L.G. Austin

Gas Reactions of Carbon

Publisher Summary This chapter reviews the majority of pertinent papers on gas–carbon reactions. The inherent chemical reactivity of the carbon and mass transport of the reactants and products can play an important role in affecting the kinetics of gas–carbon reactions. The chapter discusses the possibilities of using bulk-density and surface-area profile data on reacted carbons for better understanding of reaction mechanisms. One of the steps involved in a gas–carbon reaction is the chemisorption of the gas on the carbon surface. Some of the products of the gas–carbon reactions chemisorb on the carbon surface under certain conditions. Therefore, an understanding of the chemisorptions of gases on carbon is essential for the understanding of the gas–carbon reactions. In chemisorption, it is known that the surface atoms must have free valence electrons to form strong chemical bonds with gas molecules or atoms. Much recent work using electron paramagnetic resonance absorption techniques has confirmed the presence of unpaired electrons in various types of carbons. The number of unpaired electrons is a complex function of carbon heat-treatment temperature, apparently being affected primarily by the number and nature of imperfections in the carbon structure.

Methods for determination of breakage distribution parameters

Abstract The distribution of primary breakage products in laboratory mills can be estimated by batch grinding for short times. Three methods are given for manipulating the data, the second and third methods correcting for secondary breakage. Method III is the most accurate, but since it uses the specific rates of breakage of the various sizes in the correction procedure it is necessary to have experimental or theoretical estimates of these values. A general computer program is given for the computations.

An analysis of fine dry grinding in ball mills

Abstract The kinetics of dry grinding of several cement clinkers and two coals were investigated in a laboratory tumbling ball mill. The kinetic process is first-order at first, but the rates of breakage decrease as fines accumulate in the bed. It was demonstrated that the slowing of the breakage rates applies to all sizes in the mill, indicating that the cushioning action of fines affects the whole breakage process, even though mill power remains constant. Tests on cleaning or non-cleaning the balls showed that the major factor was not the build-up of a coating on the balls. Radio-tracing tests showed that the effect was not due to pelletizing of fines into larger particles. The quantitative magnitude of the cushioning action was different for different materials. It is, therefore, postulated that cushioning is affected not only by air trapped in the bed of fine particles but also by the cohesive attraction of fine particles, which is a function of the material.

The back-calculation of specific rates of breakage and non-normalized breakage distribution parameters from batch grinding data

Abstract This paper describes a mathematical approach for calculating parameters relating specific rates of breakage and breakage products distribution from batch grinding a known feed for several grinding times. Knowledge of such parameters leads to improved equipment design criteria and consistent operating correlations. The approach involves the use of non-linear optimization with appropriate statistical tests and gives parameter estimates close to those gained from direct experimental measurements. Some results and experiences using the technique are summarized.

Experimental methods for grinding studies in laboratory mills

Abstract The paper describes the sieving and grinding schedules necessary to express the breakage characteristics of a brittle material in terms of specific rates of breakage and primary breakage product distributions. It is demonstrated that larger particles can break abnormally, and that the primary breakage distributions are not always normalized.

Breakage properties of some materials in a laboratory ball mill

Abstract Crystalline quartz, silicon carbide, three coals of different rank and a cement clinker were studied in a small laboratory ball mill under standard conditions. The first-order specific rates of breakage and the cumulative primary daughter fragment distributions were determined. Two coals showed a slowing down of breakage rate at fine dry grinds. Anthracite showed an acceleration of grinding rate. Wet grinding was first order in all cases even to very fine grinds. Wet grinding was always faster than dry grinding for a given material but the shapes of the size distributions were the same within experimental variability.

The effect of ball size on mill performance

Abstract The specific rates of breakage of particles in a tumbling ball mill are described by the equation S i = ax α i ( Q ( z ), where Q ( z ) is the probability function which ranges from 1 to 0 as particle size increases. This equation produces a maximum in S , and the particle size of the maximum is related to ball diameter by x m = k 1 d 2 . The variation of a with ball diameter was found to be of the form a = k 2 / d 1.5 . Both k 1 and k 2 vary with mill diameter, and simple power laws have been assumed, k 1 ∝ D 0.1 , k 2 ∝ D 0.6 . If it is also assumed that the mean overall values of S i for a mixture of balls is the weighted mean of S i values for each ball size, equations are derived for calculating this mean value. As an example, the results are used in a mill simulation to show the quantitative effect of different ball mixes in a two-compartment cement mill versus a uniform mix over the whole mill.

The estimation of non-normalized breakage distribution parameters from batch grinding tests

Abstract The Harris hypothesis that a Weibull plot of grinding data should give a straight line of slope one if grinding is first-order is disproved. Due to the shape of the breakage distribution parameter B and the fact that it is not normalized, the slope is generally greater than one even for perfect first-order grinding. A computation technique is described for calculating non-normalized values of B , using the results of batch grinding tests on a closely sized sample.

Further studies of ball and powder filling effects in ball milling

Abstract The specific rates of breakage of quartz have been studied in three tumbling ball mills, two of 195 mm i.d. and one of 0.6 m i. d., as a function of fractional ball and powder loading. It was found that power results from a small mill with small lifters were anomalous, probably due to slippage, so that results reported previously from tests in this mill were not correct as a function of ball load. New results are presented for both wet and dry grinding.

An analysis of ball-and-race milling. Part I. The hardgrove mill

Abstract The basic principles of mill action were investigated in the batch Hardgrove ball-race machine, modified by the addition of a torque device. It was found that the torque to drive the mill after correction for bearing friction was almost proportional to load M on the balls and independent of rotational speed ω, so that mill power ??? Mω. The first-order specific rates of breakage were proportional to M and ω. Torque increased as the power in the race increased, then reached almost a constant value, as did the absolute rate of breakage. As fines accumulated in the charge breakage became non-first-order, showing a slowing-down effect for all sizes. An easy method of simulation of this condition was demonstrated.