Effectiveness factor analysis for non-isothermal biomass pyrolysis: a transient model for single pellet systems

The effectiveness factor (EF) concept is extended for non-catalytic pyrolysis reactions involving no gaseous reactant. A fully transient, non-isothermal model is formulated for a single biomass pellet by incorporating structural evolution, porosity variation, and temperature-dependent properties. The study presented a theoretical analysis of EF for different values of Lewis number (L _e), heat of reaction (G factor), Arrhenius number (Ē), Thiele modulus (ϕ), and heating rate (γ). The model was solved using two approaches (i) a numerical solution and (ii) an approximate solution based on the Quantized Method (QM). Good agreement was observed between the numerical and QM solutions for pellet conversion within the investigated thermicity factor range of -0.25 ≤ β ≤ 0.225, while the effectiveness factors predicted by the two approaches differed by a maximum of 7.14%. Furthermore, analytical asymptotic limits show that EF approaches unity for homogeneous behavior, while it drops to as low as 0.005 (200-fold reduction in reaction rate) under shrinking-core conditions. For practical applications in fixed-bed gasifiers, a pellet diameter of 4 mm is recommended under the investigated conditions (L _e = 0.25, G = -6), providing a favorable balance between heat and hydrodynamic constraints. The developed EF correlations enable rapid estimation of effective pyrolysis rates without detailed multiscale modeling, offering a computationally efficient tool for reactor design and optimization in biomass gasification systems.