sacaton copper prospect in Pinal County, has disclosed two porphyry copper deposits. One deposit, mineable by surface mining, has approximately 17 million tons of material averaging 0.80% Cu. A deeper deposit suitable for under- ground mining has approximately 12 million tons averaging 1.5% Cu. Although Asarco intends to place this property in production, no startup date has been determined.

Jan 1, 1970

By Howard Reiss, C. S. Fuller

A theoretical and experimental study has been made of those interactions between holes and electrons which influence the solubilities of donors and acceptors in semiconductors. The major portion of the work concerns the solubility of lithium in silicon doped to varying degrees with boron. This solubility increases with increasing boron content in a manner predicted by theory and exhibits the expected temperature dependence. A qualitative experiment in germanium is described which demonstrates, in accordance with theory, that doping with a donor decreases the solubility of another donor. SEVERAL authors have discussed the possibility that holes and electrons behave like chemical entities and influence the solubilities of ionized impurities, Wagner was the first to invoke this concept in connection with his studies on nonstoichio-metric oxides. He used it again in explaining the solubility of hydrogen in molten binary alloys. In a theoretical paper,' Reiss drew attention to the fact that solutions of impurities in semiconductors

Jan 1, 1957

By K. K. Clark

Excessive injection pressures in water injection wells may create deeply penetrating fractures, or may open up existing reservoir fractures. If these fractures are oriented toward offset producing wells, oil recovery at injected water breakthrough and ultimate recovery will be impaired. A method of calculating fracture lengths from pressure fall-off test data is presented. The method is based on a linear flow model that simulates conditions present during the early-time period after shutting in an injection well. Fracture lengths can be calculated directly if formation permeability is known. A graphical technique is presented that provides fracture lengths based on permeabilities calculated from normal fall-off tests, where those permeabilities are adjusted for flow geometry. Test data from four injection wells and results obtained from applying the method to these wells are discussed. Introduction Rates of water injection into nonstimulated wells in low permeability reservoirs frequently fall below economically desirable levels. Therefore, some form of stimulation such as hydraulic fracturing often is performed on these wells. Usually these fractures penetrate a short distance from the well — short as compared with interwell spacing — and therefore should not create problems of water channeling to offset producing wells. In the past, some operators have been tempted to increase injection pressures continually to maintain a specified injection rate. But pressures cannot be increased indefinitely. Field data indicate that continued injection above fracture opening pressure can cause excessively long fractures to approach between well distances. If these long fractures intersect or closely approach offset producing wells, premature water breakthrough can result. It is difficult to seal effectively these fractures by various workover procedures after premature water breakthrough has occurred. This paper describes testing procedures that are potentially capable of detecting premature water breakthrough before it occurs. Knowledge of fracture lengths and fracture opening pressures can assist field engineers in selecting optimum operating conditions for water injection wells. Fracture lengths should be calculated from pressure fall-off tests on injection wells, and maximum permissible iniection pressures should be determined from step-rate injectivity tests. Equipped with this information, the field engineer is in a better position to recommend for a particular injection well the optimum operating conditions that will lessen the chances of channeling to offset producers. Historically, pressure transient tests have been conducted primarily on producing wells and analysis procedures have been based on radial flow concepts. Several authors have suggested that these same procedures be applied to tests conducted on water injection wells. This application is justified for wells that are not connected to extensive fracture systems. However, if the formation is severely fractured, the interpretation methods must be modified. Several authors have presented the pressure response of various systems that are intended to simulate reservoir conditions. A paper by Russell and Truitt* on vertically fractured svstems is probablv the most useful from the standpoint bf the fieid engineer. Russell and Truitt presented the pressure-vs-time behavior of a well connected to vertical fractures with various fixed lengths. Their permeability adjustment technique is used in this paper to refine methods of calculating fracture length and interwell permeability. Theory and Definitions Three flow-system geometries are considered in analyzing injection well test data. These various geometries are applicable during specific time intervals of transient pressure tests. Schematic drawings of the flow models, and the time intervals over which they are applicable, are shown in Fig. 1 in the chronological order that they are applied to the pressure response of water injection wells in fractured formations. The very early response is simulated by an infinite linear system as shown in Fig. 1A. This representation permits the calculation of matrix surface area exposed to the fracture. The model shown in Fig. 1B is identical with the one studied by Russell and Truitt. They evaluated the transient pressure response of this vertically fractured system by finite difference techniques. The results were presented as tabulations of dimensionless pressure drop functions for a range of fracture lengths. A semilog plot of these data shows that the apparent matrix permeability can be related to the true matrix permeability by a simple exponential function. Their adjustment factor is used in this paper to improve the accuracy of matrix-permeability and fracture-length calculations.

Jan 1, 1969

By Chung Yu Wang

MINING ENGINEERING presents the fourth in a series of articles on strategic minerals. Preceding it are "Cobalt" in January, "Sulphur" in May, and "Nickel" in August. Here, an authority in the field analyzes the resources, production, uses, defense impact and future outlook of Tungsten

Jan 10, 1951

By F. Twyman

PART I.-QUALITATIVE, SPECTRUM ANALYSIS THOSE chemists (they are still greatly in the minority) who use the spectroscope, use it very often, and find it almost indispensable. As a means of detecting minute quantities of the metals it is unrivalled. A metal can be readily distinguished in the presence of any other element, compound, or mixture without the necessity of separation. The qualitative analysis of the metallic constituents of a substance, which, the spectroscope gives so easily, is a sure basis for planning a chemical analysis. As the determination of each element proceeds the purity of precipitates maybe checked as often as desired. If, possessing these advantages; the spectroscope has been neglected in general chemistry, it is not surprising that it was neglected in metallurgical chemistry; for many of the impurities which are of industrial interest, even when they are present in a metal or alloy in small quantities, are not then always easily detected by the examination of their visible spectrum. The history of the development of the art has been given in Bureau of Standards Scientific Paper No. 444.

Jan 1, 1928

By H. D. Kynor

By the term mechanical mining is meant that operation, or series of operations, that replace the hand methods of mining. The first undercutting machine to operate in anthracite was placed in the Butler mine of the Hillside Coal and Iron Co., Dec. 23, 1910, by the Sullivan Machinery Co. The first Jackhamer used in the anthracite field was installed at the Wadesville colliery of the Philadelphia & Reading Coal and Iron Co. in Oct., 1912, by the Ingersoll-Rand Co. The first longwall conveyor was installed at the Dodge mines of the Delaware, Lackawanna, & Western Coal Co. in March, 1912. The first mechanical scraper equipment was installed in the Seneca mines of the Lehigh Valley Coal Co. in January, 1914. The amount of anthracite mechanically mined since the first mining machine was installed in 1910" is as follows: Penna. Coal Co. D. L. & W.. ScRanton Temple Hudson YeaR and Hill- Tons Coal Co., Coal Co., Coal Co., Total, side Coal Tons Tons Tons Tons and Iron. Tons 1920................ 372,737b 367,000d 322,892 74,127 371,878 1,508,634 1919................ 950,786 no record 306,616 81,575 319,356 1,658,333 1918................ 917,778 744,966 24,880 44,756 288,781 2,021,161 1917................ 757,940 838,800 5,050 57,279 164,180 1,823,249 1916................ 286,780 860,663 13,960 114,173 101,475 1,377,051 1915................ 428,819 592,169 8,253 1,029,241 1914................ 219,188 153,896 373,084 1913................ 171,505 1912................ 124,267 124,267 1911................ 40,319 40,319 1910................ 1,184 1,184 a A slightly greater production was obtained than here indicated, as the tonnage from individual operations is not shown. b Decrease due to strike conditions in 1920. c Does not include tonnage of D., L., & W. d D., L., & W. decrease in 1920 due to having fewer mining machines in operation. There are about 150 undercutters in use in the anthracite region, 80 mechanical loaders, and 10 longwall conveyors.

Jan 1, 1922

By C. R. Sandberg, N. Stein, L. D. Wiener, E. B. Elfrink

this paper presents the results of a study of the slip velocity of gases rising through liquids in vertical tubes, inclined tubes, and vertical annuli. The data were obtained in gas-liquid systems which included combinations of air, propane and natural gas (over 97 per cent methane) with water, lubricating oils, and crude oils. The 214 data points obtained in this study along with 11 data points reported in the literature are incorporated in an empirical correlation which relates the mean slip velocity of gases flowing through liquids with the parameters gas rate, tube size, ratio of liquid viscosity to liquid density, gas density, liquid density, and the angle of the tube from the vertical. The average numerical deviation of the measured slip velocity data from values obtained from the correlation is 9.2 per cent. The average algebraic deviation between measured and Predicted data is 0.31 per cent, an indication that the correlation is a satisfactory representation of the data. The correlation presented in this paper will be useful primarily in the design of subsurface gas-oil separation equipment for increasing the efficiency of oil-well pumping installations. but may perhaps be extended to other situations of gases rising through liquid columns. INTRODUCTION The production of oil by pumping is often complicated by the presence of free and dissolved gas in the oil at bottom-hole conditions. This gas can be drawn into the pump barrel and result in "vapor locking" the pump, thus reducing the efficiency of the pumping operation. Large amounts of free gas may be excluded from the pump by the use of a gas-anchor, which is designed to allow the separation of free gas from the oil before it is drawn into the pump. The design of a suitable gas-anchor depends on a knowledge of the difference between the velocity of the free gas and that of the oil as the oil travels down toward the pump intake. This rate of gas rise through the oil is termed "slip velocity." AS a first step toward the full understanding of this roblem, the mean slip velocities of gases flowing through static

Jan 1, 1952

By G. F. Tagg

In an earlier paper1, the author described a method of interpreting earth-resistivity curves, based on the theoretical investigation of a single horizontal underlying stratum. If the four-electrode system of Wenner is employed, the resistivity in a homogeneous soil is given by the formula where a is the electrode separation and R is the resistance of the earth between the two inner electrodes. If the earth is not perfectly homogeneous, the application of this formula gives an apparent specific resistance varying with the electrode separation. In the special case of the single horizontal underlying stratum, there is a surface layer of thickness h and resistivity p1 and a lower layer, extending to infinity, of resistivity pz. It has been shown by Lancaster-Jones2 that the apparent resistivity obtained by an application of equation 1 is related to the true resistivities, the depth h and the electrode separation a by an expression of the formhere pa is the apparent resistivity and F is a function (actually an infinite series), of the ratio h/a, and a reflection coefficient k = (p2 — p1)/(p2 + p1). For given values of h/a and k, the right-hand side of equation 2 can be calculated, and curves drawn showing the relationship between pa/p1, h/a and k. Such a set of curves for the case when p1 > p2 is given in Fig. 1. When pl is less than pz it is more convenient to use conductivity instead of resistivity. Hence, if oa = the apparent conductivity = lip, and a1 = the conductivity of the upper layer = l/pl, it follows that GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula

Jan 1, 1940

By G. F. Tagg

In an earlier paper1, the author described a method of interpreting earth-resistivity curves, based on the theoretical investigation of a single horizontal underlying stratum. If the four-electrode system of Wenner is employed, the resistivity in a homogeneous soil is given by the formula where a is the electrode separation and R is the resistance of the earth between the two inner electrodes. If the earth is not perfectly homogeneous, the application of this formula gives an apparent specific resistance varying with the electrode separation. In the special case of the single horizontal underlying stratum, there is a surface layer of thickness h and resistivity p1 and a lower layer, extending to infinity, of resistivity pz. It has been shown by Lancaster-Jones2 that the apparent resistivity obtained by an application of equation 1 is related to the true resistivities, the depth h and the electrode separation a by an expression of the formhere pa is the apparent resistivity and F is a function (actually an infinite series), of the ratio h/a, and a reflection coefficient k = (p2 — p1)/(p2 + p1). For given values of h/a and k, the right-hand side of equation 2 can be calculated, and curves drawn showing the relationship between pa/p1, h/a and k. Such a set of curves for the case when p1 > p2 is given in Fig. 1. When pl is less than pz it is more convenient to use conductivity instead of resistivity. Hence, if oa = the apparent conductivity = lip, and a1 = the conductivity of the upper layer = l/pl, it follows that GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula

Jan 1, 1940