A Nonisothermal PEM Fuel Cell Model Including Two Water Transport Mechanisms in the Membrane

Author(s):  
K. Steinkamp ◽  
J. O. Schumacher ◽  
F. Goldsmith ◽  
M. Ohlberger ◽  
C. Ziegler

A dynamic two-phase flow model for proton exchange membrane fuel cells is presented. The two-dimensional model includes the two-phase flow of water (gaseous and liquid) in the gas diffusion layers (GDLs) and in the catalyst layers (CLs), as well as the transport of the species in the gas phase. The membrane model describes water transport in a perfluorinated-sulfonic-acid-ionomer-based membrane. Two transport modes of water in the membrane are considered, and appropriate coupling conditions to the porous CLs are formulated. Water transport through the membrane in the vapor equilibrated transport mode is described by a Grotthus mechanism, which is included as a macroscopic diffusion process. The driving force for water transport in the liquid equilibrated mode is due to a gradient in the hydraulic water pressure. Moreover, electro-osmotic drag of water is accounted for. The discretization of the resulting flow equations is done by a mixed finite element approach. Based on this method, the transport equations for the species in each phase are discretized by a finite volume scheme. The coupled mixed finite element/finite volume approach gives the spatially resolved water and gas saturation and the species concentrations. In order to describe the charge transport in the fuel cell, the Poisson equations for the electrons and protons are solved by using Galerkin finite element schemes. The electrochemical reactions in the catalyst layer are modeled with a simple Tafel approach via source/sink terms in the Poisson equations and in the mass balance equations. Heat transport is modeled in the GDLs, the CLs, and the membrane. Heat transport through the solid, liquid, and gas phases is included in the GDLs and the CLs. Heat transport in the membrane is described in the solid and liquid phases. Both heat conduction and heat convection are included in the model.

2007 ◽  
Vol 10 (06) ◽  
pp. 740-756 ◽  
Author(s):  
Stephan Konrad Matthai ◽  
Andrey A. Mezentsev ◽  
Mandefro Belayneh

Summary Fractured-reservoir relative permeability, water breakthrough, and recovery cannot be extrapolated from core samples, but computer simulations allow their quantification through the use of discrete fracture models at an intermediate scale. For this purpose, we represent intersecting naturally and stochastically generated fractures in massive or layered porous rock with an unstructured hybrid finite-element (FE) grid. We compute two-phase flow with an implicit FE/finite volume (FV) method (FE/FVM) to identify the emergent properties of this complex system. The results offer many important insights: Flow velocity varies by three to seven orders of magnitude and velocity spectra are multimodal, with significant overlaps between fracture- and matrix-flow domains. Residual saturations greatly exceed those that were initially assigned to the rock matrix. Total mobility is low over a wide saturation range and is very sensitive to small saturation changes. When fractures dominate the flow, but fracture porosity is low (10–3 to 1%), gridblock average relative permeabilities, kr, avg, cross over during saturation changes of less than 1%. Such upscaled kr, avg yield a convex, highly dispersive fractional-flow function without a shock. Its shape cannot be matched with any conventional model, and a new formalism based on the fracture/matrix flux ratio is proposed. Spontaneous imbibition during waterflooding occurs only over a small fraction of the total fracture/matrix-interface area because water imbibes only a limited number of fractures. Yet in some of these, flow will be sufficiently fast for this process to enhance recovery significantly. We also observe that a rate dependence of recovery and water breakthrough occurs earlier in transient-state flow than in steady-state flow. Introduction Oil is difficult to recover from fractured reservoirs; however, approximately 60% of the world's remaining oil resources reside in heterogeneously deformed formations (Beydoun 1998). The production dilemma is reflected in complex pressure and production histories, unpredictable couplings of wells independent of their spatial separation, rapidly changing flow rates and the risks of rapid water breakthrough, and low final recovery (Kazemi and Gilman 1993). Qualitatively, the main production obstacle is simple to conceptualize (Barenblatt et al. 1990): while the oil resides in the pores of the rock matrix, production-induced flow will occur predominantly in the fractures. However, they typically contribute less than 1% to the total fluid-saturated void space and are therefore rapidly invaded by the injected fluid. Once short-circuited by the injectant, the injection/production stream entrains only the oil that enters the fractures as a consequence of countercurrent imbibition (CCI) (Lu et al. 2006). The efficiency of this process is relatively well constrained by experimental work (Morrow and Mason 2001) and reproduced accurately by transfer functions (Lu et al. 2006). Rate predictions for fractured reservoirs require a further estimate of the area of the fracture/matrix interface captured by a shape factor (Kazemi et al. 1992). However, in cases where this measure is relatively well-constrained, predicted transfer rates appear to greatly exceed actual values. This observation suggests that, at any one time in the production history, transfer occurs over only a small part of the fracture/matrix interface. Furthermore, as is indicated by packer tests and temperature logs, only a small number of fractures contribute to the flow during production (Long and Billaux 1987, Barton 1995). This is confirmed by field-data-based numerical flow models (Matthäi and Belayneh 2004, Belayneh et al. 2006), highlighting that viscous flow in the rock matrix is usually significant, even if the fractures are well interconnected. All these findings conflict with the simple conceptual model, even qualitatively. How shall we replace it with something more accurate for the prediction of the behavior of fractured reservoirs?


Energy ◽  
2021 ◽  
Vol 218 ◽  
pp. 119543
Author(s):  
Jingxian Chen ◽  
Peihang Xu ◽  
Jie Lu ◽  
Tiancheng Ouyang ◽  
Chunlan Mo

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