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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 E. R. Smith

ANALYSIS of the requirements for gun perforation equipment suitable for penetrating casing and cement showed that these points would be involved: (1) Powder charges electrically detonated under high fluid lieads and at remote distances. (2) Selective firing of sliots in sequence. (3) Sufficient velocity for the bullet to penetrate at least two strings of seamless casing and all cement beyond the strings. (4) Heat-treatment of steels to withstand great pressures and penetration. (5) Esclusiorl of fluid under extremely high hydrostatic pressure. (6) Stranded steel wire line acting as weight - suspending and current - carrying medium. (7) Firing controls operated above the surface. (8) Determining gun depth and suspended weight by means of the wire line. (9) Portability for field use.

Jan 1, 1936

By ELIHU THOMSON

IN 1877, Professor Thomson delivered at the Franklin Institute, [Philadelphia, five lectures on electricity. The object of the lectures and the demonstrations, which were numerous and many of them original even to the employment of special apparatus constructed by the lecturer, was to show clearly that electricity, of whatever name, was the same., differing only in tension (as it was termed) and in the current flowing, or quantity (the old term), in steadiness or in wave-like character. In those days, the textbooks divided the subject into statical and dynamic electricity, with sub-divisions such as frictional electricity, voltaic electricity, magneto electricity, electromagnetism, thermo electricity, and animal electricity. The well-known Ruhmkorff coil,' or spark coil as it is now called (as when used for the ignition of automobiles), was employed to step, up a battery current to a high-tension discharge which would charge condensers, such as Leyden jars.

Jan 1, 1921

By B. DE MARE

THE No. 6 open-hearth furnace at the plant of the Worth Steel Co., Claymont, Del., is the first to be rebuilt according to the Kuehn system. This as well as the other five furnaces at Claymont, has a nominal capacity of 75 tons, but the actual charge is about 242,000 lb. No hot metal being available, the pig-iron is charged cold. Oil of low grade with an asphalt base is used as fuel. These two items have to be kept in mind when discussing the actual fuel consumption. Careful records have been kept covering a five weeks run and the following is a brief summary of them The time required to heat the furnace preparatory to charging from the time a wood fire was started until charging commenced was 36 hours. This, I understand, is much less than with furnaces of standard design. The draft of the furnace, as shown by a gage in the stack-flue, is 1.25 in. The maximum draft with new checkers on former runs was 1.50 in., this draft gradu¬ally decreasing as the checkers closed up. Both of the first helpers claim the present draft is all they need for the proper working of the furnace, and, as with the Kuehn regenerators the draft remains practically the same from beginning to end of a run, this is satisfactory.

Jan 1, 1929

By H. Foster Bain

Steel for any large structure must be imported, the Hanyang works being entirely unable to supply local demand. The United States Steel Products Co. has warehouses and small stocks at Shanghai and at normal times there are heavy importations from Europe. It is difficult to obtain any accurate index of prices, but comparison of customs valuations with Pittsburgh quotations shows angles, bars and plates to have averaged $10 gold per ton higher in China in 1914, while on galvanized and tinned plates the excess was- $38 per ton. The margin since has been greater. Previous to the war little machinery was manufactured in China. There were shipyards at Shanghai and at Hong Kong which built a small number of engines, and small foundry and repair works are found at a number of ports. Their capacity was limited and the difficulties and delays incident to transport in China so numerous that in practice every important mine has a small foundry, boiler works, and machine shop. This must be taken into account in plans for work in the country. While skilled workmen can be found it is to be noted that most of them have been trained

Jan 1, 1921

By AIME AIME

ADDRESSING the Ohio Section at a recent meeting in Columbus, Ohio, R. C. Allen, executive vice-president for Oglebay, Norton & Co., Cleveland, spoke on "The Iron-Ore Industry of the Lake Superior Region in Prosperity and Depression." The speaker considered this region in connection with the problem of national security. This is the age of minerals; progress depends on them; and next to agriculture, the mineral industry is of prime importance. The United States has no shortage of minerals rather an over-supply; but many mines have been and are being exhausted. The shifting of the sources of supplies of minerals so important as copper, petroleum, and iron to other countries would create internal strains and affect international relations. There will be no early decline of ore mining in the Lake Superior region unless it is forced by unwise public policies. Iron ore is industrial strength and self-sufficiency. A study of economic geography is important for statesmen and mining men, because the minerals essential for peace and war are haphazardly or irregularly distributed throughout the world. Of these minerals, 75 per cent are owned by 10 per cent of the population, mainly peoples of Anglo-Saxon origin.

Jan 1, 1934

By David W. Brunton

FROM the old-fashioned " grab-sample " to the modern timing- . device, which takes a machine-sample with mathematical precision, there is a wide gap which was only crossed' by many years of toil and unremitting endeavor. Even to-day, notwithstanding the advancement in the art, "grab-sampling" is still practiced-sometimes to afford the unscrupulous mine-promoter a basis for fairy-tales with which to entrap the too-gullible investor, and often by milling and smelting companies to determine the amount of moisture in custom-ores. The latter practice is almost as reprehensible as the former, and it causes more trouble and ill-feeling between seller and buyer than all other factors put together. No reputable concern to-day would think of attempting to determine by grab-sampling the amount of gold, silver, lead, or copper contained in an ore, and yet many buyers expect the miner to accept the results of grab-sampling in the determination of the amount of water contained in the ore, forgetting that accurate results are just as necessary here as in the determination of the metals, because the result determines the percentage of weight of the ore which shall be excluded and considered to have no value whatever. Samples for the determination of moisture should be taken with as great care as samples for the determination of. metallic content, and in order to avoid the extra expense of a separate operation moisture-samples should be taken from the sample-safe. As the sample reaches the sample-bin in a smaller stream and by a more circuitous route than the "reject" travels in its path to the outgoing car, it loses more moisture en route, and a constant should be added to compensate for this difference. Carefully-conducted experiments have shown that the difference in loss of moisture between the two routes does not exceed 10 per cent. in summer and 7 per cent.. in winter. For instance,

Aug 1, 1909

By E. W. Henderson

Development work in the state of Utah in 1935 consisted of additional work done on wildcat tests started in previous years and on a number of new wildcat tests started during the year. No effort was made to extend areas or to discover deeper productive horizons in proven fields. Principal areas of development were in Daggett County, northeastern Utah; Grand and Emery counties, east-central Utah; and in Washington County, southwestern Utah. Daggett County Clay Basin.—The Mountain Fuel Supply Co. deepened Murphy No. 2, sec. 21, T.3N., R.24E., from 6030 to 6790 ft. for a test of the Sundance formation. Two sandstone members at 6520 to 6644 ft. and 6737 to 6790 ft. contained water. The hole was plugged back to 5860 ft. and left as a future gas supply for the Salt Lake City-Ogden pipe line. The failure of the Sundance formation to produce in this test, in view of the recent Sundance discoveries in Colorado arid Wyoming, was disappointing Emery County Last Chance.—-Thc wildcat test of the Rainsey Petroleum Corporn-tion, Well No. 1-X, sec. 18, T.26S., R.7E., completed plugging back from total depth of 3168 ft. to 2771 ft. and was shut in as a gas well. A gas sand at 2724 to 2771 ft. produced approximately 21 million cubic fert. A deep test of the structure will be started upon approval of a wit plan of development. Grand County Cisco.—-The wildcat test of the Utah Southern Oil Co., sec. 33, T.22S., R.22E., of which the total depth was 1720 ft. on Dec. 31, 1935, is the most interesting operation ill the state. Location of the test was deter-

Jan 1, 1936

By E. W. Henderson

Development work in the state of Utah in 1935 consisted of additional work done on wildcat tests started in previous years and on a number of new wildcat tests started during the year. No effort was made to extend areas or to discover deeper productive horizons in proven fields. Principal areas of development were in Daggett County, northeastern Utah; Grand and Emery counties, east-central Utah; and in Washington County, southwestern Utah. Daggett County Clay Basin.—The Mountain Fuel Supply Co. deepened Murphy No. 2, sec. 21, T.3N., R.24E., from 6030 to 6790 ft. for a test of the Sundance formation. Two sandstone members at 6520 to 6644 ft. and 6737 to 6790 ft. contained water. The hole was plugged back to 5860 ft. and left as a future gas supply for the Salt Lake City-Ogden pipe line. The failure of the Sundance formation to produce in this test, in view of the recent Sundance discoveries in Colorado arid Wyoming, was disappointing Emery County Last Chance.—-Thc wildcat test of the Rainsey Petroleum Corporn-tion, Well No. 1-X, sec. 18, T.26S., R.7E., completed plugging back from total depth of 3168 ft. to 2771 ft. and was shut in as a gas well. A gas sand at 2724 to 2771 ft. produced approximately 21 million cubic fert. A deep test of the structure will be started upon approval of a wit plan of development. Grand County Cisco.—-The wildcat test of the Utah Southern Oil Co., sec. 33, T.22S., R.22E., of which the total depth was 1720 ft. on Dec. 31, 1935, is the most interesting operation ill the state. Location of the test was deter-

Jan 1, 1936

By T. S. Washburn

THE grades of commercial steel produced in large quantities can be divided into two general types from the standpoint of ingot structure-killed and rimmed. Killed steel covers a wide variety with carbon contents throughout the range of the steel portion of the iron-carbon diagram, and is the kind usually used in the production of alloy steels. Rimmed steel is normally associated with carbon ranges under 0.30 per cent, and is not yet used to a large extent in alloy practice, except for copper-bearing steels. The fundamental differences in the ingots made from these two types of steel can be seen most easily in Figs. 1 to 7. In the rimmed ingot shown in Figs. 5 to 7 there are two lines of blowholes approximately parallel to the sides and coming together at the top and at the bottom of the ingot. In the killed ingots shown in Figs. 1 to 4 these blowholes are not present. Also, the rimmed ingot has no well defined pipe, as com-pared to the deep pipe on the killed ingots, and there are numerous pri-mary blowholes in the lower portion of the rimmed ingot perpendicular to the surface and close to it, while on the killed ingot there are no blowholes of this type in the ingot shown in Fig. 1 and very small ones close to the surface in the lower part of the ingot shown in Figs. 2 to 4. With respect to the presence of pipe and the primary blowholes, the structure may vary considerably in both rimmed and killed ingots, therefore these cannot be considered as fundamental structural characteristics differ-entiating the two types of steel. The primary blowholes in rimmed ingots may be much less pronounced than those in the ingot shown in Figs. 5 to 7-as, for example, in "ingot iron," which is entirely free from them. An example of a cross section of an ingot-iron ingot is shown on page 16 of "Research and Methods of Analysis of Iron and Steel," published by the American Rolling Mill Co. (1920). A certain amount of pipe may also occur in rimmed ingots, though it is normally porous and not as well defined or deep as in the killed ingot of Fig. 1. In killed ingots, pri-mary blowholes may occur near the surface, as in Figs. 2 to 4, and

Jan 1, 1937

By G. H. Kesler, C. E. Dryden, J. H. Oxley

Rates of heat- and mass-transfer from rods to recirculating air were determined within a one-quarter-scale model of a metals deposition bulb. The dependence of local and averaged rates of transfer upon outlet geometry, number of rods, position upon a rod, and airflow rate was established for flow patterns created by radial and tangential air inlets. The results are given a qualitative interpretation in terms of rates and distribution of metal deposition in a prototype deposition bulb. IT is well known that a number of metals can be prepared from volatile compounds containing them by causing dissociation of their compounds to occur at heated surfaces. Examples of such metals include silicon, titanium, zirconium, and aluminum, which can be prepared from their halides. While the ability to prepare high-purity metals by this technique is of importance in itself, the rate of deposition of metal also is important in considering the commercial potential of such a process. If the over-all process of deposition is broken down into separate steps of transport of materials to and from the heated deposition surface and establishment of chemical equilibrium at the surface, as was described in a recent paper,1 then since surface temperatures are usually high and surface equilibrium is attained very rapidly, the rate-controlling step can be considered as either that of transport of reactants to the surface or of transport of products other than deposited metal away from the surface. These two transport steps are related through the reaction stoichiometry. It can be shown1 that the rate and distribution of metal in such a transport-controlled process are determined by the over-all and local mass-transfer coefficients in conjunction with the equilibrium conversions at the hot surfaces. The rate relationship is: w = [KA(y a-y s)] B.E where the bracketed group is the rate of arrival of the reactant at the surface of area A as determined by the mole fraction driving force (y a - y s) and the convective transport constant K. The factor B is the weight fraction of metal in the reactant, and E is the equilibrium fractional conversion to metal. Numerical values of y, and y, are fixed by the vapor composition and the equilibrium compositim of reactant at the surface; and E can be determined by thermodynamic calculations or by experiment. However, values for the convective coefficient K are available generally only for systems of simple geometry, such as cross-flow past a rod or sphere or parallel flow past a flat plate or through a tube. Often it is necessary to work with systems of more complex geometry and in which the vapor flow may not be uniform or exactly parallel or perpendicular to the surface. It is possible, of course, to establish working correlations for these more complex systems by direct experiment; but the experiments usually are costly in both time and money. To circumvent this objection and to aid in arriving at an understanding of the relationships and interactions of the process variables, it is helpful to construct a model of the flow system in which air, water, or other convenient fluids can be substituted for the process vapors and with which mass-transfer measurements or analogous he at-transfer measurements can be made upon a simulated deposition surface. By this means, a large number of measurements can be made in a reasonable time, and the correlation of these results can be applied to the prototype system. Examples of the application of these techniques are to be found in the literature (e.g., Ref. 2). It is the purpose of this paper to illustrate these techniques by description of a model study which was done at Battelle Memorial Institute. The work to be described was of a preliminary nature; the investigation subsequently was extended to develop quantitative relationships among the significant dimensionless transport, geometric, and flow parameters. This more detailed study will be the subject of a future paper.

Jan 1, 1962

By Julien Deby

The sinking of a deep shaft is always a serious undertaking, especially when the strata to be traversed are of great hardness, or when they are feebly coherent or highly saturated with water. In the. first case, that of solid rock, modern appliances, such as the rock-drill, put into motion by air-compressors, along with suitable explosives, will generally answer the purposes of the mining engineer until he has reached the main water-levels. When these have

By AIME AIME

THE convention which met in Washington at the call of the Joint Conference Committee was called to order at ten o'clock on Thursday morning; June 3, by Richard L. Humphrey, temporary chairman, member of the American Society of Civil Engineers, who made a brief statement of the reason for the meeting. Lieut. Col. Charles W. Kutz, Corps of Engineers, U. S. A., and Engineer Commissioner of the District of Columbia, then welcomed .the engineers composing the convention on behalf of the District of Columbia and, the Washington engineers. Although an elaborate program had been prepared on which were many well-known speakers on interesting and important topics, , it was voted to intersperse this to fill in the usual and unavoidable hiatuses in the business program of such a convention[ Calvert Townley, president of the American Institute of Electrical Engineers, was elected permanent chairman, and J. C. Hoyt, of Washington, was elected secretary of the convention. The following committees were appointed: Consti¬tution and by-laws, Richard L. Humphrey, chairman; resolutions, Philip N. Moore, chairman; and program, F. H. Newell, chairman. Then, Gardner S. Williams, member of the, A. S. C. E. and the Grand Rapids Engineering Society of. Grand Rapids, Mich., and one-time member of the American Association of Engineers, offered the following resolutions:

Jan 1, 1920

By Nathaniel Hen

IN the United States, in the 2 1/2 years since the rescinding of the wartime order closing gold mines, conditions have not yet returned to normal. Shortages of man power have prevented some mines from operating at all, and most of those in operation are still at reduced capacity. This fact, combined with shortages of materials, the high cost of supplies and labor, high tax rates, and a fixed price for the product have made the past years rather rough ones for gold producers. In foreign countries conditions are rather similar. In Canada several new mines are coming into production and some others are enlarging. Costs have not increased as much as in the United States and gold production is being encouraged. Recently a bonus of 20 per cent on increased production has been proposed. In South Africa, where gold mining is of major importance in the national economy the industry is also in a favored position with government; new discoveries of major importance there will markedly increase the gold output. Demand for labor is rap-

Jan 1, 1948

By J. B. Gayle

PRESENT flotation processes depend almost entirely on the buoyant properties of air bubbles to effect separations of mineral and gangue, but there is no convenient method for measuring aeration in flotation cells. Consequently the relation between aeration and cell performance has not been definitely established. In connection with a comparative study of kerosene and froth flotation processes, a modification of the displacement method' was developed in which air escaping from the cell surface is measured with a wet-test meter. The arrangement shown in Fig. 1 is satisfactory for use with a number of cells and is not critical, except that care must be taken to use connections and tubing large enough to avoid excessive back pressures. Attempts to use smaller tubing resulted in back pressures that caused displacement of the liquid level in the receiver, so that some air was lost around the sides, an occurrence readily visible when measurements were taken with only water passing through the cell. With the arrangement shown, the manometer indicated an average reading of about 1/2-in. water pressure. No loss of air was evident. Fig. 2 presents typical data for a standard Denver sub-A 24x24-in. unit cell operated at impeller speeds from 0 to 710 rpm. Each plotted point represents the average for five readings distributed over the entire cell surface. Readings were taken with only water passing through the cell. Results of this type have been used in a study of the influence of operating variables on cell performance and in detecting inherent differences in the operating characteristics of cells of various kinds. Although the information presented in Fig. 2 resulted only with water passing through the cell, the apparatus is suitable for use during flotation of coal when various reagents are present. Possible modi- fications that might prove convenient under special circumstances include varying the size and shape of the receiver and substituting a calibrated, inverted, water-filled carboy or other gas-measuring device for the wet-test meter. If such modifications result in excessive back pressures, some form of draft should be applied at the discharge end of the measuring system.

Jan 1, 1959

By Clyde E. Williams

MUCH has been said recently concerning the depletion of the Lake Superior iron ore re- serves. Estimates given indicate a total life of the present known reserves of twenty to thirty years. Some argue that there is no need to concern ourselves about the possible depletion of the Lake Superior iron ore supply because foreign ores can be brought in to this country at a lower price than rich agglomerated ore can be produced from the lean domestic ores. Some fear, as a result of this, a displacement of the steel business from present districts to the Atlantic seaboard. Others show that foreign ores will be brought to interior points via the projected Great Lakes-St. Lawrence waterway. Others believe that the South, given better freight rates, will extend its iron and steel market into northern territory.

Jan 1, 1931

By P. E. Fitzgerald, J. C. Gindlesperger

1. The Acidizer (Trade Publication of Dowell Inc.): No. 1. Aspects of Acidizing. No. 2. Inhibited Acid. No. 3. The Value of Acidizing. No. 4. The Chemistry of Acidizing. No. 5. Jelly Seal in Acidizing. No. 6. Loosening Stuck Drill Pipe. No. 7. The Geology of Acidizing. 2. J. C. Albright: Acid Is Being Used for Cleaning Intake Wells in Water-flooded Areas. Oil Weekly (Sept. 23, 1935) 24. 3. D. H. Bancroft: Acid Tests Increase Production of Zwolle Wells, Miller County, Arkansas. Oil and Gas Jnl. (Dec. 22, 1932) 42. 4. A. H. Bell: Possible Areas for Acid Treatment in Illinois. Pub. of Illinois- Indiana Petr. Assn. and lllinois Geol. Survey (1934) 49. 5. N. A. Best: Treating Limestone Formations Consists of More than Pouring Hydrochloric Acid in the Well. Oil and Gas Jnl. (April 5, 1934) 54. 6. L. G. E. Bignell: Sealing Off Salt Water from Oil-bearing Formations. Oil and Gas Jnl. (Jan. 30, 1936) 59. 7. L. G. E, Bignell: Acidizing Upper Limestone Formation Facilitated by the Use of Jelly Seal. Oil and Gas Jnl. (March 5, 1936) 30. 8. L. G. E. Bignell: Bailing, Shooting, Tubing and Acidizing Have All Been Tried in Deep Test at Binger, Oklahoma. Oil and Gas Jnl. (May 10, 1934) 38. 9. L. G. E. Bignell: Dowel1 Incorporated Increasing Its Field Service for Acid Treatment of Wells. Oil and Gas Jnl. (June 7, 1934) 62. 10. L. C. Chamberlain, Jr. and P. E. Fitzgerald: Oil Well Acidizing in Michigan. Mich. Acad. Sci. Papers (March 1937). 11. M. E. Chapman: Some of the Theoretical and Practical Aspects of the Acid Treatment of Limestone Wells. Oil and Gas Jnl. (Oct. 12, 1933) 10. 12. C. E. Clason and J. G. Staudt: Limestone Reservoir Rocks of Kansas React Favorably to Acid Treatment. Oil and Gas Jnl. (April 25, 1935) 53. 13. W. F. Cloud: Cleaning and Reconditioning Oil Wells—Reconditioning by Use of Acid (Petroleum Production 1937), 389. University of Oklahoma Press, 1937,' 14. K. A. Covell: Developments in Eastern Production Practice. Acid Treatment of Michigan Wells. Amer. Petr. Inst. Prod. Bull. 213 (1934) 77; Oil and Gas Jnl. (May 31, 1934) 89; Oil Weekly (May 28, 1934) 17. 15. B. A. Cunningham: Acid Treatment of Lime Formations. Amer. Petr. Inst. Paper 901 (1933) 9D, 1-7. 16. 0. I. DeSchon: Pondera Production up 22,000 Barrels. Montana Oil & Min. Jnl. (Jan. 26, 1935) 1.

Jan 1, 1937

By Joseph C. Buchen

IN principle, production of salt from sea water is a simple operation. Sea water is trapped in ponds, the sun and wind cause evaporation of the water, and what is left is principally salt. Commercial production of solar salt, however, requires a careful consideration of many factors. Obviously, sufficient evaporation must take place throughout the making season to produce an economically adequate crop. Other factors are density of soil, contour of ground, height of ground above sea level, minimum dilution from fresh-water streams, and distance from market. Unfortunately, in the United States the localities of greatest evaporation, allowing for the other factors, are not the most suitable for the manufacture of sea salt by solar evaporation. The south end of San Francisco Bay most

Jan 1, 1937

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

The introduction and development of the flotation process have proved to be of such momentous importance to the mining industry of the United States that they deserve to be considered historically.* The origin of the use of oily matter in separating minerals in ores is obscure, because its beginnings were unregarded. The story told by Herodotus concerning the recovery of gold from the mud of a lake by means of feathers daubed with pitch in the hands of apocryphal virgins is as pertinent to our inquiry as the yarn, two thousand years later, of a young school-teacher in Colorado that was washing oil-stained ore-sacks in her brother&apos;s assay-office when she noted the floating of pyrite on the water contaminated by the oil. In any event, the method patented by Carrie Everaon in 1885 was a complete failure, except as factitious evidence for trying to disprove the originality of subsequent inventions. An early and inadvertent use of the affinity of oil for metallic surfaces is suggested by the story of Jason and the Argonauts, who extracted gold from the gravel of the river Colchis by means of sheepskins. The woolly hide sewed, like the blankets used in our early stamp-mills, to arrest the gold, which was further detained by the oil on the fleece. Strabo, referring to a later period, says that in the country of the Soanes, who inhabit the valley of the Colchis, “the winter torrents are said to bring down even gold, which the barbarians collect in troughs pierced with holes, and lined with fleeces; and hence the fable of the Golden Fleece”.† William Pryce

Jan 1, 1932