*2.3. Thermodynamics Data*

Table 1 shows the information on reactants, products, and the boiling point at a reactive pressure of 20 kPa. There is no binary or ternary azeotropic phenomenon in the system [10].

**Table 1.** Information of pure components at a reactive pressure on 20 kPa.


As can be seen from Table 1, the reactants of the reaction, namely, acetic anhydride and butyric acid, have boiling points higher than the lighter product acetic acid, and lower than the heavier product butyric anhydride, which is key to the proposed SRDC process with the internal circulation of excess reactant.

Table 2 shows binary interaction parameters estimated using Aspen Plus (Aspen Plus 8.4, Aspen Tech, Bedford, CO, USA, 2014), VLE-HOC is a physical property method. The non-random two liquid (NRTL) activity coefficient model was used to calculate phase equilibrium in this work [11], which is calculated by Equations (9)–(12):

$$\ln \gamma\_i = \left(\sum\_j \pi\_{ji} \mathbf{G}\_{ji} \mathbf{x}\_j / \sum\_k \mathbf{G}\_{ki} \mathbf{x}\_k\right) + \sum\_j \left(\mathbf{x}\_j \mathbf{G}\_{ij} / \sum\_k \mathbf{G}\_{kj} \mathbf{x}\_k\right) \left[\tau\_{ij} - \left(\sum\_k \mathbf{x}\_k \tau\_{kj} \mathbf{G}\_{kj} / \sum\_k \mathbf{G}\_{kj} \mathbf{x}\_k\right)\right] \tag{9}$$

$$
\pi\_{i\dot{j}} = a\_{i\dot{j}} + b\_{i\dot{j}}/T + c\_{i\dot{j}}/T^2 \tag{10}
$$

$$G\_{i\bar{j}} = \mathcal{e}^{(-u\_{i\bar{j}}\tau\_{i\bar{j}})} \tag{11}$$

$$
\alpha\_{i\bar{j}} = \alpha'\_{i\bar{j}} + \beta'\_{i\bar{j}} T \tag{12}
$$


**Table 2.** Binary interaction parameters.

#### **3. Simulation of Two-Column RD Process for the Production of Butyric Anhydride**

According to the above reaction kinetic and thermodynamic data, and the process introduced in the literature [9], the traditional two-column RD process is operated with a 10% excess feed of butyric acid as simulated with Aspen Plus, where the pressure of both columns is 20 kPa, and the residence time of reactive tray is 6 min. Figure 1 shows the process parameters and simulation results of the process streams, where NF means feed position; Nr, Nrxn and Ns represent the number of rectifying, reactive, stripping trays, respectively; and NT means the total number of column trays. The reactants are fed into the RD column C1; the overhead discharge of C1 is acetic acid, while the bottom discharge is the mixture of excess butyric acid and butyric anhydride, which is fed into distillation column C2, whose overhead discharge is the excess butyric acid to be recycled back to C1, and the bottom discharge is the product butyric anhydride, whose purity is more than 94 mol %, as seen from Figure 1.

**Figure 1.** Traditional two-column reactive distillation (RD) process.

#### **4. Single RD Column with Internal Material Circulation**

## *4.1. Principle and Two Applications*

Before the reactants are fed, it is supposed that the excess operation has been used to prepare the initial bottom materials of the RD column before start-up, e.g., the mole ratio of acetic anhydride to butyric acid is 1.1:2 for the bottom materials. The neat operation is used for the RD column after the process is running in a steady state. As a result of the different boiling points of the pre-excessed acetic anhydride reactant and the acetic acid, they can be separated easily from in the rectifying section of the column. As shown by Figure 2a, the acetic anhydride is always excessive and circulates in the column, thus the conversion of butyric acid is very promising, similar to the case of the traditional two-column RD process with the excess feed of acetic anhydride. Of course, the condenser duty of the RD column in Figure 2a must be tuned carefully to implement the internal circulation of the excessed acetic anhydride.

**Figure 2.** A single RD column (SRDC) with internal circulating excess reactant. (**a**) SRDC with internal circulation of pre-excess AcAn; (**b**) SRDC with internal circulation of pre-excess BuAc.

Similarly, with an excess of butyric acid in the initial bottom material, the internal circulation of butyric acid can also be realized by tuning the reboiler duty of the RD column in Figure 2b carefully, since the difference in boiling points is also significant between butyric acid and butyric anhydride.

The above two applications of the single RD column with excess reactant circulating internally are the bases of the proposed SRDC process.

#### *4.2. Simulation of the SRDC Process*

The application of internal circulation of excess reactant depends on tuning the condenser duty or reboiler duty of the SRDC. Therefore, it is important to simulate the processes shown in Figure 2a,b whose corresponding flowsheets in ASPEN are shown with Figure 3a,b. The position of the reactive section is fixed, but the simulation strategy is different depending on the different excess feed. When acetic anhydride is in excess, the rectifying section and the reactive section are separated from the stripping section, the tear flow is supplemented with an excess of 10% acetic anhydride, and the rectifying section is used to separate the excess acetic anhydride and acetic acid. When butyric acid is in excess, the rectifying section is separated from the reactive section and the stripping section, the tear flow is supplemented with an excess of 10% butyric acid, and the stripping section is used for the separation of the excess butyric acid and butyric anhydride.

In Figure 3a, which represents the pre-excess of acetic anhydride, the upper column with the condenser is the only rectifying section of the SRDC, as shown in Figure 2a; the only material discharged from overhead is the acetic acid byproduct, the excess acetic anhydride circulates internally, while the lower column with the reboiler only includes the reactive and stripping sections of the SRDC, whose bottom discharge is the butyric anhydride product.

**Figure 3.** Flowsheets of SRDC with internal circulation of excess reactant. (**a**) SRDC with internal circulation of pre-excess AcAn; (**b**) SRDC with internal circulation of pre-excess BuAc.

In Figure 3b, which represents the pre-excess of butyric acid, the upper column with the condenser only includes the reaction and rectifying sections of the SRDC, as shown in Figure 2b, whose overhead discharge is also the acetic acid byproduct; while the lower column with the reboiler only represents the stripping section of the SRDC, where the pre-excess butyric acid is separated from butyric anhydride and circulates internally; the bottom discharge is also the butyric anhydride product.

#### *4.3. Simulation Results of the Optimized SRDC*

On the basis of the flowsheets presented in Figure 3, sensitivity-based optimization was carried out to optimize the proposed two applications of the SRDC process, and the results are shown in the following.

Under the condition of a pre-excess of acetic anhydride, the simulation results of the optimized SRDC process are shown in Figure 4, the SRDC3 is the SRDC with excess acetic anhydride circulating internally.

**Figure 4.** SRDC3 (SRDC with excess acetic anhydride circulating internally) with excess acetic anhydride circulating internally.

As seen from Figure 4, the purity of the butyric anhydride product is higher than in the traditional two-column process. Figure 5 shows the temperature and liquid composition profiles between the SRDC trays.

**Figure 5.** The temperature and liquid composition profile between the SRDC3 trays. (**a**) The temperature profile between SRDC3 trays; (**b**) the liquid composition profile between SRDC3 trays.

Figure 6 shows the simulation results of the optimized SRDC under the condition of excess butyric acid, where the purity of the butyric anhydride product is also higher than that of the two-column process, the SRDC4 is the SRDC with excess butyric acid circulating internally.

**Figure 6.** SRDC4 (SRDC with excess butyric acid circulating internally) with excess butyric acid circulating internally.

Figure 7 shows the temperature and liquid composition profiles between the trays of the SRDC4, which are similar to those under the condition of an excess feed of acetic anhydride.

**Figure 7.** The temperature and liquid composition profile between SRDC4 trays. (**a**) The temperature profile between SRDC4 trays; (**b**) the liquid composition profile between SRDC4 trays.

The results of the three processes are compared in Table 3.


**Table 3.** Results of the three processes.

The conversion of reactants and the purity of the product are higher than in the two-column process.
