Catalysis of Organic..

190Modeling Mass Transfer Hydrogenationwhere Sh=k Li .d p /D Reynolds number is calculated by using the turbulence theory ofKolmogoroff,1/ 3⎛ εd⎞Red= ⎜3⎟⎝ v ⎠and Schmidt number is defined as Sc= ν/DThe critical issue in the calculation of the Reynolds number is the energy dissipated.The experiments of Hajek and Murzin (15) have shown that the dissipated energycan in many cases be clearly less than the energy imposed by the stirrer of a slurryreactor.An analogous approach was applied on the calculation of the gas-liquid mass transfercoefficient of hydrogen (k LH ). The physical parameters needed for the mass transfercoefficients and the dimensionless parameters (Re, Sc) are listed in the Notationsection near the end of this chapter.Catalytic ReactorFor the semi-batch stirred tank reactor, the model was based on the followingassumptions: the reactor is well agitated, so no concentration differences appear inthe bulk of the liquid; gas-liquid and liquid-solid mass transfer resistances canprevail; and finally, the liquid phase is in batch, while hydrogen is continuously fedinto the reactor. The hydrogen pressure is maintained constant. The liquid and gasvolumes inside the reactor vessel can be regarded as constant, since the changes ofthe fluid properties due to reaction are minor. The total pressure of the gas phase (P)as well as the reactor temperature were continuously monitored and stored on a PC.The partial pressure of hydrogen (p H2 ) was calculated from the vapour pressure of thesolvent (p VP ) obtained from Antoine’s equation (p VP0 ) and Raoult’s law:VP Vp0p = p xsolvent(10)where the Antoine parameters are listed in the Notation section. The hydrogenpressure in gas phase thus becomesVPOpH= p − p xsolvent(11)2The volatilities of the reactive organic components (citral, its reaction productsas well as the sugars) were negligible under the actual experimental conditions.A general mass balance for an arbitrary liquid-phase component in the stirredtank reactor is thus written as follows,dniNi Ap= NGLiAGL+(12)dti.e. the fluxes (N i , N GLi ) negative for reactants but positive for products. Introductionof the liquid-phase concentration (n i =c i V L ), assuming a constant liquid-phase volumeand introducing the quantities a P =A P /V L and a GL =A GL /V L gives after somerearrangement: