Mixing intensiﬁcation by natural convection with application to a chemical reactor design C.T. Gonzalez-Hidalgo a,⇑ , J. Herrero a , D. Puigjaner b a Departament d’ Enginyeria Química, Universitat Rovira i Virgili, Av. Països Catalans 26, Tarragona, Catalunya, Spain b Departament d’ Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, Tarragona, Catalunya, Spain highlights " We analyze natural convection-driven mass transfer in a cubical catalytic reactor. " Highly accurate methods are used to compute the ﬂow and the concentration ﬁeld. " The concentration boundary layer thickness is ﬁtted to the problem parameters. " A simple relation between reactor efﬁciency and boundary layer thickness is given. " The Sherwood numbers are similar to those found in forced convection mass transfer. article info Article history: Received 28 March 2012 Received in revised form 19 June 2012 Accepted 21 June 2012 Available online 30 June 2012 Keywords: Catalytic chemical reactor Natural convection Reactant conversion Reactor efﬁciency abstract The current work is focused on the numerical study of mass transport inside a cubical reactor agitated by natural convection. The inner face of the bottom wall is covered with a catalytic layer, where a ﬁrst order chemical reaction takes place with negligible internal resistance to mass transfer. The reactor operates discontinuously and its time evolution is simulated until a 90% reactant conversion is reached. A Galerkin spectral method is used for the spatial discretization of the differential conservation equations of momentum, internal energy and concentration of the reactant species. The solute concentration is advanced in time by means of a 7–8th order Runge–Kutta–Fehlberg method with automatic adjustment of the time-step. The bifurcation diagram of the natural convection ﬂow is established for Rayleigh num- bers up to Ra = 1.5  10 5 and a Prandtl number of Pr = 6. Amongst the several branches of steady solutions that coexist within this range of Ra, the ﬂow pattern that has the widest stability domain and maximizes the heat transfer rate is selected. The spatial structure and the mixing capabilities of the selected ﬂow pattern are analyzed. The competitiveness of the present reactor is assessed for Pr = 6 and different values of the Rayleigh and Schmidt numbers (in the respective ranges 7.5  10 4 6 Ra 6 1.5  10 5 and 6 6 Sc 6 2000) and the Damkohler number (1 6 / 6 100). It is found that, after a short transient, the val- ues of the reactor efﬁciency, g, become time-independent. The external mass transfer rates can be there- fore characterized in terms of g and thickness of the concentration boundary layer, d c . The dependence of both g and d c on the problem parameters (Ra, Sc and /) is analysed. The effectiveness of the natural con- vection-driven catalytic reactor is at least as high as that typically found in previous studies, where mass transfer was promoted by forced convection. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Chemical and environmental engineering, biotechnology, and pharmaceutical industries are widely using bioactive materials as process catalysts to achieve their goals [1,2]. The chemical and bio- chemical reactions that occur in such processes take place on cat- alyst surfaces or pellets. Immobilized enzymes have been recently preferred over dissolved or suspended enzymes in stirred reactors since immobilization facilitates enzyme reutilization and avoids enzyme recovery and puriﬁcation processes [3,4]. Process intensi- ﬁcation, understood as a signiﬁcant reduction on the size of pro- cess units, plays a very important role in novel designs which adapt the mixing processes in their interior to improve their versa- tility and efﬁciency. In a typical reactor ﬂuid system, when immo- bilized enzymes are attached to an impermeable solid support, molecules are convected from the bulk of ﬂuid into the vicinity of the catalyst surface and then transported to the catalyst active sites by molecular diffusion. This is the reason why mixing is a very 1385-8947/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cej.2012.06.102 ⇑ Corresponding author. Tel.: +34 977558458; fax: +34 977559621. E-mail addresses: claratatiana.gonzalez@urv.cat (C.T. Gonzalez-Hidalgo), joan. herrero@urv.cat (J. Herrero), dolors.puigjaner@urv.cat (D. Puigjaner). Chemical Engineering Journal 200–202 (2012) 506–520 Contents lists available at SciVerse ScienceDirect Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej