Investigation of multiphysics in tubular microbial fuel cells by coupled computational fluid dynamics with multi-order Butler–Volmer reactions
Graphical abstract
Introduction
Microbial fuel cells (MFCs) have emerged as a promising approach for sustainable wastewater treatment with bioenergy recovery [1]. In MFCs, organic materials are biologically degraded and electrical energy is produced through interaction between microbes and solid electron acceptors [2]. Various configurations of MFCs have been developed to optimize organics removal, energy recovery and operational flexibility [3], [4], [5], [6]. Among these proposed configurations, tubular MFC systems have been studied in great detail because of its potential advantages in microbial and substrate distribution, short distance between anode and cathode electrodes, and large surface area of separator materials [7], [8], [9], [10]. Interdependent multiphysics processes are present in tubular MFCs. For example, the hydrodynamics of electrolyte flow in the anodic chamber plays a key role in the substrate transport with associated effects on the activation overpotential distribution and chemical reactions, and vice versa. The activation overpotential and chemical reactions could contribute to the substrate consumption and transport, thereby impacting the flow field. Therefore, proper understanding of multiphysics phenomena in tubular MFCs can help guide the design and operation of such systems.
Mathematical modeling is a powerful tool to complement experiments and can be used to further understand the key processes that cannot be easily measured via experiments. Several models have been developed for studying metabolic pathway in anaerobic mixed culture fermentation and MFCs [11], [12], [13], and among them, computational fluid dynamics (CFD) can be used to numerically predict fluid flow, including mass transfer and reactions by solving various advection–diffusion equations. The application of CFD techniques in studying MFCs is still limited with very few publications in the past ten years. An early study combined MATLAB, COMSOL and a self-developed Java code to study the macro-scale homogeneous concentration evolution of soluble substrates and biomass in bulky liquid, and a micro-scale heterogeneous two dimensional biofilm model [14]. In this model, liquid velocity was calculated from the Navier–Stokes equations within a laminar flow regime, and it was found that localized proton accumulation was a rate-limiting factor on MFC output, and porous bio-electrode did not necessarily generate higher current as long as convective flow was absent. Unfortunately, those findings were not substantiated by any experimental results. Numerical simulations using CFD-ACE + demonstrated in a Y-shape mixer with inset cylinders, a lower aspect ratio (micro-channel depth-to-width) and larger inlet Reynolds number ratio (Reynolds number ratio based on inlet streams) could enhance flow mixing efficiency, due to the increased side wall effect and shear stress [15]. COMSOL Multiphysics was used to simulate laminar incompressible fluid flow in an MFC and demonstrated that enlarged biofilm attachment and increased shear rate within helical flow pathways accounted for the enhanced MFC performance [16]. Subsequently, three different helical flow channels (1.5, 5.4 and 10.8 mm, based on the spacing between helices) were experimentally investigated with a maximum power density of 11.63 W m−3 achieved in the smallest channel, which was confirmed by CFD modeling using a two layer k–ε eddy viscosity turbulence model [17]. A recent study simulated a cubic-shaped MFC containing twelve different internal structures (e.g., triangular/rectangular shape, number, length and upward/downward orientation) using ANSYS CFX [18]. Numerical results demonstrated that the maximum power density of 0.54 W m−2 could be achieved with the largest working space of 0.57 m2. The CFD prediction using ANSYS Fluent 12.1 revealed that better water distribution and biomass attachment could be developed with granular graphite and stainless steel meshes due to the minimized occurrence of preferential flow ways [19].
Although the aforementioned CFD-based MFC studies have provided useful information to understand MFC systems by analyzing micro- or macro-scaled flow conditions, there are still limitations with the CFD modeling that can be further addressed. For example, analyzing flow conditions alone fails to provide any information on activation overpotential and organic distribution, which can determine anodic surface reaction rate. A simplified electron transfer mechanism (e.g., external mediators) could be applied to electrochemically-active bacteria, which exists in a complex microbial community within the anodic chamber. Furthermore, time-dependent experimental data are essential to validate the model formulation. Herein, a coupled CFD with multi-order Butler–Volmer reaction model was proposed and validated to address some of the limitations, including a simple electron transfer mechanism, and an interaction between heterogeneous substrate and overpotential distribution on the anode surface. A direct contact electron transfer mechanism between microbes and the electrode surface was applied instead of an external mediator, because adding external mediator would not be feasible in wastewater treatments. Heterogeneous species distribution and electricity generation was predicted using the Butler–Volmer equations to include species concentration and activation overpotential on reaction rates. Real time-dependent experimental results were used for model validation. The results of this work were expected to demonstrate the viability of using a high-fidelity CFD approach to model the complex reaction physics in a tubular MFC.
Section snippets
MFC setup and operation
The MFC was constructed as a tubular reactor (32 cm long and 3.8 cm inner diameter) made of anion exchange membrane (AEM-Ultrex AMI 7001, Membrane International. Inc, Glen Rock, New Jersey, USA), as shown in Fig 1. Carbon cloth (Zoltek Corporation, St. Louis, MO, USA) was used as the material for both the anodic and cathodic electrodes. Before use, the carbon cloth was soaked in acetone solvent overnight and then heated for 30 min at 450 °C. The finished anode electrode (with effective surface
Governing equations
For steady-state, laminar, incompressible flow, the continuity equation iswhere is the velocity vector. The corresponding momentum equations for a Newtonian fluid areFrom left to right, the terms represent the momentum change in a control volume due to convection, pressure gradients, viscous diffusion, and gravity. In Eqs. (1), (2), the fluid properties, i.e., density ρ and dynamic viscosity μ, are calculated as volume-weighted mixture properties. However, due to
Determination of reaction order from polarization test
The results of the polarization test show that the current generation decreased from 27.3 to 4.8 mA after the external resistance was changed from 1 to 100 Ω sequentially, as shown in Fig. 3. By fitting an equation to the experimental polarization curve, the reaction order γ was estimated to be 6.4. The reaction order of 6.4 was used in the CFD simulations and the results are also shown in Fig. 3 as a symbol, with the average relative error of 7.4% between the experimental data and numerical
Conclusions
A coupled CFD-multi-order Butler Volmer reaction model has been proposed and validated in the present work. Convective flow conditions and associated heterogeneous species distributions were simulated using the improved CFD reaction model. Comparing to the conventional Monod-limitation equation, the multi-order model was able to predict current generation and organics removal in a simplified way. The model was experimentally validated by varying organic concentrations and the anolyte flow rate.
Acknowledgements
The MFC experiment of this research and J. Li was financially supported by a Grant from the National Science Foundation (#1358145). The authors acknowledge Advanced Research Computing at Virginia Tech (http://www.arc.vt.edu) for providing computational resources and technical support that have contributed to the results reported within this paper.
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Those authors contributed equally.