Improve thermal performance of thermosyphon solar water heater using trnsys model for small building
14- Preliminary study of the implementation of a biogas production unit by mathematical modeling: case study of the abiergue basin
FOTSA-MBOGNE D. J.*, KAMBA-TATSINKOU F. G., NGASSOUM Martin B.
Department of Mathematics and Computer Science, National Higher School of Agro-Industrial Science, University of Ngaoundéré, PO Box 512 Ngaoundéré, Cameroon
*Email: jauresfotsa@gmail.com
Résumé :
Le septième objectif de développement durable (ODD) fixé par les Nations Unies (ONU) est de "garantir l'accès de tous à des services énergétiques fiables, durables et modernes à un coût abordable". Cet objectif revêt une importance particulière pour les pays en développement tels que le Cameroun. Des études montrent que le bassin d'Abiergué présente certains potentiels pour le développement d'unités de biogaz centralisées. L’objet du présent travail est de proposer une modélisation mathématique simple pour simuler le fonctionnement d’une telle unité et prendre les meilleures décisions de fonctionnement. Nous proposons un modèle d'équation différentielle de la cinétique de méthanisation prenant en compte les entrées, les sous-processus impliqués et les processus sortants (bioréacteur en mode continu). Nous réalisons une étude qualitative du modèle proposé afin d'identifier les conditions de fonctionnement admissibles. Grâce aux données disponibles dans la littérature, nous déterminons les paramètres du modèle. Nous décidons de la viabilité d'une installation de biogaz et de ses caractéristiques. Notre contribution est triple. Nous fournissons un modèle transposable, qui est simple mais réaliste pour simuler la mise en place d’une unité de production de biogaz. Les paramètres de ce modèle liés à l'étude de cas sont déterminés. Les conditions de viabilité de l'unité de traitement sont données et illustrées à l'aide d'un diagramme de fonctionnement. Ce travail met en évidence une approche plus ou moins précise des études de faisabilité de la mise en place d'une unité de production de biogaz. Une demande est faite pour le cas du bassin d'Aviergué.
Mots-clés: Bioréacteur, dynamique des espèces, équilibre de fonctionnement, stabilité Abstract
The seventh Sustainable Development Goal (SDG) set by the United Nations (UN) is to
"ensure access for all to reliable, sustainable and modern energy services at affordable cost".
This objective is of particular importance for developing countries such as Cameroon. Studies show that the Abiergué basin has some potentials for the development of centralized biogas units. The purpose of the present work is to propose a simple mathematical modeling to simulate the operation of such a unit and to make optimal operating decisions. We propose a differential equation model of the methanization kinetics taking into account the inputs, the subprocesses involved, and the outgoing ones (continuous mode bioreactor). We make a qualitative study of the proposed model in order to identify the permissible operating conditions. Thanks to the data available in the literature, we determine the parameters of the model. We decide on the viability of a biogas plant and its characteristics. Our contribution is threefold. We provide a transposable model, which is simple but realistic to simulate the
implementation of a biogas production unit is proposed. The parameters of this model related to the case study are determined. Viability conditions of the treatment unit are given and illustrated by means of an operating diagram. This work highlights a more or less precise approach to feasibility studies of the implementation of a biogas production unit. An application is done for the case of the Abiergué basin.
Keywords: Bioreactor, species dynamics, functioning equilibrium, stability a- Introduction
Needs of sustainable energies ...
_ Economic growth and sustained transformation in Africa
_ Condition of sustainability: massive investment in the energy sector
_ According to the website "planète énergies1" initiated by the multi-national Total _ Fossil energies represent more than 2/3 of the global electricity mix
_ Hydraulics intervening for more than 16%
_ Hydropower, renewable energies represent less than 5%
_ Not in accordance of United Nations Sustainable Development Goal (UN-SDG 7):
Affordable and Clean Energy.
1https://www.planete-energies.com/fr
Solution trials ...
_ Recently, [Ngono-Emgbwang et al., 2019] conducted a study on:
_ Potential for waste recovery, particularly in the Abiergué Watershed located in Cameroon
_ Mapping the sources of waste in order to optimally choose the potential site for the installation of a centralized anaerobic methanation production unit
_ Following [Gerardi, 2003], Anaerobic digesters provide many attractive features:
_ Production of biomethane
_ Reduction in volume and weight of sludges _ Reduction of sludge handling and disposal costs
_ Reduction of the numbers of pathogens due to relatively high Temperatures Reluctance to anaerobic digestion ...
_ Anaerobic digestion unfortunately has an unwarranted reputation as an unstable and di_cult-to-control process:
_ Lack of adequate knowledge of anaerobic digester microbiology (At least 300 di_erent species of bacteria are found in the feces of a single individual)
_ Lack of proper operational data
_ Designing an e_cient and reliable anaerobic digestion unit requires some attention ! _ Our goal is to propose a rigorous and simplistic approach aiming at giving conditions to respect to guarantee the perenniality and the stability of the production of biogas given a potential in substrate and methanogenic bacteria.
Objectives of this work ...
_ Specific objectives:
_ Provide a simplistic and realistic model of biogas production
_ Determining conditions to respect to guarantee the perenniality and the stability of the system
_ Application to the case of the Abiergué Watershed b- Mathematical Modeling of biogas production process
The model ...
_ We consider the following model (1):
Mathematical Modeling ...
Table 1: summarizes the parameters appearing in the model (1).
The growth function m is assumed to have the Monod form :
The hypotheses of the model ...
_ Single species of methanogenic microorganisms
_ Single source of substrate. This is not too restrictive if we assume that before entering the bioreactor the substrate is homogenized with the same proportions of its constituents.
_ Population of methanogenic microorganisms renews itself without any external supply. The reason is that it could be di_cult to guarantee a regular supply of those methanogenic microorganisms.
c- Qualitative analysis of the model Steady states ...
A stability result ...
An optimization result ...
Optimal dilution rate ...
Theorem
For given values of k > 0 and Sin, the optimal production of biogas is obtained when
d- Application to the Abiergué Watershed _ Rough description of Abiergué Watershed
_ Entirely located in Yaoundé (political capital of Cameroon) with eleven districts (Cité verte, a portion of Nkolbisson, Oyomabang, Etetack, Nkolbikok, Mokolo, Carrière, Madagascar, Melen, Nkolso'o, Madagascar)
_ A population estimated at approximately 557164 inhabitants _ From statistics provided in literature we get
e- Conclusion and prospects
_ Our main goal was to propose a rigorous and simplistic approach aiming at giving conditions to respect to guarantee the perenniality and the stability of the production of biogas given a potential in substrate and methanogenic bacteria.
_ What we achieved
_ Providing differential equation model of biogas production
_ Determining conditions to respect to guarantee the stability of the system biogas production at an optimal cadence
_ Starting estimation of key parameters for a biogas treatment plan to be installed into the Abiergu_e Watershed
_ Several prospects
_ Continue to estimate key parameters already started _ Extending the model to several species of microorganisms
_ Take into account operational factor such as pH, temperatures and the whole J. Harmand, C. Lobry, A. Rapaport, and T. Sari (2017). The Chemostat: Mathematical Theory of Microorganism Cultures. John Wiley & Sons.
M.C Ngono Emgbwang, C. Kapseu and M. Ngassoum (2019). Implementation of a Decision Support Tool for the Development of Centralised Methanation in Abiergué Watershed.
International Journal of Innovative Science and Research Technology, Volume 4, Issue 7.
Short biography :
Dr. FOTSA-MBOGNE David Jaurès has been a senior lecturer since 2017 in the Department of Mathematics and Computer Science at the National School of Agro-Industrial Sciences, University of Ngaoundere, Cameroon. Previously, he was Assistant lecturer from 2011 to 2017 in the same department. Since 2011, Dr. FOTSA has been in charge of teaching the first level of the "Industrial Maintenance and Production"
sector.He obtained his Bachelor's Degree in Computer Science
(Specialization in Scientific Computing), his Master's of Science Degree in Mathematical Engineering (specialty in Mathematical Epidemiology) and his Ph.D Degree in Applied Mathematics (Mathematical Specialty), all at the University of Ngaoundéré. Dr. FOTSA-MBOGNE focuses on research in mathematical modeling of dynamic systems (deterministic or stochastic), control (finite or asymptotic control, optimization) and observability (state and parameter estimation, observers , filters) of these. Dr FOTSA-MBOGNE offers several courses in algorithmics and programming, operational research and optimization, numerical analysis, statistics and probabilities, and analysis. Moreover, to make learning easier for students, he has undertaken to make free tutorials and course notes available a
web page that he administers and updates very regularly
(https://sites.google.com/site/mjdavidfotsa/home).