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By W. T. Cardwell

Physically absurd, triple-valued saturations appear in the straight-forward solution of the Buckley-Leverell equations for the displacement of oil by water or gas. From an engineering viewpoint, the triple value causen no difficulty. It is well known how it may be compensnted in order to obtain physically meaningful, numerical results. From a scientific viewpoint, the question still arises: What did the triple value mean? This paper explains how and why the triple value arose in non-capillary Buckley-Leverett theory. The discussion should serve as a background for the understanding and use of the modern method of characteristics in di.~pkzc(>ment theory. INTRODUCTION Displacement theory was introduced to petroleum technologists in 1 941 by Buckley and Leverett.' Their first equation, which they wrote down without derivation, was equivalent to the following: ?s/?t= - qr/F ?f/?r (1) where S = saturation of displacing fluid (a fraction) r = time q,. = total volumetric velocity of both the displacing phase and the phase being displaced (usually, but not necessarily, assumed to be a constant) F = porosity (a fraction) f - fraction of the total volumetric velocity that is the volumetric velocity of the displacing phase (assumed to he a function of S only x = distance. Buckley and Leverett called Eq. I "a material balance equation". Actually it is derived from both a continuity equation, or material balance equation, and Darcy's law. Buckley and Leverett jumped from their Eq. 1 immediately to their Eq. 2, which was the equivalent of the following: (?x/?t)x = qr/F df/ds = qr/F f'(s) (2) The jump from Eq. 1 to Eq. 2 involves apparently simple mathematics, but in that apparently simple mathematics lies a subtle point that is part of the key to the meaning of the triple value to be discussed here. Eq. 2 may be readily interpreted as saying that a point of constant saturation (on a saturation-vs-dis-tance curve) moves with a constant velocity that is proportional to the total volumetric rate, inversely proportional to the porosity, and is otherwise a function of the saturation itself. So that if one knows the derivativc with respect to saturation of the fractional flow function, f(S), for each saturation, one knows the velocity of each point of the moving saturation-vs-distance curve. The function f(S) can he determined experimentally and its derivative f'(S) can be calculated. It turns out that the experimentally derived f'(S) is not a monotonic function of S, but instead it has a definite maximum and declines away at both high and low saturations. This in turn means, in accordance with Eq. 2, that on a moving saturation-vs-distance curve, ccrtain intermediate saturations will travel faster than the saturations either higher or lower. The result is indicated in Fig. 1. In Fig. 1, the abscissas represent distances along a column of porous medium, which column is assumed to be uniform in cross-section perpendicular to the ab-scissal direction. The ordinates represent fractions of pore space occupied by the displacing phase, which may be either water or gas. It is assumed that the saturation is uniform over all planes perpendicular to the abscissal direction. The saturation is a function only of time and one space variable. Time variation of the saturation is represented by change in shape of a curve such as curve AGJ, which represents the initial saturation-vs-

By G. K. Manning, A. R. Elsea, A. B. Westerman

INTRODUCTION A CONSIDERABLE number of high-temperature alloys, that is, alloys which have load-carrying ability at elevated temperatures, have been developed on an empirical basis. In order to determine why these alloys possess this particular ability, a project was started at Battelle Memorial Institute on the fundamental factors promoting high-temperature strength of alloys. At the time of inception of this study, the cobalt-base alloy, Vitallium, was widely used because of its good high-temperature properties. One phase of this study was to include an investigation of the structures observed in Vitallium after various heat treatments. However, before investigating the structural features of Vitallium, it appeared logical to examine the phase diagrams of the related binary systems in order to develop information as to which phases- might be present in Vitallium. A preliminary survey of the pertinent alloy systems was made, with particular emphasis on the cobalt-chromium system, which is the base for the Vitallium series of alloys. The early work of Lewkonja1 and Guertler2 indicated that cobalt and chromium are completely miscible in the liquid state, and, within a narrow temperature range, in the solid state; that the liquidus shows a minimum; and that the alloys containing 45 to '85 pct chromium undergo a transformation at 1200 to 1250°C. More recently, Wever and Haschimoto,3 Wever and Lange,4 and Matsunaga5 carried out experimental work which led to the diagrams shown in Fig I and 2. Both diagrams are based on thermal analysis, metallographic, magnetic, and dilatation data; in addition, X ray diffraction results were used by Wever and Haschimoto, and electrical resistance measurements by Matsunaga. It is apparent from a comparison of the two diagrams that there was a difference of opinion as to the locations of the boundaries of the various phases, and as to the existence of a phase containing approximately 47 pct chromium. With these exceptions noted, it might be pointed out that the two diagrams are similar, and that, in general, any particular reaction which is shown on both diagrams occurs at a lower temperature on the Matsunaga diagram than on that of Wever-Haschimoto-Lange. Thus, in view of the gaps in the data and the questionable features in the published diagrams, it appeared desirable to start the fundamental study of Vitallium by determining the diagram for the cobalt-chromium system. EXPERIMENTAL WORK For the convenience of the reader, the diagram as determined by the present investigation is presented in Fig g. The liquidus and solidus data for the low-chromium alloys were taken from the work of Wever and Haschimoto,3 while the, melting point for pure chromium is the

Jan 1, 1948

By J. H. Tu

The technical paper correctly points out that the kriging variance is not a good measure of the uncertainty of the estimated (i.e., kriged) value of individual blocks. The authors claim that their proposed jack-knife method, which is a rekriging of each block by eliminating, in turn, one sample from m the original sample set and then taking the average of the rekriged estimates, not only gives good block estimates, but the resulting jackknife kriging standard deviation is a useful indicator of the "true uncertainty associated with block estimates." However, they immediately abandon the idea of using the block-by-block standard deviations, reasoning that these standard deviations are not independent and that there is no easy way to utilize them. There may be another reason for not using them. The jackknife standard deviations for individual blocks given in their example are mostly in the range of 0.004 to 0.005 oz/st (0.14 to 0.17 g/t) with only one block having a high value of 0.012 oz/st (0.41 g/ t). These individual block standard deviations are as low as the jackknife standard deviation for the mean grade of the entire shape, i.e., 0.0041 oz/st (0.14 g/t). Do they represent the "true uncertainty" .of the individual block estimates? Could the authors explain this? In a global shape consisting of a large number of blocks, any given sample will affect the kriged estimate of only those few blocks within its vicinity. This is the rationale for the authors' selective rekriging, making the jackknife algorithm more efficient. On second thought, why not do away with jackknifing altogether? Just cumulate and normalize, if necessary, the kriging weights of each sample used during the ordinary block kriging process, and then compute the global variance from these kriging weights and their respective sample grades? After all, isn't the global mean grade nothing but the weighted average of the samples used in the estimation? Reply by G.S. Adisoma and M.G. Hester The jackknife is one of the many tools in a practitioner's toolbox to solve estimation problems. The strengths of the technique lies in its simplicity, i.e., it uses the concept of mean and standard deviation and the fact that it can be easily combined with other tools, in this case kriging. Because the jackknife kriging (JK) estimate is also the mean of the pseudovalues, the JK standard deviation is attractive just as the standard deviation of the mean explains the variability of the data. The difference is that the pseudovalue calculation in jackknife kriging uses the ordinary kriging (OK) weighting scheme instead of simple arithmetic averaging. The data used to illustrate the jackknife technique in the paper con¬sist of high values that are roughly three times the low values. The resulting JK estimate of the block grades show that the highest estimate is roughly twice the grade of the lowest estimate. The contrast between the low and the high estimate is more evident in the JK estimate than in the OK estimate, even though the mean grades of the blocks for the two estimates are very similar. Nonetheless, in this paper, we are concentrating more on the need for a more realistic measure of uncertainty, or precision, for the estimate. Unlike its OK counterpart, the JK standard deviation of the blocks clearly reflects the original data variation. The highest JK standard deviation of the blocks is three times its lowest value. This follows our intuition that, when the samples used to estimate a block is more variable, the resulting estimation variance (or standard deviation) should be higher than the case where the samples are more uniformly valued. However, block-by-block standard deviation or variance is of little practical value in reserve estimation and classification, as well as in mine planning. One is usually more interested in quantifying not the variance of the individual block estimate, but the uncertainties associated with a much larger dimension, such as the minable reserve. Thus, the thrust of the paper is to find a simple way to obtain a single estimation variance or standard deviation associated with the reserve grade estimate. The discussion by J.H. Tu did not mention how one would obtain the global variance from the OK weights and the sample grades. As a technique that offers a data value-based measure of uncertainty for its estimate, the "leave-one-out" jackknife fills this need nicely through the block kriging shortcut approach described in the paper. Note: The first column and the last two columns of Table 3 in the paper should have contained a single number each, namely, an OK estimate of 0.0317, a JK estimate of 0.0333 and a JK standard deviation of 0.0041 oz/st, respectively, for the shape, as are obvious from the text.

Jan 1, 1997

By J. Duncan Wilkins

Introduction In difficult times such as these, there is a strong reaction to the current way of doing things. Typical reactions that we have all heard are "There has to be a better way," "We're pricing ourselves out of business," "We have to improve our productivity," and "We have to have more cooperation," between union and management and employees and management. All of these comments have at their roots one common factor - getting the maximum amount for your dollar. The other factor inherent in these statements is productivity. I have not yet met a person in our industry who has not expressed the opinion that we should, and that we can, improve our productivity. Reducing Labor Costs In light of these factors I suspect we have all spent a fair amount of time examining our labor costs. For some of us, labor costs are a high proportion of our total cost of doing business. To alleviate the impact of these costs, we have generally done four things. We have reduced our number of employees, shut down operations for appropriate periods, sought concessions from union employees, and placed freezes on wages, salaries, and other benefits on nonunion employees. These approaches have been made to improve current shortfalls in our cash positions - to tide us over, as it were - or to provide us with a chance for survival. These are short-term measures that help to bring immediate relief, but can pose significant problems (or challenges), for the longer term. For instance, what do we do when times improve? How much do things have to improve before we do anything? By seeking concessions from unions in bad times, what do we do when unions come to us in good times? It is a rather sad and critical fact that we have grown too fat during the good times and too thin during the bad. In the first case, we have failed to optimize our earnings. In the second, we have cut ourselves too far. Consequently, when good or better times have arrived, we have had to bulk up our requirements to meet production commitments. In mining, for example, when times become tough, we tend to reduce our development plans so that when times improve we have to really "sock it to 'em," so that we can maintain productive capacities. We should plan ahead a little more to reduce the amplitude of our cyclical wavelength, so that in good times profits are optimized and in bad time we are better able to take the strain. Of course, forecasting cycles is not a refined art, but if we properly control our work force levels and costs at all times, and therefore optimize our productivity, we would be more able to withstand the problems we face today. Unfortunately, it appears that it takes bad times to bring us to a realistic appraisal of our way of managing our businesses. Labor Practices Not all of the problems now faced are due to low metal prices. Inflation has played a major role in bringing costs to a frightening level. Trade unions alone can not be blamed for high inflation levels over the past several years, popular though that notion is. Contract negotiations, after all, require two parties. Indeed, our current levels of labor cost are due to two factors: • We have felt obliged to keep our employees whole, relative to the cost of living. • We have felt obliged to maintain our competitive position relative to our peers, in order to maintain our ability to attract and retain a skilled, efficient work force. In the first case, our felt obligation has been applied without due recognition of the factor of performance, either in individuals or groups. Average, even mediocre performers, have been amply rewarded for their average work and mediocrity, while the good performers, no doubt receiving more for their good work and effort, have not perhaps appreciated the slight premium for their effectiveness. The rather predictable result of this practice has been that the average and mediocre stay that way (why change?), while some (certainly not all) of the good performers have said "It's not worth it," and slipped into the warm, cosy pool of the average and mediocre. In the second case, that of maintaining competitiveness with other companies' employees, we have compounded an already serious problem of lack of skilled tradesmen by paying higher and higher prices for the existing pool to maintain comparability without improving the flow of more skilled people through sound and sufficient training programs. We have the rather dubious pleasure of paying more and more for the same problems. Compensation is either mutually agreed, as with unions, or it is unilaterally applied, as with nonunion employees. Generally, there is more flexibility available to the employer when dealing with nonunionized groups than there is with unionized groups. Sometimes that flexibility has not been used well, most often be-

Jan 11, 1983

By M. G. Ayat, B. C. Scott

J. Dasher Having an interest in coal slurry pipelines from a decade of arguments with Ed Wasp and crew at Bechtel about pumping thicker slurries slower, I immediately read this article and found nothing in it pertinant to the title. Ayat and Scott pumped five unidentified coals at 9% solids (50%-60% is the area of interest) in a 25-mm (1-in.) pipe around two square elbows through a 76-mm (3-in.) cyclone for up to 60 minutes and sized a large number of samples of unstated size on an unidentified wet screening device. They did not measure power consumption, discharge pressure, flow rate, or give pump tip speed or impeller diameter. They siad the cyclone had a "high" pressure drop (unmeasured) and did much of the degradation (measured) but more or less per unit of energy expended? Hargrove was not measured, so there are no data as to whether it would correlate with degradation. The authors conclude, with no attempt, correlation is "hard to establish." Please experiment before concluding. I am at a loss to know what "increasingly smaller size" means, much less what theory says such particles take "exponentially larger quantities of energy," which the authors neglected to measure. If such experiments without pertinent data or justified conclusions must be published, please attach a pertinant title. reply by M. G. Ayat The first and the last criticism of this paper is that the work is not pertinent to the title. Anybody who reads this article will immediately realize that the work describes the breakage of coal particles to finer sizes in coal slurry pipes and pumps. If this is so, why not title the work "Degradation process in coal slurry pipelines"? What could be more pertinent to this title than the investigation concerning the degradation phenomenon of coal particles in a pipe carrying a coal slurry? Mr. Dasher complains that he does not understand the meaning of the term "increasingly smaller size." The first sentence of this article defines the degradation process as "the breakage of coal particles to increasingly finer sizes." The term "increasingly finer sizes" here means successive breakage of a fine particle to finer and finer sizes. According to Hukki (Hukki, 1975), the probability of breakage is high for large particles and rapidly diminished for fine sizes. We apologize for being brief about some of these definitions. The degradation process, breakage of particles to increasingly finer sizes, is so widespread in the mineral industry that we did not feel it necessary to bore the reader with lengthy definitions of some simple terms. Mr. Dasher states that the coals examined and their original size consist are unidentified. Please look at Table I and Table 2 in the paper again where you will find the original size consist of the coals examined and their full specifications. We only named the coals A, B, C, D, and E to avoid identifying the coal seams that were more susceptible to degradation. Not identifying the name of the wet screening device used in this work has also been criticized. In our opinion, wet screening operation is such a routine and standard procedure that naming the device by which the screening is performed would serve no purpose but to promote a sales approach. This was not our intention. We did not conclude that the correlation between the degradation process and Hardgrove Grindability Index is hard to establish as Mr. Dasher writes in his letter. We stated, not concluded, that "It is reasonable to assume that some relationship between the extent of degradation and its physical properties, such as Hardgrove Grindability Index, does exist. However, any definite correlation is difficult to establish." This statement is based on other researchers work, which are clearly referenced in the article. The conclusions of this paper were based solely on the findings of the experimental work. As for the theory of comminution that Mr. Dasher asks, we would like to refer him to some basic comminution books and articles where various theories are clearly described. For example, Hukki (Hukki, R.T.,"The Principles of Comminution; An Analytical Summary," Eng. Min. 176, 106, 1975) suggests that the relationship between energy and particle size is a composite form of three laws (Bond's law, Kick's law, and Rittinger's law). A comprehensive analysis of coal breakage processes is also performed by Broadbent and Callcott (S.R. Broadbent, and T.G. Callcott, "Coal Breakage Processes, I. - A New Analysis of Coal Breakage Processes;" and "Coal Breakage Processes, II. - A Matrix Representation of Breakage," Journal of the Institute of Fuel, pp. 524-539, December 1956). These and many other relevant publications explain the relationship between the particle size and energy much better that what can be said in this short reply. We will, however, agree with Mr. Dasher on one particular point. We, too, believe that if the investigation concerning the degradation process in coal slurry pipeline were to be pursued further, one could choose to determine one or more of the variables available in the process, such as discharge pressure, power consumption, percent solid, pipe diameter, etc.

Jan 1, 1989

By W. G. K. Fleming

The general history of piling is traced up to the present time with regard to the evolution of methods and materials. The processes have been strongly influenced by developments in basic equipment and industrial change. It is noticeable that in the twentieth century more progress has taken place than in the many previous centuries. It has been strongly influenced by the general development of Soil Mechanics. Test loading is probably the most effective way to assess the success of designs and many empirical relationships have been challenged through it. As we approach a new century it appears that it will be an age of rapid equipment development, with much enhancement of understanding of what has been done. Processes of automatic construction and testing will becoming commonplace. These changes will narrow the limits of conventional scatter that have come to be accepted and to a large extent will be driven by political efforts to curtail energy consumption, to raise standards of quality and reliability, and to conserve the environment. 1. Ancient history. Piling is an ancient art. Its first mention in history is from Herodotus, the first person to commit an account of his times to the written word in the years 557 to 479 BC. He evidently had a strong interest in engineering matters because he wrote of building, brick making, reinforced brickwork, river training, canal building, bridge construction, tunnelling and its acoustic detection and piling. The piling reference comes from Book 5 at paragraph 16.

Jan 1, 1999

By Thomas V. Falkie

In bygone days, the mineral engineer spent most of his/her time on the technical aspects of designing, building, and managing mineral operations. In the last few decades, mostly since the 1960s, increasing amounts of engineering man power and time are spent dealing with federal, state, and local government agencies, laws, and regulations. It is not possible to plan, design, build, or operate mines, mills, smelters, or even office buildings without detailed consideration of government regulations and permitting requirements dealing with environment, worker health and safety, etc. The four chapters of this section provide an overview of the social, legal, political, environmental, and health and safety aspects of mineral enterprise. The section sets the stage for the working engineer/geologist in industry, government, consulting, or academe and points the direction for more detailed study in each of these areas.

Jan 1, 2008

By H. T. Rall

This report summarizes a systematic 20-year study of the organic sulfur compounds in Wasson, Texas, crude oil and, to a lesser extent, of three other crude oils, that has culminated in some 200 individual sulfur-compound identifications. The development and application of special separation and identification techniques generally suitable for the characterization of sulfur compounds in any crude oil are discussed. This report reviews early sulfur literature covering petroleum sulfur compound identifications completed before this study was begun, and cites 58 papers resulting from this work. The sulfur compounds in petroleum, both as to type and quantity, have long been of concern to the petroleum industry, and such compositional data are not only of theoretical interest, but also of practical value.

Jan 1, 1972

By P. A. Witherspoon, R. W. Donovan, T. D. Mueller

The use of petroleum-barren aquifers for underground storage has become extremely important to the natural-gas industry. A critical problem in assessing the feasibility of a specific aquifer for such use is the permeability determination of the caprock over the proposed storage project. The approach used here is to conduct both static and dynamic field tests on the aquifer being analyzed. Valuable information on the possibility of communication between the storage aquifer and any other aquifers above can be obtained by measuring hydrostatic water levels and water analyses. Significant differences in such data give evidence of the lack of communication between the intended storage reservoir and other horizons. The dynamic approach requires that one well be pumped in the storage aquifer, and changes in fluid levels recorded in both the aquifer and its caprock. The interpretation of the data from such pumping tests involves the solution of nonsteady radial flow in an infinite aquifer and the influence on such flow of a leaky caprock. A finite-difference model has been used to investigate this problem, and the transient behavior has been solved numerically with a digital computer. It has been found that the pressure transients in the storage aquifer are not affected significantly by moderate caprock leakage. The pressure behavior of the caprock is a much better indicator of the degree of leakage, and generalized solutions for this behavior are included. Field data are presented to demonstrate both the static and dynamic approach. If is concluded that appropriate investigation of the groundwater hydrology in an aquifer-type gas-storage project can provide much valuable information for determining the effectiveness of the caprock to hold gas. INTRODUCTION Underground storage of natural gas in the United States has been developing at a rapid rate over the past few years. In 1955, the total gas-storage capacity was about 1.6 trillion cu ft; by 1961, this figure was almost 3.2 trillion cu ft, an increase of 100 per cent in six years.' This trend un- doubtedly will continue because the economics favor the development of gas storage, as opposed to the construction of new pipelines, to meet the inherent cyclic demand for fuel in the metropolitan areas of this country.' About 15 per cent of the current underground gas storage has been developed in petroleum-barren aquifers, i.e., geological domes or anticlines in which no commercial quantities of oil or gas had been produced prior to the storage operations. The necessity for using barren aquifers outside many metropolitan areas of this country has been due to the lack of depleted oil or gas fields that were near enough and large enough to meet the demands of such consuming areas. Pipeline companies have developed aquifer storage along their transmission lines to meet the fluctuating needs of their complex systems. Considerable thought has also been given to the problem of storing gas in a structureless aquifer, both in this country' and in the Soviet Union outside the city of Leningrad.'," Conditions such as these have led to the development of aquifer gas-storage projects in many parts of the U. S. Most of these developments have centered in the Mid-Continent area, and the greatest amount of activity has been concentrated in Illinois.6 Thus, the use of petroleum-barren aquifers for gas-storage purposes has become extremely important to the natural-gas industry. There are three basic problems in developing aquifer-type storage: (1) finding an adequate geologic structure, (2) finding a suitable storage reservoir within the structure and (3) determining the tightness of the caprock over the intended storage zone. The first two problems can be solved by applying conventional methods of exploration geology, but once these problems are solved, the question arises as to why no oil or gas is present in an otherwise favorable setting. Two situations are possible: (1) an adequate source bed was never present, or (2) a source bed was present but the petroleum seeped away because of a leaky caprock. Determining the tightness of the caprock is one of the most critical problems in assessing the feasibility of a specific aquifer for storage purposes. In attacking this problem, one usually takes cores of the caprock and subjects them to a rigorous investigation. Such core data are desirable, but they only detail the matrix properties and cannot be expected to reveal the gross characteristics of the caprock. Several gas-storage projects in the U. S. have had considerable leakage where

By J. E. Powell, F. H. Spedding

WHILE rare earths are reported to be widely distributed in nature and are not really rare," in practice, there are only a few minerals which are sufficiently rich in rare earths to serve as practical sources. Perhaps the best known of these is monazite which is a phosphate mineral containing rare earths and thorium. This mineral occurs as a dense brown sand in gravel beds and is particularly rich in the light rare earths of the cerium subgroup. This mineral is processed commercially for its thorium, cerium, and lanthanum content, and, consequently, furnishes rich concentrates from which neodymium, praseodymium, samarium, europium, and gadolinium may be obtained. Unfortunately, monazite is rather lean in rare earths heavier than gadolinium. A second mineral which is rich in the light rare earths is bastnasite, a fluoro-carbonate. Extensive deposits of this ore have been discovered in the western United States and have received considerable newspaper publicity in recent years. While bastnasite is very rich with respect to cerium, lanthanum, and neodymium, it contains even less heavy rare earths than does monazite. One of the better sources of heavy rare earths of the yttrium subgroup is gadolinite, a black silicate rock from which the rare-earth content can be extracted readily by acid leaching. It is obtained chiefly from Norway at the present time, although there are known deposits in the United States. Other sources of heavy rare earths include fergu-sonite, euxenite, and samarskite which are refractory tantalo-columbate ores. These minerals require caustic fusion or reduction to carbides with carbon before the rare-earth content can be extracted. All of the minerals which are rich in the heavy rare earths contain yttrium as a major constituent. After the rare earths have been extracted as a group from an ore by chemical means, it is generally convenient to precipitate them from acid media with oxalic acid in order to eliminate certain non-rare-earth impurities such as iron, beryllium, etc., which are usually present. The oxalate can then be readily ignited to R2O3. The oxide can be dissolved in acid and is the starting point for subsequent separation into the pure components. Perhaps the principal reason why the rare earths have not been studied as extensively as other elements of the periodic table, whose natural abundances are comparable, is that they are extremely difficult to separate from each other by the usual chemical means. Prior to 1945, the separation of one trivalent rare earth from another was a laborious process. All separations were based on repeated fractionation processes, i.e., fractional precipitation, fractional decomposition, fractional crystallization, etc. These processes were repeated from a few hundred to many thousands of times in order to obtain individual rare-earth salts of reasonable purity. Of course, mention should be made that, in the few cases where a rare earth could be oxidized or reduced to a valence state other than three, more conventional chemical means could be utilized to separate the oxidized or reduced ion from the other normally trivalent rare earths. The ionic states which deserve special mention are CeIV, SmII, Eu11, and Yb11. When it is possible to remove an element of the series efficiently, due to an optional valence state, its immediate neighbors also become easier to isolate. For example, binary mixtures of lanthanum and cerium, and praseodymium and cerium can be obtained by a relatively small number of fractional operations. The tetravalent state of cerium then allows the complete resolution of the binary mixtures by ordinary chemical means. Although the tetravalent state of cerium has been known for a long time, the divalent states of samarium, europium, and ytterbium were not used extensively in separations prior to 1930 because they are relatively unstable in aqueous media.'-" No attempt will be made to give a comprehensive review of the extensive literature dealing with the separation of rare earths. Rather, this paper will be confined to a review of those methods which have been developed at Iowa State College during recent years, and which have proved extraordinarily successful for the isolation of highly pure rare earths in quantity. It was obvious that, if pure rare earths were to become generally available, methods would have to be developed wherein the thousands of fractional operations made necessary by the similarity of rare-earth properties could be performed automatically. The development of chromatographic techniques and ion-exchange resins appeared to offer a mechanism by which this objective could be accomplished. A number of early attempts were made to separate rare earths by these means; for example, Russell and Pearce12 passed a mixture of rare earths through a cation-exchange column and reported

Jan 1, 1955

By R. Simon

The sources of energy dissipation for concentrated loadings on rock are considered in an attempt to account for the experimentally measured magnitude of the work required to break out a unit volume of rock from the free surface of an essentially semi-infinite medium. It is concluded that most of this work probably represents the elastic strain energy developed by the loading in a much larger volume of rock beneath the loaded region than the volume of the rock fragment broken out to the side of the loaded region. This strain energy is largely dissipated in the form of stress waves generated by the high rate of unloading produced by the propagating cracks. The energies associated with the formation of the new surfaces of the cracks and with the stress waves generated directly by the loading process are computed to be negligibly small. Possibilities for improving the utilization of energy to drill rod. subject to the geometrical limitations imposed by down-hole operation, are discussed. It is pointed out that any such possible improvements would probably have to be differential ones, since each rock configuration of more favorabIe loading geometry that can be created down the hole is accompanied by a complementary configuration of less favorable loading geometry. INTRODUCTION Dislodging each cubic inch of rock from the bottom of the hole by the action of a bit requires the expenditure of an amount of energy that varies from approximately 5,000 in.-lb to approximately 100,000 in.-lb, depending on the hardness of the rock, or, more technically, upon its fragmentation strength.1 In this paper we will discuss (I) why the energy expended in drilling is so large, (2) what happens to this energy upon completion of the drilling process, and (3) what are the possibilities for reducing the magnitude of the energy required to drill rock. DETERMINATION OF ROCK DRILLING ENERGY The volume of rock removed per unit time from the bottom of a hole of diameter D is evidently (7/4)D2R, where R is the rate of penetration of the bit. If P is the rate at which work is done by the bit on the rock at the bottom of the hole, the energy required to break out a unit volume of rock is given by: Ev =(4/p) P/D2R............(i) For rotary drilling, of either the rolling-cone or drag-bit varicty, P = 2pLN, where L is the torque resistance to rotation at the bottom of the hole and N is the rate of rotation of the bit. L is essentially the same as the torque measured at the rotary table only when drilling in shallow holes. The energies expended in rotating the drill string against the frictional resistance of the walls of the hole and and against the viscous drag of the drilling fluid are extraneous to the subject under consideration, although these may be much greater in magnitude than E, when drilling in a deep hole. For percussion drilling, P = fE where f is the percussion frequency and E is the work done on the rock per impact. The latter quantity can be both computed and measured for a percussion drilling machine. 2 (Under satisfactory drilling conditions, defined in terms of ranges of numerical values of certain dimensionless parameters, E is only 30 to 50 per cent less than the impact energy of the striker.2) Alternatively, E, may be measured directly by dropping chisels shaped like bit edges, backed by rigid weights, onto the surfaces of laboratory rock samples of effectively semi-infinite extent. Under these circumstances, essentially all of the impact energy is converted to work done on the rock, and the relationships among volume of rock broken out, chisel shape, impact energy and indexing distances can be obtained.3 The values of the energy required to break out a unit volume of rock under favorable circumstances are substantially in agreement for rotary drilling, percussion drilling and drop testing at atmospheric pressure. The energy per unit volume is a quantity of the order of magnitude of roughly twice the com-pressive strength of the rock as measured by a uniaxial loading test. The phrase "order of magnitude" in this paper means from about 1/3 as much to 3 times as much; i.e., the energy per unit volume may range from roughly the same up to several times

By E. F. Poncelet

Forty years ago A. A. Griffith developed a theory explaining why brittle materials displayed such low tensile strengths.' He based his views on two points. First, he found himself compelled to assume that all brittle materials are replete with flaws, cracks, and other defects that act, although quite invisible, as large stress raisers. Second, he applied the "theorem of minimum potential energy," which says that the total potential energy of a system must pass from the unbroken to the broken condition by a process involving a continuous decrease in potential energy. By this means he satisfactorily accounted for the noted low strength of such solids and also for the wide spread obtained in experimental measurement of these strengths. So successful has the theory been that it is favored by some to this day. Unfortunately this theory is of limited use beyond the explanation of these two noted phenomena and it is keenly felt that a better theoretical insight into the physics of the fracturing process is needed as the volume of experimental evidence accumulates. The author proposes in the following to build on the fundamentally sound concepts of Griffith and, with the help of increased theoretical knowledge over that available to Griffith, develop a mechanism for frac-ture which will provide far greater understanding of the experimental evidence accumulated to date than is possible from the original Griffith idea. THE GRlFFlTH THEORY Very little progress indeed can be made without accepting the first postulate of Griffith which supposes all brittle solids to be full of microcracks. It would be difficult indeed to find a better mechanism for the small strength of such brittle materials, in conjunction with the fact that the energy that must be expended for comminution is by no means small. The postulate of the existence of the microcracks permits the breakup of the various bonds a few at a time by concentrating the stress at the tip of the progressing crack, while the total energy expended is the same as if they all had been ruptured simultaneously. The only flaw in the argument is that no reasonable explanation has been proposed to account for the genesis of such cracks. Indeed their very presence is in violation of the Griffith second postulate, the potential energy theorem. This theorem is straightforward for isothermal processes, and, in spite of Griffith, there is some doubt that treating the problem isothermally is legitimate. The surface energy of bodies is a free energy, not a potential energy as stated by Griffith, and the production of new surface free energies is not necessarily an isothermal process. There is ample evidence to the contrary. Generally speaking, if heating a body increases its surface area, then, by virtue of Le Chatelier's principle, any increase of that area by other means will tend to lower its surface temperature. Lord Kelvin calculated the actual cooling that resulted in drawing out a film of liquid.2 R. A. Houston calculated the surface cooling that resulted in stretching a metal wire.3 These calculations were made by applying the Carnot cycle to the process and evaluating the thermodynamics thereof. IRREVERSIBILITY OF THE FRACTURING PROCESS While Griffith was very careful not to say so, the impression gained from studying his papers is that he considered the fracturing process as reversible, that is, a succession of quasi-equilibrium states. There is ample evidence that it is not. The indication that the new surfaces produced by the propagation of a crack are cooler than the original body points to an irreversible heat flow from the interior to the new surfaces to equalize the temperatures. If the process be reversible, any crack accidentally formed should immediately close up as, in the absence of any strain energy, the potential energy would thereby be lowered. The fact that they do not, constitutes a paradox. Such paradoxes are nothing new where certain phenomena that propagate from minuscule nuclei are assumed to be reversible. Such is, for instance, the condensation of a pure saturated vapor that is suddenly chilled by adiabatic expansion. At the beginning the tiny droplets that are formed should be only a few angstroms in size, but the vapor pressure at such droplets is so high that they should evaporate at once. A similar situation arises if a saturated pure solution becomes super-saturated upon cooling; the first tiny crystal nuclei should dissolve as fast as

Jan 1, 1964

By G. K. Manning, A. R. Elsea, C. R. Simcoe

Boron increases the hardenability of hypoeutectoid steels by decreasing the nucleation rate of ferrite and bainite. It is postulated that concentrations of lattice imperfections, such as exist at the grain boundaries, furnish the necessary energy for nucleus formation. Boron, because of its atomic diameter, will concentrate at lattice imperfections where sites of suitable size are present. Boron will decrease the energy of these local areas by occupying these sites. This mechanism accounts for the large increase in hardenability observed with small amounts of boron. The loss of the boron hardenability effect and the boron precipitate formation are explained on the basis of increased concentration of boron at the grain boundaries either with increasing boron content of the material or with increasing temperature. COMMON alloying elements affect both the nucleation and growth rates of the austenite decomposition reactions.' This effect is largely a result of the slow diffusion rates of these elements. Although a small addition of boron markedly increases the hardenability of steel, the diffusion rate of boron, which is of the same order of magnitude as that of carbon, can hardly account for this effect. An addition of boron in the range of 0.001 to 0.003 pct is about as effective as an addition of 0.30 pct Mo, 0.40 pct Cr, or 1.25 pct Ni in increasing the hardenability of a 0.40 pct C steel;' however, increasing the carbon content of the steel decreases the effectiveness of the boron addition."' The difficulty in understanding why so small an addition of boron can replace much larger quantities of the more strategic alloys, together with the erratic behavior sometimes encountered in boron-treated steels, has interfered with their general acceptance by industry. In the belief that an understanding of the mechanism by which boron increases the hardenability of steel should lead to a more general acceptance of boron-treated steels, a research investigation to determine this mechanism was undertaken at Battelle Memorial Institute under sponsorship of Wright Air Development Center. Experimental Work In order to study the effect of boron on the transformation of austenite to ferrite and bainite, a group of steels was made with a basic composition similar to that of the SAE 8600 series. This base composition was chosen because it has sufficient hardenability to permit accurate measurement of the times required for transformation to start at various temperatures. The chemical analyses of the steels used in the first part of this investigation are listed in Table I. These steels were made as 200 lb heats in an induction furnace. The furnace charge was Armco ingot iron with the alloying elements added as ferroalloys. After the alloy additions were made, the heat was deoxidized with 0.125 pct Al. A 100 lb ingot was cast and an addition of 0.003 pct B, as ferroboron, was made to the metal remaining in the furnace. This metal was cast into a second 100 lb ingot. The ingots were forged to 11/4 in. diam bar stock from which end-quench hardenability specimens were obtained. Part of this material was further reduced by hot rolling to lx¼ in. bar stock from which specimens were obtained for isothermal transformation studies. Studies of Nucleation and Growth: End-quench hardenability tests were performed on these steels, using an austenitizing temperature of 1600°F. The hardenability curves, shown in Fig. 1, indicate that boron treatment resulted in considerable increase in hardenability of the steels. Any such change in hardenability must result from a change in the transformation rate of the austenite, and these rate changes can be established readily by isothermal transformation studies. Isothermal transformation studies were conducted on these steels as follows: specimens were austeni-tized at 1600°F for 15 min, transferred to a lead bath operating at a constant subcritical or intercritical temperature, held for various lengths of time, and water quenched. The specimens were sectioned for metallographic examination to determine the amount and the type of transformation products present. In order to determine the effect of boron on the formation rate of ferrite, isothermal transformation tests were made on the 0.20 pct C steel in both the boron-treated and boron-free condition at an intercritical temperature of 1375°F where ferrite is the only decomposition product of this low carbon austenite. The results of these tests are shown in Fig. 2, where the percentage of ferrite formed is plotted as a function of time at temperature. It is apparent that boron markedly decreased the transformation rate of austenite to ferrite at this temperature.

Jan 1, 1956

By C. E. Sims, H. M. Banta, S. L. Hoyt

Over the past few years, metallic arc welding has been extended to steels of the hardenable type. As compared with other methods of fabrication, production has been facilitated, service performance frequently has been improved, and the overall results have been so favorable that engineers and production men have placed great emphasis on this application of welding. The metallurgist and welding engineer, however, have been confronted with new problems, since, for one reason, the harder steels are more apt to crack and special precautions must be taken if sound joints are to be procured. Some of the factors that are pertinent to this problem are metallurgical, and it is an object of this contribution to discuss steel manufacture and processing methods and to show how their control assists in reducing the hazard of cracking. By this time, the problem of cracking— specifically underbead cracking, or "hard cracks," or parent-metal cracks-—is well known, and a large amount of work has been published, both here and abroad, dealing with this subject.' The tests described are made under restraint to facilitate cracking and arc so designed that a semiquantitative, or at least a relative, value of the cracking tendency is obtained. As one would expect, it has been reported that the incidence of cracking increases with the carbon and alloy content of the steel. More specifically, the cracking tendency is said to increase with the hardenability of the steel, though it is now recognized that the situation is not so simple. The phenomenon itself, on the other hand, has been but loosely described, and it is in only broad generalizations that this cracking has been related to steel metallurgy. Thus, while it has been abundantly demonstrated that the hardenable aircraft steel, S.A.E. 4130, must tend to crack when are-welded, the problem still remains of why two lots of the same composition and the same hardenability can vary so greatly in cracking tendency, or what it is about the prior metallurgical history that so strongly affects the results. Further, while the efficacy of preheating and postheating in preventing cracking is recognized and utilized in production, the mechanism by which they function seems not to have been described. These points are thought to be significant in the production of steel for fabrication by metallic arc welding and, hence, of interest to mill and process metallurgists and welding engineers. Consequently, it is another object of this paper to discuss the mechanism of parent-metal cracking, including the influence of the condition of the steel and the control of cracking by manipulation of the time-temperature conditions during and after welding. A new method of rating the cracking tendency is also discussed, and the results of the test are related to steel composition and structure or prior history. The work to be described was the outgrowth of work in 1940-41 at Battelle Memorial Institutc on two projects, one

Jan 1, 1945

By J. A. Holmes, EDWARD C. FRANKLIN, RALPH A. GOULD

The commission may be permitted to express its earnest hope that the litigation which comes to an end with the findings and recom- mendations herein set forth will be considered by both parties to the action as definitely and equitably decided. The commission trusts that its work will show the value of the commission form of settlement and that its work will serve as a prece- dent to be followed in disputes relative to technical subjects. If the work of the commission is productive of a tendency on the part of technical litigants to avoid the use of the courts for the settlement of disputes it will not have been done in vain. Such tendency will surely grow and ultimately such differences will be arbitrated by technically trained men without recourse to the courts of law. Appended to the report of the findings of the commission are to be found the detailed reports covering the several lines of inquiry and investigation carried on by the commission and upon which its findings are based, and also a detailed statement of the fiscal affairs of the commission. A word of explanation is necessary in regard to the fiscal statement. While each party to the litigation has agreed to bear one-half of the expense of the investigations of the commission, it will be noted that the Selby Smelting & Lead Co. is credited with $21,000, while Solano County is credited with but $6,000. In order that the investigations of the commission might go forward without interruption the Selby Smelting & Lead Co. has generously supplied funds at the times they were needed. This assistance has been

Jan 1, 1915

Jan 1, 1953

By Lindsay Norman

To many who for years have scrutinized the US mineral supply picture, recent, often strident debate on present-day security of many critical mineral supplies echoes sentiments repeatedly expressed in the past decade by the minerals industry. At no time since the last world war has such a flurry of public concern been expressed for the economy's mineral sector. Where once mineral availability problems were relegated to the newspaper's business section or not reported at all, today comprehensive analyses of our international mineral posture are discussed in detail by some of the nation's most respected and widely read periodicals. In past years, disinterest was also experienced whenever the mining industry attempted to carry its message to Congress, the public, and the government's executive branch. Among minerals professionals, the past decade was a time of particular frustration clue to serious erosion ill US ability to competitively produce the vast array of raw materials vital to the economy acid national defense. Fervent calls for immediate attention were simply not answered. These professionals have understood that mining and agriculture are the primary sources of wealth, fulfilling virtually all needs and creating and sustaining jobs. Why then has it been so difficult to raise the consciousness of the American public, and even more surprisingly, of the government and national leadership? The answer to this question is perhaps endemic to how government functions, but pore important, it begs that mining professionals capitalize on the opportunity and the attention now at hand. Carefully conceived and implemented actions by both private and public sectors are needed more than ever before in the past 35 years. To this end, it is vitally important to seek out and resolve the root causes of supply problems and not dwell on superficial solutions. The following discussion attempts to establish a simple framework to view this process. It does not presume to be an exposition of cause and effect, but hopefully identifies some needed steps. Growing Awareness in the 1970s Of all events stimulating current concern, certainly the OPEC oil embargo has left the deepest impression. It was inevitable that after such a shock, man. Americans would begin asking whether the US was as vulnerable to cutoffs of minerals as it was to oil cutoffs. Then, when serious trade security questions surfaced in sonic mineral-rich nations in Africa and the Persian Gulf, the ominous term ''resource war" began to be heard. Countries such as South Africa, Zaire, Zambia, and Zimbabwe have suddenly become key areas for testing our national security resolve. As the US witnesses the influx of Marxist influence in many sub-Saharan exporting nations and the rising threat to free world access to critical materials and energy, the assurance of adequate supplies is becoming a national issue at last. The US is now learning that self-sufficiency for many vitally important mineral commodities has vanished. Of course, it did not vanish overnight; it had been leaking away for years, and the trend was noted by industry and a few in government. Within the minerals community, suspected weaknesses in America's resource posture were sought and found. As a result, the country's heavy reliance on foreign sources fur more than a score of minerals, many extremely vital to security, has been forcefully documented and the case for drastically altering the supply unbalance hits been proposed. The renewed concern for national defense is central to almost all proposals for minimizing US foreign mineral dependence. It is not surprising that many of the voices heard today on the dependency issue are active members or alumni of the militate establishment. Unfortunately, their almost total focus on the security aspects of dependency has tended to obscure important underlying issues which are not directly defense-related. Some of the proposals advanced might mitigate the deeps-dency problems, but they still fall short of curing the underlying problems that have led to a steady loss in mineral self-sufficiency. In almost all instances these problems call be traced to increasing government influence on the free market minerals economy. Some national security proponents seek to attain total self-sufficiency in minerals. Such arguments must he tempered by existing realities. It is easy to demonstrate that the US obtains substantial quantities of sonic essential minerals from potentially insecure sources abroad. That the US will continue to do so in the foreseeable future is not in doubt Uncertainty begins, however, when we try to interpret the significance of these facts. It is important to understand that mineral dependency does not irrevocably lead to vulnerability. Unlike oil, no mineral commodity combines the same degree of universal indispensibility and centralized foreign control of supplies. Moreover, although many US-required minerals are produced by fewer countries than export oil, those minerals cannot approach petroleum in economic or industrial importance. Finally, most foreign supplies come front friendly, secure nations such as Canada, 'Mexico, and Brazil. This, aid more, constitutes a vital element in US economic health as a world trading nation. The Cost of Interruption The US is currently stronger and more resilient than many expected after absorbing the oil embargo shock and subsequent price increases. Nevertheless, major worldwide

Jan 6, 1981

By Persifor Frazer

THERE is always a difficulty in assigning limits to the scope of a science or art, and among the difficulties of that kind besetting practical or stratigraphical geology is that of determining what kinds of natural objects shall be considered as the goals of its search. The term mineral, in its broader sense, includes every solid, liquid, or

Jan 1, 1875

Jan 1, 1953

By Richard L. Gordon, William A. Vogely

In this chapter, the principles that determine the procedures selected to transform minerals in the ground into usable commodities are re¬viewed.a I argue here that straightforward mod¬ification of the modern general economic theory of production suffices to meet the practical needs of a mineral economist. Therefore, the chapter is largely a review of the general economic theory of production to which is added discussion of the special prob¬lems of the exhaustibility of mineral resources and the economics of finding and developing economically recoverable minerals. In many cases, propositions applicable to all industries are reviewed because they are not treated ade¬quately in prior texts. In the discussion, use is frequently made of basic concepts of differential calculus widely used in economics. However, this is supple¬mented by simpler verbal and graphical treat¬ments, so that those either untrained in the calculus or, as is often the case, whose skills have grown rusty, can still follow the discus¬sion. Where the argument depends critically on the mathematics, this is noted and the justifi¬cation for including the material is provided. In addition, an appendix outlines the critical mathematics and reviews some of the numerous books published that provide the most readable available introduction to the subject. Further¬more, mineral industries examples are used to suggest the relevance of the theory. THE RELEVANCE OF THE ECONOMICS OF PRODUCTION Three basic steps are involved in establishing the relevance of economic analysis to mineral ¬industries decision making. First, the general theory of production must be defined, and its relationship to the simpler models of production stressed in economics textbooks must be noted. Second, the critical modification-considera¬tion of the problems of discovering and devel¬oping mineral deposits-must be developed. It turns out this too involves a special case of the general theory of production. Third, the concept of an economics of exhaustible resources must be explored sufficiently to suggest why its practical relevance is doubtful (or at least far smaller than the numerous writers on the subject seem to believe). The present approach is heavily influenced by post-1945 developments in economic anal¬ysis. Particularly since World War II, economic theory has drastically changed its scope. First, stress has increased greatly upon viewing the economy as a network of intertwined markets known technically as the general equilibrium system.b In this view, not only is the economy viewed as an integrated system, but critical con¬cepts are viewed somewhat differently than was previously fashionable. Specifically, in general equilibrium models, the concepts of supply and demand are rejected as central concepts in favor of a distinction be-

Jan 1, 1985