Modelling lumped-parameter sorption kinetics and diffusion dynamics of odour-causing VOCs to dust particles

An analytical algorithm is presented for fast simulation of the adsorption kinetics and diffusion dynamics of odour-causing volatile organic compounds (VOC-odour) which originate in the stored swine manure to airborne dust particles in a ventilated airspace. The model is an extension to the well-known lumped-parameter model (LPM) that incorporates a Langmuir–Hinshelwood (LH) kinetic concept dependent on VOC-odour concentration with diffusion limitation. The basic idea behind the model implementation is to couple the calculations of the two major processes in the VOC-odour/dust particle system: VOC-odour diffusion based on the homogeneous surface diffusion model (HSDM) and surface reaction based on the LH kinetics in an LPM scheme. The LPM employs Laplace transforms and gamma distributions of the rate coefficient to produce a lumped-parameter gamma model (LPGM) for kinetic equation of VOC-odour adsorption to airborne dust particles, whereas the HSDM incorporates the age and size distributions of airborne dust for evaluating the dust-borne VOC-odour dynamics. The integrate assessment of VOC-odour sorption kinetics and diffusion dynamics allows to relate the adsorption rate coefficient, reaction order, and surface effective diffusivity in a complex VOC-odour/dust particle system. The LPGM fitted well with the data obtained numerically from HSDM and successfully determined the adsorption rate coefficient and reaction order for each sorption process.