Entropy-Driven Spontaneous Biomethane Formation: A Unified Thermodynamic Framework for Buswell’s Equation


  •  Pong Kau Yuen    
  •  Cheng Man Diana Lau    
  •  Kuok In Gabriel Yuen    

Abstract

Background: Anaerobic digestion is a microbial-mediated biochemical reaction. Buswell’s equation representing anaerobic digestion is used to understand the degradability performance of organic matter and energy conversion. Thermodynamic parameters govern energy efficiency, temperature sensitivity, and process stability. While Buswell’s equation predicts stoichiometry, there is lack of study on the integration of enthalpy change, entropy change, and Gibbs free energy change across diverse organic matter.

Method: Enthalpy change of anaerobic digestion is calculated by using parameters of organic matter, mathematical framework of Buswell’s model, and thermochemical equation. Furthermore, thermodynamic equations are applied to quantify and understand the nature of standard enthalpy change, standard entropy change, and standard Gibbs free energy change of anaerobic digestion.

Results: Using methane as a standard reference, a set of 21 organic matter (CxHyOzClwNvSuPt) is selected. (i) Through the experimental heat of formation and stoichiometric coefficient of Buswell’s equation, the standard enthalpy change is found in the range of −303.19 kJ/mol (sucrose) and +186.42 kJ/mol (naphthalene). (ii) All the calculated standard entropy change are between +110.63 J/K (formic acid) and +2289.60 J/K (triphenyl phosphate), therefore anaerobic digestion is an entropy-dominated reaction. (iii) The calculated standard Gibbs free energy change is in the range of −885.32 kJ/mol (sucrose) and −57.74 kJ/mol (acetic acid), therefore anaerobic digestion is a spontaneous reaction. (iv) As temperature increases, the product of temperature times entropy change becomes more positive, and Gibbs free energy change to become more spontaneous.

Significance: Based on the collected data of standard heat of formation and standard absolute entropy, or standard Gibbs free energy formation of any chemical formula of organic matter, a unified thermodynamic framework of Buswell’s equation is established. Thermodynamic parameters of organic matter for anaerobic digestion can be quantified.



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