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By C. Chu

An investigation has been made of the radial heat-wave process using a mathematical model in two-dimensional cylindrical coordinates. This model considers combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. From a study of the general features of the process, an important phenomenon has been revealed, namely, the feedback of heat into the reservoir on the trailing edge of the heat wave. The effects of various process variables on the performance characteristics of the process have also been investigated. It was found that up to the time when the combustion front reaches a given point, the per cent heat loss, provided it is not higher than 40 per cent, is approximately directly proportional to the square root of thermal conductivity arid fuel content, but inversely proportional to the square root of gas-injection rate and oxygen concentration. The effecr of reservoir thickness is more pronounced, since halving the thickness doubles the per cent heat loss. The most decisive factor in determining the center-plane peak temperature is the fuel content of the reservoir. Within the temperature range investigated, doubling the fuel content doubles the peak temperature in the early stage, but the rate of decline of the peak temperature is high. Reservoir thickness is also a very influential factor. The peak temperature is lowered when the thickness is reduced; however, the effect of thickness becomes less pronounced when the thickness is high. Reduction of oxygen concentration increases the peak temperature in the early stage but lowers it afterwards because of the higher rate of decline of the peak temperature. Increase in gas injection rate or decredse in thermal conductivity geives a higher peak temperature which stays high for a longer period. The propagation range of the heat wave is chiefly governed by the fuel content of the reservoir. An increase of 0.2 1b/cu ft in the fuel content increases the propagation range by 100 per cent. The propagation range is more than doubled by doubling the gas injection rate, or reservoir thickness, or by reducing the thermal conductivity by 50 per cent. Comparatively, oxygen concentration has less effect on the propagation range. INTRODUCTION Several investigators have conducted theoretical studies of a radial heat wave. Vogel and Krueger1 studied a system with a moving cylindrical heat source of constant temper- ature, considering conduction in the radial direction only. Ramey2 included conduction in the vertical direction in his studies. Bailey and Larkin2 attacked a more general problem where initial well heating, vertical heat losses and arbitrary frontal velocities were included. In all these studies, however, conduction was considered to be the only means of heat transfer. Bailey and Larkin in a later paper included the effects of convection in a study involving both linear and radial geometries. Vertical heat losses were neglected in the radial case. Katz5 studied a similar problem in a one-dimensional radial model, using a heat-loss coefficient to account for vertical heat losses. Selig and Couch6 mployed a cylindrical model and investigated two limiting cases. In one case they considered no heat loss from the reservoir whereas in the other they assumed a constant temperature at the interface between the reservoir and its bounding formations. Thomas' studied a more general case but assumed a permeable bounding formation so that the convection effect is not confined to the reservoir. In the present work a more realistic and more generalized model is used. It involves a two-dimensional cylindrical system with combustion, convection and conduction inside the reservoir, but only conduction in the bounding formations. The purpose is to establish the temperature distribution both inside and outside the reservoir, to study the general features of the radial heat wave process, and to investigate the effects of various process variables on the performance characteristics of the process. THEORY We fist consider a circular porous reservoir of thickness H extending vertically from y = — H/2 to y = + H/2. The reservoir extends from a well bore radius r, to an external radius re. A stream of oxygen-containing gas is introduced into the reservoir through the wellbore. The oxygen-containing gas reacts with the fuel contained in the reservoir and forms a combustion front wherever the prevailing temperature can support the combustion. It is here assumed that this combustion front constitutes a cylindrical surface source of heat having an infinitesimal thickness in the radial direction and extending vertically throughout the whole thickness H. This is designated as Region I. We next consider a Region II corresponding to the upper and lower formations bounding the reservoir, extending from y = — - to y = — H/2 and from y = + H/2 to y = + m. Since r, is very small, we may assume that the two bounding formations have the same dimensions, symmetric with respect to the center plane of the reservoir. In this way, we may take the upper half of the system alone into consideration. In contrast with

By R. S. Archer

THE name molybdena was employed by Pliny to denote various substances resembling lead. Later this name was applied to galena-the naturally occurring sulfide of lead-or substances of similar appearance. By the middle of the eighteenth century, it was applied to graphite and to the mineral sulfide of molybdenum (MoS2) now called molybdenite. This confusion is quite understand- able inasmuch as these substances look and feel very much alike. In 1778, the Swedish chemist Scheele published a treatise in which he pointed out essential differences between graphite and molybdenite. On treatment with nitric acid, molybdenite, unlike graphite, produced a peculiar white earth with acidic properties which he called molybdic acid. Since the same mineral gave off sulfurous fumes on heating, he concluded that it was a sulfide of molybdenum. In 1790, there appeared an account of the isolation by P. J. Hjelm of the new element molybdenum, as a metallic powder, by heating the oxide with carbon. It was not until Bertelius conducted the necessary experiments, about 1818 to 1825, that the foundation of the chemistry of molybdenum was laid. The only recorded use of molybdenum during the first century after its isolation was as a chemical reagent, primarily for the determination of phosphorus. It was not until the last decade of the nineteenth century that the use of molybdenum in steel appears to have been investigated. A

Jan 1, 1953

By Rossiter W. Raymond

THE most important event in the history of mining in the United States was the discovery of gold in California, which led to the rapid development, not only of a new industry, but of a new empire. The settlement of the Pacific slope was making but slow progress under the inducements of a scanty commerce in furs and hides. The liberal grants offered by the government to agricultural pioneers in Oregon had attracted to the Willamette valley and other favored points in that territory a limited population; but the government of the Mexicans in California was positively unfavorable to enterprise. It is true that gold was known to exist in the country. Rumors of it were current among the trappers, and placers had actually been worked in what is now Los Angeles County ; but the padres of the neighboring mission of San Fernando had discouraged the business as demoralizing to their flocks ; and the existence of the precious metal was not widely known; still less was its distribution north¬ward suspected. The discovery of gold, January 19th, 1848, at Sutter's saw-mill, on the south fork of the American River, afterward famous as Coloma, in Eldorado County, was the beginning of the new epoch. This discovery was made by James Wilson Marshall, a partner in the mill, who observed in the debris washed down by the tail-race a glittering fragment of a mineral unknown to him. Suspecting it to be gold, he sought for further specimens, and obtained, in the course of a few days, several ounces of it. Tests subsequently

Jan 1, 1875

By Rossiter W. Raymond

The most important event in the history of mining in the United States was the discovery of gold in California, which led to the rapid development, not only of a new industry, but of a new empire. The settlement of the Pacific slope was making but slow progress under the inducements of a scanty commerce in furs and hides. The liberal grants offered by the government to agricultural pioneers in Oregon had attracted to the Willamette valley and other favored points in that territory a limited population; hot the government of the Mexicans in California was positively unfavorable to enterprise. It is true that gold was known to exist in the country. Rumors of it were current among the trappers, and placers had actually been worked in what is now Los Angeles County; but the padres of the neighboring mission of San Fernando had discouraged the business as demoralizing to their flocks; and the existence of the precious metal was not widely known; still less was its distribution northward suspected. The discovery of gold, January 19th) 1848, at Sutter's saw-mill, on the south fork of the American River, afterward famous as Coloma, in Eldorado County, was the beginning of the new epoch. This discovery was made by James Wilson Marshall, a partner in the mill, who observed in the debris washed down by the tail-race a glittering fragment of a mineral unknown to him. Suspecting it to be gold, he sought for further specimens, and obtained, in the course of a few days, several ounces of it. Tests subsequently

By Nelson Severinghaus

Following the end of hostilities of World War 11, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, One near Camak, One near Lithonia and one at Stockbridge. All have had excess fines Or in in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling Of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed 'tone is generally sold with a a narrow margin Of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. By-products of Granite Dimension Stone It sometimes becomes difficult to differentiate between main product and byproduct. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of Uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I), They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1948

By A. V. Deforest, C. W. Macgregor, A. R. Anderson

One of the important problems in the design of structures and machine parts subjected to rapidly applied loads is the determination of the strength and ductility of the material itself under such conditions. Realizing the need for such information, many investigations have been carried out in the past. Most of these experiments have been made using notched bars in bending either with the Charpy or Izod impact machine. While yielding valuable data on the effect of notches in the energy absorption of the material and on the condition of heat-treatment, this form of test does not lend itself readily to a determination of fundamental stress-strain relations. For this and other reasons, more attention has been paid recently to the tension impact test. An extensive literature already exists on the subject and only those investigations somewhat closely related to the present paper will be mentioned. For a more comprehensive list, the reader is referred to the Symposium on Impact Testing or the A.S.T.M., 1938. The work of Mann.' Clark and Dätwyler,2 Nádai and Manjoine,3 Winlock and Leiter,4 Deutler,5 and Brinkmann,6 however, deserves especial mention. In most of the previous investigations on the subject, when stress-strain relations were obtained under high rates of loading, it was the common procedure to determine stresses based on the original area and strains based on the original length. Stress-strain curves were then constructed by P ALo plotting So = 1/A0 as a function of eo = ALr,o where A0 and Lo refer to the original area and gauge length, respectively. At present there exists a paucity of true stress-strain data in the impact problem. The advantages of constructing so-called true stress-strain curves in order to reveal the fundamental physical properties of the material for the tension test were discussed recently by one of the authors.7'8 It was shown that the true physical behavior of the material in the tension test could best be represented P by plotting the average true stress, S = 2P as a function of 6 = q' = log —r = log ~9L where P, A, L, S, E, and q' refer to the load, the cross-sectioned area while the load P is applied, the actual gauge length, the average true stress, the true strain and true reduction in area, respectively. Besides giving a better physical representation, the method has certain additional advantages in that the stress-strain curve so plotted becomes a straight line from the maximin load point to fracture. The construction of such curves, however, while comparatively simple for the slow rates of loading customarily used in the tension test, presents certain dificulties for tensile impact in that both loads and diameters are required throughout the test. The continuous measurement of test-piece diameters to fracture under impact conditions offers considerable experimental difficulty. In order to make it feasible to

Jan 1, 1942

By Nelson Severinghaus

Following the end of hostilities of World War 11, a resurgence of industrial and home building has given impetus to the use of many products of the stone industry. Shortage and high prices of some building materials such as lumber have aided wider acceptance of materials such as concrete products which have been relatively plentiful and which have not risen so rapidly in price. Ingredients for many of these substituting materials come from the stone industries, often from by-products of stone operations. Most of the tonnage of the stone industry in the State of Georgia comes from granite and marble. There are extensive dimension stone operations in granite in the Elberton and in the Lithonia areas. Building and monumental marble from the Tate area has been used throughout the country. Cutting operations in both types of stone have their by-products in faulty blocks and in spalls. In the State there are three large crushed-stone plants utilizing granite, One near Camak, One near Lithonia and one at Stockbridge. All have had excess fines Or in in the past but this excess is largely disappearing with development of new uses. At times this "waste" has amounted to as much as 20 pct of the stone quarried. Handling Of this large tonnage from point of screening out to storage piles presented a costly problem and large areas were taken up by the piles. Crushed 'tone is generally sold with a a narrow margin Of price over cost, so any elimination of disposal cost or increase of income by marketing of by-products is highly desirable. By-products of Granite Dimension Stone It sometimes becomes difficult to differentiate between main product and byproduct. In the cutting of granite dimension stone in the Lithonia district of Georgia, a considerable quantity of remnants of Uneven shape and size is produced. The larger of these pieces have long found use as building rubble, particularly for retaining walls and building foundations (Fig I), They are broken down to one man size by plug drilling and wedging and by hammer. In recent times, demand for this former by-product has grown so that quarries have been opened for the production of rubble as a main product. Local masons have attained skill in using these irregular shapes to form economical and attractive walls. Areas such as Elberton, Georgia, which do not have a large building market nearby, tend to accumulate piles of large pieces of reject stone. When a road job or other local construction offers a quantity market for crushed stone, a portable crusher works this material down to crushed aggregate. Spalls and finer chips from granite stone-cutting operations have generally found their way into crushers and thence to the many uses for crushed aggregate. One company near Lithonia started marketing the smaller by-product crushed sizes for chicken grit about ten years ago. This use has grown to nation-wide distribution and the tonnage is now so great that they have opened a large quarry with

Jan 1, 1948

By A. V. Deforest, A. R. Anderson, C. W. MacGregor

One of the important problems in the design of structures and machine parts subjected to rapidly applied loads is the determination of the strength and ductility of the material itself under such conditions. Realizing the need for such information, many investigations have been carried out in the past. Most of these experiments have been made using notched bars in bending either with the Charpy or Izod impact machine. While yielding valuable data on the effect of notches in the energy absorption of the material and on the condition of heat-treatment, this form of test does not lend itself readily to a determination of fundamental stress-strain relations. For this and other reasons, more attention has been paid recently to the tension impact test. An extensive literature already exists on the subject and only those investigations somewhat closely related to the present paper will be mentioned. For a more comprehensive list, the reader is referred to the Symposium on Impact Testing or the A.S.T.M., 1938. The work of Mann.' Clark and Dätwyler,2 Nádai and Manjoine,3 Winlock and Leiter,4 Deutler,5 and Brinkmann,6 however, deserves especial mention. In most of the previous investigations on the subject, when stress-strain relations were obtained under high rates of loading, it was the common procedure to determine stresses based on the original area and strains based on the original length. Stress-strain curves were then constructed by P ALo plotting So = 1/A0 as a function of eo = ALr,o where A0 and Lo refer to the original area and gauge length, respectively. At present there exists a paucity of true stress-strain data in the impact problem. The advantages of constructing so-called true stress-strain curves in order to reveal the fundamental physical properties of the material for the tension test were discussed recently by one of the authors.7'8 It was shown that the true physical behavior of the material in the tension test could best be represented P by plotting the average true stress, S = 2P as a function of 6 = q' = log —r = log ~9L where P, A, L, S, E, and q' refer to the load, the cross-sectioned area while the load P is applied, the actual gauge length, the average true stress, the true strain and true reduction in area, respectively. Besides giving a better physical representation, the method has certain additional advantages in that the stress-strain curve so plotted becomes a straight line from the maximin load point to fracture. The construction of such curves, however, while comparatively simple for the slow rates of loading customarily used in the tension test, presents certain dificulties for tensile impact in that both loads and diameters are required throughout the test. The continuous measurement of test-piece diameters to fracture under impact conditions offers considerable experimental difficulty. In order to make it feasible to

Jan 1, 1942

By James M. Stapleton

IT has long been recognized by blast- furnace men that correct top distribution of materials is very important in efficient and economical furnace operation. Thousands of experiments on top design, filling, sizing, and other operations have been carried out to improving furnace performance by securing uniform distribution. Many of these experiments have worked out satisfactorily and have been passed along to the industry. Many of them have been discarded and forgotten. It has been the custom to judge the results of such experimentation by the results shown in improved or lowered furnace efficiency. While the effect on furnace practice will have to continue to be the final criterion of experimental changes, it has always been a desire of blast-furnace men to ascertain the reason for failure or success. Efficiency in the blast furnace approaching the maximum can be measured in several ways: (I) by actual operating results as revealed in the coke rate and tonnage figures, and (2), in the degree to which the top gas approaches the limiting ratio of CO/C02 for the reduction of iron oxide by CO gas. This ratio is shown in the equilibrium curve in Fig. I for the system Fe-O-C and CO2-CO-C. The closer the top gases approach this limiting ratio (set at 1.08 by Martin1 because of the effect of limestone calcination) the more efficiently we may expect a furnace to operate. The fact that low CO/C02 ratios parallel eficient operating performance caused us to investigate the cause of good or poor distribution and the effect of filling and other changes on furnace operation. Heretofore it has been possible to take a sample of furnace gas (usually from the dust catcher) and from it determine how closely the reducing gases were to the ideal or limiting value as set by the equilibrium diagram. However, to find just where in the top area the distribution was distorted and the top-gas CO/CO2 ratios were distant from equilibrium values has been a difficult and expensive investigational procedure. In an effort to overcome this difficulty, apparatus was designed to take gas samples and temperatures across the top radius of the furnace. It was hoped that with the aid of this apparatus traverse sampling of the ascending gases could be simplified, and the cost of sampling substantially lowered. Routine experimenting could then be maintained and results checked with furnace operation. It must be emphasized that a traverse sampling is necessary for a true picture, as single samples at any one point are unreliable. This statement can be verified by an examination of Tables 3 to 6, showing results obtained at our furnaces in a large number of tests. APPARATUS The design of the equipment for taking the samples was governed by the need for providing a simple, routine test that could be performed fairly quickly without adversely affecting normal furnace operation.

Jan 1, 1943

By P. E. Rider, K. A. Gschneidner, O. D. McMasters

The solid solubilities for thirteen rare-earth metals in gold were determined by using the X-ray parametric method. Solubilities ranged from 0.1 at. pct for lanthanum in gold up to 8.8 at. pct for scandium in gold. The solubilities from lanthanum to gadolinium were very small and essentially constant, but a sharp increase occurred from gadolinium to scandium. The large solubilities for the heavy rare-earth metals were not expected because of the large size and electrochemical differences between rare-earth atoms and the gold atom. Contributions from first- and second-order elasticity theory plus an electronic contribution were found to reasonably account for a more favorable size factor. Electron transfer from the rare-earth metal to the gold Is thought to occur such that the resultant rare-earth and gold electronegativities are favorable for solid-solution formation. It was also found that this mutual adjustment of size and electronegutivity does not occur if the pure-metal size factors are greater than a critical value of 25 pet. The eutectic temperatures for ten systems were determined and these remained fairly constant at approximately 809 "C for the lighter lanthanide metal-gold systems until the Er-Au system was reached, at which Point the eutectic temperature successively increased reaching a maximum of 1040°C in the Sc-Au system. This rise was correlated to the size factor becoming more favorable for solid-solution formation at erbium. The valence state of ytterbium was found to change from two in the pure metal to three when ytterbium is dissolved in the gold matrix. RECENT results1 reported concerning the solubility of holmium in copper, silver, and gold, showed that the solubility of holmium in gold was quite large, 4.0 at. pct, compared with 1.6 in silver and 0.02 in copper. The small solubilities of holmium in silver and copper are quite reasonable in view of the large size difference (22.2 and 38.2 pct, respectively), large electronegativity difference (0.59 for both systems), and possible unfavorable valency factor (assuming one for silver and copper and three for holmium). The large solubility in gold, however, is unexpected because these same factors are also unfavorable for holmium and gold (22.5 pct size difference and 0.69 electronegativity difference), and because the light rare-earth metals, lanthanum, cerium, and praseodymium, have negligible solid solubilities in gold.2 In view of this unexpected behavior, it was felt that a study of the solid solubilities of most of the rare-earth metals in gold would be desirable to better understand the factors involved in the formation of solid solutions. Of the rare-earth metals added to gold in this study, only ytterbium is divalent in the pure metallic state (the other rare-earth metals are all trivalent) and many of its physical properties (such as the metallic radius, electronegativity, and so forth) are much different from those of the normal trivalent rare-earth metals.' The properties of ytterbium are such that one would expect solid-solution formation to be less favorable for ytterbium in gold than for any of the normal trivalent rare-earth metals. But chemically ytterbium is known to possess a stable trivalent state, and it is quite possible that ytterbium may alloy as a trivalent metal under certain conditions rather than as a divalent metal. Because of the dual valency nature and because so little is known about the alloying behavior of ytterbium, the gold-rich ytterbium-gold alloys are of special interest. EXPERIMENTAL PROCEDURE Materials. The gold used in this investigation had a purity of 99.99 pct with respect to nongaseous impurities. In general the rare-earth metals were prepared by reduction of the corresponding fluoride by calcium metal.3 The impurity contents of the metals used in this study are given in Table I. Preparation of Alloys. Two- or 3-g alloy samples were prepared by arc melting. The samples, with the exception of some of the Er-Au alloys, had weight losses of 0.5 pct or less. All alloy concentrations noted in this paper are nominal compositions. After arc melting, the alloys were wrapped in tantalum foil, sealed off in quartz tubing under a partial atmosphere of argon, homogenized for approximately 200 hr at 780°C, and then quenched in cold water. X-Ray Methods. The X-ray parametric method was used in determining the solubility of the rare-earth metals in gold. filings were sealed in small tantalum tubes by welding under a helium atmosphere. The tantalum tubes were then sealed in quartz tubing under a partial argon atmosphere, and annealed for times ranging from 1/2 to 3 hr (the length of time was inversely proportional to the an-

Jan 1, 1965

By S. J. Rothman, L. T. Lloyd

S. J. Rothman and L. T. Lloyd (Argonne National Laboratory)— Hagel's paperz0 discusses the question of the mechanism for self-diffusion in bcc transition metals. Recent work21"23 has led us to agree with him in reabandoning the ring mechanism in favor of a defect mechanism, most likely vacancies. On the other hand, we think that Hagel's attempt to group together all self-diffusion in bcc transition metals is wrong. We prefer the scheme of Peart, Graham, and omlin," who separate them into two groups. One group contains the anomalously behaved metals P titanium,', y uranium, and perhaps zirconim.' The other group contains a iron," this alloy was held at 1800°C for 2 hr before quenching, its structure was all a. B. C. Giessen, I. Rump, and N. J. Grant (Authors' reply)—We very much appreciate the discussion by Deardorff and Kato regarding the a to /3 transformation temperature of hafnium. In the W-Hf program, as well as in a current study of the system Cr-Hf, standard precautions were exercised against contamination, including vacua of less than 10"5 mm Hg and a weight control check of all specimens to insure an impurity rise of less than 100 ppm. Following receipt of the above discussion, a revision was made in the annealing process. Arc-cast specimens were etched with a 10 pct HF-90 pct HNO solution until 1 mm of surface, including a possible oxide film, was removed. Annealing was done in a hafnium container which provided a long diffusion path for gaseous contaminants. Finally, the heat treating time was shortened. Structural changes were noted to occur quite slowly. A 99.5 at. pct Hf alloy showed 70 pct /3 after 30 min at 1700°C and was 100 pct /3 after 10 min at 1715°C. After 24 hr at 1740C, the alloy was found to be 10 pct/3. This change is due to contamination; it was estimated that it corresponds to an increase of 60°C in the transformation temperature over a 24 hr period. The corresponding change in 30 rnin would be slight. Using the same hafnium as in the above publication, and three new alloys at 98, 99, and 99.5 at. pct Hf, the transformation temperature was indicated to be 1715" 15°C. Since this hafnium contained 4.4 at. pct Zr, a correction of 40 5C, based on an assumed approximately linear transformation temperature curve, must be made for pure hafnium. This yields a value of 1755 20°C in good agreement with Deardorff and Kato's value. Because the slope of the boundary is small, this permits a good extrapolation, and we regard the W-Hf alloys as well suited to check the Hf transformation temperature. niobirn,'' and molybdenum,22 whose activation energies correlate with the melting temperature and whose Do values follow Zener's predictions.28 We have no quarrel with Hagel's placing chromium into the second group; we disagree with his interpreting our data to make uranium fit into that group. Hagel considers that the measurements of self-diffusion in uranium below about 950°C represent combined volume and grain boundary diffusion. This contention is based on the curvature of the penetration plot for our 891°C run,4 which also has a nearly straight line plot of log c vs x. Hagel has extrapolated these characteristics to our 803.5C run and fitted his Arrhenius plot for self-diffusion in y uranium to our four highest temperature points only. We think this is wrong for the following reasons.

Jan 1, 1963

By W. L. Kerlie, J. H. Richards

The variation in hydrogen content of basic open-hearth steels during refining and the effect of changing from steam to air atomization were studied. The water content of the furnace atmosphere, the slag basicity, and the degree of oxidation of the slag-metal system largely control the hydrogen in the steel. SMALL amounts of hydrogen have an adverse effect on the ductility of steel and a wide range of hydrogen contents has an adverse effect on the internal soundness of both ferrous and nonferrous castings. This has been of major concern to the metal industry, both manufacturers and fabricators, for many years. As one of the results of continuing investigations of the hydrogen problem, much has been learned about methods of reducing the hydrogen content of liquid metals below the relatively high levels that are normally associated with such phenomena as rising ingots and excessive porosity in sand casting. However, it was not until a reliable and simple method for sampling and analyzing liquid metal was developed that much progress was possible in quantitatively evaluating the effect of steelmaking practice on hydrogen contents at levels below 6 to 8 ppm. Throughout all the work described in the following presentation the Geffner pintube technique was used to obtain samples of liquid metal1 * and the tin-fusion method, developed at Massachusetts Institute of Technology,2 was used to analyze the samples. Before attempting a systematic experimental program for minimizing the hydrogen content of open-hearth steels, it was necessary to determine the variation in hydrogen in the open-hearth bath during the normal processing of a heat. The logs of ten heats are illustrated in Figs. 1 through 7. The number at each point on the graphs refers to the number of pintube samples analyzed for hydrogen. An increase in the hydrogen content of the liquid metal during the early period of refining is apparent in all heats. There is evidence of a decrease in hydrogen later in the refining period, see Fig. 2, for example. Therefore, the existence of a maximum hydrogen content at some intermediate time during the refining period is anticipated. To test for the existence of a maximum, the data illustrated in Figs. 1 to 5 were grouped together so that they could be examined on a collectively comparable basis. The grouping was effected, as illustrated in Fig. 8, by superimposing Figs. 1 to 5 so that the apparent hydrogen maxima coincided at a fixed position, indicated by the zero on the time axis. Also, by vertical adjustment until the graphs appeared to the eye to be superimposed, the hydrogen scale was made to show the change in hydrogen content. That is, a standard amount was subtracted from the hydrogen values for each heat. Therefore, Fig. 8 represents a generalized presentation of the data and, for this reason, cannot be used to predict the actual hydrogen content of the bath during refining, but rather to show the probable rate of change in hydrogen during refining. Statistical examination of the grouped data in Fi.g. 8 shows that the apparent. increase and suhsequent decrease in hydrogen are real and confirms the existence of a maximum in general. The average increase In hydrogen during the early period of refining is between 0.8 and 1.3 ppm per hr, and the

Jan 1, 1958

By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

By John C. Calhoun, Frank T. Bethel

Glass beads have been surface treated with Dri-film to render them oil wet by n-octane to varying degrees, and capillary desaturation curves have been determined by the restored state method. The desaturation curves show a regularity of increasing displacement pressures as the oil wetness increases. This has been used to compute apparent contact angles between n-octane and water on glass. The family of desaturation curves also shows a regular crossover, such that the residual wetting liquid saturation values are in reverse order to the displacement pressures. A semi-logarithmic variation is shown between the apparent contact angle and the residual saturation. The desaturation data are interpreted to mean that the wetting liquid ceases to be a continuous phase within individual pores before the capillary pressure can be raised sufficiently to force out the wetting phase completely. The saturation of wetting liquid at which this break in liquid continuity occurs is higher as the oil wetness decreases. INTRODUCTION The petroleum industry has for some time been using measurements of capillary pressures on porous media for research correlations and engineering calculations. It has been generally recognized that the capillary desaturation curve reflects the character and arrangement of the pores within the media and the distribution of fluids within the pores. Methods have been proposed for computing pore size distributions, tortuosity factors. and relative permeabilities from capillary desaturation data.' There is little doubt that the interactions between porous rocks and their contained fluids resulting from surface forces play a dominant role in determining the magnitude and direction of capillary pressure measurements. There have been attempts to introduce as variables two quantities — inter-facial tension and contact angle — generally used to char- acterize surface forces, but in spile of the wide interest in these quantities as important variables, few definite conclusions have been drawn concerning their qualitative or quantitative significance. INTERFACIAL TENSION The interfacial tension appears in a capillary pressure function given by Leverett for correlating capillary desaturation type curves. Use of the interfacial tension in this function seems to be justified by other experiments reported. Apparently, interfacial tensions have little bearing on wetting phase residual by desaturation. CONTACT ANGLE The contact angle was utilized as a variable by Bartell and co-workers"." in tests on displacement pressures, later recognized as the initial point of capillary desaturation. Although Leverett did not include contact angle in his original formulation of the capillary pressure function, later workers suggested its addition. Few reports are available to show variation of residual liquid with contact angle as a result of capillary desaturation.' The problems attendant to measuring contact angle within a porous medium are great. As a consequence of the lack of a concrete approach to a measurement. the workers in this area of research have adopted the general expression of "wettability" to indicate the relative position of two liquids saturating a porous body. It has been shown that gross measurements on porous systems, including capillary desatura-tions, are sensitive to wettability. Attempts at giving a scale to wettability in terms of contact angle through capillary desaturation curves have been made and these apparently are steps in the right direction. In these attempts presence of many other variables precludes attainment of exactness. Also, as a result of other variables, it has been impossible to correlate changes in apparent contact angle with changes in other physical measurements of the systems in question. The present work is an attempt to eliminate as many variables as possible in measuring capillary desaturations resulting from changes in contact angle within a porous medium.

Jan 1, 1953

By Robert D. Pike

IN November 1939, on behalf of the Harbison-Walker Refractories Co., the author undertook the study of the problem of utilizing the dolomite of northwestern Ohio for the manufacture of calcined magnesia suitable for use in refractories. Grateful acknowledgment is made of the unfailing assistance and encouragement throughout this work from the executive and technical staff of Harbison-Walker Refractories Company. The dolomite of the Niagara formation that is exposed or near the surface of a wide area in northwestern Ohio1 constitutes a vast supply of almost pure dolomite. It offers a virtually unlimited supply of cheap raw material of uniform dependable analysis for the manufacture of magnesia. A typical analysis of dolomite from the vicinity of Luckey, Ohio, follows: [ ] Brines containing magnesium chloride or sea water can be reacted with calcined dolomite to produce magnesia.2,3 In such reactions the MgCl2 of the brine supplies some of the magnesia and the amount of dolomite required is thereby reduced by an equivalent amount, but brines of commercial importance containing magnesium chloride are some distance away from the purest grades of the dolomite of northwestern Ohio. It was decided therefore to concentrate upon the development of a suitable process for separating the lime and magnesia of dolomite, depend¬ing upon the dolomite itself as the sole source of magnesia. This would make it possible to place a plant at the dolomite quarry, thus eliminating the cost of transporting the stone and also rendering the calcined magnesia available at a most convenient production point, considering the cost of delivery throughout the steel industry. The selection of a process depending solely upon the dolomite as a source of magnesia also necessarily entails production of the lime content of the dolomite as a by-product. It was recognized that if such a lime by-product could be produced in a suitable form, a plant location in northwestern Ohio would also be advantageous for marketing the lime. The problem, therefore, was the discovery and development of a low-cost process for separating the magnesia and lime of the dolomite of northwestern Ohio and producing each in a form relatively free from the other, and meeting the respective requirements of established markets. A satisfactory solution of this problem has been found, and it is the

Jan 1, 1947

By Anton Sawatzky, Erich Vogt

By means of mathematical solutions to the appropriate diffusion equations, we describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various temperatures and concentrations encountered in a heavy water moderated reactor. When the hydrogen concentration is below terminal solid solubility only the a Phase is present. Redistributions are then described in terms of the characteristic functions of the difhsion equation. For higher concentrations both the a and 6 phases are present. We assume the two phases to be always in equilibrium. For moderately small hydrogen concentrations exact solutions of the two-phase equation approach the the approximate solutions derived by Sawatzky and for all concentrations the exact solutions exhibit the qualitative features of his result: the two-phase concentration increases with time, everywhere; in the absence of a hydrogen current at the hot end of the sample an a-phase region always exists there; the interface of the a + 6 , a-phase boundary moves toward the cold md of the sample and the hydrogen concentration is discontinuous at the interface. Simultaneous solulions of the a and a + 6 hydrogen distributims and of the concomitant interface motion are obtained and compared to the observations of Sawatzky and Markowitz. The kinetics of the hydrogen diffusion process are shown to lead to m apparent heat of transport of the a phase which is lower than the actual value (even for samples with long anneals) thus resolving at least partially the disparity between experimental measurements of this quantity. A number of recent papers1"4 have reported measurements on the diffusion and redistribution of hydrogen in Zircaloy-2 under temperature and concentration gradients. These studies were instigated by problems arising from increasing use of Zircaloy-2 as a fuel element cladding material in pressurized-water power-reactors. The Zircaloy-2 picks up hydrogen during the operation of the reactor: the consequent precipitation of zirconium hydride in the Zircaloy-2 has pronounced effects on its mechanical properties. The Purpose of the present Paper is to describe the kinetics of the thermal diffusion of hydrogen in Zircaloy-2 for the various hydrogen concentrations and temperatures likely to be encountered in reactors. When the hydrogen in the Zircaloy-2 is entirely in the solid solution phase (a phase), the differential equation for thermal diffusion is well known and the redistribution can be described by standard mathematical methods some of which are given in Section 11 below. The treatment of the a + 6 (hydride) region differs from the earlier treatment of sawatzky3 by taking into account several modifications of the two-phase diffusion equations as suggested to us by Markowitz4 and Kidson.5 Even with the modifications the results obtained in our more complete treatment are substantially the same as those found by Sawatzky. As we show, the difference between the results of sawatzky3 and kIarkowitz4 is largely due to the difference in the geometry of their experiments. In the next section we derive the modified two-phase equation for arbitrary geometry. The exact solution of this equation is given in Section III for linear and cylindrical geometry. It is shown that Sawatzky's approximate solution is quite accurate for almost all the temperatures and hydrogen concentrations which are actually encountered. In Sawatzky's approximate theory the hydrogen concentration everywhere in the two-phase region increases continuously. As his paper pointed out, this result, together with hydrogen conservation, implies that in a sample with no hydrogen current flowing into the hot end a two-phase region is always accompanied by a single-phase region at the hot end of the sample. The net hydrogen gain in the two-phase region is supplied by the decrease of hydrogen in the single-phase region and by the movement of the (a, a + 6) boundary toward the cold end of the sample. Hydrogen conservation at the (a, a + 6) boundary leads to a discontinuity in the concentration and its derivative there. In Section IV it is shown how these qualitative features of the thermal diffusion kinetics arise from the simultaneous solution of the a-phase differential equation and a + 6 phase equation. Methods derived by us previously for the solution of the redistribution in both phases and the accompanying motion of the boundary are used to obtain approximate solutions valid for large times. The solutions account well for the observed redistributions of Sawatzky and Markowitz. It is shown how the continuing motion of the (a, a + 6) boundary leads to measured values of the heat of transport lower than the actual value, even for specimens with relatively long anneals.

Jan 1, 1963

By John Wulff, J. H. Hollomon

The opinion has been widely held that the corrosion of alpha brass occurs by the selective solution of zinc. As late as 1939, Fink1 and Evans2 suggested that in the initial stage of the corrosion the selective solution of zinc produces copper-rich areas, which subsequently act as cathodes that facilitate the deposition of copper. Previously Abrams3 had shown that most of the copper found on corroded brass was re-deposited and not residual, although he did not consider the nature of the initiation of the corrosion process. Enough data exist to indicate that any metal surface is sufficiently heterogeneous to provide the anodes and cathodes necessary for the initiation of corrosion.4,5 Thus, for alpha brass we need postulate not an initial selective solution of zinc, but only the existence of local differences in electrochemical potential. The heterogeneity responsible for potential differences may arise from oxide and other films as well as from alloy concentration gradients. Even though selective corrosion may be possible in some alloy systems, previous data on alpha brass as well as the experimental work reported in this paper do not require this supposition. Bengough and May16 in a discussion of Abrams' paper, first suggested the addition of small amounts of arsenic (0.03 per cent) to a1pha brass to prevent the redeposition of copper (dezincification). This suggestion was later substantiated by Nixon.7 In their studies of the inhibiting influence of arsenic, Evans and Fink were led to the selective-solution hypothesis in order to explain the initial corrosion of such alloys. They believed that an arsenic film covered anode areas and prevented the formation of copper-rich spots capable of acting as cathodes for the deposition of copper. They did not consider, however, the mechanism by which the arsenical film was formed. Bengough and May,a in another publication, suggested that the commonly found gray or black arsenical film may act to: (I) carry oxygen to the brass surface, (2) increase the discharge potential of copper on brass, (3) precipitate cuprous chloride from colloidal suspension in chloride solutions. Masing9 assumed that the film found upon arsenical brass was metallic arsenic. His measurements of hydrogen overvoltage of bulk arsenic led him to believe that the inhibition of dezincification occurs because the overvoltage of a brass surface is lowered by the arsenic film. He reasoned that this film would permit the more rapid reduction of hydrogen at the cathode, which would prevent the redeposition of copper. In a recent paper,10 we have pointed out that the film formed during the corrosion of arsenical brass and copper in stagnant solutions is essentially arsenious oxide (As2O3),

Jan 1, 1942

By Hubert D. Keiser

An observation that is finding fresh confirmation in the leadership of the Allied Nations is "When the need arises, a man will rise to fill it." Much the same can be said of industrial advances in the current emergency. Events and circumstances have created needs for new materials and stimulated the inventive genius of man to fill them. The timely development of fibrous-glass manufacture, in relation to present war needs, is a case in point. Historical Summary It is probable that the first glass fibers produced by the hand of man were made about 4000 years ago. Successful production of glass fibers for manifold industrial and military uses, on any scale that could begin to meet present needs, has a history spanning a scant four years. The American processes that brought this young industry into being were developed between the years 1931 and 1937; research and manufacturing efforts were consolidated to create a commercially satisfactory operation as late as November 1939. In the 40 months that have elapsed since then, the industry has achieved commercial importance, supplied immense quantities of materials for pre-war industrial expansion to meet "defense" and Lend-Lease needs, and now has reached such importance that it has come largely under the control of the War Production Board for equitable distribution of its major products among 13 claimant agencies. It is worthy of note, however, that the Bureau of Ships, Navy Department, began exploratory use of fibrous-glass products in 1932, within one year after the date of the first experimental trials of the new process. This early recognition of the military importance of fibrous glass gave impetus to further research work. The foregoing rapid scanning of historical development must be filled in, lest the. impression be created that glass fibers were suddenly created out of thin air, with no antecedent trials, failures, and partial successes. The actual history of glassmaking is lost in antiquity. Probably some nomadic tribesman found molten glass beneath the bed of a hot campfire built upon sand of the proper composition. If his curiosity led him to poke the glowing, viscous pool with a green-wood stick or some handy weapon, it is probable that he drew a glass fiber on the end of his implement. Molten glass has much the same consistency as honey or molasses; it strings out tenuously. Thus, it is quite possible that the first form of glass shaped by man's action was a glass fiber. Artisans in glass, throughout the long Direc- of glassmaking as an art> drew fibers from fine rods for many decorative applications, including "spun glass" decoration in beautiful stemware and the charming millefiori (glass flowers encased in solid glass), and even to create the blood vessels in glass eyes to match a bleary mate.

Jan 1, 1948

By R. E. Mussler, F. E. Block, T. T. Campbell

An exploratovy study was made to deternzine the feasibility of preparing beryllium by the metallother-. mic reduction of beryllium oxide. The procedure involved heating a relatively nonvolatile metal reductant in contact with beryllium oxide in a vacuum. Beryllium vapors formed in the reaction were condensed as a coherent deposit on a heated surface. Reductants tested included tanthanun, yttrium, thorium, Th-Mg, and Zr- Ti alloys, and the hydrides of lanthaniir~z, yttriunz, and zirconiur?7,. Test ten7pevatures ranged from 1350'to 175O' C, and reaction times ranged frot 30 to 100 lzr. In most cases metal recoveries were lola, although yields close to 90 pct of theoretical were obtained with latzthanum, yttrium, and zirconium reductants. In most cases metal deposits were contanzinated by beryllides, /ls/cally of the Beln M or Bel3 M type. BERYLLIUM has a variety of unique properties including light weight (sp gr 1.85), low thermal neutron absorption cross section, high scattering cross section, excellent dimensional stability, high strength to weight ratio, high melting point (1285"C), high specific heat, and high thermal conductivity. Interest in beryllium as a structural material in aerospace and nuclear-reactor applications is based on these properties. In general, the potential of beryllium has been only partially realized, largely because of the brittleness of poly crystalline forms of beryllium, difficulties associated in its fabrication, and joining problems encountered in its use in structural applications. Several excellent books and monographs are available to those interested in the occurrence, extractive metallurgy, and utilization of beryllium.1"* Although an extensive amount of research on beryllium has been in progress during the past 10 years, much of the work has been concerned either with the so-called "ductility problem" or with the development of methods of fabrication and evaluation of properties of various commercial or purified grades of metal. A recent survey of the literature indicates that only limited efforts are presently being directed toward developing new methods for reducing beryllium compounds to metal. Two major commercial methods now used to produce beryllium are the magnesium reduction of beryllium fluoride and e lec trow inn ing of beryllium from fused sodium chloride-beryllium chloride salt baths. Only a limited amount of work has been done on the direct reduction of beryllium oxide. Major factors which complicate this method are the great stability of beryllium oxide and the reactive nature of beryllium metal. The stability of the oxide necessitates extremely high reduction temperatures and vacuum operation to liberate beryllium metal vapor and cause reactions of the following type to proceed: XBeO(s) +YM(s)-MYOX(s) + XBe(& As early as 1939, roll' used this reaction for the direct reduction of beryllia by zirconium and titanium, and later in 1952 ~a~el~ studied the reduction of beryl-

Jan 1, 1967

By Hubert D. Keiser

AN observation that is finding fresh confirmation in the leadership of the Allied Nations is "When the need arises, a man will rise to fill it." Much the same can be said of industrial advances in the current emergency. Events and circumstances have created needs for new materials and stimulated the inventive genius of man to fill them. The timely development of fibrous-glass manufacture, in relation to present war needs, is a case in point. HISTORICAL SUMMARY It is probable that the first glass fibers produced by the hand of man were made about 4000 years ago. Successful production of glass fibers for manifold industrial and military uses, on any scale that could begin to meet present needs, has a history spanning a scant four years. The American processes that brought this young industry into being were developed between the years 1931 and 1937; research and manufacturing efforts were consolidated to create a commercially satisfactory operation as late as November 1939. In the 40 months that have elapsed since then, the industry has achieved commercial importance, supplied immense quantities of materials for pre-war industrial expansion to meet "defense" and Lend-Lease needs, and now has reached such importance that it has come largely under the control of the War Production Board for equitable distribution of its major products among 13 claimant agencies. It is worthy of note, however, that the Bureau of Ships, Navy Department, began exploratory use of fibrous-glass products in 1932, within one year after the date of the first experimental trials of the new process. This early recognition of the military importance of fibrous glass gave impetus to further research work. The foregoing rapid scanning of historical development must be filled in, lest the impression be created that glass fibers were suddenly created out of thin air, with no antecedent trials, failures, and partial successes. The actual history of glassmaking is lost in antiquity. Probably some nomadic tribesman found molten glass beneath the bed of a hot campfire built upon sand of the proper composition. If his curiosity led him to poke the glowing, viscous pool with a green-wood stick or some handy weapon, it is probable that he drew a glass fiber on the end of his implement. Molten glass has much the same consistency as honey or molasses; it strings out tenuously. Thus, it is quite possible that the first form of glass shaped by man's action was a glass fiber. Artisans in glass, throughout the long history of glassmaking as an art, drew fibers from fine rods for many decorative applications, including "spun glass" decoration in beautiful stemware and the charming millefiori (glass flowers encased in solid glass), and even to create the blood vessels in glass eyes to match a bleary mate.

Jan 1, 1943