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.