(372q) Multiscale Modelling of Trickle Bed Reactors for Biological Methanation

The biological valorization of carbon dioxide is a new process, proposed in the context of carbon capture and reuse, which is gaining momentum due to the increasing demand of energy from renewable sources [1].

Trickle bed reactors (TBRs) can be effectively used in the production process of methane from renewable hydrogen and carbon dioxide through biological methanation since their packing structure provides high interfacial area for the multiphase reaction. Although the chemical reactions involved are well-known, the hydrodynamics resulting from the trickle regime and the tortuous geometrical structure of the packing are complex. For this reason, a better understanding of these phenomena is needed for design, scale-up and optimization purposes.

In the literature, some studies have been proposed to simulate the full TBR using computational fluid dynamics (CFD) for the volume-averaged hydrodynamics, resorting to simplified semi-empirical models to account for phase interaction phenomena [2]. Although these give good qualitative estimates of the average fluid flow and the final methane production rate, the quantitative predictions are not accurate enough for design and optimization purposes.

On the other hand, CFD simulations can also be employed to obtain accurate predictions at the pore-scale of the reactor. Nonetheless, the simulation of the complete reactor at this grid resolution would require prohibitive computational resources and would not be compatible with industrial turnovers. The main aspect that prevents us from directly simulating these phenomena is its multiscale nature. In fact, the packing elements of the porous media have a characteristic length two to four orders of magnitude smaller compared to the full geometry. Similarly, the time scale of the chemical reactions is smaller than the time scale of the mean flow advection.

Given the multiscale physics, one approach that seems appropriate to tackle the computational challenges is to resort to multiscale modelling. In this framework, we propose a multiscale model consisting of one model for the macroscale, describing the volume-averaged flow dynamics in the porous media and one model for the micro-scale, taking into account the complex interactions among the phases at the scale of the pores.

In this work, for the macroscale we employ the two-phase Darcy’s law. It is derived through a homogenization procedure and presents some parameters that need closure; the relative permeabilities. This model is deemed to be inaccurate but efficient. On the contrary, for the microscale we use the InterFoam solver of OpenFOAM which describes and simulates accurately the physics at the scale of the pores (see figure 1) but is resource intensive.

In principle, it seems reasonable to directly couple the models at run-time and at each time step call InterFoam for every cell of the macroscale solver to extract the values of the quantities that need closure. Nonetheless, following this approach the computational time becomes quickly incompatible with industrial needs even for simple cases. Once again, the reason is that microscale simulations are computationally demanding. One possible workaround is to resort to an approach similar to Marcato et al. [3]. In fact, we replace the microscale simulations with a data-driven surrogate model which gives real-time predictions of the closure terms.

To this end, InterFoam is used to create a dataset of simulations over Representative Elementary Volumes (REV) of the porous media varying the input parameters (operating conditions). Next, in the post-processing of each of these simulations we extract the values of relative permeabilities of the two phases. Finally, a data-driven model is trained to predict the relative permeabilities extracted from the simulations carried out at the scale of the pores.

The coupling between the macroscopic and the surrogate model is done at run-time. In figure 2, we report a 2D result of the multiscale model. We show the water saturation evolution at different integration times obtained reproducing a packed bed reactor with a simplified geometry of dimensions [0, 0.4] x [0, 0.8] m and a computational grid of [80 x 160] cells. Water is inserted from the top of the domain and is convected to the outlet at the bottom. For left and right boundaries are employed wall conditions.

In the coupled solver, the macroscale model gives an appropriate description of the averaged flow hydrodynamics and the surrogate model informs it about microscale phenomena through relative permeabilities. Moreover, the models influence each other mutually. On the one hand, the surrogate model inputs depend on the local (cell) flow conditions. On the other hand, macroscopic hydrodynamics is influenced by the surrogate model output.

References

[1] M. Thema et al., (2019), Biological CO₂-Methanation: An Approach to Standardization, Energies 12.9.

[2] S. Markthaler et al., (2020), Numerical simulation of trickle bed reactors for biological methanation, Chemical Engineering Science 226, 115847.

[3] A. Marcato et al., (2022), Prediction of local concentration fields in porous media
with chemical reaction using a multi scale convolutional
neural network, Chemical Engineering Journal 455, 140367.