Techno-economic and Sensitivity Analyses of Different Biodiesel Production Pathways by Adding Tetrahydrofuran as a Cosolvent

The main objective of this study is to design and simulate three different continuous processes, namely, homogeneous and heterogeneous alkali-catalyzed and supercritical methanolysis processes to produce biodiesel at a production rate of 100,000 t/year from virgin vegetable oil. Tetrahydrofuran (THF) was used as a cosolvent at different concentrations of 25 wt.%, 30 wt.%, and 1.63 wt. % for the homogeneous and heterogeneous alkali-catalyzed and supercritical processes, respectively. An economic assessment and a sensitivity analysis were performed based on the results of the process design and simulation. Technical assessment of the proposed processes indicated that the homogeneous and heterogeneous alkali-catalyzed processes were the simplest, where the least amount of process equipment were used. whereas the supercritical methanolysis process was more complex, which used a large number of transesterification and separation units. The homogeneous alkali-catalyzed process that used THF demonstrated the lowest total capital investment, after-tax net profit, and payback period of M$2.32, M$10.54, and 0.19 years, respectively, and the highest after-tax rate of return of 513%. However, the heterogeneous alkali-catalyzed process that used THF demonstrated the lowest manufacturing cost of M$82.20 and the highest after-tax net profit of M$18.20. The supercritical methanolysis process that used THF demonstrated the highest manufacturing cost of M$90.07 and the after-tax net profit of M$12.40. The results from the sensitivity analyses indicated that the methanol recovery percentage, biodiesel purification tower vacuum pressure, and costs of feedstock oil, methanol, biodiesel, and glycerin by-products are the factors that most significantly affect the economic feasibility of biodiesel production.


Introduction
Global energy consumption has been increasing daily due to the rapid population growth and industrial development [1]. Some alternative energy sources, such as solar, hydrogen, wind, and biodiesel, have attracted the interest of researchers to satisfy the increasing demand [2]. Biodiesel is a prominent alternative fuel among these renewable sources because it is nontoxic, biodegradable, renewable, and environment friendly [3]. Biodiesel is produced by transesterification reaction of vegetable oil or animal fats with methanol in the presence of a catalyst. High biodiesel yields are obtained using a homogeneous alkali catalyst during the transesterification process at mild reaction temperature, short reaction time, and atmospheric pressure [4]. However, this type of catalyst suffers from major issues in terms of emulsification, high energy consumption, catalyst separation after reaction, and generation of excess wastewater [5]. These problems can be solved by producing heterogeneous catalysts [6]. However, heterogeneous catalytic reactions are typically time-consuming because of the diffusion problem caused by the formation of three phases of reactants: methanol oil solid catalyst [7]. Therefore, identifying a solid base catalyst for transesterification under mild reaction conditions and short reaction time is difficult [8]. For biodiesel production, alkaline-earth metal oxides with high basicity are suitable. One of the most promising heterogeneous basic catalysts for biodiesel production is alkaline-earth metal oxide, specifically calcium oxide [9].
Homogeneous and heterogeneous catalysts are used for transesterification reactions in biodiesel production.
Homogeneous catalysts are classified into two types, namely, acid and base catalysts, whereas heterogeneous catalysts are classified into three types, namely acid, base, and enzymatic catalysts. The rate of reaction of base-catalyzed transesterification is faster and it produces more biodiesel in less time than the acid-catalyzed catalyst. on the other hand enzyme catalyst is a good catalyst for transesterification owing to its low temperature and high yield; however, it is expensive. Thus, homogeneous alkaline transesterification is the preferred process for biodiesel production because the catalysis is faster and less expensive than the other catalysts [10][11][12][13][14][15][16].
Most of the previous studies investigated the effect of cosolvents on the transesterification reaction of oils. For example, Encinar et al. [17] investigated the effect of various cosolvents on the transesterification of rapeseed oil, including acetone, diethyl ether (DEE), dibutyl ether (diBE), tertbutyl methylether (tBME), diisopropyl ether (diIPE), and tetrahydrofuran (THF). Thanh et al. [18] investigated the homogeneous reaction process of the transesterification of canola oil using acetone as a cosolvent. Acetone was also used as a cosolvent by Luu et al. [19] to produce biodiesel from waste cooking oil (WCO). Dabo et al. [20] investigated the cosolvent transesterification of Jatropha curcas seed oil. Alhassan et al. [21] studied the transesterification of cottonseed oil into biodiesel using cosolvents such as DEE, dichlorobenzene, or acetone. Linseed has a high potential for biodiesel production because of its high oil content, high levels of unsaturated fatty acids, inedibility, and low cost compared with the other oily seeds [22]. Hence, linseed is an excellent choice as a raw material for biodiesel production. Ambat et al. [23] investigated biodiesel production from low-cost feedstock such as lard oil and WCO using SrAl double oxides. The effects of acetone and THF as cosolvent for transesterification were compared and the best result was obtained using 5% THF.
Continuous processes were primarily evaluated in previous economic studies on biodiesel production. Kasteren and Nisworo [24] calculated the costs of producing 8000-125,000 t of biodiesel per year using a continuous supercritical methanol process and WCO. You et al. [25] calculated the costs of producing 8000-100,000 t of biodiesel per year using a continuous homogeneous alkali-catalyzed process involving soybean oil. West et al. [26] calculated the costs of producing 8000 t of biodiesel per year using four WCO-based processes: (1) continuous homogeneous alkalicatalyzed process, (2) continuous homogeneous acid-catalyzed process, (3) continuous heterogeneous acid-catalyzed process, and (4) continuous supercritical methanol process. Similarly, Marchetti and Errazu [27] calculated the costs of producing 36,036 tonnes of biodiesel per year using the same four processes. The continuous heterogeneous acidcatalyzed process demonstrated the lowest manufacturing costs among the four processes.
The objectives of the present study are to design and simulate three different continuous homogeneous and heterogeneous alkali-catalyzed and supercritical methanolysis processes, namely, Process I, II, and III, respectively to produce biodiesel at a production rate of 100,000 t/year using virgin vegetable oil. Techno-economic and sensitivity analyses of different biodiesel production pathways are performed by adding THF as a cosolvent in two steps.

Methodology
The design and simulation calculations of the different biodiesel production processes using THF as a cosolvent are performed along with the economic calculations, followed by sensitivity analyses to investigate the parameters that affect these processes.

Process Simulation Procedure
The commercial feasibility analysis of the proposed procedures and process simulations are completed. Despite the few predicted variations between the process simulation results and actual operation, most current simulation software can provide reliable data on process operation because of their comprehensive thermodynamic packages, large component libraries, and advanced calculation techniques. Process-simulation software Aspen HYSYS V8.4 which is developed by AspenTech Inc. is used in this study.
The process-simulation steps involve defining the chemical components, choosing a thermodynamic model, determining the plant capacity, selecting the proper operating units, and providing the input conditions (flow rate, temperature, pressure, and other conditions).
To set up a process flowsheet and perform a steady-state simulation, the first step involves defining the chemical components and thermodynamic model to be employed. The system mainly consists of triglyceride, methanol, methyl ester, glycerol, THF, and catalyst. Information on most of these species is available in the HYSYS component library and is not further discussed here. Vegetable oil is a mixture of different triglycerides containing various fatty acids. Because oleic acid is the most common monoenoic fatty acid in plants and animals [28], triolein (C 57 H 104 O 6 ), which contains three oleic acid chains is chosen as the representative triglyceride in the HYSYS simulation. Accordingly, methyl oleate (C 19 H 36 O 2 ) is considered as the resulting biodiesel product and its properties are available in the HYSYS component library. The components that are not found in the library, such as phosphoric acid and potassium phosphate are defined using the "Hypo manager" tool in HYSYS. For phosphoric acid, its molecular weight is 98 g/mol. Its normal boiling point and density are set to 406.9 °C and 1857 kg/ m 3 , respectively [29]. Finally, HYSYS is used to estimate the other physical properties, such as critical temperature, pressure, and volume.
Because of the presence of a highly polar component, i.e., methanol, both the universal quasi-chemical and nonrandom two-liquid (NRTL) thermodynamic/activity models are recommended to estimate the activity coefficients of the components in a liquid phase. The detailed descriptions of these models are provided by Gess [30]. The NRTL model is used in this study. Once the chemical components and thermodynamic model are defined, the next step is to develop a process flowsheet by choosing the operating units and defining the input conditions, such as composition, flow rate, temperature, and pressure. To obtain an equal basis for comparison, each process is designed for the same plant capacity. Thus, in the current process design, a plant with 100,000 tons/year biodiesel is simulated.

Process Design for the Selected Processes
As mentioned earlier, biodiesel production through transesterification includes many processes. In the present study, three transesterification processes are selected according to the following.
• The homogenous alkali-catalyzed process is selected as the most studied and conventional process [31]. • The heterogeneous alkali-catalyzed process is selected as the corresponding process for comparison with the homogenous alkali-catalyzed process [32]. • The supercritical methanolysis process is selected for its promising conversion results and shorter reaction times. This process is catalyst-free compared with the other biodiesel-production technologies. It demonstrates the fastest reaction time under elevated conditions [33,34].
The three different designed and simulated continuous processes are listed in Table S1. Figures 12 and 3 show the process flowsheets of the three processes, whereas Table S2 lists the selected process parameters for HYSYS simulation. The detailed process description is presented herein.

Transesterification
Fresh methanol (stream methanol), recycled methanol (stream 201B), and the cosolvent (stream THF) are mixed before being introduced into the reactor (R-100) with the addition of virgin vegetable oil (stream oil) and KOH catalyst in Process I or CaO catalyst in Process II. In R-100, 91%, 97%, and 98.5% of the oil are converted into biodiesel according to the experimental results in Processes I, II, and III, respectively [35][36][37], and glycerol is produced as a byproduct. The outlet stream from the reactor is introduced to methanol recovery distillation tower T-100 after being used to heat the inlet oil stream. In Process II, the outlet stream from R-100 is introduced to the catalyst removal separator (solid/liquid) before entering T-100 because of the need to remove the solid catalyst before proceeding.

Methanol and THF Recovery
Because of the low boiling points of methanol and THF (64.7 °C and 66 °C, respectively), methanol and THF are recovered from T-100; with stream 201 that contains both substances being recycled back to R-100. To keep the bottom temperature below 150 °C, vacuum distillation is performed. Fig. 1 Homogeneous alkali-catalyzed process with THF as a co-solvent flowsheet on Aspen HYSYS Fresh make-up methanol and THF are mixed with the recovered methanol and THF (stream 201B) and then sent back to reactor R-100. Bottom stream 202 is sent to the biodiesel/ glycerol separator, except in Process I where it is first sent to neutralization reactor R-200 to remove the excess liquid catalyst so as not to affect the purity of the final products.

Catalyst Removal
In Process I, to remove the KOH catalyst, the bottom stream from T-100 is fed to neutralization reactor R-200, and phosphoric acid is added. The resulting by-product, i.e. K 3 PO 4 , is removed from the solid/liquid gravity separator. The resulting potassium phosphate is used as a valuable by-product (e.g., fertilizer). In Process II, excess CaO, which is removed by the catalyst removal separator (solid/liquid), can be used as a low-quality by-product or sent to the regeneration chamber to be used again in the process.

Biodiesel/Glycerol Separation
Gravity separator V-100 is used to separate the biodiesel from glycerol and methanol. The heavy-liquid phase (aka glycerol) is removed from the bottom stream (stream glycerol), whereas the biodiesel is removed from the light-liquid stream and sent back to biodiesel purification tower T-200. The glycerol obtained from stream glycerol exhibits high purity (> 95%) which can be sold as a technical-grade substance.

Biodiesel Purification
To obtain a final biodiesel product that complies with the American Society for Testing and Materials (ASTM) specifications, biodiesel distillation T-200 is used. To prevent biodiesel degradation, T-200 is operated under a vacuum to keep the temperatures sufficiently low. A partial condenser is used to separate the biodiesel from water and In the reboiler, superheated high-pressure steam is used as the heating medium.

Economic Assessment
Technical assessment is not the only aspect considered in project assessment because different factors such as economic, environmental, and social factors must be considered. Economic performance is an essential aspect of assessing process viability. It tests the project profitability, i.e., whether it loses, or is profitable. The overall economic performance of a biodiesel plant (e.g., fixed capital cost, the total cost of manufacturing, and break-even cost of biodiesel) can be calculated once the specific factors are identified, which include the plant capacity, process technology, raw material cost, and chemical cost.
The following assumptions are considered in the economic evaluation in this study: • The operating hours are assumed to be 8000 h/year. • The pump efficiency is assumed to be 70%, which is used to determine the pump shaft power.  Table 1.
According to the definition of capital-cost estimation provided by Turton [39], the economic estimation in this study is considered as a "study estimate," which means that a process flow-diagram must be developed, in addition to rough sizing of the major process equipment. No further data, such as the layout plot or process piping and instrumentation diagram, are considered. The current study demonstrates an accuracy range from + 30 to − 20%. Accordingly, the results from this type of preliminary evaluation do not accurately reflect the final profitability of a chemical plant but can be used as an indicator for comparison among the different process alternatives. The module cost technique is a commonly used technique for calculating the cost of a new chemical plant. It is known as the best technique for making preliminary cost estimates and is used in this study. The economic assessment is developed in the literature proposed by Turton.

Purchased Cost of Equipment and Bare Module Cost
The capital cost of a chemical plant is estimated using Capcost and an Excel-based program developed by Turton. The cost data are adjusted for inflation by adding the current value from CEPCI. The equipment options available in the program include evaporators, vaporizers, reactors, towers, heat exchangers, process vessels with and without internal parts, mixers, and pumps with electric drives. The cost obtained from the program presents the bare module cost (C BM ) for each piece of equipment, which reflects the sum of the direct and indirect costs related to the equipment installation.

Total Capital Investment
The total capital investment (C TCI ) was split into fixed and working-capital investments. The fixed capital investment (C FC ) presents the investment required to make the plant ready for start-up, and it consists of two cost types: contingency, and fee costs (C FCs ), and auxiliary facility costs C AFs .

Contingency and Fee Costs (C CF )
Contingency and fee costs are included in the cost evaluation for protection against oversights and faulty information. They are calculated using Eq. (1). These costs are added to the bare module cost to obtain the total module cost (C TM ) as expressed in Eq. (2).

Auxiliary Facilities Costs (C AF )
Auxiliary facilities costs include site development, auxiliary buildings, off-sites, and utilities, and they can be calculated using Eq. (3). These terms are generally unaffected by the construction materials or operating pressure of the process. These costs are added to the total module cost to obtain the fixed capital cost (C FC ) as expressed in Eq. (4).

Working Capital Costs (C WC )
Working capital costs represent the amount of investment needed to start-up the plant and financially cover the first few months of operation before gaining revenues from the process. They are calculated using Eq. (5). These costs are added to the fixed capital cost to obtain the total capital investment (C TCI ) as expressed in Eq. (6).

The Total Manufacturing Cost
The total cost of manufacturing related to the daily operation of a chemical plant is calculated by assessing the economic feasibility of the proposed processes, including the direct manufacturing cost, fixed manufacturing cost, and general expenses (GEs) as expressed in Eq. (7).

Direct Manufacturing Cost (DMC)
Direct manufacturing costs (DMCs) include the operating expenses that vary with the production rate, and they cover the costs of raw materials, utilities, waste treatment, labor, direct supervisory cost, clerical labor, maintenance and repairs, operating supplies, laboratory charges, patents, and royalties. The costs of the used raw materials, utilities, and waste treatment are listed in Table 1.
The operating labor cost (C OL ) is calculated using Eq. (8) provided by Turton where N OL is the number of operators per shift, P is the number of processing steps including the handling of particulate solids, e.g., transportation and distribution, particulate size control, and particulate removal. N NP presents the number of nonparticulate processing steps and includes compression, heating and cooling, mixing, and reaction.
The other costs include direct supervisory, clerical labor, maintenance and repair, operating supplies, laboratory charges, patents, and royalties, which are calculated by multiplying them with a factor listed in Table S3.

Fixed Manufacturing Cost (FMC)
The fixed manufacturing costs (FMCs) are independent of the changes in the production rate, including the plant overhead cost, property taxes, insurance, and depreciation, which are considered accounted at constant rates even when the plant is not operating and calculated by multiplying them with a factor listed in Table S4.
General Expenses (GEs) General expenses (GEs) represent the required overhead burden to perform business functions, including management, sales, and research functions and are calculated by multiplying them with a factor listed in Table S5.

Profitability Analysis
Three factors are used as a basis to evaluate profitability: time, cash, and interest rate. The time and interest rate criteria are used in the current study to evaluate profitability. However, we start the evaluation, and the annual net profit (A NP ) must be calculated.

Annual Net Profit (ANP) and Income Tax (AIT)
The annual net profit (ANP) presents the money gained or lost resulting from the revenues (A R ) after subtracting all associated costs, which is calculated using Eq. (9).
Taxation has a direct effect on the profits realized from building and operating a plant. The income taxes (A ITs ) vary according to national laws and regulations. In the present study, A IT is assumed to be 30%. After deducting A IT from the A ITs , the after-tax net profit is obtained (A NNP ) as expressed in Eq. (10).

After-Tax Rate of Return on Investment (ATROR)
The aftertax rate of return on investment (ATROR) is used [40], which represents the rate at which money is generated from fixed capital investment. The project is more profitable if the ROI percentage is higher. The ROI percentage is calculated using Eq. (11).
Payback Period (PBP) The payback period represents the time required after the start-up to recover the fixed capital investment for the project and is calculated using Eq. (12). The project is more profitable if PBP is shorter as calculated by Eq. (12).

Sensitivity Analysis
Sensitivity analyses of the processes are performed to calculate the effect on the process variables with some degrees of uncertainty and to determine any operating conditions in each process that can be modified to improve the process. Computer modeling HYSYS is considered an experiment performed by the computer. It is different from traditional physical experiments but has been widely used in recent years. Usually, computer experiments provide an effective alternative to time-consuming or expensive physical experiments. For reaction conditions that are too difficult or costly to implement in practice, computer experiment is a powerful tool for predicting the system behavior.

Controlling Factors
ATROR of the biodiesel plant is used as the performance criterion. It is related to many intermediate outputs, such as CTCI, and total manufacturing cost. Although the amount of these intermediate outputs are also available in this work, the after-tax rate of return provides the primary basis for the conclusions.
In addition to the chemical costs that are directly related to the economic calculations, some design variables affect the processes, such as the recovery rate of methanol, vacuum in the methanol recovery tower, and vacuum in the biodiesel purification tower. Those factors are included in the sensitivity-analysis study to investigate their effect on the processes. In Process I, for example, 11 control variables (i.e., control factors) are found to affect the response variable (i.e., aftertax rate of return). They are the methanol-recovery percentage, vacuum in the methanol-recovery tower, vacuum in the biodiesel-purification tower, and costs of the feed oil, methanol, cosolvent, biodiesel, glycerol, catalyst, neutralization agent, and salt by-product from neutralization.
The control factors differ from one process to another. they depend on the type of catalyst and removal process of the catalyst from the system. In Process I, a liquid homogeneous catalyst is used, which requires the application of a neutralization agent to create a neutralization reaction to obtain a salt by-product. This process increases the control variables to 11 factors. In Process II, the used catalyst is a solid heterogeneous catalyst, which requires removal using a solid/liquid separator and no extra chemical is introduced into the system. This process reduces the control variables to eight factors. In Process III, no catalyst is used, which reduces the control variables to eight factors. The identification of the control variables in each process is listed in Table S6.

Experimental Design
The two-level fractional factorial design is a common screening tool that is to filter out insignificant variables without losing much important information. In this study, the two-level fractional factorial design with resolution IV is applied. In a resolution IV design, each main effect is at least confounded with one three-factor interaction. One special feature in the current research is that several factors involve chemical costs. In some cases, interactions between two chemical costs or interactions between one chemical cost and another unrelated chemical property should be made very small or zero. The description of all factors in Process I are listed in Table S7. Process I is chosen as an example because it contains the maximum number of variables, whereas the other processes have fewer control variables than Process I.
The setting of the levels of chemical costs is based on an assumption. The use of different price ranges would create some ambiguities in analyzing the practical significance of these factors. In other words, determining whether the significance of each chemical cost factor is due to the cost itself or its wide cost range. To avoid such ambiguities, the cost of each chemical is arbitrarily set at the same price range (i.e., $200/t) for the sensitivity analyses. Thus, the final results reflect the practical effect of each factor.
Today, computer programs are designed for each process. In the statistical analysis study of this research, Design Expert V7.0 is used as the software to perform the study and estimate the influencing variables. The fractional factorial experimental design includes 2 IV , which involve 11, 9, and 8 factors, respectively, 32 runs and one response for each set of experiments. these factors are used for Process I-III. The system description of each process is listed in Table S8.
After the model, control variables, and response are defined, the program randomly creates run actions. Therefore, the response values under different run conditions are obtained and input into the program. Here, the analysis of variance (ANOVA) table can be easily completed. Finally, when the P value (Prob > F) is less than 0.05, the parameter can be considered as significant. In other words, the parameter significantly affects the process.

Results and Discussion
Different cosolvents are used in the transesterification of fatty materials, e.g., acetone, THF, hexane, DEE, chlorobenzene, 2-propanol, ethyl acetate, 1,4-dioxane, diBE, and tBME. By comparing the studied cosolvents, Roschat et al. [41] found that THF resulted in higher biodiesel yields than those obtained using 1-propanol, 2-propanol, acetone, ethanol, and ethylene glycol. Encinar et al. [17] demonstrated that the use of cosolvent improved the mass transfer between the phases existing in the transesterification process. Therefore, a high biodiesel yield could be achieved within small reaction times, even at room temperature. The most effective cosolvents were DEE and THF.

Technical Assessment
Simulation of the three different processes is performed using the Aspen HYSYS simulator. A technical comparison of these processes is presented below. Table 2 lists the comparison among the three different processes for biodiesel production that use THF as a cosolvent: homogeneous alkali-catalyzed Process I, heterogeneous alkali-catalyzed Process II, and supercritical methanolysis Process III. We find that Process III exhibits adverse reaction conditions with the highest conversion of 98.5%. Meanwhile, Process II exhibits the largest reactor volume of 411.8 m 3 because of its longest reaction time of 360 min.
For the methanol and THF recovery tower T-100, Process I showed the lowest methanol-to-oil molar ratio of 4.5:1 and 25% wt.% THF, which results in a small amount of methanol that needs to be recovered in T-100.Therefore, the vapor load inside the tower is reduced to 11,431 kg/h, the condenser duty is reduced to 7.32 MJ, the reboiler duty is reduced to 11.15 MJ, and the tower diameter is reduced to 2.0 m. Meanwhile, Process II contains a methanol-to-oil ratio of 12:1 and 30 wt. % THF. The vapor load inside the tower is 19,985 kg/h, the condenser duty is 19.29 MJ, and the reboiler duty is 18.78 MJ. For Process III, a 42:1 methanol to oil molar ratio and 1.63 wt. % THF is used, which results in the increase in the condenser duty to 60.75 MJ, the reboiler duty to 34.53 MJ, the load inside the tower to 51,453 kg/h, and the tower diameter to 4.3 mas listed in Table 2.
In all processes, the use or absence of a homogeneous and heterogeneous catalyst does not affect biodiesel/glycerol separator volume V-100, because the processes have the same separator volume of 0.3 m 3 and high-purity glycerol of > 95% can be obtained.
In Process I, a neutralization step is required to remove the catalyst from the final biodiesel product. On the other hand, Process II does not require a neutralization step because of the ease in separating the heterogeneous catalyst using a filtration step. Process III also does not use a catalyst. The neutralization reaction introduces extra water into the system, which acts as a bipolar liquid and is partially removed from the glycerol stream, Thus, the purity in Process I decrease to ≈ 95% instead of ≈ 99% compared with that of the other processes.
In biodiesel-purification tower T-200, the introduction of a neutralization step before the tower in Process I introduces water into the system, which complicates the biodiesel-purification, and results in the need for a larger tower to obtain ASTM-compliant biodiesel. Thus, a 3.8-m tower diameter is required in Process I. In terms of final biodiesel purity, the three processes can produce biodiesel with a purity of more than 96.5% which complies with the ASTM and EN-14103 standards. The total number of major processing units in each process is listed in Table S9. The lowest number of units is in Processes I and II with nine pieces of equipment. Supercritical methanolysis Process III is the most complex process with 13 pieces of equipment because of the adverse reaction conditions required to perform the reaction, i.e., reaction pressure and temperature. This increase in the number of equipment indicates a potential increase in the cost of construction materials.

Economic Assessment
After the process simulation and design presented in the previous sections, the values of the fixed capital cost, total manufacturing cost, and after-tax rate of return of the processes are determined. A summary of the economic performance of each process is shown in Figs. 4, 5 and 6 and Tables 3, 4 and 5.   Table 3 lists the comparison among the three process types. We found that the volumes of transesterification reactor R-100 are 9.2, 411.8, and 220.9 m 3 . Although Process II has the highest transesterification reactor volume, Process III incurs the highest transesterification reactor cost of M$0.07. Process I incurs M$1.53 and Process II, incurs M$1.98. This result is due to the use of high pressure of 19,000 kPa in Process III and a high methanol-to-oil molar ratio of 42:1, which increases the reactor thickness and reactor volume.
For methanol-recovery tower T-100, Process I shows the lowest methanol-to-oil molar ratio of 4.5:1, which results in the need for smaller equipment sizes. The tower diameter in Process I is 2.0 m that in Process II is 2.7 m and that in Process III is 4.3 m. Thus, the cost of T-100 in Process I is the lowest than those in the other two processes, namely, M$0.54 for Process I, M$0.67 for Process II, and M$1.64 for Process III.
Because of the use of a homogeneous catalyst in Process I, a neutralization step is required to remove the catalyst from the final biodiesel product. This process adds an extra cost to M$0.07 for the total bare module cost.
The adverse conditions in Process III result in the use of more equipment to overcome the 42:1 methanol-to-oil molar ratio and 19,000-kPa pressure. Thus, supercritical methanolysis Process III incurs the highest total bare module cost among the cosolvent processes (M$1.36 for Process I,  With regard to the utilities, the transesterification reaction conversions of Process I-III are 91%, 97%, and 98.5%, respectively, which indicate that Process I has the largest amount of superheated high-pressure steam and consequently the highest cost of M$18.57. Those of Process II and III are M$7.46 and M$11.28, respectively. Two more factors affect the utility cost, i.e., low-pressure steam and refrigeration water costs, which are both used in T-100. The high methanol-to-oil molar ratio in Process III increases the load inside the tower. Thus, the amount and costs of the low-pressure steam in Process I-III are M$1.42, M$2.71, and M$4.93, respectively. This process also increases the amount and costs of the refrigeration water in the condenser to M$0.50, M$1.32, and M$4.17, respectively.

Total Manufacturing Cost
Overall, Process II incurs the lowest total cost of manufacturing, i.e., M$82.20. Process III is second at M$90.07 because of the high methanol to oil molar ratio. Finally, Process I incurs the highest total cost of manufacturing, namely, M$94.81 because of its transesterification reaction conversion of 91% and the need for a larger amount of superheated high-pressure steam.

After-Tax Rate of Return and Payback Period
The list in Table 5 indicates that all processes achieve positive net profit after taxation because of the high revenue from selling the biodiesel product at approximately M$99.4. Homogeneous alkali-catalyzed Process I demonstrates the highest ATROR of 513% and the shortest payback period of 0.19 years. This result is attributed to its low capital investment (M$2.32), and the contributions of by-product glycerol and K 3 PO 4 to the total revenue, which are M$9.24, and M$1.17 respectively. On the other hand, Process I has the lowest after-tax net profit of M$94.81 because of its high manufacturing cost.
For Processes II and III, higher after-tax net profits are realized, namely, M$18.20 and M$12.40, respectively. However, they have lower ATROR of 417% and 160%, and longer payback periods of 0.23 years and 0.59 years, respectively.

Sensitivity Analysis
Sensitivity analyses are performed in all processes to determine the effect of the process parameters on ATROR. As previously mentioned, to investigate the influencing parameters on each process, the ANOVA table must first be obtained. Finally, if P value (Prob > F) is less than 0.05, the parameter can be considered significant. In other words, the parameter significantly affects the process. The ANOVA table for each process is listed in Table 6.
Tables S10 and S11 list the summary of the sensitivity analysis results. In all processes, the methanol-recovery percentage significantly affects ATROR. The increase in the methanol-recovery percentage increases the reboiler duty of the methanol recovery tower. Thus, a larger reboiler area and a higher amount of steam are needed. As a result, FCI, COM, and ATROR are all affected.
The biodiesel purification tower vacuum pressure exerts a major effect on Processes I and II. Its slightest increase or decrease results in a change in the condenser and reboiler duties. Increasing the pressure to reach atmospheric pressure increase the temperature inside the tower. Therefore, the temperature difference between the steam and biodiesel mixture is reduced. Thus, a larger amount of steam and a larger heat transfer area for the reboiler are needed to achieve the required biodiesel purity. Process III is the only process with the methanol-recovery tower vacuum pressure as a major parameter. The use of a large amount of methanol to oil molar ratio and a large amount of cosolvent requires a large tower size and large condenser/reboiler sizes and duties. Therefore, the change in the pressure inside the tower indirectly affects FCI and COM.
For the raw materials, the oil and methanol cost positively affect all processes. Raw materials contribute approximately 54-63% of the total manufacturing cost. Therefore, a change in their costs affects COM and consequently ATROR. With respect to the products, the biodiesel and the glycerol costs introduced the greatest effect because they both contribute approximately 90% and 8% to the total revenue respectively. Thus, a change in their costs is affecting the after-tax net profit and consequently ATROR.

Conclusion
Three different continuous processes, namely, homogeneous, and heterogeneous alkali-catalyzed and supercritical methanolysis processes that use virgin vegetable oil as the raw material and THF as cosolvent were designed and simulated. The economic assessment of the three processes demonstrated that the homogeneous alkalicatalyzed process that used THF as cosolvent exhibited the lowest total capital investment, after-tax net profit, payback period, and the highest after-tax rate of return.
However, the heterogeneous alkali-catalyzed process that used THF incurred the lowest manufacturing cost and generated the highest after-tax net profit. The supercritical methanolysis process that used THF demonstrated the highest manufacturing cost and after-tax net profit.
On the basis of the after-tax rate of return and the payback period, Process II realized the highest after-tax net profit with lower ATROR and a longer pay-back period. Process I, realized the highest ATROR and shortest payback period with a lower after-tax net profit. The sensitivity analyses revealed that the methanol recovery percentage, biodiesel purification tower, vacuum pressure, and costs of the feedstock oil, methanol, biodiesel, and glycerol were the major factors that affected the commercial viability of biodiesel production.
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB). The authors gratefully acknowledge the support from the National Research Center and Faculty of Engineering, Cairo University.

Availability of Data and Materials
The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request through a material transfer agreement.

Declarations
Ethics Approval and Consent to Participate Compliance with ethical standards was considered by informing participants about the aims and methods of the respective research. Participation in the survey was voluntary and the anonymity of the participants is preserved-no inferences can be drawn from the answers to the individuals.

Conflict of Interest
The authors declare no competing interests.
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