화학공학소재연구정보센터
Inzynieria Chemiczna i Procesowa, Vol.15, No.3, 327-351, 1994
CONDENSATION OF VAPOR MIXTURES FORMING 2 IMMISCIBLE LIQUID-PHASES
Condensation of vapour mixtures forming a nonhomogeneous liquid phase (two immiscible liquids) is an important industrial operation. Such processes are frequently encountered in petrochemical industry. In Chapter 2 equilibrium relations as well as equilibrium diagrams characteristic of such systems have been analysed. This analysis, based mainly on Figs. 1 and 2, revealed that in the equilibrium diagrams for the systems considered three regions defined by equations (6)-(8) can be distinguished. For the majority of such mixtures the functions defined by Eqs. (6)-(8) can be approximated with good accuracy by linear relations (9)-(16), which have been used in subsequent considerations. The particular shape of the equilibrium curve for such mixtures suggests the occurrence of three different modes of condensation which depend on the following vapour mixture compositions: 1. The composition is the same as heteroazeotropic composition y1 = y1H. 2. The composition differs from the heteroazeotropic composition, i.e., y1 not-equal y1H. In the first case (Mechanism I) the components of the vapour mixture condense at heteroazeotropic ratio at a constant temperature (T(H)). The composition of the liquid phase formed is identical with the heteroazeotropic composition (x1P = x1 = y1H). Thus the condensation process is similar to that for a pure component; owing to the zero concentration gradient between the bulk of the vapour phase and the interface there is no diffusional resistance. In the second case there can appear two different condensation modes depending on the interfacial temperature. Mechanism II. The interfacial temperature lies between the heteroazeotropic temperature (T(H)) and the boiling point of one of the components (T1, T2). The condensate film is formed of only one liquid layer in which one of the components is present at a high concentration (0 < x1P < x'1 or x''1 < x1P < 1). Mechanism 3. The condensate film is composed of two liquid phases in which mole fractions are x'1 and x''1 but mean composition of the condensate is different from the heteroazeotropic composition (x1P not-equal x1H). Accordingly, the interfacial temperature has to be equal to the heteroazeotropic temperature T(H), and the composition of vapour at the interface - to the heteroazeotropic composition y1H. Which of the mechanisms will take place during the condensation process depends on the intensity of the condensation, which is determined by the mass and heat transport processes. In order to determine the amount of heat transported to the wall as well as the mass fluxes of the species transferred from the vapour to the liquid phase it is necessary to know the conditions at the interface, as the interfacial state variables determine the kinetics of the process. For any cross-section perpendicular to the interface the relations (22) and (23) must hold due to the continuity of fluxes at the interface. By applying the definitions of the mass and heat fluxes given by Eqs. (24)-(31) as well as assuming a segregated condensate flow (32) Eq. (33) can be derived, from the mole fraction x1P at the interface can be calculated. From this equation it is evident that for high condensing fluxes a local total condenskation takes place, i.e., x1P = y1, while for condensing fluxes tending to zero we deal with an equilibrium condensation (y1 = y1P). This holds for the whole equilibrium diagram. By applying the linear equilibrium relations (9) and (13) equations (36)-(38) are developed by means of which the mole fraction x1P at the interface can be determined in three regions of the equilibrium diagrams defined previously. The dependence of the state variables at the interface (x1P, y1P, T(P)) on the flux of the condensing vapour is illustrated in Figs. 4 and 5; in these figures the limiting value phi(G1)* at which the change in the condensation mechanism occurs is also shown. The flux of the condensing vapour can be determined by means of Eq. (47). Finally, the procedure for estimating the state variables at the interface (x1P, y1P, T(P)) as well as the flux of the condensing vapour is presented as a detailed algorithm (Fig. 6). The interfacial state variables calculated using the relations presented above determine explicitly all the mass and heat fluxes which can be employed in the appropriate balance equations characterizing the condenser under consideration. These heat and mass balances are described by the differential equations (51)-(54) and, upon the introduction of the condensation degree (55), by Eqs. (56)-(58). Moreover, in each cross-sectional area of the condenser, defined by the degree of condensation, v, relations (59)-(61) must hold, which determine the flow rates of the two phases and the average composition of the liquid phase. Accordingly, the design procedure for the condensation process consists in integrating differential equations (56)-(58) from v = 0 up to a given condensation degree, subject to initial conditions (64)-(66). For each cross-section of the condenser the flow rates of the two phases as well as the composition of the liquid are determined by Eqs. (59)-(61). Moreover, the algorithm (Fig. 6) has to be applied for each condensation degree in order to determine the interfacial state variables needed at each integration step. Verification of the model and of the design method have been performed by comparing the experimental results with numerical predictions. The inlet parameters for the experimental condenser are given in Table 1 and the experimental results and the results of calculations are presented in Table 2. As can be seen from the tables a good agreement is reached between the values predicted by the model and the experimental results. Extensive calculations performed for the mixtures considered lead to the conclusion that only in special cases the condensation mechanism II can be observed. These are: small temperature differences between the interface and the cooling medium (and thus very small condensing luxes) or, alternatively, very high (y1 --> 1) or very low (y1 --> 0) content of one of the components. This is illustrated by the temperature and composition profiles in Figs. 9, 10 and 11. Nevertheless, also in these cases, after a given condensation degree has been reached the change of the condensation mechanism occurs and mechanism III begins to take place. The results of simulation of the condensation process allow one to propose a simplified approximate method for dimensioning condensers for the mixtures considered. If inequality (62) holds it can be assumed with good accuracy that the interfacial temperature is equal to the heteroazeotropic temperature and in order to determine the heat transfer area of the condenser only the resistance of heat transfer through the condensate film has to be taken into account.