(491c) Inverse-Designed Heating Profiles for Inductively Heated Metamaterial Reactors

Electrified heating methods for chemical reactors offer a promising solution to reducing industrial carbon emissions by utilizing green electricity for high grade heat production. In particular, induction heating is a scalable, volumetric, and highly efficient heating method that can be readily adapted to various reactor configurations. Our group recently proposed the metamaterial reactor in which a helical coil is used to inductively heat a volumetric, electrically conducting open cell baffle acting as a susceptor with tailored effective electromagnetic properties. When a high frequency AC current is driven through the coil, an alternating magnetic field within the coil is produced that excites eddy currents throughout the cross section of the susceptor that dissipate into heat with high efficiency.

In prior demonstrations of metamaterial reactors containing volumetrically uniform open-cell reaction bonded silicon carbide foams serving as reaction baffles, we showed that the reverse water gas shift (RWGS) reaction could be performed near equilibrium conversion limits with a heating efficiency greater than 90%. Furthermore, the tubular reactor supported volumetric heat dissipation and a minimal radial temperature gradient, leading to reaction operation in ideal plug flow conditions. However, axial gradients were observed due to a combination of thermal losses via conduction concentrated at the baffle ends, reaction consumption, and heating of the inlet gas which increases with flow rate. The presence of such thermal gradients and thermal gradients in general impact reaction kinetics and ultimately sets limits on reactor conversion and form factor.

Inductive heating with metamaterial baffles presents a unique opportunity to fully tailor the volumetric heating profile by spatially tailoring the effective electrical conductivity of the susceptor. In this talk, we present a generalized formalism for tubular metamaterial reactors that allows for the customization of heating profiles via inverse design of the reaction susceptor geometry. We demonstrate that these heating profiles can be specifically engineered to optimize various reactions and operational conditions by considering factors like thermal conduction, convection, and reaction consumption. As proof of concepts, we illustrate designs that can facilitate the RWGS reaction under isothermal conditions under different gas flow rates and temperatures, thus achieving the maximum conversion rate possible for the specified reactor size and temperature.

We employ a multiphysics inverse design approach for optimizing the susceptor layout within a tubular reactor to achieve a desired temperature profile. In an initial step, we utilize a suite of experimental techniques to create quantitative models that capture the reaction mechanisms and heat loss parameters. With these parameters, we produce a simplified one-dimensional (1D) multi-physics model of the reactor that accounts for kinetics, thermodynamics, mass transfer, and heat transfer of the solids and gases as a function of axial position. The 1D model is valid in the limit where radial gradients of physical properties are negligible or radially averaged. Next, an inverse design optimization algorithm is used with the 1D model to specify the spatially varying effective physical properties of the susceptor that produce our desired response. Finally, a detailed susceptor geometry that has position-dependent effective physical properties corresponding with the inversely designed profile is specified.

We experimentally validate our design methodology for a set of fixed bed reactor systems that are each designed to perform the RWGS reaction at different isothermal temperatures and gas flow rates. The metamaterial susceptors are composed of additively manufactured Inconel open cell lattice susceptors and are impregnated with RWGS fixed bed catalyst. The reaction kinetics model used for inverse design is experimentally specified using differential reactor data. In one demonstration, we focus on 150 mm-long, 38 mm-diameter reactors that operate near ideal plug flow conditions. The susceptor lattice is cubic with a pitch of 4.75 mm, and its effective conductivity properties are tailored as a function of axial position by varying the wire diameter from 0.5 mm and 1.2 mm. The isothermal condition is confirmed through axial temperature measurements taken by a multipoint fiber optic probe inside a thermowell along the central axis of the reactor. A three-dimensional (3D) multiphysics model that integrates electromagnetic, heat-transfer, computational fluid dynamics, and chemical engineering modules consistent with our 1D model and experimental measurements is used to validate our results.

In a second demonstration, we show that for relatively large diameter reactors (diameter = 76 mm), radial heating and temperature gradients from the high frequency induction heating process can be explicitly reduced by engineering the radial heating profile of the metamaterial susceptor. These radial gradients naturally arise in scaled inductively heated reactor system due to skin depth effects involving the uniform magnetic field and susceptor and due to thermal losses at the reactor wall. We design and fabricate susceptor lattices with radially varying effective conductivity properties and experimentally show that radial temperature variations can be eliminated with radial susceptor engineering. We also show that the combination of radial and axial variations in susceptor geometry can lead to isothermal volumetric reaction conditions in scaled reactor systems.