Modeling and experimental investigation of the spatial heat transfer in a plate reactor with meandering millichannels
Graphical abstract
Introduction
More than 20 years after its foundation as a scientific discipline during the late 90 s, micro process engineering has come of age in the meantime [1]. The advantages of miniaturization are verified by numerous studies [[2], [3], [4]]. Nowadays, several commercial suppliers of micro and millistructured reactors are established and first full-scale continuous production reactors based on micro- or millistructures are in operation, leading to an increasing acceptance of this technology in the process industry. While the benefits of the technology as such are beyond question, it is still necessary to characterize individual micro- and millistructured reactors for the layout of processes, e.g. in terms of hydrodynamics and heat- and mass transfer.
The ART plate reactor PR37 of the manufacturer Ehrfeld Mikrotechnik GmbH is readily available, but still lacking a systematic and comprehensive characterization. In this paper, the heat transfer performance of this reactor is addressed. A mathematical model is developed that, combined with experiments, allows insights into the reactor not accessible through experiments alone. This model is a solid base for process design and optimization in the future.
In a broader sense, a microreactor is a reactor system with characteristic lengths in the range of micrometers to “a few millimeters” [5] and particularly between “about 10 μm and about 2 mm” [6]. This term is sometimes used exclusively for reactors in the micrometer range (e.g. between 10 and 100 μm [7] or 50 and 500 μm [8], while reactors at the upper end of the broader definition are also referred to as millireactors [9].
Though the process intensification is less pronounced in millireactors, they are much more suited for the process industry than microreactors as they allow throughputs that are sufficient for the production without an excessive numbering-up of process channels [10]; achieving an even flow distribution over hundreds or thousands of parallel micrometer-sized channels is challenging [11], particularly as microchannels are very prone to fouling and clogging, which leads to increasing pressure drops and flow maldistribution over parallel channels [12]. Millireactors have proven to be an excellent trade-off between the degree of process intensification and viable flowrates [13]; production quantities up to 10,000 tons per year have been realized in millireactors [14].
Millireactors are preferable used to conduct highly exothermic reactions. They are therefore typically designed as integrated heat exchangers and reactors (also referred to as HEX reactors [15]). The most common type of millireactors is the plate reactor, due to its compactness and flexibility regarding the number of plates [2]. Examples for milli-/microstructured plate reactors are the LFR and AFR from Corning [16], the MR500 from 3 M Technical Ceramics [17], the DeanHex from Boostec and Toulouse University [18,19] and the Flow Plate from Lonza and Ehrfeld Mikrotechnik [20,21]. However, also other concepts exist like the Miprowa technology from Ehrfeld Mikrotechnik [22] which is similar to a shell-and-tube heat exchanger. An overview of some plate heat exchanger/reactor concepts is given by Cybulski et al. [15].
The heat transfer in micro- and millichannels can usually be described with the same approach based on dimensionless numbers as in macroscopic devices [23], as the continuum hypothesis is practically always fulfilled in technical applications. The Nusselt number is defined as [24]:
In eq. 1, is the local heat transfer coefficient, the hydraulic diameter of the channel and the thermal conductivity of the fluid. In practice, heat transfer coefficients are often calculated with Nusselt correlations which have in most cases been determined experimentally, but might also be derived from numerical studies or, in simple cases, analytically [25]. Nusselt correlations developed for macrochannels can generally be applied for microchannels as well [23,26]. However, certain effects which can be neglected in conventional devices may have a significant influence within millistructured devices. Among others, one of these “scaling-effects” is the so-called conjugate heat transfer. This term refers to a situation where a complex three-dimensional temperature field develops within the reactor wall so that heat is not only transported from one fluid perpendicular through the wall to the other fluid, but principally in all directions. Simple boundary conditions like constant wall temperature (CWT) or constant wall heat flux (CWHF) do no longer apply and heat transfer in both the solid and the fluid system has to be computed simultaneously with the flow field [27].
Channels in the micrometer range are often straight and the flow is purely laminar. The Nusselt number of a developed laminar flow is a constant and depends only on the geometry of the channel and boundary conditions of the heat flow (e.g. CWT or CWHF). Elevated heat transfer coefficients are achieved only due to the extremely small diameter. The values for the Nusselt number of a developed flow with CWT boundary conditions are e.g. in a pipes 3.66 and in square channels 2.98 [24].
Millichannels on the other hand are typically curved, zig-zagged or have periodically changing cross-sectional areas to induce secondary flows that enhance the heat transfer. There are also straight millichannels that are equipped with static mixing elements to intensify transport processes by a steadily repeated breaking of thermal boundary layers and thus exploiting the increased Nusselt numbers of developing flows [13]. Any intensification of the heat transfer has to be paid for by an increased pressure drop; however, the increase (relative to a straight channel) of the Nusselt number is larger than the corresponding increase of the Darcy friction factor for common geometries such as sinusoidal [28], serpentine [29] and converging-diverging channels [30]. The formation of secondary flows in non-straight channels is dependent on the Reynolds number, defined as:
As it is generally known, in eq. 2 denote the mean velocity, the density and the viscosity of the fluid. In the case of converging-diverging channels, stationary secondary flows develop if is in the order of magnitude of ten; the secondary flows become oscillating at higher Reynolds numbers and chaotic already at a few hundred [31], well below the critical Reynolds number for straight channels of about 2000 [8]. Therefore, the form of Nusselt correlations developed for turbulent or transitional flows in straight pipes can be used to describe the heat transfer in millichannels [32]. However, the values of the parameters have to be re-adjusted for the actual geometry. This requires a profound base of experimental data.
Section snippets
ART plate reactor PR37
In this paper, the abovementioned plate reactor PR37 from Ehrfeld Mikrotechnik is investigated. The PR37 reactor frame takes up to ten reactor plates. Each plate has a millistructured process channel milled into the upper side and a utility channel on the lower side. The process channel has a nearly rectangular cross-section and is meandering. The channel cross-sectional area is periodically changing between the nominal value of the short straight parts of the channel and twice this value in
Demand for a novel model
In contrast to local heat transfer coefficients of channels, the overall heat transfer coefficient is directly accessible from experiment for any heat exchanger. As it is well-known, the measurement of the overall heat transfer coefficient requires only the inlet and outlet temperatures of both media and the mass flow of one medium. As long as the geometry of the device is simple enough and conjugate heat transfer is negligible, the determination of the channel heat transfer coefficients from
Nusselt correlation parameters
More than 300 experiments were used for the determination of the Nusselt parameters. A few experiments with very low utility flow rates were excluded, as heat losses (despite the thermal insulation) become significant here due to the low heat capacity. Both the utility and the process channel Nusselt correlations have been optimized simultaneously. The optimization yielded the set of parameters for the Eqs. (11) and (13) given in Table 2. The mean error was 0.5 K, which is fairly low
Conclusion
The four plate types of the millistructured ART plate reactor PR37 of Ehrfeld Mikrotechnik have been characterized in terms of heat transfer in this work. A large number of heat transfer experiments, covering a wide range of Reynolds and Prandtl numbers, have been conducted. An innovative reactor model has been developed that calculates the spatial heat flow in the plate based on a network of thermal resistances. This model allows a simulation of the heat transfer and different thermal
CRediT authorship contribution statement
Alexander Rave: Conceptualization, Methodology, Software, Writing - original draft, Investigation. Rafael Kuwertz: Validation, Writing - review & editing. Georg Fieg: Writing - review & editing, Project administration, Funding acquisition. Joachim Heck: Resources, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
Authors would like to acknowledge the financial support from German Federal Ministry for Economic Affairs and Energy through ZIM program (Zentrales Innovationsprogramm Mittelstand, project number: ZF4025906CM8).
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