Energy Optimization and Effective Control of Reactive Distillation Process for the Production of High Purity Biodiesel

: Biodiesel is a promising renewable energy option that signiﬁcantly reduces the emission of greenhouse gases and other toxic byproducts. However, a major challenge in the industrial scale production of biodiesel is the desired product purity. To this end, reactive distillation (RD) processes, which involve simultaneous removal of the byproduct during the transesteriﬁcation reaction, can drive the equilibrium towards high product yield. In the present study, we ﬁrst optimized the heat exchange network (HEN) for a high purity RD process leading to a 34% reduction in the overall energy consumption. Further, a robust control scheme is proposed to mitigate any feed disturbance in the process that may compromise the product purity. Three rigorous case studies are performed to investigate the effect of composition control in the cascade with the temperature control of the product composition. The cascade control scheme effectively countered the disturbances and maintained the fatty acid mono-alkyl ester (FAME) purity.


Introduction
The continuous depletion of non-renewable energy resources and their hazardous impact on the environment has impelled the scientific community to explore alternative energy sources. Due to consistently increasing energy demands, the need to develop renewable, non-toxic, and environmentally friendly energy options such as biofuels has grown rapidly [1][2][3].
Biodiesel is similar to petroleum diesel in terms of properties and is a promising alternative to fossil fuels [4][5][6]. Fatty acid mono-alkyl esters (FAME) are the main component of biodiesel, which can be produced by transesterification of free fatty acids (FFA) and alcohol. The biodegradable feed stocks such as animal fats, vegetables, or cooking oils are common sources of FFA. The optimization and simplification of FFA transformation to the cleanburning biodiesel fuel is a subject of active research [7][8][9][10]. While using the conventional reactor-separation system, the reaction equilibrium limits the product yield. The generation of byproducts amplifies the backward reaction, thus limiting the reaction conversion. This limitation instigates the need for multiple separation systems in the process, involving additional capital and operational costs. A potential solution to this drawback is the deployment of a reactive distillation (RD) column. An RD column is a separation column with catalysts in a particular section, which enables the reaction as well as separation to occur simultaneously in the same tray. The RD process is best suited for equilibrium-limited chemical reactions, whereby the byproducts are separated immediately after their formation. This causes the reaction to move forward and results in high conversion and product yield. Additionally, the RD process optimizes the plant economics, eliminating the need for extra separation processes and added utilities [11][12][13][14][15]. Estrada-Villagrana et al. [13] studied and complex operation composition analyzers are required to closely monitor the feed flow rates and composition [35]. Moreover, sensitive flow controllers are required for effective control system since even a slight disturbance may compromise the biodiesel product purity. The aforementioned requirements make the equimolar process infeasible to operate [37]. Therefore, excess reactant is often employed as an alternate to ease RD process control design in the industrial processes [34]. Using excess reactant may increase the capital and operational costs of the process. However, a proper energy management and integrated energy design can cope with the energy requirements and scale down the utilities expenses [8,23]. Another advantage of the proposed process is the high purity water byproduct, which eliminates the need for a water treatment process to conform to environment standards.
Moreover, an optimized heat exchange network was designed using Aspen Energy Analyzer in this study. The proposed heat integrated process is less energy intensive with energy savings of up to 33% compared to the conventional process. In order to consistently manage the product purity, a robust process control structure is an essential requirement. Therefore, a rigorous process control scheme was designed in this study and case studies were undertaken to overcome the impact of disturbances in the process without compromising the product quality. The columns are designed using the Radfrac method in Aspen Plus. The process dynamics and control mechanism were studied using the rigorous pressure driven mode of Aspen Plus.

Process Kinetics
FFA reacts with methanol in the liquid phase to produce FAME and water using sulfated zirconia, which is a solid acid catalyst [38]. This esterification reaction can be written as: The reaction kinetics of the present esterification reaction are given as: The reaction is reversible, and k 1 and k 2 are reaction constants for forward and backward reactions, respectively. Noting that the byproduct water is continuously extracted from the reaction process, the forward reaction dominates the overall esterification reaction. Since the backward reaction rate is remarkably sluggish, neglecting the backward rate is an acceptable approximation, simplifying the reaction kinetics [23]. Therefore, the reaction kinetics can be expressed as: where A is the Arrhenius factor and E a is the required activation energy. For the current study [23]: ; E a = 55, 000 J mol (4)

VLE Thermodynamics
The multi-component phase equilibrium of the reaction and separation system requires a precise thermodynamic model and relevant parameters. The thermodynamic activity model 'UNIQUAC' is used in the present work for VLE and LLE calculations. The UNIQUAC model is given as [39]: The binary interaction parameters used in the activity model are listed in Table 1. The binary parameters were deduced experimentally [37], whilst the FFA-FAME and methanolwater parameters can be extracted from Aspen properties. The components in the system can be arranged in the following order in terms of their volatility: The light key component recovered in the RD distillate is water along with excess methanol while the heavy key in the bottom is FAME with traces of FFA. The residue curve for methanol/water/FAME system at 9 bar (RD operating pressure) is reported in Figure 1a. The separation of high purity FAME is feasible, however high heat duty is required. The separation of methanol and water is performed in the conventional column.
The T-xy diagram at an operating pressure of 5 bar is plotted in Figure 1b.
The binary interaction parameters used in the activity model are listed in Table 1. The binary parameters were deduced experimentally [37], whilst the FFA-FAME and methanol-water parameters can be extracted from Aspen properties. The components in the system can be arranged in the following order in terms of their volatility: The light key component recovered in the RD distillate is water along with excess methanol while the heavy key in the bottom is FAME with traces of FFA. The residue curve for methanol/water/FAME system at 9 bar (RD operating pressure) is reported in Figure 1a. The separation of high purity FAME is feasible, however high heat duty is required. The separation of methanol and water is performed in the conventional column.
The T-xy diagram at an operating pressure of 5 bar is plotted in Figure 1b.
The following assumptions were made in the present simulation: • The liquid and vapor in all the trays are completely mixed • Both the liquid and vapor streams leaving the tray are in equilibrium.

•
The vapor hold-up in the tray is negligible • The liquid phase is homogenous in all trays.

Steady State RD Process
The process flowsheet is shown in Figure 2 and the important design parameters, reported by Ali et al. [40], are used to simulate the process. The design parameters are reported in Table 2. The tray numbers in both columns are denoted from top to bottom so The following assumptions were made in the present simulation:

•
The liquid and vapor in all the trays are completely mixed • Both the liquid and vapor streams leaving the tray are in equilibrium.

•
The vapor hold-up in the tray is negligible • The liquid phase is homogenous in all trays.

Steady State RD Process
The process flowsheet is shown in Figure 2 and the important design parameters, reported by Ali et al. [40], are used to simulate the process. The design parameters are reported in Table 2. The tray numbers in both columns are denoted from top to bottom so that the first tray represents the condenser and the last tray is the reboiler. The methanol and FFA with 100% purity at ambient temperature are used as reactants. The fresh methanol blends with recycled methanol and enters the RD column with FFA in stages 15 and 6, respectively, after preheating to the desired temperature. The liquid hold-up is set at 50 L so that flooding from the trays can be avoided. The RD column produces 99.5 mol% FAME as bottoms, while the distillate comprises of unreacted methanol and water. The stream results of the process are mentioned in Table 3. The excess methanol and water exiting from RD distillate is separated in the conventional distillation column (CC). The water purity is maintained at 99.5% in the CC bottom. The methanol-water mixture recovered from the CC top with a high concentration of methanol is recycled back and mixed with the fresh methanol feed. The first column, i.e., the RD column shown in Figure 3, involves the production of FAME and water from methanol and FFA in the reaction section and the simultaneous transfer of water from the liquid phase to the vapor phase providing an added advantage. The liquid phase and vapor phase compositions in the trays are reported in Figure 4. In the stripping section, below the reaction section, the FAME in the vapor phase moving upwards is transferred to the liquid phase further enhancing the FAME concentration in the liquid phase below. The lighter components are transferred from vapor to liquid coming downstream from the condenser as reflux in the enriching section. In order to reduce the recycling load and achieve a steady state, a 10% effluent is purged out from the recycling process using a splitter, which is 0.57 kmol/h with a methanol/water ratio of 0.47/0.53, respectively. The purge constitutes only 4.6% of the total feed input supplied in the process. The purge effluent can be used in the process, which requires dilute methanol [41]. Moreover, the purge comprises only 5 mol% of the total water produced in the process and 4.2 mol% of the total methanol fed into the system.

Heat Integration
The heat integration parameters of the streams of the process flowsheet in Figure 2, which require heating and cooling and are included in the optimized heat exchange design, are reported in Table 4. The majority of utilities required are for the preheating of reactants, whereby the utilities can be efficiently replaced by the hot process effluents, which must be cooled before their utilization. The cold utilities requirement is lessened as well. The modified heat exchange network (HEN) of the process is reported in Figure 5. There are five new heat exchangers, which replaced the process heaters and coolers in Figure 2. Since the condensers and reboilers of the distillation columns involve phase changes and require equilibrium conditions, the heat integration design becomes a complicated task. For example, the kettle type exchangers generally used for reboilers involve vapor and liquid separation as well. Moreover, there are high possibilities of involvement of multiple heat exchangers for single reboiling/condensing processes since the enthalpy of one stream may not be enough to maintain equilibrium and achieve the required process conditions. Moreover, distillation columns in some cases have condensing and reboiling processes inside the column integrated with sump or the surge tank. Therefore, the condensers and reboilers of columns are not accounted for in the heat exchange network in the present modified HEN. Table 5 compares the various economic parameters of the preliminary process reported in Figure 2 and heat integrated process reported in Figure 5. The requirement of both hot and cold utilities was reduced by 22.7% and 24.8%, respectively. Other miscellaneous energy savings, such as electricity, contributed to a further reduction. Therefore, the overall energy consumption was reduced by 33.6% while the estimated capital cost remained the same in both cases. Moreover, the temperature interval diagram plotted in Figure 6 shows that the stream S-15, which is the bottom stream from the RD column reboiler, has a temperature of around 366 • C, while the cold streams have to be heated to a maximum of 150 • C. The heaters and coolers drawn here refer to PFD in Figure 2. The minimum approach temperature is set at 10 • C. The heat available in section A in the TID diagram is the excess energy available after designing the HEN, which is removed in E-01 in Figure 5. The 140.12 kW of energy available at 366 • C can be used for preheating streams that require heating up to high temperatures, which is an added advantage of the heat integration of the process.

Process Control Structure
In the current process control structure, the objective is to maintain the purity of the product, FAME, and the other effluent from the distillation column, water, if any changes occur in the feed flow rates. The rigorous plantwide control process suggested by Luyben is used in the current study [34]. There are a total of 11 controllers used for controlling the process. The following control loops were added to the process: Level controllers (LC): Since the surge/storage tanks have a flexible range of variation and do not require stringent control, proportional controllers were installed as level controllers to maintain liquid level at reflux drum and sump of the reactive distillation column and the distillation column.
Flow controllers (FC): The equi-molar feed flow in the process employs composition

Process Control Structure
In the current process control structure, the objective is to maintain the purity of the product, FAME, and the other effluent from the distillation column, water, if any changes occur in the feed flow rates. The rigorous plantwide control process suggested by Luyben

Process Control Structure
In the current process control structure, the objective is to maintain the purity of the product, FAME, and the other effluent from the distillation column, water, if any changes occur in the feed flow rates. The rigorous plantwide control process suggested by Luyben is used in the current study [34]. There are a total of 11 controllers used for controlling the process. The following control loops were added to the process: Level controllers (LC): Since the surge/storage tanks have a flexible range of variation and do not require stringent control, proportional controllers were installed as level controllers to maintain liquid level at reflux drum and sump of the reactive distillation column and the distillation column.

Flow controllers (FC):
The equi-molar feed flow in the process employs composition analyzers and flowmeters with high precision and sensitivity, which are expensive and involve strenuous operation. Any stoichiometric misproportion may result in process dynamics instability and require complex process control arrangements to be enacted in such situations. Adding one reactant in excess in the process eliminates the equal feed flow requirement and hence the complex measurement devises. However, the excess reactant has to be separated from the feed, which employs an extra distillation column.
The PI controllers were set to control the feed flow rates in the column. The fresh methanol feed flow, along with recycled methanol, was controlled before entering the column. A ratio controller is attached to maintain the methanol feed flow with respect to acetic acid in the column at a fixed ratio at any time.
Pressure controllers (PC): In order to maintain the condenser pressure in both columns, PI controllers are installed in both columns. The heat removal from the condenser was manipulated by controlling the coolant flow in the condenser.

Temperature controllers (TC):
The temperature controller was installed to control the temperature of trays in the column. The process output was the heat duty of the reboiler. The PI controllers were installed as temperature controllers in both columns. A dead time of 1 min was used with temperature controllers.

Composition controller (CC):
The composition controller is used in Case 4 below to effectively manage the product purity of the reactive distillation column. Since the response of cascade controller is sluggish, a dead time of 3 min is used with the control scheme.
The tuning parameters of FC, PC, and LC were taken from the standard tuning parameters suggested by Luyben [42], while the tuning parameters for TC and CC controllers were calculated from the Ziegler-Nichols tuning method [32]. The details and tuning parameters used for controllers are reported in Table 6.
The following case studies were performed in the current study:

Case I
This case study was performed without using feed flow ratio control and composition control structures. As seen in Figure 7, a total of ten control loops were installed. The control scheme faceplates of all the controllers are reported in Figure 8. Although the composition control was not used, the temperature controller installed in both columns can manage the tray temperatures as well as composition to an extent. A dead time of 1 min is added to the control structure. Figure 9a shows the response of effluents when the methanol feed flow was increased from 6.3 kmol/h to 6.6 kmol/h at time 2 h. The FAME product increased from 6 kmol/h to 6.1 kmol/h, since the reaction shifted towards product side due to the increase in reactant, methanol. Moreover, the RD distillate flow (Stream S-10) increased due to excess methanol (0.2 kmol/h increase) and excess water produced (0.1 kmol/h) due to increased reactivity. However, the water in CC bottom decreased and the CC distillate flow increased (Stream S-21), and hence the effluent in the recycling process as well as columns increased. When the methanol increased in the CC column, there was a higher transfer of methanol from liquid to vapor in the stripping section, which increased the total vapor flow rate and reduced the liquid flow rate in the reboiler, which in turn resulted in lower CC bottom flow rate, which is water. Moreover, the increased vapor flow after cooling in a condenser resulted in higher amounts of distillate. Although there was slight increase in FAME concentration, the concentration of water decreased slightly due to increased methanol in the CC column. Additionally, it took 2.5 h for FAME concentration to stabilize. Henceforth, the methanol feed flow was decreased from 6.3 kmol/h to 6.0 kmol/h. The disturbance effects are reported in Figure 9b. It should be noted that the methanol feed flow is equivalent to acid feed flow. A decrease in FAME product is seen since the reaction is shifted towards the reactant side. The water product increased due to the decrease in methanol in the CC column feed flow. The FAME concentration decreased while the water concentration increased. The time taken for stable FAME concentration is approximately 2.5 h here as well.  to the increase in reactant, methanol. Moreover, the RD distillate flow (Stream S-10) increased due to excess methanol (0.2 kmol/h increase) and excess water produced (0.1 kmol/h) due to increased reactivity. However, the water in CC bottom decreased and the CC distillate flow increased (Stream S-21), and hence the effluent in the recycling process as well as columns increased. When the methanol increased in the CC column, there was a higher transfer of methanol from liquid to vapor in the stripping section, which increased the total vapor flow rate and reduced the liquid flow rate in the reboiler, which in turn resulted in lower CC bottom flow rate, which is water. Moreover, the increased vapor flow after cooling in a condenser resulted in higher amounts of distillate. Although there was slight increase in FAME concentration, the concentration of water decreased slightly due to increased methanol in the CC column. Additionally, it took 2.5 h for FAME concentration to stabilize. Henceforth, the methanol feed flow was decreased from 6.3 kmol/h to 6.0 kmol/h. The disturbance effects are reported in Figure 9b. It should be noted that the methanol feed flow is equivalent to acid feed flow. A decrease in FAME product is seen since the reaction is shifted towards the reactant side. The water product increased due to the decrease in methanol in the CC column feed flow. The FAME concentration decreased while the water concentration increased. The time taken for stable FAME concentration is approximately 2.5 h here as well.

Case II
In this case study, a feed flow ratio control was added, as seen in Figure 10 (without composition control, but with temperature control in the RD column). The ratio control ensures that one feed flow rate remains in proportion with the other feed flow. In the present study, the acid feed flow is at a ratio of 1.0/1.05 (kmol/h basis) to methanol flow feed. The first graph in Figure 11 shows that the acid feed flow immediately changes from 6 kmol/h to 6.29 kmol/h when the methanol feed flow is changed from 6.3 kmol/h to 6.6 kmol/h. It should be noted that the ratio control will be enacted only in the case of methanol feed flow disturbances. The FAME product flow increased due to the increase in reactants. However, the effluent in the process has increased (Stream S-10 and S-21). A marginal decrease in mole fractions of products is seen due to higher unreacted reactants in the product streams. The FAME composition became steady after more than 2 h.

Case II
In this case study, a feed flow ratio control was added, as seen in Figure 10 (without composition control, but with temperature control in the RD column). The ratio control ensures that one feed flow rate remains in proportion with the other feed flow. In the present study, the acid feed flow is at a ratio of 1.0/1.05 (kmol/h basis) to methanol flow feed. The first graph in Figure 11 shows that the acid feed flow immediately changes from 6 kmol/h to 6.29 kmol/h when the methanol feed flow is changed from 6.3 kmol/h to 6.6 kmol/h. It should be noted that the ratio control will be enacted only in the case of methanol feed flow disturbances. The FAME product flow increased due to the increase in reactants. However, the effluent in the process has increased (Stream S-10 and S-21). A marginal decrease in mole fractions of products is seen due to higher unreacted reactants in the product streams. The FAME composition became steady after more than 2 h. 6 kmol/h to 6.29 kmol/h when the methanol feed flow is changed from 6.3 kmol/h to 6.6 kmol/h. It should be noted that the ratio control will be enacted only in the case of methanol feed flow disturbances. The FAME product flow increased due to the increase in reactants. However, the effluent in the process has increased (Stream S-10 and S-21). A marginal decrease in mole fractions of products is seen due to higher unreacted reactants in the product streams. The FAME composition became steady after more than 2 h.

Case III
The operation with temperature controller may sometimes generate an offset in the product composition, which can be subsided using a composition controller. However, the CC control generates a delayed response, which can again compromise the composition quality. Hence, the control scheme is used in a cascade loop with a temperature controller. The control loop structure is reported in Figure 10 and the cascade control arrangement faceplate is reported in Figure 12. The temperature control scheme acts as a primary loop, while the composition control scheme is set as a secondary loop. The process output of the composition controller, which is temperature, is synchronized as the set point of the primary controller. It can be clearly seen in Figure 13 that the composition of the FAME product is almost invariant with the change in reactants feed flow, providing a steady product quality irrespective of the disturbances in the process.

Case III
The operation with temperature controller may sometimes generate an offset in the product composition, which can be subsided using a composition controller. However, the CC control generates a delayed response, which can again compromise the composition quality. Hence, the control scheme is used in a cascade loop with a temperature controller. The control loop structure is reported in Figure 10 and the cascade control arrangement faceplate is reported in Figure 12. The temperature control scheme acts as a primary loop, while the composition control scheme is set as a secondary loop. The process output of the composition controller, which is temperature, is synchronized as the set point of the primary controller. It can be clearly seen in Figure 13 that the composition of the FAME product is almost invariant with the change in reactants feed flow, providing a steady product quality irrespective of the disturbances in the process. ment faceplate is reported in Figure 12. The temperature control scheme acts as a primary loop, while the composition control scheme is set as a secondary loop. The process output of the composition controller, which is temperature, is synchronized as the set point of the primary controller. It can be clearly seen in Figure 13 that the composition of the FAME product is almost invariant with the change in reactants feed flow, providing a steady product quality irrespective of the disturbances in the process.

Conclusions
Incorporating excess methanol in the proposed flowsheet, although it required an extra distillation column, successfully circumvented the need for a complex process design, complicated control, and expensive compound composition analyzers. The process flowsheet, designed using the design parameters of the previous study [40], produced 99.5 mol% FAME and 99.5 mol% byproduct water. A 10% recycle methanol was purged to reduce the recycle load and improve the water purity. The optimized modified HEN proposed here significantly reduced the cold and hot utilities by decreasing the utility costs by 33.6%.
In the first case study, ±5% change in the methanol feed flow affected both products' flow and composition. The FAME composition was, however, stabilized after 2.5 h of disturbance. A ratio control used in the second case ensured the flow of both feeds at a fixed ratio. This strategy helped to better control the FAME composition. The third case study employed a composition control along with feed ratio control. The operation of composition control in cascade with the temperature control system successfully mitigated the product composition variations in case of any disturbances in the methanol feed flow rate.

Conclusions
Incorporating excess methanol in the proposed flowsheet, although it required an extra distillation column, successfully circumvented the need for a complex process design, complicated control, and expensive compound composition analyzers. The process flowsheet, designed using the design parameters of the previous study [40], produced 99.5 mol% FAME and 99.5 mol% byproduct water. A 10% recycle methanol was purged to reduce the recycle load and improve the water purity. The optimized modified HEN proposed here significantly reduced the cold and hot utilities by decreasing the utility costs by 33.6%.
In the first case study, ±5% change in the methanol feed flow affected both products' flow and composition. The FAME composition was, however, stabilized after 2.5 h of disturbance. A ratio control used in the second case ensured the flow of both feeds at a fixed ratio. This strategy helped to better control the FAME composition. The third case study employed a composition control along with feed ratio control. The operation of composition control in cascade with the temperature control system successfully mitigated