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By Lincoln F. Elkins, John T. Cooke

Injection of gas to increase oil recovery has been considered for almost all important discoveries during the past ten or fifteen years. However, the number of gas injection projects having sufficient history and data is too limited to permit valid generalities of effectiveness of gas injection. Management and engineers are faced with a difficult problem of selecting those reservoirs which are susceptible to profitable application of gas injection. Injection of gas to maintain high pressure favors some factors affecting reservoir performance such as viscosity, surface tension, and formation volume factor of oil by keeping gas in solution and favors some operating features such as extending flowing life of wells and storing part of the produced gas for future use or sales. Injection of gas at low pressure involves lower compression ratio, or at least a single gas-gathering system, larger displacement volume in the reservoir per unit of gas handled, and permits effective utilization of the naturally existing energy and agent for oil displacement that is gas dissolved in oil. Each program is thus a compromise to meet optimum economic conditions while striving to attain maximum recovery of this important nautral resource. The statement has often been made that pressure maintenance would greatly increase oil recovery by permitting abandonment of formation oil inflated with gas in solution rather than abandonment of the same liquid volume of tank oil, if the same terminal oil saturation could be attained. Simple calculations indicate increases in oil recov- ery as high as one hundred per cent on this basis for high formation volume factor oil encountered in current deep drilling. Important in this statement is "if the same terminal oil saturation could be attained." Implicit in this statement are the requirement of physical

Jan 1, 1949

By John T. Cooke, Lincoln F. Elkins

Injection of gas to increase oil recovery has been considered for almost all important discoveries during the past ten or fifteen years. However, the number of gas injection projects having sufficient history and data is too limited to permit valid generalities of effectiveness of gas injection. Management and engineers are faced with a difficult problem of selecting those reservoirs which are susceptible to profitable application of gas injection. Injection of gas to maintain high pressure favors some factors affecting reservoir performance such as viscosity, surface tension, and formation volume factor of oil by keeping gas in solution and favors some operating features such as extending flowing life of wells and storing part of the produced gas for future use or sales. Injection of gas at low pressure involves lower compression ratio, or at least a single gas-gathering system, larger displacement volume in the reservoir per unit of gas handled, and permits effective utilization of the naturally existing energy and agent for oil displacement that is gas dissolved in oil. Each program is thus a compromise to meet optimum economic conditions while striving to attain maximum recovery of this important nautral resource. The statement has often been made that pressure maintenance would greatly increase oil recovery by permitting abandonment of formation oil inflated with gas in solution rather than abandonment of the same liquid volume of tank oil, if the same terminal oil saturation could be attained. Simple calculations indicate increases in oil recov- ery as high as one hundred per cent on this basis for high formation volume factor oil encountered in current deep drilling. Important in this statement is "if the same terminal oil saturation could be attained." Implicit in this statement are the requirement of physical

Jan 1, 1949

By K. E. Brown, J. P. Brill, T. C. Doerr

A wide range of intermittent gas-lift tests way conducted in a 1,500-ft experimental well through 11/4- and 11/2-in, nominal size tubing. The well was equipped with two gas-lift valves, four Maihak electronic pressure transmitters and surface facilities to measure casing and tubing pressures, temperature, liquid production and the rate and volume of gas injected. For each tubing size, tests were conducted varying the slug length, gas volume injected and liquid viscosity and surface tension. From these tests, an empirical "fallback" or liquid loss correlation has been developed. No general fallback correlation could be obtained, and the correlation is presented in the form of one curve for each slug length of a given liquid and lubing size. A conceptual model has been developed which combines the fallback correlation with equarions which govern liquid slug pow. A mathematical simulation of the model in the form of a digital computer program is used to calculate total recovery, gas volume used and clearance time for a given test. Tubing pressures at the gas-lift valve and at the gm-slug interface are calculated as a function of time. Tubing pressures at the surface during slug clearance ore also calculated. The results compare favorably with the test data and verify the conceptual model. The extent to which the model can be used for other tubing sizes, depths, liquids and gas-lift valves can only be determined with additional experimental data. Data are also necessary so that a fallback curve can be constructed for the particular test conditions studied. INTRODUCTION The flow of liquid slugs in vertical conduits has long been an established production method in the petroleum industry. Under the name "intermittent gas lift", many advances have been made in engineering design. However, the unsteady-state nature of liquid slug flow has discouraged attempts to describe the problem analytically. The result has been that intermittent gas lift is dominated by rules-of-thumb engineering practices developed over many years. The advent of slim-hole completions has increased the demand for a more rigorous solution to the intermittent problem. Small-diameter conduits offer more frictional per intermittent cycle. Small-diameter conduits are defined to be 1%-in. nominal size tubing or smaller. When oil is produced from the reservoir in which it is found, and transported to surface tanks by intermittent gas lift, three separate flow stages are encountered: flow of the fluids to the wellbore through a porous medium, vertical flow of a liquid slug from the point of gas injection to the surface, and horizontal flow of the liquid slug through the surface flowlines from the wellhead to the surface tanks. The three stages are depicted schematically in Fig. 1. The present study deals with liquid slug flow in both the vertical and horizontal conduits, ending when the bottom of the liquid slug reaches the surface. Due to the large number of variables involved, the analytical study of intermittent gas lift is extremely complex. The possibility of flow regimes other than slug type, the nature of the force fields acting on the system, the interfacial instabilities involved, the varying operational principles of existing gas-lift valves and the complete unsteady-state nature of the physical phenomena occurring in an intermittent gas-lift cycle relate some of the difficulties encountered.

By T. E. Leontis

ONLY a limited amount of information has been published on the effect of thorium as an alloying ingredient in magnesium. McDonald13'2 showed that the addition of thorium in amounts up to 3 pct increases significantly both the ductility and the strength of rolled magnesium sheet. A recent publication by Sauerwald" indicates that thorium contributes strength and creep resistance at elevated temperatures to magnesium in both the cast and wrought states. The observations of Sauerwald are confirmed in this paper, which presents the results of a systematic study of the effects of compositional variation on the tensile properties, creep resistance, conductivity, density, and metallography of Mg-Th alloys containing up to 50 pct Th both in the sand-cast and in the extruded states. The effect of the addition of cerium to Mg-Th alloys is also reported. Experimental Methods The alloys studied in this investigation were pre.pared in small laboratory melts according to the melting practice described by Nelson4 as the crucible method. Electrolytic magnesium was used as the starting material to which the thorium* was introduced in metallic form. It was observed that the behavior of thorium in molten magnesium with respect to reaction with protective fluxes is similar to that of rare-earth metals. In order to obtain the highest possible alloying efficiency, it is necessary to use non-MgC1, fluxes and to apply all the precautions described by Marande6 for melting, alloying, and casting magnesium-rare-earth alloys. .Under these conditions it is possible to obtain an alloying efficiency in the range of 85 to 95 pct. The Mg-Th-Ce alloys were made with cerium of the highest purity available, not with the commercial product "misch-metal" which contains approximately 50 pct Ce. The total rare-earth content of this material was 97.1 pct, of which 0.3 pct was rare-earth metals other than cerium; the major impurities comprising the balance were iron and magnesium. The thorium and cerium contents of each alloy were determined chemically. Test bars 6% in. long with a 2% in. long reduced section of % in. diam were cast in sand molds using a four-baf pattern. In most cases, a 3 in. diam extrusion billet 10 in. long was cast in a steel mold from the same melt used for making the sand-cast test bars. For the higher thorium alloys, it was necessary to remelt the foundry scrap from the test bars in order to make the extrusion billets. The billets were scalped to a diameter of 2 15/16 in. and the ends faced to a length of 9% in. as limited by the size of the extrusion container. The alloys were extruded into % in. diam rod on a 500-ton direct-extrusion press. The details of the extrusion process are as follows: Billet preheat 925°F (2 to 16 hr) Container temperature 900 °F Die temperature 900°F Extrusion speed 10 ft per min Reduction ratio 36:1 Percent reduction 97.3 Alloys containing up to 10.2 pct Th were preheated at 925°F for 2 hr; all alloys with higher thorium contents were preheated for 16 hr. In order to establish the effect of extrusion temperature, billets of

Jan 1, 1953

By M. J. Sinnot, J. C. Shyne

Low-frequency mechanical damping measurements were made to investigate internal friction in Fe-A1 alloys. The atomic ordering of the Fe-A1 system strongly influenced the stress-induced ordering internal friction. Magnetoelastic damping was also encounteyed and was shown to be reduced by the application of a static stress. THIS paper describes some damping experiments made on alloys of Fe and Al. Stress-induced ordering internal friction was measured with samples containing from 9.8 to 31.3 at. pct Al. Aluminum is soluble in a-Fe to about 50 at. pct and forms at least two long-range ordered structures, Fe3Al and Feu.' Stress-induced ordering internal friction is known to occur in many substitutional solid solutions, but few measurements of this damping effect have been made with alloy systems that have pronounced ordering tendencies. LeClair and Lomer developed expressions relating the relaxation strength of the damping process to the degree of atomic ordering and predicted that stress-induced ordering internal friction would be zero with complete ordering.' This concept was confirmed experimentally by Lulay and Wert using the system cd-Mg It is also consistent with the weak stress-induced ordering peaks observed in P -brass by Artman and in 16 wt pct Al Fe-Al by bert.' It was expected, therefore that the ordering characteristics of the system Fe-Al would strongly influence the stress-induced ordering internal friction exhibited by the experimental alloys. SAMPLE PREPARATION The alloys used in this investigation were induction melted under vacuum using high-purity melting stock. The iron was electrolytically refined Plastiron 101 which contained 99.85 wt pct Fe. The aluminum was a special 99.95 pct pure grade supplied by Alcoa. The only other raw material was spectrographically pure graphite which was used in small quantities as a deoxidant. The amount of carbon used was slightly in excess of the amount required to completely deoxidize the melt; this resulted in residual carbon contents of 0.01 to 0.02 pct in the finished alloys. The vacuum cast 2 1/2-in. diam ingots were hot rolled to 5/8-in. diam round bars. Portions of these bars were hot swaged and hot drawn to 0.050-in. diam wire. Straight pieces of the hot drawn wire were slowly heated to a temperature of 1300°C in a He atmosphere. After holding for 4 hr, the samples were allowed to cool in the furnace. This annealing treatment resulted in grain growth in the samples, the final grain size being about the same as the wire diameter. The grain boundaries were oriented perpendicularly to the wire axis, giving a bamboo grain structure. The existence of a preferred orientation could not be detected in these coarse grained samples. If the samples had a fiber structure, this probably would have been the same in all samples because of similar processing, thus the influence of crystal orientation on the relaxation strength would have been similar in all samples. The aluminum contents of the alloys are listed in Table I. EQUIPMENT The principle of the torsion pendulum was used for the internal friction measuring device. The

Jan 1, 1961

By Harold B. Fell

MANY oil producers are in disagreement with the idea held by some that an increase in the price of crude oil would be unlikely to stimulate much production and that we will be obliged to draw upon foreign sources of petroleum to supplement our domestic production as the years go by. Supporting our con trary opinion are numerous facts and figures. The most recent official estimate of the maximum efficient rate of production from the oil wells of the United States is 5,271,000 bbl per day. The Economics Advisory Committee of the Interstate Oil Compact Commission estimates, assuming certain supplies from imports and from natural gasoline and benzol, that crude oil require-

Jan 1, 1947

By R. J. Schilthuis

In 1929, Coleman, Wilde, and Moore1 undertook an investigation of the theoretical decline in reservoir pressure as related to the production of oil and gas. The most important part of this work was presented in an equation defining the relationship between the reservoir pressure, the quantities of oil and gas produced, the oil and gas content of the reservoir, and the properties of the reservoir fluids. With this equation, it appeared that, with sufficient data, it would be possible to calculate the oil content of the reservoir and predict quantitatively the effect of gas-oil ratio on the decline of reservoir pressure. Needless to say, such an expression would be highly important in evaluating fields and in arriving at a choice of production methods to be used. Unfortunately, at the time these investigators published their work, there were not sufficient data available to permit application of the equation. The technique of measuring reservoir pressures had not been developed, gas measurements were uncommon, oil and water production records were in most cases inadequate, and little was known of the properties of the complex hydrocarbon mixtures making up the oil and gas in the reservoirs. For these reasons, little additional work of a similar nature could be done. However, during the past four years many data have been systematically accumulated on reservoir pressures and the properties of oil and gas, and it is now possible to use these data in furthering the studies on the behavior of oil and gas reservoirs. It is the purpose here: first, to present the derivation of a modified form of the equation given by Coleman, Wilde and Moore, which will permit the calculation of what later will be defined as the "active oil" content of a reservoir; second, to derive formulas for calculating the reservoir-energy changes that occur during the course of production, and finally, to discuss the limitations and application of the equations developed.

Jan 1, 1936

By R. J. Schilthuis

In 1929, Coleman, Wilde, and Moore1 undertook an investigation of the theoretical decline in reservoir pressure as related to the production of oil and gas. The most important part of this work was presented in an equation defining the relationship between the reservoir pressure, the quantities of oil and gas produced, the oil and gas content of the reservoir, and the properties of the reservoir fluids. With this equation, it appeared that, with sufficient data, it would be possible to calculate the oil content of the reservoir and predict quantitatively the effect of gas-oil ratio on the decline of reservoir pressure. Needless to say, such an expression would be highly important in evaluating fields and in arriving at a choice of production methods to be used. Unfortunately, at the time these investigators published their work, there were not sufficient data available to permit application of the equation. The technique of measuring reservoir pressures had not been developed, gas measurements were uncommon, oil and water production records were in most cases inadequate, and little was known of the properties of the complex hydrocarbon mixtures making up the oil and gas in the reservoirs. For these reasons, little additional work of a similar nature could be done. However, during the past four years many data have been systematically accumulated on reservoir pressures and the properties of oil and gas, and it is now possible to use these data in furthering the studies on the behavior of oil and gas reservoirs. It is the purpose here: first, to present the derivation of a modified form of the equation given by Coleman, Wilde and Moore, which will permit the calculation of what later will be defined as the "active oil" content of a reservoir; second, to derive formulas for calculating the reservoir-energy changes that occur during the course of production, and finally, to discuss the limitations and application of the equations developed.

Jan 1, 1936

By O. B. Buchlen, J. W. Smith

The Coal Research Bureau of the School of Mines at West Virginia University, using an experimental flotation cell designated an airlift-cyclone was able to obtain a clean coal product containing 7.64% ash with 94% yield and 97% coal recovery. This favorable performance was obtained with the experimental flotation cell operating as a simulated three-stage unit on slurry taken from the fine coal circuit of a coal preparation plant. This experimental device, consisting of a sheet metal cyclone-like unit mounted on a U-shaped uplift pipe, uses a combined flotation and cyclone action to beneficiate the minus 14 mesh partially cleaned feed product. In addition to providing comparable analytical results, the airlift-cyclone possesses other attractive features among them being a low capital expenditure, utilization of moderate plant floor space, efficient operation on high density feed slurry, and absence of moving parts. The primary shortcoming of the experimental cell is its limited capacity. The Coal Research Bureau presently has under construction a larger unit which, it is hoped, will provide the capacity and quality to establish the airlift-cyclone as a commercially feasible unit. Froth flotation of fine coal is a practice which has only recently gained wide acceptance in this country. Various explanations can be put forth for this delayed acceptance of a very selective and efficient system of coal preparation. Among these reasons would be the advent of continuous mining machines resulting in the increased production of coal fines, the change in market patterns from domestic and rail consumers who did not want fines to a predominantly utility market which normally consumes fines, and also the imposition of legal restrictions in regard to stream pollution. However, the major detriment is probably the high cost involved both in installation and operation of the flo- tation unit and auxiliary systems. These facts assume greater emphasis when considering that froth flotation installations normally process a low quality feed product. A recent estimate' of installation costs including dryers, filters, and other auxiliary equipment for a flotation system was $5000 to $7000 per ton of capacity while the operating costs, exclusive of auxiliary equipment, were estimated at 10 to 306 per ton of feed. The Coal Research Bureau of the School of Mines at West Virginia University is currently developing a simplified froth flotation cell, designated an airlift-cyclone, which may provide considerable savings in capital and operating costs without sacrificing product quality or recovery. This experimental cell consists of three primary components: 1) a vertically mounted U-shaped pipe; 2) an air injector device; and 3) an integrally mounted cyclone-like unit (Fig. 1). A feed slurry is introduced at the top of one leg of the U-pipe while compressed air is injected near the base of the other leg. The air serves both to aerate the pulp and to cause it to flow upward into the base of the cyclone unit where the floated clean coal is separated from the reject material and unfloated coal which remains in slurry. The Coal Research Bureau's experimental airlift-cyclone is somewhat similar in principle to a flotation device developed by Russian engineers in the late 1950's. In tests upon a two-stage pilot-size device, the Russians obtained very favorable cleaning efficiencies.' However, later experience with production models demonstrated that rated capacities and acceptable product quality could not always be maintained.3 Because of these limitations, Russian engineers subsequently recommended that conventional, mechanical cells be used when cleaning difficult to float slurries. Engineers at the Coal Research Bureau felt that such a device utilizing the combined actions of a cyclone and a froth flotation machine offered numerous attractive features and merited investigation. Accordingly, a small capacity experimental airlift-cyclone was designed and, with the permission of the Christopher Coal Company Div. of Consolidation Coal Co., installed in Christopher's Humphrey preparation plant near Morgantown, West Virginia.

Jan 1, 1964

By Kenzo Ikeda

The Kosaka smelter is situated in the extreme northern end of Hondo (the main island of Japan) 15 mi. east of Odate, on the government railroad, to which it is connected by a private railway. It contains ten blast furnaces having a maximum daily capacity of 1600 short tons of ore, conducting a slow pyritic smelting entirely without coke or limestone, and with a charge carrying over 50 per cent. of briquetted and agglomerated fines. The matte (35 per cent. Cu) is blown in two basic-lined barrel converters, the blister copper (98.8 per cent. Cu) being cast at once into anodes. The adjoining refinery contains 600 tanks with a maximum capacity of 1300 tons of cathodes per month, the byproducts being gold, silver, and bismuth. At present, working at about half capacity, the whole plant consumes 2000 kw. of hydro-electric power, and employs 850 men and women. The ores are derived from two principal sources: The relatively new Hanaoka mine, 20 mi. from the smelter, yielding copper pyrites by underground mining, and the old Kosaka open-cut mine, 1 1/2 mi. from the smelter, yielding three different ores: (a) kuromono, a compact finegrained mixture of barite (32 per cent.), zinc blende, galena, and pyrite, the whole carrying about 2.5 per cent. Cu; (6) cupriferous pyrites with 2.4 per cent. Cu; (c) siliceous ore with 2 per cent. Cu. The Hanaoka ore now constitutes approximately one-half of the charge, almost replacing the Kosaka kuromono which was the ore chiefly smelted until 1913.'

Jan 1, 1923

By Kenzo Ikeda

The Kosaka smelter is situated in the extreme northern end of Hondo (the main island of Japan) 15 mi. east of Odate, on the government railroad, to which it is connected by a private railway. It contains ten blast furnaces having a maximum daily capacity of 1600 short tons of ore, conducting a slow pyritic smelting entirely without coke or limestone, and with a charge carrying over 50 per cent. of briquetted and agglomerated fines. The matte (35 per cent. Cu) is blown in two basic-lined barrel converters, the blister copper (98.8 per cent. Cu) being cast at once into anodes. The adjoining refinery contains 600 tanks with a maximum capacity of 1300 tons of cathodes per month, the byproducts being gold, silver, and bismuth. At present, working at about half capacity, the whole plant consumes 2000 kw. of hydro-electric power, and employs 850 men and women. The ores are derived from two principal sources: The relatively new Hanaoka mine, 20 mi. from the smelter, yielding copper pyrites by underground mining, and the old Kosaka open-cut mine, 1 1/2 mi. from the smelter, yielding three different ores: (a) kuromono, a compact finegrained mixture of barite (32 per cent.), zinc blende, galena, and pyrite, the whole carrying about 2.5 per cent. Cu; (6) cupriferous pyrites with 2.4 per cent. Cu; (c) siliceous ore with 2 per cent. Cu. The Hanaoka ore now constitutes approximately one-half of the charge, almost replacing the Kosaka kuromono which was the ore chiefly smelted until 1913.'

Jan 1, 1923

By J. B. Goddard

Crystallization of ammonium paratungstate (APT) is frequently the last effective purification step in producing high-purity tungsten. However, crystallizer mother liquors are often several times higher in tungsten than predicted by the solubility of APT. The formation of heteropoly anions, particularly those containing phosphorus and silicon, is largely responsible. Solubility of tungsten in APT mother liquor can be linearly correlated with the concentration of these and other impurities. The problem can be overcome by direct treatment of the crystallizer feed solution with aluminum sulfate. By appropriate treatment, the aluminum hydroxide flocculates and is easily filtered, resulting in a purified low-aluminum crystallizer feed from which high APT yields can be attained.

Jan 1, 1985

By R. N. Hoffman

A new technique for determining capillary pressure curves has been developed and tested. The technique differs from previously reported centrifuge techniques in that the centrifuge is slowly accelerated from zero to the maximum desired speed rather than being held constant at particular, progressively higher speeds. An important advantage of this technique over other methods of determining capillary pressure curves is the short time required to obtain the desired amount of data over the chosen pressure range. For example, to obtain 30 data points between 1.2 and 104 psig with a 1.55-in. long, 3/4-in. diameter core using a brine-air system, 6.6 hours were required with this technique. An equally important development of this paper is an analytic method for the conversion of the data from the centrifuge experiment to capillary pressure curve data. Previously there has been only an approximate conversion available. Although the capillary pressure curves determined by this technique appear to be as accurate as those determined by other techniques, the accuracy could be improved if certain variables, not treated in this experiment, were investigated. Among these are the dynamic distortion of the centrifuge equipment and imperfect initial saturation of the cores. INTRODUCTION Pirson 1 defines capillary pressure in a porous medium as "the differential pressure that exists between two fluid phases at their interfaces when they are distributed under static equilibrium within a porous material". Capillary pressure in rocks is known to be a function of fluid saturation, among other things, and a capillary pressure curve is defined for the purposes of this paper as a plot of the capillary pressure-wetting phase saturation relationship for a particular rock sample. Several methods are used for determining capillary pressure curves for small rock cores. Prominent among these are the semi-permeable barrier, mercury injection, and, to a lesser extent, centrifuge methods. The semi-permeable barrier method is currently the most popular. It features simplicity in both execution and the mathematical conversion of the experimental data into a capillary pressure curve. The main disadvantages of the semi-permeable barrier method are the time required — as long as two months — to obtain several points for the curve, and a fairly low maximum pressure before breakthrough of the non-wetting phase into the barrier occurs, for example, about 32 psig for a brine-air system. It is for these reasons that other methods such as the centrifuge method have been introduced. High accelerations and the absence of a barrier result in quicker attainment of saturation equilibrium at a given pressure. However, the centrifuge method involves much more expensive equipment and more difficult procedures and calculations than does the barrier method. The purpose of this investigation has been to improve the equipment and procedures of the centrifuge method and to develop an analytic method for the conversion of the experimental data into a capillary pressure curve. Hassler and Brunner did the original work in the determination of capillary pressure using a centrifuge. In their work the centrifuge speed was increased in a step-wise manner, each speed being held constant until saturation equilibrium was reached in each core. Saturation equilibrium was indicated when the volume of liquid collected in the graduated pipette of the core holder remained constant. According to Hassler and Brunner, equilibrium was reached in "a few minutes to one-half hour or more". In the centrifuge method, as opposed to the barrier method, the fluid saturation of the core is not a constant throughout the length of the core, but varies with the radius of centrifugation. Also, the capillary pressure cannot be read directly but must be calculated from a knowledge of the centrifuge speed and other parameters. For these calculations, Hassler and Brunner derived the following equations:

By S. E. Szasz, E. J. Moore, B. F. Whitney

An accurate value of formation water resistivity R, is essential in calculating formation porosity and fluid saturation from electrical well logs. In the cases where R, has not been measured directly, it must be obtained from other data, e.g., the SP curve. This paper deals with another approach: how to calculate R, from the chemical analysis of the formation water. INTRODUCTION It is known that the resistivity of aqueous solutions of pure salts depends on their concentration and on the temperature; the concentrations are given in MPL (mg of solute per liter of solution), or sometimes in ppm (mg of solute per kg of solution): MPL = ppm X specific gravity. Values for different pure salts are available in the literature, but not for solutions of mixtures which are of practical interest. The major component of the dissolved material in almost all formation waters being sodium chloride, it is customary to express the resistivity of formation waters in terms of equivalent sodium chloride concentration, i.e., the concentration of a solution of pure NaCl which has the same resistivity at a given temperature as that of the formation water under consideration. Thus, the problem of calculating R, from the chemical anaylsis can also be stated as how to convert the other constituents of the solute into equivalent NaCl concentration. Salts dissolved in water are at least partly dissociated into ions, and do not conserve their identity. If known amounts of several salts are dissolved in water, the solution does not necessarily contain the same salts in the original proportion, but perhaps some other combination of the ions, along with free ions in solution. This is why the chemical analysis of formation waters is often given in terms of ions, as if all dissolved salts were completely dissociated. Our problem then boils down to how to convert the concentrations of the various ions to equivalent concentrations of Na' and C1-. Dunlap and Hawthorne' have proposed to convert the concentration of all other ions to equivalent Na' and C1-concentrations by means of constant multipliers; e.g., 0.95 for Ca"; 2.0 for Mg"; 0.27 for HCO 3-; 0.5 for SO, -, etc. Their factors were based on measurements made at 68F on 26 formation water samples from the Texas Gulf Coast, ranging in concentration from 1,500 to 75,000 ppm. The Dunlap method is widely used in electric log interpretation, and is often extrapolated beyond its original concentration range. A comparison of R, values calculated by this method and values actually measured on formation water samples has shown large discrepancies, especially at higher concentrations. Therefore, two new methods were developed at Sinclair Oil Corp.'s Tulsa Research Center to calculate equivalent sodium chloride concentration from the chemical analysis of formation water samples. FUNDAMENTAL CONSIDERATIONS The resistivity of a solution, or its reciprocal the conductivity, at a given temperature is determined by the charge, concentration and mobility of the ions actually present. Monovalent ions such as Na' or C1- always carry the same charge. Compounds of polyvalent ions, however. may show incomplete dissociation, e.g., NaSO; + Na' instead of SO,-- + 2Na'. This happens especially in more concentrated solutions. Only very dilute solutions are completely dissociated, as assumed in the chemical analysis report. At higher concentration, the degree of dissociation depends not only on the nature and concentration of the particular salt under consideration but also on the nature and concentrations of the other solutes. Mobility of the ions depends on the viscosity of the solution. It also depends on the degree of hydration of the ions, which in turn is a function of the nature and the charge of the ions and also of the amount of free water available per ion, i.e., the total ionic concentration. The net effect is that the conductivity increases slower than proportional to the concentration, even if a solution contains only one salt such as NaC1, and is different for different salts (Fig. 1). Conductivity can even decline with a further increase in concentration, e.g., if additional salt is little dissociated but ties up some of the free water and/or causes an increase in viscosity. In solutions containing more than one salt, the contribution of one salt to the total conductivity depends not only on the fractional concentration of this same salt, but also on the concentration of all other solutes. A perfect method would give the conductivity or resistivity of a solution as a function of the concentrations of all solutes present. This is so complicated as to be impractical, and a simpler method must be found which is of acceptable accuracy. The Dunlap method, on the other hand. is too simple because it askmes that at any concentration the contrih-

Jan 1, 1967

By J. L. Kenty, J. P. Hirth

The concept of a critical super saturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, is discussed with reference to vapor-solid nucleation. The necessary and sufficient conditions deduced for observations of this type of behavior are: 1) the nucleation rate must exhibit a sharp dependence on super saturation, 2) the growth rate must be sufficiently large that nuclei become observable in the time period of the experiment, and 3) the number of highly preferred nucleation sites must be small. Experiments reveal that the nucleation of silver on sodium chloride is visually detectable at all experimentally accessible super saturations and does not exhibit critical nucleation behavior. Failure to observe a critical super saturation is attributed to the insensitivity of nucleation rate to supersaturation as a consequence of the particular values of the contact angle and the surface free energy for this system. THE concept of a critical supersaturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, arises naturally in homogeneous nucleation theory. Experimentally this type of behavior has been found by Volmer1 and others for water and other low surface tension liquids, as reviewed by several authors.2'3 The same type of behavior has been predicted and observed for heterogeneous nucleation of solids by Yang et al.4 and others,596 as also recently reviewed.2,7,8 In the work reported here on the heterogeneous nucleation of silver on NaC1, however, no critical super-saturation was found. Similar observations have been made recently for other systems.9-11 These results led to a reexamination of nucleation theory which revealed that there are conditions for which critical behavior is not predicted, either for homogeneous or heterogeneous nucleation. Although heterogeneous nucleation is of primary importance in this paper, some insight into critical behavior for such a case can be gained by considering homogeneous nucleation. Accordingly both types of nucleation theory are reviewed briefly. The requisite conditions for critical supersaturation behavior are then considered. The experimental results for the nucleation of silver on NaCl are presented and interpreted in terms of the theoretical presentation. REVIEW OF NUCLEATION THEORY There are essentially two approaches to nucleation theory, the so-called classical theory involving the concepts of bulk thermodynamics, and the statistical mechanical theory in which nuclei are regarded as macromolecules. The classical theory is based on the work of Volmer and Weber12,13 and Becker and. Doring14 and has been extended by Pound et al.15 The crucial assumption in the classical theory is that the small clusters or nuclei can be characterized by the same thermodynamic properties as those of the stable bulk phase. Thus, the nuclei are assumed to have a surface free energy, y, and a volume free energy of formation (relative to the vapor phase), ,, identical to that of the bulk. For deposition under low super-saturation conditions, the nuclei are large and this assumption is satisfactory. However, in many cases of interest, the nuclei contain only a few atoms and this assumption is highly questionable. The statistical mechanical models originated, for the specific case of a dimer as the critical nucleus, with the work of Frenkel16 and were extended later to larger sizes by Walton,17,18 Hirth19 and, more recently, Ht Zinsmeister. These models describe the nucleus in terms of a partition function, the estimation of which is tractable for clusters of 2 to 10 atoms, but extremely difficult for clusters larger than 10 atoms. Although the classical and statistical mechanical models are expected to apply for the limiting cases of large and small nuclei, both are uncertain for intermediate sizes. In this paper we shall treat only the classical model, recognizing that it is exact only for large nucleus sizes and regarding it as a phenom-enological description for small nucleus sizes. When analyses of experimental data using bulk properties show the nucleus size to be small, the resulting parameters should be regarded as largely empirical parameters describing the relative nucleation potency of the system. Considerable justification for the continued use of classical theory is provided by its general success in predicting nucleation behavior as a function of supersaturation and temperature. We emphasize that the qualitative features of the statistical mechanical models, particularly the critical super-saturation behavior that is central to the present work, are the same as those of the classical model. Of course, potential energy terms and surface partition functions replace the volume and surface energy terms of the latter model. The most recent versions of classical nucleation theory have been extensively reviewed.2,3,7 so that only the results are presented here. For homogeneous nucleation of a condensed phase from the vapor phase, the volume free energy change is ?Gv=vrT = =^ln£ [1] where v is the molecular volume of the condensing species. The supersaturation ratio,

Jan 1, 1970

By Erland Johnson

BRINE was discovered at Avery Island, La., in 1790, but it was not until 1862 that rock salt was found about 13 ft below surface-the first discovery of rock salt on the continent. Maximum elevation of the island is 152 ft and elevation at the shaft 31 ft. The mining level is 530 ft below elevation at the shaft and the shallowest salt about 12 ft below surface. A shaft was sunk in 1869 when the mining operation started. In 1898 the present shaft was sunk, and the mine has been operated by International Salt Co. ever since.

Jan 6, 1957

By David P. Hale

THE Cartersville barite district is near Cartersville, Ga., in the southeastern part of Bartow County, about 43 miles northeast of Atlanta. The area over which active mining is being done extends about six miles in a northeasterly direction and is about three miles wide. Barite production in Georgia began about 1907,1but the existence of the mineral was known much earlier. At present four companies are operating washing plants and three other plants are operating on leases from those companies. The chief impurities in the ores are silica and iron oxide. The silica is easily washed and jigged out and gives little trouble. Any gravity separation between the iron and the barite is generally poor, owing to the slight difference in specific gravity. Two operators have turned to magnetic separation as the solution to the problem and have made remarkable improvements in the finished product. By very close sizing prior to jigging, the separation between iron and barite has been greatly improved. In some localities manganese occasionally appears as an impurity, but is fairly easy to eliminate by gravity methods. A considerable percentage of iron and silica is eliminated by being broken free in crushing. Until methods for the recovery of fine ore were introduced a minimum of crushing was done, but modern methods allow more than formerly. The depression years brought about the need for increased recovery of ore handled on the part of the producers and a demand for a higher grade of product on the part of the buyers. Improvements in milling and mining practice have had a far greater effect, however, than merely the production of a better grade of ore with greater recovery. They have opened for mining large areas that a few years ago were considered noncommercial deposits because of their inaccessibility and their high iron content. It is no exaggeration to say that the new methods have more than doubled present known reserves of barite ore of economic value.

Jan 1, 1938

By J. L. Huitt, B. B. McGlothlin, D. K. Lowe

Published correlations for the principal aspects of hydraulic fracturing were combined into a digital computer program to facilitate the study of interrelated variables. The computer program includes individual relationships for fracture width during pumping, fracture area generated, propping agent embedment, flow capacities of propped fractures and transport of propping agents in horizontal fractures. The effects of more than 20 treatment and formation parameters on the predicted results of hydraulic fracturing treatments were studied. The effects of these parameters were determined for (I) fracture width during injection, (2) fracture width after the overburden comes to rest on the propping agents, assumed not to be crushed, (3) generated and propped fracture area, (4) location and concentration of propping agents in the fracture when injection ceases, (5) flow capacities of the various propped sections of the fracture and (6) expected increase in the well productivity. The effects of propping agent, formation and fracturing fluid parameters on well productivity are discussed. The parameters that were found to have the most pronounced effects on hydraulic fracturing treat~nents are injection rate, treatment volume, fracturing fluid coefficient, size and amount of propping agent, spearhead volume, well drainage radius and formation capacity. INTRODUCTION Many correlations have been published for predicting effects of various parameters that are considered in the design of hydraulic fracturing treatments. The Carter equation' can be used to predict generated fracture radius as a function of fracture width, fracturing fluid leakoff and other parameters. Fracture width can be determined by use of the Perkins and Kern correlation' in which the fracture width is related to the fracture radius, fluid injection rate and certain formation and fracturing fluid parameters. Wahl and Lowe et aL4 have reported methods of predicting the location of propping agents in fractures when pumping ceases. The former study is applicable to the case where the ratio of propping agent diameter to fracture width is less than 0.1. The latter is applicable when this ratio is greater than 0.1. These studies showed that the propping agent placement in horizontal-radial fractures depends principally on how the individual particles are transported in the fracture by the carrying fluid. Particle transport in fractures is determined by local fluid velocity in the fracture, fluid and particle properties, and the size of the particle relative to the fracture width. The distribution of propping agents, effective overburden pressure and formation rock strength control the propped fracture width6 by controlling the extent to which the propping agent particles embed into the fracture faces. From the distribution of propping agents and the propped fracture width, fracture flow capacities can be calculated or the various regions of the fracture. The flow capacities and the radial extent of these regions can be combined with reservoir information to predict the productivity increases for fractured wells. In all these studies, the effects of certain treatment and/ or reservoir parameters on one facet of fracturing can be predicted only if other facets which the parameters affect are fixed. For instance, fracture width and radius are interrelated; that is, to calculate the value of one, the value of the other must be known. Also, some parameters influence more than one aspect of fracturing. For example, prop-pant transport is a function of both fracture width and fluid viscosity. but fracture width is itself a function of fluid viscosity. Since these calculations are complex and the parameters interrelated, it is not possible to write an equation with which the over-all effects of treatment parameters can be solved explicitly. For these reasons, the correlations for determining the effects of the parameters which are most significant in hydraulic fracturing treatments have been incorporated into a digital computer program. COMPUTER PROGRAM The program, which was written for an IBM 7094 computer, can be used to predict results of most of the combinations and values for the treatment parameters that are ordinarily considered for fracturing treatments. A spearhead of fracturing fluid and a propping agent-carrying fluid with different fluid properties can be taken into account. Also, the total volumes and relative amounts of the spearhead and carrying fluids can be varied. Two different propping agents (as used in tail-in operations) and a wide range of formation properties and injection rates are considered. The computer program (Fig. 12) consists of several sets of calculations. First, the final flooded fracture radius and average fracture width at the cessation of pumping are calculated. This is done by simultaneous solution of the Perkins and Kern fracture width equation and the Carter equation for flooded fracture radius (equations used in the computer program appear in the Appendix). The next step is to determine local fluid velocity in the fracture as a function of time and radius. Since it is not possible to write this function in closed form expression, a table of velocity values is generated by the program and stored for subsequent use. The time span from the beginning of

TO THE BOARD OF DIRECTORS AND MEMBERS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS GENTLEMEN Submitted herewith are the report of the Treasurer for the year 1937 and the reports for the same year of the following standing committees: Admissions, Membership, Papers and Publications, Library, Student .Relations, Speakers for Local. Sections and Student Societies, and Mining and Metallurgy. To these reports members are referred for further details. Finances.-Income for the year was the largest since 1930, the figure being $189,394, an increase of $18,803 compared with income for 1936, exclusive of a special Rocky Mountain Fund appropriation of $2500 in that year for visits to western schools and Local Sections. Major items of increase were: $8,000 from current dues and arrears; $7,700 from advertising in MINING AND METALLURGY and the two periodical "Technologies"; and $4,800 from sales of TECHNICAL PUBLICATIONS (pamphlets) and TRANSACTIONS volumes for both current and former years. Initiation fees and clues from new members declined $2,300, principally because of the larger 'proportion of Junior Members to Members among the new enrollments. Junior Members pay no initiation fee and dues are $10 compared with $15 for Members.

Jan 1, 1938

By J. C. De Haven, Harry Seltz

INTERMETALLIC compounds are formed in many binary metal systems. Some compounds are stable to their melting points, and others decompose at lower transition temperatures. Even those of the first class are dissociated in the liquid state, as indicated by the continuous form of their solubility curves at their melting points'. While the lattice structures of some of these compounds' have been determined, their thermodynamic properties have not been investigated. In this paper is described the determination of the free energy and heat of formation of the compound CdSb, which is of the first class mentioned above, melting congruently at 455° C. This compound shows a rhombic structure, and the lengths of the edges of the elementary cell containing four molecules are: a = 6.52,b=8.60,c=4.16Å2 There are three possible methods of determining the free energy of formation of a compound of this type. The first method, applying the third law of thermodynamics, requires the measurement of its heat capacity preferably to liquid hydrogen temperatures, and a calorimetric determination of its heat of formation. The second method involves the study of the equilibrium of the compound in some gas reaction, such as: CdSb + CO2 = CdO + CO + Sb. From the known free energies of formation of, CdO, CO2 and CO the free energy of formation of CdSb could be calculated. The third method measures the electromotive force of a galvanic cell in which the cell

Jan 1, 1935