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G. , Clement and J�r ge n sen ( 1 98 3 ) ) have ob ser ve d that the par am eters obtained by t he "buildin g-block" app ro ac h fail to give s ati s fac tory prediction of the reactor pe r for m an c e unde r reactin g conditions . H e n c e they feel that it is nec e ss ary to d et e r mine all ( or most ) of the parameters si m ult an eo u sly in or d er to give a reactor model that can be used for inter polation and for control purposes . One m ay argue that the failure o f the b ui l di n g - block method m ust indicate t hat there is som e misconception of the kinetic model or of the flow p attern in the reactor , and t h at these un certainties had better be re solve d .
N umerically , all these different problem s are han dled by the same general techniq ue , b ut with sli ght modific ations for different boundary conditions . ) _ Da y ( 128) au where u W hen s = 1 an d v ( u ) i s x 2 and s = 0 , 1 , and 2 . velocity distribution , we have a steady - st ate tubular reactor When v ( u ) = 1 and z is interpreted as contact time , we have transient pellet proble m . D in stead vav as t he dimensionless group of parameters . Equation ( 1 2 8 ) is discreti zed by N t h - order collocation : = the radial problem .
1 0 7 ) w hen cP 1 + oo . is a good approximation w he n h > 1 0 . Even t h o u gh i n the present ex ample a collocation solution could be found for all $ 1 values , it is worthw hile to remember than an accurate solution o f the boundary value problem c an also be o bt ain e d by forw ard inte gration from r; = 0 or from r; = 1 . T here are positive ei genvalues in the Jacobian of f , and the solution m ay e asily dive r ge , b ut an explicit Run ge - Kutta method is j u st as good as an i m plic i t method .