Population balance mass basis

In the example, all of the results are for the given sample size of 1 liter and the quantities estimated have units reflecting that basis. This basis volume is arbitrary, but use of the calculated quantities requires care in defining this basis consistently in corresponding mass and population balances. The volume of clear liquor in the sample is an alternative, and sometimes more convenient, basis. 

In some cases population balances are performed on a cumulative basis. One reason for such a population balance is so that theory can be easily compared to experimental data obtained from sieve analysis. To predict the mass on a sieve with size L, which cstme from the sieve above of size L + AL, we must perform the integrsd... 

Macroscopic Population Balance on a Discrete Mass Basis... 

The death rate in grinding is also referred to as the breakage rate and, for the population balance on a discrete mass basis, is given by [11]... 

In batch comminution, the summation term in equation (4.11) is zero because there are no flows into or out of the mill. Therefore the population balance on a discrete mass basis is simplified to... 

Several classification functions, C(L), are given in Figure 4.20. Here, the fraction of particles by mass reporting to the recycle stream is given as a function of particle size, L, for a screen and a cyclone. Several authors have used empirical classification functions instead of dassifier performance curves with reasonable results for the overall comminution-classification circuit control. The steady state (i.e., dmidt = 0) macroscopic population balance on a discrete mass basis over the grind-... 

The basis of a population balance is that the number of crystals in a system is a balanceable quantity. Such balances are coupled to the usual mass and energy balances describing any system, and the crystals are... 

The assessment on the basis of ehanges in the particle size distribution considers the left-hand side of Eq. (5), i.e., the absolute change in mass Am,- is measured. But the individual contributions that led to these changes, i.e., the terms on the right-hand side of Eq. (5), are not considered by this type of assessment. It may be possible to take the contributions of feed and system loss by means of measurements into account, but it is not possible at all to unravel the internal transfer masses rrif j and between the size intervals just by observing the changes in the particle size distribution. For this reason, it is not possible to extrapolate the description to a different duration of the attrition process or even to transfer it to other initial particle size distributions. For this purpose a description via particle population balances is needed. 

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