The methanol production process via CO₂ hydrogenation was simulated using Aspen Hysys version 8.8 process simulator. Peng-Robinson was used as the thermodynamic property package. The physical properties were predicted using the thermodynamics based equation as shown in Equations (1) and (2). Where H^ID is the Ideal Gas Enthalpy and S^ID is the Ideal Gas Entropy.

In the process simulation, two reactors were employed due to low conversion of the CO₂ hydrogenation reaction. Figure 1 represents the process flow diagram of methanol production via CO₂ hydrogenation (Wiesberg et al., 2016). In this process, the feed of 1,000 kmoles per hour of carbon dioxide at 40°C and 20 bar was mixed with the 3,000 kmoles per hour of hydrogen (at the same conditions). The mixture was then compressed, heated and sent to the first equilibrium reactor. The first reactor partially converted CO₂ to methanol as liquid product, as shown in Equations (3)–(5) (Tidona et al., 2013). The unreacted CO₂ and H₂ then entered the second equilibrium reactor to produce more methanol product. The pressure of gas phase leaving the second reactor was reduced to recover methanol as liquid phase. All liquid methanol products were sent to the first distillation column, where the light components (CO, CO₂, and H₂) leaved at the top of the column. The mixture of methanol and water leaved the column at the bottom and entered the second distillation column, where the methanol product with purity of 99.5%mole was obtained at the top of the column.

For equipment specifications, both reactors were simulated using equilibrium model. The sets of reaction used in each reactors are Equations (3)–(5). The efficiency of the pump was assumed at 75% (adiabatic). The efficiencies of all compressors were assumed at 75% (adiabatic). The specifications of column T−100 were condenser temperature at 40.1°C and reflux ratio at 0.5. The specifications of column T−101 were 99.5%mole methanol product purity, and reboiler temperature at 143.2°C.

The detailed process simulation of methanol production via CO₂ hydrogenation is provided in Appendix A.

In an economic analysis, capital, and operating costs were included in calculation of methanol production cost. The capital cost involved all major equipment, except pump, and piping. The capital cost was calculated using equations and data from the capital equipment-costing program (Turton et al., 2003). The data was adjusted for inflation from year 2001–2017 by using values of the Chemical Engineering Plant Cost Index, CEPCI. The CEPCI value in 2001 is 297, and the CEPCI value in 2017 is 541.7 (Jenkins, 2018).

The equipment costs were estimated base on total module costs (C_TM), shown in Equation (6), where n represents the total number of pieces of equipment. C_BM is the bare module cost, which can be estimated from Equation (7)

Where CPo is the purchased cost for base conditions, which can be determined from Equation (8)

F_P is the pressure factor

F_M is the material factor

In Equation (8), parameters A is the capacity or size parameter for the equipment, K₁, K₂, K₃ are the maximum and minimum values used in the correlation.

The description of major equipment, and K₁, K₂, and K₃ used in this studied are shown in Table 1.

For cost modeling of reactors, the dimension of reactors were fixed at height of 5.8674 m and diameter of 1.068 m. The values of K₁ is 3.4974, K₂ is 0.4485, K₃ is 0.1074, B₁ is 2.25, B₂ is 1.82, and F_M is 3.1. The pressure factors (Fp) for the reactors were determine using Equation (9), where P is in barg.

Assumption used in the economic analysis are listed below.

Sensitivity analysis is an efficient tool, which can be used to determine the significant parameters. In this section, the impacts of eight parameters on the methanol production cost were determined using sensitivity analysis. An increase in pressure and decrease in temperature leads to increase of the equilibrium conversion of CO₂ to methanol (Witoon et al., 2015). The eight studied parameters are (1 and 2) inlet pressure and temperature to the first reactor, ERV-100, for CO₂ and H₂ conversion conditions, (3) inlet temperature to the first separator for methanol product separation condition, (4) inlet pressure to the second reactor, ERV-101, for CO₂ and H₂ conversion conditions, (5 and 6) outlet temperature of both coolers, located after the second reactor, for methanol product separation condition from gas and liquid mixture, (7) outlet pressure at the valve VLV-102 for recovering methanol from gas phase mixture, (8) Inlet temperature to the first distillation column for separation between liquid methanol and water products, and gaseous unreacted reactant separation.

For all parameters, except inlet temperature to the first reactor, we performed the sensitivity analysis by varying value of interested parameter within the range ± 25% of its base value, and fixing other parameters at their base values. For inlet temperature to the first reactor parameter, we varied the value of temperature within the range ± 10% of its base value. Table 2 shows the base value used in sensitivity analysis of each parameter.

In this section, RSM (Nuchitprasittichai and Cremaschi, 2011) coupled with non-linear solver were employed to optimize the methanol production via CO₂ hydrogenation process. The objective is to minimize the methanol production cost per tons produced methanol ($/tons produced methanol). Response surface methodology is a statistical tool used to represent the relationship between independent variables and dependent variable(s). In this work, RSM was employed to represent the relationship between significant operating parameters and the methanol production cost per tons produced methanol. The significant operating parameters (decision variables) are the significant parameters obtained from sensitivity analysis (in section Sensitivity analysis) which are x₁: inlet pressure to the 1st reactor, x₂: inlet temperature to the 1st reactor, x₃: inlet pressure to the 2nd reactor, x₄: outlet temperature of the liquid stream cooler after the 2nd reactor, x₅: inlet temperature to the 1st distillation column.

Figure 4 represents simulation—optimization algorithm. In the algorithm, the range of each decision variables was first determined. In this work, the ranges of decision variables were obtained from literature (Shen et al., 2000; Witoon et al., 2015). Factorial design with two levels (2^k Factorial design, section 2^k Factorial design) and a center point were used as a data set of the decision variables. Then, process simulation, coupled with cost analysis, was run corresponding to operating conditions in the data set to obtained methanol production costs. The data of operating conditions and the corresponding methanol production costs were combined and fit the first order model by regression analysis (using Design Expert 11 software). If the data fit the first order model (R—squared > 0.7), it means that the region of operating conditions and methanol production costs is in linear region. The steepest descent (section Steepest descent) was performed to move operating conditions to the region of lower methanol production cost. On the other hand, if the data do not fit the first order model, it means that the data are in non-linear region. The Box—Behnken Design [BBD, section Box—Behnken design (BBD)] was performed to collect more data in non-linear region. All data were then combined to fit the second order (non-linear) model. The non-linear model was then used as the objective function in optimization problem. Microsoft Excel (non-linear programing, NLP) solver was used to solve the non-linear optimization problem (section Optimization formulation) for the minimum methanol production cost. The optimal solution obtained from this RSM is considered as a local optimal solution.

In performing simulation—optimization algorithm, the first data set (data set 1) from 2^k factorial design with initial range of each decision variable (shown in Table 3, Data set 1 column) was fitted with the first order regression model. The obtained R—squared value is 0.9995. This means the data still fit the linear model. Therefore, we performed steepest descent to search for the region of lower methanol production cost. Figure 6 shows steepest descent in moving the operating conditions to lower methanol production cost region.

From the steepest descent results, for the first reactor, an increase in inlet pressure from 56.0 to 58.0 bar, and a decrease in inlet temperature from 192.0 to 183.0°C yielded an increase in methanol product at equilibrium condition (%conversion increased from 40 to 45%). For the second reactor, a decrease in inlet pressure from 118.0 to 102.0 bar yielded an increase in methanol product in the reactor. The outlet temperature of the liquid stream cooler after the 2nd reactor decreased from 74°C to around 65°C yielded an increase in liquid methanol separated from the separator. The inlet temperature to the first distillation column increased from 48.0 to 52.0°C yielded higher efficiency to separate most of remaining CO₂ and lighter components from methanol and water.

The steepest descent moves the operating conditions to the new conditions as follows: inlet pressure to the first reactor: 58.84 bar, inlet temperature to the first reactor: 184.0°C, inlet pressure to the second reactor: 106.64 bar, outlet temperature of the liquid stream cooler after the second reactor: 65.54°C, and inlet temperature to the first distillation column 52.75°C. We then used these new operating conditions as the middle value of the range of decision variables. The ranges of the new operating conditions are shown in Table 3, Data set 2 column.

The new data set (Data set 2) was then constructed with 2^k factorial design. The corresponding methanol production costs were collected, as shown in Figure 6. Most of the data in data set 2 shows lower methanol production cost than data set 1, except the data at low inlet pressure to the first reactor. The results agree with the results from sensitivity analysis that the inlet pressure to the first reactor has inversely proportional relationship with the methanol production cost.

By fitting data set 2 with the first—order regression model, the data did not appropriately fit the model as R—squared value is 0.6353 (<0.7). This means that there is high possibility to find the non-linear region at this step. We then used theses ranges of operating condition with BBD in collecting more data for constructing the non-linear model.

The reduced non-linear model (the model with only significant terms) was constructed with 73 sample points (32 sample points from 2^k factorial design, and 41 sample points from BBD) as shown in Equation (15). The model represents the relationship between the operating conditions and the methanol production cost.

Where y is the methanol production cost per tons produced methanol ($ per ton produced methanol), x₁ is inlet pressure to the first reactor, and x₂ is inlet temperature to the first reactor. Please be noted that the obtained values of x₁ and x₂ in Equation (15) are in code variables (−1 to +1). The obtained results have to be converged to the actual operating condition values by using the ranges in Table 3, data set 2 column and Equation (10), where −1 represents the lowest value and +1 represents the highest values in the range.

Table 4 shows the local optimal operating conditions (x_i) of methanol production via CO₂ hydrogenation with the minimum production cost per tons produced methanol (y). Since three parameters, which are inlet pressure to the 2nd reactor (x₃), outlet temperature of the liquid stream cooler after the second reactor (x₄), and inlet temperature to the first distillation column (x₅), do not show significant impacts on the production cost in the non-linear model (Equation 15), the values of these three parameters were set at their lower bounds.

The prediction accuracy of the model was determined by the percent error. The percent error of the model was estimated by comparing between the predicted methanol production cost with the actual production cost. We obtained the actual production cost by running the process simulation with the corresponding optimal operating conditions. The percent error of this non-linear model is 1.05. For regression analysis of this model, the R—squared value is 0.8705, and the adjusted R—squared value is 0.8610. Therefore, with the small number of percent error, it can be concluded that this methanol production via CO₂ hydrogenation process can be represented by the second order model. The process is successfully optimized using RSM.

The optimization formulation was solved in the Intel Pentium 4 processor, core i3. The local optimal solutions were obtained in 2 s. The obtained minimum production cost ($ per tons produced methanol) is an offset between the methanol production cost and the amount of produced methanol. The methanol production cost includes energy consumption, utilities, and capital cost costs. For the optimal solution, the amount of produced methanol increased so that the minimum production cost per tons of produced methanol was obtained. The optimal methanol production rate is 964 kmoles per hours, which produced from 1,000 kmoles per hour of feed carbon dioxide and 3,000 kmoles per hour of feed hydrogen.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.