Dynamic mathematical model for biotransformation and mass transfer of livestock generated VOC-odor in a bioactive dust particle system

A multi-step mass transfer-biodegradation model is developed to describe the bioactive adsorber dynamics for the biotreatment of livestock generated odor causing VOCs (VOC-odor) based on a biologically active dust particle (BADP) process. The BADP process employs dust particles with adsorbat- acclimated microbial culture to form the bioactivated dust particles (BDP) for the simultaneously adsorption, mass transfer, and biodegradation of VOC- odor. The model incorporating age and size distributions of BDP considers the equilibrium partitioning of VOC-odor at BDP and bulk gas interface that followed by two kinetic processes occurring in the bulk and solid phases: bulk gas mass transfer-biodegradation and BDP biofilm diffusion- biodegradation. Analytical equations indicate that the overall biotransformation rate of VOC-odor in a BADP process is controlled by BDP- bulk gas equilibrium processes represented by the slowest of two kinetic processes determined by a dimensionless group: the Thiele modulus (φ²), the Damkohler number (Da) and the Biot number (Bi). Computer simulations demonstrate that the most favorable performance of a BADP system in reducing VOC-odor concentrations is operated under Bi<1, Da<1, or Bi >1 φ² < 1; indicating diffusion-biodegradation controlled. The dimensionless group can be used to identify the dominant rate-limiting processes and to evaluate the overall biomineralization rate in a BADP process. Simulation results allow the determination of preliminary design for prototype development.