Development of a Model for the Process of Anaerobic Digestion and Its Solution by the Modified Adomian Decomposition Met
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Development of a Model for the Process of Anaerobic Digestion and Its Solution by the Modified Adomian Decomposition Method M. I. Silva1 · A. L. De Bortoli2,3 Accepted: 13 November 2020 © Springer Nature India Private Limited 2020
Abstract Modeling the transformation of biomass into biogas is complex, because it involves a nonlinear and coupled set of ordinary differential equations. Thus, obtaining an analytical-numerical solution becomes attractive for this problem. In this paper, five chemical reactions are used to model the chemical kinetics of the anaerobic digestion process. The rate of production of each reaction is estimated by Gibbs free energy value. The equation system of the model is solved by the Modified Adomian Decomposition Method, applied to the time variable. The results obtained agree with the expected solution. Keywords Anaerobic digestion · Chemical kinetics · Differential equations system · Adomian decomposition method · Simulation
Introduction Many models of chemical, physical and biological processes are often expressed in terms of differential equations or systems of differential equations [1–3]. If the systems obtained in modeling these processes are non-linear, coupled or rigid, their solution becomes difficult and computationally expensive. For this reason, there is a need for efficient numerical methods to solve mathematical modeling problems.
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M. I. Silva [email protected] A. L. De Bortoli [email protected]
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Graduate Program in Applied Mathematics, Federal University of Rio Grande do Sul, Av. Bento Gonçalves 9500, Porto Alegre, RS, Brazil
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Graduate Program in Applied Mathematics, Federal University of Rio Grande do Sul, Porto Alegre, Brazil
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Graduate Program in Chemical Engineering, Federal University of Rio Grande do Sul, Porto Alegre, Brazil 0123456789().: V,-vol
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Int. J. Appl. Comput. Math
(2021) 7:5
For example, Djouad et al. [4] applied a second order Rosenbrock scheme for gas phase chemical kinetics, because the stiffness induced by different timescales magnitudes seriously restricts the integration time step of these models. Jajarmi et al. [5] presented a new mathematical model for the dengue fever outbreak based on a system of fractional differential equations. To simulate this model they used a new and efficient numerical method, in which they transform the system of equations into an equivalent integral equation. Then the trapezoidal method was used to approach the fractional integral operator. Currently, control techniques also are being used to optimize the solution of problems of great interest [6–8]. Among these applications, the Anaerobic Digestion (AD) process has become an important source of research. Anaerobic Digestion is a biochemical process of producing biogas, which is the biological degradation of biomass [9–11], the most abundant raw material in the world. Biomass is composed of substances of organic origin (plants, animals and microorganisms). Unlike fossil fuels, such as oil and coal, biomass is renewabl
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