Production of Biofuel Additives Using Catalytic Bioglycerol Etherification: Kinetic Modelling and Reactive Distillation Design

Abstract

Glycerol is an unavoidable by-product of the biodiesel production process. The conversion of glycerol into valuable biofuel additives is essential in the fuel industry. The goal of this work is to develop a reactive distillation-based process for the production of biofuel additives by bio-glycerol etherification. In this study, a kinetic model using a lumping approach for glycerol etherification with tert-butyl alcohol (TBA) over Sn (II) phosphomolybdate (Sn_1.5PMo₁₂O₄₀) catalyst was developed. Aspen Plus was used to validate the kinetic model by simulating the glycerol etherification with TBA in a batch reactor. The model predictions were in good agreement with the experimental data. A reactive distillation-based process to produce glycerol ethers was developed, and heat integration was conducted to reduce energy consumption. The energy requirements of the integrated process and the CO₂ emissions were decreased by 17% and 14%, respectively. An economic evaluation was performed to study the profitability of the process for an annual capacity of 33,000 metric tons of glycerol ethers. It was found that the process is economically attractive, with a return on investment of 29.40% and a payback period of 2.2 years. The reactive distillation-based process is green and promising for producing biofuel additives that are sustainable and environmentally friendly.

1. Introduction

Oxygenated additives are well known for producing cleaner-burning diesel fuels by increasing oxygen levels and the octane rating number of the fuel. In addition, additives decrease the fuel vapor pressure, which in turn limits carbon emissions [1,2,3]. In recent years, glycerol ethers have been considered promising oxygenated additives for diesel fuels [4]. The blending of glycerol ethers with diesel enhances internal combustion efficiency, decreases pollutant emissions, and improves fuel properties such as pour and cloud points [5].

Biodiesel is produced by the transesterification process in which vegetal oils react with alcohol in the presence of alkaline-based catalysts [6,7,8]. The biodiesel process produces glycerol as a by-product, consisting of ~10 wt.% of the total fuel [9,10,11]. The high demand for biodiesel has created an abundant supply of glycerol, which has caused the prices of glycerol to decline [12]. Accordingly, research efforts have been developed to make a more sustainable and economically viable biodiesel production process using different routes for converting glycerol into value-added chemicals [13].

One promising process is the conversion of glycol to ethers. The glycerol ethers are oxygenated additives with attractive properties. Mono-tert-butyl glycerol ether (MTBG) is typically used as an efficient surfactant, while di-tert-butyl glycerol ether (DTBG) and tri-tert-butyl glycerol ether (TTBG) are used as alternatives to replace conventional fuel additives such as methyl tert-butyl ether (MTBE), which has a fossil origin [14,15].

Glycerol etherification can be carried out using isobutylene or tert-butyl alcohol (TBA), and it was concluded that TBA is preferable compared to isobutylene [16]. In addition, isobutylene is in the gas phase during the reaction with glycerol, while TBA and glycerol are both in the liquid phase. Therefore, the use of TBA prevents oligomerization and overcomes the need for an additional solvent during the etherification reaction [8,10,16,17]. In most cases, heterogeneous solid catalysts are preferable for glycerol etherification over homogenous catalysts, and this is because homogeneous catalysts are known for their high operational costs and environmental drawbacks [18,19]. Many studies were carried out with solid catalysts for glycerol etherification using TBA to maximize conversion and selectivity. The heterogeneous catalysts include ion exchange resins, zeolites, sulfonated niobium oxides, a pillared clay, sulfonic acid-functionalized mesoporous polymers, sulfonated hybrid silicas, and amorphous organosilica-aluminium phosphates [16,20,21,22,23]. Da Silva et al. studied the synthesis of three Keggin heteropolyacid salts dopped with different Sn (II) amounts to evaluate their performance as catalysts for glycerol etherification with TBA [24]. It was found that Sn_1.5PMo₁₂O₄₀ provided the maximum selectivity toward DTBG and greater conversion among the three Keggin heteropolyacid salts.

Several studies have attempted to develop kinetic models that accurately describe the etherification of glycerol using TBA over different catalysts, but none was done for the Sn_1.5PMo₁₂O₄₀. Frusteri et al. developed a simple kinetic model that represents the reaction of glycerol with TBA catalyzed by Amberlyst 15 [8]. The reaction order was determined using the excess method conditions. Pico et al. developed both lumped and extended kinetic models for glycerol etherification with TBA catalyzed by Amberlyst 15 [10]. The lumped model contains three stoichiometric reaction equations, while the extended model has six stoichiometric reaction equations. It was reported that the two kinetic models provided a good representation of the experimental reactions.

Reactive distillation (RD) is considered a well-researched multi-functional technique for industrial applications due to its advantages which include reduced cost, improved separation process, improved selectivity, less energy consumption, and less complicated processes [25]. In addition, RD allows that chemical reaction and separation to occur at the same time inside the column, avoiding problems of equilibrium limitations that are common in a plethora of reversible reactions [26]. Even though other studies in the literature investigated etherification reactions, none of them developed a complete industrial-scale process for producing glycerol ethers using a reactive distillation-based process [15,16,17,27].

In this work, a kinetic model of glycerol etherification with TBA using the Sn_1.5PMo₁₂O₄₀ catalyst will be derived. A reactive distillation-based process will be developed to produce glycerol ethers from a catalytic etherification reaction with TBA. A heat integration will be carried out to reduce the energy consumption and CO₂ emissions of the reactive distillation-based process. The feasibility of the process will be verified through an economic analysis.

2. Results and Discussion

The diffractograms of phosphomolybdic acid and its tin salt are shown in Figure 1. It can be noticed that acid has greater crystallinity than Sn salt. However, the diffraction peaks were seen at the same 2θ angle. It is suggestive that the secondary structure of the Keggin anion was maintained even after the replacement of protons by Sn²⁺ cations.

The diffraction peaks noticed in the diffractogram of tin phosphomolybdate salt underwent enlargement and loss of intensity triggered by the presence of Sn (II) cation. The crystallite size was calculated by Scherrer Equation (Equation (1)), where λ corresponds to the Cu Kα radiation, and β is the full width at half-maximum for a reflection maximum located at 2θ.

$$\mathrm{L}=\frac{0.9 \mathsf{\lambda }}{\mathsf{\beta }\cos \mathsf{\theta }}$$

(1)

The protons exchange by Sn²⁺ led to a lower crystallite size (25.5 to 9.9 nm; phosphomolybdic acid and its tin salt, respectively). These measurements were performed in duplicate.

The elemental composition of tin phosphomolybdate was confirmed through energy dispersive spectroscopy. It was compared to the pristine heteropolyacid in

Table 1. Energy dispersive spectroscopy analysis of Sn_1.5PMo₁₂O₄₀ catalyst and its precursor H₃PMo₁₂O₄₀ *.

Mass (%)	H3PMo12O40		Sn1.5PMo12O40
	Theoretical	EDS	Theoretical	EDS
H	0.2	-	0	-
Sn	0	0	8.5	9.5
P	1.7	2.3	1.5	2.4
Mo	63.1	62.1	58.0	57.7
O	35.0	35.6	32.0	30.4

* the values presented are the average of three different regions of the catalyst surface.

.

There was a satisfactory agreement between theoretical and experimental values for both compounds, assuring the synthesis was carried out with success. Since EDS was coupled to an electronic scam microscope, the images of the catalyst surface were obtained and shown in Figure 2.

As verified by the Sherrer equation, the particle size of Sn_1.5PMo₁₂O₄₀ was smaller than pristine acid. From the N₂ adsorption/desorption isotherms (Figure 3), the surface properties of tin phosphomolybdate were obtained.

Table 2. Texture properties of H₃PMo₁₂O₄₀ and Sn_1.5PMo₁₂O₄₀ salt.

Catalyst	Surface Area m2 g−1	Pore Volume (×10−2 cm3/g)	Pore Diameter (nm)
H3PMo12O40	11.8	1.7	3.8
Sn1.5PMo12O40	11.2	1.4	2.9

shows that they were very close to those obtained from phosphomolybdic acid.

The infrared spectra of phosphomolybdic acid and its tin salt are shown in Figure 4. The main absorption bands noticed in the spectrum of H₃PMo₁₂O₄₀ acid were placed at 1015, 977, 910, and 760 cm⁻¹ wavenumbers, which were attributed to the vibrations of ν_as P-O, ν_as Mo = O, ν_as Mo-O_v-Mo, and ν_as Mo-O_a-Mo, respectively. These same absorption bands were also observed in the spectrum of tin phosphomolybdate. This observation suggests that after the protons exchange of pristine heteropolyacid, its Keggin structure was preserved.

2.1. Kinetic Modelling

A kinetic model of the glycerol etherification with TBA over the Sn_1.5PMo₁₂O₄₀ catalyst was derived by the lumping approach [7,8]. The forward (k_nF) and backward (k_nB) reaction rate constants where n = 1, 2, or 3 are shown in Equations (2)–(4):

$$\mathrm{Glycerol} + \mathrm{TBA} \begin{array}{c} k_{1F}\\ \overrightarrow{\overleftarrow{ k_{1B}}}\end{array} \mathrm{MTBG}+{\mathrm{H}}_2\mathrm{O}$$

(2)

$$\mathrm{MTBG} + \mathrm{TBA}\begin{array}{c} k_{2F}\\ \overrightarrow{\overleftarrow{ k_{2B}}}\end{array}\mathrm{DTBG}+{\mathrm{H}}_2\mathrm{O}$$

(3)

$$\mathrm{DTBG} + \mathrm{TBA} \begin{array}{c} k_{3F}\\ \overrightarrow{\overleftarrow{ k_{3B}}}\end{array} \mathrm{TTBG} +{ \mathrm{H}}_2\mathrm{O}$$

(4)

A power law approach was used to model the reaction kinetics, and the rate equations are second-order, as shown in Equations (5)–(7), where “C” refers to the concentration of a specific reactant:

$$r_1=k_{1F}{C}_G{C}_{TBA}-k_{1B}{C}_{MTBG}{C}_{H_{2}O}$$

(5)

$$r_2=k_{2F}{C}_{MTBG}{C}_{TBA}-k_{2B}{C}_{DTBG}{C}_{H_{2}O}$$

(6)

$$r_3=k_{3F}{C}_{DTBG}{C}_{TBA}-k_{3B}{C}_{TTBG}{C}_{H_{2}O}$$

(7)

The Arrhenius equation that describes the temperature dependence of the reaction rates is shown in Equation (8), where “k_0i” is the pre-exponential factor:

$$k_{i }=k_{0i }{e}^{-\frac{E_i}{RT} }$$

(8)

The reaction rate constants have been determined by plotting the inverse of concentration versus time. The mass balance equations of the reactants and products are shown in

Table 3. Mass balances of the reactants and products.

Component	Mass Balance Equation	Component	Mass Balance Equation
Glycerol	$\frac{d{C}_G}{dt}=-r_1$	DTBG	$\frac{d{C}_{DTBG}}{dt}=r_2-r_3$
TBA	$\frac{d{C}_{TBA}}{dt}=-r_1-r_2-r_3$	TTBG	$\frac{d{C}_{TTBG}}{dt}=r_3$
MTBG	$\frac{d{C}_{MTBG}}{dt}=r_1-r_2$

. The kinetic model is based on reaction stoichiometry. When one mol of glycerol is consumed, one mol of MTBG and one mol of water are formed. Consequently, when this is converted to DTBG, one mol of water is formed. The same occurs when DTBG is converted to TTBG (see Equations (1)–(3)). Glycerol is only consumed by $r_1$, and TBA is consumed by $r_1, r_2, \mathrm{and} r_3$. MTBG, on the other hand, is generated by $r_1$ and consumed by $r_2$, DTBG is generated by $r_2$ and consumed by $r_3$, and TTBG is generated by $r_3$.

The Arrhenius equation was used to find the pre-exponential (frequency) factors ($k_{0i }$) and the activation energies (E_i), as listed in

Table 4. Frequency factors (k₀) and activation energies (Ea) of the kinetic model.

Pre-Exponential Factor (m3/mol·s)		Activation Energy (kJ/mol)
$k_{0\_1F}$	$6.8\times {10}^8$	$E_{1F}$	91
$k_{0\_1B}$	$7\times {10}^3$	$E_{1B}$	52.5
$k_{0\_2F}$	$2\times {10}^6$	$E_{2F}$	61
$k_{0\_2B}$	$3\times {10}^3$	$E_{2B}$	30
$k_{0\_3F}$	$0.7\times {10}^3$	$E_{3F}$	66
$k_{0\_3B}$	$0.1\times {10}^3$	$E_{3B}$	80

. The concentrations of glycerol and products obtained experimentally at different temperatures were used to find ($k_{0i }$) and (Ei).

A batch reactor (RBatch) model of Aspen Plus was used to simulate the three reactions. The simulation results were validated and compared with the experimental data obtained from the work of Da Silva et al. [24]. The batch reactor has an initial amount of glycerol and TBA of 0.0046 mol and 0.0368 mol, respectively. The reactor was simulated at an isothermal temperature of 363 K, and the pressure was gradually increased from 1.0 bar to 3.8 bar for a 4-h duration.

Figure 5 shows the molar compositions of the experimental data and the simulation results plotted versus time for glycerol, MTBG, DTBG, and TTBG. Results in Figure 5 show that only 67% of conversion was achieved under these reaction conditions. Moreover, almost no TTBG was formed. It suggests that the performance of this catalyst using these conditions was not satisfactory when using the conventional reactor.

Figure 6 shows a parity diagram of glycerol conversions and product selectivities. In the parity diagram, the data obtained using the developed model has been plotted as a function of the experimental data. It was found that the kinetic model provided a good agreement with the experimental data in the range of ±10%. The straight-line correlation coefficient, R², equals 0.9739.

2.2. Reactive Distillation Design

A reactive distillation (RD) column has been designed and simulated using RadFrac of Aspen Plus (version 11, AspenTech, Bedford, MA, USA) software for glycerol etherification with TBA using Sn_1.5PMo₁₂O₄₀ as a catalyst to produce glycerol ethers. The reactive distillation column is used to shift the equilibrium of the etherification reactions toward the more desirable products (i.e., DTBG and TTBG). When using a conventional reactor, the reaction route favors the MTBG, which is less valuable.

The NRTL model was used for activity coefficients due to the nonideal vapor-liquid equilibrium and the presence of an azeotropic mixture in the process (TBA/water). As illustrated in Figure 7, the RD column consists of 20 sieve stages and six reactive stages, which start from stage 5 to stage 10. The RD column has a total condenser and a kettle reboiler. The glycerol is fed at the 5th stage of the RD column with a flow rate of 20 kmol/h at 363 K and 3.8 bar, while the TBA is fed at the bottom of the RD column with a flow rate of 100 kmol/h at 363 K and 4.1 bar. The ratio of glycerol to TBA was set to 5. Water and TBA are separated at the RD column’s overhead, while glycerol ethers are separated in the bottom stream. The unreacted glycerol is about 0.6 mol%. It was found that the MTBG was entirely converted to DTBG.

A parametric study was performed to evaluate the effect of the reflux ratio on the conversion of glycerol. The flow rate of the unreacted glycerol is plotted at different reflux ratios, as shown in Figure 8a. The unreacted glycerol varies from 0.13 to 0.63 kmol/h. The maximum glycerol conversion (~99%) occurred when the reflux ratio was in the range of 0.9–1.3. Figure 8b shows the molar fractions of the glycerol ethers (i.e., MTBG, DTBG, TTBG) as a function of the reflux ratio. It was found that for the reflux ratio above 0.4, the desired products are only DTBG and TTBG that are present in the bottom stream, while the undesired product (MTBG) is completely consumed.

The rectifying section is necessary to achieve higher conversion by removing water from the column [28]. The reactive zone starts after the rectifying section at the 5th stage, and a parametric study was done to identify the optimum number of stages in the reactive zone. The effect of the number of reactive stages on glycerol conversion and product purity is shown in Figure 9a,b, respectively. The increase in the number of reactive stages increases the glycerol conversion and consequently reduces the unreacted glycerol at the bottom. The maximum conversion is attained using six reactive stages, starting at the 5th stage and ending at the 10th stage.

The effects of feed ratio (TBA: Glycerol) on glycerol conversion and product mole fractions are shown in Figure 10a,b, respectively. The TBA flow rate varied from 20–150 kmol/h for a feed ratio (TBA: Glycerol) of 1 to 7.5. When the TBA flow rate is increased, the conversion of glycerol increases until the TBA feed flow rate is 100 kmol/h (TBA: Glycerol ratio = 5), when glycerol is completely consumed.

2.3. Process Development

The reactive distillation-based process for the production of glycerol ethers is shown in Figure 11. The process was developed and simulated using Aspen Plus^® for a typical plant capacity of 33,000 metric tons per year. Glycerol feed (stream 1) of 20 kmol/h is pumped using P-101 at 3.8 bar and heated in heat exchanger E-101 at 363 K. The glycerol enters the reactive distillation column at the top stage. TBA fresh feed (stream 3) is mixed with the recycled TBA (stream 10) and pumped using P-102 at 4.1 bar. The TBA is heated using E-101 at 363 K and fed to the RD column at the bottom stage with a flow rate of 100 kmol/h.

The conversion of glycerol in the RD column is ~99%. The glycerol ethers (DTBG and TTBG) are separated at the bottom of the column. The product is cooled in E-103 at 298 K (stream 6) and sent to the storage tank. The glycerol ethers consist of DTBG (94.5 mol%) and TTBG (5 mol%). The overall purity of the glycerol ethers is 99.5 mol%. °C

Water and unreacted TBA are separated at the top of the RD column (stream 5). The residue curve map of the TBA-water-glycerol mixture is shown in Figure 12. Water and TBA are saddles, and glycerol is the stable node. The azeotrope, the unstable node, happens when the mixture has 62.1% TBA and 37.9% water.

The azeotropic mixture of the TBA and water is sent to an extractive distillation unit (T-101) for purification. Glycerol is used as a solvent and fed at the top of the extractive distillation column with a flow rate of 150 kmol/h. A water-TBA mixture is fed at the 15th stage of the extractive distillation column with a flow rate of 100 kmol/h (stream 9). TBA exits the extractive distillation column as the distillate with a flow rate of 59 kmol/h (stream 10), which is recycled back and mixed with the fresh feed of TBA. The glycerol-water mixture leaves the extractive distillation in the bottom stream and is sent to the solvent recovery column (T-102). Glycerol solvent is recovered in the bottom stream and sent back to the extractive distillation column (T-101).

Table 5. Streams information of glycerol with TBA etherification process.

Stream	1	2	3	4	5	6	7
Temperature (K)	298	363	298	363	391	308	298
Pressure (bar)	1	4	1	4	4	2	1
Enthalpy flow (kW)	−3708	−3635	−4119	−9530	−8670	−4201	−30
Vapor mole fraction	0	0	0	0	0	0	0
Molar flow (kmol/h)	20	20	41.3	100.3	100.2	20.0	0
Mass flow (kg/h)	1842	1842	3061	7413	5137	4118	15
Component Flowrates in (kmol/h)
Glycerol	20.0	20.0	0.0	0.0	0.0	0.1	0.2
TBA	0.0	0.0	41.3	99.9	59.2	0.0	0.0
MTBG	0.0	0.0	0.0	0.0	0.1	0.0	0.0
DTBG	0.0	0.0	0.0	0.0	0.0	18.9	0.0
TTBG	0.0	0.0	0.0	0.0	0.0	1.0	0.0
Water	0.0	0.0	0.0	0.4	41.0	0.0	0.0
Stream	8	9	10	11	12	13
Temperature (K)	308	371	360	464	364	308
Pressure (bar)	1	2	1	2	1	1
Enthalpy flow (kW)	−27,695	−8670	−5619	−29,369	−3265	−27,665
Vapor mole fraction	0	0	0	0	0	0
Molar flow (kmol/h)	149.7	100.3	59.0	191.4	41.4	149.8
Mass flow (kg/h)	13,791	5137	4352	14,576	800	13,777
Component Flowrates in (kmol/h)
Glycerol	149.7	0.0	0.0	149.7	0.1	149.5
TBA	0.0	59.2	58.6	0.6	0.6	0.0
MTBG	0.0	0.1	0.0	0.1	0.1	0.0
DTBG	0.0	0.0	0.0	0.0	0.0	0.0
TTBG	0.0	0.0	0.0	0.0	0.0	0.0
Water	0.3	41.0	0.4	41.0	40.6	0.3

shows the stream information of the process.

2.4. Process Integration

Heat integration has been conducted to reduce the energy requirements for the base case process. The integrated glycerol etherification process using reactive distillation is shown in Figure 13. Two heat exchangers have been added to the base-case process (E-103 and E-105) to generate medium-pressure steam (MPS-1 and MPS-2) to heat the T-101 reboiler.

The two heat exchangers use the bottom stream of RD and T-102 because of their high temperatures of 560 and 572 K, respectively. The product stream (stream 7) is also used to heat the feeds in E-101 and E-102 at 363 K. The product (stream 8) is cooled in heat exchanger E-104. The product stream exiting the reactive distillation is used to heat the feed streams of glycerol and TBA in E-101 and E-102 instead of using a steam utility. The stream information of the integrated process is shown in

Table 6. Stream information of the integrated glycerol etherification process.

Stream	1	2	3	4	5	6
Temperature (K)	298	363	298	363	391	560
Pressure (bar)	1	5	1	5	4	4
Enthalpy flow (kW)	−3708	−3635	−4119	−9530	−8670	−3499
Vapor mole fraction	0	0	0	0	0	0
Molar flow (kmol/h)	20	20	41.3	100.3	100.3	20.0
Mass flow (kg/h)	1842	1842	3061	7413	5137	4118
Component Flowrates in (kmol/h)
Glycerol	20.0	20.0	0.0	0.0	0.0	0.1
TBA	0.0	0.0	41.3	99.9	59.2	0.0
MTBG	0.0	0.0	0.0	0.0	0.1	0.0
DTBG	0.0	0.0	0.0	0.0	0.0	18.9
TTBG	0.0	0.0	0.0	0.0	0.0	1.0
Water	0.0	0.0	0.0	0.4	41.0	0.0
Stream	7	8	9	10	11	12
Temperature (K)	476	374	308	298	308	371
Pressure (bar)	2	2	2	1	1	2
Enthalpy flow (kW)	−3769	−4048	−4201	−30	−27,695	−8670
Vapor mole fraction	0	0	0	0	0	0
Molar flow (kmol/h)	20.0	20.0	20.0	0.2	150.0	100.3
Mass flow (kg/h)	4118	4118	4118	15	13,791	5137
Component Flowrates in (kmol/h)
Glycerol	0.1	0.1	0.1	0.2	149.7	0.0
TBA	0.0	0.0	0.0	0.0	0.0	59.2
MTBG	0.0	0.0	0.0	0.0	0.0	0.1
DTBG	18.9	18.9	18.9	0.0	0.0	0.0
TTBG	1.0	1.0	1.0	0.0	0.0	0.0
Water	0.0	0.0	0.0	0.0	0.3	41.0
Stream	13	14	15	16	17
Temperature (K)	360	464	364	572	308
Pressure (bar)	1	2	1	1	1
Enthalpy flow (kW)	−5619	−29,369	−3265	−25,051	−27,665
Vapor mole fraction	0	0	0	0	0
Molar flow (kmol/h)	59.0	191.4	41.4	149.8	149.8
Mass flow (kg/h)	4352	14576	800	13777	13777
Component Flowrates in (kmol/h)
Glycerol	0.0	149.7	0.1	149.5	149.5
TBA	58.6	0.6	0.6	0.0	0.0
MTBG	0.0	0.1	0.1	0.0	0.0
DTBG	0.0	0.0	0.0	0.0	0.0
TTBG	0.0	0.0	0.0	0.0	0.0
Water	0.4	41.0	40.6	0.3	0.3

.

A comparison of the energy requirements between the base-case process and the improved process is shown in Figure 14a. The improved process can reduce total energy requirements by 17%. This is because the low-pressure steam was eliminated in the first two heat exchangers (E-101 and E-102), and the medium-pressure steam was generated within the process. A comparison of the CO₂ emissions of the base case and the improved process is shown in Figure 14b. The CO₂ emissions are reduced from 1898 kg/h in the base-case process to 1636.8 kg/h in the integrated process when natural gas is used to generate steam.

2.5. Economic Analysis

An economic evaluation was performed to check the profitability of the improved glycerol etherification process. Figure 15 shows the cost distribution of the main process equipment. The reactive distillation column is responsible for about 49% of the total cost. The extractive distillation column and solvent recovery column represent 25 and 17% of the total cost, respectively.

Table 7. Materials and utility costs for glycerol etherification process [28,29].

Item	Price
Glycerol ($/metric ton)	445
TBA ($/metric ton)	1150
Product ($/metric ton)	1700
Utilities
Medium pressure steam (mps) ($/metric ton)	6
High pressure steam (hps) ($/metric ton)	8
Electricity ($/kWh)	0.045
Cooling water ($/m3)	0.08

shows the prices of the raw materials, products, and utilities used in the process. The total annual cost of utilities is estimated at $1,600,000. The cost distribution of the utilities is shown in Figure 16. The cost of high-pressure steam (hps) is accountable for ~65% of the total annual costs of utilities. The total production cost (TPC) was estimated to be $43,860,000. The cost of raw materials is responsible for ~76.7% of the TPC.

Figure 17 shows the annual cost distribution of the total production cost of the glycerol etherification process. The direct costs, which are largely contributed by the raw materials costs, are responsible for 87% of the TPC, while the fixed charges and general expenses are responsible for the other 13%. The total capital cost of the investment is ~$7,391,000, and the details of the calculations of the total investment cost are provided in

Table 8. Details of total capital investment calculations [29].

	Fraction of Delivered Equipment for the Fluid Processing Plant	Calculated Values (million $)
Direct Costs
Purchased equipment, E′		1.133
Delivery, a fraction of E′	0.1	0.113
Subtotal: delivered equipment		1.246
Purchased equipment installation	0.47	0.586
Instrumentation &Controls (installed)	0.36	0.449
Piping (installed)	0.68	0.847
Electrical systems (installed)	0.11	0.137
Buildings (including services)	0.18	0.224
Yard improvements	0.1	0.125
Service facilities (installed)	0.7	0.872
Total direct costs	2.6	4.487
Indirect Costs
Engineering and supervision	0.33	0.411
Construction expenses	0.41	0.511
Legal expenses	0.04	0.05
Contractor’s fee	0.22	0.274
Contingency	0.44	0.548
Total indirect costs	1.44	1.795
Fixed capital investment (FCI)		6.281
Working capital (WC)	0.89	1.109
Total capital investment (TCI)		7.391

[30]. The economic evaluation summary of the reactive distillation-based process for glycerol etherification is shown in

Table 9. Economic evaluation summary of the reactive distillation-based process for glycerol etherification.

Item	Value
Fixed capital cost	$6,282,000
Total capital cost	$7,391,000
Return on investment (ROI)	29.36%
Payback period	2.2
Net present value	$7,853,000
The discounted cash flow rate of return	15.18%

.

3. Materials and Methods

3.1. Chemicals

All reagents were obtained from a commercial source and used without prior treatment. Glycerol (≥99.5%), tert-butanol (≥99%), SnCl₂ (98%), and H₃PMo₁₂O₄₀ were purchased from Sigma Aldrich (St. Louis, MO, USA). Dodecane (99%,) was purchased from Vetec (Sigma Aldrich, St. Louis, MO, USA). The Sn (II)-phosphomolybdate catalysts (Sn_1.5PMo₁₂O₄₀) were synthesized in the lab [24].

3.2. Synthesis of Catalysts

All the catalyst salts were synthesized according to the literature [15]. Typically, an aqueous solution (ca. 5 mL) of stannous chloride at an adequate stoichiometry was slowly dropped into another solution (ca. 20 mL) containing the solved H₃PMo₁₂O₄₀. The resulting suspension was magnetically stirred and heated at 333 K/3h. Afterward, the solvent was evaporated at 383 K, and the salt obtained was dried in an oven at 423 K/5 h and posteriorly calcined at 573 K/5 h.

3.3. Characterizations of Sn_1.5PMo₁₂O₄₀ Catalyst

SEM images and EDS analysis were performed in a JEOL JSM 6010LA microscope (Tokyo, Japan) from secondary electrons imaging (SEI) at 10 mm of work distance, electron source at 20 kV, and 1500 × magnification.

Diffractograms were recorded in a Bruker D8 Discover diffractometer (Billerica, MA, USA), operating with Cu-Ka radiation and a Ni filter, at 40 kV and 40 mA.

Porosity analyses were done through the DFT method in a NOVA 1200 Quantachrome instrument (Boynton Beach, FL, USA). N₂ adsorption/desorption isotherms were acquired at 77 K, after samples were degassed in a vacuum at 383 K/5 h. The surface area was determined from the BET method applied to the isotherms with P/P0 varying from 0.05 to 0.32.

FTIR spectra were collected by the Attenuate Total Reflectance method in a Varian 660-IR instrument (Middelburg, The Netherlands), coupled to a PIKE Technologies GladiATRTM accessory (Madison, WI, USA).

3.4. Catalytic Runs

The catalytic experimental runs of glycerol etherification with TBA were conducted in a sealed tube reactor (35 mL) equipped with a magnetic stirrer, and the reactor was placed in a thermostatic oil bath. Glycerol (0.84 mM), tert-butyl alcohol (3.37 mM), and dodecane as an internal standard (0.1 mM) were added to the reactor. The system was stirred for 5 min and heated to 363 K. Afterward, an exact amount of catalyst (9.2 × 10⁻⁴ mM, 0.2 mol% Sn (II) ions) was added to the reaction and monitored for 240 min.

3.5. Conversion and Selectivity

Glycerol and tert-butyl ethers were analyzed in a Shimadzu CG-2010 plus, equipped with a capillary Carbowax 20 M (30 m × 0.25 mm × 0.25 μm) column and FID detector. The column temperature started at 80 °C and was raised to 210 °C (10 °C/ min). The injector and detector were set to 250 °C. The carrier gas was H₂. A split ratio of 1:30 was used.

To determine the response factor of the products, glycerol ethers were previously separated from the reaction medium through chromatography in a silica column, using ethyl acetate, chloroform, and methanol as eluents at different proportions. The response factors concerning glycerol were 7.3, 5.3, and 3.1 for TTBG, DTBG, and MTBG, respectively.

The conversion of glycerol was estimated through gas chromatography analysis of aliquots collected periodically to compare the amount of glycerol consumed to the initial glycerol concentration at different time intervals. The main products were identified by GC-MS analysis (GC-MS 2010 ultra-mass, operating at 70 eV). The reaction products were identified through co-injection in GC equipment with authentic samples that were previously synthesized in the lab [24]. The compositions of reactants and products at different reaction temperatures are illustrated in

Table 10. Initial and final compositions at different temperatures.

Temperature K	Moles of Glycerol		Moles of Products			Moles of TBA
	0h	4h	MTBG	DTBG	TTBG	0 h	4 h
353	0.0046	0.0013	0.0026	0.0005	0.0000	0.0368	0.0333
363	0.0046	0.0011	0.0027	0.0008	0.0000	0.0368	0.0325
373	0.0046	0.0012	0.0024	0.0010	0.0001	0.0368	0.0323
383	0.0046	0.0014	0.0023	0.0007	0.0000	0.0368	0.0331

. The experimental conditions were: glycerol (4.6 mmol), TBA (36.8 mmol), catalyst (0.2 mol% of Sn²⁺, 195 mg of Sn_1.5PMo₁₂O₄₀), temperatures (353, 363, 373 and 383 K), time (4 h), internal standard (dodecane 0.100 mL), total volume (4 mL).

3.6. Reaction Pathway

The reaction pathway of glycerol etherification with TBA is depicted according to the literature [4]. A kinetic model of the glycerol etherification with TBA over the Sn_1.5PMo₁₂O₄₀ catalyst was derived by the lumping approach [7,8]. The kinetic model corresponds to the scheme shown in Figure 18.

It is important to note that TBA can undergo dehydration, leading to the formation of isobutylene, which could react with glycerol through another reaction pathway. It was verified that by using TBA in excess and a temperature of 363 K, the TBA concentration in the gas phase remains almost unaltered. This reaction can be minimized by having little or no impact on the overall process [25].

The reactions yield mono-tert-butyl glycerol (MTBG), di-tert-butyl glycerol (DTBG), and tri-tert-butyl glycerol (TTBG). In the first step, glycerol reacts with TBA to produce MTBG and water. MTBG produced from the first step reacts with TBA to produce DTBG and water. DTBG reacts with TBA in the third step to produce TTBG and water.

The equilibrium behavior of the etherification reactions was studied using the REquil reactor model embedded in Aspen Plus. The REquil model calculates the reaction equilibrium constants (Keq) from the Gibbs free energy of the participating components [31]. The equilibrium constants are functions of the temperature.

The compositions at the thermodynamic equilibrium for etherification reactions were evaluated at different temperatures and compared with the data obtained experimentally, as shown in Figure 19. It was noticed that the conversion of glycerol at the thermodynamic equilibrium reached more than 99.99% at all temperatures, with a very slight decrease in conversion when increasing the temperature. However, the maximum glycerol conversion achieved experimentally was 76% at 363 K after 4 h of reaction time. As shown in Figure 19a, there are large differences between the equilibrium values and the experimental data, indicating that the etherification reaction is limited by kinetics.

Figure 19b shows that only MTBG and DTBG are present in the product distribution obtained experimentally, and only a small amount of TTBG is present. In contrast, the selectivity of TTBG is almost 100% across all temperatures at the thermodynamic equilibrium.

4. Conclusions

In this work, a kinetic model for glycerol etherification with TBA over Sn_1.5PMo₁₂O₄₀ catalyst has been developed using the lumping approach. The kinetic model is proved to be valid since the simulation results are in good agreement with the actual experimental data. A reactive distillation column was designed and optimized to produce glycerol ethers with the highest purity of 99.5% and a glycerol conversion of ~99%. The achieved results were obtained using a lower TBA to glycerol feed ratio as compared to the conventional process. A reactive distillation-based process was developed for glycerol etherification to produce 33,000 metric tons per year of glycerol ethers. The energy requirements for the process were reduced by implementing heat integration into the process, and the energy requirements and CO₂ emissions were reduced by 17% and 14%, respectively. An economic analysis was carried out to evaluate the profitability of the glycerol etherification process, and it was found that the process is profitable, with a return on investment of 29.4% and a payback period of 2.2 years.