The Chemzcal Engmeermg Journal, 51 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (1993) B254333 B25 zyxwvutsr The order of micromixing and segregation effects on the biological growth process in a stirred-tank reactor zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONML M. Atiqullah Petroleum and Gas Technology Dzvzswn, The Research Instztute, Dhahran 31261 [Saudz Arabza) A K M. S. Rahman, S A Beg and M M. Hassan Chemical Engmeermg Department, KWQ Fahd Unzverszty of Petroleum and Mznerals, Dhahran 31261 {Sauda Arab@ (Fiecewed January 3, 1992) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Abstract Dependmg on the hydrodynamc conditions, a stied tank reactor may be dnnded mto two nucronuxmg environments maxunum nuxmg followed by complete segregation (case l), or wee versa (case 2) The Ng-Rlppm two-envu-onment model sunulates case 1, whereas the zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ Fan reversed two-enwonment model covers case 2 The nucro nuxmg concepts of Danckwerts and of Zurletermg have been apphed to both models m terms of the degree of segregation J to evaluate the mfluence of the order of nucronux- mg-segregation effects on blolo@cal growth processes The model predictions for both endogeneous and exogeneous cell metabohsm show that case 2 eves more substrate conversion and cell production than does case 1, for the same extent of nucro nuxmg, parkularly at low tiutlon rates At h@ ddution rates, both models predict the same reactor performance, independent of the nucronuxmg phenomenon The substrate conversion and cell production decrease urlth mcreasmg tiuhon rate, followmg a smular trend Further, the effects of nucro nuxmg are found to be strong functions of ddution rate At Hugh tiutlon rates for case 2, the nucronuxmg effects are pronounced only when the reactor approaches complete segregation However, for case 1, the effects are appreciable when the reactor deviates shghtly from perfect nuxmg For some mtermedate dllutlon rates, the Fan model, unhke the Ng-Rlppm model, shows that the reactor output decreases hnearly vvlth mcreasmg degree of segregation Beyond a cntlcal value of the dllutlon rate, the reactor output falls hnearly ullth tiution rate for exogeneous cell metabohsm (case 2) On the contrary, for case 1, the output decreases exponentially throughout the entie range of dilution rates 1. Introduction Mlcrobml growth processes, which are mherently dynamic, consist of a large number of elementary reactions Because of this mtrmsic kmetic behavlour, they are susceptible to micronuxmg or segregation effects The mrxmg phenomenon m a stirred-tank reactor can be divided mto two components macronuxmg and nucronuxmg [l-5] The macronuxmg com- ponent accounts for the variation m residence times experienced by the molecules flowmg through the reactor The micromlxmg component measures the extent to which the feed nuxes, on a molecular level, with the flmd already m the reactor. It was Dan&we& [ 2 ] who first described mathematically the nucromlxmg phenomenon by mtroducmg the concept of degree of segregation J which was further advanced by Zmetermg [ 3 I. A stirred-tank reactor behaves as a perfect mixer and a completely seg- regated reactor for J approachmg zero and unity respectively Fan and coworkers [S-S] have used the above concept of degree of segregation to model the effects of overall nuxmg on biological growth processes Fan and coworkers [S-S] considered two stirred tanks m series, and the series combmation of a plug flow reactor and a stirred-tank reactor On the basis of such a modellmg approach, they suggested the followmg possible states of nucronuxedness. (1) complete segregation, (u) plug flow reactor followed by a completely segregated reactor, (m) completely segregated reactor followed by a plug flow reactor; (iv) plug flow reactor followed by a maxlmum- zyxwvutsrqp 0300-9467/93/$6 00 0 1993 - Elsevler Sequoia All nghts reserved