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Vj-I

Fig. 27. Schematic representation of an EQ stage.

With very few exceptions, M ■ is considered to be the hold-up only of the liquid phase.

It is more important to include the hold-up of the vapor phase at higher pressures. The component material balance (neglecting the vapor hold-up) is:

= +Lhx, h +Fizu ~{\ + r] )V,yu -(l + r/ )L,xu + (49)

at k=l where x, y are mole fractions in the liquid and vapor phase, respectively. In the material balance equations given above r is the ratio of sidestream flow to interstage flow:

The E equations are the phase equilibrium relations y,j = K>.,xu where K. is chemical equilibrium constant.

The S equations are the summation equations:

The enthalpy balance is given by dM ,H, .. , ,. „ „ , ,

= +LhH'h + FjHi ~(l + r) yrf -(1 + ^)L,H'; -Q, (53)

where H is molar enthalpy, and Q is heat duty.

There is no need to take separate account in Eq. (53) of the heat generated due to chemical reaction since the computed enthalpies include the heats of formation.

The R equations are the reaction rate equations. For the reactive extractive distillation it is known that chemical reaction is reversible, and the reaction rate is assumed to be zero. That is to say, the chemical equilibrium is reached in every tray.

Under steady-state conditions all of the time derivatives in the MESH equations are equal to zero. Newton's method (or a variant thereof) for solving all of the independent equations simultaneously is an approach nowadays widely used. But other methods also are frequently used, e.g. the relaxation method where the MESH equations are written in unsteady-state form and are integrated numerically until the steady-state solution has been found, is used to solve the above equations.

7.1.2. Case studies

EQ stage model is used for process simulation of extractive distillation in order to obtain the necessary information for various purposes. In what follows we discuss the steady state of extractive distillation and extractive distillation with chemical reaction (i.e. reactive extractive distillation) in the EQ stage model.

(1 ) Steady state analysis

Analysis of operation state is still a topic of considerable interest in the distillation community. Especially in the catalytic and azeotropic distillation processes the non-linearity phenomena are very prominent, and multiple steady state is easy to appear (see chapter 4), In this chapter only steady state is analyzed.

For the separation of C4 mixture by extractive distillation with DMF, the operation state is analyzed by changing the feeding location of solvent, which is a sensitive parameter [159]. The feeding location of solvent into the extractive distillation column for recovering butane is variable, but other operating conditions are kept constant. The relation of the top molar composition of butane with the feeding stage of solvent is shown in Fig. 28 (the stage is numbered from the top to the bottom). When the solvent is fed in the vicinity of No. 20 stage, the composition change is very abrupt and two operation states (OS) are found. However, only No. 1 operation state (OS) is desirable because in this case the top molar composition of butane is much higher.

Similarly, only the feeding location of solvent into the extractive distillation column for recovering 1,3-butadicne is variable, but other operating conditions are kept constant. In this case the top molar composition of 1,3-butadiene is stable because the amount of vinylacetylene (VAC) is so small that the 1,3-butadiene composition is not affected. The function of this column is to remove VAC from 1,3-butadiene, so the change of the bottom flowrate of VAC should be obvious. The relation of the bottom flowrate of VAC (kmol h'1) with the feeding stage of solvent S is shown in Fig. 29 (the stage is numbered from the top to the bottom). It can be seen from Fig. 29 that when solvent S is fed in the vicinity of No. 30 stage, two operation states are also found. However, only No. 1 operation state is desirable because in this ease the amount of VAC removed from 1,3-butadiene is greater. Therefore, by using EQ stage model, we can find which operation state is the best or the worst.

Feeding stage of solvent S

Fig. 28. The relation of the top composition of butane with the feeding stage of solvent S in the extractive distillation column.

Feeding stage of solvent S

Fig. 28. The relation of the top composition of butane with the feeding stage of solvent S in the extractive distillation column.

Feeding stage of solvent S

Fig. 29, The relation of the bottom flowrate of VAC with the feeding stage of solvent in the extractive distillation column.

Feeding stage of solvent S

Fig. 29, The relation of the bottom flowrate of VAC with the feeding stage of solvent in the extractive distillation column.

(2) Reactive extractive distillation

In the HQ stage model, if there exists no chemical reaction, the independent equations are simplified, only solving MHSH equations. However, for reactive extractive distillation, EQ stage model is somewhat complicated, especially when there exist more than one chemical reactions. Separation of acetic acid and water with tributylamine as the separating agent is just the case.

As mentioned before, the following reversible chemical reaction may take place:

HAc + R3N « " R3NH+ * "OOCCHj where HAc. R?N and RjNH1 • OOCCHi represent acetic acid, tributylamine and the salt formed by the reaction, respectively.

In terms of the chemical equilibrium constant K at 25°C, the relation of chemical equilibrium constant with temperature can be deduced by Eq. (4).

On the other hand, it is known that aggregation of acetic acid molecules in the vapor phases occurs. If only aggregation of two molecules is considered, the following reversible chemical reaction may take place:

2A[ < * A2 where A] is the monomer of acetic acid, and A2 is the dimer of acetic acid.

In this case, the chemical equilibrium constant KA is written as nv

In addition, KA , the function of temperature, can also be calculated by the following empirical equation [137, 138], lg KAi=£Ai+a>AJT (55)

The key to the simulation of extractive distillation process is the selection of an accurate VLE model to solve the EQ stage model of the column. In general, the Wilson, NRTL and UNIQUAC equations, which are suitable for systems composed of many components and can deduce the multi-components system from binary systems, are used.

Although the VLE data can be obtained by experiments and then correlated by the iterative solution by using the maximum likelihood regression, the interaction parameters of the VLE model may be various under different assumptions. Table 26 shows the interaction parameters of Wilson, NRTL and UNIQUAC equations for the system of water (1) and acetic acid (2) under two cases: considering two-molecule aggregation and not, respectively; Table 27 shows the interaction parameters of Wilson, NRTL and UNIQUAC equations for the system of water (1) and tributylamine (2); Table 28 shows the interaction parameters of Wilson, NRTL and UNIQUAC equations for the system of acetic acid (1) and tributylamine (2) under three cases: not considering two-molecule aggregation and reversible chemical reaction; only considering reversible chemical reaction, and considering two-molecule aggregation and reversible chemical reaction at the same time, respectively.

In these tables an average deviation Ay, is calculated by

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