Experimental Investigation of Mass Transfer Intensification for CO₂ Capture by Environment-Friendly Water Based Nanofluid Solvents in a Rotating Packed Bed

Abstract

In this research, two intensification approaches for CO₂ capture via a rotating packed bed (RPB) and nanofluids were examined simultaneously to maximize the experimental mass transfer coefficient. The two intensification approaches were done by using water as a green, environmentally friendly absorption solvent and as the base fluid for preparing nanofluids and also by using centrifugal acceleration in an RPB. Physicosorption of CO₂ in an RPB was carried out by applying Al₂O₃, TiO₂, and SiO₂ nanofluids to intensify the mass transfer in water, and the operation parameters such as the angular speed of the rotor, concentration and type of nanoparticles, gas and liquid flow rates, and CO₂ concentration in mass transfer intensification were evaluated and several nanofluids were selected to survey investigate how they affect the mass transfer at low pressure. The results show that the Al₂O₃ nanofluid was more effective than other nanofluids and that the 40 nm nanofluid of this type was more efficient than the 20 nm size. Therefore, a correlation is proposed in this paper for liquid volumetric mass transfer coefficient prediction that includes the microconvection of nanoparticles and surface tension.

1. Introduction

It is well known that the main energy generation sources are still gas, oil, and fossil fuels all over the world. Pollution has led to global warming, melting ice in the South and North poles, the rising of sea and ocean levels, and climate change. Therefore, researchers are increasingly focusing on finding appropriate and optimal methods for gas treatment, especially carbon dioxide emissions [1].

There are four approaches to reducing gaseous emissions, namely, electrochemical, oxy-fuel combustion, pre-combustion, and post-combustion methods [2]. Carbon dioxide is mostly a greenhouse gas that plays a major role in climate change and is often absorbed in post-combustion processes in industries. These processes and other relevant technologies are developed to increase efficiency and decrease costs. Absorption and chemisorption are especially important in industries [2,3,4]. A good patent review on CO₂ removal technologies can be found in [5]. All technologies have their own advantages and disadvantages when used alone; therefore, to reduce the drawbacks, several intensification approaches are simultaneously applied. Song et al. called these “hybrid processes” [6]. Other techniques include the formulation of solvents [7,8] and process intensification tools such as centrifugal, vibration, mixing, nanoparticle, and magnetic field applications [9,10]. Process intensification (PI) helps to reduce equipment size, energy consumption, and effluents. and allows the systems to be compacted in smaller areas with innovations [11,12,13]. Rotating packed beds (RPBs) are a type of PI equipment that uses centrifugal acceleration [14]. Another alternative PI approach, which was mentioned above, is the use of nanofluids (NFs) that include the suspension of nanoparticles (almost less than 100 nm) in a base fluid (BF) that can transfer heat and improve MT operations such as liquid-liquid extraction [15]. A great number of investigators have worked on CO₂ capture by using NFs, and a short review of these studies was published by Zhang et al. [16]. Previous investigation reports illustrated that Al₂O₃, TiO₂, and SiO₂ NFs are most effective MeOH-based NFs in CO₂ absorption. For instance, Pineda et al. [17] examined the enhancement of Al₂O₃ and SiO₂ and demonstrated that CO₂ absorption increased by more than 9% with these NFs. Lee and Kang [18] evaluated CO₂ solubility with Al₂O₃/NaCl aqueous NFs and reported 12.5% intensifiction. Jiang et al. [19] studied amine-based NFs and showed that TiO₂ and Al₂O₃ were more efficient than SiO₂. Haghtalab et al. [20] studied water-based ZnO and SiO₂ NFs in concentrations of 0.05, 0.1, 0.5, and 1 wt.% and compared the amounts of their enhancement at high pressures. Similarly, Al₂O₃ was examined in a concentration range of 0–0.2 wt.% in pure water and the optimum concentration value of 0.05% wt was reported In the results by Ref. [21]. Another example is the examination in mass fractions of 0.02, 0.1, 0.5, and 1% of Al₂O₃, SiO₂, Fe₃O₄, and CNT NPs in water and amine solution by Rahmatmand et al. [22], who reported that Al₂O₃ and SiO₂ were more efficent NFs. Darvanjooghi et al. [23] evaluated an SiO₂ NF with different sizes at concentrations of 0.005, 0.05, 0.01, and 0.1 and the results indicated that maximum CO₂ removal occured at the concentration of 0.01 wt.% and that the rate of absorption increased with the increase in NP size.

Salami and Salimi [24] used water-based NFs to enhance the MT rate in packed bed columns and reported that Al₂O₃ and SiO₂ NFs with a nanoparticle (NP) concentration of 0.05 vol.% had MT rates of 14% and 10%, respectively. In addition, some researchers, such as Samadi et al. [25] and Salimi et al. [26], applied magnetic NFs and magnetic field induction to achieve higher MT rates. These types of NFs enjoy two benefits: They are controllable in magnetic fields and help with CO₂ capture [27]. The simple or single-block RPB includes a liquid distributor and a rotor made up of a packing and a shaft. It should be noted that the liquid acceleration is set based on the rotor speed, which can intensify micro-mixing and MT according to its pattern. The change in the flow area is more significant in RPBs than in PBCs; therefore, the MT coefficient varies at different points of the rotor because of gas velocity and surface area changes along the radius [28]. It is clear that RPBs have a larger surface area than conventional PBCs in the same operation conditions [10]. Wang et al. [29] reported that advantages of RPBs were high volumetric MT coefficients (leading to a decreased physical size, as well as lower capital and operation costs), decreased flooding tendency, micro-mixing improvement, suitability for toxic and expensive materials, and skied-mounted applicability. Recently, Luo et al. [30] studied micro-mixing by applying two intensification approaches (ultrasonic-assisted RPB), and Dashti and Abolhasani [31] examined physicochemical absorption using MEA and NPs with TiO₂/MEA (0.01–0.1 wt.%) in an RPB with blade packing. They used TiO₂ based on the results of [19] and reported precipitation of particles not possible in RPBs because of high interactions and very low resistant time of the NFs.

Because of the advantages, RPBs are still designed and developed on laboratory and industrial scales. Generally, this topic is treated and developed in four directions:

(a)

Examination of chemical solvents like propylene carbonate to evaluate the absorption ability [32]; mixed-chemical solvents, as in Ref. [33]; or new advanced-green solvent performance in acid gas treatment, such as ionic liquids [34] and nanofluids [31].

(b)

Optimization of RPB operations by improving contact surface area or mass transfer by changing the hydrodynamic features through:

• Modifications to RPB configurations such as “liquid distributor(s).” For instance, Hacking et al. [35,36] examined novel redistribution rings in a bed. Wu et al. used a multi-inlet to distribute liquid in a bed [37] whose efficiency was examined by Zhang et al. [38], and Wang et al. [39] evaluated the contacting angle of fluids,
• Modifications to the bulk zone by adding baffles/blades, as in Yang et al. [40], or mesh pin, as in Liu et al. [41,42]; or changing the number of mesh screen layers, as in Su et al. [43]; changing the packing wettability, as Lu et al. [44]; or changing the kind of packing structure, as reported in [45].

(c)

Examination of the intensification by replacing the conventional equipment with RPBs, such as deoxygenation of water and fuel [46,47], wastewater treatment [48], CO₂ absorption [49], and selective absorption [50].

(d)

Focusing on the micro-scale or micro-mixing in a heat-sensible process, controlling polymerization processes, and packing optimization [51].

All of these development were carried out by experimental methods (tests or high-speed photography), CFD (reviewed by Chen et al. [52]), and numerical methods, especially the artificial neural network (ANN) method [53,54].

Regarding the first category, numerous CO₂ absorption systems in RPBs have been investigated by researchers at different operating parameters. Jiao et al. [55] examined the performance of an RPB in a Q_L range of 0.5–1 L/min and a Q_G range of 667–1667 L/min at 1 bar and 298 K. Generally, Xing et al. [56] showed RPB performance at atmospheric pressure in different rotational speeds and a vast gas–liquid ratio (GLR) range of more than 20 and up to 20,000, as summarized in

Table 1. Temperature and GLR range selected for the CO₂ absorption system by previous investigators.

Authors	Temp., K	GLR
Wang et al. [33]	298–333	100–260
Lin et al. [57]	301	20–350
Yu et al. [58]	313–323	300–1200
Kang et al. [59]	333	67–700
Sheng et al. [60]	303–333	72–700
Wu et al. [61]	323	75–300
Sheng et al. [62]	303–323	138–242

. In addition, Xiang et al. [32] evaluated CO₂ absorption with propylene carbonate in a pilot-scale RPB at a gas flow rate of 8–25 m³/h and liquid flow rate of 100–300 L/h at high pressure and a rotating speed of 290–1450 rpm.

The higher possible GLR for CO₂ absorption in an RPB is an important parameter to provide economical performance, as reported in [63], which allows operation with the lowest absorption solvent solution.

Considering the above issues, the present study focused on physical absorption and was carried out with two intensification approaches by an RPB as a contactor that provided centrifugal force and NPs that were applied to increase the effectiveness of water-based NFs as advanced environmentally friendly water-based solvents. Therefore, this study examined the effect of NFs on the MT coefficients at low pressure and CO₂ concentrations in a centrifugal field in an RPB. In this device, the cavity zone was removed with a modification of the contactor and was filled by packing to extend the gas–liquid contact area. Injections were mounted on the shaft and the liquid was distributed through the holes on the rotor, which could cool down the bearings in operation. On the other hand, we applied TiO₂, Al₂O₃, and SiO₂ nanoparticles in CO₂ capture. In this article, first, the setup characteristics, operation, and data processing of CO₂ capture by NFs are described, and then the results are evaluated and discussed.

2. Experimental Setup and Data Processing

2.1. Materials and Solvent Preparation

NPs (>99% purity) with the physical properties listed in

Table 2. Physical properties of the nanoparticles and BF applied in this study.

Solvent		Base Fluid	Silica	Titanium Oxide	Alumina
	Parameter
Color		Colorless	White	White	White
Formula		H2O	SiO2	TiO2	Al2O3 (I)	Al2O3 (II)
Density, Kg/m3		998.2	2400	3800	3890	3920
Thermal conductivity, W/m.K		0.61	1.4	11.7	30	30
Molecular weight, g/mol		18.02	60.08	79.87	159.69
Mean size of particles (nm)		---	3–10	25	20	40
Status or morphology		liquid	Spherical solid powder
Purity		DM	>99.9%
Cp (J/Kg.K)		4182	730	689.3	840	880
Surface tension (mN/m)		72.03	52	67.4	57.4	68.9

were purchased from different companies: Al₂O₃ (40 nm) from Neutrino Nanotechnology, TiO₂ (25 nm) from Evonik Degussa Gmbh (Essen, Germany), and SiO₂ (5 nm) and Al₂O₃ (20 nm) from US Nano (South Bend, IN, USA). These NPs were applied to prepare water-based NFs (suspension) by adding NPs in pure water (DW) to produce 0.05–0.1 wt.% NFs as solvents after mixing by a magnetic stirrer. Ultrasonication of the water suspension was carried out using a probe-type device (UW-3100, Bandelin, Germany). It should be mentioned that water was selected to create an environmentally friendly BF. Then, the water–based NF was used as a solvent without adding any surfactant, but the stability of the NFs was examined by dynamic light scattering (DLS) analysis. The results are shown in Figure 1.

Investigation was performed after every 5 test runs and the NFs were sonicated again to make sure that they were dispersed well, although the turbulences of the fluid in the RPBs help the stability of the suspension, as reported by Dashti and Abolhasani [31].

2.2. Setup Characteristics, Operating, Data Gathering, and Processing

The novel RPB included a rotor that consisted of stainless-steel packing and small holes mounted on the shaft as liquid injectors, which were expected to help distribution. The cavity zone was filled by packing to increase the contacting area in the rotor. NFs as solvents were injected with a nozzle into the center of the shaft and radially distributed in the packing to help cool the bearings. A gas stream was inserted circumferentially from the side of the casing (shell) into the center of the packing, made contact with the liquid droplets, and then left from via the housing.

As shown in Figure 2a, the setup used for CO₂ capture included an RPB, an electromotor, a pump, a vessel of NFs, tubes, connections, pressure gauges, flow meters, and cylinders of CO₂ and N₂. The regeneration section of [64] was used in this study to generate the CO₂-enriched stream.

After a leak test of the setup, test runs were performed by introducing gas from the top outside edge of the RPB casing, as shown in Figure 2b, which, after passing through the packing, exited the left housing from outlet gas holes. Simultaneously, the NF was injected into the rotor and distributed radially from small holes that were mounted on the shaft to make contact with the gas stream counter-currently. The gas outlet stream was sent to a safe location, and the liquid outlet was sent to the regeneration section. After the solvent was regenerated, it was recycled to the NF storage vessel. The sampling point for titration was at beginning of the liquid stream towards to the regeneration section.

The experiment steps for NFs included:

• Introducing the mixed gas stream to the RPB under a flow control and design limitation of system, then venting it out to a safe location.
• Turning on the RPB driver at low speed and checking the operating condition.
• Turning on the solution pump, introducing the solvent to the RPB slowly, setting the operating conditions with the instrument devices, and keeping the proper situation (

  Table 3. Rotating packed bed specifications and conditions of the experimental runs.

  Packing Type	Stacked Layers of Wire Mesh
  Inner diameter of rotor (shaft diameter), m	0.035
  Outer diameter of rotor (disc diameter), m	0.255
  Packing height, m	0.034
  Total surface area (m2. m−3)	563.04
  Surface tension of packing, mN/m	75
  Porosity	0.8958
  Rotational speed (rpm)	300 & 500
  Liquid flow rate, L/hr	24–42
  Gas flow rate, L/min	6–16
  CO2 present range, %	10–50
  Temperature, °C	35
  Casing pressure, bar	3.3

  ).
• Starting the regeneration section and recycling the regenerated solution stream to the solution pump suction when a steady-state situation is reached, then closing the outlet of the solvent vessel and keeping the circulation circuit.
• At this stage, the rotating speed can be changed when stability of the system is reached.
• Sampling for titration is caried out after 10 min.

According to Section 1, CO₂ absorption was performed by NFs in the operating conditions given in Table 3—that is, above atmospheric pressure while considering the design condition of the RPB.

The RPB with stainless steel wire mesh packing shown in Figure 2b, which was used in this research, had a packing with a 0.0175, 0.1275, and 0.034 m inner radius, outer radius, and axial height, respectively.

The uncertainty errors of experimenting instruments and the maximum errors of parameters are given in

Table 4. Uncertainty of the instruments.

Instrument Name	Instrument Range	Measured Variable	Accuracy	Min and Max Values Measured in Experiment	Uncertainty (U%)
Gas flow meter	0–20 L/min	Volume flow rate of gas	0.1 L/min	6–16 L/min	0.01–0.03
Liquid flow meter	0–200 L/h	Volume flow rate of liquid	0.6 L/h	24–42 L/h	0.99–2.32
Titration glassware	0–50 ml	Volume of liquid	0.1 mL	0–30 ml	0.15–10
Thermometer	−200–850 °C	Inlet and casing temperatures	0.1 °C	30–35 °C	0.44
Scale	0–300 g	Weight of NPs	0.0001 g	0.025–0.25 g	0.05–0.15

and

Table 5. Uncertainty of the parameters.

Variable	Uncertainty Error (U%)
kLa	6.82
ReL	0.89
ReG	0.96
We	1.04
Gr	1.56
Sc	0.08
kLadp/DL.at	1.36
ReNP	1.10

, respectively.

2.3. Experimental Mass Transfer Modeling and Analysis

It should be noted that the mean MT coefficient is meaningful when the hydrodynamic condition is uniform throughout the whole system [65] and that there is no such unifurmity in an RPB. Moreover, theoretical and empirical approaches can be used for computing MT coefficients for simple systems, but there is no general theory to predict MT coefficients in RPBs [66]. Therefore, researchers present a suitable MT correlation for their system. Various empirical and statistical correlations for RPB contactors were developed and a greater number of effective parameters were considered by numerous researchers for many systems with several configurations of RPBs to raise the accuracy, as reported in [67]. For instance, Chen et al. studied RPBs with different radius values and reported that MT decreased with the increase in the outer radius of the packing at low rotational speeds, but this decrease was very low at high rotational speeds [68]. Later, they carried out a new investigation to evaluate MT in RPBs by considering the effect of packing characteristics such as size, material shape, and surface property, and they proposed a correlation that included packing characteristics and fluid surface tension [69]. Rajan et al. [70] reported that k_La_e and a_e changed with several radius values of RPB (with ring packings) due to gas and liquid superficial velocity variations with centrifugal acceleration, which could affect the Re and Fr numbers. In addition, they reported that the Weber number (We) would be changed with the packing surface area. Mohammaddoost et al. [64] also examined physical absorption with metal oxides and developed correlations that were illustrated by [71,72] and showed that the Sherwood number (Sh) depended on the geometry of the contactor, liquid Schmidt number (Sc), NP volume fraction, liquid, and NP Reynolds number.

In an RPB, the whole specific or total surface area (a_t), that is available with packing is not involved in MT. The specific surface area of packing is divided into wetted surface area (a_w) and gas–liquid MT effective interfacial surface area (a_e) due to the situation of the contacting phases in gas–liquid systems. All the wetted surface area in the vicinity of the gas phase generates the MT interface, and this determines the main value of the gas–liquid effective interfacial surface area. The dynamic status of hydrodynamics and their variation through an RPB within various radius values may cause alterations in the amount of gas–liquid interfacial effective surface area and MT rate. On the other hand, changes in the flow area in RPBs, contrary to that in PBCs, is significant when the MT coefficient varies with the position on the rotor because of gas velocity and surface area changes along the radius [28]. There are also significant parameters that can enhance the gas–liquid MT interfacial effective surface area. These parameters are summarized below according to the results of [73,74,75,76]:

• Rotating speed, (affecting liquid elements);
• Gas and liquid rate;
• Packing form and configuration;
• Liquid distribution;
• Temperature.

The simplest technique that is used in chemical methods to calculate the amount of a_e is has been applied by numerous investigators using CO₂-NaOH or CO₂-N₂-NaOH systems. For calculations, it is assumed that steady-state isothermal physical absorption occurs through the packing of an RPB and gas feed, assuming ideal gas.

In this study, the diffusivity, density, and viscosity of pure water and NFs were calculated according to [77,78], and Table 2 illustrates the NP specifications. The mean centrifugal acceleration was calculated using the following equation [79]:

$$a_m={\left(\frac{R_o^2+R_i^2}{2}\right)}^{\frac{1}{2}}{\left(\frac{2\pi N}{60}\right)}^2$$

(1)

In addition, the gravity ratio can be calculated by dividing a_m by the earth gravity [55].

Physical absorption of CO₂ by NFs is related to NP surface active sites where ions and H₂O molecules are adsorbed and released in solution. HCO₃⁻ ions that interact with polar groups on NPs are generated through the reaction of CO₂ with water as follows [21]:

$${\mathrm{CO}}_2+{\mathrm{H}}_2\mathrm{O}\leftrightarrow {\mathrm{H}}_2{\mathrm{CO}}_3\leftrightarrow {\mathrm{H}}^{+}+{\mathrm{HCO}}_3^{-}$$

(2)

Data gathering from the RPB setup was carried out using acid–base titration, which is used to estimate the amount of absorbed CO₂ by NFs, and finally the experimental k_La was calculated by considering the following stoichiometric reactions for acid-base titration:

$$2\mathrm{NaOH}+{\mathrm{CO}}_2\to {\mathrm{Na}}_2{\mathrm{CO}}_3+{\mathrm{H}}_2\mathrm{O}$$

(3)

$$2\mathrm{NaOH}+{\mathrm{H}}_2{\mathrm{SO}}_4\to {\mathrm{Na}}_2{\mathrm{SO}}_4+2{\mathrm{H}}_2\mathrm{O}$$

(4)

A total of 15 mL of NaOH of 0.01 M was consumed for titration of 2 mL of the solvent sample with H₂SO₄ (0.0024 M). The CO₂ rate at the RPB inlet (from the regeneration section) and outlet was computed using Equation (5). Then, the overall volumetric MT coefficient in the RPB was calculated using Equation (6).

$$\dot{N_{\mathrm{CO}2}}=\frac{0.5\left[\left({\upsilon }_{\mathrm{NaOH}}.M_{\mathrm{NaOH}}\right)-\left(2{\upsilon }_{{\mathrm{H}}_2{\mathrm{SO}}_4}.M_{{\mathrm{H}}_2{\mathrm{SO}}_4}\right)\right]}{{\upsilon }_{NF}\times 0.001}\times Q_{NF}$$

(5)

$$k_{L}a=\frac{{\dot{N}}_{\mathrm{CO}2}^{L,inlet}-{\dot{N}}_{\mathrm{CO}2}^{L,outlet}}{\mathsf{\Delta }{C}_{ln}}$$

(6)

$$\mathsf{\Delta }{C}_{ln}=\frac{{\mathsf{\Delta }C}_1-{\mathsf{\Delta }C}_2}{ln\left(\frac{\mathsf{\Delta }{C}_1}{\mathsf{\Delta }{C}_2}\right)}$$

(7)

$$\mathsf{\Delta }{C}_1=HE.P_{g,inlet}-C_{L,outlet}$$

(8)

$$\mathsf{\Delta }{C}_2=HE.P_{g,outlet}-C_{L,inlet}$$

(9)

$$C_L=\frac{{\dot{N}}_{\mathrm{CO}2}^L}{Q_{NF}}$$

(10)

where C_L is the CO₂ concentration and HE is the Henry coefficient, which was taken from [77]. The MT intensification parameter, k_eff, which was described as a ratio of the MT coefficients by Saeedina et al. [80], can show that NFs are more effective than BFs.

$$k_{eff}=\frac{{\left(k_{L}a\right)}_{NF}}{{\left(k_{L}a\right)}_W}$$

(11)

After the above calculations, the density and viscosity of the NFs were estimated by the following equations [81]:

$${\mu }_{NF}=\left(1+2.5\phi \right){\mu }_w$$

(12)

$${\rho }_{NF}=\phi {\rho }_p+\left(1-\phi \right){\rho }_w$$

(13)

$$\phi \left(vol\%\right)=\frac{\left(wt\%\right)}{\left(wt\%\right)+\frac{{\rho }_p}{{\rho }_{BF}}\left(100-wt\%\right)}$$

(14)

The diffusivity values of water were calculated with Equation (15), which was proposed by Versteeg and Swaaij [77], and the values for the NFs were extracted from the findings of [78]. The NP Reynolds number (Re_NF) was determined by Equation (16) [64].

$$D_{\mathrm{CO}2,w}=2.35\times {10}^{-6}\exp \left(\frac{-2119}{T}\right)$$

(15)

$$R{e}_{NP}=\frac{2k_{B}T{\rho }_p}{\pi {\mu }_{NF}^2{d}_{particle}}$$

(16)

3. Results and Discussion

In the setup of this work, the gravity ratio increased from 30.06 to 219.04 from the inner radius of the packing to the outer radius, and from 53.45 to 389.40 at the low and high rotating speeds of the rotor, respectively. Regarding this issue, it was necessary to survey the effect of the rotating speed on the MT volumetric coefficient. Figure 3 shows the values of k_La of pure water and various NFs versus the CO₂ content of the gas feed, which reveals how the concentration of NPs and kind of NPs affected the MT performance. It was also found that the MT coefficient of Al₂O₃ NF- 0.01 wt at high/low rotating speeds (Figure 3a) and TiO₂ NF-0.05 wt.% were the highest values (Figure 3b), and the Al₂O₃ and TiO₂ NFs’ MT volumetric coefficient v alues were higher than those of the SiO₂ NF at a concentration of 0.1 wt.% (Figure 3c). Figure 3d demonstrates that an increase in the rotating speed of the RPB led to an increase in the k_La values. The figure indicates that there was a relationship between k_La and the rotor speed. It also reveals that higher rotor speeds improved a_w. Therefore, the a_e values change along the radius for solvents, as reported by Agarwal et al. [82], and are influenced by changes in the NF concentration, type of NF, and CO₂ content. This may be due to the microconvection ability of NPs and its dependency on concentration values. A higher amount of CO₂ content also makes for a higher driving force due to further concentration differences between the phases.

To evaluate the effect of Al₂O₃, TiO₂, and SiO₂ concentration on MT performance, concentrations of 0.05, 0.01, and 0.1 were selected and examined at a constant gas flow rate of 10 L/min with different CO₂ content values (10–50 vol.%) and various solvent flow rates, as shown in Figure 4a–d. The figure demonstrates that k_La was influenced by the kind of nanoparticle as well as nanofluid concentration and flow rate, but it was not changed by varying the CO₂ content. This figure also indicates that NFs had substantially higher MT performance than water, which may be due to the shuttle effect, as well as hydrodynamic and bubble breaking effects in NFs, which can increase the contact area and reduce the boundary layer’s thickness, which, as discussed by Kim et al. [83], can intensify the diffusion of CO₂ molecules [84]. Furthermore, it was found that the concentration of 0.01 wt.% of the NF was more efficient than other concentrations of the suspension. This result confirms Krishnamurthy et al.’s and Kim et al.’s reports [71,85], which demonstrated that an increase in the concentration values of NPs intensifies the diffusion up to a certain value and then decreases. In addition, viscosity does not have a significant effect because of low concentrations, as reported by Samadi [25].

As Figure 3a and Figure 4, reveal, the NF concentration of 0.01 wt.% was tested at different flow rates and a constant gas flow rate (10 L/min) with two CO₂ content values (50 and 10 vol.%) which also included Al₂O₃ NFs (II). The results of these tests are shown in Figure 5.

Figure 5a,b reveal that the TiO₂ and Al₂O₃ NFs (II) were more effective than other NFs and pure water. In addition, as can be seen, the Al₂O₃ (II) NF was more effective than the Al₂O₃ (I) NF, which may have been due to high turbulence that occurs at higher gas and liquid flow rates, and more importantly due to effective surface area values and the microconvection ability of NPs.

Considering the data shown in Figure 5 and using Equation (11), the MT intensification parameter at high rotating speeds was calculated for Al₂O₃ (II), Al₂O₃ (I), TiO₂, and SiO₂. The average amount of k_eff at the high speeds of the RPB were 1.99, 1.47, 1.82, and 1.77 for Al₂O₃ (II), Al₂O₃ (I), TiO₂, and SiO₂, respectively, and the maximum value reached 2.59 for Al₂O₃ (II), which may have been due to its nanoscale mixing abilities in liquid.

In addition, the results shown in Figure 3, Figure 4 and Figure 5 indicate that the performance of metal- oxide NPs was better than that of SiO₂ NF, which could be related to the microconvection, diffusion, and surface-active site ability of NFs, which can adsorb ions. In addition, surface renewal rate or acidic, basic, or amphoteric properties of NF can change the concentrations of H₃O⁺ and OH⁻ [20].

On the other hand, it can be claimed that the Al₂O₃(II) NF performance was better than that of Al₂O₃(I), which may be related to surface area, as indicated in Refs. [23,86]. Based on the study carried out by Ali et al. [87], who showed that a nanofluid’s thermal conductivity coefficient increases with the size of the NPs, and considering the similarity between heat and mass transfer, it may be argued that the better performance of the Al₂O₃(II) NF was due to the increase in the NPs.

The effect of gas feed and solvent flow rates on the performance of Al₂O₃ (I) and (II) NFs-0.01 wt.% was examined (Figure 6). It is clear that the amount of k_La increased with an increase in the gas feed/solvent flow rate, and its values were higher at high rotating speeds than lower ones. Therefore, there was a relationship between the above-mentioned operating parameters and MT performance. Figure 6a shows the performance of Al₂O₃ (I) and (II) NFs (0.01 wt.%) at high rotating speeds, a constant CO₂ content of 50 vol.%, and two constant solvent flow rates of 24 and 42 L/h based on changes to the gas flow rate through the two upper solid curves along with the upper horizontal and right vertical axes, as well as the two lower dotted lines along with the lower horizontal and left vertical axes. Figure 6b similarly shows the performance of these two NFs at the same concentration, with a CO₂ content of 50 vol.% and at the constant gas flow rates of 6, 16, and 24 L/h based on changes to the solvent flow rate. It is also shown that sovereignty was related to Al₂O₃ (II). It is possible that the microconvection strength of Al₂O₃ (II) was higher than that of Al₂O₃ (I) in the solvent.

According to the flow regime, to predict the absorption performance of a contactor, it is necessary to determine the liquid-phase MT coefficient and Peclet Number (Pe) [72].

Based on the MT correlations reported in [67], the above reported results, and evaluations of the correlations, it can be concluded that the volumetric MT coefficient was mostly proposed by investigators using Reynolds (Re), Schmidt (Sc), Weber (We), Froud (Fr), Grashof (Gr), and φ. For dimensional analysis, it is necessary to take into account parameters such as the geometry of the system, the process nature, kinematic viscosity, and external forces. Therefore, according to the above experimental results, the fact that external forces affect the turbulent situation of the fluid flow; the packing geometry; the liquid surface tension, which can be affected by the NP concentration and size; and the effect of rotational speeds considered with the Re, Sc, We, and Gr numbers should be all taken in to consideration. On the other hand, the relationship between k_La and the above-mentioned parameters can be expressed as follows:

$$k_{L}a=f\left(u_L, d_p,{\rho }_L,{\mu }_L,D_L,a_t,a_c,\sigma \right)$$

(17)

Taking into account the analogy of heat and mass transfer and considering the results of Kristiawan et al. [88] and Mohammadoost et al. [64], investigations in mass transfer have shown that when the absorbing solvent is an NF, the NF’s Reynolds number and concentration of NFs can affect the MT performance. Therefore, the above-mentioned issues, critical surface tension, and Brownian Reynolds number (Re_NF), which show the NP’s role in micro-convention, lead to the following equation:

$$\frac{k_{L}a{d}_p}{D_L{a}_t}=AR{e}_G^{a}R{e}_L^{b}W{e}_L^{c}S{c}_L^{d}G{r}_L^e{\left(\frac{\sigma }{{\sigma }_c}\right)}^f{\left(B+\phi R{e}_{NF}\right)}^g{\left(B-\phi R{e}_{NF}\right)}^h$$

(18)

In the present study, the constants of the empirical correlation of MT performance were found with regression analysis of the experimental data of water and NFs. This equation, known as the predicted model, showed a 29.7% discrepancy with the experimental data that were shown and compared with Rajan et al.’s [70] correlation (in Figure 7):

$$\frac{k_{L}a{d}_p}{D_L{a}_t}=112.67R{e}_G^{0.993}R{e}_L^{2.119}W{e}_L^{0.331}S{c}_L^{0.5}G{r}_L^{0.294}{\left(\frac{\sigma }{{\sigma }_c}\right)}^{0.021}{\left(\frac{1}{4}+\phi R{e}_{NF}\right)}^{3.543}{\left(\frac{1}{4}-\phi R{e}_{NF}\right)}^{2.747}$$

(19)

The limitations of dimensionless numbers in the correlation were 5.29 × 10⁻¹ ≤ Re_L < 9.26 × 10⁻¹, 1.55 ≤ Re_G < 4.13, 1.89 × 10⁻⁶ ≤ We ≤ 7.68 × 10⁻⁶, 6.66 × 10¹ ≤ Sc ≤ 3.18 × 10⁻², 4.12 × 10⁵+ ≤ Gr ≤ 7.33 × 10⁵, 0.00 ≤ Re_NP ≤ 1.31.

k_La had higher Re_L and Re_NP power compared to other dimensionless groups, which shows that k_La was strongly connected to the liquid flow rate and NP concentration.

Considering the above-mentioned points about dimensionless groups, the above-mentioned relationship form can be used to scale up the RPB.

4. Conclusions

In this investigation, MT performance in a CO₂-N₂-NF system with centrifugal acceleration and several NPs was examined. The values of k_La for water, TiO₂, Al₂O₃, and SiO₂ NFs in various concentrations were obtained and the effect of changing operation parameters was analyzed. The metal oxides of TiO₂ and Al₂O₃ (I) and (II) were more efficient than the mineral oxide of SiO₂. Moreover, the concentrations of 0.01 wt.% were more efficient in comparison with the base fluid (water) and other concentrations of the suspension, and the NFs of TiO₂, Al₂O₃, and SiO₂ to some extent affected the liquid volumetric interfacial MT coefficient at the high rotating speeds of the RPB. The results clearly show that at high rpms, NPs in suitable concentrations can enhance the MT performance considerably, even when using low-solubility solvents like water at low pressure. In this study, Al₂O₃ (II) showed better performance and increased the amount of k_La approximately 2.6 times more than water.

Additionally, it can be pointed out that MT coefficients are a function of fluid properties and flow rates and change by variation of these quantities in the flow direction. A new correlation was also proposed (Equation (19)) in this study for k_La prediction at low pressure, which includes both the microconvection of NPs and the surface tension of packings. For future research on physical absorption, examining the process at higher system pressure and CO₂ concentration, adding extra intensification tools such as external magnetic forces, the use of the hybrid water-based NFs with Al₂O₃-TiO₂, a higher concentration of NPs and rpm, examination of MT interfacial effective surface area for NP participation, and more tests on other mineral NPs and advanced solvents such as biphasic, phase change, ionic liquids, and deep eutectic solvents are recommended.