Pareto-optimal design and assessment of monolithic sponges as catalyst carriers for exothermic reactions
Graphical abstract
Introduction
Monolithic sponges, also called open-cell foams, are considered to be promising catalyst carriers in fixed-bed reactors for exo- and endothermic conversions [1], [2], [3], [4]. Since they provide a continuous solid network and high porosities, monolithic sponges combine excellent heat transport characteristics with low pressure losses.
First studies at the lab scale already demonstrated that monolithic sponges lead to lower hot-spot temperatures and comparable or higher yields than conventional packed beds of pellets or extrudates [5], [6], [7], [8], [9], [10]. Regarding the design of monolithic sponges in terms of material, open porosity (volume of accessible void space per unit sponge volume), and window diameter (see Fig. 1 a) Mülheims and Kraushaar-Czarnetzki [6], Gräf et al. [9], and Fischedick et al. [11], among others, emphasized that a high thermal conductivity of the solid is the main parameter to obtain excellent heat transport properties. More recently, Bracconi et al. [12] used a Voronoi tesselation to artificially create realistic sponge geometries (see also Wehinger et al. [13]) with precisely controlled strut diameter. Based on their finite-volume simulations, they concluded that next to a low porosity, thick and preferably uniform strut diameters are required to allow unhindered conduction in the struts and to fully exploit the thermal conductivity of the material. Further, Donsìet al.[14] and Mülheims and Kraushaar-Czarnetzki [6] speculated that small window diameters are necessary to provide large specific surface area for effective heat and mass transfer between the gas and the solid phase. Patcas et al. [15] compared monolithic sponges, honeycombs, and packed beds of pellets regarding mass transfer and pressure loss. They concluded that sponges provide the best tradeoff between high mass transfer rates and low pressure losses because of their open but tortuous flow path.
Recently, Montenegro Camacho et al. [16] presented the use of monolithic sponges in a pilot reactor for the autothermal production of hydrogen from biogas, indicating that monolithic sponges now move from the lab scale towards the pilot and production scale, and that an efficient coupling of the monolithic sponges to the reactor wall (see [17], [18], [19]) can also be realized at larger scales. In contrast to the lab scale, the pressure loss and the space-time yield become important figures of merit at the production scale as they determine the operational and capital costs. Regarding the design of monolithic sponges, this leads to conflicting design goals (see Fig. 1b). For low pressure losses sponges should exhibit high open porosities and large window diameters. This conflicts with the need for a large specific surface area, or equivalently a high catalyst inventory, and thus small window diameters. On the other hand, high porosities substantially reduce the effective thermal conductivity of monolithic sponges and thus might cause heat transport limitations and severe hot spots. For open porosities higher than 90 %, the specific surface area and thus the catalyst inventory also decreases with the porosity.
Reitzmann et al. [3] conducted early simulations of the production of phthalic anhydride with monolithic sponges at the production scale. They concluded that higher space-time yields are possible with monolithic sponges because the high porosity allowed high throughputs without significantly lower yields.
Philippe et al. [20] simulated Fischer-Tropsch synthesis in monolithic sponges and packed beds at the production scale. They found that under identical operating conditions sponges provide better heat control than packed beds at low flow rates, mainly because of the higher porosity and thusless catalyst material per reactor volume. Further, they outline the possibility of tuning the porosity of monolithic sponges to balance high heat transport rates and high catalyst inventories. Nevertheless, both studies compared only selected sponge designs and, due to the lack of available correlations at that time, applied premature or oversimplified models for heat transport in solid sponges.
To date, design guidelines for solid sponges regarding the open porosity and the window diameter to balance high catalyst inventories, low pressure losses, and high thermal conductivities to facilitate scale-up to the production scale have not been available. Therefore, a state-of-the-art multiscale reactor model for monolithic sponges is used in this study to solve the outlined multi-objective optimization problem (Fig. 1 b). The resulting Pareto-optimal sponge designs are analyzed to quantify the tradeoffs in the design of monolithic sponges. Further, the performance of selected Pareto-optimal sponge designs is further analyzed for the methanation of CO2 and compared to the performance of conventional packed beds under identical conditions. The comparison allows to assess the potential of monolithic sponges as catalyst carrier in fixed-bed reactors.
Section snippets
Reactor models
To generate the Pareto-optimal sponge configurations, a 2-d heterogeneous multiscale model was applied. It has been described in detail and validated in previous studies [21], [22]. In brief, the model considered coated monolithic sponges in a single cooled cylindrical reactor tube to resemble the application of sponges in a multi-tubular fixed-bed reactor.
In contrast to pseudo-homogeneous reactor models, heterogeneous reactor models explicitly consider heat and mass transport in the solid
Convergence of the NSGAII algorithm
As the NSGAII algorithm belongs to the class of genetic algorithms, it requires to set the number of individuals that form the set of Pareto-optimal solutions and the number of generations (iterations) over which the population is evolved. Both parameters should be high enough to populate the complete Pareto-front and to avoid dominated solutions that are not Pareto-optimal. Fig. 2 shows the influence of both the number of individuals (Fig. 2a) and the number of generations (Fig. 2b) on the
Conclusions
Monolithic sponges as catalyst carriers in fixed-bed reactors were found to be a promising option for small-to-medium scale conversions, especially for exothermic reactions. Since heat conduction in the continuous solid phase is the dominant mechanism for removing the reaction heat, they can be operated at lower gas loads than conventional packed beds of pellets. In addition, the dominance of heat conduction in the solid phase allows safe operation of monolithic sponges over a wide range of
Acknowledgements
This work was supported by the German Research Foundation (DFG) within the Research Training Group GRK 1860 ’Micro-, meso-, and macroporous nonmetallic Materials: Fundamentals and Applications’ (MIMENIMA).
Declaration of interest
None.
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