Catalysis of Organic..

Salmi et al. 189andn−1( ) ( 1)) 1'−a − a k n − tn 1, n ≠ 1*a = +−jaj 0 * j(4b)Some special cases of eq. (4) are of interest: for irreversible first (n=1) and second−kjt'(n=2) order deactivation kinetics we get a a e and a = a / + a k tj= 0( )jj0 j1respectively.In case that the effective diffusion coefficient approach is used for the molar flux, it⎛ dci⎞is given by Ni= −Dei⎜ ⎟ , where D ei =(ε p /τ p )D mi according to the random pore⎝ dr ⎠model. A further development of eq. (1) yields2dc ⎛⎛⎞⎞i −1d c⎜i s dciε ⎟∑ +⎜ +⎟pρpνijRjajDei(5)2dt⎝⎝ dr r dr ⎠⎠The boundary conditions of eq. (5) are0 jjanddc i = 0drat r = 0(6a)⎛ dci⎞Dei⎜ ⎟ = kLi( ci− ci( R)) at r = R (6b)⎝ dt ⎠r=Rwhere c i is the bulk-phase concentration of the component. The initial condition att=0 is c i (r)=ci, i.e. equal to the bulk-phase concentration.The molecular diffusion coefficients in liquid phase were estimated from thecorrelations Wilke and Chang (9) for organic solutions and Hayduk and Minhas (10)for aqueous solutions, respectively. The solvent viscosities needed in the correlationswere obtained from the empirical equation based on the experimental data,⎛ η ⎞ln ⎜ ⎟ = A + B / T , where the parameters A and B are given in (11). Spherical⎝ cP ⎠(s=2) and trilobic s=0.49, were used in the experiments. Hydrogen solubility in theorganic reaction mixture was obtained from correlation of Fogg and Gerrard (12),ln ( x * *H) = A + B / T , where x is the mole fraction of dissolved hydrogen in2H 2equilibrium, and A and B are experimentally determined constants. For aqueoussugar solutions, a correlation equation proposed by Mikkola et al. (13) was used.The liquid-solid mass transfer coefficient was estimated from the correlationprovided by Temkin et al. (14). The method is based on the estimation of Sherwoodnumber (Sh), starting from Reynolds (Re) and Schmidt (Sc) numbers,α βSh = a Re(7)iSc i