Numerical Solution of nth Order DAEM for Kinetic Study of Lignocellulosic Biomass Pyrolysis

The aim of the present study was to explore the most optimal configuration to numerically solve Distributed Activation Energy Models (DAEMs). DAEMs are useful in obtaining the kinetic parameters in non-isothermal kinetic studies using a thermogravimetry analyzer (TGA). Compared to other kinetic models, DAEMs provide an additional kinetic parameter that quantifies the extent of the reaction (σ) for each reaction’s mean activation energy (E ̅). Although DAEMs are efficacious in kinetic studies, solving DAEMs numerically is challenging. The DAEM equation includes double integration with respect to activation energy and temperature, which involves various numerical discretizations. Previously, many researchers utilized a DAEM to explicate complex reactions such as lignocellulosic biomass pyrolysis. However, most of them have yet to propose a numerical approach to solve DAEMs. Therefore, by exploring multiple numerical calculation configurations, here we present a general structure to numerically solve nth order and first-order DAEMs. The exploration includes determining the optimal integration limit of activation energy and the discretization of activation energy and temperature integration. From the investigation, we came up with a configuration that limits the integration of activation energy from E ̅-3σ to E ̅+3σ. Meanwhile, the number of integration points for temperature and activation energy must be 51 and 21, respectively. By using this configuration, DAEM can be utilized optimally in kinetic studies.