# Simultaneous numerical solution of particle scale and reactor

Several models are available for the overall thermal conductivity inside the particle [30], [31] and [32]. It is important to take into account for the effect of macroscopic (1–10 μm) pore structure on thermal conductivity due to the differences in isotropic wood pellets and anisotropic wood logs. We applied the model developed by Kollmann and Cote [31] and [32], which attributes the contribution of gas-phase, solid-phase, and Bruceine A across the pore on the overall thermal conductivity by porosity. We applied the weighting bridge-factor to account for the macroscopic pore structure, which can be expressed as the mixture of the direction parallel to and perpendicular to fibers. Thermal conductivities in the ideal directions (parallel/perpendicular) can be expressed in the same way as the electrical conductance of parallel and series circuits. The bridge factor for wood pellets was 0.33 [33], and wood logs was 0.68 [34].

Different methods are available to incorporate particle shrinkage in the particle model [9], [35] and [27]. We assumed that radial direction of shrinkage occurs uniformly over the particle during conversion because of numerical stability. Temporary radius of the particle was simply calculated as the product of initial radius, final shrinkage ratio, and the temporary overall conversion. The final shrinkage ratio, the ratio of the particle radius before and after the devolatilization, was experimentally determined in this study, which was around 0.75 for wood pellets and 0.8 for wood logs.