Biogas production modeling: Developing a logistic equation satisfying the zero initial condition

IF 9 1区 工程技术 Q1 ENERGY & FUELS
M. Meraz , P. Castilla , E.J. Vernon-Carter , J. Alvarez-Ramirez
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Abstract

Biogas produced by the fermentation of organic waste has emerged as a viable alternative for displacing fossil fuels. The accurate characterization of the biogas production kinetics is an important issue for management, optimization, and control purposes. The classical logistic equation (CLE) and its modifications are widely used for modeling biogas production. Although a tight-fitting can be obtained, these models have the physical inconsistency of predicting a non-zero value of initial biogas production. This work fixes the problem found with CLE by deriving a new function, named biogas logistic equation (BLE), from a simple kinetics scheme. The derivation departs from the differential equations for substrate, biomass and biogas obtained via the law of mass action to reduce these equations to a differential equation having an analytical solution. The parameters of the BLE are linked to the parameters of the kinetics scheme, having a meaningful physical interpretation. An extension to the multi-substrate case was proposed, leading to an expression with the flexibility of detecting phase transitions in the biogas production dynamics. Experimental data from the literature showed that the proposed logistic equation has superior fitting performance than the modified Gompertz equations and in most instances to the CLE.
沼气生产模型:建立满足零初始条件的logistic方程
由有机废物发酵产生的沼气已成为取代化石燃料的可行替代品。准确表征沼气生产动力学是管理、优化和控制的重要问题。经典logistic方程(CLE)及其修正被广泛应用于模拟沼气生产。虽然可以得到一个紧密的拟合,但这些模型在预测初始沼气产量的非零值方面存在物理上的不一致性。这项工作通过从一个简单的动力学方案中导出一个名为沼气逻辑方程(BLE)的新函数来解决CLE发现的问题。推导从质量作用定律得到的基质、生物量和沼气的微分方程出发,将这些方程简化为具有解析解的微分方程。BLE的参数与动力学方案的参数相关联,具有有意义的物理解释。提出了对多基质情况的扩展,从而可以灵活地检测沼气生产动态中的相变。来自文献的实验数据表明,所提出的logistic方程比修正的Gompertz方程具有更好的拟合性能,并且在大多数情况下对CLE具有更好的拟合性能。
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来源期刊
Renewable Energy
Renewable Energy 工程技术-能源与燃料
CiteScore
18.40
自引率
9.20%
发文量
1955
审稿时长
6.6 months
期刊介绍: Renewable Energy journal is dedicated to advancing knowledge and disseminating insights on various topics and technologies within renewable energy systems and components. Our mission is to support researchers, engineers, economists, manufacturers, NGOs, associations, and societies in staying updated on new developments in their respective fields and applying alternative energy solutions to current practices. As an international, multidisciplinary journal in renewable energy engineering and research, we strive to be a premier peer-reviewed platform and a trusted source of original research and reviews in the field of renewable energy. Join us in our endeavor to drive innovation and progress in sustainable energy solutions.
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