3.3.2. H2/EC

In this work, a higher H2/EC means lower EC partial pressures under almost the same H2 partial pressure (the variation in the H2 partial pressure is negligible for H2/EC > 80). As shown in Figure 8a–c, higher H2/EC inhibits EC conversion because the EC consumption reactions (R1 and R2) are positive-order with respect to EC. For the adiabatic reactor, the MeOH selectivity increases slightly with H2/EC (Figure 8a). The reason is that *S*MeOH is related to parallel reactions R1 and R2, which are 0.65-order and 1-order with respect to EC, respectively. The lower the EC partial pressure, the lower the relative rate of Reaction 1 to Reaction 2, and therefore the higher the MeOH selectivity. The EG selectivity increases more significantly with H2/EC, because enhanced axial convective heat transfer by the gas mixture under high H2/EC alleviates the adiabatic rise of bed temperature, which favors EG selectivity. For the boiling water-cooled reactor, the variation of *S*MeOH with H2/EC in Figure 8b resembles that for the adiabatic reactor. However, *S*EG and *S*Alcohol of the water-cooled reactor only increase by 1% and 3%, respectively, for H2/EC from 80 to 200, because the catalyst bed is close to isothermal. In Figure 8c, almost identical behavior is observed for the oil-cooled reactor as the boiling water-cooled reactor, except that *X*EC of the latter is slightly higher for H2/EC > 160, and that *S*EG and *S*Alcohol of the latter is slightly lower for H2/EC < 120. EC condensation happens when inlet H2/EC is smaller than 120 regardless of the type of the reactor, provided that EC most likely liquefies at the reactor inlet when its partial pressure is the highest.

**Figure 8.** *Cont*.

**Figure 8.** Reactor performance under different H2/EC: (**a**) adiabatic reactor, (**b**) boiling watercooled reactor, (**c**) conduction oil-cooled reactor. Operating conditions: reactant and coolant inlet temperatures 463 K, 3 MPa, 0.3 gEC·gcat−1·h<sup>−</sup>1, 80–200 H2/EC.

3.3.3. Pressure and Space Velocity

Pressure and space velocity have a great impact on the catalytic reaction but a minor influence on the transport characteristics. The influence of pressure and space velocity on the reactor performance is exemplified by the case of the boiling water-cooled reactor in view of the consistent behaviors among the different types of reactors. Figure 9a shows that the increase of operating pressures accelerates EC hydrogenation as the partial pressure of EC is increased (R1) and (R3). Meanwhile, since R1 and R2 are boosted at higher pressure while remaining unaffected, an increase in EG selectivity is observed. The MeOH selectivity is determined by the relative rates between R1 and R2. With a higher total pressure and EC partial pressure, the rate of R1 increases less than that of R2 (EC orders 0.65 and 1), resulting in lower MeOH selectivity. Although a higher operating pressure favors both EC conversion and the selectivity of EG—the more value-added product—it may also lead to EC condensation when exceeding 4.8 MPa. The optimal operating pressure is around 3 MPa when all performance metrics achieves a reasonable trade-off.

**Figure 9.** Reactor performance of the boiling water-cooled reactor under the conditions of (**a**) 1–5 MPa, 0.3 gEC·gcat−1·h<sup>−</sup>1, (**b**) 3 MPa, 0.1–0.5 gEC·gcat−1·h−<sup>1</sup> (*T*in = 463 K, *<sup>T</sup>*<sup>c</sup> = 463 K and H2/EC = 200).

Figure 9b depicts the influence of space velocity on the reactor performance. Lower space velocity is beneficial for both *X*EC and *S*MeOH. To ensure a conversion over 90%, the space velocity should be maintained below 0.3 gEC·gcat−1·h−1. The slightly higher MeOH selectivity at low *SV* and high *X*EC originates from the fact that the main reaction R1 has a smaller reaction order of EC than the parallel side-reaction R2 (i.e., R1 decays slower at high EC conversion than R2). In contrast to MeOH, the EG selectivity is boosted at high *SV* when the secondary EG hydrogenation reaction proceeds inadequately. Since

high space velocity results in too large bed pressure drop (Figure S5b), a space velocity of around 0.3 gEC·gcat−1·h−<sup>1</sup> is deemed feasible with balanced operational cost and reaction performance.

The specific effects of key operating variables *T*, *P*op, *SV* and H2/EC on the reactor performance are summarized in the Table S7.

## *3.4. Operation Windows*

Informed by the preceding illustrations, the different types of reactors response differently to variations of operating parameters. The major variables that affect the reactor performance and could be frequently changed in industrial practice include the inlet temperature of reactants and coolant (*T*), the operating pressure (*P*op), and space velocity (*SV*). Therefore, the *T*, *P*op and *SV* values required to reach certain *X*EC, *S*EG and *S*Alcohol are further calculated for the different types of reactors to shed light on their respective operating windows.

Figure 10 shows the demanded temperature and operating pressure for *X*EC, *S*EG and *S*Alcohol to reach 90/95/98%, respectively. In brief, the contour lines for *X*EC = 90% and 98% indicate that higher temperatures are required should the EC conversion be kept constant at decreasing operating pressures. The contour lines for *S*EG = 90% and 95% indicate that the operating pressure has negligible effects on *S*EG, which only decreases with the increase of temperature. The 85% *S*Alcohol contour line shows a downward trend with temperature for *P*op > 3.5 MPa. This is because higher pressures decrease *S*MeOH with *S*EG unaffected; thus, lower temperatures are demanded to compensate for the decrease in *S*Alcohol. Additionally, EC condensation restrains the allowable scope of the operation variables; the condensation regimes for the different types of reactors are marked in cyan in Figure 10. As *P*op increases, the dewpoint temperature of EC rises, thus enlarging the condensation regime. In Figure 10b,c, EC condensation is unavoidable regardless of the coolant temperature for *P*op > 4.9 MPa because the reactants condensate at the reactor inlet with the given inlet temperature of 463 K.

For all types of reactors under investigation, the contour lines divide the reactor's operating window (*T* and *P*op) into different regimes with distinct reactor performance. For instance, the red, triangular zone in Figure 10a denotes the *T*in and *P*op window for the adiabatic reactor to achieve *<sup>X</sup>*EC > 90% and *<sup>S</sup>*EG > 95% under the *SV* of 0.3 gEC·gcat−1·h−<sup>1</sup> and inlet H2/EC of 200. Figure 10a also indicates that the adiabatic reactor is not operable if *X*EC > 98% and *S*EG > 95% are desired, as the corresponding regimes would overlap inside the EC condensation regime with pressures over 5 MPa and inlet temperature below 450 K. It can be concluded that the adiabatic reactor is difficult to operate under pressures >4 MPa owing to a very narrow range of feasible inlet temperatures for adequate product yields. In contrast to the adiabatic reactor, Figure 10b−d demonstrate that the boiling water and conduction oil-cooled reactors exhibit wider operating windows of the inlet/coolant temperatures under higher pressures. The reason is twofold: First, heat removal uplifts the contour lines of *S*EG in the case of boiling water cooling and in the case of oil cooling with varying inlet temperatures (Figure 10b,d). Second, the ascending temperature profile along the oil-cooled reactor drastically lowers the EC condensation line on the oil inlet temperature-reactor pressure diagram (Figure 10c). The reactors with heat exchange would allow *X*EC > 98% and *S*EG > 95% with the demanded *T*<sup>c</sup> and *P*op being 463–465 K and 4.8–4.9 MPa for the boiling water-cooled reactor (green zone, Figure 10b), and 458–461 K and 4.8–4.9 MPa for *T*in = 463 K, or 466–474 K and 4.8–5.0 MPa for *T*<sup>c</sup> = 453 K, respectively, for the conduction oil-cooled reactor (Figure 10c,d). In all, the conduction oil-cooled reactor demonstrates the best operability in terms of allowable reactant/coolant inlet temperatures, especially under lower pressures.

**Figure 10.** Operation windows of reactors for demanded *T*in/*T*<sup>c</sup> -*P*op parameters on outlet EC conversion, EG selectivity and total alcohol selectivity under *SV* = 0.3 gEC·gcat−1·h−<sup>1</sup> and H2/EC = 200. Reactor type: (**a**) adiabatic, (**b**) boiling water-cooled, (**c**) oil-cooled, *T*in = 463 K, (**d**) oil-cooled, *T*<sup>c</sup> = 453 K.

As the production capacity of reactors might be varied during industrial operation, we further investigated the reactors' operating windows with respect to various *T*in/*T*<sup>c</sup> and *SV* in with *P*op and H2/EC set to 3 MPa and 200, respectively. Figure 11 shows that increasing temperature with the space velocity is required in order to maintain certain EC conversions, and in contrast, the maximum temperature limits to keep the EG selectivity and total alcohols selectivity above thresholds are uplifted under a higher *SV*. An exception is found for the oil-cooled reactor with varying inlet temperatures, where the maximum inlet temperature allowable for 85% total alcohols selectivity decreases again with the increase of space velocity at above c.a. 0.4 gEC·gcat−1·h−1. The EC condensation regime remains invariant with the space velocity for the adiabatic and boiling water-cooled reactor, as well as for the oil-cooled reactor with varying reactant inlet temperatures. In these cases, whether EC condensates in the catalyst bed is determined by the inlet conditions. For the oil-cooled reactor with varying oil inlet temperatures, the EC condensation regime shifts to lower temperatures with increasing space velocity, under which conditions the initial sink of bed temperature due to cooling is less prominent.

**Figure 11.** Operation windows of reactors for demanded *T*in/*T*<sup>c</sup> -*SV* parameters on outlet EC conversion, EG selectivity and total alcohol selectivity under 3 MPa and 200 H2/EC. Reactor type: (**a**) adiabatic, (**b**) boiling water-cooled, (**c**) oil-cooled, *T*in = 463 K, (**d**) oil-cooled, *T*<sup>c</sup> = 453 K.

A very small operation window for *X*EC > 98% and *S*EG > 95% (green zone; *T*in of 448–449 K, *SV* of 0.19–0.20 gEC·gcat−1·h<sup>−</sup>1) is shown for the adiabatic reactor in Figure 11a. However, common fluctuations in industry makes it difficult to keep *T*in and *SV* static in the range. For the boiling water-cooled reactor, the corresponding ranges of *T*c and *SV* are c.a. 448–463 K and 0.10–0.22 gEC·gcat−1·h−1, respectively, while for the conduction oil-cooled reactor with varying oil inlet temperatures, the ranges of *T*c and *SV* are c.a. 432–454 K and 0.10–0.21 gEC·gcat−1·h<sup>−</sup>1. As in Figure 11b–d, the larger *<sup>T</sup>*c*-SV* window of the boiling watercooled reactor benefits from an isothermal temperature profile that avoids deteriorating *S*EG at higher water temperatures, while that of the conduction oil-cooled reactor from a wide non-condensable regime. To sum up, the conduction oil-cooled reactor has the greatest allowable scope of space velocity for a wide range of reactant/coolant inlet temperatures.

#### **4. Conclusions**

In this work, multiscale reactor models for heterogenous EC hydrogenation to coproduce MeOH and EG in industrial-type adiabatic, water-cooled and oil-cooled tubular fixed-bed reactors are established and validated with bench-scale and pilot plant data. The main and side reactions occurring during the heterogeneous EC hydrogenation over Cu-based catalysts are described by a power-law engineering kinetics model involving three independent reactions.

EC hydrogenation under typical operating conditions in the adiabatic reactor renders a mild temperature rise of c.a. 12 K. However, bed temperatures above 473 K would significantly reduce the selectivity to the primary product EG due to its secondary hydrogenation, which is more temperature-sensitive than the main EC hydrogenation reaction. If the inlet temperature is lower than 453 K, however, EC condensation might happen and deactivate the catalyst, especially under low H2/EC and high operating pressures. The boiling watercooled reactor behaves close to isothermally regardless of the reactant inlet temperature, with temperature gradients only existing in the first 10% of the catalyst bed, which is beneficial for the improving the yield of EG. The conduction oil-cooled reactor shows a minimum bed temperature near the bed entrance as the cold oil gets constantly heated up towards the bed outlet. Such a U-shape temperature profile allows a relatively wide scope of both the reactant inlet temperature and the oil inlet temperature with adequate reactor performance.

Model-based operational analysis of the three different types of reactors further suggests that the application of the adiabatic reactor in EC hydrogenation is restrained by a very narrow operating window of the inlet temperature, especially under higher pressures and space velocities, if practical EC conversion and alcohols selectivity are to be acquired within the non-condensable regime of EC. The boiling water-cooled reactor exhibits no restraint on the reactant inlet temperature and a relatively wide window of the coolant temperature under different pressures and space velocities. The conduction oil-cooled reactor has a sufficiently wide window of the reactant inlet temperature and a larger operating window of the coolant temperature than the water-cooled reactor. This enables reactor operation under higher pressures and space velocities, thus providing a greater production flexibility. Understanding of these operational characteristics of representative industrial-type reactors for EC hydrogenation not only reveals the key in reactor design, but will also pave the way to further process optimization.

**Supplementary Materials:** The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/pr10040688/s1, Figure S1: Model and experiment values deviation of EC hydrogenation reaction; Figure S2: EC condensation zone under the condition of *T* = 410–530 K, *P*op = 1–5 MPa and H2/EC = 40–200; Figure S3: Contours of *P*EG in different heatexchange-type reactors: (a) (d) (g) adiabatic, (b) (e) (h) boiling water-cooled, (c) (f) (i) oil-cooled, under the conditions of 3 MPa, 0.3 gEC·gcat–1·h–1, 200 H2/EC and inlet/coolant temperatures of (a) (d) (g) inlet temperatures 443, 463, 483 K, (b)/(c) (e)/(f) (h)/(i) inlet temperature 463 K, coolant temperatures 423, 443, 463 K; Figure S4: Contours of *u*<sup>0</sup> in different heat exchange type reactor: (a) adiabatic (b) boiling water-cooled (c) oil-cooled under the conditions of 3 MPa, 0.3 gEC·gcat–1·h–1, 200 H2/EC, 463 K inlet temperature and 463 K coolant temperature; Figure S5: The influence of *SV* on (a) superficial velocity and (b) bed pressure drop, in boiling water-cooled reactor under the conditions of 3 MPa, 0.3 gEC·gcat–1·h–1 and 200 H2/EC; Figure S6: The influence of reactant/coolant inlet temperatures on *<sup>S</sup>*EG under the conditions of 3 MPa, 0.3 gEC·gcat–1·h–1 and 200 H2/EC: (a) boiling water-cooled, (b) conduction oil-cooled reactor; Figure S7: Under the conditions of 3 MPa, 0.3 gEC·gcat–1·h–1 and 200 H2/EC, (a) bed and coolant temperatures in the axial direction; bed temperatures in the radial direction: (b) adiabatic, *T*in = 443 K, (c) boiling water-cooled, *T*in = 463 K and *T*<sup>c</sup> = 443 K (d) conduction oil-cooled reactors, *T*in = 463 K and *T*<sup>c</sup> = 423 K; Table S1: Intrinsic kinetic parameters; Table S2: Specific heat capacity; Table S3: Thermal conductivity; Table S4: Viscosity; Table S5: Bed voidage; Table S6: Influence of catalyst sizes and shapes on reactor performance; Table S7: Effect of key operating variables on *X*EC, *S*EG, *S*MeOH. Refs. [62,64,65] are cited in supplementary materials.

**Author Contributions:** Conceptualization, C.C.; Funding acquisition, Y.W., J.L. and J.X.; Investigation, H.H., C.C. and Y.Y.; Methodology, C.C. and Y.W.; Project administration, Y.W., J.L. and J.X.; Supervision, C.C. and J.X.; Writing—original draft preparation, H.H.; Writing—review and editing, C.C., Y.W., J.L. and J.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Fund for Distinguished Young Scholars (61725301), International (Regional) Cooperation and Exchange Project (61720106008), National Natural Science Foundation of China (21878080, 61973124), and the Dean/Opening Project of Guangxi Key Laboratory of Petrochemical Resource Processing and Process Intensification Technology.

**Data Availability Statement:** Data available on request due to restrictions e.g., privacy or ethical.

**Conflicts of Interest:** The authors declare no conflict of interest.
