2. Methods
Microchannel reactors exchange heat between chemically reacting fluid streams. In this design, enclosed channels are formed by stacking plates separated by spacers, and the stack is fitted with appropriate headers so that alternating channels contain the reaction fluid with heat exchange fluid in the intermediate channels. The reaction channels can be filled with catalyst, and the heat exchange channels can have a structured packing to increase the heat exchange area. Another approach to increasing the surface area for reaction on each side of the separating plate is to add fins or other surface features. Indeed, this approach is adopted in plate-type reactor designs. Although somewhat successful, the reactor designs still add complexity and the alternating coupled reaction chambers continue to restrict the overall size of each chamber. All of these designs share the same general flow geometry where thermal energy transfers between chemically reacting fluid streams that flow parallel to and on opposite sides of a separating plate [29, 30]. These reactor designs suffer from a fundamental limitation resulting from the flow configuration in which a reacting stream flows parallel to a heat transfer surface through which the majority of heat is transferred perpendicular to the direction of fluid flow [31, 32]. Regardless of the reaction taking place in the reaction channels, its reaction rate will vary along the flow length of that channel due to changes in concentration and temperature. Balancing the heat requirements of an endothermic reaction with heat generated by an exothermic reaction flowing parallel to and on the opposite side of a separating plate is extraordinarily difficult since the endothermic reaction is likely to have a very different dependence upon concentration and temperature than the endothermic reaction. Along the flow length of the plate that divides these reactions, the heat flux through the plate that is perpendicular to fluid flow will vary due to temperature and reaction rate differences along the flow length of the plate. Since the thermally coupled reactions are so closely coupled, neither reaction can run at a significantly different reaction rate at any point along the channel length. Thus, each reaction will exhibit a peak in reaction rate at nearly the same position within the reactor with slower reaction rates before and after this peak, which leads to the need for a long reactor channel to ensure complete conversion. A specific example of this reaction rate problem encountered in the parallel flow arrangement is demonstrated by attempts to drive endothermic steam reforming with exothermic combustion in microchannel and alternating parallel plate reactors [33, 34]. A convenient way to supply heat is to couple the endothermic reaction with an exothermic combustion reaction in the heat exchange channels [35, 36]. Thus, the stacked reactor becomes an alternating series of endothermic and exothermic reactors separated by thin heat exchange walls. Unfortunately, the combustion reaction is difficult to control with convenient combustion catalysts and fuels, and most of the combustion occurs near the fuel inlet. This uneven combustion results in uneven heat transfer to the endothermic reaction and poor overall reactor performance.
Various approaches are directed to resolving the problem of uneven combustion, typically such approaches add extraordinary complexity to the stack design so as to attempt to distribute combustion along the heat exchange surface [37, 38]. The key feature of these designs is to add a fuel dispersion channel between each unit stack consisting of combustor-reformer-combustor [39, 40]. The plate separating the combustor and dispersion channel is a porous plate that is intended to facilitate even distribution of fuel across the entire combustion chamber. Even still, the combustion reaction is somewhat uneven because air is introduced to the combustion channels at one end rather than evenly like the fuel. Moreover, the increased complexity of this design requires the addition of multiple plates and internal feed channels to keep air out of the dispersion channels, which adds to system mass, construction costs, and system limitations. A further disadvantage of the parallel flow reactor geometry is that the operating temperatures of the two reactions must be similar since the separate streams are separated only by the thin separating and heat transfer plate. For example, maintaining the temperature of methanol steam reforming at or below a temperature of 300 °C is very difficult when heat is supplied by catalytic combustion, which typically runs above a temperature of 500 °C. Thermally matching the reactions is still further complicated by the inherent temperature gradients that are present along the flow length of the reaction channel. Any solution directed to resolving this thermal matching problem in a parallel flow configuration will add significant complexity or mass to the system [41, 42]. Further disadvantages of the parallel flow reactor geometry include the complicated hindering necessary to distribute and separate flows through alternating channels and the difficulty of independently sizing the exothermic and endothermic sides of the coupled reactor [43, 44]. Since these reactors comprise an alternating stack of reformer and combustor reactor channels, it is difficult to match the size and requirements for each side. In essence, the coupled reactors cannot be separated since the alternating channel design precludes separation of reformer and combustor. The shortcomings of microchannel reactors are fundamentally related to the direct coupling of reforming and combustion reactions by performing them on opposite sides of the separating plate in a parallel flow configuration. Many of the preceding reactor examples pursue a combination of microchannel reactor technology with heat exchange in a direction perpendicular to the reacting fluid flow to achieve a compact catalytic reactor [45, 46]. This combination places several demands on the design, requiring additional complexity or mass for effective operation [47, 48]. Therefore, a new reactor design that maintains effective operation in a compact device constructed with less complexity would be greatly beneficial. Such a design has, until now, remained elusive. The present study aims to resolve the foregoing problems and concerns while providing still further advantages.
The reactor performance is evaluated by performing numerical simulations using computational fluid dynamics. Computational fluid dynamics is the study of fluid flows and the effect of fluid flows on processes such as heat transfer or chemical reactions in fluid systems. Computational fluid dynamics facilitates the analysis of systems from relatively simple fluid flows through stationary channels and pipes, to complex systems with moving boundaries such as combustible flow in internal combustion or jet engines. Physical characteristics of fluid motion are defined by fundamental governing equations, including conservation relationships such as those of mass and momentum, which may be expressed as partial differential equations. Computational fluid dynamics facilitates the determination and analysis of fluid system properties by providing for the numerical solution of these governing equations using discrete approximations. A method is provided for treating boundary cells in a computational fluid dynamic process employing a computational mesh of cells that represents a fluid system, each cell having faces, vertices and a volume, the system characterized by governing equations and having a set of boundaries. More specifically, computational fluid dynamics methods provide for the discretization of the differential forms of the governing equations over a computational mesh that represents the fluid domain. Converting partial differential equations into a system of algebraic equations allows respective solutions to be calculated through the application of numerical methods. The algebraic equations may be solved in light of specific initial conditions and boundary-condition constraints to simulate the system fluid flow and determine the values of system properties and parameters.
In the context of computational fluid dynamics analysis, arbitrary Lagrangian Eulerian methods for numerically solving the related mathematical equations incorporate advantages of Lagrangian and Eulerian solution approaches, while minimizing their disadvantages. For example, arbitrary Lagrangian Eulerian techniques provide for the precise interface definition of Lagrangian methods, while allowing displacement of a computational mesh over time, as in purely Eulerian methods, without requiring frequent remeshing. Taking advantage of the Eulerian characteristic wherein a fluid continuum under study moves relative to a fixed computational mesh facilitates accurate analysis of large distortions in the fluid motion. As a result, more accurate treatment of greater-scale distortions of the mesh is possible than would be through purely Lagrangian solution techniques, while the resolution of flow details and precision of interface definition are improved over purely Eulerian methods. Arbitrary Lagrangian Eulerian solution algorithms may be used in combination with body-fitted mesh fluid system models, where the mesh edges conform to the boundaries of a fluid system being studied. However, despite their flexibility for allowing advantageous positioning of nodes in the computational domain, disadvantages of using body-fitted meshes include difficulties of generating the mesh and automating the meshing process. Moreover, structured body-fitted meshes cannot easily be generated for systems with complex geometries, such as those that include curved walls, inlets, outlets, or moving parts. Traditional methods to overcome these difficulties, such as increasing cell density, stretching and distorting cell shapes to fit geometric irregularities of the system, or utilizing unstructured meshes are liable to reduce solution accuracy and stability, as well as to increase compute time.
As an alternative to body-fitted methods, immersed-boundary or embedded-boundary approaches is employed in computational fluid dynamics analysis. Such methods facilitate the use of a Cartesian computational mesh throughout fluid system, with special treatment of cells near the system boundary, albeit without significant stretching and distortion of cells relative to the coordinate axes. Employing immersed or embedded boundary mesh generation techniques results in reduced mesh irregularity, as well as relative simplicity and increased speed in an automated mesh generation process. Since the sources of solution error decrease as a mesh approaches a perfect Cartesian alignment, embedded boundary approaches improve solution accuracy and stability. There are two classes of immersed boundary approaches. One immersed boundary approach involves the use of irregularly-shaped cells, at the fluid system boundaries, and the computational algorithm includes methods to account for these irregularly-shaped cells. In such approaches, cells are cut linearly along system boundary lines or surfaces that intersect the cells. An advantage of the cut cell approach is that it tracks the exact location of moving boundaries so that the computational domain conforms to the physical geometry. Thus, it is straightforward to apply a moving boundary velocity directly to let the interior fluid feel the compression and expansion effect due to the boundary motion. However, a disadvantage of the cut cell approach is that the flow transport computational algorithms need to be modified extensively to account for a large variety of irregularly-reshaped cells at the boundaries. The cutting or reshaping of cells to fit the system geometry may also result in a large number of relatively tiny cells near system boundaries, which may cause deterioration of solution accuracy and stability.