A fractional mass transfer model for simulating VOC emissions from porous, dry building material. (April 2019) - Zhang, Yan
Abstract: Dry building material is a complex porous medium with a fractal structure. A developed fractional mass transfer model can accurately simulate anomalous diffusion in complex media, such as dry building material. In this work, a new time and space fractional diffusion model is first established to study the transport and emission behaviors of volatile organic compounds (VOCs) in a dry building material in an environmental chamber. In this model, the space fractional derivative is expressed by the weight coefficients of the upward and downward transfer probabilities, and the time fractional derivative and areal porosity of the material are introduced to describe anomalous diffusion. With the newly developed finite difference and parameter estimation methods, the present model can describe the early breakthrough and heavy-tailed phenomena well. Furthermore, the results of the present model show good agreement with the experimental data, as the error value (67.44 μg/m 3 ) is much less than that of Deng and Kim's model (190 μg/m 3 ). The advantages of long-term prediction are shown. Moreover, the effects of key parameters on VOC transport are revealed. Highlights: A mass transfer model is built with time and space fractional derivatives. A modified fractional Fick's law is developed for VOC emissions. Space fractional derivatives are expressed by different weight coefficients. The boundary condition of convective mass transfer related porosity is developed. A parameter estimation method is utilized to optimize the relevant parameters.