Occurrence of 2-Phase Flow

Let us consider the P-T diagram in Fig. 8.1, where XY is the saturation vapour pressure-temperature line, or alternatively the pressure versus boiling point curve. In addition to showing the saturation vapour pressure curve, the diagram can also be regarded as a thermodynamic state diagram, with the curve separating liquid and vapour phase thermodynamic states. 

Consider liquid with thermodynamic state A at pressure P and temperature T. The liquid is undercooled, or subcooled, with respect to its boiling point at pressure P. 

During a transfer operation, the liquid state can cross the saturation vapour pressure curve XY resulting in the creation of two phases by two separable paths, or by combinations of the two paths, i.e., 

To prevent the occurrence of 2-phase flow during a hquid transfer, the change in thermodynamic states represented by both paths AB and AC must not end on, or cross, the saturation vapour pressure curve XY. 

This can be simply achieved with adequate pressure subcooling of the liquid, by pressurising the hquid along AA before the transfer commences. 

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Useful empirical correlations have been developed by Martinelli and Lockhart [1] for calculating frictional pressure drops at ambient temperature, which have been extended with reasonable accuracy to low temperature flows [2, 3]. The net result is that the occurrence of 2-phase flow with a fixed available overpressure for hquid transfer, will lead to a significant fall in mass flow and a mass transfer rate close to zero. 

During the cooldown of liquid transfer lines and storage tanks or containers, the occurrence of 2-phase flow, albeit transient, is unavoidable. 

Mobile phases employed for the separations are housed in a cartridge and delivered to the LC columns through a set of binary HPLC pumps (Shimadzu Corporation), as shown in Figure 6.2. The pumps provide a flow rate accuracy of 2% or 2 fiL (whichever is greater) in constant flow pumping mode, with a flow rate precision of 0.3%. A degasser (two channels internal volume of 195 /.d. /channel) is also housed in the pump module employed to minimize the occurrence of air bubbles. 

Tphe rate-limiting processes in catalytic reaction over zeolites remain A largely undefined, mainly because of the lack of information on counterdiffusion rates at reaction conditions. Thomas and Barmby (7), Chen et al. (2, 3), and Nace (4) speculate on possible diffusional limitations in catalytic cracking over zeolites, and Katzer (5) has shown that intracrystalline diffusional limitations do not exist in liquid-phase benzene alkylation with propene. Tan and Fuller (6) propose internal mass transfer limitations and rapid fouling in benzene alkylation with cyclohexene over Y zeolite, based on the occurrence of a maximum in the reaction rate at about 100 min in flow reaction studies. Venuto et al (7, 8, 9) report similar rate maxima for vapor- and liquid-phase alkylation of benzene and dehydro-... 

Liquid-liquid systems are encountered in many practical applications involving physical separations of which extraction processes performed in both sieve-tray and packed columns are well-known examples. In principle, all three methods discussed in Section III,B,2 can be used to model liquid-liquid two-phase flow problems. The added complexity in this case is the possible deformation of the interface and the occurrence of flow inside the droplet. 

Gas flow processes through microporous materials are important to many industrial applications involving membrane gas separations. Permeability measurements through mesoporous media have been published exhibiting a maximum at some relative pressure, a fact that has been attributed to the occurrence of capillary condensation and the menisci formed at the gas-liquid interface [1,2]. Although, similar results, implying a transition in the adsorbed phase, have been reported for microporous media [3] and several theoretical studies [4-6] have been carried out, a comprehensive explanation of the static and dynamic behavior of fluids in micropores is yet to be given, especially when supercritical conditions are considered. Supercritical fluids attract, nowadays, both industrial and scientific interest, due to their unique thermodynamic properties at the vicinity of the critical point. For example supercritical CO2 is widely used in industry as an extraction solvent as well as for chemical... 

We attribute these disturbances to the occurrence of slug flow just prior to cool-down. Much research has been done on two-phase flow, and several flow regime plots, similar to Fig. 2 [1, 2] are available in the literature. Since liquid flow velocity in the test system after cool-down was about 7-8 ft/sec, we would expect our system to pass through the slug-flow region just before cool-down. If slug flow is to be avoided, the system must be designed to have a liquid flow rate over 10 ft/sec. 

In the Mint model, we have to take into account the following considerations (i) the initial filtration coefficient Xq, which is a parameter, presents a constant value after time and position (ii) the detachment coefficient, which is another constant parameter (iii) the quantity of the suspension treated by deep filtration depends on the quantity of the deposited solid in the bed this dependency is the result of the definition of the filtration coefficient (iv) the start of the deep bed filtration is not accompanied by an increase in the filtration efficiency. These considerations stress the inconsistencies of the Mint model 1. valid especially when the saturation with retained microparticles of the fixed bed is slow 2. unfeasible to explain the situations where the detachment depends on the retained solid concentration and /or on the flowing velocity 3. unfeasible when the velocity of the mobile phase inside the filtration bed, varies with time this occurrence is due to the solid deposition in the bed or to an increasing pressure when the filtration occurs with constant flow rate. Here below we come back to the development of the stochastic model for the deep filtration process. 

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