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By J. W. Marx, R. H. Langenheim

The authors are to he complimented for a timely presentation of useful information concerning application of heat to oil reservoirs to increase the rate and ultimate recovery of oil. The solution for heated area resulting from constant rate injection of a hot fluid, presented by the authors, and the fluid-flow analogy, solved by Carter,' are particularly interesting in that 110 restriction is placed on the direction of development of the heated area. It is not necessary that the heated area grow radially. Thus the solution could provide useful information for heat injection in any type of well pattern with any specified swept area data. However, it was assumed in the development that the heated region would remain at a constant clevatcd temperature. Vertical heat losses were computed on this basis. Physically. the assumption that the heated region will remain at a constant temperature (independent of distance from the injection point) appears to require that the heat injection medium be stcam, or other condensible gases near the boding point at injection pressure. If a hot liquid below the boiling point or a hot gas considerably above saturation temperature were used, the temperature of the heated region would decrease with distance from the injection well. Lauwerier2 has discussed this problem for a linear system. (See also Jenkins and Aronolsky; and McNiel and Nelson.') Thus, the authors' solution applies more nearly to steam injection than to hot water injection or hot, non-condensable gas injection. Assuming steam as the injection medium, it appears that steam would pass through the constant-temperature heated region and condense upon contact with the unheated sand. The tempcrature in the condensing region would probably be governed by the release of heat of vaporization required for phase equilibrium at the existing pressure distribution. Temperatures in the region would also be influenced by vaporization of hydrocarbon. Thus, it is doubtful that an expression for radial temperature distribution based on heat conduction only (such as the authors' Eq. 9) would have practical significance. As pointed out by Marx and Langenheim, the growth of the heated area under constant rate steam drive will eventually be limited economically by vertical heat loss. The possibility of continuing to move heat economically by cold water injection or by increasing the steam injection rate appears to be a very important consideration. (Movement of liquids away from the injection well should increase injectivity.) Fortunately, the solution presented by the authors may be generalized to thc case of a variable heat injection rate. The general solution is:

By Warden A. Moller

(Pittsburg Meeting, March, 1910.) THE Fushun coal-field, now being opened up by the South Manchurian Railway Co., is connected with the main line by a branch, 30 miles long, from Sui Chia Tun, 10 miles south of Mukden, the capital of Manchuria. The coal-field, which lies on the southern bank of the Hun river, 25 miles east of Mukden, consists of a long narrow valley,. running east and west between hills composed of granitic and volcanic rocks. At the foot of the northern hills, the Hun river flows westward towards the Liao river, which drains the greater part of South Manchuria. At the foot of the southern hills, resting immediately upon volcanic rocks, and overlain by 20 ft. of alluvial, is a thick layer of Tertiary shales, carrying near the base two coal-seams. In many places the lower of these two seams is in immediate contact with volcanic lauds and basalts, the flows of which were evidently both prior and subsequent to the formation of the coal-seams. This contact has practically destroyed the lower seam for commercial purposes. The value of the field lies in the upper seam, which, for a length of nearly 8 miles, varies from 100 to 130 ft. thick. Of this seam, 85 per cent is good coal. The seam dips to the north conformably with the shales, at angles of from 25° to 30°, and appears to have an uninterrupted dip for about 1.5 miles before being possibly cut o$' by the northern hills. The coal-bearing shales extend east and west for a length of about 20 miles, but towards the east the continuity of the seams is broken by intrusive rocks. The coal is of the sub-bituminous variety, low in ash, bright in appearance, and breaks with a conchoidal fracture. It has the usual qualities of Tertiary coal-quick steam-raising and poor stacking-qualities. Pieces of resin, varying in size from

Apr 1, 1910

By Eugene W. Pearson

In a marked departure from conventional practice, the Power Plate process combines the two unit operations of leaching and electrowinning into a single continuous step for direct recovery of copper from sulfide concentrates, cement copper, copper scrap, and copper oxide slurries. Considering how environmental controls are pre- venting development of smelters for additional capacity or new construction, the Power Plate process provides a welcome pollution-free alternative to the smelting-electrorefining routes. And its low capital investment and low operating costs also recommend it to copper producers who are now using or investigating various hydrometallurgical methods.

Jan 12, 1974

By Fred C. Bond

AN improved method of measuring the surface area of a comminution product down to any desired particle size has been developed. The method is largely graphical, and requires relatively little calculation. It can be used with materials containing large amounts of clay, or excess fines of any kind. The surface area S is expressed in terms of square meters per100 c.c. of solids. This expression is based upon volume rather than weight, and is considered to be more suitable for crushing and grinding problems, where the machines ordinarily are operated under constant volume conditions. It has the advantage that surface areas of different materials can be compared directly, even though their specific gravities may be unknown. The "specific surface" of a material, or the number of square centimeters of surface area per gram, is equal to 100S divided by the specific gravity. Particle diameters are expressed in microns, K being the diameter of the largest particle present and L the grind limit, or lower size limit of the particles formed directly by grinding. The value of K does not always coincide exactly with the diameters of the largest particles retained on the coarsest testing sieve, since the largest particles formed in crushing and grinding are often slabby, or have other irregular shapes. L has been chosen as 0.700 microns, or number 27.5 in the size number series,1 for reasons to be explained later. S is the total surface area of all particles larger than L microns in diameter. When a homogeneous comminution product is separated into fractions whose diameters bear a constant geometrical relationship [p] to each other, and the log per cent weight retained upon each size and passing the next larger size is plotted against the log diameter, a straight line results, which is called the distribution line, and which has a slope in called the distribution modulus. The distribution line can be extended to any desired limiting size, and the total surface area of all particles larger than that size can be calculated. The equation of the distribution line is w = Cxm [I] where w is the per cent weight retained on each successive sieve; x is the particle diameter; and C is the per cent weight retained on an opening of unit diameter.2 Theoretically, the distribution line can be extended to include infinitely small particles. When it is so extended, and the assumption is made that no fine particles are present other than those accounted for by the equation; the log per cent cumulative weight passing any series of sizes, plotted against the log diameter passed, will result in a straight line lying parallel to and above the plotted distribution line.

Jan 1, 1941

By W. A. Young

Polynomial functions of temperature were obtained for the specific heats, thermal diffusivities, and thermal conductivities of zirconium hydrides containing 4 at. pct U. Three hydrides (H/Zr atom ratios of 1.58, 1.65, and 1.70) were studied over the range a" to 900°C and a fourth (H/Zr = 1.81) was studied over the range 0° to 760°C. The specific heats were determined from enthalpy measurements which were obtained using a unique drop calorimeter specifically designed for use with materials in which high temperature phase transitions and/or high dissociation pressures occur. Thermal diffusivities were measured by the flash method using a pulsed laser. The thermal conductiuities were obtained as the product of specific heat, thermal diffusivity, and density. The specific heats agree, within 10 pct, with values derived using a theoretical model in which the hydrogen and zirconium atoms are treated as Einstein and Debye oscillators, respectively. RELIABLE values of the thermophysical properties of the fuel are required to predict the operating temperatures and temperature response of SNAP nuclear reactors. Among the most important of these properties are the thermal conductivity, specific heat, and thermal diffusivity. A considerable number of investigations1-4 have been made of these properties for the Zr-H and Zr-H-U systems.* However, little of the drides, however, this direct method cannot yield meaningful results, since the hydrogen will redistribute under the influence of the thermal gradient, thus forming a concentration gradient; hence, one has a spectrum of compositions, rather than a homogenous alloy. Although the "average" composition of the material may be identical to the initial uniform concentration, the directly measured value of conductivity will be dependent on the thickness of the specimen, due to the highly sensitive dependence of transport properties on hydrogen content. This dependence is strikingly illustrated by the work of Bickel,5 who found that the electrical conduction of zirconium hydrides ranges from primarily hole conduction to primarily electronic conduction, depending upon the hydrogen content. Fortunately, the direct measurement of thermal conductivity is unnecessary, since it can be expressed as the product of the specific heat, thermal diffusivity, and density, all of which can be directly measured with considerable accuracy. EXPERIMENTAL Specimen Preparation. The combined fuel-moderator material used in SNAP reactors is a hydrided zirconium-uranium alloy containing -10 wt pct U. The alloy used in this work was representative of that used in nuclear reactors except that normal uranium was substituted for the enriched uranium required for reactor usage. It was produced by a triple-arc-melt and double-extrusion process. All specimens were prepared from a single cylindrical extrusion which contained 10.30 pet U, 89,35 pct Zr, and 0.35 pct impurities, The specimens for each composition were hydrided simultaneously with ultrapure hydrogen (10 ppm total impurities) using standard fuel production techniques which routinely yield homogeneous, crack-free fuel with negligible increases in the impurity levels. The hydrogen content of each specimen was determined from its weight gain and the density was measured by liquid displacement, Chemical analyses yielded hydrogen concentrations which agreed with the weight gain data within ±0.02 in H/Zr atom ratio) the concentrations of all other elements agreed almost exactly with the initial values after adjustment for the added hydrogen. The specimens used for the determination of specific heat were centerless ground to 2.00 cm diam after hydriding. A thin slice was carefully removed From each end for metallographic examination. In every case, this examination revealed a uniform structure as evidenced by the appearance and distribution of the two phases present in the fuel at the hydrogen concentrations used. TWO specimens (H/Zr = 1.600 and 1.632) appeared to be entirely 6 phase with equi-axed grains; the specimen with H/Zr = 1.756 showed

Jan 1, 1970

By AIME

THE history of the Mine La Motte area covers a greater period of time than any other mining operation west of the Mississippi, for it was almost exactly four centuries ago that the white man first visited the region. In May 1541 a few men from the party of Fernando de Soto traversed the place looking for silver which they understood the Indians had found in the vicinity. Some historians say that De Soto himself visited the place sometime later. No other white man came through again until the early 1700's. In 1712 King Louis XIV of France granted to Antoine Crozat a charter for transacting all business and government in the vast domain of the New Continent stretching from the Gulf of Mexico northward indefinitely. This

Jan 1, 1947

By A. M. Gaudin

Activation of sphalerite with silver ions results from the exchange of two Ag ions for one Zn ion in the sphalerite lattice. The exchange is proportional to the logarithm of time and proceeds until either of the reactants is consumed. Sodium cyanide prevents the activation of sphalerite by controlling the ratio [Zn++]/[Ag+]' in solution. If sphalerite has already been activated with excess silver, cyanide ions can deactivate sphalerite provided oxygen is present. SOLUBLE: silver salts are effective activators for flotation of sphalerite with potassium ethyl xan-thate as collector.* Since sphalerite takes up large quantities of silver ions rapidly,2-4 investigation of this system appeared fruitful for studying the mechanism of sphalerite activation and deactivation. Experimental data presented here comprise studies of the mechanism and rates of activation and deactivation of sphalerite with silver and cyanide ions. A 20-lb sample of sphalerite from Ottawa County, Oklahoma, was handpicked, crushed, screened, hy-drosized to produce a 65/100-mesh fraction, and purified by electrostatic separation. The sphalerite was then leached with benzene and absolute ethyl alcohol to remove possible organic contaminants and with 0.1 M NaCN to remove any copper that might have been picked up during screening. The benzene had been specially purified by grinding with fine sphalerite for 12 hr to remove trace impurities that might have had a specific affinity for sphalerite. Ii'inally, the mineral was washed, dried in flowing nitrogen, and stored in large ground-glass stoppered weighing bottles under a small nitrogen pressure. The specific surface of two samples from the 65/100-mesh sphalerite stock, measured by krypton gas adsorption," was 420 cm2 per g. Compared with spheres of the same size and specific gravity, the prepared mineral had five times as much surface. Results of a wet chemical analysis and of a spectro-graphic study are given in Table I. Manganese, nickel, tin, indium, thallium, cobalt, and magnesium were not detected spectrographically. All solutions were preparid by -adding reagent-grade chemicals to conductivitv water. which had been previously saturated with the desired gases. Nitrogen and oxygen were purified, but no attempt was made to purify the laboratory air. Radioanalysis was carried out with prepurified Ag110 tracer obtained from the Oak Ridge National Laboratory. The complete decay scheme for Ae is complex. Its primary emissions are 0.09 and 0.55 mev ß rays and 1.48 mev y raysB and its half-life is believed to be 270 days. In preparation of solutions of AgNO3, the amount of Ag110 added was negligible compared to that of the inert silver. Abstraction of silver from solution by sphalerite was measured after agitation of 1.5 g sphalerite with 20 ml of solution in 50-ml pyrex flasks. All sample preparations were carried out in a dry box so that the proper atmosphere could be maintained. After the mineral had been agitated in the silver nitrate solution, an aliquot of the solution and a sample of the wet mineral were transferred to separate counting vials and weighed. The solid sample was dried and re-weighed and the activity in both vials measured by means of a scintillation counter. With scintillation counting it is possible to count y radiation from the solid and liquid, a distinct advantage over the older ß-ray counting techdiques.4 All measurements of silver activity were made using a sodium-iodide well-type scintillation counter. The amount of zinc in solution was measured colorimet-rically by the monocolor method of Sandell.7 Activation Studies Exchange Between Zinc Ions and Silver Ions During Activation: The increase of Zn++ in solution during activation with Ag+ is shown in Table 11. These data indicate a replacement of one Zn++ by two Ag+. Analysis of a separate two-month agitation test indicated that the replacement of Zn++ by Ag+ was, as expected, in the molar ratio of 2.0.

Jan 1, 1958

By W. A. Backofen, D. H. Avery, W. F. Hosford

Sheets of the magnesium alloys AZ31B, HK31A, and ZE10A in several different tempers were tested in tension and determinations were made of the ratio of width-to-thickness strain. A marked increase in the ratio with tensile straining and a dependence upon alloy and test direction are rationalized in terms of a balance between the amounts of basal and prism-plane slip. All such variations are related, in turn, to the prevailing crystallographic texture. Fracture appearance is explained on the basis of anisotropy in plastic flow, and implications for developing texture -hardening effects in these alloys are discussed. ThE crystallographic texture or preferred orientation of a given material is determined by details of processing history. Such texture is known to influence many aspects of material behavior, in particular both the yielding and strain-hardening characteristics which are of special interest in the present work. Traditionally, the resulting plastic anisotropy has not been regarded as especially desirable. Earing in drawn sheet is perhaps the most common example of an unwanted effect of texture. However, it has also been recognized that suitable textures may be usefully employed to improve drawability,1,2 as a specific example, and generally to control yielding resistance under combined-stress loading.374 Texture would seem to be a detail of structure not yet exploited to nearly the fullest extent. A convenient basis for characterizing anisotropy in plastic behavior is the ratio of width-to-thickness strains obtained in a tension test;5&apos;6 the parameter is frequently labeled "R" and its value is revealing with respect to the nature of the prevailing texture. R gives a useful measure of a material&apos;s "thinning resistance". For an isotropic material, R = 1. With R > 1 the increased through-thickness strength in a sheet means greater resistance to yielding under biaxial tension, or "texture hardening";3&apos;4 if R < 1 the result may be a "texture softening" under the same loading conditions.4 Most R data relate to steel sheets for deep-drawing applications. Values for steel and other materials of cubic structures are not often much greater than 1 and nearly constant with strain in testing.1,2,7,8 To explore the implications of plastic anisotropy further, it was felt that experiments with much more strongly textured materials would be useful, and this led to the choice of magnesium alloys. The "ideal" sheet texture for magnesium contains the (0001) plane in the rolling plane, which ought to lead to R values approaching infinity. However, departures from the ideal texture, the possibility of slip in non-close-packed directions, and deformation by twinning would all be expected to introduce some range of R. Accordingly, studies on these materials were undertaken. EXPERIMENTAL Alloys in sheet form, Table I, were selected to obtain a variation in crystallographic texture, in the expectation that this would be reflected in differences in plastic anisotropy. Pole figures constructed by the Schulz surface-reflection technique9 were provided with the experimental materials by the Dow Metal Products Co. Profiles of pole density along great circles through the rolling (0 deg) and transverse (90 deg) directions were prepared from the pole figures and are collected in Figs. 1 and 2; considerable departure from the "ideal" (0001) alignment in the rolling plane is evident, with the largest angular spread in both directions being found in the ZEl0 alloy. Results of tensile tests on full-thickness specimens of 6-in. gage length by 1/2-in. width are given in Fig. 3 as engineering stress-strain curves* in rolling and transverse directions. All tests but one were made at a constant drive rate of 0.02 in. per min, and the final values of percent elongation at fracture, over the initial 6-in. gage length, are noted at the ends of the curves; one test on ZE10A-

Jan 1, 1965

By Donald E. Garrett

The processing of brines from Searles Lake, California, yields one of the world&apos;s largest supplies of borax and boron chemicals, second probably only to the massive deposit at Boron, California. Two companies produce from this deposit, the American Potash & Chemical Corp. and the West End Chemical Co., a division of the Stauffer Chemical Co. Two processes are employed in recovering borax from the brines; one is used by both companies and consists of carbonating the brine to form sodium bicarbonate, removing this, and then cooling the liquor to crystallize a crop of borax. Only American Potash uses the second process, evaporating the brine to concentrate it and remove (crystallize) much of its NaCl, Na2CO3, Na2SO4, and NaLi2PO4 content, quick cooling the remaining liquor to remove KCI, and then seeding the filtrate to remove borax. Both methods will be briefly described. Searles Lake is a large evaporite body formed during the most recent two Sierra Nevada ice stages, the Tahoe and the Tioga. Runoff waters from the Sierra Nevada Mountains collected in the large Owens Valley drainage basin and from there overflowed into the Indian Wells basin and then into Searles Lake. In each Lake, evaporation took place. To a large extent the Owens and Indian Wells lakes acted as settling basins, for much of the mud, and insoluble calcium and magnesium precipitates were deposited there. Recent volcanic activity in the mountains to the north and east of Owens Lake had scattered considerable mineral-rich volcanic ash and debris throughout the drainage area, and several hot springs were formed that contained boron and other salts. The present flow rate and concentration of several springs, and the known age of at least the Tioga zone, can fairly well account for all of the boron present in Owens and Searles Lakes.1 The tungsten content can be accounted for in a similar manner.2 Most of the salts thus originally present in the fresh water runoff-from ice, snow, and rain-accompanying these two ice stages were ultimately deposited in Searles Lake. During the Tahoe period, from 25 to 40 ft of massive, mixed salts were deposited, along with six interspersed layers of mud (four inches to two feet thick) representing comparatively brief interglacial periods. Before the final desiccation of the lake, from 10 to 14 ft of new mud was deposited, representing the Tioga stage. The crystals subsequently deposited were from 70 to 90 ft thick, and form the present lake surface. The extent of the salt body is about 34 square miles, of which 12 square miles are exposed salt; the remaining area is covered by recent alluvial deposits (chiefly mud). The present lake is generally dry on the surface but floods to a shallow depth following heavy rains. The crystal body of both zones consists of continuous clusters of salts, and the voids between crystals (about 45 pct of the total volume) are occupied by brine. The level of this brine never recedes more than several inches below the salt surface. The brine pumped to the plants for processing is generally saturated with all of the solid phases present in that area, and thus is a complex mixture containing about 35 pct solids (see Table 3). The brine composition varies somewhat at different areas of the lake and from upper to lower structures, so wells are drilled in the areas and to the depths desired. A casing is cemented in the hole to within a short distance from the bottom, and pumps with about 14-ft suctions are mounted on the casing to pump the brine into the plants. The evaporation process of the American Potash & Chemical Corp. treats upper structure brine, evaporating all of the water from

Jan 1, 1960

By L. H. de Wald, J. Walter Scott

The removal of lead by fire refining methods from copper of electrolytic quality is growing in importance. Particularly is this true of the refining of secondary copper and copper cathodes obtained from electrolytic cells where lead is used as the anode material, as in the electrolysis of ore-leaching solutions and foul electrolyte. When investigating the removal of small amounts of lead from molten copper in a reverberatory furnace during the refining of secondary copper of otherwise electrolytic copper quality,&apos; it was found necessary first to know something about the distribution of the lead throughout the bath. The authors believe that it is not generally known how small amounts of lead as an impurity are distributed in a molten copper bath; that is, whether the lead is concentrated at the bottom or at the top, or whether it occurs more or less uniformly throughout the bath. The data contained in this report may help, therefore, in the development of a satisfactory fire refining method for the removal of this obstinate element from a molten copper bath. The first step was the development of a method for taking samples from various locations in the bath, at the surface and at various depths. The sampling device used, shown in Fig. 1, consisted of a 10-gram fireclay assay crucible fitted into a ring on the end of a steel rod handle of suitable length. A fireclay scorifier, 2 in. dia., with a ½-in. hole bored in the

Jan 1, 1930

By H. E. Hostetter

Grossmann&apos;s method1 for calculating the hardenability of steel from the composition and grain size has gained wide acceptance, and when properly used, has been well proved in practical application, both for estimating the hardenability of known compositions and for selecting compositions to meet known hardenability requirements. The Grossmann method uses as the criterion of hardenadility the "ideal critical diameter," DI, which is the&apos; size round that will just harden to a structure of 50 per cent martensite at the center when given the theoretically fastest quench, or "ideal quench." The DI can be related to actual quenching practice if the severity of quench is known; or the DI can be correlated with hardenability as determined by the Jominy end-quench method.2 The effect on hardenability of each element present in a steel can be represented by a multiplying factor, the value of which depends on the amount of the element present and the degree of effectiveness of the particular element. (The value of the factor for a given carbon content varies with the grain size.) When the factors for all elements present in a steel have been determined from charts, they are multiplied, and the resultant product is the DI of the steel. The validity of Grossmann&apos;s scheme of multiplying factors has been confirmed in a number of other investigations.3-6 It can be appreciated that a certain desired level of hardenability can be obtained by adding chromium, molybdenum, nickel and vanadium to a base composition containing carbon, manganese, silicon and the usual impurities. Many of the ranges of hardenability used commercially can be obtained by any of the foregoing alloying elements used singly in the base composition. The same hardenability levels also can be obtained through use of any of a great number of multiple element combinations of these alloying elements. In this report a method will be presented for determining what one combination is the most efficient (based on hardenability and cost of added alloy) for a given level of hardenability. It should not be assumed from the emphasis given to hardenability, that hardenability is the only criterion for the selection of an alloy composition. Such properties as the hot-working characteristics, machinability, carburizing characteristics, amount of distortion during quenching and the retention of austenite may be considerations of importance in many applications. However, hardenability is one of the most important properties of an alloy steel and one that must be considered in almost all cases involving heat-treatment by quenching. Therefore, a method for determining the lowest-cost alloy combination should be of considerable value. Determination of Most Efficient Combinations For comparing the alloying elements on standards of cost and hardenability, it

Jan 1, 1947

By H. E. Hostetter

Grossmann&apos;s method1 for calculating the hardenability of steel from the composition and grain size has gained wide acceptance, and when properly used, has been well proved in practical application, both for estimating the hardenability of known compositions and for selecting compositions to meet known hardenability requirements. The Grossmann method uses as the criterion of hardenadility the "ideal critical diameter," DI, which is the&apos; size round that will just harden to a structure of 50 per cent martensite at the center when given the theoretically fastest quench, or "ideal quench." The DI can be related to actual quenching practice if the severity of quench is known; or the DI can be correlated with hardenability as determined by the Jominy end-quench method.2 The effect on hardenability of each element present in a steel can be represented by a multiplying factor, the value of which depends on the amount of the element present and the degree of effectiveness of the particular element. (The value of the factor for a given carbon content varies with the grain size.) When the factors for all elements present in a steel have been determined from charts, they are multiplied, and the resultant product is the DI of the steel. The validity of Grossmann&apos;s scheme of multiplying factors has been confirmed in a number of other investigations.3-6 It can be appreciated that a certain desired level of hardenability can be obtained by adding chromium, molybdenum, nickel and vanadium to a base composition containing carbon, manganese, silicon and the usual impurities. Many of the ranges of hardenability used commercially can be obtained by any of the foregoing alloying elements used singly in the base composition. The same hardenability levels also can be obtained through use of any of a great number of multiple element combinations of these alloying elements. In this report a method will be presented for determining what one combination is the most efficient (based on hardenability and cost of added alloy) for a given level of hardenability. It should not be assumed from the emphasis given to hardenability, that hardenability is the only criterion for the selection of an alloy composition. Such properties as the hot-working characteristics, machinability, carburizing characteristics, amount of distortion during quenching and the retention of austenite may be considerations of importance in many applications. However, hardenability is one of the most important properties of an alloy steel and one that must be considered in almost all cases involving heat-treatment by quenching. Therefore, a method for determining the lowest-cost alloy combination should be of considerable value. Determination of Most Efficient Combinations For comparing the alloying elements on standards of cost and hardenability, it

Jan 1, 1947

By J. Parker

As a practicing mining engineer, I face many rock mechanics&apos; problems daily and would like to mention one or two examples to illustrate the current gap between laboratory investigations and actual field problems. I would like to endorse Dr. Obert&apos;s suggestion that more field measurements and observations should be undertaken. There is an ever-increasing body of data beginning with Hast&apos;s results in Sweden,l then measurements at Elliot Lake, Canada, and so on, including our own measurements at White Pine, which clearly indicate that the horizontal stresses underground. are often at least as large as the vertical stresses. Visual observation of the deformation of roof and pillars (including failure due to horizontal compres- sion) also demonstrates that the horizontal stresses are often most important: Yet almost every laboratory investigation begins with the assumption that the only stresses acting are vertical. Roof spans in layered formations. for example, are calculated on the assumption that the rock behaves as a gravity loaded beam. This is all too often unrealistic.

Jan 1, 1967

By OTTO HERRES

TO operate the bituminous coal industry in the United States in 1929 cost $770,237,000, of which $30,739,000 was paid for purchased power and $34,947,000 for new machinery and equipment. Equipment aggregated 3,124,000 hp. A mining industry that spends $65,000,000 a year for power and machinery is likely to be fairly well mechanized, and when the machinery in use takes three million horsepower to drive it, the probabilities are that mechanization has been in progress in at least some of the mines for quite a few years. Mechanization in its broadest sense implies machine cutting, power drilling, mechanical loading, electric haulage, mechanical sizing and cleaning, and lesser applications of machinery to mining operations. But the introduction and development of mechanical loading has been the feature of coal mining recently and its extraordinary progress is causing great changes within the industry. First, let us look at the records. The quantity of coal loaded mechanically in bituminous mines was:

Jan 1, 1933

By J. S. Dodge, I. M. Krieger

The laminarturbulent transition was studied for monodisperse rigid polymer latices as functions of particle diameter and concentration at several tube diameters. Breaks in the graph of friction factor US Reynolds number were used to characterize the transition; rates of shear were sufficiently high so that Newtonian behavior at the high shear limiting viscosity could be assumed. No abnormal behavior was noted at concentrations below 30 volume percent. At higher concentrations, suppression of turbulence was observed with critical Reynolds numbers rising to as high as 5,500 at 50 volume percent. No definite effect on the transition was noted due to variation of particle size or tube diameter. The type of surfactant used to stabilize the latex was found to have an important influence on the critical Reynolds number. INTRODUCTION For some polymer solutions and solid-in-liquid suspensions, the transition from laminar behavior to turbulence in pipeline flow has been reported to take place at unusually low1-5 and in some cases at higher than normal6,7 critical Reynolds numbers. Extreme values of critical Reynolds numbers (NRe*) have been found to range from 1 to 6,000, as opposed to the values of 2,000 to 3,500 which are obtained for ordinary liquids. Observations have also been reported of drag reduction in fully developed turbulent flow, i.e., a decreased value of the friction factor in the Reynolds number-friction factor plot6*10-14 in colloidal and polymeric fluids. In some cases, turbulence suppression (unusually large values of Nre*) was noted to occur preceding the drag reduction,6 while a normal transition was noted in other cases of drag reduction.14 To relate the occurrence of turbulence suppression and drag reduction to the molecular or particulate structure of the fluid, it is desirable to characterize the structural variables with some precision. For most colloidal dispersions and polymeric fluids, this is very difficult; particle sizes, shapes and stiffnesses may vary over wide ranges in the same sample. Recently, however, a colloidal fluid has become available which consists of rigid spherical particles of highly uniform diameter dispersed in a simple Newtonian liquid. These are monodisperse polymer latices, prepared by carefully controlled emulsion polymerization reactions. The purpose of this research was to study the transition to turbulence in these well-characterized colloidal fluids as a function of concentration, particle diameter and tube diameter. Typical flow curves of latices of high solids content are shown in Fig. 1. While these curves were obtained with monodisperse latices, the general shape of the curve is also typical of a polydisperse latex. It is observed that a shear-thinning region occurs for low to moderate rates of shear. At sufficiently high shearing rates a limiting Newtonian viscosity is reached. The viscosity µ diminishes with decreasing volume fraction 4 at all shear rates. For 4 less than 0.25, latices are Newtonian at all rates of shear.15 An increase in average particle size (at a given extends the Newtonian viscosity region to lower rates of shear. A third factor which influences the

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

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&apos; 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&apos; 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

By R. E. Holmes, T. W. Leland

The solution to the unsteady-state mass- and heat-transfer equations describing the adsorption of a dilute component from a gas stream flowing through a packed bed is readily applicable to the design of hydrocarbon recovery units. The solution to these equations depends on the assumption of a linear equilibrium equation to relate concentrations on the surface to concentrations in the gas. This assumption is shown to be justifiable for components which are very dilute in the gas stream. This approach permits the prediction of the effects of bed shape and size, cycle time, and gas mass velocity on the recovery of each component. It also allows the time and gas flow rate needed for regeneration to be determined. The equations involve a constant for each component and another constant characterized by the type of adsorbent. These constants must be evaluated from operating data. Values of these constants determined for silica gel are presented. This paper points out the type of experitrrental data needed for a thorough design of hydrocarbon adsorption units. INTRODUCTION The growing importance of adsorption processes to recover hydrocarbons from natural-gas streams has created an urgent need for better methods to design and predict the performance of these processes. Since the original use of solid adsorbents in natural-gas processing was for dehydration, most of the current design methods for hydrocarbon recovery re extensions of those developed earlier for dehydration. These methods are based on an adsorptivity or bed loading factor defined as the amount of a particular component adsorbed per unit weight or per unit volume of the packed bed. The recovery of a given component is then expressed as an empirical function of its adsorptivity on a given adsorbent. In spite of the simplicity and initial utility of these methods, they are not completely satisfactory in that they do not predict the effect of the dimensions of the bed in relation to flow rate and cycle time, and do not predict the distribution of various components along the length of the bed. It is possible, however, to make a considerable improvement in the design of these processes by applying the basic equations of mass and heat transfer applicable to gases containing small concentrations of adsorbing components flowing through granular beds. These equations have been developed and solved by Anzelius,&apos; Furnas,% nd Hougen and Marshall." where G = mass velocity of the inert constituents (assumed to be methane), lb/hr-sq ft, y = weight of an adsorbing component in the gas per unit weight of inert, lb of a given constituent per lb of methane, x = bed length, ft, p, = packed bed density, lb/cu ft, P, = gas density, Ib/cu ft, f = void fraction in the bed, t = time, hours, and w = weight of a given component adsorbed per unit weight of adsorbate free solid, Ib/lb pure adsorbent. The term on the left side of Eq. 1 represents the flow rate per unit bed volume of a component entering less the flow rate per unit bed volume of that component leaving the differential bed length. The terms on the right side represent, respectively, the accumulation rates per unit bed volume on the solid and in the gas phase within the differential bed section. The last term is negligible for this application since pgfv is quite small in comparison with p, and G. The partial differential is determined by the mass-transfer rate between gas and solid in the differential section.

By J. Chipman, N. J. Grant, R. Rocca

Desulphurization of liquid iron by reducing slags of the electric-furnace type was studied from 65 heats. Variations were made in basicity over a wide range and in FeO up to about 5 pct for their effects on desulphurization. The role of FeO in desulphurization from the blast furnace, to the electric furnace, to the oxidizing conditions of the open hearth is shown to fit a relatively simple pattern of behavior. THE mechanism which controls the desulphurization of molten iron by basic slags has been the object of several investigations. In particular, equilibrium determinations have been made both in the field of basic open-hearth slags, which have a high iron-oxide concentration, and in the field of blast-furnace slags which have a very low iron-oxide concentration. In both cases the desulphurization ratio has been found to increase with increasing basicity of the slags; however, the mechanism of desulphurization differs in the two cases. In basic open-hearth slags desulphurization occurs mainly as a partition of iron sulphide:&apos; FeS * (FeS) and the desulphurization ratio is approximately independent of iron-oxide concentration in the slag. In blast-furnace slags the concentration of iron oxide is very low as a result of the highly reducing conditions in which they are formed. The controlling reaction for desulphurization is then:2,3 FeS + (CaO) <=* (CaS) + (FeO) The slags of the reducing stage in the electric furnace have an iron-oxide concentration which is intermediate between blast-furnace and open-hearth slags. The study of the mechanism of desulphurization for these slags has been the object of this investigation. The importance of low (FeO) in the slag for desulphurization was first verified by Bardenheuer and Geller,& who found that high desulphurization ratios were obtained in highly reduced slags. It was recognized" hat iron oxide in the slag becomes a controlling factor in desulphurization only at FeO concentrations approximately under 5 pct. A recent investigation conducted by Buehl,7 upon the suggestion of one of the authors, confirmed this opinion from the results obtained from a heat conducted in a small arc furnace. In the present investigation, slags of very high basicity, such as often are encountered in the basic electric furnace, could not be studied, but equilibrium data have been obtained for slags in a wide basicity range. The iron-oxide concentration in these slags ranged from 0.08 to 15 pct and was controlled by the addition of silicon to the metal. Other constituents of the slags were mainly CaO, MgO, SiO2, A120,, and CaF,. The experimental technique was essentially the same as that of previous investigations.1 8-lo In an open magnesia-lined induction furnace, 65 lb of Armco ingot iron was melted. An atmosphere of hydrogen was maintained over the melt for 1 hr to bring the carbon content down to approximately 0.010 pct maximum. The bath then was exposed to air for 25 min to remove hydrogen. The electrodes were put in place, and the furnace was operated from this point on in an atmosphere of nitrogen. A synthetic slag was added to which additions of silicon and iron sulphide were made. A rate study conducted at the beginning of this investigation had

Jan 1, 1952

By R. H. Hiltz

Three titanium alloys, known to provide a mechanically unstable p structure after quenching, were selected as material for a study of the Origin and nature of stress-induced transformation. Data from hardness and tensile tests were used to study the initiation of marten site and the effect of the transfornation and transformation products on the mechanical properties of B titanium, particularly the stress-strain relationships. With the exception that the materials investigated showed a natural aging reaction in the P condition, their behavior is analogous to that of&apos; stress-transforming stainless steels. The transformation starts after initial yielding and is essentially complete just prior to .maximum loading. Once initiated, the martensite itself is capable of propagating the transformation. The deforn-ing materials show low strength, high ductility, and a high strain-hardening exponent. In metallic systems which undergo a diffusionless transformation on cooling, it is possible to produce a similar transformatiorl by plastic deformation under special conditions. Dewez&apos; in delineating Ms temperatures for the titanium-rich end of most titanium binary systems:, established the point of intersection of Ms with room temperature for those particular alloys. Alloy compositions which would quench to mechanically unstable p were established from these data. The first investigation into the possibility of stress-induced transformation occurring in titanium met with little success. It was concluded that such a transformation in titanium was possible only under very special conditions. Continued effort in this direction, however, showed certain Ti-Mo binaries to be highly susceptible to this phenomenon. This fact was utilized by Liu to study the habit planes of martensite and by Machlin and wenig5 to study the effects of stress and plastic deformation on the P to a prime transformation in titanium alloys. The first investigation of the mechanical properties of these alloys was conducted by Holden and his coworkers at Battelle Memorial Institute.&apos; The potentiality of the alloys i3s sheet-forming material was recognized, and the data reappeared in a survey of this type of titanium material.? The initial optimism was tempered by the difficulties in obtaining homogeneous 2i-Mo alloys in commercial-size ingots. The increasing need for good sheet-forming material kept investigation in this direction active, resulting in the development of a commercial alloy of this type.&apos; This study was undertaken to obtain a clearer picture of the mechanism of stress-induced transformation in titanium. MATERIALS AND TEST PROCEDURE Three alloys were selected for this investigation: one a Ti-Mo alloy; another a Ti-Cr-Mo alloy, known to deform martensitically; and the third, a Ti-V alloy with an Ms below room temperature and an Md above room temperature, but known to contain w phase in the quenched condition. The compositions of these alloys are given in Table I. These alloys were cast as 5-lb experimental ingots, employing skull melting. The ingots were hot-forged into 1-in.-round bars. Two 72-in.-thick slices were cut from each bar for hardness testing; the remainder was cut into 0.252-in. tensile blanks. The tensile blanks and one hardness disc from each bar were heated in salt to a temperature 100°F above the 0 transus, held 2/2 hr, and brine quenched. X-ray analysis showed the pieces to be 100 pct 8.* *Omega cannot be distinguished from p by the technique employed. Tensile blanks were machined to size after this treatment. TO prevent transformation due to machining stresses, the shoulders and gage length were ground. True stress-true strain curves were

Jan 1, 1960