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By T. R. A. Davey

IN 1947 the author became interested in the fundamental aspects of the desilverizing of lead by zinc, conducted some experimental work, and searched the technical literature for all available fundamental data. Since then a revival of interest in the subject in Europe resulted in the appearance of quite a number of papers. It became evident that it would be more profitable to collect together and examine thoroughly the results of various workers, than to attempt to duplicate the experimental determinations. There are many inconsistencies in the various publications, and it is opportune to review at this time the present status of knowledge on the Ag-Pb-Zn system. There is also a need for a clear description, in fundamental terms, of the various desilverizing procedures. This paper is presented in four sections: 1—There is an historical review of the origins of the Parkes process, of the results of many attempts to find a satisfactory fundamental explanation for the phenomena, and of the modifications proposed to date. 2—A diagram of the Ag-Pb-Zn system is presented. This is believed to be free of obvious inconsistencies or theoretical impossibilities, although thermodynamic analysis subsequently may reveal errors. 3—The fundamental bases of the various desilverizing procedures, which have been used up to the present day, are described; and a new method is suggested for desilverizing a continuous flow of softened bullion in which the bullion is stirred at a low temperature in two stages producing desilverized lead at least as low in silver as that from the Williams continuous process and a crust which, on liquation, yields a very high-silver Ag-Zn alloy. 4—A suggestion is made for the revival of de-golding practice, following a recently published account which does not seem to have attracted the attention it deserves. The terms "eutectic trough" and "peritectic fold" as used in this paper are synonymous with "line of binary eutectic crystallization" and "line of binary peritectic crystallization" as used by Masing.' The German literature on ternary and higher systems is rather extensive and a fairly general system of nomenclature has arisen, whereas in English usage the corresponding terms are not as well established. For this reason the meanings of terms used in this paper, together with the equivalent German terms, are given as follows: 1—Eutectic trough—eutektische rinne: line at which a liquid precipitates two solids S1 and S2 simultaneously. If the composition of a liquid which is cooling reaches this line, it then follows the course of this line until a eutectic point is reached, or until all the liquid is exhausted. The tangent to the eutec-tic trough cuts the line joining S1S2. 2—Peritectic fold—peritektische rinne: line at which a solid S1 and a liquid L transform into another solid S2. If the composition of a liquid which is precipitating S1 reaches the line, on further cooling only S2 is precipitated. The liquid composition moves from one phase region (L + S1) into the other (L + S2), and does not follow the course of the boundary. The tangent to the peritectic fold cuts the line S1S2 produced nearer S,. 3—Liquid miscibility gap, or conjugate solution region—mischungslucke: the region within which two liquid phases coexist in equilibrium over a certain range of temperature. A system whose composition is represented by a point in this region comprises one liquid at high temperature; then as the temperature is progressively reduced, two liquids, one liquid and one solid, one liquid and two solids, and finally three solids. 4—Liquid miscibility gap boundary—begrenzung der flussigen mischungsliicke: the line along which the surface of the miscibility gap dome, considered as a solid model, intersects the surrounding liquidus surfaces. 5—Tie lines—konoden: lines joining points representing the compositions of two liquids, a liquid and a solid, or two solids, in equilibrium. In binary systems the only tie lines customarily drawn are those through invariant points, e.g., through the eutectics of the Pb-Zn and Ag-Pb systems, or the various peritectics of the Ag-Zn system, as in Figs. 1 to 3. In ternary systems it is desirable to draw sufficient tie lines to indicate the slopes of all possible tie lines. 6—Ternary eutectic point—ternares eutektikum: point at which liquid transforms isothermally to three solids, S1, S2, and S Such a point can lie only within the triangle 7—Invariant peritectic (transformation) point— nonvariante peritektische umsetzungspunkt: (a) — On the miscibility gap boundary, the point at which two liquids and two solids react isothermally so that L, + S, + L, + S2. (b)—On the eutectic trough, the point at which a liquid and three solids react iso-thermally so that L + S, + S2 + S3. Such a point must lie on that side of the line joining S,S which is further from S,. (c)—A further possibility, not found in this ternary system, is that the point is at the intersection of two peritectic folds when the reaction concerned is L + S, + S, + S Historical Introduction Karsten discovered in 1842 that silver and gold may be separated from lead by the addition of zinc.2 Ten years later Parkes used this fact to develop the well known desilverizing process which bears his

Jan 1, 1955

By Walter Miller

A surprising development during the year was the continued high demand for petroleum products and the high level of crude oil charges to the stills. Generally speaking, the petroleum industry during 1946 succeeded in producing a greater quantity of crude oil and petroleum products than in any of the war years, and considerably exceeded the production of any prewar year. Daily crude still charges averaged between 4,700,000 and 4,800,000 bbl per day for 1946 and about equaled the 1945 record, although most pessimistic 1945 guesses, predictions, or fears ranged, for 1946, from only 3,900,000 to 4,400,000 bbl per day. In spite of the high crude charge to the stills, total stock of crude oil was higher at the end of the year by some 7,000,000 to 8,000,000 bbl. A similar story holds regarding stocks of the principal refined products. Gasoline on hand at year's end was two to three million barrels lower, and was considered low for the expected demand during the coming high consuming season, while stocks of light and heavy fuel oils, although some higher than a year previous, hardly reached a comfortable level. The trend in gasoline of high octane number, which has resulted in a marked rise in. the antiknock quality by the end of 1945 (five or six numbers higher than during the war and one number higher than the prewar quality of civilian motor gasoline of 1941) was abruptly arrested by an acute shortage of metallic lead for manufacturing tetraethyl lead. Government action in the form of lead price control, rationing, and the setting of octane ceiling specifications to conform to the reduced ethyl lead compound available were enforced until abrogated at the end of the year. It will be interesting to see how rapidly the octane levels will resume the rising trend, as more metallic lead slowly becomes available for making greater quantities of ethyl lead compound. As octane quality rises over present levels the disadvantage of the refiner without catalytic cracking equipment will increase. Gasoline made by catalytic cracking, without addition of ethyl lead, approximates 77 octane by the official ASTM Motor Method test, compared with 66 for gasoline generally similar in volatility made by the older thermal cracking operation. Catalytic gasoline shows an even greater improvement in the Research octane number, the comparison being roughly 86 Research versus 71 Research octane for the thermal cracked product. This higher differential in Research octane is credited by many, although not universally so, as contributing to better road performance, and consequently resulting in a more desirable product marketwise. In some parts of the country a premium of roughly one fourth cent per gallon is now being paid for gasoline with higher Research octane made possible by including catalytic cracked product in the final blends. If such price differentials in favor of catalytic gaso-

Jan 1, 1947

By Walter Miller

A surprising development during the year was the continued high demand for petroleum products and the high level of crude oil charges to the stills. Generally speaking, the petroleum industry during 1946 succeeded in producing a greater quantity of crude oil and petroleum products than in any of the war years, and considerably exceeded the production of any prewar year. Daily crude still charges averaged between 4,700,000 and 4,800,000 bbl per day for 1946 and about equaled the 1945 record, although most pessimistic 1945 guesses, predictions, or fears ranged, for 1946, from only 3,900,000 to 4,400,000 bbl per day. In spite of the high crude charge to the stills, total stock of crude oil was higher at the end of the year by some 7,000,000 to 8,000,000 bbl. A similar story holds regarding stocks of the principal refined products. Gasoline on hand at year's end was two to three million barrels lower, and was considered low for the expected demand during the coming high consuming season, while stocks of light and heavy fuel oils, although some higher than a year previous, hardly reached a comfortable level. The trend in gasoline of high octane number, which has resulted in a marked rise in. the antiknock quality by the end of 1945 (five or six numbers higher than during the war and one number higher than the prewar quality of civilian motor gasoline of 1941) was abruptly arrested by an acute shortage of metallic lead for manufacturing tetraethyl lead. Government action in the form of lead price control, rationing, and the setting of octane ceiling specifications to conform to the reduced ethyl lead compound available were enforced until abrogated at the end of the year. It will be interesting to see how rapidly the octane levels will resume the rising trend, as more metallic lead slowly becomes available for making greater quantities of ethyl lead compound. As octane quality rises over present levels the disadvantage of the refiner without catalytic cracking equipment will increase. Gasoline made by catalytic cracking, without addition of ethyl lead, approximates 77 octane by the official ASTM Motor Method test, compared with 66 for gasoline generally similar in volatility made by the older thermal cracking operation. Catalytic gasoline shows an even greater improvement in the Research octane number, the comparison being roughly 86 Research versus 71 Research octane for the thermal cracked product. This higher differential in Research octane is credited by many, although not universally so, as contributing to better road performance, and consequently resulting in a more desirable product marketwise. In some parts of the country a premium of roughly one fourth cent per gallon is now being paid for gasoline with higher Research octane made possible by including catalytic cracked product in the final blends. If such price differentials in favor of catalytic gaso-

Jan 1, 1947

By Harold S. Morgan

INTRODUCTION The Waste Isolation Pilot Plant (WIPP) is being developed in southeastern New Mexico by the United States Department of Energy as a research and development (R&D) facility to demonstrate the safe disposal in salt of radioactive wastes resulting from defense activities. As part of the WIPP R&D program, a series of in situ tests will be performed to determine the behavior of drifts and storage rooms in the creeping salt medium (Matalucci, et al. 1982). Data obtained in these tests will be used to evaluate and improve numerical models used to compute the structural response of these drifts and rooms. Stress has been proposed as one of the parameters to be measured in the tests, and borehole inclusion stressmeters have been included in the instrumentation package. Cages of this type provide an indirect measurement of stress change in that they actually monitor borehole displacements which are then related to changes in the in situ stress away from the borehole. The relationship between stress and displacement is highly dependent upon the constitutive behavior of the rock in which the gage is emplaced. This relationship is well understood for rocks with linear stress-strain behavior (Fossum, et al, 1976), but, for creeping rocks like salt, the relationship has yet to be determined. Thus, inclusion gage response in salt must be investigated fully before stress measurements from the WIPP in situ tests can be used for comparisons with computed stresses The calculations presented in this paper were performed as part of an investigation of inclusion stressmeter performance in salt. They focus on the strain gaged stressmeter (SGS) (Cook and Ames, 1979) and on a hypothetical solid cylindrical inclusion with variable stiffness Issues addressed include the effects of creep and the effects of gage stiffness on stressmeter output for various loading conditions. The

Jan 1, 1984

By A. Raman, P. P. Singh

The constitution of the La-Rh system was studied by powder X-ray diffraction, metallopaphic, and differential thermal analysis techniques and an equilibrium diagram is presented. Eleven intermediate phases occur in the system and the crystal structural data for nine of them were determined. La3Rh crystallizes in an orthorhombic structure of undetermined type, whose unit cell is obtained by doubling the 'a; and 'c,,' edges of an FesC type unit cell. The other intermediate phases of the system are LarRh-3( undetermined structures also occur in the system. LaRh, undergoes a polymorphic phase transformation at 1240°C. LaRh3 and La2Rh7 also exhibit polymorphisnz. The phases Laah and LazRh7 melt congruently. The latter undergoes a eutectoid transformation into LaRh, and Rh at 1205°C. Laah3 is formed by a peritectoid reaction between Laah and La,Rh,,. The other Phases result from peritectic reactions between the liquid and the adjacent rhodium-rich phases. The intermediate Phases of the La-Rh system are compared with those of the La-Co and La-Ni systems. DURING the course of a detailed investigation to study the occurrence of CrB, FeB, A1B2, and related structures in the rare earth alloys it was found that much information is lacking for the rare earth noble metal systems. Although the structures of several rare earth alloys containing the noble metals at the AB and AB2 stoichiometries have been reported, the occurrence of related structures at other stoichiometries has not been studied. We have initiated a project to study the crystal structural features of selected rare earth-rhodium alloys and to map the equilibrium diagrams of representative systems with conventional methods. The results of our investigation in the La-Rh system are presented in this paper. Two phases were known in the La-Rh system. LaRh has the CrB-type structure.' LaRhz is a MgCu2-type Laves phase.z EXPERIMENTAL PROCEDURE Alloys weighing less than 1 g were prepared from commercially pure lanthanum (99.9 pct +), supplied by Lunex Company, Pleasant Valley, Iowa, and rhodium (99.92 pct +), supplied by Engelhardt Industries, Newark, N.J., in a conventional arc melting furnace under argon atmosphere. The buttons were turned upside down and remelted three times to insure homogeneity in the samples. Since negligible loss of material was encountered during melting, a chemical analysis of the alloy buttons was not undertaken. Powder specimens for X-ray diffraction studies in the as cast state were then prepared. The buttons were wrapped in thin molybdenum foils and homogenized by heating in vacuum at suitable high temperatures for more than 1 week. They were then broken into three or four pieces for annealing experiments. The pieces were wrapped in molybdenum foils and annealed at various temperatures in evacuated quartz capsules. The annealing was carried out for 2 hr at or above 1200°C, 1 day at temperatures close to llOO°C, 2 days at 1000°C, and for 1 week at temperatures below 1000°C. After annealing the alloy pieces were again broken and powder specimens for X-ray diffraction were prepared. The powders of the lanthanum rich alloys with more than 80 at. pct La were prepared by filing. The filings were sealed in molybdenum tubings and stress-relieved at 600°C in vacuum. It was not deemed necessary to stress-relieve the powders of the other alloys, since the alloys were very brittle and were ground easily. POWDER X-RAY DIFFRACTION X-ray diffraction photographs of powders (-325 mesh size) of the alloys in the as cast and annealed states were prepared in a Guinier-de Wolff focussing camera with copper K, X radiations. These patterns were studied to identify the stoichiometries and the crystal structures of the intermediate phases. The lattice parameters of the phases were calculated after minimizing the differences between the observed sin2 6 values, calculated from the diffraction angles 8, and the sin2 8 values, calculated using approximate lattice constants obtained from a few lines. These differences were minimized manually to less than 0.0005. The latLice constants are judged to be accurate to *0.005A for values less thp about 10A and to k0.01~ for values greater than 10A. The relative intensities of the lines were calculated using a computer program written by Jeitschko and Parthk.~ No attempt was made to refine the atomic positional parameters in the phases. METALLOGRAPHY The phase equilibria in the investigated alloys in the as cast and annealed states were also studied by metallographic examination. The polished specimen surfaces were etched with 10 pct picric acid in alcohol (alloys up to 25 pct Rh), concentrated picric acid (from 25 to 37.5 pct Rh), 2 pct nital (40 to 50 pct Rh), 10 pct nital (from 50 to 66.7 pct Rh) and with concentrated 48 pct HF for the other rhodium-rich alloys. Selected microstruture~ were then photographed using a Po-laroid Land camera. THERMAL ANALYSIS Differential thermal analysis of the alloys was carried out in DTA-668 Stone differential thermal ana-

Jan 1, 1970

By William P. Blake

This camp is just now startled by the alarming suggestion that unless there shall speedily be an appreciation in the value of silver, and a decrease in the cost of salt, it will be prudent business policy to close the Alice mines and mills until the conditions of production are more favorable. Such an event would be a great blow to the prosperity of Butte. It would throw some hundreds of men out of employment, and it might lead to the adoption of the same policy by other companies, which, like the Alice, have not been able to pay dividends to their shareholders for a long time. The question arises, and becomes emphatic: If, under the present adverse conditions, the mines and mills cannot be made to pay a proper profit, why should they continue to be worked ? The owners mentally ask: Shall we go on exhausting our mines, pouring out a stream of silver for the maintenance of the community, and the support of the rail ways, or shall we husband our reserves, withdraw the miners from our slopes, and wait for more favorable conditions ? This is the impending question, and all concerned dread to meet and answer it. Let us briefly review the situation and forecast, if possible, what the solution of' the problem will be. It must be understood that the discussion does not include, or refer to, the immense copper-producing interests of the camp, which may or may not be upon a very much more satisfactory basis. It will be confined chiefly to the operations of the Alice company, sta tistics of which are at hand, without involving the other silver com panies in the conclusions beyond those inevitable from well-known facts, patent to all. There are at present in Butte and in its vicinity in the principal mills an aggregate of 290 stamps dropping upon silver-ores: Alice,...........80 stamps. Moulton,. .........40 " Lexington,...50 " Silver Bow,.........30 " Blue Bird,..........90 " The Alice mills at present, with their 80 stamps, devour, in round numbers, from 100 to 120 tons a day. The actual amount

Jan 1, 1888

By L. D. Hall, D. R. Mash

The paper presents the results of experiments on the anelastic. behavior of gold, as manifested by grain boundary relaxation. Two grain boundary internal friction peaks are found for 99.9998 pct Au. It is found that the peaks are associated with primary and secondary recrystallization. However, the existence of two discrete peaks cannot be explained on the basis of grain size and shape alone. It is suggested that grain boundary stability, as determined by orientation, plays a role in the observed effects. EVIDENCE for the viscous behavior of grain boundaries in metals has been presented in recent years by several investigators, based upon studies of various anelastic effects, especially internal friction. KG1 has contributed greatly to this field, having put forward a coherent body of evidence for stress relaxation by the viscous intercrystalline flow mechanism. In this connection, he has made extensive use of pure aluminum (99.991 pct) as the test material, although he has also studied other metals and alloys, including pure iron (Puron).² Rotherham, Smith, and Greenough³ have studied the internal friction of pure tin, interpreting their results in a manner similar to that of KG. In view of the importance of such studies in shedding light upon the fundamental structure and behavior of the grain boundaries in pure metals, it appears that the use of a very pure test material which is inert to its environment should provide useful information on anelastic properties and the source of such behavior in pure metals. The present work was carried out on spectrograph-ically pure, 99.9998 pct Au, free of all impurities except for a trace of silver, estimated to be present to the extent of about 0.0002 pct. The term "pure gold" will hereafter refer to this very pure material. Gold of commercial purity, 99.98 pct, was also studied to observe the effects of small amounts of impurities. A pure gold "single crystal" specimen was also tested for comparison. The variation of the internal friction and rigidity modulus as a function of temperature was determined by means of a torsion pendulum apparatus employing extremely low stress amplitudes and a frequency of vibration of the order of 1 cycle per sec. A 12 in. length of 0.031 in. (20 gage) gold wire formed the suspension element. The apparatus was similar to that described by Ke.l The test procedure and the basic requirements to be met for obtaining useful experimental data by this method have been given elsewhere.1,2 It should be made clear that in all of the experiments to be described, the internal friction and rigidity were independent of the amplitude of torsional vibration. The semilog plot of amplitude of vibration vs ordinal number of vibration was a straight line. This was carefully verified for each internal friction measurement. The linear variation shows that the internal friction was independent of stress; i.e., that the specimens were not being cold-worked during testing. The reproducibility of the internal friction curves, which were obtained by cyclic heating and cooling, indicates that the gold was unaffected by its environment during the tests. The measure of internal friction adopted in the present study is the conventional "logarithmic decrement," defined as follows: log. dec. = l/n In A0/An [I] where n is the number of cycles or vibrations; A,, the initial amplitude of vibration; and An, the amplitude after the nth cycle. When the logarithmic decrement is small, the shear modulus, G, of the wire is proportional to the square of the frequency of vibration provided the length and radius of the wire are kept constant. A plot of frequency squared vs temperature gives the following ratio:' This expresses the fraction of the stress which has not been relaxed at a given temperature. Gr and Gv are the relaxed and unrelaxed moduli, respectively. The frequency of vibration in the polycrys-talline specimen is fp, and the frequency of vibration of a single crystal is f8. This latter quantity is obtained simply by extrapolating the linear, low temperature portion of the curve of frequency squared vs temperature for the polycrystalline specimens. The theory of viscous grain boundary stress relaxation as demonstrated by the anelastic behavior of metals has been discussed in detail by Zener4 and need not be reproduced here. Experimental Results Initial measurements of the internal friction of pure gold were carried out on specimens which had been drawn with no intermediate annealing, resulting in a material which had undergone approximately 99 pct reduction of area in final processing. Annealing was then carried out at successively higher temperatures starting at 400°F for 1 hr and proceeding in this manner to as high as 1600°F in 100°F intervals. After each annealing treatment an internal friction and rigidity vs temperature curve was obtained over the range from room temperature to the particular annealing temperature. The resulting internal friction curves did not exhibit well defined maxima (peaks), but rather several fairly flat

Jan 1, 1954

By AIME AIME

CHARLIE WARNER, Chairman of the Petroleum Division, is no stranger to the problems of the oil industry or to those of the Petroleum Division, after more than 25 years of experience in locating and producing oil and more than 22 years of membership in the Institute. He was born at Jefferson, N. Y.. April 27, 1894, and educated in the public schools of New York State and at Cornell University where he studied geology and allied sciences from 1913 to 1917 and received a B.A. degree. Immediately upon completion of this training, he was employed by the Empire Gas & Fuel Co. as a field geologist in Oklahoma and Kansas. Two years later he became district geologist for the Emerald Oil Co. in Oklahoma and Kansas, and in 1920 he rejoined the Empire Gas & Fuel Co. in the capacity of district geologist in Oklahoma. In September of 1921 he began his association with the Houston Oil Co. of Texas. He was district manager for the company in the Mid-Continent area until 1932 when he was transferred to the head office at Houston, where he became superintendent of the land and lease department in 1934 and was elected a director of the company in 1941. In these capacities, and also as petroleum engineer for the company, he keeps in intimate touch with all phases of field activity and with the regulation of the industry by State and Federal agencies.

Jan 1, 1943

By Jerome Strauss

IN his review of developments in 1943, Gilbert Seil, Chairman of this Committee on Reduction of the Ferroalloy Ores, tabulated the consumption of the alloying metals in relation to the steel production of that year. In the year just closed the approximate tonnage was of the same order, differing only to a minor degree or suffering some correction with more precise figuses available, as indicated in the following estimates: Consumption Metals in Tons Steel 92,000,000* Manganese 700,000 Silicon 200,000 Chromium 200,000 Nickel 75,000 Molybdenum 20,000 Tungsten 8,000 Vanadium 1,700 Titanium 1.600 Boron 10 `Production figure. The technologic studies instituted during 1942 and carried forward with such great vigor during 1943 continued into 1944 although in some instances were brought to a close either by completion of the specific development

Jan 1, 1945

By John V. Beall

There is an underlying surge to mining in the Philippines." So said A. R. "Ham" Reed, general manager Itogon-Suyoc Mines, Inc., to this reporter last November. Itogon-Suyoc is a small company with a struggling gold mine, a mixed sulfide mine and some prospects. In the Republic of Philippines (ROP), politics, which have an effect on mining, create some uncertainties. By July 1974, no mining company may have more than 40% foreign ownership. The ownership provision is a matter of concern to such important companies as Atlas and Benguet Consolidated and is generally considered a deterrent to new foreign investment. Under these circumstances, Reed's comments are of interest. On foreign prospectors: Don't come in cold; find a Philippine partner or buy into a company already here. Physical conditions of exploration are tough-terrain, communications -but the mineral potential is excellent.

Jan 4, 1969

By N. W. Lord

The process of molten-zone refining is analyzed for long ingots and many zone passages. Formulas are derived which give the resultant impurity distribution in terms of finite series. A comparison with the approximate procedure of Hamming is given. HE physical principles and applications of an extremely physicalprinciple efficient form of metallurgical refinement has been described by Pfann. The purpose of the present paper is to describe a method of analyzing exactly the particular program used which enables the segregation effect to be predicted for any number of molten-zone passages in a long ingot. The method is applied to the particular case of refinement of an ingot whose impurity initially is uniformly distributed throughout its length. A number of molten zones of equal length are passed through the ingot effecting a radical redistribution of impurity. Pfann has indicated an approximate method, due to R. W. Hamming, of calculating the resultant concentration after each successive zone pass for a particular value of the segregation constant defined in his paper. Here a solution will be presented in terms of the number of zone passes and the segregation constant. The expression, though cumbersome, is exact and susceptible to ordinary numerical computation procedures. The results of a similar computation using the procedure of Hamming are presented in a table together with the exact results of the present method. The discrepancy in terms of absolute concentrations is tabulated for the first eight zone-lengths. To establish the notation (which follows that of Pfann1 as closely as possible) and physical basis of the analytical equations, the physical model and principal assumptions may be reviewed. An alloy of two elements, where there is formed a continuous range of solid solutions, usually does not melt as a simple compound. Rather, a temperature is reached where the solid solution is in heterogeneous phase equilibrium with a liquid solution of different composition. The temperature dependence of these equilibrium compositions forms part of the phase diagram. For very small concentrations of a solute B in a solvent A, this usually takes the form of Fig. 1. Sometimes the solidus and liquidus slope upward. This corresponds to a segregation constant (defined below) which is greater than unity. The segregation constant is now defined as k = Cn(x)/CnI(x) [1] where C,,(x) is the impurity concentration in the solid ingot at distance x during the nth passing of a molten zone and Cnl (x) is the impurity concentration of the liquid zone from which the solid at dis- tance x is formed (see Fig. 4 of ref. 1.) C (x) remains the same after passage of the zone. The constant k may be either greater or less than unity in general. Purification in the former case is effected only in a finite ingot and in the portion that is melted last. For k less than unity purification is effected even in an infinite ingot. The method which follows gives, in the former case, the successive increases in impurity concentration and, in the latter case, the successive decreases in concentration. The general case of impurity redistribution will be considered first, and purification will be discussed later on. The analysis rests on the following assumption: The movement of the zone is too rapid to allow appreciable atomic rearrangement in the solid sections and too slow to disturb the uniform impurity distribution in the liquid zone characteristic of equilibrium. Hence, the composition in the solid at the left solidifying interface will be determined by Eq. 1 while the impurity concentration of the liquid zone will be uniform throughout its length. The reasoning which follows closely parallels that of Appendix 11 in Pfann&apos;s paper. It is reviewed here for the case of the nth zone pass in order to make clear the meaning of an operator essential to the present method. Fig. 4 of ref. 1 shows the movement of a molten zone of length 1 in an ingot of total length d. Each Cn(x) can be determined from the condition that the amount of solute added to the zone during an incremental advance, dx, is due to the melting in of a solid portion C(x)dx and the freezing out of kCnl(x), that is d I —r- CnL (x) dx = Cn-1 (x+l)- kCnL (x) dx or, in terms of Cn(x) d k k —— C,(x) +—c.(x) =— Cn-1 (x + l). [2] dx l l This, of course, is derived from the main assumption, the fact that 1 is constant, and that the total impurity content previously present up to x + 1 is constant . A correction has to be made for the region (d — nl) < x < d. This is due to the zone length changing during the passage of the solidifying interface beyond x = d — 1. Since the general solution would be too complicated otherwise, only the region 0 < x < d — nl is considered. The general solution of Eq. 2 is

Jan 1, 1954

By Joseph R. Crump, Francois Ville, Frank M. Tiller

Several simplifications have been accepted in filtration theory during the past fifty years in an effort to avoid apparently intractable mathematical problems. In effect, these simplifications ignored the variation in average cake porosity and average filtration resistance with variation in pressure drop or with time. This study examines the traditional approach and shows that, in many cases, it cannot give correct design guidance. Using a set of dimensionless parameters because of the large number of significant variables, a revised theory is developed which does not require that porosity and resistance values be set constant. Graphs developed in the traditional approach (e.g., dt/dv versus v or t/v versus V) have substantial curvature near the ordinate; but this curvature is frequently ignored in theory and is easily missed in experiments. The revised theory allows more accurate design calculations, especially for compressible cakes.

Jan 1, 1980

By Donald Barton

THIS paper outlines a time-saving graphical method of calculation for application to the interpretation of observations with the Eötvös torsion balance. Preliminary to the treatment of this short cut method which has been found practicable, the principal formu-las by which the student of interpretation can calculate the gradient and differential curvature produced by different types of bodies in different types of situa-tions are presented and discussed. It is necessary to split most geologic bodies into a series of simpler ones for which not too complicated formulas are avail-able. The gradient and differential curvature effects are calculated for each of the simple bodies and then summed to the total effect for the whole body. The calculations are considerable in number and, though more tedious than difficult, should be&apos; entrusted to an experienced calculator. Considerable facility in qualitative interpretation can be acquired by the geophysicist from experience and from a thorough study of the types of gradient and differential curvature anomalies produced by the dif-ferent types of possible structural situations. How-ever, semi-quantitative calculations&apos; of the probable structure bring out many relations that are not evident in a simple inspection of torsion balance results ; it throws out as impossible or improbable certain of the alternative structural possibilities that may seem equally probable under simple inspection of the results; it will determine more accurately the position of the crest of the structure; and reduce considerably the un-certainty in the interpretation and it is necessary to intelligent interpretations. The calculation of such cross-sections consists of a trial-and-error calculation of a body that will give gradient and differential curvature effects as closely as possible the same as those observed. From his knowledge of the gradient and differential curvature produced by different types of bodies, the geophysicist sketches a tentative cross-section of the structure as indicated-to him-by the observed results of the torsion balance survey, and the calculator then splits the struc-ture into blocks, and calculates the gradient and differ-ential curvature block by block. If, as rather usual, the calculated .gradient and differential curvature pro-files diverge considerably from, the respective observed ones, it is necessary to add and subtract blocks from the cross-section until a close agreement is obtained .between the calculated and observed profiles. The com-plete calculations have to be gone through for each block that is added or subtracted.

Jan 9, 1928

By N. D. Shutler

This paper describes a numerical mathematical model of the steamflood process that depends on fewer restrictive assumptions than models previously reported. The solution, however, is obtained economically. Example calculations are presented that, on comparison with experimental results, tend to validate the model. Results that expose certain process mechanics are discussed. The model describes the simultaneous flow of three phases — oil, water and gas — in one dimension. It includes the effects of three-phase relative permeabilities, capillary pressure, and temperature- and pressure - dependent fluid properties. Interphase mass transfer of water-steam is allowed, but the oil is assumed nonvolatile and the hydrocarbon gas insoluble in the liquid phases. The model allows heat convection in one dimension and two-dimensional heat conduction in a vertical cross-section spanning the oil sand and adjacent strata. The hydrocarbon-steam gas composition is tracked, but the effect of gas composition on water-steam phase behavior is neglected. The model is solved numerically in three separate stages. The three-phase mass balances are solved simultaneously using Newtonian iteration on nonlinearities occurring in the accumulation terms. The energy balance is solved separately by noniterative application of the alternating-direction implicit procedure. Separate solution of the composition balance is accomplished by straightforward solution of the finite difference equations. The method of effecting nonsimultaneous, stable solution of the mass and energy balances is the key to the success of the model. INTRODUCTION Mathematical tools as well as laboratory and field experiments are necessary to help us understand the complex steamflood process. A mathematical model can expose process mechanics and show the relative importance of process variables, but this ability is often limited by restrictive assumptions. Most known models of steam processes,l-5 with the exception of the model of Gottfried,6 are "simplified" in that they involve analytic approximations and require many restrictive assumptions. The primary utility of these methods lies in the routine use as an aid in engineering design. By contrast, the comprehensive model presented here is numerical and requires far fewer restrictive assumptions. It finds its primary utility as a research tool. It serves as an aid in understanding the nature of the process, in interpreting laboratory experiments and in evaluating and developing simpler mathematical models for engineering design. The major reason why previously presented models have been confined to the "simplified" class is evidenced by the one published exception. In 1965, Gottfried6 presented a numerical model for the combustion process of which the steam process is a subset. The result is a comprehensive tool (though it neglects capillarity and two-dimensional heat conduction) that is troubled with convergence problems and that requires 2 to 3 hours of IBM 7094 time to complete a calculation. Though our present model does not simulate combustion, it does consider capillarity and two-dimensional heat conduction and it overcomes the convergence and computer-time problems. MATHEMATICAL DESCRIPTION OF STEAMFLOODING FLUID FLOW The equations employed to describe three-phase fluid flow are of a familiar form. Darcy&apos;s. law provides expressions for the velocities of the three phases (oil, water and gas), which, when combined with oil, water and gas mass balances, give the partial differential equations governing flow of the

Jan 1, 1970

By R. C. Hassinger, D. V. von Rosenberg

Transverse dispersion has received considerably less treatment in the literature than has longitudinal dispersion. Different methods for determining transverse dispersion coefficients have been used in different investigations, and the results obtained have not been consistent enough to permit accurate generalizations as to the effect of various physical parameters on the magnitude of these coefficients. A numerical solution to the differential equation describing transverse dispersion in the absence of longitudinal dispersion was obtained to enable one to calculate the dispersion coefficient from experimental results. The more general dispersion equation including longitudinal dispersion also was solved numerically to give quantitative limits of a dimensionless group within which the assumption of negligible longitudinal dispersion is justified. Possible experimental procedures were examined, and one utilizing a cylindrical packed column was chosen for the determination of transverse dispersion coefficients. Values of these coefficients were determined for a system of two miscible organic fluids of equal density and viscosity, for two sizes of packing material over a wide range of flow rates in the laminar regime. The dispersion coefficient was found to decrease, for a constant value of the product of packing size and interstitial velocity, as the size of the packing material particles increased. INTRODUCTION Longitudinal dispersion has received extensive treatment in the literature, and consequently is better understood than its orthogonal counterpart, transverse dispersion. Many mathematical models of dispersion processes assume that transverse dispersion is rapid enough to damp out any radial** concentration gradients and therefore may be neglected. Laboratory and production results, however, indicate that this is a poor assumption.l,2 Various experimental procedures for determining transverse dispersion coefficients have been used in previous investigations, but the results have generally been expressed by similar correlations. The transverse dispersion coefficients obtained, however, have often varied considerably for given values of the correlation parameters. We feel that further experimental determinations of transverse dispersion coefficients will help alleviate some of the inconsistencies in these empirical correlations. One assumption implicit in all previous investigations is that of negligible longitudinal dispersion in the experimental system. An attempt to justify this assumption often is made using intuitive reasoning, but it is apparent that this reasoning must break down as the condition of zero flow rate is approached. A mathematical examination of the equations describing the system yields physical limits outside of which the assumption of negligible longitudinal dispersion is invalid. BACKGROUND In a porous medium, the "effective molecular diffusivity" De is less than the molecular diffusivity D measured in the absence of a porous medium, due to the tortuous path which a diffusing molecule must travel. Various authors3-5 have reported values of the ratio De/D in the range of 0.6 to 0.7. When there is fluid flow within the porous medium, mass transfer occurs by convective dispersion as well as by molecular diffusion. These are separate phenomena and can be treated as such on a microscopic scale. However, the mathematical complexity is such that only extremely simple geometries could be considered, and the results hardly would be applicable to the complex geometries existent in actual porous media. A more

Jan 1, 1969

By Charles H. Jacoby, Stanley J. LeFond

Salt, or halite, has a long and most varied history. While we know the Chinese were producing salt as early as 3000 B.C., the first written reference to salt appears in the book of Job recorded about 2250 B.C., which reads: "Can nothing which is unsavory be eaten without salt?" We do not know when man first used or realized that he needed salt. Perhaps one of our early Eolithic ancestors noted a piece of salt shining along the shore of a salt lake or a bay. He may have been attracted by its shining luster and tasted it. He found that it had a tart, zesty, distinctive flavor and perhaps chewing a large piece, became ill. However, by experimentation he soon learned that taken in the proper proportions salt was a very pleasant additive to his food. He may have noticed, too, that it increased his feeling of well-being. Thus, when the curtain of recorded history rises, we find man using salt for his health&apos;s sake, seasoning his food with it, feeding it to his animals, and using it in many superstitious and religious ceremonies. These uses, however, are a far cry from the uses for salt today. The first attempts of white man to make salt in continental United States were reported in the year 1614, while the first commercial production was in 1753 from the Kanawha licks. Practically all this salt was for human consumption, preserving food, and curing hides. Prior to the coming of the white man, Indians are known to have made salt from salt springs such as those that existed at Avery Island, LA, Charleston, WV, Saltville, VA, and Onondaga, NY. In 1862 the first rock salt was mined in the US from the Avery Island salt dome. Almost immediately thereafter, rock salt was mined at Saltville, VA and then at Retsof, NY in 1885. Of the more than 39 million tons produced annually in the United States, about 58% or 23 million tons are consumed by the chemical industry in the production of chlorine, caustic soda, hydrochloric acid, sodium metal, and some 30 other basic chemicals. These basic chemicals, in turn, are used in the preparation of approximately 14,000 chemicals which range from soap and detergents, to such chlorinated hydrocarbons as DDT, BHC, carbon tetrachloride, etc. Utilization of cavities created in salt beds and domes has grown rapidly since 1947 until now the waste salt is creating an ecological problem. The uses for both dry- and solution-mined cavities range from the storage of liquid hydrocarbons to containerized storage of toxic wastes, from compressed air for the peak shaving of power to storage of nuclear wastes. Geology Mineralogy Properties: Because of its simple structure, halite, the mineralogical name for salt, was the first structure to be analyzed by X-rays. It has the following properties: Formula: NaCl (Na-39.34%. Cl2-60.66% ) Crystallography: isometric, hexoctahedral, 4/m 32/m Space group: Fm3m A0: 5.627 kX Cell contents: Na4CI4 Habit: usually cubic, rarely octahedral, massive, granular to compact Physical properties: Refractive index: 1.554 Twinning: observed on {111} Cleavage: {001} perfect Fracture: conchoidal, brittle

Jan 1, 1983

By F. F. Aplan, P. H. de Bruyn

The adsorption density of hexyl mercaptan was measured at the gold-solution and the gold-vapor interfaces. This collector is strongly adsorbed at low concentrations, a monomolecular layer being formed at the gold-solution interface at concentrations as low as 2 x 10&apos;6 moles per liter. A maximum contact angle of 83 ± 3° is observed. From a thermodynamic analysis of the experimental data the changes in surface tension at the gold-gas and gold-solution interface are calculated. The data also suggest that the adsorption density of mercaptan at the gold-gas interface exceeds that at the gold-solution interface. In the equilibrium state, a simple flotation system consists of three phases, the solid to be floated, air, and an aqueous solution in stable contact along a line. During the process leading to this final state, a solid-gas interface is created at the expense of a portion of the liquid-gas and solid-liquid interfaces. This change of state is achieved by addition of a collector and, if necessary, suitable modifying agents to the system. By a combined application of the Gibbs Adsorption and the Young Equations, de Bruyn, Overbeek and Schuhmannl were able to show theoretically that the equilibrium distribution of the collector at all three interfaces determines the magnitude of the contact angle. Their analysis led them to conclude that the equilibrium adsorption density of the collector at the solid-gas interface exceeds its density at the solid- liquid interface. This paper succeeded in focussing attention on the neglected role of the solid-gas interface in flotation. In recent years the application of radiotracer, infrared, electrochemical and electro-kinetic techniques to studies of the solid-liquid interface2-5 enhanced our understanding of adsorption processes at this interface. Except for the measurement of contact angles, the solid-gas interface received no attention in fundamental flotation studies. In an attempt to apply the analysis of de Bruyn, Overbeek and Schuhmann to a simple flotation system, an investigation of the adsorption of hexyl mercaptan onto gold was undertaken. Gold was chosen as the solid phase in order to keep the number of dissolved chemical species in the solution phase to a minimum. Hexyl mercaptan (1 - hexanethiol) was selected as collector because its relatively high vapor pressure at room temperature makes it possible to obtain adsorption measurements at the solid-gas interface. This flotation system consists, therefore, of a pure solid phase (gold), an aqueous solution of a weakly dissociated collector (1 -hexanethiol), and a gaseous phase, nitrogen saturated with respect to both water vapor and mercaptan vapor. EXPERIMENTAL MATERIALS AND METHODS Materials: Liquid 1-hexanethiol (C6H13SH) was obtained from Distillation Products Industries and was further purified by double distillation. The purity of the final product was established by boiling point and refractive index measurements. For the adsorption studies from aqueous solution, the radiotracer element, sulfur-35, (half life 87.1 days, 0.169 Mev beta ray) was synthesized into the mercaptan by Tracerlab Inc., Boston, Mass. A close boiling fraction of the synthesized compound was used in the adsorption studies. The specific activity of the radioactive compound was 10 millicuries per gram.

Jan 1, 1963

By B. M. Larsen, K. Heindlhofer

THIS paper describes a relatively simple electrical apparatus that, through the close analogy between the flow of heat and of electricity, enables one to solve quickly and with satisfactory accuracy many complex problems in heat flow. This device, developed in 1935, has proved especially useful in the solution of certain practical problems relating to the design and efficiency of regenerators for an open-hearth furnace or coke oven, yielding within a few hours information that would take weeks or even months to acquire by mathematical1.2 or experimental3 methods of comparable accuracy. Its description now is prompted by growing interest in such analogues, as shown by several recent papers.4.5 The analogy between flow of heat and of electricity appears to have been recognized first by Maxwell who, in his famous Treatise on Electricity and Magnetism (1881) says: The analogy between the theory of the conduction of electricity and that of the conduction of heat is at first sight almost complete. If we can take two systems geometrically similar, and such that the conductivity. for heat at any part of the first is proportional to the conductivity for electricity at-the corresponding part of the second, and if we also make the temperature of any part of the first proportional to the electric potential at the corresponding point of the second, then the flow of heat across any area of the first will be proportional to the flow of electricity across the corresponding area of the second. .. Thus, in the illustration we have given, in which flow of electricity corresponds to flow of heat, the electric potential to temperature, electricity tends to flow from places of high to places of low potential, exactly as heat tends to flow from places of high to places of low. temperature He noted, however, that this analogy is restricted: ... there is, however, one remarkable difference between the phenomena of electricity and those of heat. Suspend a conducting body within a closed conducting vessel by a silk thread, and charge the vessel with electricity. The potential of the vessel and of all within it will be instantly raised, but however long and however powerfully the vessel be electrified, and whether the body within be allowed to come in contact with the vessel, or not, no signs of electrification will appear within the vessel, nor will the body within show any electrical effect when taken out. But if the vessel is raised to a high temperature, the body within will rise to the same temperature, but only after a considerable time, and if it is then taken out it will be found hot, and will remain so till it has continued to emit heat for some time. The difference between the phenomena consists in the fact that bodies are capable of absorbing and emitting heat, whereas they have no corresponding property with respect to electricity. According to this statement the application of the analogy would be limited to problems of steady flow that do not involve heat-capacity effects. In spite of this

Jan 1, 1945

By J. E. Pavlick, A. G. Guy

The total creep of tin alloys containing antimony in solid solution was observed to decrease with increase in antimony content. However, near the solubility limit an anomalous maximum in deformation was. found, in agreement with similiar observations by Bochvar. IT has long been recognized that alloys may deform more rapidly under stress if there is a tendency for a phase change or other structural change to occur simultaneously. However, the phenomena involved are complex and in some instances the opposite effect, strengthening, may result.&apos; This area of research has not attracted much interest in the western world, and although Russian investigators have studied it for the past 15 years their work has not received due attention here. Recently diametrically opposing views on one aspect of this problem have been espoused by two Russian investigators, Kornilov and Bochvar. The question is this: in certain binary alloys tested in creep at the temperature where the solute is at the limit of solid solubility, does the incipient formation of the second phase strengthen or weaken the alloy? Korni-lov&apos;s arguments in favor of strengthening were presented at the 1954 Symposium at the National Physical Laboratory, =Creep and Fracture of Metals at High Temperatures.The most recent statement of Boch-var&apos;s theory of weakening is in Oding&apos;s new book on creep and rupture.3 Although Bochvar agrees that strengthening occurs in some alloy systems, he argues that in certain alloys an anomalous weakening is observed. However, the extensive work of Korni-lov&apos;s group on creep properties of alloy systems has not revealed any anomaly of this type, but instead has tended to refute Bochvar&apos;s theory. This clear-cut controversy offered a good opportunity for a simple experiment to resolve the problem. The experiment and its results supporting Bochvar are the subject of this paper. However, it will be helpful first to sketch the present status of the larger question of the effect of a phase change or other structural change on plastic deformation. PREVIOUS WORK One of the first researches in this area was by Pfei1,37 who investigated the creep resistance of an 80 Ni-20 Cr alloy containing varying amounts of titanium. He found that the resistance to creep increased rapidly as the solid solubility limit in the alloy at 775&apos;c was approached and slightly exceeded. With further addition of titanium the creep resistance decreased, presumably because of precipitation effects. Bochvar&apos;s first work in this field was a study in 1945 of "superplasticity" in zinc alloys containing 15 to 25 pct Al.4 He found that alloys quenched from about 400 had anomalously low hardness when tested below this temperature. The following year, in a paper on the dependence of mechanical properties on the composition and structure of alloys,5 he extended some observations of Kurnakov to predict that at high temperatures of testing the hardness values for solid-solution alloys might be lower than those for the component metals. He also pointed out the influence of changes in solidus temperature in affecting curves of hardness vs composition, and he

Jan 1, 1962

By J. W. Halley

THE effects of tin on steel have become increasingly important because of the necessity of using poorly detinned scrap, tin cans, and terne plate, in the open hearth. Since a tin can contains about 1.5 per cent tin, it would be possible to have up to 0.75 per cent tin in steel made with a 50 per cent scrap charge. In order to use tin-containing scrap, it is necessary to know the effect of tin on various grades of steel. The following investigation is by no means comprehensive but covers a number of steels in which tin content is important. PUBLISHED WORK A number of investigations of the effects of tin on rolling quality and physical properties have been published. It has been found that tin increases strength and hardness and reduces ductility and notched impact resistance. The decrease in ductility and notched impact resistance becomes more marked as the carbon decreases. McKimm1 found no change in Olsen ductility, Rockwell hardness, yield strength, tensile strength or elongation in cold-reduced strip containing up to 0.124 per cent tin. A tin content of 0.15 per cent gave difficulties in rolling and increased the hardness but 0.21 per cent tin showed no change in properties from material containing very little tin. No explanation of this contradiction is offered. Andrew and Peile2 investigated steels containing 0.01 to 0.25 per cent carbon and up to 0.63 per cent tin. They found an increase in tensile strength of from 100 to 200 lb. per sq. in. for each 0.01 per cent tin on normalized samples. The elongation and reduction of area were decreased and the notched impact resistance was reduced markedly. Quenched and drawn samples did not show embrittling if water-quenched from the draw temperature of 1148°F. (620°C.). They could find no evidence of tin under the microscope. Whitely and Braithwaite3 investigated the effect of tin on rail steel containing 0.55 to 0.06 per cent carbon. They found that 0.08 per cent tin caused a marked decrease in elongation, notched impact resistance and the degree of bend. The tensile strength was increased in some tests and not in others. Bolsover and Barraclough4 investigated the effect of tin up to 0.50 per cent on a 0.35 per cent carbon steel and on several alloy steels with from 0.30 to 0.40 per cent carbon. They found a comparatively uniform decrease in notched impact resistance with increasing tin on quenched and drawn samples. If the samples were quenched from the drawing temperature or reheated to the drawing temperature and quenched, the embrittling was much less severe. Steels containing molybdenum suffered much less embrittlement than other steels. EXPERIMENTAL WORK Effect of Tin on Low-carbon Rimmed Steel Increasing quantities of tin were added to four ingots of a heat of the following ladle analysis: carbon, 0.08 per cent; manganese, 0.39; phosphorus, 0.009; sulphur, 0.025.

Jan 1, 1942