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

Heidebrecht, Peter; Sundmacher, Kai

doi:10.1016/s0009-2509(02)00644-9

Cited by 53 publications

(25 citation statements)

References 7 publications

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“…In the industrial sized fuel cells, the difference in the temperature distributions can be up to hundreds of degrees at the surface causing several disadvantages and difficulties. For the DIR-MCFC, with both advantages and disadvantages, many modellings (Wolf and Wilemski, 1983;Standaert et al, 1996;He, 1998;Yoshiba et al, 1998;Bosio et al, 1999;Park et al, 2002;Heidebrecht and Sundmacher, 2003;Wee and Lee, 2005) have been presented for decades. However, some of them have not quantitatively and directly described the results in relation to the three reactions at each point within the cell and others have not presented the experimental data for their modelling.…”

Section: Introductionmentioning

confidence: 99%

Simulation of the performance for the direct internal reforming molten carbonate fuel cell. Part I: distributions of temperature, energy transfer and current density

Wee

Lee

2006

Int. J. Energy Res.

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SUMMARYThis study examined the temperature distributions of the anode and cathode gases of the cell body as well as the current density distributions at each point of the direct internal reforming molten carbonate fuel cell (DIR-MCFC) using numerical modelling. The model was based on assumptions and experimental data from a 5 cm Â 5 cm sized unit cell operation. The results showed there was an approximately 138C temperature difference between the initial point (0, 0) and end point (1, 1) of the cell body and the temperature increased steadily along with the direction of the anode gas flow. The temperature distribution of the anode gases showed a similar trend to those of the cell body. The temperature of the anode gases was an average 118C lower than that of the cell body. The temperature distributions of cathode gases were relatively higher than those of the anode gases and the cell body. The temperature distributions at each point of the cell body, including the anode and cathode gases, could be explained by the different rates of the electrochemical, methane steam reforming and water-gas shift reactions at each point in the cell body. The current density distribution at the entrance of the cell was the highest at 290 mA cm À2, and decreased steadily to 150 mA cm À2 at the exit. These results were also confirmed by the amount of hydrogen reacted in the electrochemical reaction (referred to Part II). Finally, modelling simulations showed a non-uniform distribution of the temperature and current density throughout the DIR-MCFC were observed. In addition, it was confirmed that the distributions of the reaction rates and gas compositions at each point of the cell also showed a great deal of difference throughout the DIR-MCFC. The non-uniformity of these temperature distributions can lead to deterioration in the cell performance. These might provide the necessary information for solving these problems.

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Section: Introductionmentioning

confidence: 99%

Simulation of the performance for the direct internal reforming molten carbonate fuel cell. Part I: distributions of temperature, energy transfer and current density

Wee

Lee

2006

Int. J. Energy Res.

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“…are the heats of reaction for reaction (5), (6), (1) and (2), respectively; U AC , U CC are the electrical potentials of the anode and the cathode; U AM , U CM are the electrical potentials of the electrolyte membrane on the anode side and on the cathode side; I Cell is the total cell current; L y , L z are the lengths of the electrodes in the y and z directions; F is the Faraday constant.…”

Section: Energy Balance Of the Mcfcmentioning

confidence: 99%

Nonlinear Model Reduction of a Two‐Dimensional MCFC Model with Internal Reforming

Mangold¹,

Sheng

2004

Fuel Cells

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A reduced nonlinear model of a planar molten carbonate fuel cell is presented. The model is derived from a spatially distributed dynamic model of the cell by applying the Karhunen Loève Galerkin procedure. The reduced model is of considerably lower order than the original one and requires much less computation time. The comparison between the two models shows that the reduced model can describe the dynamics of the temperature field with sufficient accuracy and has good extrapolation qualities with respect to changes in the model parameters.

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“…A complex practical application is a model for molten carbonate fuel cells with e few second-order temperature equations and about 20 additional transportation equations, see Heidebrecht and Sundmacher [24] or Pesch et el. [34].…”

Section: Introductionmentioning

confidence: 99%

Parameter Identification in One‐Dimensional Partial Differential Algebraic Equations

Schittkowski

2007

GAMM-Mitteilungen

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In this paper we discuss a couple of situations, where algebraic equations are to be attached to a system of one-dimensional partial differential equations. Besides of models leading directly to algebraic equations because of the underlying practical background, for example in case of stationary equations, there are many others where the specific mathematical structure requires a certain reformulation leading to time-independent equations. To be able to apply our approach to a large class of real-life problems, we have to take into account flux formulations, constraints, switching points, different integration areas with transition conditions, and coupled ordinary differential algebraic equations (DAEs), for example. The system of partial differential algebraic equations (PDAEs) is discretized by the method of lines leading to a large system of differential algebraic equations which can be solved by any available implicit integration method. Standard difference formulas are applied to discretize first and second partial derivatives, and upwind formulae are used for transport equations. Proceeding from given experimental data, i.e., observation times and measurements, the minimum least squares distance of measured data from a fitting criterion is computed, which depends on the solution of the system of PDAEs. Parameters to be identified can be part of the differential equations, initial, transition, or boundary conditions, coupled DAEs, constraints, fitting criterion, etc. Also the switching points can become optimization variables. The resulting least squares problem is solved by an adapted sequential quadratic programming (SQP) algorithm which retains typical features of a classical Gauss-Newton method by retaining robustness and fast convergence speed of SQP methods. The mathematical structure of the identification problems is outlined in detail, and we present a number of case studies to illustrate the different model classes which can be treated by our approach.

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

Cited by 53 publications

References 7 publications

Simulation of the performance for the direct internal reforming molten carbonate fuel cell. Part I: distributions of temperature, energy transfer and current density

Simulation of the performance for the direct internal reforming molten carbonate fuel cell. Part I: distributions of temperature, energy transfer and current density

Nonlinear Model Reduction of a Two‐Dimensional MCFC Model with Internal Reforming

Parameter Identification in One‐Dimensional Partial Differential Algebraic Equations

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