Catalysis of Organic..

Salmi et al. 191dci= Niap− NGLiaGL(13)dtThe initial condition is c i =c i (0) at t=0. The flux at the particle surface is givenby (see eq. 6b),N = k c − c R(14)iLi( ( ))iiwhile the flux at the gas-liquid interface is estimated from the two-film theoryresulting in the expressionb bcGi− KicLiNGLi= (15)Ki1−kLikGiIn the actual case, this expression is used for hydrogen only, since thevolatilities of organic reactants and products were negligible, and thus N GLi =0 for theorganics.The concentration of hydrogen in gas phase was obtained from the ideal gaslaw, c H2 =p H2 /(RT) (eq. 11), and the equilibrium ratio of hydrogen (K H2 ) wascalculated from the equilibrium solubility (x * H2, Fogg and Gerrard (12)) and Henry’slaw:pH2KH= (16)2 *x c RTwhere C TOT,L =ρ L /M L (Table 1).Numerical ApproachH2TOT , LThe partial differential equations describing the catalyst particle were discretizedwith central finite difference formulae with respect to the spatial coordinate.Typically about 9 discretization points were used for the particle. The ordinarydifferential equations (ODEs) created were solved with respect to time together withthe ODEs of the bulk phase. Since the system is stiff, the computer code ofHindmarsh (3) was used as the ODE solver. In general, the simulations progressedwithout numerical troubles.Case StudiesMany organic hydrogenation and isomerization reactions have a parallel-consecutivereaction scheme of the typeABCD