Peter Heidebrecht

Molten carbonate fuel cell (MCFC) with internal reforming: model-based analysis of cell dynamics

A transient mathematical model for a single counter-flow cell of a molten carbonate fuel cell has been developed. The model is based on the description of physical phenomena related to the concentration, temperature and potential field within the gas and the solid phases. Simplifications like plug flow and constant pressure in the gas phase as well as a lumped solid phase for energy balance are used. The rate expressions for the electrochemical reactions include mass transport resistances. The potential field is described by a set of algebraic equations allowing for the calculation of a spatially distributed potential field. Some results of the model are presented using the example of a stepwise change in load demand. The results include the steady states of the system as well as the transient functions of concentrations, temperatures, current densities and cell voltage. Due to the general notation of this model in dimensionless form it can easily be extended to describe cross-flow 2D cells as well as 3D stacks.

Dynamic Model of a Crossflow Molten Carbonate Fuel Cell with Direct Internal Reforming (DIR-MCFC)

A dynamic model for a single, spatially distributed molten carbonate fuel cell (MCFC) in cross-flow configuration is presented. The equations are formulated in dimensionless terms and are based on balances of mass, enthalpy, and charge. They include a detailed description of the electric potential field, reforming reactions inside the anode channel, mass transport resistance between the bulk gas phase and the electrochemical reaction zone inside the electrode pores, a catalytic combustion chamber, and the recycling of cathode exhaust gas. The simulation yields transient and spatially distributed profiles of temperatures, concentrations, gas fluxes, and current density as well as the cell voltage and the electric power over the full range of operating conditions. It is therefore a useful basis for system design, optimization, and control design of MCFC, applicable to any size of MCFC and transferable to other high-temperature fuel cells such as the solid oxide fuel cell. The complete set of model equations is presented in detail. Some exemplary steady state and transient simulation results are presented and compared to results from other models.

Conceptual Analysis of a Cyclic Water Gas Shift Reactor

The cyclic water gas shift reactor (CWGSR) is based on the repeated reduction of a fixed bed using a mixture of hydrogen and carbon monoxide and its subsequent oxidation with steam to produce pure hydrogen. The reactor is analyzed on a conceptual level using a spatially distributed, dynamic model. The model assumptions and the resulting model equations are presented, and important parameters are discussed. Simulation results show that the CWGSR reactor has a poor performance for co-flow configuration of the gases during reduction and oxidation phase, but the reverse-flow configuration seems to be a very attractive option. Parameter variation of the duration of the reduction phase indicates that especially short cycling times not only yield high energetic performance, but they also decrease thermal and morphological stress on the fixed bed material. In addition, the counter-flow CWGSR with short cycling times shows an inherent heat integration like in a Matros reactor, which opens attractive options for system integration of this reactor with other process steps. The behavior of the CWGSR is compared to a pressure swing adsorption reactor (PSA), which shows common features, but also significant differences between both types of cyclic fixed bed reactors.

Validation of a Mathematical Model Using an Industrial MCFC Plant

The parameter identification of a mathematical model of a molten carbonate fuel cell (MCFC) is presented. The model is spatially distributed in two dimensions and describes the strongly non-linear coupling of the temperature field and reactions inside a MCFC. It contains a high number of unknown parameters that need to be validated by experimental means. Therefore, measurements from an industrial 250 kW fuel cell power plant are used. This validation approach requires an elaborate strategy, which is presented in detail. The resulting set of parameters can predict the behavior of the MCFC over a broad operating range with a very good precision. The validated model is an important basis for further process optimization and for control system design.

Optimal design of non-linear Temperature Programmed Reduction (TPR) experiments

Abstract The experimental method of temperature programmed reduction (TPR) is extended by application of non-constant temperature gradients. An optimal control problem is formulated with the D-optimality criterion as the objective function and ordinary differential equations (ODEs) as constraints. The problem is solved for systems with a single reaction and with two consecutive reactions. The results show that optimal nonlinear temperature profiles promise to yield lower variances of the estimated parameters when compared to experiments with the best linear temperature profile. To improve the applicability of this approach under lab conditions, reduced problems are formulated with considerably fewer degrees of freedom that can be solved more reliably. The optima of the reduced problems approximate those of the full problems very well.

Multiscale CFD simulation of a methane steam reformer for optimization of the spatial catalyst distribution

Abstract This paper studies the coupled mass and heat transport as well as the reactions in an Indirect Internal Reforming (IIR) unit of a Molten Carbonate Fuel Cell (MCFC). The aims are first to identify the dominating processes for a specific design. Because temperature is one major issue in MCFC, the second aim is to predict the spatially distributed thermal behavior of the unit. In a first step several detailed models, describing only a small section of the IIR, are created. The results of these simulations, especially the temperature and gas composition, are discussed. In a second step the whole IIR unit is modeled. The results of the detailed models and some simplifications of the geometry are used to create this model.

Development of a Hierarchical Model Family for Molten Carbonate Fuel Cells with Direct Internal Reforming (DIR-MCFC)

This contribution deals with the mathematical modelling of a high temperature molten carbonate fuel cell (MCFC) and serves as a basis for the following three contributions of this mini-symposium. After a motivation and a short introduction into the working principle of the MCFC, the most important equations of the model are presented. This model is applied for optimisation purposes and as a basis for the derivation of reduced models specifically designed for different tasks.