Estimation of temperature transients for biomass pretreatment in tubular batch reactors and impact on xylan hydrolysis kinetics

A combined heat transfer/kinetic model was developed to quantify temperature variations in small tubular batch reactors and estimate the effect of deviations from isothermal operation on the kinetics of biomass pretreatment. Assuming that heat transfer was dominated by conduction in the radial direction, a classic parabolic time-dependent partial differential equation was applied to describe the temperature in the system and dedimensionalized to provide a single solution for application to all situations. A dimensionless expression for the reaction kinetics for xylan hydrolysis was then developed, and a single parameter expressed as the dimensionless ratio of the first-order rate constant times the tube radius squared divided by the thermal diffusivity was found to control the reaction rate. Three different characterizations of the deviation between the concentration profile predicted for isothermal xylan hydrolysis and that based on the transient temperature were directly related to this dimensionless rate constant parameter for both catalyzed and uncatalyzed hydrolysis kinetics. These results were then used to project the relationship between deviations in yield from isothermal results and the tube radius and reaction time.