CFD simulation of CO2 absorption by water-based TiO2 nanoparticles in a high pressure stirred vessel

This work presents the modeling and simulation of CO2 capture by a water-based Titanium dioxide (TiO2) solid nanoparticle in a stirred high-pressure vessel at a constant temperature. Photocatalytic material such as TiO2 has excellent properties, namely it is nontoxic, inexpensive, and non-polluting. CFD model equations are developed and solved using COMSOL software package. The effect of the concentration of a solid nanoparticle in a water-based TiO2 solution, the size of TiO2 nanoparticles and the rate of mixing on the CO2 absorption rate is investigated. A 2D mathematical model considers both shuttle and micro-convention mechanisms. Results reveal that the best TiO2 concentration range is between 0.5 and 1 kg/m3 and that a particle size of 10 nm is more efficient than higher particle sizes. A moderate mixing rate maximizes the CO2 removal rate. The theoretical predictions are validated using lab experimental data and those in the available literature. Results confirm that the model calculations match with the experimental results. Accordingly, the model successfully predicts the experimental data and can be used for further studies.

efficiency reaching 20% and 40% at high and low liquid flowrates, respectively. A study of the removal efficiency of CO 2 at two different concentrations of the nanoparticles, namely 0.25 wt% and 0.5 wt%, found that, for both cases of SiO 2 and CNT nanofluids, the removal efficiency was positively affected by the increase in concentration of nanoparticles 12 . Darabi et al. 13 obtained similar results for a comparison between CNT and SiO 2 nanofluids with enhancement values of 32% and 16%, respectively. Results were obtained via modeling and simulation in a membrane module. Rezakazemi et al. 14 evaluated the absorption effectiveness of nanofluids in a membrane contactor using a 2D mathematical model. The nanoparticles of interest in this study were CNT and SiO 2 in water. For a concentration range of 0.06-24 wt%, a decrease in the percentage of CO 2 separation was observed for both CNT and SiO 2 . Jiang et al. 15 studied four nanoparticles, namely: silica (SiO 2 ,), titanium oxide (TiO 2 ,) magnesium oxide (MgO) and aluminum oxide (Al 2 O 3 ), as well as two base fluids, namely monoethanolamine (MEA) and diethanolamine (MDEA), through a bubbling reactor. Results revealed that absorption of CO 2 by the nanoparticles was better in MDEA compared to MEA. The experimental enhancement factor at specific nanoparticle loading of 0.1 wt % was found to be 0.99, 1.07, 1.09, and 1.29 using SiO 2 , Al 2 O 3 , MgO, and TiO 2 , respectively. The work by Jiang et al. 15 also noticed an optimum solid loading in terms of the effectiveness of the process; in particular, the enhancement factor increased to a maximum value, then subsequently decreased for TiO 2 and Al 2 O 3 . The range of studied concentrations was 0.2-1 kg/m 3 . Peyravi et al. 16 16 . CO 2 absorption by Al 2 O 3 nanoparticle in an NaCl aqueous solution was investigated 18 .
Haghtalab et al. 19 performed the experiment in a stirred high pressure cell at a constant temperature and concluded that the ZnO nanofluid is more efficient than SiO 2 nanofluid with water as a base fluid. They studied the effect of the ZnO concentration on the absorption of CO 2 at 0.05 wt%, 0.1 wt%, 0.5 wt% and 1 wt% at different pressures (1-22 bar) and noticed that, at the same pressure, the effectiveness of the CO 2 absorption decreases with the concentration. The reasoning behind such a result is attributed to the aggregation of the particles caused by the increase in concentration of the nanoparticles whereby, as a result, less CO 2 is absorbed. Zhang et al. 20 evaluated TiO 2 nanoparticles in a stirred cell and found an optimum value for the concentration of TiO 2 in a propylene carbonate-based fluid at which the enhancement factor was the highest, by covering the range of 0.6-1.4 kg/m 3 . In the study conducted by Irani et al. 21 , the nanoparticle graphene-oxide (GO) was synthesized and used in MDEA in a process of gas sweetening. It was shown that this absorbent mixture has favorable CO 2 absorption behavior since GO is characterized by its high surface area and the presence of hydroxide (OH) groups on the surface of the particles. Little change was observed in the absorption enhancement by increasing the concentration of GO from 0.1 to 0.2 wt%. Through a numerical approach while neglecting agglomeration, Koronaki et al. 22 concluded that the effectiveness of CO 2 removal increases with the increase in a CNT's equivalent diameter. In contrast, Zhang et al. 20 found that, when the concentration of TiO 2 is low, the effectiveness of CO 2 removal progressively decreases with an increase in the diameter of the particles while, at higher concentrations, an increase in the size of particles leads to a gradual increase in the enhancement factor. The suggested mechanism behind such an observation is that when the concentration of the particles is low, smaller particles means that more particles are present in the nanofluid that takes up the gas. In contrast, when the concentration is higher, larger particles suggests the presence of a smaller number of particles within the solution and, as a result, viscosity is decreased, which gives a better CO 2 capture process. Darvanjooghi et al. 23 used a bubble column to evaluate the effects of the nanoparticle size on the capture of CO 2 . In this study, a mixture of silica-water is used. The tested particle sizes are: 10.6, 20, 38.6 and 62 nm. At the same concentration of silica particles (0.01 wt%), the increase in particle size increased the rate of CO 2 removal as well as the mass transfer coefficients.
Farzani Tolesorkhi et al. 24 investigated the removal of CO 2 by silica nanofluid in water in a cell with no stirrer. It was observed that although increasing the temperature (from 35 to 45 °C) increases the carbon dioxide's diffusion coefficient in water, the adsorption rate decreases. Pineda et al. 25 studied the removal rate of CO 2 by nanofluids in an annular contactor at low rotational speeds. Three nanoparticles in a methanol-based solvent, namely Al 2 O 3 , SiO 2 and TiO 2, were studied. The nanofluids achieved better absorption enhancements in the counter-current flow configuration. The addition of trays further improved the absorption rate for all nanofluids. Kim et al. 26 investigated the mass transfer through the removal of CO 2 via a bubble absorption and diffusion process for Al 2 O 3 in a methanol-based solvent. The Al 2 O 3 particles positively affected the absorption rate of CO 2 while the viscosity increased by 11% at a particle concentration of 0.01 vol%. The influence on the surface tension was insignificant. Jorge et al. 27 aimed to study amine-functionalized multiwall carbon nanotubes (MWCNTs) in water. While enhancing CO 2 absorption, the amine functional groups also increases the hydrophilicity of the MWCNTs, which enables the particles to remain suspended in water for long periods (at least three months at room temperature). Compared to pure water, the absorption capacity of these MWCNTs is 36% higher at a particle concentration of approximately 40 mg/L. The present work studies the possible enhancement of CO 2 absorption by water-based TiO 2 solid nanoparticles in a high-pressure stirred cell. The study investigates the influence of TiO 2 loading, particle size and mixing rate on the CO 2 absorption rate. A transient 2D mathematical model is developed to describe and predict the CO 2 pressure drop and absorption rate in the high-pressure stirred cell at a constant temperature.  Figure 1 is a schematic diagram of the experimental setup used to measure the CO 2 pressure in a high-pressure stirred cell. A precise volume of water-based TiO 2 nanoparticles was added to the cell and a vacuum pump evacuated the cell's empty space. Pure CO 2 gas filled the displaced space of the cell. The controller of the stirred cell recorded the temperature and pressure, and manipulated the rotation speed of the magnetic stirrer. The chiller controlled the stirred cell temperature by circulating water in the jacket of the cell. The vacuum pump removed any air or gas above the surface of the liquid as well as any gas bubbles in the nonabsorbent fluid. The nanofluid was prepared by mixing a specific amount of TiO 2 solid nanoparticles (size 10 nm) dispersed in 500 ml of water. A high intensity ultrasonic liquid processor was used for at least 30 min to form a homogenous solution.

Model development
A dynamic 3D mathematical model considers both micro-convection and a shuttle mechanism in a cylindrical coordinate system (r, z, θ). The model is employed to depict a concentration profile in radial, axial and angular directions. The micro-convections described by the Brownian movement of the nanoparticles cause fluctuations of the liquid around the nanoparticles. Accordingly, the liquid-gas mass transfer is enhanced due to the convective mass transfer in the bulk of the liquid. By contrast, the shuttle mechanism resulting from the movement of the nanoparticle to and from the liquid-gas interface absorbs the gas and desorbs it to bulk the liquid (regeneration of nanoparticles). Hence, the continuous movement of nanoparticles between the bulk liquid and liquid-gas interface enhances the mass transfer. It is assumed that the nanoparticles are of spherical shape and surrounded by a liquid layer, due to the small size of nanoparticles, the mass transfer resistance inside the particles is neglected.. In order to simplify modeling of the process, the system is divided into three sub areas: gas, liquid and dense phase regions. The model equations were solved using finite element methods built in the efficient COMSOL Multiphysics software package 28 . www.nature.com/scientificreports/ Gas phase region. The transport of CO 2 from the gas phase to the nearby liquid and dense phases is by diffusion and is described by Eq. (1): The arbitrary boundary conditions are: The initial conditions: at t = 0 C Ag = C Ag0 (initial concentration of CO 2 in the cell above the liquid solvent nanofluid).
Liquid phase region. The mass transport of CO 2 in the liquid phase is defined by the component balance equation in the cylindrical coordinate: where the concentration of CO 2 in the liquid phase is C AL , Dense phase region. The CO 2 mass transfer in the dense phase is described by the following equation: The suitable boundary conditions are: where k 1 is the mass transfer coefficient in the presence of nanoparticles (m/s) obtained from the experimental data as a function of nanoparticle loading in the base fluid. The concentration of CO 2 in the liquid dense phase is C Ad , the mass transfer coefficient of the convective phase is h, the surface area of one nanoparticle to its volume is A s /V s , and C AS is the concentration of CO 2 at the solid surface. The mass transfer of CO 2 in the dense phase between the liquid and solid particles is achieved by the following equation: where q is the amount adsorbed of CO 2 per unit mass of solid particles. The adsorption mechanism is described by a Langmuir adsorption isotherm: Rearranging the equation for C AS At z = z 1 N A = k l C Ag − C Ad (molar flux) www.nature.com/scientificreports/ where q m is the maximum amount of CO 2 being adsorbed at the surface of the solid nanoparticles. The trend understood by the nano motion and the Einstein-Stokes equation quantifies the Brownian diffusion of a single particle: where D is the diffusion coefficient, k B is the Boltzmann constant (1.38 × 10 −23 m 2 kg/s 2 K), μ is the solvent viscosity, and d p is the droplet diameter.
The volumetric mass transfer coefficient obtained experimentally for nanofluids is as follows 29 : where V G (m 3 ) is the gas volume, P A (Pa) the gas pressure, H (m 3 Pa/mol)) is the Henry coefficient, C Ad (mol/m 3 ) is the solute concentration in the dense phase, and A (m 2 ) is the liquid-gas contact area. The mixing rate (φ) of the liquid phase is described by the following equation: where ω is the mixing rate constant in (rad/s), and π is 3.14.

Results and discussion
Effect of nanoparticle concentration. The increase in the concentration of nanoparticles in the base fluid does not essentially improve mass transfer. In certain cases, the increase in nanoparticle concentration decreases the mass transfer at a lower level than the base fluid without nanoparticles 12,30-32 . Figure 2 illustrates the pressure of carbon dioxide removed with time for variable solid concentrations in base fluids. The size of the nanoparticles used in the study was 10 nm nanoparticles TiO 2 . The results reveal that the (9) C As = q/ q m k q 1 − q/q m www.nature.com/scientificreports/ solids loadings have strong impact on increasing the rate of the CO 2 pressure drop. Results also demonstrate that there is a solids loading limit beyond which the CO 2 absorption rate decreases. This is attributed to the interaction of the dispersed phases. No interaction of nanoparticles occurs at a very low concentration of solid nanoparticles (< 0.005 wt%). Accordingly, the solid nanoparticles move freely. As the solid nanoparticle concentration increases, the effect of convectional mass transfer increases, hence promotes the performance of the CO 2 absorption rate (in the range of 0.005-1 wt%). By contrast, as the concentration of the solid nanoparticles exceeds a certain value, the free spacing between the solid nanoparticles decreases, which suppresses their interaction and free movement, hence the CO 2 absorption rate decreases 33 . At high nanoparticle concentration, the distance between dispersed nanoparticles decreases, hindering the movement of particles, hence decreases the local convection. The high solid concentration also reduces the interfacial area between the absorbent nanoparticles and the CO 2, hence reduces the absorption rate. The performance of CO 2 absorption decreases at high nanoparticle concentration because of the increase in the viscosity of the absorbent nanofluid. Viscosity increases as nanoparticle concentration increases. This increase in viscosity is negligible at low nanoparticle concentrations. The increase of the nanoparticle concentration beyond a critical value slows the Brownian fluid motion due to the interactions of inter particles 34 .
Validation of the developed mathematical model is obtained by comparing the present model predictions with the experimental data obtained from the absorption of pure CO 2 gas in a high-pressure stirred cell reactor. Figure 3 demonstrates the absorption of CO 2 without mixing with a propylene carbonate-based TiO 2 nanoparticle inside the stirred cell 20 . The results were in good agreement with model predictions. Furthermore, the model can be used for investigating the effect of other operating parameters on the CO 2 removal rate. Figure 4 demonstrates the CO 2 concentration profile throughout the high-pressure stirred cell. The diagram reveals that the CO 2 concentration in the gas phase is initially 80 mol/m 3. With time, the concentration declines to around 50 mol/m 3 while the concentration of CO 2 in the liquid phase increases due to the absorption of CO 2 from the gas phase to the liquid phase. The increased mixing rate homogenizes the concentration profile of the liquid phase. The dead zone at the center of the tank is attributed to the low mixing rate.
Effect of mixing rate. Figure 5 shows the effect of mixing rate with time on the CO 2 pressure drop in the gas phase region of the stirred cell. The gas pressure decreased significantly as the mixing rate increased from ω from 0 to 0.1. With further increase in the mixing rate (ω = 0.1-0.2), the effect on the pressure removal rate is insignificant. After 60 min of operation, increasing the ω value from 0.0 to 0.1 decreases the gas pressure from 171 to 166 kPa. Increasing the ω value from 0.1 to 0.2 results in a decrease to 165 kPa. Further increase of ω results in an insignificant decrease in the rate of the CO 2 pressure drop. A high mixing rate results in perfect The pressure is atmospheric; temperature is 24 °C; initial CO 2 concentration is 80 mol/m 3 ; the particle diameter is 10 nm, with 0.1 wt particle loading. Image generated using Comsol Multiphysics version 5.5 (comsol.com). www.nature.com/scientificreports/ mixing, hence a homogenous phase where more CO 2 is being absorbed by the nanofluid. Mixing accelerates the convective motion of the nanoparticles, such as the Brownian motion that forces the nanoparticles to interact with the CO 2 at the liquid-gas interface, decreases the thickness of the diffusion boundary layer, and assists the CO 2 gas to diffuse into the bulk base fluid 22 .
Effect of initial gas pressure. Figure 6 shows the effect with time of the initial gas pressure on the rate of the CO 2 pressure drop. The results reveal that as the initial CO 2 gas pressure increases, the rate of the gas pressure drop also increases, as expressed in Fig. 7. The increase in the solubility of the CO 2 in the nanofluid is attributed to the pressure that increases the concentration gradient, hence increases the CO 2 removal flux. The rate of decrease in the CO 2 gas pressure is directly proportional to the initial gas pressure in the gas compartment of the absorption cell. A similar result was observed for the effect of pressure on the CO 2 absorption performance in the existing nanoparticles 35 . The absorption enhancement of nano absorbent increases with increasing pressure. According to the Einstein-Stokes equation, for most fluids, the viscosity increases monotonically with the pressure, hence hinders the Brownian motion 36 . In contrast, high pressure increases the absorption performance because of the exterior force exerted by the high pressure, which reduces the size of the clusters. The effect of the mixing rate on the CO 2 removal rate is illustrated in Fig. 7. The rate of the pressure drop increases with an increased mixing rate to a certain limit. A further increase in the mixing rate has an insignificant effect on the CO 2 removal rate. According to Henry's law of solubility, for the physical absorption method, the solubility of the gas increases as the temperature decreases and the pressure increases.
Effect of nanoparticle size. Figure 8 shows the effect of particle size on the CO 2 pressure drop at a constant mixing rate of 1 kg/m 3 TiO 2 nanoparticle. The figure also illustrates that there is an optimum size of nanoparticle, that is 10 nm, beyond which the absorption rate of CO 2 declines. According to the Einstein-Stokes equation, the particle size is inversely proportional to the particle diffusion coefficient. The inverse relations between particle size and absorption performance were reported by many researchers 32,[37][38][39] . Comparison of model predictions and experimental data obtained from the literature 20 are in good agreement. Particles in nanofluids can move as single or aggregated state. If particles move in aggregated state, their influence on absorption rate is insignificant. This may contribute to the reason for the decrease in absorption performance at high nanoparticle concentration. Similar results were observed by Lee and Kang 18 .

Conclusion
This paper presents the influence of a water-based TiO 2 solid nanoparticle on the performance of CO 2 absorption in a high-pressure stirred cell. The addition of TiO 2 nanoparticles to classical water-based solvents offers advantages to the overall performance of the base solvents. Nevertheless, the enhancement in the CO 2 removal process relies on many factors concerning either the added component to the base solvent or the operating mechanism and conditions of the absorption process such as TiO 2 concentration, mixing rate, size of the nanoparticles. Results reveal that a stirred cell reactor is efficient in CO 2 removal using TiO 2 nanoparticles. There is optimum concentration of around 0.1 wt%, beyond which the removal rate declines. There is also an optimum mixing rate and particle size; a low particle size performs more reliably than a large particle size. The developed CFD mathematical agreed well with experimental data at low operating time and no mixing rate. By contrast, discrepancy increased with time and with mixing rate. Moderate mixing rate improves rate of CO 2 absorption.