Development of a Population Balance Model to Simulate Fractionation of Ground Switchgrass

Abstract

The population balance model represents a time-dependent formulation of mass conservation for a ground biomass that flows through a set of sieves. The model is suitable for predicting the change in size and distribution of ground biomass while taking into account the flow rate processes of particles through a grinder. This article describes the development and application of this model to a switchgrass grinding operation. The mass conservation formulation of the model contains two parameters: breakage rate and breakage ratio. A laboratory knife mill was modified to act as a batch or flow-through grinder. The ground switchgrass was analyzed over a set of six Tyler sieves with apertures ranging from 5.66 mm (top sieve) to 1 mm (bottom sieve). The breakage rate was estimated from the sieving tests. For estimating the breakage ratio, each of the six fractions was further ground and sieved to 11 fractions on a set of sieves with apertures ranging from 5.66 to 0.25 mm (and pan). These data formed a matrix of values for determining the breakage ratio. Using the two estimated parameters, the transient population balance model was solved numerically. Results indicated that the population balance model generally underpredicted the fractions remaining on sieves with 5.66, 4.00, and 2.83 mm apertures and overpredicted fractions remaining on sieves with 2.00, 1.41, and 1.00 mm apertures. These trends were similar for both the batch and flow-through grinder configurations. The root mean square of residuals (RSE), representing the difference between experimental and simulated mass of fractions, was 0.32 g for batch grinding and 0.1 g for flow-through grinding. The breakage rate exhibited a linear function of the logarithm of particle size, with a regression coefficient of 0.99.