**4. Results**

#### *4.1. Example 1: Isopropyl Acetate*

Taking the process of synthesizing isopropyl acetate (IPAc) with acetic acid (HAc) and isopropanol (IPOH) as an example, the esterification reaction is a reversible exothermic reaction, and the conversion rate is limited by the chemical equilibrium. Zhang et al. proposed reactive and extractive distillation technology for the synthesis of IPAc, and the extraction agen<sup>t</sup> dimethyl sulfoxide (DMSO) was added in the tower to obtain high-purity IPAc [6]. Zhang et al. conducted a steady-state simulation of the reactive distillation column, and performed dynamic optimization control, based on the results. In this work, the improved Inside–Out method was used to solve the esterification process, and the steady-state simulation results were compared with that of Zhang et al. [6]. The chemical reaction equation of this esterification reaction was as follows:

$$\text{CH}\_3\text{COOH} + (\text{CH}\_3)\_2\text{CHOH} \rightleftharpoons \text{CH}\_3\text{COOCH} (\text{CH}\_3)\_2 + \text{H}\_2\text{O}$$

Kong et al. determined the kinetic model of the esterification reaction through kinetic experiments [24]. The kinetic expressions and parameters are as follows:

$$r = k^{+} \mathbf{C}\_{I \text{MAC}} \mathbf{C}\_{I \text{POH}} - k^{-} \mathbf{C}\_{I \text{PA} \subset \text{C}\_{I} \mathcal{O}\_{2} \text{O}},\tag{41}$$

$$k^{+} = 2589.1 \exp\left(-\frac{14109}{RT}\right) \text{k}^{-} = 2540.2 \exp\left(-\frac{18890}{RT}\right) \text{.}\tag{42}$$

where r is the reaction rate, mol·L−1·min−1; Ci is the molar volume concentration of the i component, mol·L−1; *k*<sup>+</sup>, and *k*– are the forward and reverse reaction rate constants; *R* is the gas constant, with avalue of 8.314 J·mol−1·K−1; and *T* is the temperature, in K.

The improved Inside–Out method was used to simulate the isopropyl acetate process. The property method was non-random two liquid (NRTL). The operating conditions of the isopropyl acetate reactive distillation column is shown in Table 1.


**Table 1.** Operational conditions of the reactive distillation column.

The schematic diagram of the isopropyl acetate reactive distillation column and the parameters of the feed stream are shown in Figure 5.

Figure 6 is a comparison between the initial value of the reaction extent and the simulation result. It can be seen that the initial value and the simulation results were relatively close, which increased the possibility of convergence. The error behavior at each iteration, calculated by Equation (38), for the program using the improved Inside–Out method is shown in Figure 7. The outer loop calculation reached the convergence through 10 iterations, and the error decreased steadily, without oscillation.

**Figure 5.** Schematic diagram of the isopropyl acetate reactive distillation column.

**Figure 6.** Comparison of the initial values of the extent of reaction and simulation results.

**Figure 7.** Error at each iteration for the simulation of isopropyl acetate reactive distillation column.

Table 2 shows the comparison between the simulation results of the isopropyl acetate reactive distillation column and the literature. It can be seen that the temperatures at the top and bottom of tower obtained in this work were similar to that in the literature, and the relative deviation was within 1%. The relative deviation of the condenser heat duty was 1.82% and the relative deviation of the reboiler heat duty was 2.47%.


**Table 2.** Comparison of the simulation results of Example 1.

Table 3 shows the comparison between the simulation results of the molar composition of the top and bottom products and the literature. It can be seen that the molar composition of the top and bottom product obtained in this work presented a grea<sup>t</sup> agreemen<sup>t</sup> with the literature, except for the smaller part, and the simulation results were accurate and reliable.


**Table 3.** Comparison of product composition of Example 1.

## *4.2. Example 2: Propadiene Hydrogenation*

Taking the depropanization column in the propylene recovery system of the ethylene production process as an example. The Inside–Out method was used to simulate the depropanizer column, and the results were compared with the measured values. The top of the depropanizer column was equipped with a catalyst. In the reaction section, propadiene was hydrogenated into propylene and propane. The conversion rate of the first reaction was 0.485, the conversion rate of the second reaction was 0.015. The chemical reaction equation were as follows:

$$\begin{array}{c} \mathrm{C\_3H\_4 + H\_2 \to C\_3H\_6} \\ \mathrm{C\_3H\_4 + 2H\_2 \to C\_3H\_8} \end{array}$$

The improved Inside–Out method was used to simulate the depropanization column. The property method was Soave–Redlich–Kwong (SRK). The depropanizer column had 3 feeds, and the feed stream parameters are shown in Table 4. The operating conditions of the depropanization column are shown in Table 5.


**Table 4.** The parameters of feed stream for the depropanization column.

**Table 5.** Operational conditions for the depropanization column.


Table 6 shows the comparison between the simulation results of the depropanization column and the measured value. It can be seen that the temperatures in the top and bottom products, as calculated by the Inside–Out method were close to the measured value, and the relative error was about 1%. The liquid product flow rate at the top and bottom of the tower coincided with the measured value, only the relative deviation of the vapor product flow at the top of the tower was 2.74%. Table 7 shows the comparison between the mass composition of the top and bottom liquid products and the measured value. The simulation results of the product mass compositions were basically consistent with the measured value, except for the smaller composition values.

**Table 6.** Comparison of the simulation results of Example 2.



**Table 7.** Comparison of the mass compositions of the product flow of Example 2.
