Hydrodynamics of cocurrent three-phase fixed-bad reactors .2. Verification of the parameters of the hydrodynamic model

The objective of the present study is to verify the parameters (estimated elsewhere, 1]) of the hydrodynamic model of Grosser et al. [2]. This model formed the basis for the derivation of a mathematical criterion defining the change-over of the hydrodynamic mode from the gas continuous flow regime to pulsing flow regime. The parameters verified are: relative permeabilities of the liquid (k(L) = delta(L)(n)) and gas (k(g) = s(g)(m)) phases and a numerical coefficient at the logarithmic function in the Leverett J-function. The verification requires the knowledge of the gas pressure drop in the reactor and the liquid hold-up. The gas pressure drop was determined experimentally for the following systems: nitrogen-water, nitrogen-aqueous glycerol solutions and nitrogen-aqueous ethanol solutions (the physicochemical properties of the solutions studied are given in Table 3 of ref. [1]). The values of the liquid hold-up were taken from the literature (cf. Table 1 and Figs. 1-3). Upon analysing the available data concerning the liquid hold-up, considerable discrepancies were found between the experimental values of this parameter. Since both in the hydrodynamic model and in the mathematical criterion of Grosser ct al. [2] defining the regime change-over these parameters (i.e. epsilon(L) and epsilon(g) appear risen to high powers, the discrepancies in the experimental values of the liquid hold-up are reflected by the calculated values of n(cal) and m(cal) (Figs. 6-8) and, therefore, in the values of the relative permeabilities of the two phases. This suggests that without reliable values of relative permeabilities, k(L) and k(g), both the hydrodynamic model and criterion of Grosser et al. [2] should be employed with great care. It has to be remembered that the forces <(F-i)under bar> which are calculated basing on the values of relative permeabilities of the two phases) are very high and play a dominant role in the momentum balance equations. This is especially true with regard to measurement systems of physicochemical properties different than those of water; in this case, the values of the model parameters estimated in the present work may prove inadequate.