Dynamic mathematical model for biotransformation and mass transfer of livestock generated VOC-odor in a bioactive dust practice 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 (phi 2), 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 phi 2 < 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.