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By L. B. Pankratz

Heat contents were measured for Na2CaSi04 and Na2Ca2S02 between 298° and 1,300° K, for Na2Ca2Si309 between 298° and 1,500° K, and for Na4CaSi3O9 between 298° and 1,350° K. Copper-block drop calorimetry was employed. Reversible, first-order transitions were found for Na2CaSi04 and Na2Ca2Si309. The transition for Na2CaSi04 is at 830° K with a heat absorption of 160 cal/mole; that for Na2CagSi309 occurs at 750° K with a heat absorption of 1,550 cal/mole. Results for the other two silicates showed no irregularities. A table of heat content and entropy increments above 298.15° K and heat con-tent equations are included for use in thermodynamic calculations.

Jan 1, 1968

By Dong Joon Min, Joo Hyun Park, Mi Sun Choi, Jae Hong Shin

Sublimation of ZrCl4 is important for the production of nuclear grade metallic Zr in Kroll’s process. The sublimation kinetics of ZrCl4 was investigated by TGA under both isothermal and non-isothermal conditions. The sublimation rate of ZrCl4 increased with increasing temperature under isothermal conditions. ZrCl4 sublimation was confirmed to be a zero-order process under isothermal conditions, whereas it was first-order kinetics under non-isothermal conditions. The activation energy of ZrCl4 sublimation under isothermal conditions was 21.7 kJ/mol. The activation energy for non-isothermal sublimation was 101.4 kJ/mol and 108.1 kJ/mol with the Kissinger method and Flynn- Wall-Ozawa method, respectively. These non-isothermal activation energies were very close to the heat of sublimation (103.3 kJ/mol). Sublimation occurs by two elementary steps: surface reaction and desorption. Therefore, the overall activation energy of ZrCl4 sublimation is 104.8(±3.4) kJ/mol. The activation energy of the surface reaction and desorption steps are proposed to be 83.1 kJ/mol and 21.7 kJ/mol, respectively.

Jan 1, 2014

By E. D. Levine

A study was made to delineate the dislocation mechanistns controlling prismatic and basal slip at low temperatu.ves in titanium containing approximately 100 ppm interstitial impurities. Mechanical tests were performed on single crystals prepared from electron-beam zone-refined crystal bar by a thermal cycling technique. Measurements were made of critical shear stress and activation volume as functions of temperature. The study revealed that, for prismatic slip, two overlapping thermally activated processes aye rate-controlling below 300°K. From absolute zero to 220°K, reasonable agreement is obtained between experiment and the mechanism which involves overcoming 01. the Peierl's stress by the formation of double kinks in dislocation lines lying in close-packed directions. Between 220°and 300°K prismatic slip is controlled by a difierent thermally activated process which is characterized by a stronger temperature dependence of critical shear stress. Above 300OK, prismatic slip is controlled by an athermal process. Basal slip is controlled by a thermally activated process between 195' and 400°K. An approximate analysis suggests that it is the Peierl's mechanism that is rate-controlling in this range. Below 195°K, the occurrence of mechanical twinning obscures the features of basal slip. Above '400 X, basal slip is controlled by an athermal process. TITANIUM, an hcp metal with a less-than-ideal axial ratio of 1.587, deforms primarily by {1010}( 1210) slip at low temperatures.'-3 The critical shear stress is strongly affected by the presence of interstitial impurities. For example, churchman3 reported that a decrease in the combined nitrogen plus oxygen content from 0.1 to 0.01 pct decreased the critical shear stress for prismatic slip from 9.19 to 1.4 kg per sq mm at room temperature. Basal slip, however, is less strongly affected by interstitials; Churchman's data for {0001}( 1210) slip show a smaller decrease in critical shear stress from 10.90 to 6.3 kg per sq mm at room temperature, for the same decrease in interstitial content. In the present study, an attempt has been made to delineate the dislocation mechanisms controlling prismatic and basal slip in titanium. In view of the strong effects that impurities may have on at least some of these mechanisms, experiments were performed on material of reasonably high purity, so that comparisons could be made with investigations on material of both lower and higher impurity contents. EXPERIMENTAL PROCEDURE Single crystals were prepared from 1/4-in.-diam electron-beam zone-refined crystal bar, furnished by Materials Research Corp. The analysis of the zone-refined material is given in Table I, indicating that the interstitial content is of the same order as the purer of the two materials investigated by Churchman. The Vickers diamond pyramid hardness number of this material was 85.6. This value agrees quite well with the correlation between hardness and interstitial content proposed by Ogden and Jaffee.4 On the basis of hardness, the material investigated in this study is, therefore, intermediate in purity between that studied by Churchman (Vpn = 97) and that studied by Spangler and Herman (Vpn = 62.4).5 Single crystals were grown by thermal cycling through the a-ß transformation. Two-in.-long by 1/2-in.-diam bars were heat-treated in vacuum for 4 hr at 1160°C. The temperature of the furnace was then lowered to 865°C, and the specimens were maintained at this temperature for 7 days. This procedure was repeated several times, resulting in the growth of individual crystals up to 14 in. in length. Specimens for testing in direct shear along either {l010}(1210) or {0001}(1210) were obtained by electrical-discharge machining. The specimens were in the form of cylinders 1/4 in. in diam by approximately 1/2 in. in length, with a reduced section 1/8 in. in diam and a in. in length. All specimens were electropol-ished subsequent to electrical-discharge machining. The ends of the test specimens were cemented in stainless-steel collars. Shear tests were conducted in an Instron Tensile Tester at various temperatures from 4.2° to 508°K. Measurements were made of critical shear stress and activation volume. The latter measurements were performed by measuring the change in flow stress upon cycling the strain rate between ?1 = 2.62 x 10-3 per sec and ?2 = 2.62 x 10-4 per sec. Activation volume, I)*, is defined as u* =ßkT [11

Jan 1, 1967

By K. K. Kelley, L. B. Pankratz, W. W. Weller

Mullite is a substance of prime importance in ceramic technology . Despite this fact , its thermodynamic properties have received little attention . A Bureau of Mines literature survey disclosed the absence of lowtemperature heat capacity data , the absence of an experimental entropy value for 298.15 ° K , and the lack of heat content data beyond the temperature range from 298° to 576 ° K. Data supplied in this Bureau report fill these gaps in the thermodynamic knowledge of mullite . According to equilibrium phase studies of Aramaki and Roy ,3 the mullite phase melts congruently at 2,123 ± 15 ° K , and the equilibrium crystallinephase composition extends from Al Si2013 to Al6.8 Si₂ Q4.2 . The results in this report are for the stoichiometric composition , Al Si¿Qз . • Heat capacity measurements were made over the temperature range from 50 ° to 298 ° K , and the entropy at 298.15 ° K was evaluated . Heat content measurements covered the temperature range from 298 ° to 1,800 ° K. Heat content

Jan 1, 1963

By M. J. Ferrante

Relative enthalpies of CuBr from 298.15 to 1,301 K were measured at the Bureau of Mines to provide thermodynamic data needed for the advancement of mineral technology. The temperatures of transition were measured by differential scanning calorimetry (DSC) and the standard enthalpies of transition[ (IlH~r) by drop calorimetry. The combined results gave reversible transitions at 657 K with llH~r= 1.10 kcal/mol, at 741 K with lm~r == 0.51 kcal/mol, and at 759 K with an enthalpy of fusion (AH~) of 1.22 kcal/moL ] An anomalous increase in heat capacity preceded the first crystal transition at 657 K. Tabulated values are listed for the standard relative enthalpy, heat capacity, entropy, and Gibbs energy function from 298.15 to 1,500 K. Standard relative enthalpies are also given in equation form and combined with thermodynamic data from the literature to derive values of standard enthalpies of formation and Gibbs energies of formation.

Jan 1, 1984

By P. J. Spencer, J. N. Pratt

The vapor pressure of manganese over liquid Mn-Sn alloys has been determined by a high-temperature torsion-effusion technique. Alloys containing from 8 to 100 at. pct Mn were investigated in the temperature range jrom 1280" to 1580" and the measured pressure values were used to calculate the partial and integral thermodynamic properties of the liquid alloys. The activities show small negative departures from ideality while the integral heats and excess entropies of mixing are asymmetric inform, changing from positive to negative with increasing manganese content. The possible contribution of various factors to the observed thermodynamic properties is discussed. COMPARATIVELY few thermodynamic data are available for manganese alloy systems.' Therefore, as part of a continuing program of studies of the thermodynamic properties of transition metal alloys, measurements have been made on various binary alloys involving this element. In recent publications,2~3 investigations of liquid Mn-Cu alloys and of the Mn-Au system in both solid and liquid states have been reported. For the first-mentioned system the work suggested that magnetic interactions may be responsible for the observed form of the thermodynamic properties, while in the second the influence of the electrochemical factor appears to be dominant. The present paper describes a similar study of liquid Mn-Sn alloys. Again the thermodynamic properties have been obtained from vapor pressure measurements made by use of a high-temperature torsion-effusion technique.4 A detailed description of the apparatus and of the experimental procedures used in alloy preparation and pressure measurement may be found elsewhere.2'4 EXPERIMENTAL RESULTS Sixteen alloys, ranging in composition from 8 to 100 at. pct Mn, were prepared from spectroscopically standardized manganese of 99.99 pct purity and tin of 99.999 pct purity, both supplied by Johnson-Matthey and Co., Ltd. One-gram samples of the alloys were obtained by carefully weighing appropriate amounts of the pure components into an effusion cell; this was then suspended in the apparatus and the metals melted together in situ by heating under vacuum to approximately 1550°K. After allowing sufficient time for a homogeneous liquid alloy to be formed, vapor pressure measurements were commenced. These were determined as rapidly as possible at a series of steady temperatures within the range of interest. The duration of experimental runs on individual samples was kept sufficiently short to ensure insignificant varia- tion of alloy composition during investigation. After completing pressure measurements, the alloys were rapidly cooled and their compositions checked by weighing or chemical analysis. All experiments were conducted using effusion cells machined entirely from boron nitride. Measurements were made using a variety of cells with orifice areas ranging from 0.0032 to 0.0075 sq cm and lengths of the order of 0.04 cm; the usual effusion correction factors for orifice geometry and molecular distribution were calculated using Freeman and Searcy's equation5 and had values between 0.6 and 0.75 for the orifices employed here. The vapor pressures of manganese over the alloys were measured at approximately 20°K intervals in the temperature range 1280" to 1580°K. In view of the close approximation of the measured pressures to Clausius-Clapeyron behavior in the experimental temperature range, the data for each alloy have been expressed by equations of the form: logp(atm) =-A/T + B A least-squares computer treatment was applied to the vapor pressure values in order to obtain the coefficients A and B with their associated error. The resulting equations are listed in Table I, together with the equation for pure solid manganese obtained from a previous study.4 To minimize the effect of possible apparatus calibration errors, the activities and partial free energies of manganese in the alloys were calculated by initial reference to the latter equation, obtained from identical torsion-effusion measurements. The immediately resulting thermodynamic quantities, based on a solid manganese reference state, were then converted to refer to the more appropriate supercooled pure liquid manganese standard; tabulated values of the free energies of solid and liquid manganese from Hultgren et al.' were used for this purpose. Partial entropies of solution of manganese were calculated from the temperature coefficients of the free energies and partial heats from the Gibbs-Helmholtz relationship.

Jan 1, 1969

By A. R. Taylor

The Bureau of Mines has determined the heat capacity and enthalpy values for beryllium sulfate (BeS04) throughout the temperature ranges of 10° to 300° K in an adiabatic calorimeter, and 350° to 860° K in a Bunsen-type ice calorimter, The heat-capacity data were extrapolated to 0° K, and smooth values of heat capacity, entropy, enthalpy function, and free-energy function were reported at 10-degree intervals between 0° and 300° K. The method of least squares was used to fit the enthalpy data with an algebraic equation. The equation also was used to calculate values of heat capacity, entropy, enthalpy function, and free-energy function at 50-degree intervals between 300° and 900° K.

Jan 1, 1963

By T. Estelle Gardner

The Bureau of Mines made enthalpy measurements on sodium bromide and sodium iodide in the temperature range 400° to 1,200° K using an ice calorimeter. Equations representing enthalpy as a function of temperature were derived from the data by the method of least squares. These equations were used to calculate smooth values of heat capacity, enthalpy, and entropy at 50° K intervals from the ice point to 1,200° K. The melting point determined for sodium bromide was 1,020° K; the melting point of sodium iodide was 934° K. The heats of fusion of sodium bromide and sodium iodide were calculated to be 6,270 and 5,680 cal/mole, respectively.

Jan 1, 1967

By G. R. St. Pierre, A. Ghosh

In the Si-C-0 system at temperatures of interest in process metallurgy there are four stable condensed phases—silicon, carbon, silica, and silicon carbide (Sic). Silicon melts at 1683oK1 and shows negligible solubility for carbon and oxygen at 1700°K. However, silicon dissolves approximately 1.5 at. pct C at 2500oK.2 Carbon in the form of graphite remains pure and dissolves negligible amount of silicon.' Silica (crysto-balite) melts at 2001°K' and is essentially a stoichio-metric compound. Silicon carbide is a solid and shows negligible deviation from stoichiometry up to approximately 2800oK.2 Besides the condensed phases there is a gas phase

Jan 1, 1970

By R. L. Bell, T. G. Langdon

A technique was developed- for determining the grain strain, and hence the grain boundary sliding contribution, occurring during the high- temperature creep of a magnesium alloy, from the distortion of a grid photographically printed on the specimen surface. The results were compared with those obtained from measurements of grain shape, both at the surface and interrwlly, and it was concluded that the grain shape technique may substantially underestimate the grain strain and overestimate the sliding contribution due to the tendency for migration to spheroidize the grains. ALTHOUGH a considerable volume of work has been published on the role of grain boundary sliding in high-temperature creep, many of the estimates of Egb (the contribution of grain boundary sliding to the total strain) have been in error due to the use of incorrect formulas or inadequate averaging procedures.' One of the most easy and convenient measurements from which to compute Egb is that of v, the step normal to the surface where a grain boundary is incident. Unfortunately, this parameter is also the one associated with the treatest number of pitfalls. Values of v have been used to calculate Egb from the equation: egb =knrVr [1] where k is a geometrical averaging factor, n is the number of grains per unit length before deformation, v is the average value of v, and the subscript ,r denotes the procedure of averaging along a number of randomly directed lines. If the dependence of sliding on stress were assumed, it would be possible, in principle, to calculate k from the known distribution of angles between boundaries and the surface. This in itself is difficult because the distribution depends on the history of the surface,' but the problem is even further complicated by the fact that v depends on other factors such as the unbalanced pressure from subsurface grains.3 However, the great simplicity of the measurement procedure for v makes it highly desirable that this problem of k determination should be overcome. In the present experiments, this was achieved by the use of an indirect empirical method in which the grain strain, eg, at the surface was determined by the use of a photographically printed grid. The assumption here is that the total strain, et, is simply the sum of that due to grain boundary sliding, egb, and that due to slip or other processes within the grains, eg. SO that: Et = Eg + Egb [2] Thus k is given by: In practice, it is customary to indicate the importance of sliding by expressing it as a percentage of the total creep strain; this quantity is termed y (= 100Egb/Et). The determination of Eg from a printed grid within the grains avoids the difficulties due to boundary migration which should be considered when the grain strain is calculated from measurements of the average grain shape before and after deformation. As first pointed out by Rachinger,4,5 however, this latter technique has the particular advantage that it can also be applied in the interior of a polycrystal. Recently, several workers have produced evidence on a variety of materials6-'' to support the observation, first made by Rachinger on aluminum,4,5 that 7 can be very high, 70 to 100 pct, in the interior, even when the surface value, determined from boundary offsets, is very much lower.10'11 Although there have been criticisms both of the shortcomings of the grain shape technique'' and of the different procedures used to determine y at the surface,' it seemed important to check whether measurements of sliding by grain shape gave values of y which were truly representative of the material. In the present experiments, grain shape measurements were therefore made both at the surface and in the interior for comparison with one another and with the independent measurements of grain strain using the surface grid technique. EXPERIMENTAL TECHNIQUES The material used in this investigation was Magnox AL80, a Mg-0.78 wt pct A1 alloy supplied by Magnesium Elektron Ltd., Manchester. Tensile specimens, about 7 cm in length, were prepared from a 1.27-cm-diam rod, with two parallel longitudinal flat faces each approximately 3 cm in length. The specimens were annealed for 2 hr in an oxygen-free capsule, at temperatures in the range 430° to 540°C, to give varying grain sizes, and, prior to testing, the grain size of each was carefully determined using the linear intercept method. This revealed that the grains were elongated -0.5 to 5 pct in the longitudinal direction. Testing was carried out in Dennison Model T47E machines under constant load at temperatures in the range 150" to 300°C. At temperatures of 200°C and below, tests were conducted in air with the polished flat faces coated with a thin film of silicone oil to prevent oxidation; at higher temperatures, an argon atmosphere was used. To determine v,, each test was interrupted at regular increments of strain and the specimen removed from the machine. At the lower strains, when v, was less than about 1 pm, measurements were taken on a Zeiss Linnik interference microscope;

Jan 1, 1969

By R. E. J. Putman

Introduction Self-tuning regulators are a class of controllers built around the concepts of sampled data theory, and are especially suitable for implementation in a digital microprocessor or minicomputer control system. The algorithms used are distinctly different from those based upon analog control techniques and include automatic adjustment features which permit them to adapt to unmeasured changes (in, for example, ore grindability) or process nonlinearities (as exhibited by cyclone classifiers). They are also designed to handle transport lags in a simple manner, for example, anticipating the effects of a variable recycle rate on particle size distribution. The advent of distributed control systems will encourage the exploration of these techniques in the minerals processing industries, and particularly for improving the control of comminution circuits, which are especially energy intensive. This paper outlines some current work in progress on this topic. Background Those engaged in the practice of process control have long had two philosophical problems for which solutions have been actively sought - what is optimal control and how can we attain it in some heuristic fashion automatically. The basic analog controller can be represented by the differential equation: [V = Ko + K1 f y • dt + K2 dt(1)] where: v and y are the instantaneous values of output and error respectively and K0, K1, and K2 are tuning constants. The empirical rules for establishing the values of K0, K1, and K2, which provide stability, have evolved from the initial suggestions of Ziegler and Nichols(9) in 1942 and have served their purpose well. However, later analyses demonstrated that there are in fact many combinations of the values of K0, K1, and K2 which, besides being stable, behave better or worse in relation to other process control criteria; some examples are duration of error, amplitude of a damped response, magnitude or rate of movement of control valve or adjustment of speed regulator, etc. The definition of optimality had broadened. In 1964, Kalman(4) published his classic paper which tried to resolve these problems. He defined a

Jan 1, 1982

By J. S. Tosh

An equilibrium study of the system potassium carbonate, potassium bicarbonate, carbon dioxide, and water has been conducted with solutions of 20-, 30-, and 40-percent equivalent potassium carboaate concentrations. These equilibrium data cover the operating range of the hot carbonate scrubbing system for removing carbon dioxide from gas mixtures. Such data are necessary to establish the limits of purification and are used to design absorption and regeneration towers. Values of K in the relationship K = (KHCO3)2/(K2CO3)PCO2 were determined for higher temperatures of 70" to 140° C. and greater concentrations, I 20 to 40 percent, than employed by previous investigators. For the 20- and 30-percent concentrations, K is constant at a given temperature; thus, once K has been determined the equilibrium pressure of carbon dioxide can be calculated for any conversion. Variation of & values with changing conversion was observed with the 40-percent solutions, so that equilibrium calculated pressures are less reliable from average K values.

Jan 1, 1959

By L. Piga, P. Cipriani, F. Pochetti

High-temperature roasting of alunite in the presence of K2CO3 gives rise to a reaction that results in up to an 80% recovery of its potassium content as K2SO4 by leaching of the roasted mixture. K2SO4 is also generated from the reaction between the added K2CO3 and the SO3 driven off during roasting of the alunite. This limits the environmental and corrosive problems involved in the thermal treatment of this mineral. A solid residue containing mainly aluminum oxide is also obtained. This could be used as raw material for the production of aluminum, as the use of K2CO3 does not introduce different cations than are in the ore. A statistical study was performed on the factors assumed to affect the recovery of potassium, namely, roasting temperature, K2CO3- alunite stoichiometric ratio and leaching temperature.

Jan 1, 2000

By J. M. Stuve

This Bureau of Mines investigation measured the low-temperature heat capacities of FeOC1(c) and FeC13(c) in the temperature ranges of 6 to 305 K and 4.6 to 300 K, respectively. The standard entropies (S°, 298.15 K) of FeOCl(c) and FeC13(c) were derived as 19.73±0.03 cal/deg-mole and 35.33±0.07 cal/deg-mole. A large lambda transition was observed in the heat capacity of FeC13(c) at 8.4 K. The standard enthalpy of formation (?H°f, 298.15 K) of FeOC1(c) was determined to be -98.23±0.22 kcal/mole by HC1 solution calorimetry. High-temperature enthalpy measurements (H-H298.15) of FeOC1(c) were determined to 700 K by precision drop calorimetry. Standard thermodynamic formation data and related functions were tabulated at various temperatures for FeOC1(c) and FeC13(c).

Jan 1, 1980

By W. J. Pearson

"""POTASH"" is a term applied to the compounds of the element potassium (K) and when used in agriculture and industry is ex-pressed in terms of potassium oxide (K2O), regardless of the actual com-position of the compound. When a chemical analysis is made of a fertilizer, the amount of K is deter-mined and then calculated to the equivalent amount of K2O. However, the compound K2O does not exist in nature. Most of the world's potash supply is derived from mineral deposits similar to those in Saskatchewan and New Mexico. However, there is some production from concentrated surface brines such as occur in Searles Lake, California; Salduro Marsh, Utah; the Dead Sea; and from well brines in Micl1igan."

Jan 1, 1960

By C. Fuellenbach, J. Brune

"INTRODUCTION Mining activities must be safe and profitable. These two requirements influence each other. The purchase and implementation of safety improvements costs money. Injuries and illnesses at mines stop or delay production and may result in additional costs or a loss of profit. Other effects of injuries and illnesses include the negative influence on employee morale, corporate reputation and conflicts with contract partners. Based on this researchers asked the question: are mines with lower rates of injuries and illnesses more profitable than mines with a higher frequencies? One aspect of this research is the evaluation of the safety situation and the measurement of benefits of safety improvements in the German mining industry. In the following paper, this part of the research will be examined. The main aim is the evaluation of injury rates in different German mining sectors and regions in Germany. SELECTION OF GERMAN MINING OPERATIONS The research team decided to focus the study on the salt and potash and the aggregate and industrial minerals mining industries in Germany. These two mining industries are different in the number and size of operators, structure of the industry, pricing and markets. The selection of two different industries adds to the clarity of the evaluation. Salt and potash mining industry The German salt and potash industry is primarily located central Germany. All salt and potash mines in Germany are underground operations. In 2015, the German potash industry employed 8,100 employees and generated a total revenue of 2 billion Euros. German potash reserves include magnesium compounds like kieserite (MgSO4·H2O), in addition to sylvite (KCl) and carnallite (KMgCl3·6(H2O)). The German salt industry employed 2,300 people in 2015 and generated revenue of 800 million Euros (Krueger, 2015) There are seven mining companies with salt and potash operations: esco-european salt company GmbH & Co. KG, K + S Kali GmbH, Saline Luisenhall GmbH, GSES Glückauf Sondershausen Entwicklungs- und Sicherungs-gesellschaft GmbH, Südwestdeutsche Salzwerke AG, Wacker Chemie AG and Südsalz GmbH. In this way, esco – european salt company GmbH & Co. KG is an affiliated company. Esco was founded as a joint venture of K + S and Solvay in 2002, since 2004 K + S is the sole holder (esco - european salt company GmbH & Co. KG, 2016). Likewise, the Südwestdeutsche Salzwerke AG has a controlling interest in Südsalz GmbH (Südsalz GmbH, 2016). Aggregate and industrial minerals mining industry The aggregate mining industry in Germany is comprised of many small mining operations and relevant companies. According to the German Department of Economics (BMWi, 2015), the following industrial materials are classified as aggregates: fluorite, barite, kaolin, quartz and quartz sand, quartzite, silica, loamy and foundry sand, pegmatite sand, shale, clay, bentonite, schistose, limestone and dolomite, gypsum and anhydrite, basaltic lava and lava sand, gravel and split, pebble and silicic sand and peat."

Jan 1, 2017

By D. W. Fuerstenau, L. M. Berlioz

In 1957, Charles1 first presented an analysis of a relationship between the energy expended in comminution and the extent of size reduction achieved. Subsequently, Schuhmann extended and interpreted Charles' approach to comminution. According to their analysis, the energy, E, expended in comminuting unit mass of fairly uniformly-sized material is related to the size modulus of the product, k, by where a is the distribution modulus (slope of the log-log cumulative size distribution plot) and C is a constant, which is primarily determined by properties of the solid. If there is any fundamental basis for the E vs k relationship, E must necessarily be concerned with the useful work for the size reduction process and not necessarily the work input, as discussed in detail by Harris.3 Charles and numerous other investigators tested this equation only by relating k to the grinding time, assuming expended energy to be directly proportional to time, but never directly measuring power. In our laboratories, we recently constructed a special batch ball mill with which the power could be accurately determined with torque measuring apparatus.4 With this device, a direct test of the Charles relationship could then be made for ball milling. 5 EXPERIMENTAL A stainless steel mill, 11.5 in. long and 10 in. in inside diam, lined with eight low-silhouette lifter bars, was used for these experiments. The grinding media consisted of 30 kg of single sized, 1-in. diam, stainless steel balls, which occupied about 50% of the total mill volume under static conditions. The void fraction of the static ball load was approximately 0.4, and for the dry grinding conditions used, the corresponding interstitial volume was filled when about 3300 g of the dolomite feed material was present. The 7x9 mesh dolomite used as feed was obtained as a natural, uncrushed product thus as- suring a random distribution of feed particle shapes. Charge weights of 660, 1320, 1980, 2480, 3300, 3960 and 5280 g, which correspond to 20%, 40%, 60%, 80%, l00%, 120%, and 160% of the interstitial load, respectively, were used. Grinding times of 20, 40, 60, 80, 100, 150, 200 and 300 revolutions were considered, with the mill operating at 54 rpm (approximately 60% of critical speed). The tests were made sequentially, in that the size distribution obtained after a certain grinding interval was utilized as the feed for the subsequent period of grinding. Agreement with control experiments where the mill ran continuously for the entire interval was excellent. Torque measurements were made utilizing a Baldwin-Lima-Hamilton SR-4 torque pickup in the manner that has been described previously.3 Standard wet (to obtain the -400 mesh material) and dry sieving procedures were followed using the Tyler full screen series. RESULTS The Gaudin-Schuhmann size distributions obtained in all of these experiments are characterized by distribution moduli (slopes), a, of about 0.66 and are representative of normal dry batch ball milling of a material like dolomite. As an illustration of typical

Jan 1, 1968

By M. Felsenthal

Engineers are frequently faced with the problem of having to predict oil recovery from a solution gas drive reservoir in the early life of a field. This is often the time when actual laboratory or field-derived gas-oil permeability (kg/k0) data are not yet available. Although excellent collections of k0/k0 data for various types of rocks may be found in the literature,1,2,3 a need exists for a more detailed correlation of k0/k0 data with core properties such as porosity, permeability, clay content or pore-size distribution. It is the purpose of this article to present this type of correlation for sandstone material. The correlation is based on laboratory tests performed on over 300 core samples from 19 reservoirs in the United States and Canada. EXPERIMENTAL Cores were analyzed by routine procedures, using samples of conventional size (7/8-in. diameter, 7/8-in long) cut parallel to the bedding planes. Air permeability was measured at 1.67 atm mean pressure in a Hassler-type apparatus. Porosity was determined with the aid of a Ruska bulk volume meter and a Boyle's Law rock volume meter, An evaporation method' was used to evaluate irreducible water saturations. Core samples were saturated with 25,000 ppm NaCl brine. The brine was reduced to the irreducible saturation, and the remainder of the pore space was filled with kerosene. This was followed by multiphase flow tests using the so-called "dispersed feed" technique.5 n this technique, gas and oil (kerosene and kerosene-saturated air) were dispersed with the aid of a porous Alun-durn feed head, the face of which contained a waffle-shaped system of Lucite-lined grooves. Oil entered the back side of the feed head and emerged at the raised areas of the front face. Gas was introduced directly into the system of grooves at the front face. The gas-oil mixture then entered the test core which was kept in capillary contact with the feed head. Permeabilities were determined from rate and pressure measurements and saturations from weights. All determinations were performed at equilibrium or steady-state conditions. Pore-size distributions were determined on selected samples by a mercury injection technique.6 GENERAL CORRELATIVE TRENDS When examining data from a given reservoir, it was noted that k0/k0 vs saturation curves became generally less steep as specific air permeability increased, a development that has a favorable effect on oil displacement efficiency by solution gas drive. This trend has also been reported by others in the literature.' An effect of porosity on k0/k0 data was also noted. This effect was not generally discernible in a study of relative permeability data for a given reservoir but became apparent when data for sandstone reservoirs of similar lithology but differing average porosity were compared. For instance, in a comparison of argillaceous and/or calcareous sandstones from 11 reservoirs ranging in average porosities from 14 to 28 per cent, a definite trend was noted, indicating that for a given permeability k0/k0 curves became less favorable (i.e., steeper) as porosity increased. A similar trend was observed for a group of comparatively clean sandstones from five reservoirs ranging in average porosities from 15 to 21 per cent. For a given permeability and porosity, comparatively clean sandstones gave more favorable k0/k0 curves than argillaceous and/or calcareous sandstone or chert reservoirs. The laboratory studies also showed that least favorable k0/k0 curves were exhibited by shaly sandstone, conglomerate, and sandstone containing carbon inclusions. Table 1 lists the various source reservoirs classified by lithology types. To facilitate a correlation of k0/k0 data with core characteristcis, it was found expedient to work with

By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat's' The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K'(tn), related by K(m) = K'(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K'(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K' (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K' (m)] is a streamline of value $[K(m), K' (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K' (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

By P. C. Chaubal

The overall kinetics of oxidation of single partic1es of chalcopyrite have been studied for temperatures up to 1273 K. The experiments were conducted in a stationary bed reactor using a non-isothermal technique. Any mass and heat transfer effects on the kinetics of oxidation were eliminated by using a high-enough gas flowrate. Up to temperatures of 873 K, pore-bl1ocking kinetics were applicable, whereas above 873 K, power-law kinetics gave a satisfactory fit of the data. The activation energy was 215 kJ/mol below 754 Kand 23.7 kJ/mol above 1,060 K. Predominance area diagrams were constructed at various temperatures and used in conjunction with X-ray analyses of partially oxidized samples to determine the intermediate phases formed during the reaction. The analysi1s also provides a justification for the kinetic models used. The results indicate that the reaction rate is first order with respect to oxygen concentration and inversely proportional to the square of the particle size throughout the ranges of temperature studied.

Jan 1, 1985