*2.5. Process Optimization*

The most interesting aspect of the response surface graphs was their wide area of high ester yield. This implies stability, being a desirable effect because high ester contents can be obtained under various experimental conditions. In particular, it is possible to find lots of reaction conditions which lead to an ester content greater than 96.5%, the minimum value specified by the European Standard UNE-EN 14214. According to Equation (1), the maximum ester content would exceed 100%; using 0.10 mol·L−<sup>1</sup> KOH and 3:1 CH3OH/oil molar ratio in the first step and 0.05 mol·L−<sup>1</sup> KOH and 5:1 CH3OH/oil ratio in the second step, the predicted ester content would be 101.2% (Table 3). However, experimental ester content higher than 98% was not obtained in any reaction. It was expected that the empirical ester content would be close to 98% when the predicted ester content was higher than 98%. This hypothesis was supported by the first reaction in Table 3, whose conditions led to predicted ester contents higher than 100%, and the measured one was close to 98%. On the other hand, the second reaction of this table was carried out under conditions which led to ester content over 96.5%, and the measured one was also higher than 96.5%, so this biodiesel would be within the European standard.

**Figure 1.** Response surface plots of ester content: (**a**) Catalyst concentration vs. MeOH/oil molar ratio first step; catalyst concentration second step: 0.03 mol·L−1, MeOH/oil molar ratio second step: 3:1; (**b**) Catalyst concentration vs. MeOH/oil molar ratio second step; catalyst concentration first step: 0.06 mol·L−1, MeOH/oil molar ratio first step: 4.5:1; (**c**) Catalyst concentration vs. MeOH/oil molar ratio first step; catalyst concentration second step: 0.05 mol·L−1, MeOH/oil molar ratio second step: 4:1; (**d**) Catalyst concentration vs. MeOH/oil molar ratio second step; catalyst concentration first step: 0.10 mol·L−1, MeOH/oil molar ratio first step: 6:1.


**Table 3.** Optimization of the process.

Since the experimental conditions to obtain biodiesel from castor oil were optimized, an economic evaluation was carried out. For this economic evaluation, the conditions assuming that the predicted ester content was higher than 96.5% were considered. These conditions are collected in Table S1 of Supplementary Material. The main variable costs of the process, such as the consumed methanol, catalyst, and neutralizer, were determined for each condition. To simplify, only the levels of the factors integrated in the model were considered to this calculation, although similar conditions would be expected to achieve similar results and there would be infinite options. Since four factors and five levels were considered, 54 alternatives were evaluated. Among them, the ester content was predicted to be greater than 96.5% under 74 conditions.

Firstly, a biodiesel plant which uses 50,000 tons of castor oil per year was considered. Since biodiesel yield is usually close to 100%, this yield was assumed to the following calculations of this section [19,26]. The process is composed by two heated series reactors. The biodiesel and glycerol phase of the product of the first reactor would be separated, and biodiesel phase would be transferred to the second reactor. Fresh alcohol catalyst solution would also be added. From the products of the reaction, methanol would be recovered in about 90% of unreacted alcohol [2]. The neutralizer was H3PO4, so an input from the sale of K3PO4 to the industry of fertilizers was added. The prices to purchase one kilogram of CH3OH, KOH, and H3PO4 were \$0.47, \$1.87, and \$0.40, respectively. The price of selling one kilogram of K3PO4 was \$0.64. These data were obtained from local companies and the Methanex Methanol Price Sheet [36]. According to these values, the annual cost of methanol, catalyst, and neutralizer in the aforementioned biodiesel plant were evaluated. These expenses were calculated for each condition (Table S1 of Supplementary Material) and they were plotted in Figure 2 as variable cost per liter of biodiesel. The cost of castor oil was not considered because it would be the same for all conditions. The numbers in the x-axis represent the experimental conditions considered to calculate the cost. According to the model, all of these conditions will lead to an ester content greater than 96.5%. Among them, the reaction conditions which showed the cheapest processes in terms of feedstock cost would be the numbers 57, 58, 39, and 65. These numbers represent the conditions collected in Table 4. As an example, the number 57 represents 0.06 mol·L−<sup>1</sup> as catalyst concentration and 6:1 as MeOH/oil molar ratio for the first step and 0.01 mol·L−<sup>1</sup> as catalyst concentration and 3:1 as MeOH/oil molar ratio for the second step. When these conditions were used in a biodiesel plant of 50,000 tons of castor oil, a cost saving close to \$400,000 could be obtained in comparison to the most unfavorable conditions collected in Figure 2. On the other hand, the optimal conditions as shown in a previous work, where one-step process was used, were 0.064 mol·L−<sup>1</sup> CH3OK and 18.8:1 as catalyst concentration and MeOH/oil molar ratio, respectively [8]. Considering these conditions and the same biodiesel plant, close to \$800,000 per year could be saved if the process with two steps were used. Therefore, the use of two-step transesterification for this process will suppose important saving costs for reagents.

**Figure**  millions **Table 4.** Experimental conditions with the lowest variable costs per liter of biodiesel.

of

dollars

for

the

selected

conditions.


## *2.6. Process Simulation*

**2.**

Annual

variable

cost

in

Experimental conditions related to run 39 were considered to simulate the process. Due to the high solubility between methanol and castor biodiesel, phase separation was extremely slow when the conditions of run 57 and 58 were used. Therefore, the third condition with lower cost was taken into account. The simulation of a plant of 50,000 tons·year<sup>−</sup><sup>1</sup> of castor oil was carried out. A continuous process was considered because it is common in industry, especially in plants with high capacities [2]. The process flowsheet is shown in Figure 3. The simulation was carried out with the software UniSim Design, and the properties of the main streams of the process were collected in Tables 5 and 6. The process could be improved by energy integration and a study in-depth of the pumping system.

**Figure 3.** Process flowsheet.

**Table 5.** Properties of the main streams (part I).


**Table 6.** Properties of the main streams (part II).


Firstly, the chemical components were defined for the simulation process. Methanol, glycerol, NaOH (instead of KOH) and water were available in the software component library. The

castor oil feedstock and biodiesel were defined as the triglyceride of ricinoleic acid and methyl ricinoleate, respectively. Both compounds were added as hypothetical components [19,37]. Due to the presence of highly polar components, non-random two liquid (extended NRTL) was recommended as thermodynamic model. In addition, liquid–liquid equilibrium data for the system of methanol–glycerol–methyl ricinoleate were faithfully provided by the model [38,39].

Plant capacity was established as 50,000 tons·year<sup>−</sup><sup>1</sup> of castor oil transformed to biodiesel; therefore, 6.25 tonnes·hour−<sup>1</sup> were considered (8,000 annual operating hours) [10]. As shown in Figure 3, castor oil and fresh methanol were fed to the process by stream 1 and 2, respectively. The stream 3 was a 30% catalyst solution in methanol. Conditions and compositions of these streams are shown in Tables 5 and 6. Methanol was added in excess, so the surplus was recovered and purified, and 89.2% of unreacted methanol was recycled. In the first reactor, the reaction was carried out with a 5.25:1 methanol/oil molar ratio, 0.08 mol·L−<sup>1</sup> NaOH, 45 ◦C, and 10 min as residence time. In the second reactor, composition and flow of the streams were regulated to use a 3:1 methanol/oil molar ratio, 0.01 mol·L−<sup>1</sup> NaOH, 45 ◦C, and 10 min as residence time. These conditions were the established in run 39, Table 4.

The reactors used in the simulation were conversion reactor models with 89% oil conversion in the first reactor (CRV-100) and 77.5% remain oil conversion in the second reactor (CRV-101). As previously checked by other authors, the presence of the theoretical reaction intermediates, diacylglycerols and monoacylglycerols, was only observed in the initial stages of the reaction, due to high methanol to oil ratios [40].

In the process flowsheet (Figure 3), the product of the first reactor was led to a liquid–liquid separator (V-100). In the process design, a high-speed disc bowl centrifuge was considered because this separation is very slow for castor oil biodiesel and glycerol [41]. Biodiesel rich phase was led to the second reactor and fresh catalyst and methanol were also added. After this reaction, the product was a monophasic mixture. Methanol was recovered by two in series vacuum distillation (V-101 and V-102) at 50 kPa. The temperatures of these operations were 150 ◦C in the first separator and 50 ◦C in the second one. The recycled stream had 99.9% methanol.

The streams of biodiesel from the separators were washed in a water washing column (T-100) with hot water (40 ◦C). It was a column with four theoretical stages at atmospheric pressure [2,40], and in this step, the total removal of the remaining catalyst, methanol, and glycerol was achieved.

Final biodiesel refinement was conducted through vacuum distillation, in order to obtain biodiesel which was within the EN 14214:2013 standard. According to these specifications, water and methanol contents were lower than 0.05% and 0.20%, respectively. The final amount of biodiesel obtained in the process was 6016 kg·h−1, with a yield of 96.3% based on the initial oil.

Glycerol rich phase was neutralized with H3PO4 and this operation was simulated by the tool "Component Splitter" (X-100). This tool allowed for the separation of NaOH. The real operation requires a reactor where H3PO4 reacts with KOH and a following step for the separation of the synthesized salts [2]. Finally, a distillation column (T-101) was used for methanol recovery and glycerol purification. The design of this column was carried out according to previous works [40,42] and using the "Short Cut Distillation" software. The achieved glycerol purity was 86.4%, but depending on its desired use, additional purification could be necessary.

## *2.7. Cost Evaluation*

Once the production process was established, a cost evaluation was carried out. Firstly, the main units were identified and their sizes calculated. To determine the volume of the transesterification reactors, the volumetric flow of reagents and their residence time were considered; the reactor was a stirred tank with 0.5 as a fill factor. The size of the high-speed disc bowl centrifuge was estimated based on the flow of product that had to be separated. Flash distiller sizes were obtained according to the guidelines established by Silla [43]. The evaporator V-101 was a vertical vessel with cylindrical shape, 4.5 m<sup>3</sup> as total volume and 3 as the length/diameter ratio. The design of V-102 was carried out considering that the inlet stream was mainly composed of vapor. In this case, the length to diameter ratio was 2 and its volume was 0.70 m3. The most suitable shape of the distiller V-103 was a horizontal cylinder with 50% as liquid level and 10 min as residence time. Under these assumptions, the volume of the vessel was 2.7 m3.

The cost of the water washing column and the neutralization and salt removal units was estimated based on the inlet flow rate [16,40]. Regarding the distillation column for glycerol purification (T-101), design criteria for this type of unit were used [44]. A packed column was chosen instead of a plate column, because of its short dimensions. The packing material was INTALOX®, 1". The diameter and length of the column were 0.30 and 5.2 m, respectively, considering 65% efficiency [43–45]. The cost of the reboiler and condenser were considered in the heat exchanger section.

The costs of the processing units were calculated based on its size and previous data. In addition, the exponential rule of economy of scale was applied, following Equation (2), where S0 and CS0 are the capacity and cost of the known unit, respectively, and S and CS are the capacity and cost of the unit of which the cost is unknown. Exponent, δ, is characteristic of each technology and δ = 0.65 for the estimation of tanks, reactors, and columns, and δ = 0.80 for the pumps [46].

$$\mathbf{C}\_{\rm S} = \mathbf{C}\_{\rm S0} \left(\frac{\rm S}{\rm S\_0}\right)^{\rm s} \tag{2}$$

This rule was also applied to determine the cost of the equipment in an additional plant. A plant which used 16,000 tons·year<sup>−</sup><sup>1</sup> of castor oil was also evaluated. This plant was considered because the production of castor oil could be smaller in some areas. Fifty thousand tons of castor oil and about one-third of this amount were considered. The cost of the equipment has to be updated, following changes in the value of money due to inflation and deflation according to the chemical engineering plant cost index. Equation (3) was employed, where CA and CB are the current capital cost and the cost in the base period, respectively, and CEPCIA and CEPCIB are the index published in *Chemical Engineering Journal*. The costs of the major processing units are presented in Table 7.

$$\mathbf{C}\_{\text{A}} = \mathbf{C}\_{\text{B}} \frac{\mathbf{C} \mathbf{E} \mathbf{P} \mathbf{C} \mathbf{I}\_{\text{A}}}{\mathbf{C} \mathbf{E} \mathbf{P} \mathbf{C} \mathbf{I}\_{\text{B}}} \tag{3}$$


**Table 7.** Estimation of equipment costs.

The total capital cost of the plant was estimated by the method of factors developed by Lang and improved by Peter and Timmerhaus [47]. This method was based on the cost of the major processing units. In Table 8, factors and capital costs of the plant were collected. As seen in this table, the cost of the plant increased because of the increase of capacity, however, one plant was more than three times bigger than the other, while its cost was only double.


**Table 8.** Estimated fixed capital cost (year 2015).

The price of castor oil was considered as an average price of this oil for the European region. However, this price strongly depends on Indian producers, because this country accounts for more than 60% of the global yield [48]. The prices of the rest of the raw materials were also obtained. As shown in Table 9, the costs of the utilities, and fixed costs were collected to obtain the final manufacturing cost of biodiesel in plants with capacity of 50,000 and 16,000 tonnes·year<sup>−</sup>1.


**Table 9.** Annual manufacturing costs.

As seen in Table 9, vegetable oil represents 81% of the biodiesel costs in the plant of 50,000 tons·year<sup>−</sup><sup>1</sup> and 78% in the smallest plant. Castor oil can be a promising raw material for biodiesel production on account of the low production requirements. Castor bean can be grown in poor or low fertile lands with low rain indexes, making it a good option for poor regions. However, this oil shows high price on the international market, possibly due to its dependence on the Indian market and its use as lubricant and in the chemical industry. The issue of this type of biodiesel is its high viscosity, which make its direct use in injection engines di fficult. However, there are some works where castor oil is used to obtain biodiesel because it has good behavior in engines when it is mixed with other biofuels or diesel [4,49].

#### **3. Materials and Methods**
