Cocurrent turbulent tube reactor with multiple gas injections and recycle of slurry: A treatment in terms of green functions

Abstract

A system of integral equations based upon momentum and mass balances, apt for the modeling of a multiphase gas-slurry turbulent tube reactor operating in the dispersed bubble-flow pattern, with slurry recycle and allowance for multiple injections of a gaseous reactant, has been developed using the Green function formalism. This mathematical treatment results adequate for the systematic handling of the solutions representing the different combinations of initial- and boundary-value problems which arise whenever the recycle ratio becomes nonzero. A multi-point gas injection operation of the ITR can be accounted for with the simple introduction of as many point source terms in the mass balance for the dissolved gaseous reactant as needed. An iterative solving routine, combined with the topological concept of homotopy, has been implemented and applied as an example for a particular process. The iterative numerical resolution schemes that were implemented starting from said integral equations have, in general, a narrower convergence region than that attainable via a more standard integration method. A split of the driving force terms of the sensitive mass balance equation enlarges it, as it was also found by other authors who have analyzed similar problems. However, a noticeable advantage in favor of iterative schemes (as measured by computing times) is found whenever the boundary-value problem resulting from the presence of a process recycle has to be dealt with. This advantage becomes even greater if multiple injections of gas are considered. The modelling of the turbulent tube reactor serves only as an illustration of using Green functions in chemical engineering systems. Moreover, after the model assumptions, the remaining model is not a characteristic one for a slurry reactor, but can also be used for other heterogeneous gas-liquid reactors, provided no enhancement of gas absorption occurs.