Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Heuristic methods in optimization of selected parameters of Two-Phase Anaerobic Digestion (TPAD) model Karol Postawa ⁎ , Jerzy Szczygieł, Marek Kułażyński Departament of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland ARTICLE INFO Keywords: Biogas TPAD Model Parameters Thermophilic Mesophilic Anaerobic digestion ABSTRACT The article aims to define and optimize the key parameters of Two-Phase Anaerobic Digestion model (TPAD). This kind of anaerobic digestion utilizes a separation of selected process steps in two, different reactors. The reason for this modification is to achieve the best possible conditions for all reactions and transformations – which are significantly different for hydrolysis/acidogenesis and acetogenesis/methanogenesis. It can be done differently: by pH control, selective inoculation and so one. However this article focus on temperature phasing, in which the first step is kept in thermophilic conditions, which promotes a high rate of hydrolysis, while the second is mesophilic, usually in higher pH, which expands optimal conditions for methane generating archaea. Thus the model parameters in each of two reactors have to be adjusted to the specific environmental conditions. In this work, as the most important, three reaction rates were recognized: for hydrolysis (k dis ), for propionate- related conversions (k _ m pro ), and acetate-related conversions (k _ m ac ). The optimization leads to the conclusion that in the value of k _ m pro and k _ m ac decrease with the temperature, while the temperature-dependence coef- ficient is accordingly 0.019487 ° − C 1 and 0.01068 ° − C 1 . The hydrolysis rate indicated the opposite trend, and the coefficient value was -0.0534 ° − C 1 . The reference reaction rates are defined for 35 ° C and are respectively: 7.964313, 12.3536, 1.048912 − d 1 . To calculate these values, a two-stage heuristic algorithm was utilized, starting with initial values based on selected other models available in the literature. The data to validation was taken from the most complete and most recent publications and scientific databases. 1. Introduction Biogas is a renewable fuel produced from organic feedstock in the process of anaerobic digestion. Usually, it is described as four-stages conversion (hydrolysis, acetogenesis, acetogenesis, methanogenesis) in which different species of bacteria are involved [1]. They also indicate different sensibility for temperature, so the environment needs to be adjusted to ensure their survivability and efficiency of biocatalysis. In the topic of biogas production, two types of bacteria are the most im- portant – meso- and thermophilic. The first, typically requires the temperature around 35 ° C, while the second one a significantly higher – even around 55 ° C. The thermophilic group is also more sensitive for any changes [2], as it’s less diversified [3], so it is more difficult to control fully thermophilic fermentation. In this work, the scope will be focused on Two-Phase Anaerobic Digestion (TPAD), and to be precise, its temperature-phased variant [4,5]. This method extends the concept of separating the processes which take place during digestion to improve the overall performance and quality of the product. In a classical biogas plant, all conversions – hydrolysis, acidogenesis, acetogenesis, and methanogenesis [6,7], occur in the same reactor. As a result, the conditions, need to be compatible with all types of microorganisms. In the TPAD system, the production is split into two sequent tanks. First is kept in thermophilic conditions – usually in the temperature around 55 ° C, which significantly promotes hydrolysis [8]. The second, in mesophilic conditions, so at a lower temperature, fits perfectly with the requirements of methanogens [9]. As a consequence, better overall performance of all conversions is achieved. The mathematical modeling is an interesting and applicative tool for predicting the efficiency of real installations with biological systems [10]. In the age of pervasive digitalization, computational methods become more and more important. In the opposite of traditional, in- scale experiment, the model returns result optimized for the final size. What’s even more interesting in this approach – it let to perform screening of many possible configurations with low cost and a very short time. Thus it can be a part of the decision making in designing installation [11]. In the presence of this fact, it can be said that de- veloping such methods can be the future of engineering. https://doi.org/10.1016/j.fuel.2020.118257 Received 7 October 2019; Received in revised form 24 April 2020; Accepted 27 May 2020 ⁎ Corresponding author. E-mail address: karol.postawa@pwr.edu.pl (K. Postawa). Fuel 281 (2020) 118257 0016-2361/ © 2020 Elsevier Ltd. All rights reserved. T