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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 R. P. Agarwala, M. S. Anand, S. P. Murarka

Using the residual radioactivity technique, grain boundary diffusion of chromium in the a phase and lattice diffusion in the a and the ß phases of zirconiuttz have heen studied. The diffusivities (in units of square centiwzeters per second) have heen expressed as THE rate of diffusion of atoms along surfaces and grain boundaries is much greater than that through the bulk of metals. These processes dominate over volume diffusion at lower temperatures and can be isolated from it by virtue of the fact they yield high diffusion coefficients and low activation energies. In zirconium, however, it has been difficult to identify the volume-diffusion parameters separately. The values of diffusivities in a and ß phases yield activation energies which are much lower than those for volume diffusion calculated from semiempirical or empirical relations.1-3 Diffusion frequencies (Do) are also low, especially in the a phase, and they yield negative entropies of activation.4 Similar results have been obtained for the diffusion studies in titanium.5 It is yet to be investigated whether in these cases diffusion is controlled by some extraneous factor like high reactivity of these metals, or some different mechanism is operative as suggested by Pound et a1.6 However, Federer and Lundy,7 in a recent study of the diffusion of zir-conium-95 and columbium-95 in zirconium, and Gibbs et al.,8 in the study of impurity diffusion in titanium, found a temperature dependence of D, Do, and Q. Their study yielded low values of Do and Q at low temperatures, as has been found by other workers, and fairly high values at high tempera-

Jan 1, 1965

By D. W. Fuerstenau

Recently R. J. Charles1 showed that comminution of brittle or semi-brittle materials in batch operations is described more appropriately by a variable energy relationship than by the specific relationships proposed by Rittinger,2 Kick,3 and Bond.' That is, the value of n in the empirical differential operation which applies to crushing and grinding (Eq. 1) is variable. Independently, Holmes' developed an identical generalized equaton for size reduction. The experimental data of Charles and Holmes show that the value of n is determined by the material and the comminuting machine and is constant for a given combination of these two conditions. The general objective of the present article is to extend the Charles-Holmes concepts to continuous ball milling. The specific objective is to analyze the operation of a vibratory ball mill dry-grinding chromite in a continuous open circuit and to develop an equation for the comminution of chromite in this mill. Basic Principles: In a batch mill the length of time during which the material is ground is a direct measure of the energy expended on the material, except possibly for exceedingly fine grinding. However, in a continuous operation, the fraction of the total expended energy which is useful for grinding will vary according to feed rate and amount of material in the mill. If the amount of material within a continuously operating vibratory mill is low enough so that only part of the expended energy is used for grinding, the extent of size reduction at constant power input must depend upon the length of time the material is retained within the mill, namely, upon retention time. The following analysis pertains to a continuous mill operating under these conditions. The empirical differential equation that applies to the comminution of brittle materials is:" dE = -Cdx/x" [1] where dE is an infinitesimal energy expenditure, C a constant, dx an infinitesimal size change, x the particle size, and n a constant. For continuous grinding in an open circuit at constant power input, P, Eq. 1 must be written as (dtr)P = -C dx/x" [la] where dt, is an infinitesimal time during which a particle of size x is in the mill, and C' is a constant. A ground product never consists of particles of single size but always comprises a distribution of sizes. In comminution, the expenditure of energy causes a lateral shift in the size distribution.', ' " The general objective of any engineering study of comminution is to correlate the magnitude of this size distribution shift with the energy expended, the ultimate aim being to cause the greatest shift with the least amount of expended energy. Although a number of criteria can be used to measure this shift, Schuhmann's size modulus has been found convenient.' Mathematically, the Schuhmann size distribution can be expressed as follows:" y = l00(x/k) [2] or in differential form: dy = [F- xa-' dx ] K, where y is percentage of material finer than size x, a is a constant that determines weight distribution among particles of various sizes, and k the size modulus that denotes the theoretically maximum-sized particle in any size distribution. By considering the energy required to reduce an element of weight of material, dy, from size x, to size x, the element of time during which the material must remain in the mill at at power will be (dt..).= J'-Cax!(dy) [3] Summing up all the elements of weight from zero to 100 for a product that conforms to the Schuhmann size distribution yields C C f Cdx,\( 100«x°-'dx\

Jan 1, 1960

By R. P. Rothwell

Jan 1, 1885

By P. A. Witherspoon, S. P. Neuman

Evaluating the permeability of a caprock overlying a potential gas storage reservoir is a very critical problem. Pumping water from the reservoir can be used as an evaluation tool in analyzing this problem. Fluid level changes that occur in the aquifer us well as in the caprock can be measured with appropriately placed wells. If the leakage of water from the caprock into the aquifer is considerable, the effects will be apparent in the aquifer. If the leakage is slight, however, it will not be possible to detect it with certainty from observations in the aquifer alone. Fluid level measurements in the caprock must be relied upon. and improved methods of analyzing such effects have been developed which are based on a theoretical analysis of fluid flow through a caprock of infinite thickness. An example applying these methods to field data is discussed. INTRODUCTION One of the most critical problems in evaluating an aquifer gas storage project is determining the tightness of the caprock overlying the formation to be used as the storage reservoir. A formation that has previously held oil or gas obviously has a suitable caprock, but an aquifer that contains only water gives no such assurance. A number of aquifer projects in the United States have been troubled by gas leaking out of the intended storage zone, and the ensuing difficulties have led to the development of new evaluation methods. One of these new methods is pump testing wherein water is removed from the aquifer at some controlled rate prior to injection of gas. This fluid withdrawal causes a pressure drop to move out through the aquifer for considerable distances in a matter of days or weeks. Depending on the properties of the caprock, a pressure transient can also pass upward (as well as downward) through the caprock layers adjacent to the aquifer. Thus, if the operator has placed observation wells at appropriate distances from the pumping well, the rapidity with which the pressure transients reach different points in the system can be used to investigate the fluid transport properties of both the aquifer and its caprock. The usefulness of pump testing has been recognized by groundwater hydrologists for many years as a means of determining the potential yield and properties of aquifers used in water supply They have introduced the term "leaky aquifer" for a system in which an aquifer is overlain (or underlain) by semipermeable caprock layers. The ease with which water leaks into the aquifer during pumping can, of course, be very beneficial in bringing additional water to the pumped well. Hydrologists have therefore devoted considerable attention to this prob-lem. From the gas storage standpoint, however, the tighter the caprock layers that overlie the intended storage reservoir, the better are the conditions for minimizing or eliminating any vertical migration of gas. Thus, after a suitable geologic structure has been found, the emphasis in aquifer storage projects is in determining that the caprock is tight. Attention has recently been focused on the use of pump testing as one approach to solving this problem.23,24 This paper presents a further development on evaluating the permeability of a slightly leaky caprock when the caprock is of infinite thickness. From the practical standpoint, this means that the caprock layers are thick enough that pressure transients do not reach the outer boundaries of the system during the pumping test. In a subsequent paper, an analysis of the case where the caprock is of finite thickness will be presented. PREVIOUS WORK ON LEAKY AQUIFERS Jacob" developed a partial differential equation describing the flow of water in an aquifer of permeability k that is overlain by a leaky caprock of permeability k'. Fig. 1 shows a schematic cross-section of the system under consideration. One of his principle assumptions was that if k > > k', the direction of flow is essentially vertical in the caprock and horizontal in the aquifer. Neuman19 confirmed the validity of Jacob's assumption using a mathematical model. Another assumption was that a permeable source layer overlies the caprock (Fig. 1) and is able to maintain a constant hydraulic head at the upper boundary of the caprock. By neglecting the effects of compressibility within the caprock, Jacob1* developed a solution for a bounded circular aquifer. Later, Hantush and Jacobx5 used the same assumptions to solve the case of an infinite radial aquifer that is pumped at a constant rate. Their solution may be expressed in di-mensionless parameters by

By Persifor Frazer

"The nebular theory is a noble speculation supported by plausible argument, and the verdict of science on the whole subject cannot be better expressed than in the words of Newcomb :—'At the present time we can only say that the nebular hypothesis is indicated by the general tendencies of the laws of nature, that it has not been proved to be inconsistent with any fact, that it is almost a necessary consequence of the only theory by which we can account for the origin and conservation of the sun's heat, but that it rests on the assumption that this conservation is to be explained by the laws of nature as we now see them in operation. Should any one be skeptical as to the sufficiency of these laws to account for the present state of things, science can furnish no evidence strong enough to overthrow his doubts until the sun shall be found growing smaller by actual measurement, or the nebulæ be actually seen to condense into stars and systems.' " Leibnitz2 is credited by Cuvier3 (who associates with him Descartcs) with " amusing their imaginations " by conceiving the world to be an extinguished sun or vitrified globe upon which the vapors, condensing in proportion as it cooled, formed the seas, and afterwards deposited the calcareous strata. Whiston4 believed the earth was crested from the atmosphere of one comet and deluged by the tail of another. The heat which remained from its origin excited the whole antediluvian population, men and animals, to sin, for which they mere all drowned in the deluge, except the fish, whose passions were apparently less violent. De Maillet5 held that the globe had been covered by water for many thousand years. The terrestrial animals were originally inhabitants of the sea, and man himself began his career as a fish. He adds it is not uncommon to meet with fishes in

Jan 1, 1905

By L. S. Darken

IN the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be repre-sented satisfactorily by the simple equilibrium expression K - (p1)p1 (p2)p2 . (R1)r1(R2)r2 . where (P) denotes the concentration of a product and (R) the concentra-tion of a reactant in the reaction r1R1 + r2R2 + . . . Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a com-ponent is not proportional to its true mol fraction, But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple com-ponents and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satis-factorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature as ionization or the occurrence of polar and nonpolar molecules-are presumably less effective in metal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

By Fred C. Bond

IN crushing and grinding the larger particles are more exposed to the work input. They absorb most of the work and protect the smaller neighboring particles from destructive contact with the crushing surfaces or grinding media. The importance of this exposure differential upon the reduction efficiency and product size distribution has long been recognized. Unfortunately, there has heretofore been no direct method of evaluating it, and such indirect methods as observing the slope of the plotted product size distribution line have been used as an indication. In this presentation the Third Theory of Comminution1 has been used, together with the exponential formula for size distribution, to evaluate the exposure ratio and exposure constant and to illustrate examples of their utility in crushing and grinding applications.

Jan 12, 1957

By H. H. Campbell

Many attempts have been made to write a formula by which to calculate the strength of steel from its chemical composition, but most of these endeavors have failed because there were too many disturbing conditions. It is idle to collect from the pages of trade-papers, books, or the proceedings of scientific societies, a multitude of observations. The combination of such results will simply show that steel of the same composition will vary in tensile strength through wide limits—a fact that has been known for generations. That cold-working, overheating, and many another form of heat-treatment alter fundamentally the strength of steel, is ancient history, although it is only recently that the microscope has pointed out the road to an explanation of the phenomena. It mag be urged that the microscopic structure must betaken into consideration in any formula giving the ultimate strength, but from the standpoint of the present investigation this is unnecessary. We are trying to determine primarily, not what changes in ultimate strength may be made by variations in the condition of carbon, but what effect is produced by changes in the amount of carbon, when its condition remains constant. For such an inquiry, in order that the condition of the carbon should remain as nearly uniform as possible, it is essential that all testrpieces be made under the same conditions; and it is believed that the tests described in this paper satisfy that requirement. The investigations were made at the works of the Pennsylvania Steel Company, Steelton, Pa.; the ingots from which the tests were made were 6 in. square in every case; they were heated in the same furnace and forged at the same ham-

Jan 1, 1905

By S. S. Clarke

THEN sufficient ore has been blocked out on a lease to warrant a shaft, the proposed. Location of the shaft should be carefully considered, as the old promoter's method of sinking wherever his hat landed is a sad mistake as some: of us have learned by trying to operate such mines. In some instances certain conditions exist, such as mill location, railroad right of way, etc., that necessitate a change of location from the. ideal, but under average conditions and with the knowledge of the formation gained from the drill logs and with the general trend of the orebody known, the shaft can be located from. the standpoint of its future relation to the mine with re-gard to hauling and' hoisting a maximum tonnage: at a minimum cost per ton, also taking into account the minimum amount of expense and trouble- in sinking. Quite a few shafts are located in the wall of a run or just in the thin edge of the orebody: As a general rule the formation here is solid and permits rapid and safe sinking, and the shaft pillars are left in practically valueless material. This permits the withdrawal of pillars and still keeps the shaft protected. By opening a shaft in thin ground, you are not tempted to cut it high, wide, and handsome, but to shape it up-with ample clearance for lay-bys and with more of an idea of permanency, as a few hundred extra dollars spent around the shafts for proper track installation will re-turn, a good rate of interest in ease of handling "cans," quick get-away; and fewer wrecks. Nearly all the shafts in this district are sunk on a contract basis, the con-tractors furnishing all labor and explosives, and the company building the sinking-derrick, dump-track, and furnishing, all equipment, material, and power. The following costs are the averages, for three shafts sunk through good solid formation, with no water to, contend with, and approximately 260 -ft., deep, having about-100 ft. of shale. The contract price was $9 per foot with the shale and $13 per foot in the solid, making a total of $2,980 paid to the contractor. The wages paid by the contractor were, $5 per shift for the hoist-man, who also sharpened steel, $6 for the lead shaft man, and $5 for the helper;, the cribbing was sawed on contract for 40c. per shaft: foot; about. 94 board feet. of cribbing was used per foot of staggered cribbing and 168 board feet per foot of solid cribbing.

Jan 8, 1928

By Joseph F. Shirley

A froth flotation plant to recover byproduct molybdenite must be designed specifically for the selected separation process and the type of ore being treated. However, some general rules concerning byproduct molybdenite plant design can be suggested that would be valid for most processes. The term byproduct molybdenite in this paper is limited to the recovery of molybdenite from copper porphyry ores, which essentially amounts to selectively separating molybdenite from copper and iron sulfide concentrates. In addition, most of the discussions would apply only to the almost universally used approach of floating the molybdenite and depressing the copper and iron sulfide minerals. Thickener It is considered essential that the feed to a byproduct molybdenite plant be thickened prior to being treated for molybdenite recovery for the following reasons: 1) Thickening allows the rougher and any preconditioning stages to be operated consistently at the optimum percent solids. 2) Generally, the size of equipment used for pretreatment and the rougher flotation is considerably smaller and less expensive than if the copper flotation concentrates were treated directly. 3) The removal of as much water as practical by thickening removes flotation reagents added in the copper flotation circuit, especially frother which can be quite troublesome in a byproduct molybdenite plant. Although thickening of the molybdenite plant feed has long been recognized as necessary to optimum metallurigcal results, very often this area has been designed poorly. The thickener should be sized so that it can produce a consistent thickened product containing 60 to 65% solids without the use of flocculants. Some plants are only able to thicken to 45 to 50% solids consistently while other plants let the percent solids vary from 45 to 60% over a 24-hr period. While the former is more desirable than the latter, in many cases better metallurgical results could be obtained if the percent solids could be held consistently close to 60%. Probably the simplest and most satisfactory system of handling the thickener underflow is to spigot it into a sump, using a sphincter type valve for the orifice, controlled by a density meter. Another satisfactory approach is to use an ODS type pump to meter the underflow. There are other methods of handling thickener underflow which work satisfactorily as long as the amount of copper concentrates entering the thickener is relatively uniform. However, they often fail to operate satisfactorily when there are large fluctuations in the thickener feed rate due to fluctuations in ore tonnage and/or copper grade. If the percent solids in the plant feed could be held close to 65%. There is the possibility the molybdenite plant tailing would not have to be thickened prior to the copper filter plant. This means that the molybdenite rougher float would have to be conducted at 45 to 50% solids with all the cleaner tailings returned to the rougher for dilution. Admittedly, in some situations this approach would be impossible, but if capital or plant area is limited, it should be considered.

Jan 1, 1981

By J. Jones-Parra, J. C. Calhoun

INTRODUCTION The purpose of this paper is to present the results obtained by solving the fractional flow' and frontal advance' equations to obtain oil recovery at water breakthrough as a function of the length of the system being flooded, the linear velocity of injection and the displacing phase viscosity. The method of solution makes use of the stabilized zone concept first presented by Terwilliger, et al3 when calculating saturation distributions in a gravity drainage system. In order to check the calculated results, the equations and method of solution were applied to the system on which Rapoport and Leas' reported experimental data. METHOD OF SOLUTION The solution of the fractional flow equation and the frontal advance equation is obtained by assuming that a water front forms to sweep the oil out ahead of it. There is ample evidence that under the proper conditions a water 'front does form. If this water front is not to dissipate, the water saturations which comprise it must have equal linear velocities. These water saturations are said to comprise the stabilized zone. Equation (2) indicates that for all these saturations and hence fw must plot as a straight line against saturation for those water saturations comprising the stabilized zone. The water saturations lying between the highest in the stabilized zone and the highest that can be achieved in the porous medium comprise the variable zone. Regardless of the numerical value of the length of the system, the variable zone must eventually span all of it, so that for long enough systems in Equation (1) will be small enough to be neglected. Hence, for the saturations in the variable zone Equation (1) can be simplified to In order to determine the composite fw function applicable to the entire range of saturations in the porous medium, it is necessary to find the water saturation which separates the stabilized zone from the variable zone. This dividing saturation must be on the curve defined by Equation (4), and a tangent curve at that point must pass through the initial water saturation to satisfy Equation (3). Hence, the valid fw curve is given by a straight line starting at the initial water saturation, tangent to the curve of Equation (4): and along the curve of Equation (4) from the point of tangency on. The point of tangency determines the water saturation dividing the zones. The length and shape of the stabilized zone can be found by solving Equation (1) for Integrating this expression numerically between any two saturations in the stabilized zone gives the distance separating these two saturations. By repeated integration, the saturation distribution of the stabilized zone can be determined. The total length of the stabilized zone is given by The integral appearing in Equation (5) is a function of the viscosity ratio, the capillary properties of the rockfluid system, the relative permeabilities, and the initial water saturation. Considering these variables fixed and designating the value of the integral by writing caw for and v/60 for q/A; Equation (5) becomes The saturation distribution of the stabilized zone can be integrated over its length and divided by the length to obtain the average water saturation The volume of water in the stabilized zone is then given by The average water saturation in the variable zone can be found by extending the straight line segment of (the segment joining Sw and Sw) until it intersects fw = 1.00. The saturation at the intersection is. This method of finding is nothing more than the graphical solution of the equation The volume of water in the variable zone at breakthrough is then given by Assuming no initial water saturation, the recovery at breakthrough expressed as percent pore volume is given by

Jan 1, 1953

By J. O. Whiteley, C. Dietz

It is difficult to give a refining outline that may be followed for any and all combinations of the platinum metals; different combinations require different methods of attack. This paper does not pretend to go into all of the reactions of the metals of the platinum group, but will outline the commercial refining of platinum scrap. Typical Platinum Scrap As a concrete case, let us take 100 oz. of miscellaneous scrap, made up of jewelry scrap, dental scrap and laboratory ware. This lot will contain some platinum, palladium, iridium, ruthenium, rhodium, gold, silver and copper. The first problem is to get all of the metals in solution. If the scrap is principally platinum, palladium and gold, a treatment with aqua regia is the course to pursue; but if the scrap contains alloys high in iridium or ruthenium, aqua regia will act too slowly. In the case in hand, we are going to presume that we have scrap high in iridium and ruthenium, and proceed accordingly. Obtaining Residue A Place the scrap, together with six times its weight of granulated test lead, in a solid carbon crucible. This crucible may be placed inside a clay graphite crucible packed with charcoal, to prevent the excessive oxidation of the carbon crucible by the furnace blast. Place a tight cover on the carbon crucible; heat gradually to a good red heat and allow it to soak in the heat for 4 or 5 hr. After the leaded mass is cool, dissolve in dilute nitric acid (1-6) on a steam plate or sand bath. This dissolves practically all of the lead and most of the palladium, silver and copper, together with seme of the platinum and rhodium, and leaves the iridium, ruthenium, gold, and most of the rhodium and platinum as a finely divided residue. Siphon off the clear solution and treat the residue with another portion of dilute nitric acid to insure the solution of the lead and copper. The second nitric acid solution is added to the first, and the residue is filtered on suction and washed thoroughly with hot

Jan 1, 1928

By Arthur Phillips

THE study of anisotropy in metals has been greatly stimulated in recent years by the rapid development of X-ray methods for determining the crystallographic relationships of wrought and annealed materials. Prior to this time the knowledge regarding the directional properties of commercial alloys consisted almost exclusively of observations of a practical nature made during the fabrication of metal objects, supplemented by a limited number of mechanical tests on specimens cut at various angles to the direction of working. Such observations clearly indicate that the common methods of cold-working metals cause both a crystallographic and a mechanical fibering varying in character and degree according to the nature and extent of the deforming process. Even after annealing, following certain not too well known combinations of reductions and anneals, a preferred orientation may exist, thereby constituting a residual fiber effect sufficiently pronounced to manifest directional properties. With the application of the X-ray the experimental horizon was extended chiefly because the study of anisotropic metals promised to offer direct and quantitative evidence regarding the involved mechanism of fragmentation and plastic flow. As a natural consequence the intensive studies in this direction have yielded a vast accumulation of data of ultimate potential value. Unfortunately, however, as is commonly the case in entering a virgin field of experimentation, many of the data cannot be molded into complete and coherent form because of the many unrelated conditions of the experimental projects. Again, the results of the study of single crystals have been rather naturally but at times indiscriminately applied to polycrystalline metals. Furthermore, sweeping statements have been made regarding the behavior during working and annealing of metals and alloys, entirely on the basis of similarity in lattice arrangement. There is abundant reason for believing that relatively small concentration variables, differences, in magnitude and distribution of applied stresses, and the character of associated annealing treatments may in some cases greatly influence the mechanics of flow and consequently largely determine the final structural characteristics of the metal.

Jan 1, 1932

By J. P. Neumann, Y. A. Chang

Lattice parameter measurements of the hcp phase in the system Ag-A1 near the stoichiometric composition Ag2Al were carried out for specimens quenched from 825°K, annealed for 10 days at 453°K, and annealed for 100 days at 413°K. The three heat treatments resulted in the same lattice parameters at room temperature. None of the specimens showed any superlattice lines. The lattice parameters of this alloy were also measured at temperature from 77° to 750°K. An anomaly in the temperature variation of the lattice paramete.rs occurs in the region near 400°k, which may be associated with local ordering. FROM measurements of the diffuse scattering of X-rays, it is known that the [ phase in the system Ag-A1 near the stoichiometric composition Ag2A1 ex- hibits a considerable degree of short-range order at room temperature.' Moreover, based on the position of the short-range order peaks a superlattice model had been proposed in the same study and it was suggested that lowering the annealing temperature to 420°K might result in long-range order. In the present study, the diffraction patterns and the lattice parameters of three differently heat-treated specimens, i.e., quenched from 825°K, annealed for 10 days at 453°K, and annealed for 100 days at 413°K, were determined from 77" to 750°K. The purpose of these measurements was to investigate 1) whether long-range order could be established by prolonged annealing and 2) whether the lattice parameters at room temperature depended on the heat treatment, since it had been proposed earlier2 that the lattice parameters in this phase are related to the atomic arrangement. 1) EXPERIMENTAL TECHNIQUES Silver and aluminum, both 99.99 pct purity, were melted in a zirconium oxide crucible under helium in

Jan 1, 1969

By R. J. Woody

Design of the most economic continuous counter-current decantation (CCD) circuit is based on selection of the number of stages and the wash volume that will give the minimum summation of the following items: 1) Capital and operating costs of the CCD circuit. 2) Capital and operating costs of the precipitation circuit. 3) Value of the dissolved product lost.

Jan 1, 1959

By Charles E. Carlsen

Underground construction involves all the legal problems common to the construction industry and adds a nice little group of its own. Elements which will ultimately affect contractor-owner relationship commence to form almost as soon as the owner conceives of the project. A few of these with emphasis on their application to underground construction will be mentioned. (1) During the design stage, determination must be made as to whether the specifications will be general or restrictive. To what extent will the operations of the contractor be controlled? Can he proceed to use any method of tunnel excavation that he desires and only be responsible for the end result or will specific excavation procedures be required? Can explosives be used? Under what restrictions? Are tunnel supports required? How long can the crown behind the heading remain unsupported? What kind of supports are required? What restrictions on the placement of tunnel-lining concrete will be required? Each of you could extend this list for many pages but these illustrations are indicative of decisions that must be made in advance of bidding, and the ultimate decision on each question can have a significant effect on the legal relationships that exist between the contractor and the owner. The owner wants a good job at a fair price. On the other hand, nothing is worse than having a tunnel collapse during the construction period, with its extra costs, loss of life, and delay to the entire project. If the specifications are too restrictive, increased costs of performance are bound to occur. Owners save tremendous amounts of money by obtaining a contractor who has been ingenious in devising the most economical construction procedure. Care must be taken in drafting the specifications so that the benefits of such ingenuity will not be lost. (2) HOW is the contract to be awarded? Will there be open bidding, a restricted list of bidders, or will there be negotiations with a comparatively few contractors? If it is a government project, whether Federal, state, or

Jan 1, 1970

By P. Pollard

A method has been developed for evaluating acid treatments in fractured limestone fields by breaking down pressure drawdown into three component parts: (I) pressure differcntial across "skin" near the borehole face, (2) pressure differential due to flow resistance in the coarse communicating fissures and (3) pressure differential between the fine voids and the coarse fissures. It is apparent that in most successful acid treatments the first term, skin resistance, has been reduced or eliminated. Further, it is often possible to estimate the volume of coarse fissures associated with the second term, coarse fissure flow resistance. In cases where this volume is comparable with practical acid volumes it seems likely that this resistance also may be attacked with a suitably retarded acid. INTROD UCTION Acid treatment has been successfully applied as a general practice in the limestone wells in the Mara/ Maracaibo districts of Venezuela for some 10 years. At the same time the need has been felt for a more precise method of: (1) evaluating the effect of an acid job and (2) selecting wells which should benefit from an acid treatment. The following method, based on an analysis of build-up curves for wells producing from fractured limestone, provides a means of forecasting the effect acid will have on a well and in many cases the probable order of production rate increase which may be expected. In certain cases it is also possible to calculate the fissure volume through which the acid has to be displaced for best results. Various approximations are introduced in the method, but within the limitations of these the analysis gives an indication of how a well, whether previously acidized or not, may be expected to respond to acid treatment. Suitable build-up curves cannot be obtained on "tight" wells which do not give sustained production and the method is not applicable to such wells. Figs. 1 through 7 illustrate various types of build-up curves obtained from limestone wells in Western Venezuela. Curves are included showing (1) both skin and coarse fissure resistance, (2) skin resistance only, (3 and 4) reduction of skin resistance by acidization, (5) fissure resistance only, (6) reduction of coarse fissure resistance by acidization, and (7) acidization failure. This theory has been successfully applied for over three years during which 22 acid treatments have been carried out specifically to reduce skin resistance and three treatments to reduce coarse fissure resistance. The method has been found to be a useful aid in the selection of wells for acidization.

By C. M. Wayman, R. Bullough

The rediffraction of Bragg diffracted beams by differently oriented regions (such as twins) of a crystal may give rise to "extra" reflections or reciprocal lattice points. These two papers are concerned with predicting these additional reflections which result from twin related regions of a lattice. Analysis is made for {111}fcc twins, (112)bcc twins, and {hkil}hcp twins. It is first required, knowing the specific variant of the twinning plane in each case, to predict the positions of the twin reflections relative to the matrix reciprocal lattice. Once this is done, the positions of the "extra" multiply diffracted reflections may be deduced. Part I is devoted to establishing "selection ru1es" for twinning, i.e., the necessary and sufficient conditions for the existence of twinned reciprocal lattice points. 1. INTRODUCTION. Transmission electron diffraction patterns are frequently complicated by multiply diffracted beams. Pashley and stowell1 have recently demonstrated that certain extra reflections in evapo- rated films of gold result from the rediffraction of matrix Bragg diffracted beams by (111) microtwins in the gold. It was previously (and erroneously) suggested 2,3 that observed "irrational" reflections in fine-grained gold were due to the presence of some hcp gold. A similar situation exists, apparently, for some bcc materials; fine (112) twins in bcc martensite in Fe-Ni alloys4 give rise to extra reflections. There are many other examples. The number of transmission electron microscopic investigations is continually increasing, and because of the importance of double (and multiple) diffraction in the interpretation of diffraction patterns, it was judged that a detailed elaboration of the principles involved is desirable, as well as the extension of these principles in reasonably closed form to other crystal structures, particularly bcc and hcp. The present analysis considers double diffraction caused by (111) twins in fcc metals, (112) twins in bcc metals, and {hkil} = {hkl) twins in hcp metals. For each case of twinning, the various possible (variants of) twins give rise to a set of interpenetrating reciprocal lattices. The relative spatial arrangements of these reciprocal lattices can be deduced (Part I) and are expressed in terms of simple "selection rules". The resulting sets of interpenetrating reciprocal lattices are then analyzed for possible doubly diffracted reflections (Part II). The notation used, and some important formulas are given in Appendices I and 11.

Jan 1, 1967

By E. R. Phelps

A determination of feasibility of a new surface mining project requires a study in orderly fashion through the procedures outlined in Section 2 and the previous two chapters of this section. The information and data collected as described in Chapters 3.1 and 3.2 must be correlated, and the many variables that affect the venture must be reviewed. This review will furnish the mining engineer with the information required to make a preliminary evaluation of estimated profit in the venture. It is at this time that management must make yet another decision whether to drop or continue the project. 3.3-1. Maps. For the purpose of collecting, outlining, and correlating a large portion of the data required for a surface mining feasibility study, maps are essential. A map to a mining engineer is like a sheet of music to a musician, or a blueprint to a designer. It provides a pictorial method of presenting mining information not only for practical application in estimating and planning, but also for demonstration of physical relationships to those charged with decision-making responsibilities. GENERAL AREA MAP. The first step in the process of graphic information assembly is the preparation of a "small scale" general area map. Such a map may cover a mining district, a market area, a watershed area or district, or the whole or a section of a geologic feature such as an iron formation or coal seam. An example of such a general area map is shown in Fig. 3.3-la which outlines the various coal mining areas in the vicinity of a proposed "mine-mouth" power station, the Liddell Power Station Project. If Quadrangle Maps of the United States Geological Survey, or their equivalent, are available for an area, a common and very effective technique is to superimpose mining data on these maps, either directly or by means of transparent overlays. Valuable topographic information

Jan 1, 1968