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By R. V. Higgins, A. J. Leighton

Interest by petroleum engineers in the flow of three phases—oil, gas and water—in irregularly bounded porous media lies mostly in the performance calculation of water floods of reservoirs that have been partially depleted as the result of expansion of much of the originally dissolved gas. The authors present a method to forecast three-phase flow in complex geometry and explain the details by the use of a specific example of a five-spot water flood of a partially depleted stratified reservoir. In this example, the fluid and rock properties of a field given by Prats, et al,' were used. The computed results fit the field performance more accurately than Prats, et al, and Slider.' The time required for the high-speed digital computer to make the calculations, including the contributions from the different layered zones, is about one minute. INTRODUCTION The declining rate of discoveries of new oil fields in the United States makes the recovery of more oil from known reservoirs more attractive than previously. Water flooding has an excellent proved background for recovering additional oil economically. Accordingly, the main interest of this paper is in this type of recovery. In petroleum engineering studies, commercial interest in three-phase flow is mostly in the water flooding of reservoirs in which the oil has been partially produced by the expansion of dissolved gas. When water is pumped into these reservoirs, three-phase flow takes place. Although this paper is concerned with these conditions, the principles involved could be used for other conditions when and where they come to the fore. Many investigators have made contributions to non-empirical forecast methods using basic scientific engineering principles. Several of these used the oil in place at the start of the water flood and the oil remaining after a large quantity of water has passed through a core for key values in their calculations. Recently, Prats, et al,' and Slider have reduced assumptions by adding the third phase—gas—in their forecasting methods. Slider uses the mobilities in the immediate vicinity of inlet and outlet wells as an aid to simulate the resistance effect in the five-spat pattern of the flow of oil, gas and water. Prats, et al. minimize assumptions by using previously determined laboratory data for determining sweep efficiency in the five-spot pattern. In neither of these papers is the saturation profile continuously affected by permeability-saturation curves. Sheldon and Dougherty- recently described a method that employs continuously changing saturation profiles using permeability curves, has a minimum of assumptions and needs no prior sweep efficiency. The Higgins-Leighton method, described in this paper, has all of these features; however, many of the techniques are different from those of Sheldon and Dougherty. The Higgins-Leighton method, tested in May, 1961, is direct and easy to apply and requires very little computer time to calculate a forecast. The short computer time is especially helpful in the study of a reservoir containing many layers of different relative permeabilities. In the Higgins-Leighton method, the individual pressures do not have to be calculated, as the resistance to flow in each cell in the flow pattern is readily determined without the use of any iterative techniques. The saturation and permeability distributions are readily determined. These data and the shape factor, which is measured only once from the potentiometric model when mobility ratio is one, determine the resistance to flow in each cell. THEORY The authors showed in a previous paper4 that, as an aid to calculating performance, the reservoir can be divided into channels using the streamlines of a potentiometric model as a guide. See Fig. 1. This procedure also was used in this paper. The authors also showed that, by treating conduits as approximately one-dimensional and neglecting pressure gradients transverse to the main flow, the Buckley-Leverett equation may be expressed as The principles expressed by this equation are employed extensively in the three-phase flow, as they were in two-phase flow. In the three-phase flow, the channels (the size and shape of which are taken from a potentiometric model)

By J. W. Snavely

A practical mathematical treatment is presented for the determination and control of conveyor belt acceleration, particularly for conditions of starting where vertical curves are involved. A typical sample problem is analyzed, with required calculations, to clarify the procedure. THE part that acceleration plays in starting a belt conveyor and its effect on belt conveyor design are well understood in a general way. Its practical importance is easily overlooked, however, and under some conditions, it is absolutely necessary to give the problem of acceleration detailed study. Most handbooks on conveyor belting design adequately present basic data for the determination of acceleration values. This paper will only attempt to present practical thinking and a convenient method of treatment of acceleration in belt conveyor design. Mathematical Analysis In working out the various problems of conveyor belt acceleration, the starting point, as presented by the handbooks, is the familiar formula of "force of acceleration is equal to the mass times acceleration." By expressing these fundamental quantities in terms of belt conveyor design, it is possible to arrive at the unsuspected conclusion that the acceleration time for horizontal belt conveyors is independent of the load, and instead, dependent upon the belt speed, the type of drive arrangement and drive pulley, and the idler coefficient of friction. The mathematics leading to this conclusion are shown in Table I, which has been prepared to show this derivation. While at first the conclusion just given may not seem to be reasonable, further reflection indicates that obviously the type of drive pulley and the type of drive do affect materially the tension in the conveyor belt, and thus, as clearly shown, the time of acceleration is dependent upon the factors mentioned. Inasmuch as all of the factors except time are predetermined by the belt conveyor design, it becomes relatively easy to establish the accelerating time and to reduce further this time determination to a simple graph from which the time in seconds can be read directly. Such a graph is given in Fig. 1. The table appearing on Fig. 1 should be explained further. For a given belt speed, the time of acceleration can be expressed as a percentage of the belt speed. The time of acceleration is also dependent on the drive arrangement, and changes in the drive arrangement consequently change the time of acceleration. It further follows that for a given belt speed, the time expressed as a percentage of that belt speed also changes with the type of drive. Obviously then, it becomes possible to graph the percentage of speed for .each type of drive against the belt speed and accelerating time, after which, for a given belt speed and type of drive, the time can be read directly in seconds. Two constants were established for Fig. 1, the first one being the limiting of the maximum acceleration tension to 35 pct of the full load operating tension in the belt. The purpose of this is to limit the total tension imposed upon the belt during the acceleration period to 135 pct of the full load operating tension, 'which is the amount required to start or breakaway the fully loaded belt conveyor from rest. The other constant is the friction factor used for the idler equipment, which has been established as 0.022. For installations where it is necessary to establish the values of acceleration, invariably high grade idler equipment is used, and it has been established from field experience that 0.022 for the idler friction factor is amply conservative. The use of this friction factor for idlers must be tempered with judgment, of course, for occasions will arise where more power than indicated is required to start, even with the very best of equipment, such as low temperature operations that tend to congeal the grease in the bearings and thus produce additional friction drag. An inspection of the table in Fig. 1 affords a convenient rule of thumb method for determining the acceleration time, which conveniently can be 5 pct of the belt speed in seconds. The 5 pct of belt speed figure is close to the average for most types of drives. In using Fig. 1 it must be emphasized that it applies accurately to horizontal belt conveyors only.

Jan 1, 1953

By Anthony Tuke

Members of the Society of Mining Engineers may well regard it as rather unusual that a paper on this subject is being presented by someone whose first taste of mining came at the age of 60 or so - someone who last heard of cathodes and anodes in 1938. On the other hand, the title does refer to the financing of a mine and at least I can claim to have spent all my business life since the war until 1981 in the world of banking, though this inevitably means that I have been used to looking at these and other problems through what you might regard as the wrong end of the telescope. The lending of money, and more particularly the provision of finance for commerce and industry, is the central job of a banker and I have been involved in this in various ways over many years, but regrettably only very marginally in the world of mining. As you will see from what follows, the rather specialised form of finance which RTZ required was, to my regret, not provided by the British banking community since the great majority of the finance came from American banks and, to a lesser extent, from German banks. I am most indebted to Mr. Roy Wright for a great deal of the nuts and bolts in this paper. He was one of the three central figures in the growth and expansion of RTZ during the 1950's and 1960's and was right at the centre of the negotiations with bankers, with governments and with many others. The going, as you will see, was far from easy. The essential basis for the financing of each of the RTZ group's mining projects was a firm long-term sales contract for sufficient of the output of the particular mine to produce the cash flow necessary to service the loans. Wherever possible, loans were raised in the same currency as the sales contracts were made. Each sales contract was designed to give the customer the product he wanted with a long-term assurance of supply and at the same time to give the bankers the protection they required. Thus the marketing concept and the financing concept for a particular mine formed one overall plan, and talks with the customers and the bankers were conducted in parallel until a satisfactory marketing/financial package was agreed in principle. Preliminary talks were begun soon after the discovery of a potentially viable orebody. As confidence about a discovery increased, customers were persuaded to enter into contingent sales contracts before the very detailed and costly business of the economic and technical feasibility study of the mine was launched; such a study might cost 10% or more of the estimated total capital cost. At the same time provisional understandings were reached with the bankers. The contingent sales contracts usually gave a period of grace of eighteen months to two years, during which time the decision whether or not to continue with the mine had to be made. This decision rested mainly on the result of the feasibility study and also on coming to a firm agreement with the bankers. If all went well and the mine went ahead, then the contingent sales contracts became firm, but they fell away if the decision was negative. The Company was fortunate that during the whole period when its major mines were being developed, world trade was increasing rapidly and Japan was becoming a dominant industrial power. The Japanese supported many of the mines, including Hamersley Iron Ore, Lornex Copper, Bougainville Copper to name a few, with the basic long-term sales contracts that enabled their development. The Germans supported Palabora and to a lesser extent Bougainville. The mines were financed as individual projects generally with a loan/equity ratio of about 65/35, without legal recourse to RTZ for the loans. RTZ was, however, responsible for providing any capital overruns required to bring the mines into commercial operations. Nevertheless, the RTZ management regarded itself as morally responsible to the lenders because, Palabora aside, the sales contracts had either a fixed selling price (like Hamersley), an indexed price (like the Elliot Lake Uranium Mines and Mary Kathleen), or a floor price (as in Lornex, Bougainville and Rossing). Thus the Company believed that any financial failure would have been due to poor management or technical

Jan 1, 1985

By D. W. Philips

The problem of strata control has of necessity been prominent in mining, and accounts of individual experience and research abound in the literature of most mining countries. Organized rescarch began in Britain by the formation of a committee, upon the recommendation of the Safety in Mines Research Board in 1923, to investigate methods of reducing accidents from falls of roof in coal mines. This committee examined current practice in supporting underground workings in the principal coal fields, and its findings have been published in the Board's publications.' - Toward the end of these investigations it was suggested by the Chief Inspector of Mines that committees of the several mining institutes be formed to examine the problem in their respective districts. The formation of these committees marked a new phase in research on strata control. The work, though being done in the separate coal fields, followed a scheme outlined by the chief Mining Engineer of the Research Board, and was coordinated by his office. FACTORS INVOLVED The subject is being considered in Britain from two aspects: 1. To provide. by supports, means to prevent falls of fractured ground. 2. TO develop methods whereby the strata can be maintained in the least broken condition and thus make falls less likely. The first aspect is the one that will most likely lead to immediate results from the accident standpoint. It depends largely upon the assimilation of already acquired knowledge regarding the properties of supports and their correct application. The second aspect is perhaps more fundamental, and involves also the properties of the strata and their behavior under the influence of the forces induced by mining. The problem involves many natural factors that cannot be controlled, such as depth, inclination and thickness of seam and nature of the rocks. Other factors, which may be considered to a certain extent controllable, cannot be varied readily and with sufficient frequency to facilitate easy investigation; some of these are: rate of advance of the working face, length of face, direction of the face with regard to cleat and inclination, system and arrangements of rock packing behind longwall faces. In any given case the very many factors present have a mutual influence upon the effects produced in the mine. For example, a study of the effects of rate of advance cannot be done without considering the effects of other factors such as nature of strata, direction of face and quality and arrangement of supports. Conversely, the length and direction of a working face

Jan 1, 1947

By D. W. Philips

The problem of strata control has of necessity been prominent in mining, and accounts of individual experience and research abound in the literature of most mining countries. Organized rescarch began in Britain by the formation of a committee, upon the recommendation of the Safety in Mines Research Board in 1923, to investigate methods of reducing accidents from falls of roof in coal mines. This committee examined current practice in supporting underground workings in the principal coal fields, and its findings have been published in the Board's publications.' - Toward the end of these investigations it was suggested by the Chief Inspector of Mines that committees of the several mining institutes be formed to examine the problem in their respective districts. The formation of these committees marked a new phase in research on strata control. The work, though being done in the separate coal fields, followed a scheme outlined by the chief Mining Engineer of the Research Board, and was coordinated by his office. FACTORS INVOLVED The subject is being considered in Britain from two aspects: 1. To provide. by supports, means to prevent falls of fractured ground. 2. TO develop methods whereby the strata can be maintained in the least broken condition and thus make falls less likely. The first aspect is the one that will most likely lead to immediate results from the accident standpoint. It depends largely upon the assimilation of already acquired knowledge regarding the properties of supports and their correct application. The second aspect is perhaps more fundamental, and involves also the properties of the strata and their behavior under the influence of the forces induced by mining. The problem involves many natural factors that cannot be controlled, such as depth, inclination and thickness of seam and nature of the rocks. Other factors, which may be considered to a certain extent controllable, cannot be varied readily and with sufficient frequency to facilitate easy investigation; some of these are: rate of advance of the working face, length of face, direction of the face with regard to cleat and inclination, system and arrangements of rock packing behind longwall faces. In any given case the very many factors present have a mutual influence upon the effects produced in the mine. For example, a study of the effects of rate of advance cannot be done without considering the effects of other factors such as nature of strata, direction of face and quality and arrangement of supports. Conversely, the length and direction of a working face

Jan 1, 1947

By J. Weertman

It is shown that conditions suitable for the conversion of straight dislocations into helices are common in crystals hardened either through long-range dislocation interaction or by jog formation on dislocation lines. For dislocations other than screw dislocations or dislocations nearly screw in orientation, helices can be formed with the aid of core difhsion at temperatures low relative to the melting point of the material. It is assumed that, once formed, helices will degenerate into dislocation tangles. THE dislocation tangle is one major dislocation arrangement observed by the transmission electron microscope which had not been predicted previously from dislocation theory. Since first being observed, the tangle itself has become important in applied dislocation theory. The Cambridge school (P. Hirsch) bases part of its theory of work hardening upon this phenomenon.' In spite of the fact that the tangle obviously is a structure of prime importance to a cold-worked crystal, until recently relatively little attention has been paid to the question of exactly why or how tangles arise. It was generally assumed at first that cross slip and perhaps jog formation will lead to tangles. However Wilsdorf and schmitz2 concluded that cross slip cannot markedly contribute to the tangles. The Wilsdorfs and Maddin3'* have proposed that tangles arise by means of prismatic dislocation loops and superjogs which are produced by a precipitation of point defects. Dislocations with superjogs or which have joined with prismatic loops are themselves dislocation sources and they can produce new dislocations, a process they call "mushrooming", which then tangle with each other. There is no question that the Wilsdorfs et al. mechanism as well as the cross slip one can pro- duce tangles. However these may not be the only paths leading to tangle formation. In this paper we wish to consider another way tangles can form. Our work will be based on the theory of dislocation screw We wish to show that whenever a crystal is cold-worked there always is present a "driving force" leading to helix formation and thus to tangle formation. We do not expect to observe well-developed, regular helices in cold-worked metals. Rather we would expect that after a helix is formed random interactions with nearby dislocations will cause a well-developed helical dislocation to go over into an irregular form. A dislocation tangle is, of course, a grouping of dislocations with irregular forms. Therefore we feel that, in accounting for the formation of dislocation tangles, it is sufficient to show that many dislocations in a cold-worked crystal will take on helical form. The crucial step is helix formation. In order to have a straight dislocation assume a helical form, diffusion of vacancies, or interstitials, must occur. Our discussion of tangle formation therefore will be limited to crystals which have been deformed at temperatures ranging from about one fifth to half their absolute melting point. In this tem per a ture range appreciable core diffusion is possible. (There is no problem in explaining tangle formation at temperatures greater than half the melting point. At such temperatures dislocation climb through a bulk diffusion of point defects gives an extra degree of freedom to dislocation motion. This extra freedom of motion makes tangle formation easy.) At temperatures much below one fifth the absolute melting temperature diffusion processes are sufficiently slow that helix formation does not occur. Of course helix or tangle formation could occur in material deformed at very low tempera-tures which was subsequently warmed in order to make the thin specimen necessary for electron-microscope examination. Since within the temperature range of approximately one fifth to half the melting temperature the diffusion of point defects in the core of the dislocation is rapid, we can reasonably assume that within

Jan 1, 1963

By E. E. Schumacher

IN a laboratory devoted to the furtherance of the science of communication, the breadth and variety of the problems encountered are challenging to a metallurgist. In my own long association with the Bell Telephone Laboratories, our metallurgical group has dealt with a vast number of alloys, both ferrous and nonferrous, and with many materials in the border range of metallic properties., The objectives of our design engineers embrace every phase of telephony, and the properties they desire in metals are generally unusual, frequently unique, and often conflicting. Commercial alloys have not always been available with properties to meet a special requirement in the telephone plant, and many alloys have had, therefore, to be custom-made. Anyone who has had the opportunity to observe the results of tests of all types on numerous such alloys, both commercially and specially produced, or who has taken part in the development of an alloy of some necessary, but new or unusual combination of properties, could not fail to be impressed by the frequency with which a desired goal has been reached or adequately approached through the presence of decimal quantities of alloying elements. Nor could One fail to be struck by the occasions when, conversely, of a minute amount Of impurity element has rendered an alloy useful. It is no exaggeration to state that the content be- hind the decimal point often spells success or fail-ure, and the critical content is sometimes far to the right of the decimal point as I shall later illustrate. The great effects of small additions have long been recognized and have, in fact, been described by many investigators. The importance of the minute, however, cannot be overemphasized. Therefore, in this discussion, I propose to illustrate for you some of the startling instances, drawn primarily from our own experiences, wherein small, even vanishingly small, proportions of stranger elements in otherwise common aggregates have com-pletely changed the customary pattern of behavior. No one property has a monopoly as to being dis-proportionately affected by minor elements. Nearly all properties are affected, but there is time here to include only a selected few. I have chosen, there-fore, three of general interest: strength, magnetic, and electrical properties. I shall inquire into both the mechanisms and consequences of these disproportionate effects and try to share with you the fascination and challenge of this field. Strength Properties of Lead and Lead Alloys To illustrate the effect of the minute on strength properties I have selected lead and its alloys, with which we have worked extensively for many years. Lead has the advantages of being available in quantity in a state of high purity and of being fairly easy to melt and fabricate without contamination to any extent detectable by the spectrograph. It has the interesting disadvantages of recovery and recrystallization at room temperature. Whether I

Jan 1, 1951

By A. M. Sarem

For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady - state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two - phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-pbase relative permeability as it does in two-phase flow. INTRODUCTION In the light of increasing demand for three-phase relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis 1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between I/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression for determining the outflow face saturation from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. PROPOSED METHOD The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three - phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

Jan 1, 1967

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

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

Jan 1, 1970

By C. G. Dunn, W. W. Martin

Various X ray diffraction techniques have been developed for determining orientations of crystals. Transmission and back-reflection Laue methods1,2,3 in particular have been found to be very useful. In many applications, however, a need still exists for a simplification of the details of analysis so that orientations can be determined more rapidly, and operators with little or no training in crystallography can be easily instructed in the necessary procedures. Filling this need in part is a system of analysis that has been in use for several years in the Metals Section of the Laboratory, General Electric Co., Pittsfield, Mass. This method is an extension of the one of Majima and Togino,4 which uses fifty-five indexed standard transmission Lauemams to cover the entire range of crystal orientations. Greater rapidity in determining the orientation of a crystal is achieved by using a slightly larger set of standard Lauegrams and by systematizing the steps followed. This system of analysis in its present form constitutes the subject matter of the present paper. Although the method uses transmission X ray Laue patterns, many of the operations are applicable to the analysis of back-reflection Lauegrams. Very briefly the method is based on the fact that Bragg and azimuthal angles for two or more identified Laue diffraction spots completely determine the orientation of a crystal, and standard Laue photographs of the Majima and Togino type provide a ready means for identifying Laue spots. After a preliminary analysis, which consists of identifying the pattern in terms of one of the standard patterns, a correctly marked Lauegram is selected to carry out the final analysis. From measured Bragg and azimuthal angles, the normals (poles) of the reflecting planes for the selected Laue spots are located on a stereographic projection and the orient.at.ion of the crystal determined (in terms of the positions of cube poles for example) by a few additional operations on a \I1ulff net. The actual procedure followed will be illustrated in detail after a brief treatment or X ray problems connected with orientation determinations and a discussion of useful principles and techniques. X Ray and Plotting Problems RELATIVE ADVANTAGES OF BACK-REFLECTION AND TRANSMISSION LAUE DIFFRACTION METHODS In the back-reflection Laue method it is easy to make a direct measurement of the tilt of a zone of Laue spots. Specimen thickness also is generally no problem. In the case of thin specimens, however, the time of exposure is less for the transmission Laue method. For example, with silicon ferrite this advantage holds up to a thickness of 0.6 mm if tungsten radiation at 40 kv peak voltage is used. Furthermore, the transmission photograph represents the entire thickness of the crystal whereas the back-reflection picture represents only a surface layer (a thickness of less than 0.05 mm for silicon ferrite), the deeper layers supplying a negligible amount to the diffraction pattern. If a crystal is distorted, the transmission Laue pattern gives more information particularly with regard to the orientation of the crystal and the overall amount of spread in orientation. Finally a 3 1/4 X 4 in. film suffices for transmission photograms; a 4 X 5 in. or 5 X 7 in. film with a central hole is needed for back-reflection patterns Not only is the manipulation of film easier because of the size of film, but

Jan 1, 1950

By F. Selig, A. S. Odeh

A second-order approximation to the exact solution of the diffusivity equation corresponding to the pressure build-up of a well producing at a variable rate is derived. This approximation is applicable when the well's shut-in time is larger than the total time elapsed since the well was first produced. The resulting equations are compact in form and easy to use. Thus, the need for Horner's' theoretically precise but rather laborious solution to the above problem is eliminated. In addition, these equations apply where the use of Horner's widely known approximate method is questionable. From a practical point of view, the reported method is best suited for analysis of drill-stem tests and short production tests conducted on new wells. INTRODUCTION The utility of drill-stem and short production tests in reservoir studies has long been recognized by the reservoir engineer. If interpreted correctly they could lead to a wealth of information upon which may depend the success or failure of reservoirs' analyses. Initial reservoir pressure and the average flow capacity are two quantities that are normally sought from a drill-stem and/or a short production test analysis. Pressures are the most valuable and useful data in reservoir engineering. Directly or indirectly, they enter into all phases of reservoir engineering calculations. Therefore, their accurate determination is of utmost importance. The flow capacity kh of the reservoir is indicative of its commercial capability. In addition, it can indicate the presence of a darnaged zone around the wellbore and, thus, the necessity for remedial measures. Of the several methods used to analyze drill-stem and short production tests, Horner's' method is by and large the most common. It applies to an infinite reservoir and or a limited reservoir where the effect of production has not been felt by the boundary. Horner's method makes use of the so-called "point-source" solution of the diffusivity equation. The point-source solution is approximated by a logarithmic function and the superposition theorem is utilized to give the familiar pressure build-up equation where is the shut-in time, q is in reservoir barrels per day and the rest of the symbols conform with AIME nomenclature. Eq. 1 was derived for a well which produced at a constant rate q from time zero to time t and was then shut in. In actuality, such a constant rate of production does not normally obtain. Therefore, a correction must be applied to Eq. 1 to account for the varying rates of production. Horner suggested two methods. The first, which results in a theoretically accurate solution, is rather lengthy and laborious and, thus, it is not suited for routine analysis. The second which has been termed a "good working approximation" is the one used by the majority of the reservoir engineers. In the second method, Eq. 1 is modified by simply introducing a corrected time t, and writing where q is the last established production rate prior to shut-in, and t, is obtained by dividing the total cumulative production by the last established rate. Horner's original paper does not give any indication that this method of correction is based on any theoretical justification. In addition, there is a question as to what constitutes the last established rate. In case of a drill-stem test some engineers use the average rate obtained by dividing the total fluid produced by the total flow time, while others calculate the average rate by dividing the total fluid produced by the last flow-period time. Obviously, different results obtain for the different flow rates used. Because of this, a simple method to the varying-rate case was developed which is theoretically sound and which defines clearly the flow rate and its associated time to be used in the calculations. The final equation arrived at is where q* and t* are a modified rate and time, respectively, and can be easily calculated. In addition, it is shown theoretically that Horner's approximate method, if used for a variable-rate case, gives the correct pressure but would not be expected to give the correct flow capacity. MATHEMATICAL ANALYSIS The general equation governing the flow of slightly compressible fluid in porous media may be written as The elementary solution to Eq. 4, representing an instantaneous withdrawal of Q units volume of fluid at the origin at t = 0, is known as the instantaneous sink

By R. Wild, F. A. Wright

When a blast furnace has a certain defined burden and is operated under fixed conditions of blast temperature, etc., the fuel efficiency is determined by the extent to which the reducing gases can remove oxygen from the burden in the furnace stack. This is determined by two distinct factors: 1) The uniformity of gas-solid contact, and 2) The ease with which oxygen can be removed from individual pieces of burden. This latter is often called burden reducibility. When burdens were poorly prepared the first factor was by far the most important and a study of the reducibility of individual lumps was of rather academic interest. In recent years good burden preparation with emphasis on uniformly sized material has led to greatly improved gas distribution in the stack, and thus the second factor has become much more important and there has been a marked increase in interest in methods of measuring reducibility. This paper explores the Linder method of measuring such reducibility. The measurement of reducibility of burden materials must be carried out under conditions duplicating, as nearly as possible, those of the blast furnace stack. This is very difficult since the blast furnace process is a counter-current one, and thus the initial conditions encountered by the solid (gas temperature, composition, etc.) are the result of heat and mass transfer occurring lower down the stack. Any method of burden testing which does not take this into account is, at least to some extent, based on arbitrary assumptions. In an attempt to study blast furnace reactions under non-arbitrary conditions BISRA adopted the SCICE technique as a method of investigation. This technique has been used with a measure of success.' The SCICE technique, however, was found to be too slow for use as a routine test for burden materials and it was decided to construct additional equipment for burden testing. A test was required which would: 1) Be as realistic as possible. 2) Be quick and easy to operate. 3) Give some indication of the breakdown likely to take place during reduction in addition to a reducibility index. After a critical assessment of the reducibility tests which have been proposed it was decided to adopt the Linder test equipment and procedure as a basis for burden testing. THE LINDER TEST APPARATUS AND PROCEDURE The apparatus which was constructed (Fig. 1) was the same as that described by Linder2 except for minor changes in design. Linder also laid down a test procedure which he had derived from the results of investigations on Swedish blast furnaces. The variations of temperature and gas composition during the test were defined; these are shown diagram-matically in Fig. 2. BISRA's intention was to use the standard temperature and gas composition programmes for testing a variety of burden materials and also to investigate the influence of different programmes on standard burden materials, making use of information from the SCICE apparatus wherever this is possible. Up to the present, effort has been concentrated on the first part of the programme, and work on the second part has only just commenced. For each test 200 g of coke and 500 g of burden material were used. Linder had recommended that the coke and burden material should be between 1 and 1 1/2 in. and this was adhered to in early experiments on ores and sinters. Since the eventual aim of this work was to relate the test results to blast furnace operation, it was decided to carry out subsequent experiments using burden material in the size range used in the blast furnace, as far as this was possible. If the main interest was, for example, a comparison of the products resulting from different methods of agglomeration, then there would be advantages in using burden materials as close as possible to a standard size. After the charge had been placed in the reaction tube and this had been connected to the gas supply, rotation of the reaction tube at 30 rpm was started and the reduction programme was commenced, the gas temperature and composition being manually controlled according to the programme shown in Fig. 2. After the reduction test the charge was cooled in a nitrogen atmosphere. It was then removed from the reaction tube, the coke and burden separated, and the extent of burden breakdown assessed by screening it at 10 and 30 mesh. The extent of reduction was then

Jan 1, 1964

By P. Greenfield, C. C. Smith, A. M. Taylor

J. E. Harris (Berkeley Nucclear Laboratories, England)—Greenfield et al.11 attribute abrupt changes in slope of their log o/log i curves for heat-treated Mg/0.5 pet Zr alloy (zA) to &apos;atmosphere&apos; locking. It is proposed here that a more reasonable explanation of the apparent strengthening at low rates of strain can be based on precipitation either during the preanneal or during the creep tests. All the tests were carried out above 0.5 Tm where solute atmospheres are likely to be largely evaporated2 and can migrate sufficiently rapidly so as not to impose any &apos;drag&apos; on the moving dislocations. McLean3 has derived an expression for determining the temperature Tc above which, due to the high-migration rate of the atmospheres, Cottrell or Suzuki locking can play no part in determining creep strength. This expression, which holds for an applied shear stress of not greater than 5 X 107 dynes per sq cm is: Tc/Tm= 7/6.8 - log10? where i = secondary creep rate The values for T, corresponding to the maximum and minimum reported creep rates at each temperature have been calculated from the data of Greenfield et al. These are given in Table VII. All the test temperatures were above T,, the margin being greater for the higher temperatures and for the lower strain rates where the breaks in the log s/log ? curves occurred. Dorn and his collaborators14, 17 have studied systematically the effect of solute hardening on the creep properties of an A1/3.2 at. pet Mg alloy. In the temperature range where strain aging occurred in tensile tests, abnormally high-activation energies for secondary creep were obtained but at temperatures above 0.43 Tm, solute alloying did not have any effect on the creep parameters. Moreover, there have been no reports of any strain aging phenomenon during elevated temperature tensile tests with ZA material.18 Instead of the observed strengthening being due to atmosphere locking, it is now proposed that precipitates play an important role in enhancing the creep strength of the material. There are two possibilities—precipitation of zirconium hydride during the high-temperature preanneal and/or precipitation of the hydride or a-zirconium during creep. On the basis of the former the results can be interpreted in terms of a critical stress being necessary to force the dislocations through or over preexisting precipitates. From the latter, if the strengthening is due to pre- cipitation during the test then hardening should be associated with a critical strain rate. At low rates of strain, time is available during the tests for precipitation to occur either directly onto dislocations (thus pinning them) or generally throughout the matrix (which would impede dislocation movements). Examination of the data of Greenfield et al. suggests that both mechanisms may be operative since they observed precipitation during creep and also found that their alloys exhibited high-creep strength in the early stages of the low-stress tests, i.e., before creep-induced precipitation had time to occur. It is not easy to understand why they considered that precipitation of zirconium hydride is unlikely to occur at 600°C while it can take place in tests in air at as low a temperature as 200°C. Precipitation of the hydride during the preanneal cannot be ruled out merely on the basis of metallographic examination. Hydride precipitates in ZA type alloys are very small and can only be accurately resolved in the electron microscope.9 For example, in this laboratory20 hydride platelets with major dimensions <(1/10) µ have been observed by electron transmission through thin film specimens of hy-drogenated ZA material. Complex interactions between dislocations and such particles are illustrated in Fig. 12. Additional evidence for precipitation during pre-annealing is provided by the data presented in Greenfield&apos;s Fig. 1 and Table IT. These show that the creep strength at 200o and 400°C increases with the time of preanneal at 600°C. Such increases cannot be explained on the basis of increases in grain size alone for further improvements in strength were observed when the material was annealed for longer times than that required to stabilize the grains. Although the main discussion is confined to ZA material, similar arguments can be used against the strain aging hypothesis proposed to explain the binary Mg/Mn alloy data. In this case no precipitation is possible during the preanneal, but precipitation-hardening during creep can occur.

Jan 1, 1962

By Lyman H. Hart

Some of the significant facts that will affect the supply and demand for metals during the next few decades are given in this presentation. This is important because the only hope for intelligent guidance of the national destiny depends upon presenting a consistent and accurate picture of basic problems. The metals problems now fomenting are only slightly less important than those precipitating the energy crisis. Admittedly, it is difficult to generate serious thinking on this subject when the world is enjoying easy access to all metals at modest prices. This is possible because of the current world capacity to over-produce, and United States credit standing, at least up to now, has permitted buying freely on world markets. Although both these vital conditions are subject to change, there is little doubt that if the U.S. financial house is kept in order, we can muddle along for a while on a generally expanding, metal-based economy. But should our credit standing be permitted to collapse, or should there be a tightening of world supplies of metals, the nation would immediately find itself in trouble. Unfortunately, clear signals indicate that both of these conditions are threatening. The metal age started many centuries ago, and with the exception of the noble metals, barely a dent was made in world reserves until the present century. Then, as a result of the pioneering ideas of D. C. Jackling and Paul Gemmel, and the willingness of the McNeals, Penroses and Guggenheims to back ideas with money, a virtual explosion of metal production was propagated throughout the world. It is important to examine the causes of this expansion to determine whether it is a trend that may be sustained or whether it is anomalous and therefore attributable to circumstances not likely to be repeated or continued. This period of plenty is a once only phenomenon. Vast metal resources have been sitting around here for eons, while the world was unaware of or unconcerned with their existence. But when population began to grow exponentially, and ways were discovered to use metals to develop machines to do the work of men and animals, the exploitation of raw materials increased at a staggering rate. And now the realization is dawning that minerals are a wasting asset and are beginning to present supply problems that should begin to be of concern. Two main factors have caused this condition; One is the population growth, and the other is the expanding demand for irreplaceable raw materials as nations become more developed. A group of systems analysts, at Massachusetts Institute of Technology in a book Limits of Growth, has warned that at present rates of population growth and resource consumption together with environmental constraints, a point will be reached within 100 years when the world population will become totally incapable of supporting itself. The authors conclude that this end result could be avoided if a planned equilibrium could be established at a lower rate of population growth and resource consumption. Fortunately, there is evidence that the population problem is moderating. The growth rate in the U.S. has decreased from 2.3% per year in 1900 to 1.1% in 1970. But, even at the lower rate, population will double in 70 years. The world rate is greater, and if it continues, world population will rise from 3.5 billion to nearly 10 billion in 50 years. All of these projections are questionable because the dangers of growing population are now being recognized. A marked decrease in growth rate has been noted in the more developed countries-in fact, it was zero in the U.S. in 1972. The other factor affecting consumption of raw materials is the increase in per capita use of most items as individuals become more affluent. Many economists believe that developing countries such as China and India represent a vast future potential market; but there are others, with whom the author agrees, who believe over-population tends to stagnate development. Nevertheless, it is a fact that vigorously developing societies increase consumption at a rate far above their population growth rate.

Jan 1, 1974

By Louis A. Panek

INTRODUCTION AND SUMMARY With respect to the geomechanics aspects, the primary technical objectives in mining by an undercut-cave method are to achieve a controlled, sustained caving of the mineral body and to remove the fragmented ore with a minimum of dilution from surrounding unmineralized rock, while maintaining stability or control of the rock structure around the access openings. The structurally ideal ore body probably does not exist. If the rock mass is so weak as to cave on a short span, it may tend to be too sticky for easy drawing and handling, or create special problems in regard to support of the access openings. If the ore is strong, caving may be difficult and the caved fragments may be of such a large size as to require special equipment for transferring the ore from the caved zone. Given enough time and money to generate data and conduct trials, engineering and ingenuity can devise an appropriate combination of mine layout, sequence of extraction, and mechanical equipment to achieve a technically successful caving extraction operation to meet the foregoing requirements in many types of deposits. The large capital investment involved, however, reduces the freedom to make major changes once the mine development is well under- way, and the penalties for failure to accurately anticipate operating conditions militate against selecting any but the most obvious candidates for mining by an undercut-cave method. The demonstrated capability to extract large, deep, economically marginal deposits by this low-cost, high-volume method of mining provides an incentive to develop a rationale for predicting the cavability and stability characteristics of a deposit prior to mining, so that the undercut-cave method may be extended to a much wider range of mineral deposit characteristics. The ultimate goal is to establish as explicitly as possible the quantitative interrelationships between the measured rock-mass characteristics, the caving span, the size distribution of caved ore fragments, and the sizes and locations of stable access openings. Lacking an understanding of these relation- ships, a designer may readily change some factor in the wrong direction (e.g., excessively reduce the distance between the extraction level and the undercut to increase the convenience of operations for the undercutting crew, increasing the frequency of repairs to the extraction-level support system) or create unnecessary problems elsewhere in the system by introducing a design change that can achieve only minimal improvement in the factor of direct interest (e.g., unnecessarily complicate the ore-transfer system by changing the orientations of the openings, with- out succeeding in the objective of improving the ground support conditions). Although successful predesign is the prime objective, subsequent modifications in mine lay- out and sequence of extraction operations are inevitable. In developing the modified solution, systematic experimentation based on an understanding of the underlying structural relationships, coupled with monitoring measurements of selected diagnostic structural-behavior parameters, can achieve an acceptable solution in a minimum number of steps, which is far superior to the typical operational trial-and-error approach, in view of the cost of implementing each successive change. Since a drill-core sample of ore rock from a successful undercut-cave operation may exhibit a uniaxial crushing strength in excess of 100 MPa, the caving of such a rock mass is now commonly believed to be ascribable to the presence of discontinuities such as joints or fractures throughout the ore body. An essential part of the present investigation was therefore to characterize the natural discontinuities at each of the test sites by measuring their attitudes and spacings. The term "fracture" is used herein in a general sense to include any planar discontinuity without implication as to its suggested mode of origin. Most, but not all, of the fractures are properly termed joints. As a point of departure we may consider the possibility that the rock mass is transected by three families of joints, each family possessing a distinct orientation, such that parallelepipeds of intact rock are delineated by the jointing. Even if cementation is absent between adjoining parallelepipeds, the undercutting of the rock mass will not necessarily initiate sustained caving--owing to the all-around confinement, an arch may tend to stabilize over the undercut unless prevented from doing so by the failures of key blocks of intact rock. Thus, although the jointing can be assumed to weaken the rock mass, creating preferred directions of

Jan 1, 1981

By C. Y. Ang, C. Wert

Quench aging of supersaturated solid solutions of nitrogen in columbium takes place in reasonable times in the temperature range 300&apos; to 500°C. Changes in internal friction, hardness, and electrical resistivity are found to accompany this change. THERE is practically no detailed information in the literature concerning interstitial solid solutions in either columbium or tantalum. The fact that both of these metals are used extensively commercially in both pure and alloyed states makes studies of their properties of value. While the plan is to study both these metals and their alloys extensively, so far only a small number of measurements have been made. This paper presents data obtained in the initial investigations of columbium. The principal interstitial impurities of columbium are likely to be hydrogen, carbon, oxygen, and nitrogen. The first of these, hydrogen, is outside the scope of internal friction measurements at present and nothing quantitative is known about the initial hydrogen content of the specimens. However, it is believed that it is completely absent after the preliminary heat treatments are carried out. The carbon content of the original samples is low and can be reduced still further during sample preparation. Oxygen is normally present to some extent in columbium and can also be added or removed easily. Nitrogen is also normally present in small amounts and can also be controlled within limits. Since it is not possible yet to remove all the nitrogen from columbium and since it is possible to remove essentially all the oxygen and carbon, initial measurements were made on the alloy system nitrogen in columbium. In this sense then, the alloys are true binary alloys. Little is known about the effects of nitrogen on the physical and metallurgical properties of columbium, so it was necessary to perform some rather elementary measurements on the specimens. These measurements are described briefly in the next section and are discussed in detail in later sections. Scope of the Work That internal friction is associated with diffusion of nitrogen in columbium has been known for some time. It is similar in nature to that for carbon and nitrogen in a-iron. In these latter cases, the information obtained from internal friction has been useful metallurgically.&apos; and it is not too much to expect useful information from similar studies on columbium containing nitrogen. The technique of internal friction measurements is adequately described by Ke2 At a frequency of 1 cps the internal friction peak for nitrogen in columbium occurs at 300°C and that for oxygen at 160°C." So that all the measurements will be meaningful metallurgically, the internal friction has been calibrated by making a measurement of the damping at the two peaks and a measurement of oxygen and nitrogen content by chemical analysis. A comparison of the two gives the following calibration factor: To go from damping capacity expressed in terms of 1/Q to weight percent of oxygen and nitrogen in solid solution in columbium, multiply the peak values of internal friction by about 4 and 3 respectively." Data from which these factors were calculated are presented in Table I. The increase of electrical resistance of columbium caused by the addition of oxygen and nitrogen as interstitial impurities has been quantitatively determined. At room temperature the percentage increase is small for small additions of impurities (<0.1 wt pct); as the temperature is lowered it becomes an increasingly larger factor of the total resistance. An empirical relation has been established to express the resistivity at — 195°C in terms of weight percent of oxygen and nitrogen in solid solution. It is easy to make supersaturated solid solutions of nitrogen in columbium and to observe aging phenomena. The optimum aging temperature, as in the case for carbon and nitrogen in a-iron, occurs at the temperature for which the time necessary for a single place-change in diffusion is about 1 to 10 millisec. This means for nitrogen in columbium that significant property changes should take place for this alloy at about 400" to 500°C in reasonable time intervals. Results of such aging experiments are

Jan 1, 1954

By M. F. Williams, L. G. Hendrickson

IN classification of pulps bearing magnetized ferromagnetic particles, depolarizing is of great importance. If size separation is to be effective, particles must be individual rather than in floes. Depolarizing is also practiced in heavy medium separations in which ferrosilicon or magnetite is the medium. When particles of ferromagnetic material have been removed from a magnetic field, residual magnetism causes agglomeration. The term depolarizing refers to the operation of reducing or eliminating this residual magnetism and may thus be considered magnetic deflocculation. The terms demagnetizing and randomizing are also used. At the Research Laboratory of Oliver Iron Mining Div. in Duluth a method was developed for measuring depolarization of the pulp of ferromagnetic material. Experiments were made with Mesabi taconite,&apos; a natural magnetite of low coercive force. Ferromagnetic materials of higher coercive force, such as lodestone or the artificial magnetite produced by reduction roasting of hematite, present a more difficult problem, which was not within the scope of this investigation. It is possible, however, that some of the techniques evolved for measuring and calculating electrical characteristics of alternating current coils would be of use in depolarizing high coercive force material, particularly in conjunction with high-frequency alternating current, as proposed by Hartig and others.&apos;," Properties of Ferromagnetic Materials:&apos;7 Experimental work, described below, has shown that if a sample in the magnetized state is heated above the Curie point and cooled, much of the preferred orientation is destroyed and the sample is substantially depolarized. It has been thought that when the sample cools below the Curie point the domains cancel each other, leaving a zero net moment. However, such particles still exhibit a tendency to cohere, and undoubtedly this is caused by the forces of residual magnetism. -AS measured by the percent depolarization, this tendency is reproducible for any sample upon repeated heating above the Curie point and subsequent cooling and is independent of the initial state of magnetization. It is postulated, therefore, that as the material is cooled below the Curie point the domains in any particle do not completely cancel each other, but rather are preferentially oriented to some extent. Mechanism of Depolarizing with Alternating Current Magnetic Fields: It is believed that when ferromagnetic material is passed through an alternating magnetic field, depolarizing occurs in the decaying portion of the field. As the particles pass through the portion of highest intensity they become magne- tized. If the particles are not free to move, the polarities of the particles will be reversed (by a mechanism similar to that described above for magnetism) at a frequency equal to that of the applied field. As the material moves through the decaying field, intensity levels become such that a domain does not completely reverse, but stops on an axis of easy magnetization. By the time the material reaches the point of zero field intensity, a state of fairly random orientation of domains is achieved. If conditions are such as to give a completely random orientation, the particle will have little or no external magnetic field, and a pulp of such particles will be depolarized. Previous Work In 1918 E. W. Davis was granted a patent for demagnetization of magnetite pulps.&apos; His method consisted of passing the pulp through a tapered coil, activated by alternating current of normal frequency (60 cycle). This method, with minor modifications, has been used almost universally in all pilot plants and commercial installations in which depolarization of low coercive force materials has been required. Hartig, Onstad and Foot2,3 avd made a detailed study of the factors involved in depolarizing both low (below 100 oersteds) and high (above 100 oersteds) coercive force material. They developed a method for evaluating the relative degree of depolarization of any pulp based on the settling characteristics of the pulp. Their standard of comparison was a sample heated to above the Curie point and cooled in a zero field, all in a neutral atmosphere.* For low coercive force material they found treatment.Thisprocedure is subsequently called, in this report,theCurie that results equivalent to Curie treatment could be

Jan 1, 1957

By A. Kenneth Schellinger

THE terms surface tension .and surface energy are well known when applied to liquids and are generally described by referring to the excess energy of the air: liquid interface as a result of unsaturated molecular forces surrounding the surface molecules of the liquid due to the presence of the air phase on one side. Such unbalanced forces produce the familiar water droplet of spherical form and are generally summed up as a surface tension measured in dynes per centimeter which can be shown mathematically to be equal numerically to a corresponding surface energy expressed in ergs per square centimeter. A specific surface energy, however, is best thought of as the energy necessary to produce one unit of new surface on a substance. Hence, in producing a bubble in a flotation cell the impeller must supply surface energy corresponding to the air: liquid interfacial area on the interior of the bubble. Inasmuch as it is relatively easy to extend or contract the surface of a liquid, there are a number of successful methods for liquid surface tension, or energy, measurement based upon surface deformation. This happy state of affairs does not, however, extend to solids, which are considered to possess surface energies for the same reasons as do liquids, i.e. because of unsaturated ionic bonds at the solid gas interface. As in the case of the flotation cell producing surface on liquids as new bubbles, it takes energy to produce new surface on solids as new particles. As every mill man knows, this surface is produced on mineral solids in a grinding mill by the action of a tumbling mass of iron balls. But here so much energy usually is wasted by the inefficient action of these balls that a large amount of heat is generated, and the surface energy production may be easily confused with the energy necessary to produce this ineffective heat. The tumbling balls and fracturing minerals ultimately take their energy from a rather large electric motor. It has been variously estimated that from 10 to 20 pct" only of this energy from the motor does not appear as heat and may be presumed to appear as surface energy on the minerals present.. Such a production of new surface on the mineral phases is accompanied, of course, by a size reduction that is inevitable as more and more mineral interior molecules become surface molecules by the fracture exposure. This size reduction of mineral particles, although the most obvious feature and perhaps the sole object of the milling operation, is from this energy viewpoint the outward manifestation of the production of surface energy only. Measurement of the characteristic surface energies of pure minerals and their various mixtures in ores would be a step towards understanding of the energetics of the commercial grinding operation. In addition, the characteristic surface energy of a mineral is probably a physical property specific for that mineral, and therefore, from a scientific standpoint, should be measured. It is interesting to note that, in contrast to the large body of work on the surface tensions of liquid systems and biological systems, the field of solid surface energies has been neglected. Prior to. 1920 it is difficult to find more than one or two references to work on solid surface energies in Chemical Abstracts. Since 1920 such references number somewhat less than 100, while those on liquid systems are numbered in the thousands. Much of this apparent neglect of the field of solid surface energies (the term is intended to be somewhat inclusive at this point and refers both to the solid: gas, and the solid: liquid interface) is because of the lack of a reliable method of measurement rather than any lack of scientific curiosity. It was, and still is, difficult to produce new surface on a solid without the simultaneous production of interior changes in the same solid which may consume part of the energy used. The extension in the surface area can be measured, but the interior crystal-

Jan 1, 1952

By E. R. Buchanan, R. E. Reed-Hill

Cylindrical magnesium single crystals were deformed in torsion. The axis of torsion was the basal pole. Five crystals were deformed to different strains between 0.08 and 1.03 and then sectioned in order to determine their dislocation densities using the transmission electron microscope. The work hardening rate of all specimens was at least an order of magnitude higher than that normally associated with easy glide in a tension test and comparable to that obserzed in stage B of a tension test. The correspondence between stage B in a tension test and the initial stages of a torsion test is believed to result from the fact that in both cases deformation occurs in a structure containing roughly equivalent densities of the dislocations associated with the three basal slip vectors. THERE are three basic ways of changing the shape of a crystal using slip dislocations. The crystal can be sheared along a slip direction in a slip plane; it can be bent about an axis in the slip plane normal to the slip direction; and, if the slip plane contains multiple slip directions, it can be twisted or rotated about the slip plane normal. Of the three processes, generally known as translational, flexural, and rotational slip, only rotational slip has not been extensively investigated. The object of the present research was to obtain basic information about this phase of crystalline plasticity. This paper is concerned with some aspects of the stress-strain curves obtained by twisting magnesium crystals about their basal poles. Magnesium was selected for four reasons. One, its recovery rate at room temperature is relatively low. Two, single crystals may be easily grown. Three, at room temperature the critical resolved shear stress for basal slip is about two orders of magnitude lower than that for nonbasal slip, so that rotational slip might be expected to occur primarily by basal slip. Finally, relationships between flow stress, shear strain, and dislocation density have been determined for tensile deformation of magnesium crystals,&apos; thereby providing a basis of comparison for the torsional results. EXPERIMENTAL PROCEDURES Crystals were grown from 0.5 in. diam extruded sublimed magnesium rod furnished by the Dow Chemical Co. who reported that it contained in weight percent less than 0.0003 Al, 0.01 Ca, 0.01 Cu, 0.0012 Fe, 0.001 Mn, 0.0005 Ni, 0.003 Pb, 0.001 Si, 0.01 Sn, and 0.02 Zn, with the balance magnesium. All crystals were grown in a dried argon atmosphere using Jill-son&apos;s2 modified Bridgman technique. Two different methods were used to obtain crystals with the basal plane normal to the specimen axis. These included direct growth from seeds of the proper orientation, and spark machining (trepanning) of 0.5 in. diam cylinders from larger (1.5 in. diam) randomly grown crystals. The crystals thus produced were polished in a 20 pct HC1 water solution and then etched in a 1 pct HC1 water solution to develop etch pits lying in rows parallel to the basal plane trace. The crystals were then revolved about their axes on the stage of a low-powered microscope. Torsion specimens were prepared only from those crystals whose axes were normal to the rows of etch pits. It is estimated that this simple orientation method was accurate to about 51 deg. 1.625 in. long cylinders were next cut from these selected crystals and then acid machined in a 20 pct HC1 water solution into torsion specimens with a 1 in. long by 0.30 in. diam reduced gage section. Following this, they were annealed in air at 400°C and furnace cooled to room temperature. The specimens were given a final polish in a 10 pct HC1 water solution, rinsed in ethanol, dried, and cemented into brass grips with an epoxy resin. In addition to the torsion specimens, several tensile specimens with their basal planes at 45 deg to the stress axis were also prepared with similar dimensions except that the gage sections were increased to 4 in. in length. The torsion specimens were tested in the apparatus

Jan 1, 1970

By Donald A. Brobst

The minerals barite (BaSO4-barium sulfate) and witherite (BaCO3-barium carbonate) are the chief commercial sources of the element barium and its compounds whose many uses are nearly hidden among the technical complexities of modern industrial processes and products. Barite, the major ore mineral, is extremely vital to the petroleum industry which in 1980 consumed at least 90% of the world&apos;s production of 8.8 million tons as a major ingredient of the heavy fluid, called mud, that is circulated in rotary drilling of oil and gas wells. The remaining 10% of the barite production was consumed chiefly in the manufacture of barium chemicals and glass and as a pigment, filler, and extender. Barite occurs throughout much of the world and is available from three major geologic types of deposits-vein and cavity filling, residual, and bedded-in sufficient quantity at competitive prices to meet current demands. The world&apos;s demand for barite is expected to increase, and geologic circumstances are favorable for the discovery of new deposits of commercial value. Witherite is much less common and abundant than barite, although it is more desirable in many ways as a raw material for the production of barium chemicals. The United States has not produced witherite since about 1950; England is currently the chief producer of witherite. End Uses Most of the world&apos;s barite production since 1926 has been used as a weighting agent for the muds circulated in rotary drilling of oil and gas wells. The muds fundamentally are mixtures of water, clay, and barite in different proportions that vary according to local reservoir conditions. Muds with a specific gravity as great as 2.5 are used. The mud is pumped down the hollow drill stem, passes through the bit at the bottom of the hole, and rises to the surface in the space between the drill stem and the wall of the hole. In the course of this circulation the drill bit is cooled, cuttings are removed, the drill stem is lubricated, the walls of the hole are sealed, and the hydrostatic head of the column of weighted fluid helps to confine high oil and gas pressures. The latter feature aids in prevention of gushers, thus reducing both environmental pollution and waste of oil and gas resources as well as conserving the natural reservoir pressure for greater production and rate of recovery of the products contained in the rocks. Barite is particularly well suited for drilling mud because it is clean, easy to handle, soft (nonabrasive), heavy, virtually inert chemically, and relatively inexpensive compared to many other available heavy materials. Barite is used in the manufacture of glass in continuous tanks. The addition of barite homogenizes the melt and gives greater brilliance and clarity to the finished glass. Ground barite, both unbleached and bleached by sulfuric acid, is a common industrial filler, extender, and weighting agent. The rubber industry is a major consumer of barite as a filler. Barite also is added to bristolboard, heavy printing paper, playing cards, rope finishes, brake linings, clutch facings, plastics, and linoleum, to name but a few uses. Bleached barite has long been an extender in white lead paint because of its weight. The low index of refraction of barite, however, makes its ability to cover marks poorer than some other substances, but its low capacity for absorption of oil is a good feature. Off-color or unbleached barite can be used as a filler in colored paints. In the construction industry, some lump barite is used in concrete aggregate to weigh down pipelines buried in marshy areas and to shield nuclear reactors. Because barite absorbs gamma radiation well, its use reduces the amount of expensive lead shielding otherwise

Jan 1, 1983