In our recent work, we demonstrated an inductively heated packed bed metamaterial reactor that could be volumetrically heated. Our reactor consisted of a helical copper coil around a quartz tube which contained a monolithic, additively manufactured open-cell silicon carbide foam susceptor. This susceptor severed as both an inductively heated medium and a support for potassium carbonate catalyst that could facilitate the reverse water gas shift (RWGS) with high selectivity. We refer to the reactor as a "metamaterial" reactor due to its design principle: the silicon carbide foam’s microscopic geometry was designed to achieve a homogeneous effective electrical conductivity that enables efficient coupling with the magnetic field, achieving over 90% heating efficiency in our experiments. These demonstrations were limited to the uniform heating of a homogeneous susceptor, which is suboptimal due to the presence of significant axial temperature gradients during flow reactor operation.
In this presentation, we discuss concepts and progress in digital metamaterial reactors in which the volumetric heating profile can be fully tailored through metamaterial geometry and composition design. First, we discuss the development of an inverse-design framework consisting of a 1D pseudo-homogeneous model, assuming negligible radial temperature gradients, which describes the energy and mass balance within the inductively heated metamaterial reactor. By tuning the model with experimental data, it is possible to create a high-fidelity description of the reactor that relates the axial temperature profile to the power dissipated, which in turn is a function of the metamaterial geometry. It is further possible to control the axial heating response through discretizing the reactor by segmenting it into different sections that are one of two metamaterial reaction bonded silicon carbide lattice types, each with differing silicon content, to control the reactor temperature environment. With machine-learning driven inverse design to produce optimal reactor geometries, we demonstrate heating profile control for a 38 mm OD reactor performing RWGS and achieve a near isothermal environment, which represents a regime of maximum conversion for reactions following elementary kinetics.
Next, we discuss the extension of this inverse design framework to larger reactors with diameters on the order of hundreds of millimeters to meters. Larger reactors are susceptible to non-trivial radial temperature gradients, particularly at high flow rates, as well as axial gradients characteristic of small-scale reactors. We employ a 2D two-phase energy and mass balance that describes the heat and mass transfer between the gaseous reactants and products, the packed catalyst, and the metamaterial susceptor, which we verify using 2D Multiphysics simulations. With this model, we design a 2D profile of the metamaterial susceptor electrical conductivity that can produce a desired temperature profile at a given flow rate. This electrical conductivity profile can be realized in a number of ways: a monolithic structure of a single bulk material with varying geometry to achieve local changes in electrical conductivity, multiple susceptors packed together with different compositions, or a combination of both.
Finally, we demonstrate this scaled up method with a set of fixed bed reactors designed to maintain an isothermal environment while performing the RWGS reaction. The reactor consists of a 76 mm OD metamaterial monolith with axial and radial thermal and electrical conductivities that are a function of position, thereby producing a spatially varying heating response when coupled to the induction coil. The metamaterial susceptor consists of discrete sections of reaction bonded silicon carbide lattices with varying geometry and silicon content to produce the inversely designed heating profile, resulting in a near isothermal reactor environment and increased conversion. We demonstrate multiple inversely designed configurations optimized for varying flow rates, which result in a notable increase in conversion compared to uniform reactors due to the mitigation of radial temperature gradients.