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By J. K. Kerver, J. S. Osoba, J. G. Richardson, J. A. Hafford

A detailed study of a number of methods of relative permea-abilitv measurement has been made in a search for the tech-niqrle most suited to routine analysis of cores taken from reservoir rock. It has been found from tests run on the same samples of core material by a number of techniques that the Penn State, Hassler, Hafford, and dispersed feed techniques all yield results which are felt to be reliable. Conditions under which the faster single core dynamic technique may be used are described. Further work on the calculation of relative permeabilities to oil from data obtained by the gas drive method is needed before this latter rapid method can be utilized. Correlations between theoretical studies and experimental results have been obtained in studies of the boundary effect. pressure distribution in two-phase flow, and gas expansion effects. Previous conclusions that the effects of the outflow boundary could be made negligibly small have been substantiated. Results of experimentally determined oil and gas pressure distributions along a core sample during flow are presented. Further studies of the effects of rate of flow in the measurement of relative permeability-saturation relations have shown that results are independent of the rate of flow as long as the flow rate is below the point where inertial effects commence. An analysis of the effects of a severalfold expansion of gas along the flow path indicates that while saturation gradients are induced in the test sample, the errors caused by this phenomenon in relative permeability measurements are small. INTRODUCTION Many pages of literature have been devoted to pointing out the need for relative permeability-saturation relations in reservoir engineering. One of the most attractive ways of obtaining this information is by the analysis of samples of core material taken from the formation in question, and again literature has described man); methods for obtaining these data. It is the purpose of this paper to present the work that has been done in the study of some of these published methods together with some other methods that have been recently developed in this laboratory. Also, a study of some of the factors that influence the laburatory determination of relative permeability-saturation relations is presented. FACTORS WHICH AFFECT LABORATORY STUDY OF FLUID FLOW THROUGH RESERVOIR ROCK To determine relative permeability-saturation relations of samples of reservoir rock in the laboratory, it is important to know what factors affect these measurements in order that the magnitude of these effects can be ascertained and steps then can be taken to eliminate or, in some cases, to minimize them. The factors that have been investigated are the boundary effect, the effect of gas expansion. and the rate effect. Boundary Effect In laboratory experiments in which two immiscible fluids are flowed through a porous medium, there exists a discontinuity of capillary properties at the outflow face. This discontinuity exists became the fluids pass from a region of finite capillary pressure in the sample to a region of zero capillary pressure in an open receiving vessel. The capillary forces existing in the core caupe the rock to tend to retain

Jan 1, 1952

Jan 1, 1896

By E. S. Wheeler, M. W. Murphy

A LARGE part of the molybdenum produced in Colorado is converted and consumed in the Eastern States. As the raw materials and the power needed for the conversion of the Colorado concentrate are also accessible in the Eastern States, the conversion plant has been installed some 1500 miles east of where the ore is mined and milled. When concentrate was first produced at Climax in 1918, a custom smelter converted the product into ferromolybdenum. By 1924, the Company had decided to produce calcium molybdate and rented a building and installed equipment for that purpose at Langeloth, near Burgettstown, Pa., about thirty miles west of Pittsburgh. For the first few years the plant was a simple one of small capacity. A small hand-rabbled roaster was used, the product of which was made iota calcium molybdate by a conventional method; then an eight hearth mechanically rabbled roaster was installed to increase and speed up production. The output was considerably less than a million pounds of contained molybdenum annually until 1928, when a small part of the produc-

Jan 1, 1946

F. E. Thompson, Pottstown, Pa.: If Mr. Webster's endeavor to open up the subject of cast-iron should prove as prolific of results as did the discussion on " The Physics of Steel," he must certainly feel richly repaid. His remarks concerning the secretiveness and conservatism of the average foundry-man recall to my mind an instance of a blast-furnace which, for the last year, has been producing much foundry-iron. The manager, believing that much more of his product could be used in the foundry than the foundry-men were will-

Jan 1, 1896

By Frank T. Wheby

The cost of tunneling is highly sensitive to the rock characteristics through which the tunnel is to be driven. These characteristics affect in a major way the rates at which tunnels and shafts can be driven and the degree to which the openings must be supported to maintain them in a permanent stable condition. Tunnel and shaft design and cost criteria have been computerized, permitting estimates of tunnel-shaft systems to be made directly from inputs of rock mechanics characteristics and other data. Curves of quantities of steel, rock bolts, and other rock support items as related to tunnel size and rock quality designation are presented. An illustrative example of the use of the program in calculating the cost of a hypothetical tunnel system is included.

Jan 1, 1971

"Minerals in Transition" is the timely theme of this year's SME-AIME Fall Meeting and Exhibit, to be held September 10-12 at the Salt Palace, Salt Lake City, Utah. Approximately 2000 members and guests are expected to attend the meeting, which will include 117 technical papers, presented during 27 sessions. To complement the technical program, a record number of mining manufacturers and suppliers will be on hand to exhibit the latest in equipment innovation and professional services.

Jan 8, 1975

By C. J. Rosa, W. C. Hagel

An attempt is made to determine the diffusion coefficients of oxygen ions in hypostoichiometric zirconium oxide. A phenomenological theory is developed for three-phase, unidirectional volume diffusion of a gaseous species from a planar source. Knowledge about oxygen diffusion in a and ß zirconium and experimentally measured rates of movements of interfaces permit the evaluation of oxygen ion diffusivi-ties in ZrO2-x. The results conform to the relationship: sq cm per sec, for the temperature range of 875" to 1050° C. DIFFUSION coefficients of oxygen ions in stoichio-metric oxides have been studied by many investigators. The obtained results not only supplement the knowledge about the lattice-defect structures of oxides and conduction mechanisms but also provide information of technological importance. Rate processes such as oxide sintering, high-temperature creep deformation, and oxidation of metals and their alloys are directly dependent on diffusion phenomena. Unfortunately, diffusion coefficients obtained from studies on stoichio-metric oxides cannot be treated without restraints when applied to oxidation kinetics, if precise evaluations of oxidation rates are desired. Oxides formed on metals are usually nonstoichiometric and exhibit nonuniform distribution of either cation or anion vacancies across their thicknesses. Debuigne and Lehr1 extended Danckwerts'2 mathematical analyses and furnished a semitheoretical treatment for evaluating oxygen diffusion coefficients in zirconium oxide in terms of weight gain measurements during oxidation of zirconium in the temperature range 400° to 850°C. Their calculations are based on theoretical partitioning3 of the total amount of oxygen between a zirconium and its oxide phase. An inherent discrepancy appears to continue throughout their calculations. The amount of oxygen confined to the oxide phase should be corrected by multiplying the calculated oxide thickness by the inverse of Pilling-Bedworth ratio, if expansion of zirconium dioxide is taken into account. The purpose of the present investigation is to provide a new semitheoretical treatment for evaluating diffusion coefficients of moving species in hypostoichiometric oxide. The analyses are relevant to unidirectional volume diffusion. Although the presented method is quite general, its applicability will be discussed in terms of kinetic measurements from oxidation of zirconium at temperatures above the a/ß transition, for reasons stated in the later part of this paper. EXPERIMENTAL Pure, 99.93 wt pct, zirconium samples of approximately 2 by 1 by 0.35 cm were exposed to oxygen for various times at four temperature levels: 875°, 950°, 1000°, and 1050°C. High-purity, better than 99.9 vol pct oxygen was passed through a cold trap and columns containing anhydrous CaSO4 to remove residual water vapor. Before exposing to oxygen at a pressure of 500 Torr, specimens were subjected to wet abrasion on 200- through 600-grit Sic papers and polished with 1—p diamond dust. Prior to oxidizing, all zirconium samples were vacuum-annealed at 10-6 mm Hg for about 15 min at the test temperature. The temperature variation across the uniform heat zone was ±2°C from the preset value. Final polishing, for phase thicknesses measurements, was performed by using 8- and 1-p diamond dust and followed by vibrator polishing with 0.05-µ ? Al2O3 solution. Measurements of phase thicknesses were made by projection on a metallographic viewing screen. Conventional powder X-ray analyses for the oxide were employed. RESULTS Fig. 1 is an example of the cross section of oxidized zirconium. Designations of phases given below this figure are the same as those used in the three-phase diffusion system represented by Fig. 5 in the following section. Zirconium oxidized for longer exposure times showed two types of oxides: white oxide at the surface and an underlaying layer of gray oxide. X-ray powder patterns of these oxides at room tern-

Jan 1, 1969

By J. P. Savely, D. E. Nicholas, R. D. Call

Progress in the technology of slope design over the past 15 years now permits the selection of rational slope angles if suitable data on geology, hydrology, and rock properties are available for a specified project. Although a full-scale slope design study remains the best course of action, there are situations where an extensive study is not feasible due to time or budget constraints. Two typical examples are: (a) selecting pit slope angles for a preliminary feasibility study at the exploration stage; and (b) coping with a slope failure in an operating mine. In both instances, slope angles must often be chosen on the basis of data that are currently available or can be readily obtained. All too often during exploration programs, a feasibility study is initiated shortly before the decision deadline to drop the property or proceed to purchase. If the only existing data at this point are a few cross-sections at odd angles showing ore and waste contacts or a dog-eared map of the surface geology, there may not be time to collect and organize sufficient information for the design of slope angles. On the other hand, if during the drilling program geologic cross-sections were constructed and the structural data compiled in tabular form, rational slope angles could be computed within the allotted time.

Jan 4, 1977

By Roy C. Kirkman

It is with great pleasure that I read Mr. Howard M. Wells article in the December 1978 issue of MINING ENGINEERING entitled: "Optimization of Mining Engineering Design in Mineral Valuation." Mr. Wells very adequately presents the case and point that there are a great number of variables which must be analyzed during an economic evaluation of an FUND RESOURCE, such as copper or uranium.

Jan 4, 1979

As already said Pattin's map and the later one of Evans' showed coal in several places in Ohio as early as 1750, and possibly 1748; the reference on the latter map was' to an exposure near Bolivar, in Tuscarawas County, as well as along the Hocking River. So far. as now known, it 'was not mined in either place until 1810. George Croghan, in descending the Ohio with his party in 1765, mentions an "Alum Hill" which they saw near the present site of Pomeroy, probably an exposure of saline deposits, but does not mention coal. As settlement north of the Ohio River was prohibited until 1787, no coal was mined until long after that date. In 1785 a survey of seven ranges in the Ohio country was made, the line running west from a point on the north bank of 'the Ohio River, due north of the western termination of the southern boundary of Pennsylvania. The surveyors noted, "from hence to Stoney Brook between two very steep and high Ridges; it is eight yards wide, its bottom is of Slate and Sand Stone, and in many parts of it are large pieces of excellent Coal washed by, the Rains from the Neighboring Hills."' This was the present Yellow Creek, and the coal was from some of the lower measures. The Scioto Company published a pamphlet in French in 1787, to promote the sale of their lands and emigration to them, in which was said,

Jan 1, 1942

?ADAIR, ARTHUR C., Corp 4th Co., 1st. Training Bat., 154th Depot Brigade. ADAMS, HENRY, Major: Chemical Warfare Service. ARLUCK, A. A Headquarters, 1st Corps of Artillery. ASKIN, THOMAS B. H Ensign. BANKS, H. R., 2d Lieut Canadian Engineers. BAYLESS, G. E. S Supply Dept. U. S. Submarine Base. BELL, L. R Co. C, 302d Engineers. BELLIS, ARTHUR E., Capt Ordnance Reserve Corps. I BIRRETT, HOWARD, Lieut., Aviation Section, U. S. Signal Corps, Ellington Field. BOISE, PAUL T 2d Regiment, 24th Squadron. ?BRADLEY, CLARENCE I Convois Automobile Section 585. BROWN, GEORGE M Co. G lot Engineer Replacement Regiment. BUCKINGHAM, ALBERT U. S. S. " Coronet," S. P. 194, Section Base No. 7. BURNS J. J Co. 1-B, E. R. O. T. C. BURT, Co. B, let Engineers Replacement Regiment. ||BYERS, WHEATON B., 2d Lieut Ordnance Dept. CANTON, WILLIAM R., Sgt Headquarters Co., 80th F. A. CARSON, JOSEPH A., Capt A.S. S. R. C.' CHAPMAN, LEWIS C. Corp 29th engineers. CHETNEY, P. C., 2d Lieut 15th Bat. Headquarters Co. CHEVRILLON Louis French Red Cross. CHIDESTER, W. B., 1st Lieut 24th Machine Gun Bat. CHURCH, JOHN L., Capt 308th Engineers. CLAGHORN, D. MONTGOMERY, 1st Lieut 45th Engineers. CLAQHORN, JAMES L., Lieut Aviation Section, Signal Corps. CLARKE, ALEXANDER F U. S. Naval Aviation Service. COMINS, WALDO H. Ca t 41st Co., 164th Depot Brigade. COOK, FREDERICK A., Capt., Engineer Reserve Corps, Asst. to Div. Engr. 79th Division. COOPER, CLAUDE H. Capt C. A. R. C., 50th Artillery. COPELAND, N. R., Lieut. ||CORBY H.. G., 1st Lieut Co. D, 109th Supply Train. CORSA, BEAN, Capt Co. D, 612th Engineers. CORTESE, EMILIO Italian Army. COULDREY PAUL S., Corp British Expeditionary Forces. || CRAGIN, RODNEY S Co. E, 115th Engineers. CURRIE, JOHN M., Ca t Royal Engineers. || CUTTING, G. W., 2d Lieut U. S. Reserves, Field Artillery. V DARRINGTON, PAUL N., 1st Lieut U. S. Infantry. DAVIS, ANGUS W., Lieut-Col British Expeditionary Forces. || DAVIS, THORNTON, 1st Lieut 13th Field Artillery. ELAND, FREDERICK A., Major Engineer Reserve Corps. DOUGLAS, JAMES $ American Red Cross. DOVE, D. R., Candidate 21st Training Battery, F. A. C. O. T. C. Dover JAMES J 6th Co. C. B. DOWS, DAVID,Capt Coast Artillery, Officers Reserve Corps. || DRAKE, M. 6., 2d Lieut Headquarters Co., 325th Infantry. I || EMMERSON, E. Roy British Navy. EVERIT, RICHARD STURTEVANT Heavy Artillery Officers' Training Camp.

Jan 1, 1923

By C. H. Cheng, C. E. Birchenall

The fundamental problem in the thermodynamics of solid solutions is the determinatiorl or calculation of the activities of the components as a function of temperature and composition. Since the theory of metals is not suficiently developed to allow a priori calculation of these quantities, they must be obtained from experiment. C. Wagner1 has reviewed the literature of this subject for the period before 1940. Although several important and extensive studies have been made in the meantime, the number of systems to which any sort of quantitative information can be assigned is vanish-ingly small. These data have become of great potential importance in studies of the structure of solid solutions2 and intermetallic compounds, the nature of the diffusion process,3,4 and perhaps even the mechanism of mechanical deformation.5 For these reasons, it. seems very worthwhile to extend the experimental data in this field. Although there is little use in duplicating Wagner's review, attention should be directed to the most recently reported investigations. A brief enumeration of the methods of measurement previously employed also should be valuable. The most direct method is the determination of the partial pressure of the components in the vapor phase in equilibrium with the solution. Both equilibrium and kinetic methods have been tried in metal systems, but almost exclusively on liquid phases. Only in the ease of carbon in iron alloys and in the copper-zinc system have extensive measure- ments been made which include solid phases. When one of the components is an element, such as nitrogen or carbon, which forms compounds which are very volatile and stable at normal temperatures and pressures (CH4, Co2, CO NH3), it is frequently possible to equilibrate mixtures containing these (such as CH4-H2, CO2-CO, NH3-H2) independently with the elernents (C, X) and with the metal (Fe, Ni, etc.). Such measurernents have been made for carbon in iron, iron-silicon, and iron-manganese alloys by Smith6 and in iron and iron-nickel alloys by Toensing.7 Differences between carbon activity values at the same temperature and carbon content when carboil is introduced from CH4-H2 rnixtures or CO-CO. mixtures indicate that the effects of hydrogen and oxygen in the system are not negligible, and one can only hope that the true value lies somewhere between these sets of results, probably nearer the CH4-H2 data since hydrogen is less soluble in iron than oxygen. This is essentially an equilibrium method, although flowing gas is employed. A kirletic method has been employed which consists of sweeping an inert gas (generally hydrogen) over the alloy at a series of rates, condensing the metal vapor out,, and analyzing it. The metal content can be extrapolated to zero flow rate (equilibrium). Wejnarth's8 work on Cd-Mg and Zn-Mg is a good example of this frequently used method. A variant of this consists of equilibrating a known volume of inert gas with the alloy, sweeping it out quickly, and analyzing for metal. In common with the above method, it has the disadvantage that the "inert" gas is generally somewhat soluble in the alloy. Moreover, the former continuously displaces the system from equilihrium and may give low values if solid diffusion is involved. The dew point method applied by Hargreaves9 to the alpha and beta brasses and by Schneider and Stolll0 to A1-Zn avoids the introduction of another component to the system, but is useful only in systems in which one component is much more volatile than the other. The alloy sealed in one end of an evacuated silica tube is heated to the desired temperature. The temperature of the other end is lowered until droplets of the volatile component condense. When the temperature is raised slightly, the droplets will evaporate. By careful adjustment of temperature, the range between evaporation and condensation can be narrowed appreciably. An independent determination of the vapor pressure of the . pure volatile component is necessary to give the partial pressure over the alloy. This is the method employed here to determine the vapor pressures of zinc and cadmium over their silver alloys up to 34 pct in cadmium and 76 pct in zinc. The former involves only the a solid solution, but the latter covers the a, ß, y, and e fields. In recent determinations, Herbenar, Siebert, and Duffenbarkl1 used the

Jan 1, 1950

By B. H. Bergstram, C. L. Sollenberger

When glass spheres are crushed by slow compression loading, the outer lune-shaped fragments resulting from the fracture consistently fly outward at high velocity. About 45 pct of the strain energy fed into the sphere-platen system reappears in the form of the kinetic energy possessed by these fragments. These measurements were obtained from high-speed photographs. This kinetic energy can be utilized for addtional comminution if the fragments are allowed to impact against a suitable structure. Comminution theory has advanced considerably in recent years by the study of this unit operation under laboratory conditions. Some of the parameters have been isolated, but the experimental measurements of the pertinent quantities, such as energy, particle size, etc., are still only made prior to and after the conclusion of a fracture sequence. The catastrophic fracture process itself has not been adequately studied from a comminution point of view. It has recently been suggested by Gilvarry that the fragments which result from the free crushing of a single glass sphere by slow compression contain a considerable amount of kinetic energy after fracture. This kinetic energy, if properly directed, possibly can be partially utilized to cause additional fracture. In this paper a hypothesis will be presented which suggests that this kinetic energy is necessarily present and that its dissipation is the process by which a large part of the thermal energy imparted to the crushed product is generated. Evidence supporting the existence of kinetic energy and its utilization for secondary fracture will also be presented. THEORETICAL A previous paper4 has shown that the load-deformation curve of a system composed of an elastic sphere gripped by a pair of parallel platens, can be predicted by a consideration of the theories of Hertz as summarized by Timoshenko.' The deformation A, of one half of the system is given by which states that the deformation is a function of the mutually applied load, P, the radius of the sphere, R; and the respective physical properties of Poisson's ratio, v, and Young's modulus of elasticity, Y. The shape of experimental load-deformation curves conform to this relationship. The energy input to the sphere-platen system, can be predicted from the integral of the load acting through the appropriate distance, dA. Since dA can be evaluated in terms of P from the derivative of Eq. 1, this integral can be integrated between limits of 0 and P. The test sphere, however, is loaded at not one but at two points of contact, i.e., at both ends of a diameter, and hence the total energy input, E, is twice the energy input at each end, or The energy input to the system calculated from this equation corresponds to the energy computed from the measured area under the load-deformation curve. Timoshenko, considering the impact of two perfectly elastic spheres, has shown that the inter-penetration distance A is given by - m f (D (^ * ^t w as modified for the special case where one sphere is of infinite radius, i.e., its surface is a plane; where M is the mass of the finite sphere of radius R, and V is the velocity of approach at the start of an impact and also equals the final velocity of separation for perfectly elastic bodies. Because A is also a function of the load and the elastic properties, as shown in Eq. 1, the velocity, V, can also be calculated in terms of the elastic properties and maximum load, P, or

Jan 1, 1961

By E. Miller, J. M. Eldridge, K. L. Komarek

The thermodynamic properties of- liquid Mg-Pb allojs have been determined by an isopiestic method from 18 to 42 at. pct Pb and by a thevmodynumic analysis of the phase diagram frofiz 0 to 100 at. pct Pb. In the overlapping composition range the magneszupn activity values derived by the two methods are in excellent agreement, thus mutually supporting the correctness of the Mg-Pb phase diagram previously determined by the authors and of the acticitzes deriz~ed isopiestically. SEVERAL studies have been made of the thermody-namic properties of liquid Mg-Pb alloys. Wagner and Engelhardt,1 Lantratov,2 Knappwost,3 Sryvalin et al.* and Wilson5 used the electromotive-force method, Scheil and Wolf8 and Schmahl and Sieben" applied the transpiration technique, and the present authors8 utilized the phase diagram to determine the activity of magnesium in the Mg-Pb system. The results of these studies are not in very good agreement and could not be incorporated into a general systematic analysis of the thermodynamic properties of the homologous series of the Mg-Group IV B systems Mg-Pb,8 Mg-Sn,° Mg-Ge,10and Mg-Si.11 The thermodynamic properties of the Mg-Pb system were therefore re investigated by an isopiestic technique which has been developed for similar studies in the Mg-SnB and Mg-Ge10 systems- Lead specimens, contained in iron or graphite crucibles, were heated in a temperature gradient in an evacuated and sealed titanium reaction tube and equilibrated with magnesium vapor of known vapor pressure to form alloys of compositions which depended on their temperatures, the temperature of the magnesium vapor source, and the thermodynamic properties of the system. EXPERIMENTAL PROCEDURE Magnesium (Dominion Magnesium Ltd., Toronto, Canada) of 99.99+ pct purity and lead (American Smelting and Refining Co.) of 99.999 pct purity were used. In the early experiments, Runs 2 and 3, the alloys were contained in uncovered high-purity iron crucibles. Alloys formed in the uncovered iron crucibles had to be chemically analyzed owing to the slight volatility of lead under the imposed experimental equilibration conditions. The compositions of these alloys were determined by a gravimetric analysis of lead as lead chromate. To avoid this problem, the remaining runs were made in covered graphite crucibles machined from high-density (1.92 g per cu cm) graphite rods (Basic Carbon Corp., Sanborn, N.Y.) which had a maximum ash content of less than 0.04 pct. The non- i reactivity of graphite with lead and magnesium has been previously established,' and the experimental procedure has been described in full detail.' In the runs using covered graphite crucibles it was found that the weight increases of the crucibles and their contents after equilibration equaled the magnesium contents of the alloys within the accuracy of the chemical analysis (i0.3 at. pct Pb). Clearly, the small lid openings of the graphite crucibles prevented significant lead losses during a run, and the weight increase was therefore taken as the magnesium content of the alloys. EXPERIMENTAL RESULTS At thermodynamic equilibrium the magnesium partial pressure of the specimens equaled that of the reservoir. Since the magnesium reservoir was always maintained at the temperature minimum of the system, the activity of magnesium of any specimen was given by the ratio of the magnesium reservoir pressure to the vapor pressure of pure magnesium at the specimen temperature. The standard state was chosen as liquid magnesium and the vapor pressure of liquid magnesium

Jan 1, 1968

By F. M. Lewis, J. F. Myers

W. I. Garms-—The authors state that when they added 11 tons of balls to the 45 pct volume ball load, the power needle did not budge. The question arises as to whether any increase in capacity accompanied the 11-ton addition. It is hardly conceivable that all of the balls making up the 11-ton addition were sterile. However, as the work done in the ball mill is not by kilo-watthours per se or balls per se but by kilowatthour-balls, it is possible that the kilowatthourballs in the mill before the 11-ton addition had a different amperage, voltage or robustage than those in the mill after the addition and that the overall outcome was that equal work was done before and after the addition. The authors can keep the efficiency that they got with the 45 pct volume 1-in. ball charge and get additional capacity by putting more kilowatthourballs to work in the form of the addition of 11 tons of 2-in. balls to the present ball charge, and subsequent makeup additions by weight of 20 pct 2-in. balls and 80 pct 1-in. balls. J. F. Myers (authors' reply)-—Mr. Garms points his finger at the 11 tons of "sterile" balls added to the Tri-cone mill. A fact so interesting to us that we felt it should be reported. Clearly, ball slippage at the existing mill speed prevented any further transfer of power from the shell to the ball mass. We agree that the kilowatthourballs would increase, were we charging rough 2-in. balls as suggested by Mr. Garms. The assumption is, of course, that we would get a corresponding increase in work done. Our reported data (CIME meeting, Vancouver, 1946) shows a gain of work accomplished of 7.6 pct as we decreased the ball size from 2 in. to 11/2 in. and a further gain of work accomplished of 2.1 pct when we went from 11/2 in. to 1 in. The small ball results reported by H. R. Banks at Chapman Camp are also very convincing. In the case of 2-in. balls they would take the conventional ball path and start cascading. They would thus destroy the classifying pool over the "foot" of the

Jan 1, 1951

By J. F. Myers, F. M. Lewis

W. I. Garms-—The authors state that when they added 11 tons of balls to the 45 pct volume ball load, the power needle did not budge. The question arises as to whether any increase in capacity accompanied the 11-ton addition. It is hardly conceivable that all of the balls making up the 11-ton addition were sterile. However, as the work done in the ball mill is not by kilo-watthours per se or balls per se but by kilowatthour-balls, it is possible that the kilowatthourballs in the mill before the 11-ton addition had a different amperage, voltage or robustage than those in the mill after the addition and that the overall outcome was that equal work was done before and after the addition. The authors can keep the efficiency that they got with the 45 pct volume 1-in. ball charge and get additional capacity by putting more kilowatthourballs to work in the form of the addition of 11 tons of 2-in. balls to the present ball charge, and subsequent makeup additions by weight of 20 pct 2-in. balls and 80 pct 1-in. balls. J. F. Myers (authors' reply)-—Mr. Garms points his finger at the 11 tons of "sterile" balls added to the Tri-cone mill. A fact so interesting to us that we felt it should be reported. Clearly, ball slippage at the existing mill speed prevented any further transfer of power from the shell to the ball mass. We agree that the kilowatthourballs would increase, were we charging rough 2-in. balls as suggested by Mr. Garms. The assumption is, of course, that we would get a corresponding increase in work done. Our reported data (CIME meeting, Vancouver, 1946) shows a gain of work accomplished of 7.6 pct as we decreased the ball size from 2 in. to 11/2 in. and a further gain of work accomplished of 2.1 pct when we went from 11/2 in. to 1 in. The small ball results reported by H. R. Banks at Chapman Camp are also very convincing. In the case of 2-in. balls they would take the conventional ball path and start cascading. They would thus destroy the classifying pool over the "foot" of the

Jan 1, 1951

By W. A. Rachinger, C. Graeme-Barber, R. L. Bell, R. C. Gifkins, T. G. Langdon

R. L. Bell. C. Graeme-Barber, and T. G. Langdon (Imperial College. London)— The internal-marker technique developed by Ishida, Mullendore, and Grant has enabled them to make some interesting observations on the role of grain boundary sliding in creep. Certain of their conclusions are supported by our own similar experiments on Magnox AL80 (Mg-0.8 pct Al) specimens containing several markers, full details of which will be published shortly. In particular, we would agree that: 1) Using the internal-marker method, there is little difference between Egb, the contribution made by grain boundary sliding to the total strain, measured at the surface and in the interior of a specimen. 2) The measurement of the change in grain shape during creep leads to an underestimation of the grain strain, and hence an overestimate of Egb.. However, the discrepancies between the values obtained by this method and those obtained using markers are not as great as Tables IV and V of Ishida, Mullendore, and Grant would suggest; see below. The authors' Eq. [I] which is used to compute Egb from the transverse displacement ITt of longitudinal marker lines is not given in the reference quoted,'' where in fact only relations for Egb in terms of the longitudinal displacements of markers were developed. As first pointed out by Gifkins and Gittins,12 a problem arises in the use of longitudinal markers. and we will show that Eq. [1] underestimates Egb in the interior by a factor of 2. In Fig. 12, two grains X and Y have become displaced by the vector AC which lies in the plane of the grain boundary ABCD separating them. A longitudinal marker has been split by this displacement into the two parts LA and CAW. If these were surface grains the transverse displacement, Ut. could be obtained by viewing normal to the "top" surface. If interior, a section through CD parallel to the top surface would show the same result, provided the longitudinal internal markers delineated planes normal to the top surface. (This is an essential feature of the markers not pointed out in the paper.) The important point is that the quantity Ut tan B (=BE=DF) only gives the elongation due to the one component AB of the sliding. The elongation V/tan 8 (=GD) due to the component AD must be added to produce the total elongation resulting from the boundary displacement AC. If the grain boundaries in a poly crystalline specimen are randomly oriented with respect to the stress axis it follows that In the interior of a specimen the two sums depend for any difference simply on the definitions "top'' and "side". On the surface it is possible that the two sums could differ somewhat. In either event it is clear that the authors' Eq. [I] underestimates Egb, and in the interior, and perhaps at the surface also, the appropriate formula is given by The suggested modification probably makes little difference to the comparison between surface and interior values of Egb where both were obtained from marker measurements. For the estimation of the correction becomes extremely important where the boundary contribution is large. In our own work on magnox, for example, we have obtained values of as large as 70 to 80 pct, under conditions of high temperature and low strain rate. The use of planar markers transverse to the stress axis would simplify the comparison between surface and interior behavior, because measurement of the longitudinal offsets Us of these markers could be summed to give the total elongation di-

Jan 1, 1965

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By Arthur Taggart

Recent jig practice has shown such marked departures from the pronouncements of the textbooks, particularly as to particle size recovered and size range of feed, as to make it desirable to reexamine the mechanism of jig action. This paper presents the results of such a study. The general conclusions of the Paper are: I. A jig bed is a bi-functioned as well as bi-parted body. The upper layer comprises a plastic stream moving slowly in a substantially horizontal direction from feed lip to tail board. It serves to rough out tailing and light middling and to pick up heavy middling and lift it out 01 the jig box. The lower layer acts as the ultimate separating means by absorbing concentrate and rejecting heavy middling. 2. The separating function of the lower layer is performed in three definitely diflerent ways, depending upon the relative sizes of the grains presented to it and those composing it. Experimental The experimental work consisted of close and long-continued visual observations of operating beds in a plunger jig, eccentric driven, and in determinations of the settling rates of various metal spheres through a quartz bed under various conditions of operation. Falling velocities were measured by an ingenious method devised by A. 6. Dorenfeld, a student in the Mining Department at Colum- bia. Spheres of different metallic alloys, 3/8-in. diameter, were cast with a short piece of fine copper wire frozen in to Serve for suspension-A short piece of black cotton thread was looped to the top of the wire to serve as an indicator. The set-up for a test is shown in Fig. I. The thread should be boiled, if necessary, to make it freely water absorbent. The piece of clean plate glass D is supported rigidly at the proper height in a vertical position. The white scale E is similarly supported behind the glass. At the beginning of a test, D is filmed with water by holding it (best with clean rubber finger cots) under running tap water. It is then clamped in approximate position and C, already wet, is laid across it and drawn straight and vertical with the upper end at or near the top of D, and the ball A slightly above the top of the expanded bed. The water film holds the string to the glass. For a test the string is released, its upper end position noted just after the top of the ball becomes submerged, when the corresponding time is read, and thereafter simultaneous readings of position and time are taken as desired. Results of the visual studies of the bed are given at the pertinent places in the following discussion. Results of the settling tests are summarized in Figs- 2 and 3. Definitions The name bed as used herein refers to the entire mixture of solids and water filling the jig box. A layer is a stratum of a bed composed of particles of substantially the same specific gravities. A granular product is long-range when it approximates a crushed or ground product limited as to upper size only; a short-rafzge product is one closely sized. A bed is loaded when operating with continuous feed and discharge of products; it is unloaded when pulsating norma11y but neither being fed nor

Jan 1, 1943