{'fraction_non_alphanumeric': 0.03687150837988827, 'fraction_numerical': 0.004469273743016759, 'mean_word_length': 5.446043165467626, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Clayton Copula as an Alternative Perspective of Multi-Reaction Model

Abstract This study proposes to assess the effect of some relevant parameters of biomass pyrolysis on the numerical solutions of nthorder distributed activation energy model (DAEM) or multi reaction model (MRM). The two-step process mechanisms of pyrolysis is described by replacing the initial distribution function of f (E) with the Clayton copula. The upper limit (E∞) of ‘dE’ integral, activation energy (A), heating rate (m), and the shape and scale parameters of bivariate distribution function. Temperature ramp rate is assumed to vary linearly with time. Thermo-analytical data is obtained with the help of thermogravimetric (TG) analysis. Asymptotic technique is adopted to approximate double exponential and bivariate distribution function f (E1, E2), where E1and E2are the activation energies for bivariate scheme.