Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
15th International Conference on Nuclear Engineering Nagoya, Japan, April 22-26, 2007 ICONE15-10639 MODELING A FILTER PRESS ELECTROLYZER FOR THE WESTINGHOUSE HYBRID CYCLE USING TWO COUPLED CODES DRAFT Florent Jomard Commissariat à l’Énergie Atomique DEN/DTEC/STCF/LGCI Site de Marcoule BP 17171 30207 Bagnols sur Cèze, France e-mail: [email protected] Jean-Pierre Feraud Commissariat à l’Énergie Atomique DEN/DTEC/STCF/LGCI Site de Marcoule BP 17171 30207 Bagnols sur Cèze, France e-mail: [email protected] Jacques Morandini Astek Rhone-Alpes 1 place du Verseau 38130 Echirolles, France e-mail: [email protected] Yves Du Terrail Couvat Laboratoire EPM, Madylam 1340 Rue de la Piscine Domaine Universitaire 38400 Saint Martin d’Hères, France e-mail: [email protected] Jean-Pierre Caire LEPMI, ENSEEG 1130 Rue de la Piscine 38402 Saint Martin d’Hères, France e-mail: [email protected] Keywords: model, Westinghouse cycle, coupling, electrolyzer compartments separated by a membrane. Hydrogen is reduced at the cathode and SO2 is oxidized at the anode. In a complex reactor of this type the main coupled physical phenomena involved are forced convection of the electrolyte flows, a plume of hydrogen bubbles that modifies the local electrolyte conductivity, and irreversible processes (Joule effect, overpotentials, etc.) that contribute to local overheating. The secondary current distribution was modeled with a commercial FEM code, Flux Expert®, which was customized with specific finite interfacial elements capable of describing the potential discontinuity associated with the electrochemical overpotential. Since the finite-element method is not capable of properly describing the complex two-phase flows in the cathode compartment, the Fluent® CFD code was used for thermohydraulic computations. In this way each physical phenomenon was modeled using the best numerical method. The coupling implements an ABSTRACT Mass production of hydrogen is a major issue for the coming decades particularly to decrease greenhouse gas production. The development of fourth-generation high-temperature nuclear reactors has led to renewed interest for hydrogen production. In France, the CEA is investigating new processes using nuclear reactors such as the Westinghouse hybrid cycle [Brecher, 1977]. A recent study was devoted to electrical modeling of the hydrogen electrolyzer, which is the key unit of this process. An extensive literature review led to the choice of electrolyte and electrode materials, and the preliminary design of a new cell for production of hydrogen was evaluated. This paper describes an improved model coupling the electrical and thermal phenomena with hydrodynamics in the electrolyzer. The hydrogen electrolyzer chosen here is a filter press design comprising a stack of cathode and anode 1 Copyright © 2007 by JSME iterative process in which each code computes the physical data it has to transmit to the other one: the two-phase thermohydraulic problem is solved by Fluent® using the Flux Expert® current density and heat sources; the secondary distribution and heat losses are solved by Flux Expert® using Fluent® temperature field and flow velocities. The computations use two different meshes and interpolations from of one mesh to the other require a 3D algorithm to localize the calculation points. A set of dedicated library routines was developed for process initiation, message passing, and synchronization of the two codes. The first results obtained with the two coupled commercial codes give realistic distributions for electrical current density, gas fraction and velocity in the electrolyzer. A design optimization phase is in progress before proceeding to the final design and manufacturing of a pilot electrolyzer. out to model a filter press electrolyzer for producing hydrogen via the Westinghouse hybrid cycle. In view of the complexity of the strongly coupled phenomena that occur in this type of electrolyzer, no numerical method is currently capable of satisfactorily describing both the thermohydraulic and electrochemical aspects of the electrolyzer. The idea behind this work was to account for the coupled physical phenomena by coupling two software packages that together are perfectly suitable for describing the physical problems encountered. Flux Expert® and Fluent® were coupled to solve a highly nonlinear steady-state problem involving the coupling of equations from electrokinetics, fluid mechanics, and thermal analysis. The following solution was adopted for this purpose: – Solve the electrokinetic equation using the Flux Expert® finite-element code. One feature of this model is the use of specific “interfacial finite elements” developed to handle the overpotential at the electrode/electrolyte interfaces. – Solve the fluid mechanics equations of two-phase turbulent flow in the electrolytes where gas bubbles are generated by electrolysis. This step is performed using the Fluent® code, which includes recently developed effective models for modeling compressible and incompressible two-phase fluid flows. In Fluent®, the energy equation in terms of temperature can be associated with the fluid equations and solved at the same time. The coupling is handled and each calculation is initiated through the following steps: – Create the models. – Load the models in their respective codes. – Start the coupled simulation: first Fluent® then Flux Expert® or vice-versa. NOMENCLATURE u Velocity vector (m·s-1) Density (kg/m-3) g Gas concentration σ;= Viscous stress tensor (Pa) g Acceleration of gravity (m·s-2) T Temperature (K) Cp Heat capacity (J·K-1·kg-1) k Thermal conductivity (W·m-1·K-1) QV Volume heat sources (W·m-3) QS Surface heat sources (W·m-3) S Dirac surface distribution J Current density (A·m-2) jn Current density normal to the interface (A·m-2) Electrical conductivity (-1·m-1) V Electrical scalar potential (V) V Electrical potential jump (V) t Time (s) n Normal vector S Dirac surface distribution Nabla vector differential operator ( x , y , z ) 1. 2. COUPLING PHENOMENA AND ELECTROLYZER MODELING The physics of the electrolyzer can be broken down here into a two-phase thermohydraulic problem and an electrokinetic problem with activation overpotentials. These physical phenomena are schematically described in the following paragraphs. INTRODUCTION 2.1 Coupling of Physical Phenomena The thermohydraulic phenomena are described by the Navier-Stokes continuity and heat transfer equations: u (u )u g t ( u) 0 t T cp ( u T ) ( k T ) QV QS S t The hydraulic aspect consists of a two-phase problem involving a continuous liquid phase, sulfuric Within the framework of the Generation IV International Forum the Commissariat à l’Énergie Atomique (CEA) is investigating the possibility of producing hydrogen in industrial quantities. One of the main objectives is to take advantage of the very hightemperature heat source (> 1100 K) made available at low cost by new nuclear reactors such as the VHTR. Large-scale hydrogen production is also being considered using thermochemical or hybrid cycles such as the Westinghouse cycle, which is based on sulfur chemistry and electrochemical reduction of protons to form hydrogen. This paper describes the work carried 2 Copyright © 2007 by JSME acid, and a dispersed gas phase, the bubbles generated at the cathode/catholyte interface. The electrokinetic phenomena with activation overpotentials are described by the current conservation equation and by overpotential laws at the electrode/bath interfaces: (V ) 0 The electrokinetic problem with overpotentials is solved using Flux Expert®, which gives the electrical potential and current density fields and the losses due to Joule effect over the finite-element mesh. Flux Expert® requires the following inputs: – T over the full calculation domain – g in the fluid. The following results are provided by Flux Expert®: – J and V at the electrode boundary – QS at the electrode interfaces – QV in the electrically conductive zones. Communication between the two codes is based on the use of a simple and robust message-passing library developed to allow two calculation codes to communicate without requiring them to be merged into a single executable. The codes can thus be installed on one or even two different UNIX machines. The two programs can share the same physical inputs and results. The message-passing function calls in this library were developed as subroutines in Fluent® and Flux Expert® specially designed for coupling. The shared data include: – Initial coupling definition data: the two programs initially exchange the coordinates of the points for which the expected physical quantities will be computed. – Coupling data, which are exchanged throughout the resolution process. Before each iteration, the two programs exchange the values of the physical quantities computed during the preceding step, for those required in the next iteration. – Solution strategy data, i.e. the data that must be exchanged between the programs to reach the same solution: number of iterations, calculated precision, etc., or events such as the end of the solution. The algorithms developed are mainly location and interpolation algorithms. Each of the calculation points for the volume and surface heat sources of the Fluent® mesh must be localized on the Flux Expert® mesh. At the beginning of the iterations the heat sources are interpolated over these points and supplied to Fluent®, while the gas volume fraction and temperature must be calculated by Fluent® for the Flux Expert® mesh points and transmitted to Flux Expert®. The combined operating procedure for the two codes is shown schematically in Figure 1. “UDF” in the Fluent® portion refers to User-Defined Functions in Fluent®: the coupling routines are shown in green in the flowchart. V f ( J n ) where V represents the overpotential, the electrical potential discontinuity V at the electrode/electrolyte interface. This constitutes a system of nonlinear partial differential equations with the following unknowns: { u , P, αg, T, V}. The nonlinearities are due to the differential operators (the velocity transport term, for example) but also to the physical properties (overpotentials in particular) and the coupling quantities, which depend on one of the unknowns: – Gas production at the electrode interfaces contributes to the electrolyte motion; the production is proportional to the current density (Faraday’s law). – The presence of a bubble plume modifies the local electrical conductivity of the electrolyte. – Losses by Joule effect result in a heat release. – The physical properties, such as the electrical and thermal conductivity of the bath, depend on the temperature and on the local bubble production. 2.2 Software Coupling The two types of physical phenomena described above are solved using Fluent® and Flux Expert® with different meshes (which may be structured or unstructured) and in some cases even in different calculation domains. Although the hydraulic problem is generally solved under transient conditions and the electrokinetic problem under steady-state conditions, the coupling implemented can deal with both steady-state and transient problems. The two-phase thermohydraulic problem is solved using Fluent®, which gives the velocity, pressure, and temperature fields and gas volume fraction (bubble concentration) on the finite-volume mesh. Fluent® requires the following inputs: – Jn at the electrode boundary; the current density can be used to compute the gas production term at the interface. – QS at the electrode/electrolyte interfaces; this is the source term per unit area in the heat transfer equation corresponding to the heat release related to the overpotential irreversibility. – QV in the electrically conductive zones, i.e. the power density irreversibly generated by Joule effect; this is the volume source term in the heat transfer equation. The following results are provided by Fluent ®: – T over the full calculation domain – g in the fluid. 3. PILOT ELECTROLYZER GEOMETRY AND CALCULATION HYPOTHESES The filter press electrolyzer investigated here is a laboratory prototype. The electrolyzer was modeled to partially optimize the design of a small-scale pilot before fabrication. The device operating principle is shown in Figure 2. 3 Copyright © 2007 by JSME Main memory Main memory UDF Swap functions FEcoupling.c UDF FEcoupling.c FLUENT® where an additional hydrogen release zone ( in light blue in Figure 2) had to be defined for Fluent® to simulate hydrogen release at the electrode. Within the adjustable thickness of zone the gas release is calculated according to the local current density. 3.1 Calculation Hypotheses The electrolyzer measures 0.04 × 0.013 × 0.16 m. The code is a 3D model. The study was carried out under steady-state conditions. The physical properties of all the electrolyzer components (, , k, Cp) are temperature-dependent. The anolyte consists only of a single-phase fluid, in this case a sulfuric acid solution. The catholyte consists of a two-phase fluid formed by a sulfuric acid solution with small-diameter (about 100 µm) hydrogen bubbles produced by an electrochemical reaction at the cathode. All the outer walls of the electrolyzer are thermally insulated. The two fluids with different sulfuric acid concentrations pass through the vertical countercurrent electrolyzer at equivalent rates. The Flux Expert® input data are representative of the operating conditions frequently described in the literature [Goosen, 2003; Lu, 1980], i.e. a fluid inlet temperature of 323 K and a pressure of 1 bar. The sulfuric acid mass concentrations are 30% in the catholyte and 50% in the anolyte. The overpotential values at current densities of 2000 A·m-2 are about 0.6 V at the anode and 0.05 V at the cathode, which is very low compared with other types of electrolysis [Struck, 1980; Roustan, 1998]. Data files FLUX EXPERT ® Property operators : prxxxx.F Swap functions Main memory Main memory Figure 1. Fluent®–Flux Expert® coupling flowchart H2SO4 H2SO4 + SO2 H2 3.2 Boundary Conditions To simplify the fluid mechanics computations, fluid inlet and outlets at right angles in the cell were not taken into account. A uniform velocity profile of 0.07 m·s-1 is therefore applied at the inlets to the cathode and anode compartments. The boundary conditions for the two codes are shown in Figure 3. 0.16m + - Overpotential Area 160 0V 2000 -2 A.m z x -1 V = 0.07 m·s , 323K 0.04m Figure 2. Electrolyzer operating principle ( cathode; hydrogen release zone; catholyte; membrane; anolyte; anode ANODE CATHOLYTE membran CATHODE CATHOLYTE ANODE Hydrogen area Z -3 (10 m) The electrolyzer mesh was prepared in Gambit®. The electrolyzer geometric definitions for Fluent® and Flux Expert® are practically identical except for the gas release zone at the cathode /catholyte interface CATHOLYTE 0.013m membran CATHODE H+ +H2SO4 H2SO4 + SO2 CATHOLYTE y -3 Y (10 m) 0 1.5 6.5 6.6 11.2 V =13.1 0.07 m·s , 323K -1 Figure 3. Boundary conditions 4 Copyright © 2007 by JSME 4. nates of the integration points, after which the physical values are exchanged. A sudden increase in the residuals is observed after 40 iterations in Fluent, i.e. at the second iteration for Flux Expert®, corresponding to the transmission of fresh data between the two codes. For example, a data exchange concerning the mean temperature in the electrolyzer for each iteration in Fluent® is shown in Figure 5. 1 2 3 FE Fluent data swap T (K) MODELING RESULTS FOR A FILTER PRESS ELECTROLYZER PRODUCING 5 NL·h-1 4.1 Code Coupling Behavior The interaction between the two codes is demonstrated by the convergence of the computational residuals with successive iterations. This data is available in Fluent®. The residual is computed as follows: A A1 Résidual i 1 Ai 2 where Ai+1 is the value of the variable at iteration i+1 and Ai its value at iteration i. As fluid mechanics models are more complex to solve than electrokinetic models, exchanges between the two codes are performed at each iteration for Flux Expert® and only every twenty iterations for Fluent®. The ratio between the number of iterations in the two codes is user-adjustable. Figure 4 shows the variation of the residuals in Fluent® from iteration 1 to iteration 180 (data transfers from Flux Expert® to Fluent® corresponding to iterations 1 to 9 in Flux Expert®). 1 2 Figure 5. Mean temperature at each iteration 3 FE Fluent data swap Figure 5 reveals a temperature rise in steps of decreasing amplitude with each successive iteration, and confirms the convergence of the temperature parameter. 4.2 Results of Heat Transfer and Fluid Mechanics Computations with Fluent® The initial results concerning the thermohydraulic behavior of the filter press electrolyzer are shown here under operating and modeling conditions that are subject to optimization and improvement in subsequent work. The thermal behavior of the electrolyzer is shown in graded color in Figure 6: Catholyte Residuals continuity u residual sulphuric acid u residual hydrogen v residual sulphuric acid v residual hydrogen w residual sulphuric acid w residual hydrogen T1 residual sulphuric acid T2 residual hydrogen K residual sulphuric acid residual sulphuric acid (1–K) residual hydrogen Anolyte Figure 4. Variation of residuals over 180 iterations in Fluent, where: Figure 4 illustrates the quality of the system convergence. Data transfers between the coupled codes occur at each iteration or every 20 iterations, depending on the direction. During the first exchange after 20 iterations of Fluent®, the codes exchange the coordi- Catholyte Anolyte Figure 6. Graded color temperature map 5 Copyright © 2007 by JSME The temperature depends on the volume heat sources due to losses by Joule effect, on convective transport in the countercurrent liquid flows, and on heat exchange by conduction in the solids and liquids. Countercurrent flow was selected here because it allows greater control over the heat transfer properties of the electrolyzer operating as a filter press plate-type heat exchanger. A cross-sectional view of the electrolyzer through the middle of each compartment provides a better indication of the temperature rise versus height. 0 .1 6 0 .1 4 0 .1 2 T e m p e r a tur e (K ) H e ig h t (m ) Catholyte flow. Fluent allows the use of a quantity of substance term that represents the electrochemically produced hydrogen. The gas released at the cathode in bubbles 100 µm in diameter is transported by the bath and exits at the top of the electrolyzer. Figure 8 shows the variation of the gas volume fraction. Cathode H2 catholyte 0 .1 A n o ly te C a th o ly te 0 .0 8 3 mm 0 .0 6 0 .0 4 Figure 8. Graded color representation of the gas volume fraction 0 .0 2 0 322 324 Figure 8 illustrates the hydrogen production along the interface between cathode and the sulfuric acid solution (catholyte); the gas volume fraction increases along the cathode wall. It is interesting to note that the bubble plume proposed by the first model appears too localized at the cathode/catholyte interface. The local maximum gas volume fraction (which reaches 97%) appears overestimated. This problem is probably attributable to the definition of zone 2 in Figure 1 being too narrow. If spherical hydrogen bubbles are assumed to be stacked in a hexagonal close-packed or face-centered cubic structure at the electrode, the hydrogen volume fraction should not exceed 74% [Arnaud, 1988]. The velocity vector plot in Figure 9 shows the influence of the gas volume fraction on the electrolyte flow velocity, notably the following aspects: – The velocity in the anode compartment varies only slightly and tends toward two parabolic profiles. – The velocity in the cathode compartment varies significantly with the gas volume fraction: the greater the quantity of gas, the higher the velocity along the electrode. At a constant feed rate, this observation is directly related to the apparent restriction of the free flow cross section. The maximum velocity reached is 0.825 m·s-1, which represents an acceleration by a factor of 12 between the inlet and outlet velocity along the cathode. 326 Anolyte Figure 7. Temperature versus height in the anolyte and catholyte Figure 7 shows a temperature variation in both electrolyzer compartments comparable to that observed between the heat sink and source in a plate-type heat exchanger [Roure, 2007]. Figures 5 and 6 show a temperature rise limited to 4 K between the coldest point (liquid inlets) and the hottest (anolyte outlet). The temperature rise inside the electrolyzer reaches a maximum where the electrical conductivity of the cell is the lowest, and where the liquid flow velocity is also the lowest. For lack of experimental data, the results shown here do not yet take into account the surface heat sources generated by overpotentials, although their effect on the temperature can be estimated at about 6 to 8 K given the overpotentials obtained (see paragraph 4.4). Similarly, it would be of interest in future calculations to take into account the heat produced by exothermic reactions such as dissolution in the anolyte of the H2SO4 formed by oxidation of SO2. 4.3 Results of Two-Phase Flow Calculations with Fluent® Fluent® was selected for modeling the hydrodynamic characteristics in order to allow for two-phase 6 Copyright © 2007 by JSME Although this initial numeric result must still be confirmed by experimental tests, it highlights the importance of optimizing the anode overpotential to lower the cost of hydrogen production. Electrical potential (V) Anolyte Catholyte Cathode Anode 0,73 V 0.6 Cathodique Potential jump 0.03 V 0.3 Anodique potential jump 0.47 V 0 0 0.00655 0.0131 Lenght (m) -1 Figure 9. Vector plot of electrolyte velocity (m.s ) at the top of the cell Figure 11. Potential variation between the cathode and anode 4.4 Results of Electrokinetic Simulations with Flux Expert® The data supplied to Flux Expert® by Fluent® are used to calculate the electrical potential of the cell taking into account the gas volume fraction and the local temperature. The potential gradient in the electrolyzer is shown in graded color in Figure 10. Cathode 5. CONCLUSIONS AND OUTLOOK The model described here was designed to simulate the operation of the electrolyzer that is the fundamental component in the Westinghouse process for producing hydrogen by a hybrid electrochemical-thermochemical cycle at high temperature (VHT reactor). The filter press electrolyzer selected for its compact size was modeled by coupling the Fluent® and Flux Expert® codes. This approach allowed us to take into account under optimum conditions both the electrochemical phenomena (overpotentials in particular) and the complex two-phase flow due to hydrogen production at the cathode. The calculations showed the significant influence of fluid mechanics and gas production on the reactor heat transfer properties. The fluid flow velocity along the cathode increased by a factor of 12 in the reactor due to the release of hydrogen bubbles. This finding of particular importance for the preliminary design of a future fully optimized electrolyzer was one of the principal results obtained by coupling the Flux Expert® and Fluent® codes. The overpotentials and highly exothermic chemical reactions were not taken into account with sufficient accuracy for lack of experimental measurement data, but the coupled model is capable of doing so without difficulty. The initial calculations showed that the plume of hydrogen bubbles was apparently slightly too narrow. Population balance models allowing for bubble coalescence and breakage should also be taken into account through the development of specific physical operators. Finally, the two-phase flow model will have to be calibrated by bubble concentration measurements along the cathode in the laboratory pilot device specified from the model. Anode Potential (V) Figure 10. Electrical potential variation in the cell Observing the secondary current distribution reveals the positive overpotential (yellow) due to the irreversibility of electrochemical oxidation of SO2 into H2SO4. This phenomenon is detailed in the cross section below by plotting the potential variation at the center of the electrolyzer along a horizontal path. Figure 11 shows the individual contributions to the overall potential of the electrolysis cell. Here the anode overpotential accounts for 70% of the cell potential. Hydrogen production results in a potential drop of 30 mV, or only 4% of the cell potential. 7 Copyright © 2007 by JSME of Electrochemical Society, 127/12, 2610–2616, 1980. Roure A., Caire J.P., ICONE 15, 10493 Roustan, H., Caire, J.P., Nicolas, F., Morandini, J., Improving the numerical stability of advection equations in a fluid: example of an electrolyzer, CHISA’98, 12th International Congress of Chemical and Process Engineering, Prague, Czech Republic, 23–28 August 1998. Struck, B.D., Junginger, R., Boltersdorf, D. and Gehrmann, J., The anodic oxidation of sulfur dioxide in the sulfuric acid hybrid cycle, International Journal of Hydrogen Energy, 5, 487– 497, 1980. REFERENCES Arnaud, P., Cours de chimie physique, Dunod, 1988 Brecher, L.E., Spewock, S. and Warde, C.J., Westinghouse sulfur cycle for the thermochemical decomposition of water, International Journal of Hydrogen Energy, 2, 7–15, Pergamon Press, 1977. Goosen, J.E., Lahoda, E.J., Matzie, R.A. and Mazzoccoli, J.P., Improvements in Westinghouse process for hydrogen production, pp.1509–1513, New Orleans, LA, USA, November 16-20, 2003. Lu, P.W.T. and Ammon, R.L., An investigation of electrode materials for the anodic oxidation of sulfur dioxide in concentrated sulfuric acid, Journal 8 Copyright © 2007 by JSME