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【正文】 d x r d V r d l??? () AAd x d V Vr F F????To pare the equations for the PFR with a batch reactor, the molar feed rate is expressed as the volume feed rate F times the concentration of A: () 45 Homogeneous Reactions 0AAF FC??0 0 011A A Ad x Vr F C S V C C?? ? ? ??() Equation () can then be presented using the space velocity SV or the space time , which is the reciprocal of the space velocity: where 1FSVVFSV V?????volumetric feed rate reactor volume () 46 Heterogeneous Reactions ?For a heterogeneous catalytic reaction in an ideal packedbed reactor, the material balance is written for a differential mass of catalyst, dW. The basic equation for the conversion of the key reactant A is the same as for any type of reaction, or bination of reactions, including reversible reactions. A B C??A B C D? ? ?For or A B+C Or 47 Heterogeneous Reactions AAAAF dx rdWFdx dW Wr F F??????where Moles A fed/hr r=total moles A consumed/hr,kg W=mass of catalyst Integration of the rate equation gives the mass of catalyst needed per unit feed rate of A for a specified conversion. () 48 Heterogeneous Reactions ?The reactor volume is determined from the mass of catalyst and the bed density : b?bWV?? () The dimensions of the reactor are not fixed by these equations, The reactor dimensions are selected to give reasonable proportions and a tolerable pressure drop. Often the mass velocity is chosen first, which gives the crosssectional area, and the bed length is determined from the required volume. 49 Heterogeneous Reactions 0011(),bBA A AVd x Wr F F C S V CS V F V h r???? ? ???To relate the conversion to the space velocity, the feed concentration and the bed density are introduced into Eq. (): where () It is not really necessary to use the concept of space velocity in designing a reactor, since the mass of catalyst needed and the bed volume are determined directly from Eqs. and . However, some patents and technical reports give the conversion as a function of space velocity and temperature rather than presenting fundamental kiic data. To use such data, the space velocity must be carefully defined and interpreted. 50 Heterogeneous Reactions 39。()AAAAC S T RC S T Rdxr C CdtF C x r V C s lo p e VVxtF s lo p eVxttF x t??????? ? ?39。2 2 2A B Ac B cr k C C k Cr k C C k C????() () The concentration of A falls exponentially, as was shown earlier in Eq. (): 10 ktAAC C e ??() 12 Consecutive Reactions ?The material balance for product C is 12CACdC k C k Cdt??Combining these equations gives 12 1 0ktCCAdC k C k C edt??? () () 13 Consecutive Reactions If no C is present at the start, integration of Eq. () gives 121021()k t k tAC kCC e ekk????? The concentration of C goes through a maximum with time, can be found by differentiating Eq. () and setting the derivative to zero: 21m a x21l n ( )kktkk??() () 14 Consecutive Reactions 2 2 1()1, m a x 02() k k kCA kCCk??The concentration of D is obtained by a material balance: 1202101 2 2 1( 1 )A A C Dk t k tDAC C C Ck e k eCCk k k k??? ? ?? ? ???() () () 15 Consecutive Reactions maximum of 67% conversion of A is % and the selectivity is 77%. the conversion is 63% and the yield of C is 56% for a selectivity of 89%. 16 Parallel Reactions ? Selectivity effects can also be important with parallel reactions having different reaction orders. Consider the case where the main reaction is first order to both reactants and the byproduct reaction is second order to one of the reactants: 1211222ABAA B CA A Dr k C Cr k C? ???? ?????byproduct formation main reaction 17 Parallel Reactions ?The local or instantaneous selectivity is the ratio of to the total rate of consumption of A: 1r1 1 21 2 1 21r r rSr r r r????1 1 122 2 2( ) ( )A B BAAr k C C k Cr k C k C??() () 18 Parallel Reactions 0 0 2 k k = ?Higher sele
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