A Minimum Entropy Production Approach to Optimization of Tubular Chemical Reactors with Nature-Inspired Design

Abstract

The problem of the shape optimization of tubular-type plug-flow chemical reactors equipped with a fluid flow-based cooling system is considered in this work. The hydraulic radius Rh(z) = 2A(z)/P(z) and an equivalent surface area-based radius Rs = P(z)/(2π) were computed from the cross-sectional area A(z) and perimeter P(z) measured along the nasal duct of Northern reindeer and used for shape optimization as nature-inspired design. The laminar flow in the cooling system was modeled using the Navier–Stokes equations for an incompressible liquid. In the central tube, a set of chemical reactions with temperature-dependent rates was considered. The temperature and flow velocity fields, pumping pressure, mass flow rate, and total heat flux Jth were obtained by numerical methods. Comparative analyses of the efficiency of different geometries were conducted on Pareto frontiers for hydraulic resistivity Zh, thermal resistivity Zth, thermal inlet length Lth, and entropy production Sirr as a sum of contributions from chemical reactions, thermal, and viscous dissipation. It was shown that the tube with Rs(z) as an interface between the reactor and cooler has the best Pareto efficiency using the (Zh,Zth,Lth) objective functions. Surprisingly, this design also exhibits the lowest Sirr and a more uniform distribution Sirr(z) (i.e., equipartition) among other designs. This geometry is suggested for densely packed tubular reactors.