*2.5. Detailed Plant Simulation in Aspen Plus*

After analyzing the results of the Matlab simulations, optimum parameters were selected for each approach (i.e., the number of reactor modules, purge fraction, cooling fluid temperature) and a detailed plant simulation including heat integration was implemented in Aspen Plus V10.

The Peng–Robinson property method was selected for the reactor modules. All other equipment were simulated with the Non-Random Two-Liquid Model with a second set of binary parameters (NRTL2) as the property method.

The methanol synthesis reactor was simulated with the rigorous plug flow reactor model (RPLUG unit) and the kinetics described in Section 2.3 were implemented as a Langmuir–Hinshelwood–Hougen–Watson (LHHW) reaction model. The rearrangement of the model parameters to follow the software's specific input format is detailed in the Supplementary Material (Section D). Since the reactor cooling fluid is at a constant temperature due to water evaporation, both co-current and counter-current operations give

the same results. Therefore, the co-current operation was selected in order to simplify the mathematical calculations.

The combustion of the purge streams in a fired heater was simulated with the RGIBBS unit, which considers that chemical equilibrium is achieved when the free Gibbs energy of the system is minimized.

The heat exchangers were simulated in counter-current flow with the HeatX unit, with a minimum temperature approach of 25 ◦C for the heat exchangers located inside the fired heater and a minimum temperature approach of 10 ◦C for all the other heat exchangers.

The compressors were modeled using the ASME method, assuming a mechanical efficiency of 0.95 and an isentropic efficiency of 0.80 [22]. The pump was simulated assuming an efficiency of 0.70. The turbine was simulated with the ASME method, assuming a mechanical efficiency of 0.95 and an isentropic efficiency of 0.90 [52].

The distillation column was simulated with the rigorous RadFrac model, considering a kettle reboiler and a partial condenser at 53 ◦C with liquid and vapor distillate. A Murphree efficiency of 0.75 was set to all intermediate stages [53,54]. In both processes, the column had 30 stages and a reflux ratio of 2, with the feed entering above the 24th stage.

The relative tolerance of all equipment calculations was set to 10−5. Flowsheet convergence was achieved using the Broyden method, with a relative tolerance of 10−4, which corresponds to a mass balance closure of 99.99%.

#### *2.6. Efficiency Evaluation*

The chemical conversion efficiency (*ηCCE*) accounts for how much fuel energy remains in the final product in relation to the reactants. For methanol synthesis from H2/CO2, it is calculated as follows: [55] .

$$\eta\_{\rm CCE} = \frac{\dot{m}\_{\rm McOH} \cdot LHV\_{\rm McOH}}{\dot{m}\_{\rm H\_2} \cdot LHV\_{\rm H\_2}} \tag{13}$$

where . *mMeOH* is the methanol mass production, . *mH*<sup>2</sup> is the hydrogen feed demand, and *LHV* is the low heating value. The maximum possible efficiency (*ηCCE*,*max*) occurs at 100% overall H2 conversion to methanol (stoichiometric conversion):

$$\eta\_{\rm CCE,max} = \frac{M\_{\rm McOH} \cdot LHV\_{\rm McOH}}{3 \cdot M\_{H\_2} \cdot LHV\_{H\_2}} = 0.876\tag{14}$$

Here, *Mj* is the molar mass of component *j*. In order to also account for heat and the work input, the exergy efficiency (*ηEx*) is calculated: [39]

$$\eta\_{Ex} = \frac{\dot{m}\_{McOH} \cdot \varepsilon\_{McOH}}{\dot{m}\_{H\_2} \cdot \varepsilon\_{H\_2} + \dot{m}\_{CO\_2} \cdot \varepsilon\_{CO\_2} + P\_{cl} + E\_Q} \tag{15}$$

where *ej* is the specific exergy of component *j*, *Pel* is the total required electric power, and *EQ* is the total exergy input associated with heat demand.

The specific exergy of a component (*ej*) is divided between thermal and chemical exergy: [39]

$$\left[\boldsymbol{e}\_{j}(\boldsymbol{T},\boldsymbol{p})=\left[\boldsymbol{e}\_{j,therm}\right]+\boldsymbol{e}\_{j,chem}=\left[\boldsymbol{H}\_{\dot{j}}-\boldsymbol{S}\_{\dot{j}}\cdot\boldsymbol{T}\_{0}-\boldsymbol{H}\_{\dot{j}}^{0}+\boldsymbol{S}\_{\dot{j}}^{0}\cdot\boldsymbol{T}\_{0}\right]+\boldsymbol{H}HV\_{\dot{j}}\tag{16}$$

Here, *ej*,*therm* and *ej*,*chem* are the thermal and chemical exergies, *Hj* is enthalpy, *Sj* is entropy, *H*<sup>0</sup> *<sup>j</sup>* and *<sup>S</sup>*<sup>0</sup> *<sup>j</sup>* are the enthalpy and entropy at reference conditions (298.15 K and 1 bar), *T*<sup>0</sup> is the reference temperature, and *HHVj* is the high heating value. In the exergy efficiency calculation, the *HHV* is used instead of the *LHV*, as water is liquid at reference conditions.

#### *2.7. Techno-Economic Evaluation*

In order to calculate the production costs, the standardized methodology from Albrecht et al. [56] was considered, which is a further development based on the work of Peters et al. [57].

The main equipment costs (*EC*) were estimated based on reference equipment costs [57,58]. The scale up to the required capacity was performed with specific equipment scaling factors, and price inflation was corrected to 2020 with the Chemical Engineering Plant Cost Indexes (*CEPCI*). In Equation (23), the costs of equipment *j* (*ECj*) is described:

$$EC\_j = EC\_{j,ref} \cdot \left(\frac{C\_j}{C\_{j,ref}}\right)^M \cdot \left(\frac{CEPCI\_{2020}}{CEPCI\_{ref}}\right) \tag{17}$$

Here, the subscription ref relates to the reference equipment, *C* is the characteristic capacity, and *M* is the equipment scaling factor. The equipment is constructed with carbon steel. When the reference price is in US dollars (USD), a conversion to euros (EUR) of 1.13 USD·EUR−<sup>1</sup> is applied (February 2022) [59].

The dimensions of the flash drums and the packed distillation column were calculated with the methodology reported by Towler and Sinnott [60]. The required heat transfer area of the heat exchangers, column condenser, and reboiler were estimated by assuming the typical global heat transfer coefficients reported by the VDI Atlas [43], according to each specific situation. Equipment dimensioning is detailed in the Supplementary Material (Section G).

The fixed capital investment (*FCI*) was estimated by multiplying the total EC with the Lang Factor (*LF*), which accounts for all direct and indirect costs related to the plant construction. In this work, *LF* was assumed to be 4.86 (details are provided in the Supplementary Material, Section H) [56,57]. A working capital (*WC*) of 10% of the total capital expenses (*CAPEX*) was considered [56]. Summarizing the equations:

$$FCI = LF \cdot \sum EC\_j \tag{18}$$

$$
\mathbb{C}APEX = FCI + \mathcal{W}\mathbb{C} \tag{19}
$$

$$\text{WC} = 0.10 \cdot \text{CAPEX} \tag{20}$$

The equivalent annual capital costs (*ACC*) were estimated by applying the annuity method on the *FCI*, assuming an annual interest rate (*IR*) of 10%, a plant operating life (*tP*) of 20 years, and no salvage value [61]. The working capital does not depreciate in value, and only its interest has to be taken into account [56].

$$A\mathbb{C}C\_{FCI} = \frac{FCI \cdot IR \cdot (1 + IR)^{t\_P}}{[(1 + IR)^{t\_P} - 1]} \tag{21}$$

$$\text{ACC}\_{\text{WC}} = \text{WC} \cdot \text{IR} \tag{22}$$

$$\text{ACC} = \text{ACC}\_{FCI} + \text{ACC}\_{WC} = \frac{FCI \cdot IR \cdot (1 + IR)^{t\_P}}{[(1 + IR)^{t\_P} - 1]} + \text{WC} \cdot IR \tag{23}$$

The operating expenses (*OPEX*) were divided between direct and indirect costs. The costs related to the direct OPEX (*OPEXdir*) are presented in Table 2, which include raw materials, catalysts, process water treating, and electricity. A catalyst lifetime of three years was considered. In the Rankine water cycle, a clean water replacement of 1% of the total flow was considered [62].

The indirect *OPEX* consisted of operating labor (*OL*), operating supervision, maintenance, operating supplies, laboratory charges, taxes on property, insurance, plant overhead, administration, distribution, marketing, research, and development. The estimation of each of these items was based on typical values, which are dependent on *OL*, *FCI*, and the net production costs (*NPC*) (see Section H of the Supplementary Material) [56,57]. The total indirect *OPEX* (*OPEXind*) is calculated as follows:

$$OPEX\_{ind} = 2.2125 \cdot OL + 0.081 \cdot FCI + 0.10 \cdot NPV \tag{24}$$

**Table 2.** Costs of feedstock, catalyst, water treating, and electricity.


The required number of operators in a shift (*nOP*) was estimated with the following equation: [65,66]

$$m\_{OP} = \left(6.29 + 0.23 \cdot N\_{np}\right)^{0.5} \tag{25}$$

where *Nnp* is the number of non-particulate main processing units. Considering daily working shifts, resting periods and vacations, the number of operators to fulfill each position in a continuous operation is approximately *FOP* = 4.5. Therefore, the total number of operators (*NOP*) is: [65,66]

$$N\_{OP} = F\_{OP} \cdot \eta\_{OP} \tag{26}$$

The total costs of operating labor (*OL*) is then calculated as follows:

$$OL = \mathcal{W}\_{\mathcal{OP}} \cdot \mathcal{N}\_{\mathcal{OP}} \tag{27}$$

where *WOP* is the wage rate of each operator (*WOP* = 72,000 €·a<sup>−</sup>1) [53].

The net production costs (*NPC*) are calculated in terms of average annual costs and in terms of average costs per kg of methanol:

$$NPC\left[\frac{\mathbf{f}}{a}\right] = A\mathbf{CC} + OPEX\_{dir} + OPEX\_{ind} \tag{28}$$

$$NPC\left[\frac{\text{€}}{\text{kg}}\right] = \frac{(ACC + OPEX\_{dir} + OPEX\_{ind})}{\dot{m}\_{MEOH}}\tag{29}$$

#### **3. Results and Discussion**

In this section, process simulation and analysis are presented separately for the onestep and the three-step approaches. Finally, the techno-economic analysis of both approaches is presented and discussed jointly.

## *3.1. One-Step Process*

#### 3.1.1. One-Step Process—Selecting Key Parameters

The one-step process was successfully implemented in Matlab. Different scenarios were simulated by varying the number of reactor modules and the purge fraction, with the optimal temperature for a fixed methanol production (145 ton·h−1) being estimated in each case. In Figure 5, several contour plots are shown, where CO2 single-pass conversion (*XCO*2,*SP*) (Figure 5a), the required feed excess (Figure 5b), the optimal temperature (Figure 5c), and the total recycle stream (Figure 5d) are plotted against the number of reactor modules and the purge fraction.

CO2 single-pass conversion (Figure 5a) was considerably enhanced by increasing the number of reactor modules. This was not only because the gas hourly space velocity (GHSV) decreased, but also because the optimal temperature had lower values (Figure 5c), shifting the thermodynamic equilibrium towards higher methanol concentrations. In contrast, reducing the purge fraction had little effect on *XCO*2,*SP*. This should be the result of two competing effects: on one hand, a lower purge fraction means higher recycle streams (Figure 5d), which increases the GHSV, reducing *XCO*2,*SP*. On the other hand, the recycle stream has a H2:CO2 ratio greater than three due to a limited rWGSR extension.

By increasing the recycle stream, the H2:CO2 ratio of the reactor feed stream is enhanced, positively contributing to *XCO*2,*SP*.

**Figure 5.** One-step process—CO2 single-pass conversion (**a**), required feed excess (**b**), optimal temperature (**c**), and total recycle stream (**d**) as a function of the number of reactor modules and the purge fraction.

The required feed excess was significantly decreased both by increasing the number of reactor modules and by reducing the purge fraction. This occurred because the former procedure increased *XCO*2,*SP* and the latter maintained *XCO*2,*SP* roughly constant while increasing the gas flow inside the reactor modules.

Since the reactants (H2, CO2) represent the highest costs of the plant, it is important to minimize the required feed excess, which according to Figure 5b, occurred at 0.5% purge fraction. However, with such a low purge fraction, the total recycle stream was considerably high, demanding larger heat exchangers, flash drums, and compressors, as well as higher power consumption. Therefore, an intermediate value of 2% as the purge fraction was selected for the detailed simulation in Aspen Plus, agreeing with other studies and typical industrial values [22,39,58].

With the purge fraction fixed at 2%, six reactor modules were used in the detailed study, because further increasing the number of reactor modules only slightly reduced the required excess feed, not justifying further expenses in equipment and catalyst.

The value of the global heat transfer coefficient was updated point by point within mathematical integration along the reactor length. For the selected condition, *Uz*=<sup>0</sup> = 160 W·m−2·K−<sup>1</sup>

and *Uz*=12.5 = 150 W·m−2·K−1. Since Aspen Plus requires a constant value, the average value was used (*Uavg* = 155 W·m−2·K<sup>−</sup>1).

#### 3.1.2. One-Step Process—Detailed Plant Simulation and Process Analysis

A detailed flowsheet of the one-step process presented in Figure 3 was implemented in Aspen Plus, considering 2% purge fraction, six reactor modules working in parallel, and the optimized temperature of the reactor cooling fluid (*Tw* = 247.5 ◦C). A picture of the flowsheet in Aspen Plus, the properties of the streams, and a detailed plant description are provided in the Supplementary Material (Section E).

In Figure 6, the concentration of the products along the reactor length is shown. The methanol and water feed concentrations were close to zero, and their outlet concentrations were 7.4 and 7.2% mol/mol, respectively. The nitrogen concentration remained relatively low (inlet: 4.95% mol/mol, outlet: 5.65% mol/mol). Due to the recycle streams, CO entered the reactor modules at 1.50% mol/mol, although it was not a feedstock in the plant. CO was produced through the rWGSR until the length of 1.5 m, where its concentration reached 3.3% mol/mol. Then, due to the high water concentration (4.30% mol/mol), the WGSR became faster than its reverse reaction and started to consume CO, which exited the reactor at 1.76% mol/mol and a marginal selectivity (0.5%). This virtually stabilized CO content in the plant led to a high methanol selectivity (99.5%).

**Figure 6.** One-step process—product concentration along the reactor length. Reactor feed concentration: H2/CO/CO2/CH3OH/H2O/N2 = 71.3/1.5/21.9/0.3/0.0/5.0% mol/mol.

The CO2 single-pass conversion was 28.5%, close to the equilibrium conversion (30.4%), while the feed excess was 6.05%, which corresponded to an overall CO2 conversion to methanol of 94.3%. These values are in agreement with the Matlab simulations (*XCO*2,*SP* = 29.7%, feed excess = 5.75%, overall CO2 conversion to MeOH = 94.6%).

The chemical conversion efficiency (*ηCCE*) of the process was 82.6%, which was close to the maximum possible value (*ηCCE*,*max* = 87.6%). With the heat integration, the one-step process was not only self-sufficient, but had a heat excess that could be supplied to other processes, in agreement with the literature [21,39]. In our case, as is commonly performed in industrial methanol synthesis plants, the heat excess was used to generate electricity via a water Rankine cycle, reducing the electricity consumption from 47.4 to 17.6 MW.

In Figure 7, a global exergy balance and an exergy loss distribution are provided. No distinction was made between exergy destruction and exergy losses via side output streams (i.e., cooling water, process water, and flue gas). The exergy efficiency (*ηEx*) of the process was 76.4%, with a total exergy loss of 281.9 MW. The main losses occurred due to the exothermic chemical reactions with heat recovery at low temperatures (reactor modules: 58.1%, fired heater: 14.8%). Additionally, exergy losses in the heat exchangers (11.1%) and in the column (9.0%) were also significant, mainly due to heat transfer to cooling water.

**Figure 7.** One-step process—exergy analysis. (**a**) Global exergy balance. Total exergy input: 1194.5 MW. (**b**) Distribution of exergy losses (total = 281.9 MW).
