Modeling and Simulation of the Simultaneous Absorption/Stripping of CO2 with Potassium Glycinate Solution in Membrane Contactor.

Global warming is an environmental problem caused mainly by one of the most serious greenhouse gas, CO2 emissions. Subsequently, the capture of CO2 from flue gas and natural gas is essential. Aqueous potassium glycinate (PG) is a promising novelty solvent used in the CO2 capture compared to traditional solvents; simultaneous solvent regeneration is associated with the absorption step. In present work, a 2D mathematical model where radial and axial diffusion are considered is developed for the simultaneous absorption/stripping process. The model describes the CO2/PG absorption/stripping process in a solvent-gas membrane absorption process. Regeneration data of rich potassium glycinate solvent using a varied range of acid gas loading (mol CO2 per mol PG) were used to predict the reversible reaction rate constant. A comparison of simulation results and experimental data validated the accuracy of the model predictions. The stripping reaction rate constant of rich potassium glycinate was determined experimentally and found to be a function of temperature and PG concentration. Model predictions were in good agreement with the experimental data. The results reveal that the percent removal of CO2 is directly proportional to CO2 loading and solvent stripping temperature.


Introduction
Carbon dioxide (CO 2 ) is the main contributor to global warming, which is a worldwide concern. Pre-and post-combustion capture of CO 2 is the main solution to avoid this problem. The prominent technology nowadays is the absorption of CO 2 in amine solution, such as monoethanolamine (MEA) and diethanolamine (DEA) that takes place in a reversible chemical reaction. Despite the success of these chemicals in absorbing CO 2 from natural gas and flue gas, they suffer from certain drawbacks such as the regeneration of the alkanolamine solutions, which require high-energy consumption, solvent evaporation and degradation losses, and corrosion to pipes and equipment [1][2][3]. An alternative solvent of CO 2 capture is the amino acid salts such as potassium glycinate (PG) [4]. The PG aqueous solvents have high reactivity toward CO 2 and less regeneration energy consumption [5], the aqueous PG solvent has a comparable functional group as alkanolamine. The amino acid salts overcome the drawbacks of the alkanolamine solution in terms of low volatility because of their ionic structure, high surface tension, and low opportunity to degradation due to their resistance to oxidative degradation [6]. The reaction mechanism and reaction rate constants are essential for the simulation, evaluation, and design of the absorption/stripping process of CO 2 in potassium glycinate (PG) in conventional absorption towers and solvent-gas membrane separation processes. Several researchers have studied the kinetics of these amino acid salts (AAS) [7][8][9][10][11][12][13]. Absorbent based on potassium glycinate showed higher reactivity than sodium based absorbent toward CO 2 [14]. The kinetic data of the absorption of CO 2 in several AAS are summarized elsewhere [8].
The traditional packed bed and plate column and cryogenic are the most commonly used techniques for the removal of CO 2 gas from gaseous mixtures in alkanolamine solutions [5,15,16]. In spite of the success of these units, they suffered from certain weaknesses such as flooding, channeling, foaming, and high operating cost [17]. The alternative emerged technique is the solvent-gas membrane interaction system that can compete with the traditional solvent system; the membrane has a small structure size, liquid absorbent and gas stream flow in separate channels, is easy to scale up, and a high surface area per unit volume [2,[17][18][19]. Many researchers recommend a hollow fiber membrane contacting system for the absorption and stripping of CO 2 from rich solvent because of its noticeable advantages compared to conventional processes [13,16,[20][21][22][23]. The effective absorption of CO 2 in lean solvent and the desorption process of CO 2 from rich liquid solvent (regeneration process) in hollow fiber membrane contactor depends preferably on the high membrane porosity and less on membrane moistening as wetting depends mainly on the reactivity of membrane material with solvent being used. Accordingly, the membrane material is preferred to be from hydrophobic polymeric material such as polyvinyl fluoride (PVDF) [1,22,24,25]. On the other hand, the absorbent liquid is designated to have high surface tension to prevent the penetration of liquid into the pores of the membrane [26]. Amino acid solvents have high surface tension properties such as glycinate family, potassium glycinate (PG), and sodium glycinate [23,[27][28][29][30]. Membrane fabricated from polyetherimide (PEI), polysulfone (PS), and polytetrafluoroethylene (PTFE) have acceptable CO 2 absorption and stripping efficiency and have high liquid entry pressure and, hence, were used for absorption and regeneration of carbon dioxide from flue and natural gas by several researchers [22,25,31,32].
Most of the literature work has focused on modeling and simulation of CO 2 absorption in membrane contactors; less attention has been given to CO 2 stripping from rich solvents in membrane contactors [16,[33][34][35][36], and almost none were established for simultaneous modeling and simulation of the absorption/stripping process in the solvent-gas membrane separation process. Accordingly, the purpose of this work is the modeling and simulation of the simultaneous absorption/stripping of CO 2 in lean and rich PG aqueous solution in membrane contactor, respectively. The validated model was used to study the effect of gas and solvent flow rates, solvent temperature, and CO 2 loading in rich PG on membrane separation efficiency. The simulation results were compared with experimental data.

Model Development
The model equations that describe the absorption/stripping of CO 2 in aqueous PG through a gas-solvent membrane contactor were developed. Table 1 outlines the dimensions of the hollow fiber membrane used in the experimental and model development. Figure 1 shows the experimental setup for the absorption of CO 2 in potassium glycinate solvent and stripping of rich solvent using solvent-gas membrane contacting modules for both absorption and stripping. The feed is 10% CO 2 /90% CH 4 gas mixture flows into the membrane module shell side at variable gas inlet flow rate adjusted by Alicat mass flow controllers (Alicat Scientific, Tucson, AZ, USA). The solvent was 0.5 M aqueous potassium glycinate. The inlet solvent flow rate to absorber is monitored by a peristaltic pump (Masterflex L/S). The solvent (0.5 MPG) is supplied to the membrane lumen side at variable feed rates. The effluent of the absorber is heated to temperature range 20-80 • C. The heated stream is supplied to the tube side of the stripper (membrane module). The sweeping gas is nitrogen; the exit gas concentrate is measured using gas chromatography (Shimadzu, Kyoto, Japan) and a CO 2 gas analyzer (CAI, 600 Series, Orange, CA, USA). Membranes 2020, 10, x 3 of 14 Figure 1. Schematic of the absorption/stripping process using a gas-solvent membrane system. Table 1. Dimensions membrane module [1].

Property Value
Inner hollow fiber diameter (mm) 0.42 Outer hollow fiber diameter (mm) 1.10

Number of fibers 15
Inner surface area (m 2 ) 5.15 × 10 −3 Outer diameter of module (mm) 8.0 Effective length module (mm) 260 The developed 2D axisymmetric, transient mathematical model describes the absorption/stripping process in the solvent-gas hollow fiber membrane contacting process ( Figure  2), considering a cylindrical coordinate, isothermal, and nonwetting mode of operation assumptions. While absorption operates at room temperature, stripping operates at variable solvent feed temperatures (25-80 °C). The model considers the ideal gas, incompressible liquid, and Newtonian fluid assumptions. Henry's law measures the solubility of CO2 in the solvent at the solvent-gas interface. The CO2 and PG in the liquid phase is transported in the tube side by both diffusion and convection. CO2 diffuses across the membrane film by diffusion only. The following mass transport equations describe the absorption of the CO2 in lean PG and the stripping of CO2 from rich PG solvent.
In the model development, the subscripts in the material balance equations, , , , refers to the tube, membrane, and shell sides of the absorber, respectively, where , , , refers to the The developed 2D axisymmetric, transient mathematical model describes the absorption/stripping process in the solvent-gas hollow fiber membrane contacting process (Figure 2), considering a cylindrical coordinate, isothermal, and nonwetting mode of operation assumptions. While absorption operates at room temperature, stripping operates at variable solvent feed temperatures (25-80 • C). The model considers the ideal gas, incompressible liquid, and Newtonian fluid assumptions. Henry's law measures the solubility of CO 2 in the solvent at the solvent-gas interface. The CO 2 and PG in the liquid phase is transported in the tube side by both diffusion and convection. CO 2 diffuses across the membrane film by diffusion only. The following mass transport equations describe the absorption of the CO 2 in lean PG and the stripping of CO 2 from rich PG solvent.
In the model development, the subscripts in the material balance equations, ta, ma, sa, refers to the tube, membrane, and shell sides of the absorber, respectively, where ts, ms, ss, refers to the tube, membrane, and shell sides of the stripper, respectively. For example, C CO 2 ,ta refers to the concentration of CO 2 of the solvent present in the tube side of the absorber module. PG is the aqueous liquid solvent, r i is the forward reaction of component i, and R i is the reverse reaction rate of component i.

Hollow Fiber Lumen
The mass balance equation for CO2 in PG rich solvent flowing in the tube side is described by Equation (1): The solvent circulation velocity ( , ) is described by the parabolic equation: Qt is the solvent circulation volumetric rate, and is the number of fibers. The boundary settings: Since the PG contain amino groups similar to traditional amines, the reaction between CO2 and PG can be described by the zwitterion mechanism [21,37].
The forward reaction rate is expressed as follows [36].
where and 2 are the concentrations of PG and CO2; T (K) is the liquid temperature.

Hollow Fiber Lumen
The mass balance equation for CO 2 in PG rich solvent flowing in the tube side is described by Equation (1): The solvent circulation velocity (v z,t ) is described by the parabolic equation: Q t is the solvent circulation volumetric rate, and n is the number of fibers. The boundary settings: at r = r 1 , C CO 2 ,ta = m C CO 2 ,ma (solubility) Since the PG contain amino groups similar to traditional amines, the reaction between CO 2 and PG can be described by the zwitterion mechanism [21,37].
The forward reaction rate is expressed as follows [36].
where C pg and C CO 2 are the concentrations of PG and CO 2 ; T (K) is the liquid temperature.

Membrane Layer
The mass transfer of solute gas (CO 2 ) in the membrane section bounded between r 1 and r 2 is expressed in Equation (9) by diffusion only [38]: Equation (10) describes the material balance for the CH 4 in membrane layer Equations (11) to (14) are the boundary conditions of the membrane layer (i : CO 2 , CH 4 )

Shell of the Module
Equations (15) and (16) express the mass transfer of CO 2 and CH 4 gas in the shell side, respectively: The velocity of gas in the shell side is estimated by [39]: The appropriate boundary conditions are as follows: The radius of the free surface (r 3 ), is expressed as follows: The module void fraction (ϕ): where R, r 2 , n are the inner radius of the module, fiber outer radius, and the number of fibers, respectively.

Hollow Fiber Lumen
The mass balance equation for CO 2 in PG rich solvent in the tube side of the stripper membrane module is described by Equation (24): where the velocity of liquid inside the hollow fibers (v z,t ) is described by the parabolic equation: where Q t is the liquid solvent volumetric flow rate in the tube side, and n is the number of hollow fibers. The appropriate set of boundary conditions are outlined as follows: at z = z 1 , C CO 2,ts = C CO 2,ta (concentration of CO 2 in rich PG exits the absorber) (26) at z = z 2 , ∂ 2 C CO 2 ,ts at r = 0, ∂C CO 2,t ∂r = 0 (axis symmetry) (28) at r = r 1 , C CO 2 ,ts = m C CO 2 ,ms (solubility) (29) where m is the distribution coefficient (m = 8.314 × T/H CO 2 ) determined from Henry's law [10,11]: The Henry's constant for CO 2 in aqueous PG is determined by Where α m 3 mol = 62.183 T The reversible reaction rate is considered first order with respect to rich PG (C Pg−CO 2 ,ts ) in the tube side of the stripping unit r CO 2 = k r C Pg−CO 2 ,ts where k r is the reversible reaction rate constant.

Membrane Layer
The transport of the regenerated solute gas (CO 2 ) and the sweep gas (N 2 ) components in the membrane section restrained between r 1 and r 2 can be designated by the material balance equation (Equation (34)), where diffusion is the only transport mechanism in the membrane phase [38]: Equation (35) describes the material balance for the sweep nitrogen gas in the membrane section.
Equations (36) to (39) are the boundary conditions of the membrane film (i : at r = r 2 , C i,ms = C i,ss

Shell of the Module
Equations (40) and (41) express the steady-state mass transport of CO 2 and sweep N 2 gas in the shell side, respectively: The velocity profile in the shell side is described by Happel's free surface [39].
The relevant boundary conditions are as follows: at z = z 1 , at r = r 3 , ∂C i , ss ∂r = 0 (symmetry) The model governing equations were solved simultaneously using COMSOL software version 5.5 (COMSOL Inc., Stockholm, Swedon). The software implies a finite element method to solve the model equations. Table 2 outlined the values used in the model predictions.

Results and Discussion
The surface plot of CO 2 concentration across the membrane modules (absorption/stripping) is predicted in Figure 3. The inlet concentration of CO 2 that enters the shell side of the absorption unit (bottom) is 8 mol/m 3 , and initial fresh solvent concentration (0.5 M PG) exists in the tube side. The CO 2 being absorbed in the absorption unit with the PG solvent. The absorption efficiency declined with time. Initially, the CO 2 concentration is the inlet of the membrane (absorber) shell side. With time (after 1 and 10 min), the percentage of CO 2 absorbed dropped. The decreased in the absorption efficiency is due to the consumption of the PG solvent available for the absorption of CO 2 in the hollow fiber lumen and the week regeneration of the rich PG in the stripping unit (top). After 30 min, almost no CO 2 removal is observed in the absorber, the CO 2 concentration across the absorber shell side is almost close to inlet concentration (8 mol/m 3 ). This is attributed to the consumption of the available PG for the CO 2 absorption and the week regeneration of the solvent.   At a low liquid circulation rate (50 mL/min), no noticeable percentages of CO2 removal were observed after 10 min of operation due to the consumption of PG accessible for CO2 absorption. As the fresh solvent circulation rate increased to 110 mL/min, the reachable solvent to remove more CO2 increased. After 30 min of operation, and a solvent circulation rate of 170 mL/min, 30% CO2 removal efficiency was reached. This phenomenon is expected because when the solvent circulation amount increases, there is sufficient fresh solvent in the membrane to capture more CO2 gas.
The stripping efficiency as a function of CO2 loading in aqueous PG is demonstrated in Figure  5. The results revealed that the stripping efficiency increased with CO2 loading. Regeneration efficiency increased with increased initial CO2 loading. That is attributed to an increased CO2 concentration gradient. Based on Fick's first law, the molar flux is directly proportional to the gradient of the CO2 concentration. Accordingly, the increase in the initial concentration of CO2 in rich solvent increases regeneration efficiency; simulation predictions agree with previously published work [43][44][45][46].  Figure 4 describes the effect of the solvent flow rate in the absorption unit with time. At a low liquid circulation rate (50 mL/min), no noticeable percentages of CO 2 removal were observed after 10 min of operation due to the consumption of PG accessible for CO 2 absorption. As the fresh solvent circulation rate increased to 110 mL/min, the reachable solvent to remove more CO 2 increased. After 30 min of operation, and a solvent circulation rate of 170 mL/min, 30% CO 2 removal efficiency was reached. This phenomenon is expected because when the solvent circulation amount increases, there is sufficient fresh solvent in the membrane to capture more CO 2 gas.  The influence of rich solvent inlet temperature on regeneration efficiency along membrane dimensionless length is illustrated in Figure 6. As the stripping temperature of rich solvent increases, stripping efficiency increases. That is accredited to the decrease of CO2 solubility in rich solvent with temperature; CO2 solubility is inversely proportional to the temperature of solvent. At high temperatures, the dissolved CO2 in the rich solvent escapes and increases the stripping driving force of CO2 mass transfer, and more CO2 released leads to higher CO2 stripping efficiency [1]. The stripping efficiency as a function of CO 2 loading in aqueous PG is demonstrated in Figure 5. The results revealed that the stripping efficiency increased with CO 2 loading. Regeneration efficiency increased with increased initial CO 2 loading. That is attributed to an increased CO 2 concentration gradient. Based on Fick's first law, the molar flux is directly proportional to the gradient of the CO 2 concentration. Accordingly, the increase in the initial concentration of CO 2 in rich solvent increases regeneration efficiency; simulation predictions agree with previously published work [43][44][45][46].  The influence of rich solvent inlet temperature on regeneration efficiency along membrane dimensionless length is illustrated in Figure 6. As the stripping temperature of rich solvent increases, stripping efficiency increases. That is accredited to the decrease of CO2 solubility in rich solvent with temperature; CO2 solubility is inversely proportional to the temperature of solvent. At high The influence of rich solvent inlet temperature on regeneration efficiency along membrane dimensionless length is illustrated in Figure 6. As the stripping temperature of rich solvent increases, stripping efficiency increases. That is accredited to the decrease of CO 2 solubility in rich solvent with temperature; CO 2 solubility is inversely proportional to the temperature of solvent. At high temperatures, the dissolved CO 2 in the rich solvent escapes and increases the stripping driving force of CO 2 mass transfer, and more CO 2 released leads to higher CO 2 stripping efficiency [1].
The effect of solvent liquid flow rate on stripping efficiency along the membrane dimensionless length at 25 and 80 °C is depicted in Figure 7. Results revealed that the increase in solvent flow rate at low temperature (25 °C) has an insignificant increase in the CO2 stripping efficiency; by contrast, at high temperatures, there is a significant increase in the stripping efficiency. That is attributed to the noteworthy impact of temperature on the CO2 solubility of absorbed CO2 in liquid solvents. As previously mentioned, the CO2 solubility is inversely proportional to temperature. Hence at high temperatures, the CO2 solubility decreases and CO2 escapes from the solvent and is brushed by nitrogen-sweeping gas.
For the model validation, the experimental data of the CO2 percent removal efficiency as a function of temperature ( Figure 8) and CO2 removal flux as a function of liquid feed flow rate ( Figure  9) were plotted and compared with the simulation predictions. The experimental results are presented with standard error bars. Figure 8 illustrates the influence of rich solvent temperature on the percentage removal of CO2. The experimental results agreed with simulation predictions. As the PG rich solvent temperature increases, the removal percentage of CO2 increases due to decreasing CO2 solubility in liquid with temperature.  Figure 7. Results revealed that the increase in solvent flow rate at low temperature (25 • C) has an insignificant increase in the CO 2 stripping efficiency; by contrast, at high temperatures, there is a significant increase in the stripping efficiency. That is attributed to the noteworthy impact of temperature on the CO 2 solubility of absorbed CO 2 in liquid solvents. As previously mentioned, the CO 2 solubility is inversely proportional to temperature. Hence at high temperatures, the CO 2 solubility decreases and CO 2 escapes from the solvent and is brushed by nitrogen-sweeping gas.  Figure 7. Results revealed that the increase in solvent flow rate at low temperature (25 °C) has an insignificant increase in the CO2 stripping efficiency; by contrast, at high temperatures, there is a significant increase in the stripping efficiency. That is attributed to the noteworthy impact of temperature on the CO2 solubility of absorbed CO2 in liquid solvents. As previously mentioned, the CO2 solubility is inversely proportional to temperature. Hence at high temperatures, the CO2 solubility decreases and CO2 escapes from the solvent and is brushed by nitrogen-sweeping gas.
For the model validation, the experimental data of the CO2 percent removal efficiency as a function of temperature ( Figure 8) and CO2 removal flux as a function of liquid feed flow rate ( Figure  9) were plotted and compared with the simulation predictions. The experimental results are presented with standard error bars. Figure 8 illustrates the influence of rich solvent temperature on the percentage removal of CO2. The experimental results agreed with simulation predictions. As the PG rich solvent temperature increases, the removal percentage of CO2 increases due to decreasing CO2 solubility in liquid with temperature.  For the model validation, the experimental data of the CO 2 percent removal efficiency as a function of temperature ( Figure 8) and CO 2 removal flux as a function of liquid feed flow rate (Figure 9) were plotted and compared with the simulation predictions. The experimental results are presented with standard error bars. Figure 8 illustrates the influence of rich solvent temperature on the percentage removal of CO 2 . The experimental results agreed with simulation predictions. As the PG rich solvent temperature increases, the removal percentage of CO 2 increases due to decreasing CO 2 solubility in liquid with temperature.
Membranes 2020, 10, x 11 of 14 Figure 8. Effect of solvent temperature on CO2 removal efficiency. Hollow fibers were made of 28% PVDF/72% Triacetin, module (length is 260 mm, inner diameter is 8 mm), hollow fibers (ID/OD: 0.42/1.1 mm), sweep gas is nitrogen. Initial CO2 concentration in rich PG is 0.54 mol/L. Liquid flow rate is 20 mL/min and gas flow rate is 600 mL/min. The experimental uncertainty of CO2 percent removal is ±1.57. Figure 9 illustrates the comparison between experimental data and simulation results for the effect of the solvent circulation rate on CO2 stripping flux. The temperature and gas feed rate were kept constant at 80 °C and 100 mL/min, respectively. The experimental results were presented with standard error bars. Based on the experimental error bars in Figures 8 and 9, the experimental results and simulation predictions were in good agreement between the experimental and simulation results. The percent efficiency was calculated as follows: The CO2 stripping flux is calculated as per Equation (47): where the is the inlet gas feed rate (m 3 /s), A is the total hollow fiber surface area L is the length of the hollow fiber and n is the total number of fibers,   Figure 9 illustrates the comparison between experimental data and simulation results for the effect of the solvent circulation rate on CO 2 stripping flux. The temperature and gas feed rate were kept constant at 80 • C and 100 mL/min, respectively. The experimental results were presented with standard error bars. Based on the experimental error bars in Figures 8 and 9, the experimental results and simulation predictions were in good agreement between the experimental and simulation results. The percent efficiency was calculated as follows: The CO 2 stripping flux is calculated as per Equation (47): where the F g is the inlet gas feed rate (m 3 /s), A is the total hollow fiber surface area L is the length of the hollow fiber and n is the total number of fibers, C CO 2,in and C CO 2,out are the inlet and exit CO 2 concentrations at experimental temperature and pressure in mol/m 3 .
Membranes 2020, 10, x 12 of 14 Figure 9. Effect of solvent feed rate on the flux and CO2 removal flux. Fiber made of 28% PVDF, 72% triacetin, module (length is 260 mm, inner diameter is 8 mm), hollow fibers (ID/OD: 0.42/1.1 mm). Initial CO2 concentration in rich PG is 0.54 mol/L. Solvent feed temperature = 80 °C and gas feed flow rate is 100 mL/min. The experimental uncertainty of CO2 removal flux is ±0.0005.

Conclusion
The absorption of CO2 in lean aqueous PG and the stripping of CO2 from rich PG were simultaneous modeled and solved using COMSOL Multiphysics version 5.5. The trend of the model predictions were in good agreement with experimental data. Results revealed that the stripping efficiency was enhanced with increased solvent temperature, solvent circulation rate, and CO2 initial concentration in rich solvent. The effect of the solvent circulation rate on stripping efficiency at low temperature was insignificant; by contrast, there is ra emarkable increase in the stripping efficiency with the solvent circulation rate at high solvent temperature. A high solvent circulation rate increases the efficient stripping time of the absorption/stripping solvent-gas membrane contactor module. Figure 9. Effect of solvent feed rate on the flux and CO 2 removal flux. Fiber made of 28% PVDF, 72% triacetin, module (length is 260 mm, inner diameter is 8 mm), hollow fibers (ID/OD: 0.42/1.1 mm). Initial CO 2 concentration in rich PG is 0.54 mol/L. Solvent feed temperature = 80 • C and gas feed flow rate is 100 mL/min. The experimental uncertainty of CO 2 removal flux is ±0.0005.

Conclusions
The absorption of CO 2 in lean aqueous PG and the stripping of CO 2 from rich PG were simultaneous modeled and solved using COMSOL Multiphysics version 5.5. The trend of the model predictions were in good agreement with experimental data. Results revealed that the stripping efficiency was enhanced with increased solvent temperature, solvent circulation rate, and CO 2 initial concentration in rich solvent. The effect of the solvent circulation rate on stripping efficiency at low temperature was insignificant; by contrast, there is ra emarkable increase in the stripping efficiency with the solvent circulation rate at high solvent temperature. A high solvent circulation rate increases the efficient stripping time of the absorption/stripping solvent-gas membrane contactor module.