Modelling Mass Transfer And Reaction In Porous Materials Using Discrete And Continuum Approaches

Porous materials are widely used in catalysis and separation, because of their high specific surface area and abundant pore structures. To reasonably design and optimize catalysts and adsorbents for better performance, modelling mass transfer and reaction in porous materials is needed. This work applies discrete and continuum modelling approaches to study mass transfer and reaction in porous materials, and would serve to guide the controllable synthesis of porous materials. The main contents and results are summarized as follows:(1) Construction of discrete models. Pore network model and pore-throat model, which can precisely describe spatial distributions of pores and catalytic active sites, are built. Besides, a cutting algorithm is proposed, and this algorithm can generate pore network models and pore-throat models with arbitrary outer shapes (e.g., sphere, cylinder, and hollow cylinder, which reflect structures of many industrial porous materials). This cutting algorithm is simple, efficient, and versatile, and can reduce the computational time for generating pore models to a very large extent. Embedding equations of mass transfer and reaction into the pore models, discrete models are completed. These discrete models can simulate gas-solid, liquid-solid, and gas-liquid-solid reactions in porous catalysts, and therefore are highly flexible.(2) Construction of continuum models. A novel pore model, which is able to describe spatial distributions of pores and catalytic active sites to some extent, is proposed. Dynamic continuum models, which describe mass transfer and reaction at particle level, crystal level, and particle/crystal level respectively, are constructed. These models can be applied to study catalytic processes in catalysts and adsorption/desorption processes in adsorbents.(3) Pore blocking effects in porous catalysts. A discrete model is proposed to quantify these effects on multiphase reactions in porous catalysts. The discrete model can describe coupled mass transfer, reaction, capillary condensation, and pore blocking in porous catalyst particles. This discrete model is validated by comparing with experiments and a continuum model, for the hydrogenation of benzene to cyclohexane in Pd/γ-alumina catalyst particles. The results show that pore blocking significantly affects the effectiveness factor and can contribute to up to 50% of the hysteresis loop area for multiphase reactions, indicating that pore blocking must be accounted for. Moreover, these pore blocking effects are significantly enhanced when the pore network is poorly connected and the pore size distribution is wide.(4) Pore network effects on performance of catalysts. A discrete model is employed to probe these effects, and hydrogenation of benzene to cyclohexane over Pd/y-alumina is chosen as the reaction system. These pore network structures of catalysts are statistical parameters of pore network structures (i.e., pellet size, average connectivity, and pore size distribution), spatial distributions of pore size, and bidisperse pore structures. The simulations display hysteresis loops of the effectiveness factor as a function of benzene partial pressure in the bulk or particle temperature. The hysteresis loop area can be significantly enlarged when pore connectivity is low, volume-averaged pore radius is small, and pore size distribution is wide; the hysteresis loop area is also strongly affected by spatial distributions of pore size and bidisperse pore structures. Pore network structures directly influence mass transfer, capillary condensation, and pore blocking, and subsequently pass on these influences to the hysteresis loop of the effectiveness factor.(5) Pore network effects on performance of adsorbents. A continuum model is used to optimize the spatial distribution of pore size and porosity in adsorbents. The adsorption/desorption performance of adsorbents is evaluated under a square wave concentration perturbation with a wide range of cycle period (10-100,000s) for the adsorption of n-pentane on 5 A zeolite adsorbents. The uniformly distributed pore size and porosity is the preferred spatial structure, which is confirmed by using four empirical tortuosity-porosity relations. Further optimization of the uniform structure shows that its optimal average porosity is in the range of 0.4 to 0.6 when the perturbation cycle period is between 100 s and 2000 s and the volume-averaged pore diameter is between 10 nm and 150 nm. The relationships between optimal average porosity, cycle period and volume-averaged pore diameter are determined and explained.(6) Approximations of micropore diffusion model for adsorbents. Average diffusivity linear driving force (AD-LDF) approximation and concentration-dependent diffusivity linear driving force (CDD-LDF) approximation are introduced to simplify the precise model describing the concentration-dependent micropore diffusion in bidisperse adsorbents, and are compared with the precise model in predicting the dynamics of a sorption process under two different perturbations (i.e., step change perturbations and sinusoidal wave perturbation) with different concentrations imposed at the exterior surface of the bidisperse adsorbent. The performance of the two approximations is validated by the precise model and experiments. The AD-LDF performs better in step adsorption and CDD-LDF does better in step desorption. Under sinusoidal wave perturbation, the CDD-LDF performs better. The different levels of consistency of the two approximations with the precise model are attributed to the different definitions of the diffusivities.