Low-dimensional models for homogeneous stirred tank reactors

A novel approach is used to derive a low-dimensional model for a CSTR by spatial averaging of the three dimensional convection-diffusion reaction (CDR) equations. For the isothermal case, the model may be expressed in the two-mode form as d(C)/dt + R((C)) = 1/tau(c) (C-m(in) - C-m); C-m - (C) = I/tau(c) (t(mix,2)C(m)(in) - t(mix,1)C(m)), where (C) and C-m are the spatial average and cup-mixing concentrations, while tau(c), t(mix,1) and t(mix,2) are the space time and mixing times, respectively. The first mixing time captures the effect of micro as well as macromixing in the tank, while the second one accounts for the feed distribution (e.g., premixed, unmixed etc.). This two mode model reduces to the classical one-mode model of Bodenstein and Wolgast [Z. Phys. Chem. 61 (1908) 4221 in the limit of t(mix,i) --> 0. It is argued that for 0 < tmix,i/tau(c) << 1, the two mode model has the same accuracy as the full CDR equation while retaining qualitative features for any finite values of. The new model is used to illustrate the influence of feed distribution and mixing on conversion for the bimolecular reaction A+B -> P-tau c and competitive-consecutive reaction between A and B of the type A+B -> R and B+R -> S. The new model explains experimental results in the literature, including the opposing trends observed for series-parallel reactions under different operating conditions. (c) 2004 Elsevier Ltd. All rights reserved.