Transient mass diffusion and convection of volatile organic compounds (VOCs) from walls is an important issue for air quality in buildings. In the present work, a new model of these processes that captures mass transport within the wall structure is presented and applied for a ventilated enclosure. Porous wall structures composed of two solid phases (one carrying the VOC and one inert) and one fluid phase air are generated by the Controllable Structure Generation Scheme (CSGS) based on discrete Gaussian quadrature space and velocity. Mesoscopic scale parallel non-dimensional lattice Boltzmann method (P-NDLBM) simulations are performed for relevant ranges of wall porosity, Reynolds and Schmidt numbers for a two-dimensional enclosure with a top inlet and bottom outlets. The effect of the wall structure on mass transfer in the enclosure"is investigated for two wall structures: type (A) a wall with randomly immersed particles, and type (B) a shape-separated wall structure. Results include transient VOC concentration and streamlines in the porous wall and the enclosure for a vary of porosities and diffusivities for each phase. The pore structure and porosity of the wall have significant impact on mass transfer. Type (B) structures are more favorable for rapid mass transfer within the wall. (C) 2017 Elsevier Ltd. All rights reserved.