Mass transfer area

Effective Interfacial Mass-Transfer Area a In a packed tower of constant cross-sectional area S the differential change in solute flow per unit time is given by... 

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

The mass-transfer coefficients depend on complex functions of diffii-sivity, viscosity, density, interfacial tension, and turbulence. Similarly, the mass-transfer area of the droplets depends on complex functions of viscosity, interfacial tension, density difference, extractor geometry, agitation intensity, agitator design, flow rates, and interfacial rag deposits. Only limited success has been achieved in correlating extractor performance with these basic principles. The lumped parameter deals directly with the ultimate design criterion, which is the height of an extraction tower. 

Ogl gas-liquid mass transfer area to reactor volume relation c concentration D diffusion coefficient... 

Quite new ideas for the reactor design of aqueous multiphase fluid/fluid reactions have been reported by researchers from Oxeno. In packed tubular reactors and under unconventional reaction conditions they observed very high space-time yields which increased the rate compared with conventional operation by a factor of 10 due to a combination of mass transfer area and kinetics [29]. Thus the old question of aqueous-biphase hydroformylation "Where does the reaction takes place " - i.e., at the interphase or the bulk of the liquid phase [23,56h] - is again questionable, at least under the conditions (packed tubular reactors, other hydrodynamic conditions, in mini plants, and in the unusual,and costly presence of ethylene glycol) and not in harsh industrial operation. The considerable reduction of the laminar boundary layer in highly loaded packed tubular reactors increases the mass transfer coefficients, thus Oxeno claim the successful hydroformylation of 1-octene [25a,26,29c,49a,49e,58d,58f], The search for a new reactor design may also include operation in microreactors [59]. 

The high surface-to-volume ratio can also significantly improve both thermal and mass transfer conditions within micro-channels in two ways firstly, the convective heat and mass transfers, which take place at the multi-phase interface, are improved via a significant increase in heat and mass transfer area per unit volume. Secondly, heat and mass transfers within a small volume of fluid take a relatively short time to occur, enabling a thermally and diffusively homogeneous state to be reached quickly. The improvement in heat and mass transfer can certainly influence overall reaction rates and, in some cases, product selectivity. Perhaps one of the more profound effects of the efficient heat and mass transfer property of micro-reactors is the ability to carry potentially explosive or highly exothermic reactions in a safe way, due to the relatively small thermal mass and rapid dissipation of heat. 

The state of mixing generally controls tire mass transfer. In a liquid-liquid system, for example, the reaction rate is based on the mass transfer which depends on the interface area of the two liquid layers. This area is dramatically changed by a change in the mixing rate. If, for example, the agitator is started late, the increase in mass transfer area will lead to a rapid increase in the conversion rate and hence in the heat production rate. 

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. 

The one with the higher flow rate to obtain the maximum mass transfer area... 

For the PFTR the mass transfer area is simply the total interfacial area between the phase in question and the other fluid, while for the PFTR, where Cj is a function of position, [areaWolume] is the area per unit volume of that phase at position Z- The steady-state mass balance is therefore... 

We next need A/ V, the mass transfer area per unit volume of the reactor. The residence time of a bubble is L/m . The volume of each bubble is D, and the surface area of a bubble is 7t D. The volumetric flow rate of gas is... 

The agitated cell reactor consists of two chambers, one for the liquid phase and another for the gas-phase, which can both be independently mixed by two mixers. In this reactor the mass-transfer area can be varied independently of the gas flow rate by installing various porous plates with a defined number of holes, i. e. a defined contact area gas-liquid, between the two chambers. The value of kL can then be determined from the measurement of kLa. 

The third factors to control and keep constant are the gas pressure and superficial gas velocity. This probably will involve gas recirculation with either a small compressor, or through a hollow shaft or some other pumping device. As seen before, the bubble diameter, the mass transfer area, the gas hold-up, and the terminal bubble-rise velocity, all depend on the superficial velocity of the gas and the power input per unit volume. When these are kept constant, the various mass transfer resistances in the pilot plant and in the large unit will be the same, hence the global rate will be conserved. The last factor is the input power to the agitator. As required for mass transfer, the scale-up must be made on the basis of constant power input per unit volume. If turbulent conditions and geometrical similarity prevail, this rule imposes the following relationship ... 

The available mass transfer area for the catalyst loading is given by equation (5.3-7), that is... 

We note that RM can also be expressed per unit of mass-transfer area between the two phases. 

Alternatively, a third, low boiling-point additive such as water or inert gas can be added to strip the residual volatiles, which (a) provides more mass transfer area, (b) reduces diffusion distance for the molecules that we wish to remove, (c) increases the driving force for the separation because of the lower concentration of the volatile in the bubbles, and (d) the vaporization of the stripping agent offsets some of the heat generated by viscous dissipation. Of course, after separation we have to deal with a dilute mixture of the volatile in the stripping agent, which may need to be separated for recovery and/or environmental reasons. 

The results demonstrate that for liquid mass fluxes, which do not lead into the direct proximity of the state of saturation of air, a stoichiometric relationship does not play an unimportant role. Rather, the mass transfer area of the fluidized bed is the limiting factor of the absorption. Over-stoichiometric operation does not lead to any improved separation of the SO2 (Figs. 16.14 and 16.15), the reason being the permanent destruction of the liquid film by particle-particle collisions and the consequent production of inactive reactants. 

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... 

For calculating the external mass transfer k a value of Sh = 2 can be safely assumed. The specific mass-transfer area per unit of bed volume is p - 6(1-Eb)/dp, in which b is the bed void fraction. The combination of resistances leads to the following expression for the apparent kinetic constant ... 

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