Before of the FT process, the catalysts are reduced to hydrogen or H₂/CO ratio. Due to the complexity of catalytic systems, the microscopic understanding of the effects of catalyst reduction on iron-based catalysts is a great help in evaluating the activity of this catalyst. In the H₂ atmosphere, in both locations, the surface and volume of the iron-based catalyst, initially the hematite phases (Fe₂O₃) are converted into magnetite phases (Fe₃O₄), this is possible even at low temperatures and within two hours. Then, proportional to the support used, the Fe₃O₄ shape changes to a FeO that has a semi-stable shape. FeO is reduced to α-Fe at the catalyst level and volume. The recovered iron phases (Fe₃O₄, FeO and α-Fe), in the presence of CO or synthesis gas, are converted slowly into the iron carbide phase. It should be kept in mind that magnetite and hematite are not the catalytic active phases, but converting them into carbide is a prerequisite for the FT activity. The carbonization power of the reduction iron species is α-Fe> FeO> Fe₃O₄. With the gradual carburization of the recovered iron phases, hydrocarbon species are formed on the catalyst slowly. As a result, it could be seen that iron carbide formed on the surface layers plays a positive role in relation to active sites in FT [12, 13].

Fig. (1). Total world energy consumption by energy source, 1990-2040 [1].

Temperature, pressure and H₂/CO ratio are three effective factors in the process of producing hydrocarbon derivatives in FT synthesis [14] and their increase and decrease have a serious impact on the degree of selectivity of the products. Table 1 [15-27] describes the investigations were performed by researchers in various operating conditions. However, none of these studies provided a comprehensive model for predicting the performance of iron-based catalyst under the three factors; temperature, pressure and H₂/CO ratio.

As stated, in the FT process, the production rates are different by the change in temperature, pressure and H₂/CO ratio. Therefore, several experiments must be carried out to achieve the conditions that most of the production of the favorable product is achieved at a temperature, pressure and H₂/CO ratio of process being essential for the design of petrochemical equipment, especially in the design of the reactor and all equipment after it, that result in, costs and time will increase. The objective of this study is to achieve optimal conditions for the most production of hydrocarbon products in the synthesis of Fischer-Tropsch under the iron-based catalyst to reduce costs at industrial scale.

Preparation of the catalyst is presented in the previous study [28]. The diameter and the surface area (BET) of the iron-based catalyst are 0.18-0.25 mm and 11.78 m²/g respectively. 4.01 g of the catalyst was placed inside a fixed bed reactor. The catalyst had been reduced in the temperature of 543K, the pressure of 0.25-0.3 MPa and GHSV=1000 h^-1 for 36 hours. Then the catalyst was placed under the reaction condition, the temperature of 450 to 600 K, the pressure of 1-2 MPa and the H₂/CO ratio of 1-2.

The meaning of optimization is the change of the independent parameters to achieve optimal conditions, so that the value of the dependent variable is optimized. Changes in each parameter require that other parameters be constant, which is why it involves a lot of time and cost. The response surface methodology is used to overcome this problem. The RSM is a set of mathematical relationships that provides a logical relationship between several independent and dependent parameters. Using the obtained relationships, the effect of each independent parameter and their interaction upon the value of the dependent parameter can be observed and the optimal values are obtained. The steps of the RSM are illustrated with Fig. (2) schematically.

After determining the independent and the dependent parameters by applying equation (1), mathematical relations are established.

(1)

Here, λ ₀, λ_i, λ_ii, λ_ij are constant terms, the coefficients of the linear parameters, and the coefficients of quadratic, denotes the coefficients of the interaction parameters respectively. Y is the dependent variable or response, X is the independent variable and is the fitting error. Then, assessments are made to approve its accuracy. The analysis of Variance (ANOVA) is a collection of mathematical relationships that, with the aid of the R², R²_adj and P-value parameters, validates the model's results. To calculate R² (the coefficient of determination), Equation (2) is used; if the R² value is closer to 1, the accuracy of the model will be greater. By increasing the number of experiments, the R² value is closer to one, as when the dependence of R² value to the number of experiments is eliminated, Equation (3) (R²_adj) is achieved. The R²_adj value is also closer to one, the model is more stable. The P-value (probable value) expresses the probability of the placing an answer in the wrong area, and typically, if that is less than 0.05, the model will be meaningful from the statistical point of view.

(2)

(3)

y is the empirical response value; is the mean of responses, the amount calculated by the model. n represents the number of observed responses and p represents the number of variables in the model.

Fig. (2). Schematic of step of the Response Surface Methodology.

The selectivity variations of total hydrocarbons (HC) with temperature, pressure and H₂/CO ratios are shown in Fig. (3). The temperature is more effective than the two pressure and H₂/CO ratio factors on the selectivity of the total hydrocarbons, so that, with the increasing temperature, the selectivity of HC decreases. The pressure factor has the least effect on the selectivity of total hydrocarbon, therefore, by increasing it the total hydrocarbon selectivity increases. The selectivity of total hydrocarbons with the H₂/CO ratio has the reverse relation so that with increasing the amount of H₂/CO ratio the selectivity of HC decreases and vice versa. To obtain the highest selectivity of HC, the reaction conditions must be set to P=1 MPa, H₂/CO=1, T=468 K.

Fig. (3). The effect of reactions condition on the selsectivity of HC.

Figure 4 shows how the three factors of temperature, pressure and H₂/CO ratio influence the selectivity variations of light hydrocarbons. The images show that the temperature has the most impact on the selectivity of C2-C4, such that the selectivity of light hydrocarbons increases by increasing the temperature, however, with increasing P and H₂/CO ratio, the selectivity of C2-C4 decreases. In order to obtain the highest hydrocarbon production, the reaction conditions shall be T=600 K, P=1 MPa, H₂/CO=1.

Fig. (4). The effect of reactions condition on the selsectivity of C2-C4.

The C5+ selectivity changes with the three factors; temperature, pressure and H₂/CO ratio are shown in Fig. (5). Increasing temperature, pressure and H₂/CO ratio result in the reducing, increasing and increasing in the selectivity of heavy hydrocarbons, respectively. In the optimization section, if the goal is to minimize the production of heavy hydrocarbons, the reaction conditions will be set to T=600 K, P=1 MPa, H₂/CO=1.

Fig. (5). The effect of reactions condition on the selsectivity of C5+.

Table 5 summarizes the amount of laboratory matching with output data of the selectivity models, clearly highlighting that the RSM is efficient. Also, since the R²-Perd value is closer to 1, we can use the models to predict the products selectivity in different values of temperature, pressure and H₂/CO ratio. For example, in the reference [29], the total selectivity of hydrocarbons on the catalyst 50% Fe/50%Mn/6%K at P=1atm, H₂/CO=2, T=250°C was obtained to be 94.5, which in the model was obtained in this study with less than 2% difference, being 96.38.