Environmental and political pressure to mitigate the effects of global warming has fostered a growing interest in renewable and clean energy resources, particularly in the development of Ethanol- and Hydrogen-based transportation and energy generation solutions. While Ethanol can be derived from US-based resources such as corn via well known processes, the quest for efficient and economical Hydrogen sources continues. Autothermal reactors that combine, in a single unit, endothermic Hydrogen generation and exothermic reactions that create the thermal energy necessary to support it, represent a very promising technology in this field. These devices are compact and efficient, lending themselves naturally to on-board or on-site hydrogen production for transportation/power applications.

The above applications typically assume that hydrogen can be produced at a variable rate that can satisfy the changing demands of a downstream consumer. Consequently, steady-state performance and safety criteria notwithstanding, autothermal reactors need to meet stringent transient performance requirements. Prior work [1,5] has considered the dynamics of unidirectional autothermal reactors featuring hydrogen generation via endothermic methane steam reforming and water gas shift, supported by the catalytic combustion of methane. Using singular perturbation arguments, it was demonstrated that such systems exhibit a two time scale behavior. Also, it was shown that, ceteris paribus, counter-current designs, whereby the reforming mixture and the fuel flow in opposite directions in dedicated channels of a monolith reactor, exhibit are more robust to disturbances and production rate changes than their co-current counterparts. It was also shown that, in the absence of a control system, autothermal reactors-- regardless of flow configuration--suffer a significant performance degradation (measured in terms of energy efficiency and conversion rates) when operated in a transient manner.

Owing to its ability to handle non-square systems with constraints, model predictive control (MPC) constitutes an obvious choice for tackling the stringent operating requirements and limited degrees of freedom of autothermal reactors. Traditional linear MPC lends itself well to slow-varying systems that are operated in the vicinity of a steady-state, being, however, is ill-suited to highly nonlinear systems operated in a transient manner. In view of the above, the present work addresses the control of the transient operation of autothermal reactors within the framework of Nonlinear Model Predictive Control (NMPC). Initially, we define a performance index based on the energy efficiency of the reactor. Subsequently, the index is embedded in the formulation of the nonlinear control problem, thereby addressing, in a unified manner, the operational, dynamic and economic constraints typically posed by autothermal reactors for hydrogen production.

NMPC implementations are oftentimes hindered by the dimensionality of the underlying optimization problems. In the second part of the work, we present the use of modern, fast optimization strategies [2] to alleviate these difficulties. Exploiting the special structure of the optimization problems that arise in NMPC [3], the OptCon package [4] (based on the HQP[2] solver) provides an extremely efficient solution strategy based on a multiple shooting algorithm. Within this approach, the control interval is divided into a series of grid points. Using local control parameterizations, a shooting method is employed to transition between successive points. The differential equations and the cost function on these time intervals are integrated independently during each optimization iteration, based on the current guess of the controller's output, while the continuity/consistency of the final state trajectory is enforced with additional constraints. This multistage formulation is advantageous to the efficient application of the sequential quadratic programming (SQP)-type solver in HQP, leading to very short solution times. A sparse interior point algorithm is used for the efficient treatment of the linear-quadratic subproblems in the nonlinear SQP iterations.

The proposed control strategy is demonstrated on a detailed, first principles reactor model [5]. Our simulation results exhibit a significant increase (compared to the open loop case) in the dynamic performance of the reactor, as well as improved operation economics, while the short control execution times represent an incentive for real-time implementation.

References

[1] Baldea, M. and Daoutidis, P., Dynamics and Control of Autothermal Reactors for the Production of Hydrogen, Chem. Eng. Sci., 64, 2007, 3218-3230

[2] Franke, R., Arnold, E., and Linke, H., HQP: A solver for nonlinearly constrained large-scale optimization. http://hqp.source¬forge.net.

[3] Diehl, M., Bock, H. G., Schloeder, J. P., Findeisen, R., Nagy, Z. K., and Allgoewer, F., Real-time optimization and nonlinear model predictive control of processes governed by differential algebraic equations, Journal of Process Control, 12, 577-585, 2002.

[4] Nagy, Z. K., Mahn, B., Franke, R., and Allgower, F., Efficient output feedback nonlinear model predictive control for temperature control of industrial batch reactors, Control Engineering Practice, 15, 839-859, 2007.

[5] Baldea, M., Zanfir, M. and Daoutidis, P. Counter-Current Autothermal Reactors For Hydrogen Generation: Modeling And Dynamic Analysis, In Preparation