Bubble phase component mass

The diffusivity in gases is about 4 orders of magnitude higher than that in liquids, and in gas-liquid reactions the mass transfer resistance is almost exclusively on the liquid side. High solubility of the gas-phase component in the liquid or very fast chemical reaction at the interface can change that somewhat. The Sh-number does not change very much with reactor design, and the gas-liquid contact area determines the mass transfer rate, that is, bubble size and gas holdup will determine reactor efficiency. 

Given any complex system of heterogeneous catalytic first order reactions the mass balance on a differential volume element of the reactor at the height h yields the following system of differential equations for the j-th reaction component i) for the bubble phase... 

As a first approximation a convective term in the film region has been negleted, u is the superficial gas velocity and u f denotes the gas velocity at minimum fluidization conditions. Tne specific mass transfer area a(h) is based on unit volume of the expanded fluidized bed and e OO is the bubble gas hold-up at a height h above the bottom plate. Mathematical expressions for these two latter quantities may be found in detail in (20). The concentrations of the reactants in the bubble phase and in film and bulk of the suspension phase are denoted by c, c and c, respectively. The rate constant for the first order heterogeneous catalytic reaction of the component i to component j is denoted... 

In the case of a total condenser, the vapor-phase compositions used in the calculation of the equilibrium relations and the summation equations are those that would be in equilibrium with the liquid stream that actually exists. That is, for a total condenser, the vapor composition used in the equilibrium relations is the vapor composition determined during a bubble point calculation based on the actual pressure and liquid compositions found in the condenser. These compositions are not used in the component mass balances since there is no vapor stream from a total condenser. 

The quantity kg is sort of the odd-man-out in most work on slurry reactors (and even also for fluid-bed and gas-liquid reactors). If the bubble (gas) phase consists of pure reactant only, then a mass-transfer resistance in a film inside the bubble loses its meaning and kg drops out of the problem. Even in the case of mixed gas-phase components, gas phase mass-transfer coefficients are so much larger than their liquid-phase counterparts that the gas-phase transport rate would seldom be of importance in determining the overall rate of chemical reaction. 

The state of the gaseous phase at each moment of time t at any point P of the volume can be characterized by a continuous distribution of bubbles over the mass of i-th component t, P). This distribution must obey the kinetic equa-... 

An important finding that is consistently reported in the literature is explained by CFD simulations the impact of holdup is limited. If a liquid slug is completely saturated with the gas-phase component and if the film thickness can be assumed to be the same for the slug and the bubble, mass transfer is indeed completely independent of the holdup. 

A spray cyclone is based on the same idea as tiie bubble cyclone. A gas is introduced with a high velocity (say, 40 m/s) tangentionally into the cyclone, and liquid is sprayed in the axis (see figure 4.14). The liquid drops travel with great speed towards the wall, and flow downward as a thin film. Because of the greatly enhanced gas phase mass transfer coefficients, gas phase components can be separated on the basis of their effective liquid phase mass transfer coefficients (Schrauwen, 1986). These effects are discussed further in section 5.42.2 see eq. (5.45). 

In Equation 5.231, the indexes b, c, and e refer to the bubble, cloud, and emulsion phases, respectively. The mass balance for component i is valid in the bubble phase... 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

One therefore has to decide here which components of the phase interaction force (drag, virtual mass, Saffman lift, Magnus, history, stress gradients) are relevant and should be incorporated in the two sets of NS equations. The reader is referred to more specific literature, such as Oey et al. (2003), for reports on the effects of ignoring certain components of the interaction force in the two-fluid approach. The question how to model in the two-fluid formulation (lateral) dispersion of bubbles, drops, and particles in swarms is relevant... 

Let us try to describe some of these phenomena quantitatively. For simphe-ity, we will assume isothermal, constant-holdup, constant-pressure, and constant density conditions and a perfectly mixed liquid phase. The gas feed bubbles are assumed to be pure component A, which gives a constant equihhrium concentration of A at the gas-liquid interface of CX (which would change if pressure and temperature were not constant). The total mass-transfer area of the bubbles is Aj j- and could depend on the gas feed rate f constant-mass-transfer coefficient (with units of length per time) is used to give the flux of A into the liquid through the liquid film as a flinction of the driving force. 

---