Application of a mathematical model to predict simultaneous reactions in anaerobic plug-flow reactors as a primary treatment for constructed wetlands

Abstract

Anaerobic digestion technologies offer a set of advantages when they are implemented as a primary treatment phase prior to the use of constructed wetland systems in low cost wastewater facilities. The aim of this study is to describe a model capable of reflecting the complex functioning of anaerobic lagoons, subject to continuous flux in the feed pipe, taking into account that physicochemical properties are subject to a concentration gradient and biochemical ones to simultaneous reactions which depend on each other. Based on both Stokes and advection-diffusion-reaction equations, the proposed model includes twenty-one variables to describe hydraulic, physical, biochemical and physicochemical characteristics that take place in different points of the system and at different moments of time. Drawn up by the International Water Association, the anaerobic digestion model ADM1 is included for the purpose of incorporating the anaerobic processes in the calculation. The finite element method was used to solve the nonlinear, second order partial differential equations of the model. The calculation strategy was designed using a flowchart. Using the open-source FreeFem++ software, a simulation of the mathematical model, in bi-dimensional space, is presented to demonstrate the dynamic behaviour of the proposed model. This yields essential information about the performance of the substrate, cells, and the biochemical reaction products in each of the points within the reactor. Simulations show the potential of this methodology to carry out studies of the behaviour of each of the variables contemplated in the model, as well as comparative studies of the various possible options. In addition, this methodology can be used to help modify the behaviour of the variables based on digester geometry and the boundary values the system is subject to. From the results, it can be concluded that the proposed methodology can be a useful tool for calculating and designing the aforementioned synergistic systems of anaerobic digester plug-flow reactors and constructed wetlands.