*2.6. Coolant Heat Transfer*

For the heat exchange by pressurized boiling water, a large heat transfer coefficient (4000–6000 W·m−2·K<sup>−</sup>1) and a constant wall temperature (*T*w) are considered:

$$T\_{\mathbf{w}} = T\_{\mathbf{b}} \tag{34}$$

where *T*<sup>b</sup> is the boiling point of pressurized water.

In contrast, the heat conduction oil has a low specific heat capacity, and thus is heated up easily. The oil temperature is therefore considered as a function of the transferred heat. The oil-to-tube heat transfer coefficient is set as a function of the space in between adjacent baffle plates *<sup>t</sup>* and the coolant mass flow rate . *m*oil.

$$
\pi\_{\rm oil} = \overline{\alpha}\_{\rm oil}(t, \dot{m}\_{\rm oil}) \tag{35}
$$

The detailed expressions are given in the Supporting Information. The heat transferred between the oil and the tube wall is

$$Q\_{\rm oil} = \overline{\pi}\_{\rm oil} \cdot (T\_{\rm oil} - T\_{\rm w}) \cdot S\_{\rm wall} \tag{36}$$

As the oil temperature *T*oil varies with the axial position, the steady-state coolant temperature profile is determined by iteration. The single reaction tube is divided into 10 segments (each 0.8 m long) in the flow direction with the oil temperature in each segment calculated as

$$T\_{\rm oil,i+1} = \begin{cases} \begin{array}{c} T\_{\rm oil,in\prime} \quad i = -1 \\\ T\_{\rm oil,i} + \frac{Q\_{\rm oil,i}}{3600c\_{p,\rm oil} \cdot \dot{m}\_{\rm oil}} \end{array} 0 \le i \le 9 \end{cases} \tag{37}$$

when the iteration converges, the oil temperature as a continuous function of the the axial position is calculated by linear interpolation of the above discrete temperatures.

$$T\_{\rm oil}(\mathbf{x}) = T\_{\rm oil, i-1} + \frac{T\_{\rm oil, i} - T\_{\rm oil, i-1}}{\mathbf{x}\_{i} - \mathbf{x}\_{i-1}} \cdot (\mathbf{x} - \mathbf{x}\_{i-1}), \ (\mathbf{x}\_{i-1} < \mathbf{x} < \mathbf{x}\_{i}) \tag{38}$$

#### *2.7. Chemical Reactions*

The global reaction of ethylene carbonate hydrogenation to ethylene glycol and methanol is described by three separate reactions as shown in (R1)–(R3), respectively. This scheme allows for investigation of the effect of operating variables on the reactant conversion and product selectivity. The intrinsic kinetics of these reactions are modeled by power-law equations. The kinetic parameters were fitted to bench-scale experimental data covering a wide range of reaction conditions of *T* = 175–220 ◦C, *P*op = 3.0 MPa, H2/EC = 120–200 and *SV* = 0.5–2.2 h−1. Details regarding the kinetic equations and parameters are given in the Supporting Information (Section S1).

$$\begin{array}{ll} \text{R1:} & \begin{aligned} \stackrel{\cdot}{\\_} & \stackrel{\cdot}{\\_} + 3\text{H}\_{2} \rightarrow \text{OH(CH}\_{2})\_{2}\text{OH} + \text{CH}\_{3}\text{OH} \\ \text{R2:} & \stackrel{\cdot}{\\_} + \text{H}\_{2} \rightarrow \text{OH(CH}\_{2})\_{2}\text{OH} + \text{CO} \\ \\ \text{R3:} & \text{OH(CH}\_{2})\_{2}\text{OH} + \text{H}\_{2} \rightarrow \text{CH}\_{3}\text{CH}\_{2}\text{OH} + \text{H}\_{2}\text{O} \end{aligned} \\\\ \text{R4:} & \begin{aligned} \text{OH(CH}\_{2})\_{2}\text{OH} + \text{H}\_{2} \rightarrow \text{CH}\_{3}\text{CH}\_{2}\text{OH} + \text{H}\_{2}\text{O} \end{aligned} \\\\ \end{cases}$$

Since the two EC hydrogenation reactions ((R1) and (R3)) are dependent on the gas phase EC concentration only, their effective reaction rates over the catalyst particle surface are:

$$r\_{\text{obs}} = \eta\_{\text{EC}} \cdot r\_{\text{chem}} \left( \mathcal{C}\_{\text{EC,s}} \, \, T\_{\text{s}} \right) \tag{39}$$

The EG hydrogenation reaction (R3) is zeroth order; therefore, its effective reaction rate is equal to the intrinsic reaction rate:

$$r\_{\text{obs}} = r\_{\text{chem}}(\mathbb{C}\_{\text{EG}, \mathbb{W}} \, T\_{\text{s}}) \tag{40}$$

The performance metrics of the reaction, EC conversion *X*EC, EG selectivity *S*EG, MeOH selectivity *S*MeOH and total alcohols selectivity *S*Alcohol, are defined by the following definitions:

$$X\_{\rm EC} = \frac{\dot{m}\_{\rm EC,in} - \dot{m}\_{\rm EC,out}}{\dot{m}\_{\rm EC,in}} \tag{41}$$

$$S\_{\rm EG} = \frac{\dot{m}\_{\rm EG,out} / M\_{\rm EG}}{\left(\dot{m}\_{\rm EC,in} - \dot{m}\_{\rm EC,out}\right) / M\_{\rm EC}} \tag{42}$$

$$S\_{\rm MeOH} = \frac{\dot{m}\_{\rm MeOH,out} / M\_{\rm MeOH}}{\left(\dot{m}\_{\rm EC,in} - \dot{m}\_{\rm EC,out}\right) / M\_{\rm EC}} \tag{43}$$

$$S\_{\rm Alcohol} = \frac{S\_{\rm EG} + S\_{\rm MeOH}}{2} \tag{44}$$
