Liquid-phase mass balance

Liquid reactant (nonvolatile component) liquid-phase mass balance ... 

The liquid-phase mass balance (3.367) is used for volatile reactants being originally in the liquid phase and for reactants that are in the gas phase and are dissolved in the liquid phase. This mass balance is also called volatile liquid-phase mass balance (Hopper et al., 2001). 

The mass transfer coefficient for ozone can be calculated from both the liquid and gas phase mass balances as described by equations 3-26, 3-27 or 3-28. Difficulties arise with the liquid phase mass balance if a reaction is present. The reaction rate under the operating conditions investigated must be used, considering especially the cL prevalent in the system. Since this can be very difficult to assess, and use of inaccurate reaction rates leads to inaccurate kLa, application of the gas phase mass balance is an elegant way to avoid this problem. 

The numerator contains all hydroxyl radical forming reactions and all initiating reactions are summarized (Sk c(/()). The denominator contains all hydroxyl radical consuming reactions. The second term includes all reactions with intermediates (EkPi c(P,)), the third the reactions with scavengers(Lksi c(S,)). Similarly, the steady-state concentrations of ozone and hydrogen peroxide can be calculated from the liquid phase mass balances. 

The CNMMR model with laminar flow liquid stream in the annular region consists of three ordinary differential equations for the gas in the tube core and two partial differential equations for the liquid in the annular region. These equations are coupled through the diffusion-reaction equations inside the membrane and boundary conditions. The model can be solved by first discretizing the liquid-phase mass balance equations in the radial direction by the orthogonal collocation technique. The resulting equations are then solved by a semi-implicit integration procedure [Harold etal., 1989]. 

These are generally classified as either CSTRs, semiflow batch reactors (SFBR), or plain batch reactors, which we treated in the previous section. If the reactor is well-mixed, the liquid-phase mass balance is the same general form for all. For component j. 

LIQUID-PHASE MASS BALANCES WITH CHEMICAL REACTION... 

Dimensionless Form of the Liquid-Phase Mass Balances... 

All liquid-phase mass balances, given by equation (24-8) ... 

Hence, the final form of the dimensionless liquid-phase mass balances is... 

Step 3. Write all of the liquid-phase mass balances in condensed form using the a-parameters defined by equations (24-78) ... 

Step 4. Group all terms and coefficients in equation (24-79) that are specific to component j on one side of the generic liquid-phase mass balance ... 

For packed columns, a promising approach is represented by differential models like the axial dispersion model [82] and the piston flow model with axial dispersion and mass exchange [83], Experimental studies show that the axial dispersion model gives an appropriate description of the nonideal flow behavior of the liquid phase in catalytic packings (see Fig. 10.4) [77]. When applying the axial dispersion model to cover this nonideality, the liquid-phase mass balances (Eqs. (10.3)) transform to the following equations ... 

For the simulation of gas-liquid reactors used in the synthesis of chemicals, a complete set of gas- and liquid-phase mass balances is usually needed. The reason is that the concentrations of chemical components are high in both gas and liquid phases, and chemical reactions proceed both in the liquid film and in the liquid bulk phase. 

Figure 7.22 illustrates the numerical solution of concentrations in the liquid phase of a tank reactor. The simulation also gives the concentration profiles in the liquid film, as shown in Figure 7.22b. The algebraic equation system describing the gas- and liquid-phase mass balances is solved by the Newton-Raphson method, whereas the differential equation system that describes the liquid film mass balances is solved using orthogonal collocation. To guarantee a reliable solution of the mass balances, the mass balance equations have been solved as a function of the reactor volume. The solution of the mass balances for the reactor volume, Vr, has been used as an initial estimate for the solution for the reactor volume, Vr -F A Vr. The simulations show an interesting phenomenon at a certain reactor volume, the concentration of the intermediate product, monochloro-p-cresol, passes a maximum. When the reactor volume—or the residence time— is increased, more and more of the final product, dichloro-p-cresol, is formed (Figure 7.22a). This shows that mixed reactions in gas-liquid systems behave in a manner similar to mixed reactions in homogeneous reactions (Section 3.8) [11,12].

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