## Introduction

Mass transfer mechanisms of chemical and physical absorbents control the absorption performance of CO2 from a flue gas or natural gas streams1. The flue gas diffuses in a chemical solvent (such as monoethanolamine), followed by chemical bonding. By contrast, the flue gas diffuses in a physical solvent (such as pure water) and the CO2 dissolves in the solvent. Adding nanomaterial to the base fluids (chemical or physical) affects only the diffusion rate2. The system operating conditions highly influence the selection of the type of base solvent. Physical solvents are appropriate at high pressure and low temperature while low pressure, a low CO2 concentration and a moderate temperature are suitable for chemical-based fluids3.

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 SiO2 nanofluid with water as a base fluid. They studied the effect of the ZnO concentration on the absorption of CO2 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 CO2 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 CO2 is absorbed. Zhang et al.20 evaluated TiO2 nanoparticles in a stirred cell and found an optimum value for the concentration of TiO2 in a propylene carbonate-based fluid at which the enhancement factor was the highest, by covering the range of 0.6–1.4 kg/m3. 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 CO2 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 CO2 removal increases with the increase in a CNT’s equivalent diameter. In contrast, Zhang et al.20 found that, when the concentration of TiO2 is low, the effectiveness of CO2 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 CO2 capture process. Darvanjooghi et al.23 used a bubble column to evaluate the effects of the nanoparticle size on the capture of CO2. 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 CO2 removal as well as the mass transfer coefficients.

Farzani Tolesorkhi et al.24 investigated the removal of CO2 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 CO2 by nanofluids in an annular contactor at low rotational speeds. Three nanoparticles in a methanol-based solvent, namely Al2O3, SiO2 and TiO2, 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 CO2 via a bubble absorption and diffusion process for Al2O3 in a methanol-based solvent. The Al2O3 particles positively affected the absorption rate of CO2 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 CO2 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 CO2 absorption by water-based TiO2 solid nanoparticles in a high-pressure stirred cell. The study investigates the influence of TiO2 loading, particle size and mixing rate on the CO2 absorption rate. A transient 2D mathematical model is developed to describe and predict the CO2 pressure drop and absorption rate in the high-pressure stirred cell at a constant temperature.

## Experimental

Figure 1 is a schematic diagram of the experimental setup used to measure the CO2 pressure in a high-pressure stirred cell. A precise volume of water-based TiO2 nanoparticles was added to the cell and a vacuum pump evacuated the cell’s empty space. Pure CO2 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 TiO2 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 package28.

### Gas phase region

The transport of CO2 from the gas phase to the nearby liquid and dense phases is by diffusion and is described by Eq. (1):

$$\frac{{\partial C_{Ag} }}{\partial t} = D\left( {\frac{1}{r}\frac{\partial }{\partial r}\left( {r\frac{{\partial C_{Ag} }}{\partial r}} \right) + \frac{1}{{r^{2} }}\frac{{\partial^{2} C_{Ag} }}{{\partial \theta^{2} }} + \frac{{\partial^{2} C_{Ag} }}{{\partial z^{2} }}} \right)$$
(1)

The arbitrary boundary conditions are:

\begin{aligned} & {\text{At}}\quad z = z_{1} \quad N_{A} = - k_{l} \left( {C_{Ag} - C_{AL} } \right)\quad \left( {{\text{molar}}\,{\text{flux}}} \right) \\ & {\text{At}}\quad z = L \frac{{dC_{Ag} }}{dz} = 0\quad \left( {{\text{convective}}\,{\text{flux}}} \right) \\ & {\text{At}}\quad r = R \frac{{dC_{Ag} }}{dr} = 0\quad \left( {{\text{convective}}\,{\text{flux}}} \right) \\ & {\text{At}}\quad r = 0 \frac{{dC_{Ag} }}{dr} = 0\quad \left( {{\text{axial}}\,{\text{symmetry}}} \right) \\ \end{aligned}
(2)

The initial conditions:

at $$t = 0\, C_{Ag} = C_{Ag0}$$ (initial concentration of CO2 in the cell above the liquid solvent nanofluid).

### Liquid phase region

The mass transport of CO2 in the liquid phase is defined by the component balance equation in the cylindrical coordinate:

$$\frac{{\partial C_{AL} }}{\partial t} = D\left( {\frac{1}{r}\frac{\partial }{\partial r}\left( {r\frac{{\partial C_{AL} }}{\partial r}} \right) + \frac{1}{{r^{2} }}\frac{{\partial^{2} C_{AL} }}{{\partial \theta^{2} }} + \frac{{\partial^{2} C_{AL} }}{{\partial z^{2} }}} \right)$$
(3)

where the concentration of CO2 in the liquid phase is CAL,

\begin{aligned} & {\text{at}}\quad z = z_{1} \quad N_{A} = k_{l} \left( {C_{Ag} - C_{AL} } \right)\quad \left( {{\text{molar}}\,{\text{flux}}} \right) \\ & {\text{at}}\quad z = 0\quad \frac{{dC_{AL} }}{dz} = 0\quad \left( {{\text{convective}}\,{\text{flux}}} \right) \\ & {\text{at}}\quad r = r_{1} \quad C_{AL} = C_{Ad} \\ & {\text{at}}\quad r = 0\quad \frac{{dC_{AL} }}{dr} = 0\quad ({\text{axial}}\,{\text{symmetry}}) \\ \end{aligned}
(4)

### Dense phase region

The CO2 mass transfer in the dense phase is described by the following equation:

$$\frac{{\partial C_{Ad} }}{\partial t} = D\left( {\frac{1}{r}\frac{\partial }{\partial r}\left( {r\frac{{\partial C_{Ad} }}{\partial r}} \right) + \frac{1}{{r^{2} }}\frac{{\partial^{2} C_{Ad} }}{{\partial \theta^{2} }} + \frac{{\partial^{2} C_{Ad} }}{{\partial z^{2} }}} \right) - h\frac{{A_{s} }}{{V_{s} }}\left( {C_{AL} - C_{As} } \right)$$
(5)

The suitable boundary conditions are:

\begin{aligned} & {\text{At}}\quad z = z_{1} \quad N_{A} = k_{l} \left( {C_{Ag} - C_{Ad} } \right)\quad \left( {{\text{molar}}\,{\text{flux}}} \right) \\ & {\text{at}}\quad z = 0\quad \frac{{dC_{Ad} }}{dz} = 0\quad \left( {{\text{convective}}\,{\text{flux}}} \right) \\ & {\text{at}}\quad r = r_{1} \quad C_{Ad} = C_{AL} \\ & {\text{at}}\quad r = R\quad \frac{{dC_{Ad} }}{dr} = 0\quad \left( {{\text{convective}}\,{\text{flux}}} \right) \\ \end{aligned}
(6)

where k1 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 CO2 in the liquid dense phase is CAd, the mass transfer coefficient of the convective phase is h, the surface area of one nanoparticle to its volume is As/Vs, and CAS is the concentration of CO2 at the solid surface. The mass transfer of CO2 in the dense phase between the liquid and solid particles is achieved by the following equation:

$$\frac{\partial q}{{\partial t}} = h\frac{{A_{s} }}{{m_{s} }}\left( {C_{Ad} - C_{As} } \right)$$
(7)

where q is the amount adsorbed of CO2 per unit mass of solid particles. The adsorption mechanism is described by a Langmuir adsorption isotherm:

$$q = q_{m} \frac{{k_{q} C_{As} }}{{1 + k_{q} C_{As} }}$$
(8)

Rearranging the equation for CAS

$$C_{As} = \frac{{q/\left( {q_{m} k_{q} } \right)}}{{1 - q/q_{m} }}$$
(9)

where qm is the maximum amount of CO2 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:

$$D = \frac{{k_{B} \cdot T}}{{3\pi \cdot \mu \cdot d_{p} }}$$
(10)

where D is the diffusion coefficient, kB is the Boltzmann constant (1.38 × 10−23 m2 kg/s2K), μ is the solvent viscosity, and dp is the droplet diameter.

The volumetric mass transfer coefficient obtained experimentally for nanofluids is as follows29:

$$\frac{{V_{G} }}{RT}\frac{{dP_{A} }}{dt} = k_{L} A \left( {\frac{{P_{A} }}{H} - C_{Ad} } \right)$$
(11)

where VG (m3) is the gas volume, PA (Pa) the gas pressure, H (m3 Pa/mol)) is the Henry coefficient, CAd (mol/m3) is the solute concentration in the dense phase, and A (m2) is the liquid–gas contact area.

The mixing rate (φ) of the liquid phase is described by the following equation:

$$\varphi = \omega \pi$$
(12)

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 nanoparticles12, 30,31,32.

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 TiO2. The results reveal that the solids loadings have strong impact on increasing the rate of the CO2 pressure drop. Results also demonstrate that there is a solids loading limit beyond which the CO2 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 CO2 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 CO2 absorption rate decreases33. 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 CO2, hence reduces the absorption rate.

The performance of CO2 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 particles34.

Validation of the developed mathematical model is obtained by comparing the present model predictions with the experimental data obtained from the absorption of pure CO2 gas in a high-pressure stirred cell reactor. Figure 3 demonstrates the absorption of CO2 without mixing with a propylene carbonate-based TiO2 nanoparticle inside the stirred cell20. 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 CO2 removal rate.

Figure 4 demonstrates the CO2 concentration profile throughout the high-pressure stirred cell. The diagram reveals that the CO2 concentration in the gas phase is initially 80 mol/m3. With time, the concentration declines to around 50 mol/m3 while the concentration of CO2 in the liquid phase increases due to the absorption of CO2 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 CO2 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 CO2 pressure drop. A high mixing rate results in perfect mixing, hence a homogenous phase where more CO2 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 CO2 at the liquid–gas interface, decreases the thickness of the diffusion boundary layer, and assists the CO2 gas to diffuse into the bulk base fluid22.

### Effect of initial gas pressure

Figure 6 shows the effect with time of the initial gas pressure on the rate of the CO2 pressure drop. The results reveal that as the initial CO2 gas pressure increases, the rate of the gas pressure drop also increases, as expressed in Fig. 7. The increase in the solubility of the CO2 in the nanofluid is attributed to the pressure that increases the concentration gradient, hence increases the CO2 removal flux. The rate of decrease in the CO2 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 CO2 absorption performance in the existing nanoparticles35. 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 motion36. 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 CO2 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 CO2 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 CO2 pressure drop at a constant mixing rate of 1 kg/m3 TiO2 nanoparticle. The figure also illustrates that there is an optimum size of nanoparticle, that is 10 nm, beyond which the absorption rate of CO2 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 researchers32, 37,38,39. Comparison of model predictions and experimental data obtained from the literature20 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 Kang18.

## Conclusion

This paper presents the influence of a water-based TiO2 solid nanoparticle on the performance of CO2 absorption in a high-pressure stirred cell. The addition of TiO2 nanoparticles to classical water-based solvents offers advantages to the overall performance of the base solvents. Nevertheless, the enhancement in the CO2 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 TiO2 concentration, mixing rate, size of the nanoparticles. Results reveal that a stirred cell reactor is efficient in CO2 removal using TiO2 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 CO2 absorption.