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By William Schriever

The flow of a gas-free liquid through a spherical-grain sand has been investigated by S1ichter.l By theoretical considerations involving a rather large number of approximations he arrives at the following flow-formula: V = CPd2At NLB{1 - m) where V is the volume of liquid delivered in time t through a cylindrical column of sand of length L and cross-sectional area A by a pressure-drop P when the sand grains of diameter d are packed to a porosity m and the coefficient of viscosity of the liquid is n. C and B are constants which were determined from geometrical relations; B was in reality a function of . Values of B(l — m) for various values of m were given in a table. In the same Annual Report of the U. S. Geological Survey, King reported the results of his experiments on the flow of water through porous media. He found that there was a departure of about 86 per cent. from a linear relationship between rate of flow and pressure, for a specimen of Dunnville sandstone for pressure drops not exceeding 60 cm. of mercury. The specimen was approximately 4 cm. in diameter and 5.1 cm. in length. Over the same range of pressure he found a departure of 45 per cent. for a specimen of Madison sandstone. For unconsolidated sands he found departures as great as 49 per cent. for pressure drops of 70 cm. of mercury; for pressure drops not exceeding a few inches of water he obtained a close approximation to a linear relation. He also investi-

Jan 1, 1930

By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.' and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By R. W. Powers, M. V. Doyle

ThE solution of a diatomic gas such as 0, or N2 in a metal usually follows Sieverts' law; i. e., Here C is the solute concentration at equilibrium and P, the gas pressure. The proportionality constant Ks is also the equilibrium constant for the reaction 1/2 02 (at pressure, P) - 0 (in solution at [21 concentration., C). to use oxygen as an illustrative gas. Sieverts' law is therefore interpreted to indicate that diatomic gases go into metallic solution atomically and that the solute "gas" atoms interact negligibly with each other. Of course, this interpretation is strictly valid only over the temperature interval in which the reaction indicated in [Z] can be investigated. At temperatures several hundreds of degrees below this interval, the possibility of interactions between solute atoms is conceivable. Indeed, from internal-friction measurements some evidence for the existence of groupings of oxygen atoms in tantalum solid solutions was presented a few years ago.1,2 Over a range of solute concentration, the experimental oxygen internal-friction peak in tantalum, measured as a function of temperature at constant frequency of vibration, can be described as the sum of two elemental peaks, each corresponding to a separate relaxation process. At 0.7 cps, the height of the elemental peak found at 137°C is proportional to the oxygen content, whereas the height of the one at 162°C varies as the square of the oxygen concentration. The 137°C peak was presumed to arise from the stress-induced ordering of oxygen atoms among various classes of octahedral sites in the manner proposed by Snoek.3 The 162°C peak was attributed to a somewhat similar stress-induced ordering process, in which each oxygen atom was interacting with a neighboring oxygen atom. Similarly, the experimental peak due to nitrogen in tantalum can also be described as the sum of two peaks. The height of one varies as the nitrogen concentration and the other as the square of this quantity. In fact, some evidence of solute interactions exist for all oxygen and nitrogen solid solutions of Group V transition metals. However, the interaction energy was not obtained previously for any alloy. The determination of this quantity, as a part of a more intensive study of the interaction between oxygen atoms in solid solution in tantalum, is reported in this paper. PRINCIPLE OF THE EXPERIMENT Consider an equilibrium in a solid solution of tantalum between oxygen atoms which are bound together pairwise and those solute oxygen atoms which are not so associated. 20 (Ta) - O2 (Ta) [3]

Jan 1, 1960

By AIME AIME

FOR the use of workmen and employees, the company should establish a dispensary and a -hospital where workmen who suffer accidents or professional diseases may be taken care of; and at suitable places in the mine or metallurgical plant it should install first-aid stations. Workmen have a right to receive 75 per cent of their wages while they are unable to perform their work as result of a professional disease; but some companies pay full wages and in the case of natural disease, with the exception of venereal, alcoholism, injuries from fights, and chronic illnesses, 50 per cent of their wages up to a period of two months. The number of diseases the Law considers as professional is large and increases almost daily. Among the professional diseases, the one which has caused greatest harm to the miners and expense to the companies is silicosis. To avoid its propagation, companies should take every possible precaution that the working atmosphere is free from dust, abating this by frequent sprinkling of the workings using, wet drills and furnishing the workmen adequate protective apparatus such as respirators.

Jan 1, 1937

By O. N. Wampler

UNDERGROUND lighting in the zinc mines of the Tri-State district can be separated into four di-visions. 1. Foot of shaft. 2. Pumps, fans. incline hoists and other stationary machinery. 3. Haulage ways. 4. Headings and stopes. One of the main improvements in lighting around the bottom of the shaft is in the use of skidoo flash lights, which have replaced the old electric skidoo bells. These bells were used as signals from the hoisterman to the tub hooker. In the event that a can bumped the side of shaft or a rock spilled from the can when dumping; the hoisterman rang the skidoo bells as a signal for all to leave the vicinity of the shaft bottom on a dead run. These bells were much better than no signal at all, but many of them were often out of order; the worst feature being that when out of order this fact was not immediately indicated. The electric flash-light signals work on the opposite principle and are burning at all times except when the hoisterman breaks the circuit when signaling danger. Therefore should a break or short occur in this arrangement, the shaft bottom is immediately thrown in darkness. Since the reaction from the eye is quicker than from ear, there is a slight saving of time- to the men escaping from the point of danger. Even this brief period of time may save a life. One other, point, to be emphasized, is that all lights near the shaft bottom should be on the signal circuit so that the entire area is momentarily darkened. I. have inspected mines where only one or two lights are used as signals, with the remaining lights around the shaft on another fixed circuit. In this case the flashing of the signal lights is almost drowned out by the stationary lights. These flash signals must be as startling as possible, which can only be done by flash-ing all the lights.

Jan 6, 1928

By W. M. Peirce

Commencing in 1922, each year a lecture has been presented to the Institute of Metals Division at this February meeting. The range of subjects has been very- broad. Some speakers have dealt with the most advanced work in the very heart of the science of physical metallurgy. Others have stimulated our imaginations by discussing the most recent progress in related fields of science. Others have told us of the latest art, which is at any moment of greater practical importance than the latest science, of metals. I feel that this broad precedent in the choice of subjects will justify my choosing to talk about some of the prosaic details of how, during the last generation, industry has effectively organized research to accelerate progress in our own and all other fields of science and related art. A number of years ago I visited one of this country's well-known research laboratories and had the pleasure of chatting for a few minutes with its equally well-known director. Being particularly interested at the time in the organization problems connected with industrial research, I broached that subject. My host stated in effect that he didn't believe in organized research. He was, of course, resorting to a rhetorical hyperbole. to pain: out the danger of overorganization which can so easily drift into regimentation and destroy individual initiative. Actually nearly all of us, much as we cherish our personal freedom of action, believe in organization because the history of progress in every field of human activity has been a history of men learning to work together, to cooperate, to create an efficient division of labor. We use organization to achieve this coordination. At the same time our form of organization must not stifle individual initiative or it will prove a deterrent rather than an aid to accomplishment. Research, too, must be organized for greatest achievement but especial skill and care are perhaps needed to avoid stifling the initiative of the individual workers. I have, of course, followed with keen interest and much benefit the vast amount . that has been said and written on this subject in the past twenty years but I still find new stimulation in discussions with my good friends working in this field. It is my hope that this discussion may serve a like purpose. It would be ungracious not to make due acknowledgment to the many able contributors to this particular phase of human progress, but their very number and the great volume of their writing makes it impossible to trace to any one individual a particular significant and valuable idea. I shall content myself therefore with this general acknowledgment and with acknowledgment of the specific debt that every research man owes to those who have so ably kept before the public, and in particular before industrial executives, the place of research in the modern scheme of things' Because of the legitimate publicity thus given to research, the day is past when any

Jan 1, 1944

By W. M. Peirce

Commencing in 1922, each year a lecture has been presented to the Institute of Metals Division at this February meeting. The range of subjects has been very- broad. Some speakers have dealt with the most advanced work in the very heart of the science of physical metallurgy. Others have stimulated our imaginations by discussing the most recent progress in related fields of science. Others have told us of the latest art, which is at any moment of greater practical importance than the latest science, of metals. I feel that this broad precedent in the choice of subjects will justify my choosing to talk about some of the prosaic details of how, during the last generation, industry has effectively organized research to accelerate progress in our own and all other fields of science and related art. A number of years ago I visited one of this country's well-known research laboratories and had the pleasure of chatting for a few minutes with its equally well-known director. Being particularly interested at the time in the organization problems connected with industrial research, I broached that subject. My host stated in effect that he didn't believe in organized research. He was, of course, resorting to a rhetorical hyperbole. to pain: out the danger of overorganization which can so easily drift into regimentation and destroy individual initiative. Actually nearly all of us, much as we cherish our personal freedom of action, believe in organization because the history of progress in every field of human activity has been a history of men learning to work together, to cooperate, to create an efficient division of labor. We use organization to achieve this coordination. At the same time our form of organization must not stifle individual initiative or it will prove a deterrent rather than an aid to accomplishment. Research, too, must be organized for greatest achievement but especial skill and care are perhaps needed to avoid stifling the initiative of the individual workers. I have, of course, followed with keen interest and much benefit the vast amount . that has been said and written on this subject in the past twenty years but I still find new stimulation in discussions with my good friends working in this field. It is my hope that this discussion may serve a like purpose. It would be ungracious not to make due acknowledgment to the many able contributors to this particular phase of human progress, but their very number and the great volume of their writing makes it impossible to trace to any one individual a particular significant and valuable idea. I shall content myself therefore with this general acknowledgment and with acknowledgment of the specific debt that every research man owes to those who have so ably kept before the public, and in particular before industrial executives, the place of research in the modern scheme of things' Because of the legitimate publicity thus given to research, the day is past when any

Jan 1, 1944

By A. W. Ambrose

The underground losses of oil exceed by hundreds of thousands of barrels all the oil that has been lost in storage, transportation, or refining. The quantity lost is, of course, indeterminate; but when it is considered that the contents of an entire oil field have been excluded from recovery by invading waters, some idea of the amount wasted may be gained. Similarly, enormous quantities of gas have been lost underground. Conservation of the oil, therefore, should start before it is brought to the surface rather than after it is placed in storage tanks. Water is one of the most important causes for underground losses and the operator should give as serious consideration to an underground flood of water as he would to a destructive surface flood. The best insurance, of course, is to have the wells drilled in such a manner that water has no access to the productive oil and gas horizons, and on abandonment the wells should be properly plugged. The encroachment of edge water and the occurrence of waterin;the base of an oil sand present a very serious problem to an oil company sooner or later these waters are bound to cause considerable damage, if they do not entirely destroy the possibilities of further production. Too often, however, a field has been considered to be in a hopeless condition, whereas wells in as bad a condition in other areas have been repaired and the life of the field appreciably lengthened. The corrections are very often suggested by technical study. Very successful results have been accomplished by detailed underground work in the California oil fields, in Cushing, Oklahoma, and in other areas. The purpose of this paper is to outline briefly1 general methods of analyzing oil-field water problems in a producing or in a producing and developing oil field, with a view to suggesting repair work on offending wells. Reference is continually made to producing oil wells; the same general method of procedure, however, should be adopted in a gas field.

Jan 1, 1921

By Edward L. Fidler, Thomas E. Finch

Thin seam coal mining in the western US nominally equates to recovery of stray seams associated with thicker, major seams. The thin or stray seams encountered are generally recovered, but not in all cases. The alternative to extraction is, of course, spoiling. The majority of thin seams are encountered somewhere in the overburden above the major seam or in the parting between thick seams. Although some are true strays and appear anywhere in the geologic sequence, others might be classified as thin "rider" seams immediately above or below a thick seam and separated by some equally thin parting. For the purpose of this discussion, stray or thin seams are defined as those which are less than 1.2 m thick or represent less than 10% of the expected extractable coal. [Figure 1] is a graphic representation of typical thin, stray, or rider seams which actually appear in a western operation. Operationally, stray seams create irritating scheduling problems and require special handling techniques which do not always lead to efficient equipment utilization. Additionally, coal recovery from a thin seam is considerably less than the 95% usually recovered from thick seams. Higher recovery in thin seams leads to dilution problems, which depreciates Btu quality, and most western coals are not in a position to lose heating value. Thin western seams also undulate and pinch or swell more than thick seams, and this leads to more difficult recovery. Often they are associated with equally dark carbonaceous shales and visual selectivity is difficult at best during daylight hours. Resource Recovery Regulations Thin seam recovery in western mines is encouraged by both federal and state regulations and by the mining industry's concern for total resource recovery. [Table 1] lists the western coal states and their recovery regulations. The federal regulations are found in the Surface Mining Control and Reclamation Act of 1977. They state, "General performance standards shall . . . require the operation as a minimum to … conduct the surface coal mining operations so as to maximize the utilization and conservation of the solid fuel resource being recovered." Economic stimulation for thin seam recovery appears to be marginal or at the least controversial. Scheduling and operational problems often outweigh the nebulous profits created by engineering analysis. The only alternative to extracting thin seams occurring above major production seams is to strip directly through them and lose the resource to the spoil pile. Although this is not palatable to environmental emotions or resource promoters, it is the most simple expedient to operations people.

Jan 1, 1981

By C. W. Binckley, F. R. Burgess, E. R. Haymaker

A method of establishing stabilized back-pressure curves for gas wells producing from formations of extremely low permeability is presented. Actual well performance under many different operating conditions is shown by the stabilized back-pressure curve. By use of the method. it is possible to conduct back-pressure tests with a critical-flow prover on wells that stabilize slowly, and save approximately 88% of the gas ordinarily vented to obtain satisfactory test data, with a great reduction in time required for testing. INTRODUCTION The reasons for establishing dependable back-pressure curves on gas wells have been pointed out by previous publications. The publication most referred to. of course, is the United States Bureau of Mines Monograph 7, titled "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices". The technique generally established therein has been accepted and used by many engineers; and, when proper tests are conducted, the results can be used for the analysis and solution of several practical problems concerning field operation and development. Even where formations of low specific permeability are encountered, the determination of a well's actual performance by the back-pressure test method permits the engineer to analyze many problems in individual well operation and also to predict necessary future field development. Such problems as the determination of the ability of a well to produce into a pipe line at a predetermined line pressure, the design of gas gathering systems and meter settings, and the determination of the time and the number of wells required to be drilled to meet future market obligations, can be solved, in part., by the use of a reliable back-~ressure curve. In addition, the computed well delivery rates determined by data from backpressure tests ordered by state regtilatory bodies, when compared with the true back-Pressure curve, permit the operator to ascertain whether such data represent unstable or relatively stabilized delivery rates for given pressure conditions of the well. The technique of back-pressure testing, as described in this report, was developed by Phillips Petroleum Company engineers from data obtained during a testing program that started in 1944 and has been continued to date. Three hundred and eleven back-pressure tests were conducted on 299 wells located in the southern part of the Hugoton Field. The gas-bearing zone is composed of several dolomitic formations of the Permian Age; the important ones are the Herington, Upper Krider, Lower Krider, and Winfield. The average bottom-hole temperature is approximately 91 °F.. and the initial wellhead shut-in pressures range from 400 to 440 psig. The spacing pattern is 640 acres per well with each well located near the center of the section. The range of back-pressure potentials on wells tested was from 500 to 23,000 Mcfd. All gas wells were acidized, and the quantity of acid used, expressed in 1574 hydrocloric acid, varied from 12,000 to 22,000 gallons per well. The quantity and concentration of each treatment depended on the stage, the formation being treated, and experience gained from previously completed wells. The gas in the Hugoton Feld is a "dry" gas. It has a gasoline content of approximately 0.25 gallons per thousand cubic feet, as determined by charcoal test, and its specific gravity averages about 0.71 as compared to air (air = 1.00 at 60°F.). Of the wells tested, 71 were completed with 7" casing, 3 with 9 5/8" casing, and 1 with 6%" casing set on top of the upper producing formation with the well bore through the gas bearing formations being open hole. Two hundred and twenty-four were completed with 5 1/2'' O.D. casing set through the gas bearing formations and perforated. For the purpose of establishing reliable back-pressure curves in the area, Phillips Petroleum Company personnel has computed data on the basis of 24-hour flows per point. Early in the program, many tests were actually permitted to flow 24 hours to obtain data for each plotting point, at great expense in man power and time. Presently, however, such tests have been replaced by tests of short duration flows which can be made to effect results that correspond to the tests obtained by flows of much longer duration. METHOD When a gas well producing from a reservoir of low permeability is opened for production through a constant size orifice, both the rate of flow and working pressure decline. first at a high rate and later at a lower rate until after several hours the decline becomes difficult to ascertain. In this paper the rae of flow and working pressure are considered to be stabilized when it becomes difficult to observe changes in working pressure during a period of three hours by the use of a deadweight pressure gage. Stalibization of pressure in the literal sense is never obtained in a producing gas well. In formations of low permeability. such as those in the Hugo-ton Field, most wellhead working pressures approach stabilization closely enough to be used satisfactorily in the determination of a back-Pressure potential curve after flow periods of 24 hours. We shall therefore describe the backpressure curve calculated from ohserved rates of flow and working pressure at the end of 24-hour flow periods.

Jan 1, 1949

By E. R. Haymaker, C. W. Binckley, F. R. Burgess

A method of establishing stabilized back-pressure curves for gas wells producing from formations of extremely low permeability is presented. Actual well performance under many different operating conditions is shown by the stabilized back-pressure curve. By use of the method. it is possible to conduct back-pressure tests with a critical-flow prover on wells that stabilize slowly, and save approximately 88% of the gas ordinarily vented to obtain satisfactory test data, with a great reduction in time required for testing. INTRODUCTION The reasons for establishing dependable back-pressure curves on gas wells have been pointed out by previous publications. The publication most referred to. of course, is the United States Bureau of Mines Monograph 7, titled "Back-Pressure Data on Natural Gas Wells and Their Application to Production Practices". The technique generally established therein has been accepted and used by many engineers; and, when proper tests are conducted, the results can be used for the analysis and solution of several practical problems concerning field operation and development. Even where formations of low specific permeability are encountered, the determination of a well's actual performance by the back-pressure test method permits the engineer to analyze many problems in individual well operation and also to predict necessary future field development. Such problems as the determination of the ability of a well to produce into a pipe line at a predetermined line pressure, the design of gas gathering systems and meter settings, and the determination of the time and the number of wells required to be drilled to meet future market obligations, can be solved, in part., by the use of a reliable back-~ressure curve. In addition, the computed well delivery rates determined by data from backpressure tests ordered by state regtilatory bodies, when compared with the true back-Pressure curve, permit the operator to ascertain whether such data represent unstable or relatively stabilized delivery rates for given pressure conditions of the well. The technique of back-pressure testing, as described in this report, was developed by Phillips Petroleum Company engineers from data obtained during a testing program that started in 1944 and has been continued to date. Three hundred and eleven back-pressure tests were conducted on 299 wells located in the southern part of the Hugoton Field. The gas-bearing zone is composed of several dolomitic formations of the Permian Age; the important ones are the Herington, Upper Krider, Lower Krider, and Winfield. The average bottom-hole temperature is approximately 91 °F.. and the initial wellhead shut-in pressures range from 400 to 440 psig. The spacing pattern is 640 acres per well with each well located near the center of the section. The range of back-pressure potentials on wells tested was from 500 to 23,000 Mcfd. All gas wells were acidized, and the quantity of acid used, expressed in 1574 hydrocloric acid, varied from 12,000 to 22,000 gallons per well. The quantity and concentration of each treatment depended on the stage, the formation being treated, and experience gained from previously completed wells. The gas in the Hugoton Feld is a "dry" gas. It has a gasoline content of approximately 0.25 gallons per thousand cubic feet, as determined by charcoal test, and its specific gravity averages about 0.71 as compared to air (air = 1.00 at 60°F.). Of the wells tested, 71 were completed with 7" casing, 3 with 9 5/8" casing, and 1 with 6%" casing set on top of the upper producing formation with the well bore through the gas bearing formations being open hole. Two hundred and twenty-four were completed with 5 1/2'' O.D. casing set through the gas bearing formations and perforated. For the purpose of establishing reliable back-pressure curves in the area, Phillips Petroleum Company personnel has computed data on the basis of 24-hour flows per point. Early in the program, many tests were actually permitted to flow 24 hours to obtain data for each plotting point, at great expense in man power and time. Presently, however, such tests have been replaced by tests of short duration flows which can be made to effect results that correspond to the tests obtained by flows of much longer duration. METHOD When a gas well producing from a reservoir of low permeability is opened for production through a constant size orifice, both the rate of flow and working pressure decline. first at a high rate and later at a lower rate until after several hours the decline becomes difficult to ascertain. In this paper the rae of flow and working pressure are considered to be stabilized when it becomes difficult to observe changes in working pressure during a period of three hours by the use of a deadweight pressure gage. Stalibization of pressure in the literal sense is never obtained in a producing gas well. In formations of low permeability. such as those in the Hugo-ton Field, most wellhead working pressures approach stabilization closely enough to be used satisfactorily in the determination of a back-Pressure potential curve after flow periods of 24 hours. We shall therefore describe the backpressure curve calculated from ohserved rates of flow and working pressure at the end of 24-hour flow periods.

Jan 1, 1949

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By J. E. House, J. L. Drobnick, R. R. Swanson, D. W. Agers

Since the commercial acceptance of the liquid ion exchange process in the mineral processing industry, it has been predicted that eventually the hydrometallurgist would have a wide selection of commercially available chemical reagents to make separations efficiently and economically of virtually all metals in solution under a wide range of conditions. Several years ago, General Mills began a research and development program to determine if it were possible to develop a reagent to extract a specific metallic ion from solution at a cost that would allow large scale commercial application. A giant step toward reaching this objective was announced in late 1963, when development quantities of LIX®-63 reagent, a highly selective reagent for the extraction of copper, were first offered to industry. The properties of this reagent were de- scribed in a previous paper.1

Jan 12, 1965

By J. H. Swisher

When an Fe-Mn alloy is internally oxidized, the inclusions formed are MnO which contains some dissolzled FeO. In the internal oxidation reaction, not all of the manganese is oxidized; some remains in solid solution as a result of the high Mn-0 solubility product in iron. Taking these factors into consideration, the rate of internal oxidation of an Fe-1.0 pct Mn alloy is computed as a function of temperature, using available thermodynanzic data and recently published data for the solubility and diffusivity of oxygen in iron. The predicted and experimentally determined rates for the temperature range from 950 to 1350°C are in good agreement. ThE rates of internal oxidation of austenitic Fe-A1 and Fe-Si alloys have been studied extensively.1"4 Schenck et al. report the results of a few experiments with Fe-Mn alloys at 854" and 956C, and Bradford5 has studied the rate of internal oxidation of commercial alloys containing manganese in the temperature range from 677" to 899°C. When Fe-Mn alloys are internally oxidized, the inclusions formed are solutions of FeO in MnO, the composition depending on the experimental conditions. Since the thermodynamics of the Fe-Mn and FeO-MnO systems have been investigated,6"9 and since the solubility and diffusion coefficient of oxygen in y iron have been determined recently,&apos; it is possible to predict the rate of internal oxidation from known data. The calculations used in predicting the rate of internal oxidation will first be outlined, then the results of the prediction will be compared with the experimental results of this investigation. PREDICTION OF PERMEABILITY FROM THERMODYNAMIC AND DIFFUSIVITY DATA Oxygen is provided for internal oxidation in these experiments by the dissociation of water vapor on the surface of the alloy. The dissociation reaction is: + H2(g) + [O] [1] where [0] denotes oxygen in solution. The equilibrium constant for this reaction is known as a function of temperature:&apos; log As oxygen diffuses into the alloy, oxide inclusions are formed which are MnO with some FeO in solid solution. The reactions occurring are: [Mn] + [0] = (MnO) [31 and [Fe] + [0] = (FeO) [41 where [ Mn] is manganese dissolved in iron and (FeO) is iron oxide dissolved in MnO. The overall reactions may be written as follows: [Mn] + HOte) = (MnO) + H2(£) [5] and [Fe] + H20(g) = (FeO) + Hz(R) [61 The standard free-energy changes and equilibrium constants for Reactions [5] and [6] are known.6 Therefore the equilibrium constants for Reactions [3] and [4] may be obtained by combining known thermodynamic data for Reactions [I], [5], and [6]. For Reactions [3] and [4]: K = and For the present purpose, both the Fe-Mn7,8 and FeO-~n0&apos; systems can be considered to be ideal, i.e., [amn] = [NM~] and (aFeO) = (NM~~) = 1 - (NFeO) where the Ns are mole fractions. These relations, together with Eqs. [I] and [8], permit us to compute both the oxide and metal compositions as a function of temperature and oxygen potential at any point in the specimen. For cases where the oxygen concentration gradient between the surface and the subscale-base metal interface is linear, the kinetics of internal oxidation is an application of Fick&apos;s first law: where dn/dt is the instantaneous flux of oxygen into the specimen, g-atom per sq cm sec; 6 is the instantaneous thickness of the subscale, cm; Do is the diffusion coefficient of oxygen in iron, sq cm per sec; p is density of iron, g per cu cm; h[%O] is the oxygen concentration difference between the surface and sub-scale-base metal interface, wt pct. B6hm and ~ahlweit" derived an exact solution to the diffusion equation for systems in which there is a stoichiometric oxide formed. They showed that the oxygen concentration gradient is given by a rather complex error function relation. For the Fe-Mn-0 system and for most other systems that have been studied, however, variations in oxide compositions are small and rates of internal oxidation are sufficiently slow that the deviation from linearity in the concentration gradient of oxygen is negligible. The mass of oxygen transported across a unit area of the specimen for the total time of the experiment is given by the mass balance equation:

Jan 1, 1969

By C. Gatlin, N. E. Garner, A. Podio

Experimental data from single chisel blows on Leuders limestone are presented. A pressure chamber, similar in design to well known microbit drilling chambers, was utilized to impose variorcs stress states on the sample. Confining pressure of zero to 10,000 psi and borehole pressures from zero to 5,000 psi have been used in the studies. Pore pressure was zero and the rock samples dry in all instances. Force-displacement records and visual examination of the craters indicate that the mode of failure depends on both confining and borehole pressure in certain ranges, ranging from brittle, through a transition, to near plastic. The mode of failure is reflected in the observed blow force and energy data, as well as the shape of force-penetration curves. INTRODUCTION A previous paper&apos; presented initial data from the project on which this paper is the second report. While the first paper dealt with impact studies on synthetic rocks, the literature cited there is also pertinent to this paper, but will not be listed again in order to avoid needless repetition. This paper presents experimental data from single chisel impacts on limestone at certain simulated wellbore stress states. Specific variables investigated were combinations of borehole and confining pressure, crater geometry, a narrow range of impact velocity and the forces required to drive the chisel into the specimens under the varying conditions. EXPERIMENTAL PROCEDURE The same basic apparatus described in our earlier paper, except for the pressure vessel, was used in this study. Fig. 1 shows the complete experimental system. Fig. 2 shows details of the pressure cell, which is quite similar to the well known microbit drilling chamber. The confining (overburden) pressure system provides independent pressure control over the sample except for two, 21/4 in. diameter areas located on the sample ends. These two areas provide a pore pressure entrance on the bottom and a striking surface on the top where borehole pressure can be controlled. The ends are isolated from the confining pressure by O-ring seals. The borehole and pore pressures are related through the striking surface; they will be the same unless a seal is deposited on the borehole surface, either a mud cake or some other impermeable membrane. In these studies pore pressure control was not used, as the rocks were dry and unsaturated in all cases. Rock samples were prepared from 4-in. cubes as illustrated by Fig. 3. The circular disks of adhesive vinyl plastic protected the impact surface from the resin coating (Scotchcast No. 2) and were removed just prior to each test. This procedure insured a fresh uncontaminated surface for the impact. Fig. 4 shows the dimensions and loading of the sample, including the concentrations around the "borehole" periphery (O-ring seal). The rock used in this study was Leuders limestone, of Permian age (Leonard), quarried near Leuders, Tex. Geologically, Leuders limestone is a light gray, fossili-ferous limestone (oolitic foraminifera1 biosporite). Its fossil content is 80 to 90 per cent and consists primarily of calcitornellid, ostracods, pelecypods and oolites with the remaining part intraclasts. There are hematite or limo-nite rims on some of the intraclasts. The porosity is approximately 20 per cent, but the permeability is less than 1 md. There is no apparent orientation in the structure. Triaxial tests have been conducted to determine the variation of the physical properties of Leuders limestone in three orthogonal directions&apos;, and it is known to be unusually isotropic and uniform. Physical parameters for this rock are: uniaxial compressive strength = 9,700 psi; F = 32 and C = 2,700 psi; where + and C are Coulomb equation values (t = C+u tan +). Impact tests were run under the combinations of confining and borehole pressures shown in Table 1. Samples were dry with atmospheric pore pressure in all cases. Tests, in which elevated borehole pressures were applied, used a single layer of household Saran-Wrap to prevent horehole fluid invasion into the sample. This proved to be simple and reliable. The blunt wedge used in all the tests was 0.75 in. long and had an included angle of 60" with a 0.05-in. flat. In addition, a sharp 60" wedge was used for all confining pressures at zero borehole pressure. The chipper speed

By J. R. Thoenen

IF ASKED whether limestone production was a mining problem I would; not hesitate to answer emphatically in the affirmative. The question, "When is a quarry a mine?" is familiar. The immediate mental picture induced by the thought of limestone production is that of an open quarry. All are familiar with the open pit in the iron-producing districts of Minnesota and Michigan and the open cuts of the so-called "porphyry" coppers of the West. If these are mines, they differ little from limestone quarries in general mode of operation; if quarries, why do they need the attention of mining engineers? During 1923, the United States produced in round numbers 70,000,000, tons of ore. The limestone production of the United States for the same period was something over 100,000,000 tons. In tons, it about equals the oil production of the United States. The uses of limestone are legion. A paper read by a prominent engineer of Chicago, at the meeting of the National. Crushed Stone Association held last February in St. Louis says: "There is no industry in the United States today that is more basic in its operation or by itself controls. more industries. There is hardly a chemical operation, hardly a metallurgical operation or building operation that a crushed-stone man does not control if he will jump in and make the full utilization of it." Some of the many uses are for road metal, concrete, railway ballast, building stone, riprap, and rubble, the manufacture of iron and steel, alkalies, calcium carbide, magnesia, carbolic and carbonic acids, asphalt filler, mineral wool, poultry grit, sulfuric acid, phosphates, nitrates, soap, baking powder, the purification of copper and prevention of coal-mine explosions, to say nothing of the quantities used in the making of lime and cement. It has been said that without iron we would revert to the Stone Age; how much iron would we have without limestone? From the point. of view of the mining engineer, using the term in its broad sense to include geologists and metallurgists, the production of limestone is important because of its occurrence, volume, commercial importance, and the problems presented by its recovery and treatment.

Jan 2, 1925

By Walter R. Hibbard, George H. Eichelman, William P. Saunders

INTEREST in the various products of the austenite eutectoid transformation in iron-carbon alloys, particularly as produced by the isothermal sub-critical techniques introduced by Davenport and Bain,1 has resulted in the application of similar heat treatments to other eutectoid transformations. Studies2.3.4 of the beta copper-aluminum alloy eutectoid transformation revealed microstructures very similar to those found in iron-carbon alloys. Investigations5,6 of the kappa phase in the copper-silicon alloy system have established the eutectoid type transformation of this phase into terminal alpha and intermediate gamma phases. This transformation has been reported&apos; as forming a eutectoid type structure in a very sluggish manner by a long time isothermal treatment. The purpose of the present investigation is to study the products of the kappa eutectoid transformation as affected by transformation temperatures by means of microscopic and hardness methods. PREPARATION OF ALLOYS The copper-silicon alloy equilibrium diagram is shown in Fig I. The kappa field converges to a minimum silicon solubility at the eutectoid composition and all other completely kappa alloys are hypereutectoid. Thus, kappa decomposition involves first the proeutectoid precipitation of gamma, followed by the eutectoid transformation of a lower silicon content kappa (5.2 pct). Smith5 has indicated that alloys containing between 5.4 and 5.7 pct silicon could be hot rolled, but that the latter composition was desirable in order to permit a wider kappa temperature range. The alloy was prepared by adding Baker&apos;s commercially pure silicon to an ingot of copper-silicon alloy containing 2.34 pct silicon remaining from the investigation of Brick, Martin and Angier.7 Following the casting techniques of Krynitsky, Saunders and Stern,8 the ingot was melted under a heavy layer of dried charcoal in a clay-graphite crucible in a gas-fired pot furnace. Small lumps of silicon were held under the melt surface with a graphite rod. After the silicon had dissolved, the alloy was chill-cast and then remelted without a cover, stirred thoroughly, skimmed and poured into a preheated cast iron mold. The cast microstructure is shown in Fig 2. The casting, 10 X 4 X ¾ in., was annealed at 750°C for 21 brand furnace cooled. About 1/16 in. was milled from all surfaces. The plate was cut in half longitudinally and the bottom half analyzed by A.S.T.M. methods.9 The composition by weight was as follows: copper 94.24 pct, silicon 5.56 pct, iron 0.11 pct.

Jan 1, 1948

By Fred H. Lippold, Wm. H. Wolf

Methods of fair payment for excavating, supporting, and concrete lining tunnels have been sought by various owners for years. Tunneling techniques have changed with the development of equipment-from the hand-mucking operation to the machine mucker and, most recently, to machine-boring; from tunnel supports using timber sets to steel sets to rock bolts and, most recently, to shotcrete support; and from hand-placing the concrete lining using wooden forms to pumping or pneumatic placing using steel forms. As tunnel construction techniques advanced, so did methods for payment for the work performed. The recent development of tunnel-boring machines, or "moles," is precipitating another change. These changes have led to some difficulty in providing proper payment for the various items of work for different types of tunnels. As a major construction agency engaged in water-resources development in the western states, the U.S. Bureau of Reclamation has long been aware of the need for clarification of payment provisions in tunnel construction. The Bureau has some 150 miles of tunnels completed on its projects and about 50 miles of tunnels under construction. In this construction, the Bureau has benefited by the advance made by contractors in improving the techniques of tunnel excavation. To assure that the Bureau has an up-to-date approach to payment provisions, the Chief Engineer recently established a "standard" method of payment for all types of tunnels. It is believed that this new method of payment will be equitable for all contractors bidding on various types of tunnels using the diversity of methods of excavation now available to them. These payment provisions provide for different quantities for excavated tunnels using the blasting technique or using machine-boring techniques. In this way, the contractors have a choice in excavation methods and an equal opportunity to be low in their bids. We believe this will be an incentive to all contractors to be as progressive as the development of new equipment economically allows.

Jan 1, 1970

By B., Hoyaux

A first requirement for assessing the safety of a rock slope, either artificial or natural, particularly if the rock behaves in an elastic-brittle manner, is a proper knowledge of the distribution of stresses within the slope and their development with time and advancement of workings.

Jan 1, 1972

By Carl F. Cline, Richard R. Vandervoort, Willis L. Barmore

THE objective of this investigation was to determine the high-temperature plastic deformation behavior of stoichiometric uranium mononitride as a function of stress and temperature. Interest in the properties of this material stems from its potential use in high-temperature nuclear reactor systems. The creep of other refractory compounds containing uranium (e.g., U02, UC) has been studied by various investigators.1"4 Fassler et al.4 have studied the creep of UN in vacuum from 1100° to 1350°C at stresses of 6000 and 8000 psi. In the present work, the creep of stoichiometric UN was investigated from 1500° to 1800°C at stresses from 2000 to 5000 psi in a partial pressure of 200 mm of nitrogen. The specimens were prepared by hot isostatic pressing of UN powder into cylinders of $ in. diam by about 1 in. high. After pressing, the specimens were heat-treated in nitrogen at 1900°C for 50 hr. The densities of individual specimens were determined by the water displacement method. All specimens were theoretically dense, based on a value of 14.32 g per cu cm.5 Principal metallic impurities in ppm by weight were: Ca, 50; Cu, 5; Fe, 30; Mg, 5; Ni, 10; and Si, 20. Oxygen content was 400 ± 50 pprn and carbon content was 100 i25 ppm. The nitrogen content was 5.56 ±0.05 wt pct. The average grain size for five specimens, as determined by the intercept method, was 0.14 i 0.01 mm. One specimen had a grain size of 2.0 mm. This large grain size is an anomaly, since all specimens had the same chemical and thermal histories. Specimens of 1/4 in. diam by 1/2 in. high were creep-tested in compression in a clam shell furnace heated by W-25 pct Re sheet elements. Temperature was measured to ilODC by an optical pyrometer which had been calibrated by a standard source. The distance between fiducial marks on the specimen was measured before placement into the furnace. The furnace chamber was evacuated to 10-5 Torr and back-filled to 200 mm N2. After heating rapidly to temperature, the load was applied and controlled to ±2 pct by an Instron testing machine. Upon initial loading, the specimen was deformed until a constant crosshead rate was obtained, then quenched to room temperature, remeasured, and replaced in the furnace. Upon subsequent reloading at temperature, the crosshead rate was constant for the selected condition indicating steady-state creep.

Jan 1, 1969