Analysis of deviation from classical $$d_0^2$$-law for biochar conversion in an oxygen-enriched and temperature-controlled environment

Abstract

AbstractCombustion of char has conventionally been reported to be diffusion controlled. Analytically, the process is reported to follow second order initial diametric ($$d_0$$ d 0 ) dependence $$(d_0^\beta ; \beta =2)$$ ( d 0 β ; β = 2 ) for both single-film (no CO combustion) and two-film models (CO burns in a concentric sphere over the particle). However, experimental investigations indicate deviation from classical diffusion limit with $$\beta$$ β exceeding 2.00 and going as high as 2.37. Videography investigations depict luminous film engulfing the particle for certain Temperature-Oxygen concentration-Particle diameter combinations (for which, $$\beta \ge 2$$ β ≥ 2 ). The observed deviation is hypothesized to convective resistance offered by the CO generated on the surface to motion of $$CO_2$$ C O 2 towards the surface. This results in reduced $$CO_2$$ C O 2 concentration at the surface with enhanced conversion time being the implication (hence, $$\beta >2$$ β > 2 ). Such convective resistance remains unaccounted for in the prevailing analytical models. The CO dominated film thickness is enhanced with temperature and reactant concentration, increasing the convective resistance, and further deviating from $$d_0^2$$ d 0 2 behaviour. The analytical solution shows that in presence of a convectively expanding CO film, total conversion time is a function of film diameter while also being dependent on $$d_0^2$$ d 0 2 . The hypothesis is validated by comparing analytical estimates with experimentally observed film diameter and conversion time.