Gas/Liquid Operations in the Taylor-Couette Disc Contactor: Continuous Chemisorption of CO₂

Abstract

Gas/liquid contactors are widely used in chemical and biotechnological applications. The selection and design of bubble-column-type gas/liquid contactors requires knowledge about the gas distributor design to provide appropriate gas flow patterns. This study presents the continuous chemisorption of CO₂ in 0.1 molar sodium hydroxide solution in a counter currently operated gas/liquid Taylor-Couette disc contactor (TCDC). This vertical-column-type contactor is a multi-stage agitated gas/liquid contactor. The performance of a lab-size TCDC contactor in gas/liquid mass transfer operations was investigated. The apparatus design was adjusted for gas/liquid operations by installing perforated rotor discs to provide a rotational-speed-dependent dispersed gas phase holdup in the column. The parameters of dispersed gas phase holdup, volumetric mass transfer coefficient and residence time distribution were measured. In the first step, hydraulic characterization was performed. Then, the efficiency in gas/liquid operations was investigated by continuous neutralization of 0.1 molar sodium hydroxide with a gas mixture of 30 vol% CO₂ and 70 vol% N₂. Temperature, rotational speed and gas flow rate were varied. The desired pH value of pH 9 at the column outlet was kept constant by adjusting the sodium hydroxide feed. From the experimental results, the volume-based liquid-side mass transfer coefficient k_La was deduced in order to model the reaction according to the two-film theory over the column height. The CSTR cascade model fitted the experimental data best. The experimental results confirm stable and efficient reactive gas/liquid contact in the Taylor-Couette disc contactor.

1. Introduction

Continuously operated liquid/liquid extraction columns are designed to intensively contact two immiscible liquids aiming at the optimization of mass transfer. Agitated extraction columns use mechanical energy to control the droplet size distribution and the dispersed phase holdup. These general design aspects can be transferred to the requirements of multiphase reactions. The simple and effective design of the Taylor-Couette disc contactor (TCDC) is perfectly suited to provide continuous multiphase contact [1]. Modification of the basic contactor design enables contact of a gas phase and liquid phase(s) in co- and countercurrent operation. The phase contact principle of the Taylor-Couette disc contactor is based on stabilized Taylor vortex flow. Gas/liquid contact in Taylor-Couette reactors has been investigated by several authors [2,3]. Stabilization of two-phase flow and the limitation of axial back mixing in the Taylor vortex flow regime using rotor discs or ribs was confirmed by Richter et al. in 2008 [4], resulting in confirmation of the applicability of TCDC columns in continuous countercurrent gas/liquid operations. Continuous gas/liquid contactors such as bubble columns, packed bed or spray columns have been well investigated, and design algorithms are available [5]. These columns make use of gas flow to provide mixing energy. The bubble size distribution and mass transfer area are mainly controlled by the sparger design. Sufficient mixing without back mixing over the entire volume of the column requires the sophisticated design of a multiphase operation. Large gas/liquid reactors may suffer from insufficient cross-sectional mixing, which significantly limits process efficiency. The TCDC design is supposed to overcome these drawbacks by providing several compartments along the entire column height. Each compartment has the same flow condition depending on the rotational speed of the shaft, enabling uniform dispersed gas phase holdup and mass transfer area along the entire column height. Mixing energy is provided by the rotor shaft and rotor discs. The vertical arrangement of mixing compartments is a multi-stage agitated gas/liquid contactor. These contacting devices are used to provide sufficient residence time combined with minimal axial back mixing even at low gas loads [6]. To demonstrate the applicability of the TCDC in gas/liquid operations, continuous chemisorption of CO₂ in 0.1 molar sodium hydroxide solution was performed for different process conditions, aiming at providing a cost-effective CO₂ capture technology by chemisorption in sodium hydroxide [7]. The same process can be used to neutralize alkali wastewater streams before further processing. The neutralization of sodium hydroxide in bubble columns is well investigated and design algorithms are available [8,9,10,11]. Continuous countercurrent neutralization of 0.1 molar sodium hydroxide solution in the TCDC was performed using a gas mixture of 30 vol% CO₂ and 70 vol% N₂. The experimental parameters of flow rate, temperature (25 °C, 40 °C, 60 °C) and rotational speed were varied. For modelling of the chemisorption process over column height, the residence time distribution of the continuous liquid phase, the dispersed gas phase holdup, the pH value at the column outlet and the CO₂ concentration at the column outlet were monitored. The performance and modelling of a lab-size TCDC column in reactive gas/liquid operations is reported. The continuous chemisorption of CO₂ in 0.1 molar sodium hydroxide solution was chosen for investigating gas/liquid phase contact in the TCDC.

2. Materials and Methods

2.1. Chemisorption of CO₂

According to Pohorecki et al. [12], the absorption of CO₂ into aqueous alkaline solutions is divided into three steps (Equations (1)–(3)). Reaction 1 represents the physical absorption of gaseous CO₂ into the liquid solution. Due to the high rate of absorption equilibrium, concentration at the interface can be assumed. In reaction 2, the dissolved carbon dioxide reacts with hydroxide ions to form the intermediate hydrogen carbonate (${\mathrm{HCO}}_3^{-}$). The rate of reaction 3, where the intermediate ${\mathrm{HCO}}_3^{-}$ reacts with hydroxide ions (${\mathrm{OH}}^{-})$ to carbonate (${\mathrm{CO}}_3^{2-})$, is significantly higher than the rate of reaction 2. Therefore, the rate of the second-order reaction (reaction 2) is defined as a rate-controlling step for chemisorption of CO₂ in 0.1 molar sodium hydroxide solution. For a high pH, the pH-depending equilibrium concentration of ${\mathrm{HCO}}_3^{-}$ is very small (Figure 1). According to Fleischer et al. [13], the reaction of ${\mathrm{CO}}_2$ with water to form bicarbonate and hydrogen ions becomes dominant at low pH and can be neglected in this study because a steady-state pH value at the liquid phase outflow at the column outlet was adjusted to pH 9. At high pH values, absorption of CO₂ is considered as rate controlling [8,13,14].

$${\mathrm{CO}}_{2\left(\mathrm{g}\right)}\rightleftharpoons {\mathrm{CO}}_{2\left(\mathrm{l}\right)}$$

(1)

$${\mathrm{CO}}_{2\left(\mathrm{l}\right)}+{\mathrm{OH}}^{-}\to {\mathrm{HCO}}_3^{-}$$

(2)

$${\mathrm{HCO}}_3^{-}+{\mathrm{OH}}^{-}\rightleftharpoons { \mathrm{CO}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}$$

(3)

For this study, reactions 1 to 3 are considered. Concentration of ${\mathrm{CO}}_3^{2-}$ and ${\mathrm{HCO}}_3^{-}$ are needed for further calculations of the reaction rate. The ratio between the hydrogen carbonate and the carbonate species is calculated using the Henderson–Hasselbach equation (Equation (4)), as deduced from the law of mass action for step 3. The concentration related pKa value of ${\mathrm{CO}}_2$ in water is affected by ionic strengths and was fitted to close the overall mass balance [15]. The obtained pKa values are in the range between 10.14 and 10.36 depending on the temperature. These results agree well with the literature [14]. Figure 1 illustrates the concentration of ion species over decreasing pH value.

$$pH=p{K}_a+\log \left(\frac{c_{{\mathrm{CO}}_3^{2-}}}{c_{{\mathrm{HCO}}_3^{-}}}\right)$$

(4)

2.2. Experimental Setup

A schematic diagram of the experimental setup is given in Figure 2. This lab-scale TCDC DN 50 column is a flexible plant for multiphase operations. The rotor is powered with a laboratory drive M (Heidolph Hei-TORQUE Precision 200). The peristaltic pump P1 (ISMATEC Ecoline VC-280) equipped with Tygon^® ELFL 6.4 × 9.6 × 1.6 mm tubing was used as a feed pump for the 0.1 molar NaOH solution which was added on the top of the column. For fixed gas flow rate, the NaOH feed was adjusted via pH control at the column outlet. To monitor continuous neutralization of sodium hydroxide over the column height, the plant was equipped with a pH sensor at the column outlet (SI Analytics BlueLine 22 connected to Knick portavo 904). The flow meter FL (Bio-Tech FCH-m-PP-LC) was used to monitor the NaOH flow rate. A calibrated mass flow controller MFC (Bronkhorst F-201CV) was used to adjust the gas flow rate at the bottom of the column. The CO₂ concentration on top of the column was measured using a FlowEvo NDIR sensor (smartGas). For hydraulic characterization, a pressure differential transducer PDT (ICM 331, Schneider Messtechnik, Bad Kreuznach, Germany) was used to monitor the dispersed gas phase holdup. The oxygen concentration was recorded by WTW CellOx 325 sensors at the column outlet (O₂1) and in the feed tank (O₂2). To ensure constant temperatures between 25 °C and 60 °C, the column was adjusted with a double jacket and a Julabo DYNEO DD-600F (C1) temperature controller. The NaOH feed was preheated with a glass heat exchanger (HE) connected to the Julabo CORIO CD-601F (C2) controller before entering the column. The double-jacket feed tank B1 was connected to a second Julabo CORIO CD-601F controller. The temperature along the active column was measured using the upper TI1 probe (MGW Lauda R 24/2) and lower TI2 probe (MGW Lauda R 40/2). For neutralization experiments, a gas mixture of 30 vol% CO₂ and 70 vol% N₂ (Air Liquide) was used. Hydraulic characterization and mass transfer experiments were performed with synthetic air. Nitrogen (Air Liquide, 99.8%) was used for oxygen desorption in mass transfer experiments. Measurement of the residence time distribution was performed using a custom-made conductivity probe that can be installed at the pH port. The NaOH tracer was injected into the NaOH inlet port. The geometric data of the TCDC column are shown in

Table 1. Geometric data of the lab-scale TCDC DN 50 column.

TCDC DN50
active length	H	0.875	[m]
column diameter	dC	0.05	[m]
shaft diameter	dSh	0.025	[m]
number of compartments	N	24	[-]
compartment height	HC	0.025	[m]
column volume	VC	1.35	[l]
rotor disc diameter	dR	0.043	[m]

and illustrated in Figure 3 (right) according to the design recommendations of Aksamija et al. [16]. Detailed information about the rotor discs is given in Section 2.3.

2.3. Rotor Disc Design for Gas/Liquid Contact

Controllable dispersed gas phase holdup requires adjustment of the rotor disc design. Therefore, the rotor discs are perforated with 5 holes with a diameter of 1.5 mm, which are located next to the rotor shaft. These holes come with the effect of decreasing dispersed gas phase holdup over increasing rotational speed. The rotor disc design is illustrated in Figure 3 (left).

2.4. Column Hydrodynamics

2.4.1. Dispersed Gas Phase Holdup

The dispersed gas phase holdup φ_g is defined as the volume fraction of dispersed gas phase bubbles V_g in the active reactor height and the total active reactor volume. It is calculated according to Equation (5).

$${\mathsf{\phi }}_{\mathrm{g}}=\frac{{\mathrm{V}}_{\mathrm{g}}}{{\mathrm{V}}_{\mathrm{g}}+{\mathrm{V}}_{\mathrm{l}}}$$

(5)

The static pressure equilibrium between a reference tube, filled with the continuous phase, and the aerated column (PDT in Figure 2) corresponds to Equation (6).

$${\mathsf{\rho }}_{\mathrm{l}}·\mathrm{g}·\mathrm{h}=∆\mathrm{P}+\mathrm{g}·\mathrm{h}·\left({\mathsf{\phi }}_{\mathrm{g}}·{\mathsf{\rho }}_{\mathrm{g}}+\left(1-{\mathsf{\phi }}_{\mathrm{g}}\right)·{\mathsf{\rho }}_{\mathrm{l}}\right)$$

(6)

The dispersed gas phase holdup can be calculated from the differential pressure ∆P measured with the differential pressure transducer at steady-state operation. Because of the high-density difference between the gaseous and aqueous phase, the gas phase density can be neglected for holdup calculations. The dispersed gas phase holdup can be simplified to Equation (7).

$${\mathsf{\phi }}_{\mathrm{g}}=\frac{∆\mathrm{P}}{\mathrm{g}·\mathrm{h}·{\mathsf{\rho }}_{\mathrm{l}}}·100$$

(7)

2.4.2. Residence Time Distribution

Residence time distribution is analyzed by measuring the response signal of the conductivity sensor at the column outlet after tracer injection on top of the column. For this study, spiking of the aqueous phase with 0.5 mL of saturated sodium chloride was used for residence time distribution measurements. Calculation of the exit age function E_i according to the measured relative conductivity g_i is performed according to Equation (8). The measured mean residence time is given by Equation (9).

$${\mathrm{E}}_{\mathrm{i}}=\frac{{\mathrm{g}}_{\mathrm{i}}}{\sum ({\mathrm{g}}_{\mathrm{i}}·∆{\mathrm{t}}_{\mathrm{i}})}$$

(8)

$$\overline{\mathrm{t}}=\frac{\sum ({\mathrm{t}}_{\mathrm{i}}·{\mathrm{g}}_{\mathrm{i}}·∆{\mathrm{t}}_{\mathrm{i}})}{\sum ({\mathrm{g}}_{\mathrm{i}}·∆{\mathrm{t}}_{\mathrm{i}})}$$

(9)

The exit age function and the time are normalized to the dimensionless exit age function E_ϴi and the dimensionless time ϴ with Equations (10) and (11).

$${\mathsf{\theta }}_{\mathrm{i}}=\frac{{\mathrm{t}}_{\mathrm{i}}}{\overline{\mathrm{t}}}$$

(10)

$${\mathrm{E}}_{{\mathsf{\theta }}_{\mathrm{i}}}=\frac{{\mathrm{E}}_{\mathrm{i}}}{\overline{\mathrm{t}}}$$

(11)

According to Octave Levenpiel [17], large deviation from ideal plug-flow behavior can be approximated using the CSTR cascade model. The number of CSTRs in series is obtained from E_ϴ,max according to Equation (12).

$${\mathrm{E}}_{\mathsf{\theta },\max }=\frac{\mathrm{N}·{\left(\mathrm{N}-1\right)}^{\mathrm{N}-1}}{\left(\mathrm{N}-1\right)!}\exp -\left(\mathrm{N}-1\right)$$

(12)

The dispersion model uses the Bodenstein number (Bo) as an indicator for axial back mixing. For large deviation from ideal flow and open-open vessel boundary condition, Bo can be calculated from the variance σ of the E function according to Equation (13) [17].

$$\mathrm{Bo}=\frac{1}{{\mathsf{\sigma }}_{\mathrm{E}{\mathsf{\theta }}_{\mathrm{i}}}^2}+\sqrt{{\left(\frac{1}{{\mathsf{\sigma }}_{\mathrm{E}{\mathsf{\theta }}_{\mathrm{i}}}^2}\right)}^2+\frac{8}{{\mathsf{\sigma }}_{\mathrm{E}{\mathsf{\theta }}_{\mathrm{i}}}^2}}\hspace{1em}\mathrm{with} {\mathsf{\sigma }}^2={{\displaystyle \int }}_0^{\infty }{\left(\mathrm{t}-\overline{\mathrm{t}}\right)}^2 · \mathrm{E}\left(\mathrm{t}\right)·\mathrm{dt}$$

(13)

The ratio between convective flow and axial dispersion (D_ax) is defined by the Bodenstein number according to Equation (14).

$$\mathrm{Bo}=\frac{{\mathrm{u}}_{\mathrm{l}}·\mathrm{L}}{{\mathrm{D}}_{\mathrm{ax}}}$$

(14)

2.4.3. Liquid Phase Volumetric Mass Transfer Coefficient k_La

The experimental procedure to determine the volumetric mass transfer coefficient of oxygen in water is described by Skala and Veljkovic [18]. The dissolved oxygen concentration is measured at the column inlet (O₂2 in Figure 2) and outlet (O₂1). The data of both sensors were recorded using a custom LabVIEW routine. A continuous steady-state measurement of oxygen concentration for specific experimental conditions (temperature, flow rate, rotational speed) requires successive absorption and desorption in a loop. Therefore, the feed tank was bubbled with nitrogen. The nitrogen flow rate in the feed tank was adjusted to keep the dissolved oxygen concentration at the column inlet below 1 mg L⁻¹. Synthetic air was then added to the column and the dissolved oxygen concentration in water was measured at the column outlet at steady state. The k_La value was calculated according to Equation (15). The determination at steady-state mass transfer conditions in countercurrent flow regimes excludes errors resulting from low-sensitivity oxygen probes. This method is also described by Chaumat et al. [19] and is successfully used for investigating mass transfer in bubble columns [20].

$${\mathrm{k}}_{\mathrm{La}}=\frac{{\mathrm{u}}_{\mathrm{l}}}{\mathrm{H}}·\ln \frac{{\mathrm{c}}^{*}-{\mathrm{c}}_{\mathrm{out}}}{{\mathrm{c}}^{*}-{\mathrm{c}}_{\mathrm{in}}}$$

(15)

The superficial phase velocity u of a single phase is related to the free cross-sectional area between the rotor shaft and the column wall A_ring (Equation (16))

$$\mathrm{u}=\frac{\dot{\mathrm{V}}}{{\mathrm{A}}_{\mathrm{ring}}}$$

(16)

For specified temperature and pressure, the equilibrium concentration c* at the middle of the column was calculated using Equation (17), according to Schumpe et al. [21]. The temperature was measured simultaneously using WTW CellOx325 sensors. The pressure P in the middle of the column was calculated from the column height and measured dispersed phase holdup. The column outlet is open to the atmosphere and the pressure at the column outlet was set to ambient pressure.

$${\mathrm{c}}^{*}\left[\frac{{\mathrm{mg} \mathrm{O}}_2}{\mathrm{L} }\right]=2.954·\left(\mathrm{P}-{\mathrm{P}}_{\mathrm{s}}\right)·\mathsf{\alpha }$$

(17)

The pressure P in Equation (20) is given in kPa and α was calculated according to Equation (18) with the temperature T in °C. Coefficients a to e are given in

Table 2. Coefficients of the power series to calculate O₂ solubility with Equation (18) as a function of temperature (0–50 °C) [21].

Parameter	Value
a	4.900·10−2
b	−1.335·10−3
c	2.759·10−5
d	3.235·10−7
e	1.614·10−9

[21]. The coefficients are defined for oxygen solubility in a temperature range from 0 °C to 50 °C.

$$\mathsf{\alpha }=\mathrm{a}+\mathrm{b}·\mathrm{T}+\mathrm{c}·{\mathrm{T}}^2+\mathrm{d}·{\mathrm{T}}^3+\mathrm{e}·{\mathrm{T}}^4$$

(18)

The saturation pressure P_s in Equation (17) was calculated according to the Antoine equation (Equation (19)) with T given in K and the pressure P in bar. Antoine parameters for the temperature range from 293 K to 343 K are: A = 6.20963, B = 2354.731 and C = 7.559 [22].

$${\log }_{10}\left({\mathrm{P}}_{\mathrm{s}}\right)=\mathrm{A}-\frac{\mathrm{B}}{\mathrm{T}+\mathrm{C}}$$

(19)

2.5. Reactor Modelling

Heterogeneous chemisorption of CO₂ in aqueous NaOH solution has been studied by many authors. The design algorithm proposed by Darmana et al. [11] is commonly used to describe the chemisorption of CO₂ in bubble columns [8,10,14,23,24]. Therefore, the neutralization of NaOH with CO₂ is modelled in respect to CO₂ consumption according to the two-film theory. Equation (20) shows the general reaction equation for component A (CO₂) being transferred from a gaseous phase to a liquid bulk phase and consecutive reaction with component B (OH⁻) to form product C (CO₃²⁻) whereas the stoichiometric factor b = 2. This reaction is a second-order irreversible reaction as reactants B and C are not soluble in the gaseous phase [24]. Octave Levenspiel defined different reaction regimes in respect to the rate-limiting step. The general reaction rate for gas/liquid reactions according to Levenspiel is expressed in Equation (21) [17].

$${\mathrm{A}}_{\left(\mathrm{g}\to \mathrm{l}\right)}+{\mathrm{bB}}_{\left(\mathrm{l}\right)}\to {\mathrm{C}}_{\left(\mathrm{l}\right)}$$

(20)

$$-{\mathrm{r}}_{\mathrm{A}}^{″″}=\frac{{\mathrm{p}}_{\mathrm{A}}}{\frac{1}{{\mathrm{k}}_{\mathrm{AG}}\mathrm{a}}+\frac{1}{{\mathrm{He}}_{\mathrm{A}}·{\mathrm{k}}_{\mathrm{AL}}\mathrm{a}·\mathrm{E}}+\frac{1}{{\mathrm{He}}_{\mathrm{A}}·{\mathrm{k}}_{\mathrm{A}}·{\mathrm{c}}_{\mathrm{B}}·\left(1-{\mathsf{\phi }}_{\mathrm{g}}\right)}}$$

(21)

The gas solubility of CO₂ in the liquid phase, dependent on the partial pressure p, is described by Henry’s law (Equation (22)).

$${\mathrm{c}}_{{\mathrm{CO}}_2,\mathrm{l}}={\mathrm{p}}_{{\mathrm{CO}}_2}·{\mathrm{H}}_{{\mathrm{CO}}_2}$$

(22)

The Henry constant of CO₂ in pure water ${\mathrm{H}}_{\mathrm{w},{\mathrm{CO}}_2}$ [mol m⁻³ Pa⁻¹] is calculated according to Equation (23) with the temperature T in K [25].

$${\mathrm{H}}_{\mathrm{w},{\mathrm{CO}}_2}=3.54·{10}^{-7}\exp \left(\frac{2044}{\mathrm{T}}\right)$$

(23)

The effect of electrolyte solutions on the Henry constant is taken into account by Equation (24), with ci indicating the ion concentration [26].

$$\log \left(\frac{{\mathrm{H}}_{\mathrm{w},{\mathrm{CO}}_2}}{{\mathrm{H}}_{{\mathrm{CO}}_2}}\right)=\sum \left(\mathrm{hi}+\mathrm{hg}\right)·\mathrm{ci}$$

(24)

Ion specific parameters for hi and hg are summarized in

Table 3. Ion specific parameters according to Weisenberger and Schumpe [26].

Ion	hi [m3 kmol−1]	Gas	hg [m3 kmol−1]	bi [m3 kmol−1]
Na+	0.1143	CO2	−0.0172	−0.0857
OH−	0.0839			−0.1088
${\mathrm{HCO}}_3^{-}$	0.0967			−0.115
${\mathrm{CO}}_3^{2-}$	0.1423			−0.245

.

According to Pohorecki and Moniuk [12], the reaction rate of the second-order reaction rate constant ${\mathrm{k}}_{{\mathrm{OH}}^{-}}$ [m³ kmol⁻¹ s⁻¹] for the chemisorption of CO₂ into aqueous NaOH solution is influenced by temperature and ionic strength. Therefore, the reaction rate constant at infinite solution k_∞ is calculated according to Equation (25) and the ionic strength is considered with Equations (26) and (27) [12].

$$\log {\mathrm{k}}_{\infty }=11.895-\frac{2382}{\mathrm{T}}$$

(25)

$$\log \left(\frac{{\mathrm{k}}_{{\mathrm{OH}}^{-}}}{{\mathrm{k}}_{\infty }}\right)=0.221·\mathrm{I}-0.016·{\mathrm{I}}^2$$

(26)

Whereas, the ionic strength I is defined as:

$$\mathrm{I}=0.5·\left({\mathrm{c}}_{{\mathrm{Na}}^{+}}·{\mathrm{z}}_{{\mathrm{Na}}^{+}}^2+{\mathrm{c}}_{{\mathrm{OH}}^{-}}·{\mathrm{z}}_{{\mathrm{OH}}^{-}}^2+{\mathrm{c}}_{{\mathrm{HCO}}_3^{-}}·{\mathrm{z}}_{{\mathrm{HCO}}_3^{-}}^2+{\mathrm{c}}_{{\mathrm{CO}}_3^{2-}}·{\mathrm{z}}_{{\mathrm{CO}}_3^{2-}}^2\right)$$

(27)

Gas/liquid reactions are mainly affected by the diffusion of the reactants. Mass transfer of reactants is enhanced when the transferred component is consumed by the chemical reaction. This increased mass transfer can be described by the enhancement factor E, which describes the ratio of mass transfer with and without chemical reaction. The Hatta number Ha (Equation (28)) and the enhancement factor for an instantaneous reaction E_∞ (Equation (29)) are used to categorize the reaction regime [17,24,27]. For this study, the approximation according to Westerterp et al. [28] is used for calculation of the enhancement factor E (Equation (30)) [8,11,24,29].

$$\mathrm{Ha}=\frac{\sqrt{{\mathrm{k}}_{{\mathrm{OH}}^{-}}·{\mathrm{D}}_{{\mathrm{CO}}_2,\mathrm{l}}·{\mathrm{c}}_{{\mathrm{OH}}^{-},\mathrm{l}}}}{{\mathrm{k}}_{\mathrm{L},{\mathrm{CO}}_2}}$$

(28)

$${\mathrm{E}}_{\infty }=1+\left(\frac{{\mathrm{D}}_{{\mathrm{OH}}^{-},\mathrm{l}}·{\mathrm{c}}_{{\mathrm{OH}}^{-},\mathrm{l}}}{2·{\mathrm{D}}_{{\mathrm{CO}}_2,\mathrm{l}}·{\mathrm{c}}_{{\mathrm{CO}}_2,\mathrm{l}}}\right)·{\left(\frac{{\mathrm{D}}_{{\mathrm{CO}}_2,\mathrm{l}}}{{\mathrm{D}}_{{\mathrm{OH}}^{-},\mathrm{l}}}\right)}^{\frac{1}{2}}$$

(29)

$$\mathrm{E}=\left\{\begin{array}{c}1 {\mathrm{E}}_{\infty }\le 1\\ -\frac{{\mathrm{Ha}}^2}{2\left({\mathrm{E}}_{\infty }-1\right)}+{\left(\frac{{\mathrm{Ha}}^4}{4{\left({\mathrm{E}}_{\infty }-1\right)}^2}+\frac{{\mathrm{E}}_{\infty }·{\mathrm{Ha}}^2}{{\mathrm{E}}_{\infty }-1}+1\right)}^{\frac{1}{2}} 1<{\mathrm{E}}_{\infty }\end{array}\right.$$

(30)

For the calculation of Ha and E, further parameters are needed. Therefore, the diffusion coefficient of pure CO₂ in water ${\mathrm{D}}_{\mathrm{w},{\mathrm{CO}}_2} \left[{\mathrm{m}}^2{ \mathrm{s}}^{-1}\right]$ was calculated using Equation (31) [25].

$${\mathrm{D}}_{\mathrm{w},{\mathrm{CO}}_2}=2.35·{10}^{-6}\exp \left(\frac{-2119}{\mathrm{T}}\right)$$

(31)

The influence of electrolyte solutions on the diffusion coefficient is considered with Equation (32). Ion specific parameters for bi are listed in Table 3 [30].

$${\mathrm{D}}_{{\mathrm{CO}}_2}={\mathrm{D}}_{\mathrm{w},{\mathrm{CO}}_2}·(1+0.624·\sum {\mathrm{b}}_{\mathrm{i}}·{\mathrm{c}}_{\mathrm{i}})$$

(32)

Temperature-dependent diffusion coefficients for OH⁻ ions ${\mathrm{D}}_{{\mathrm{OH}}^{-}} \left[{\mathrm{m}}^2{ \mathrm{s}}^{-1}\right]$ are calculated according to Equation (33) [31]. The parameters are summarized in

Table 4. Parameters for determination of OH⁻ diffusivity [24].

ψ	${\mathbf{D}}_{\mathbf{O}{\mathbf{H}}^{-}}^0 \left[{\mathbf{m}}^2 {\mathbf{s}}^{-1}\right]$	T0 [K]
1.658	2.665·10−8	216.5

.

$${\mathrm{D}}_{{\mathrm{OH}}^{-}}={\mathrm{D}}_{{\mathrm{OH}}^{-}}^0·{\left(\frac{\mathrm{T}}{{\mathrm{T}}_0}-1\right)}^{\mathsf{\psi }}$$

(33)

2.6. Chemicals

The chemicals used for the neutralization experiments were technical grade according to

Table 5. Chemicals used for neutralization experiments and hydraulic characterization.

Name	Manufacturer	CAS	Purity
sodium hydroxide	J.T. Baker	1310-73-2	≥98%
deionized water	in-house source
synthetic air	Air liquide		≥99%
nitrogen	Air liquide	7727-37-9	≥99.8%
gas mix 30% CO2 and 70% N2	Air liquide		≥99%

.

3. Results

3.1. Neutralization Experiments

The 0.1 molar NaOH feed was prepared in a 10 L container by dissolving 40 g of solid NaOH pellets in deionized water. The measured start pH value of 0.1 molar NaOH solution at ambient temperature was pH 13. Calibration of the pH probe was performed between pH 7 and pH 12 prior to each neutralization experiment. Knick CaliMat buffer solutions were used for calibration. The steady-state pH value at the column outlet was set to pH 9 to avoid further reaction of CO₂ with water. The gas flow rate was fixed to 1, 2 and 3 L min_STP⁻¹ (30 vol% CO₂ and 70 vol% N₂). The 0.1 molar NaOH flow rate was experimentally adjusted to obtain a constant pH of 9 at the column outlet. The entire set of neutralization experiments for different temperatures and rotational speeds is listed in

Table 6. List of neutralization experiments.

$\mathbf{T}$	$\mathbf{r}\mathbf{p}\mathbf{m}$	$\dot{{\mathbf{V}}_{\mathbf{g}}}$	$\dot{{\mathbf{V}}_{\mathbf{l}}}$
[°C]	[L min−1]	[L minSTP−1]	[L min−1]
25	300	1	0.18
	400
	700
25	300	2	0.28
	400
	700
25	300	3	0.42
	400
	700
40	300	1	0.18
	400
	700
40	300	2	0.28
	400
	700
40	300	3	0.42
	400
	700
60	300	1	0.18
	400
	700
60	300	2	0.28
	400
	700
60	300	3	0.42
	400
	700

.

The experimentally obtained molar ratio between the NaOH feed and CO₂ is shown in Figure 4 and is approached with a second-order polynomial (Equation (34)). The NaOH feed was adjusted to 25 °C at a rotational speed of 300 rpm and was kept constant for all temperatures and stirrer speeds.

$${\dot{\mathrm{n}}}_{{\mathrm{CO}}_2}=-0.26·{\dot{\mathrm{n}}}_{\mathrm{NaOH}}^2+2.07·{\dot{\mathrm{n}}}_{\mathrm{NaOH}}-1.12$$

(34)

During column startup, the column outlet was connected to the feed tank and the NaOH feed was set to 60 mL min⁻¹ until constant flow and constant temperatures were reached. Column startup at a low NaOH feed rate was performed in order to decrease the spent amount of sodium hydroxide and to provide comparability of startup at different process parameters. The stirrer speed was adjusted to the desired rotational speed and the gas phase was set to the desired flow rate. After adding CO₂, the neutralization reaction started, and the aqueous phase column outlet was connected to the waste tank. During neutralization experiments, the feed tank was permanently refilled with 0.1 molar NaOH. The pH value at the column outlet decreased over time. After reaching pH 9, the NaOH feed was adjusted to the experimental conditions given in Table 6. Figure 5 illustrates this process with the overswing of the pH and CO₂ outlet concentration after increasing the NaOH feed. At steady-state operation, the entire amount of CO₂ was consumed by the neutralization reaction.

3.1.1. Influence of Rotational Speed

Figure 6 shows the pH over time during the column startup. The rotational speed was varied at a constant temperature of 25 °C and constant gas flow rate. It was expected that the changing flow regime with decreasing dispersed phase holdup (Figure 12), and thus also the decreasing mass transfer area, would show a different trend of decreasing pH, which was actually not monitored.

3.1.2. Influence of the Reaction Temperature

Figure 7 shows the influence of temperature on pH during column startup. The decreasing starting pH is explained by the strongly temperature-dependent dissociation of water [32]. The temperature-dependent pH value makes it more difficult to directly compare the neutralization process. Steady-state operation at the desired pH of 9 was reached earlier at elevated temperatures, which agrees with the temperature-dependent reaction rate constant in Equation (2) [12]. The concentration of sodium hydroxide was 0.1 molar for all experiments.

3.1.3. Influence of Gas Flow Rate

Figure 8 shows the influence of gas flow rate on the pH during column startup. The general expected trend shows a faster pH decrease at higher gas flow rate. With increasing gas flow rate, the dispersed gas phase holdup also increases and therefore, the specific mass transfer area significantly increases.

3.1.4. Steady-State Operation

For the neutralization experiments, steady-state pH is defined for the operation state after flow rate adjustment and constant pH value at the column outlet for at least 15 min. Although the influence of the rotational speed is identified as not significant, the steady-state pH was averaged in terms of rotational speed. Figure 9 shows the dependence of steady-state pH on gas flow rate and temperature. The lowest pH values were reached at a gas flow rate of 2 L min_STP⁻¹. The corresponding NaOH feed rate for each gas flow rate is shown in Table 6.

As shown in Figure 5, the CO₂ concentration at the column outlet was continuously recorded. Rpm-averaged steady-state CO₂ outlet concentrations are shown in Figure 10. The starting concentration of 30 vol% CO₂ was almost depleted to 0 ppm for 1 L min_STP⁻¹. A maximum CO₂ outlet concentration of 490 ppm was reached at 25 °C and 3 L min_STP⁻¹. The reactor enabled at least 99.9% efficiency with respect to CO₂ consumption.

3.2. Column Hydrodynamics

Characterization of column hydrodynamics was performed with the non-reactive test system using deionized water and synthetic air. The process parameters were the same as those used for the neutralization experiments (Table 6).

3.2.1. Dispersed Gas Phase Holdup

The perforated rotor discs (Figure 3: left) enable uniform dispersed gas phase holdup over the entire reactor height. At low rotational speed (0 rpm to 300 rpm), the gas phase rises in the gap between the column wall and the rotor disc which is specified as external flow (Figure 11a). Between 300 rpm and 700 rpm, the gas phase partially passes through the 1.5 mm holes and the gap between the rotor disc and the column wall. This flow regime is characterized as mixed flow (Figure 11b). Beyond 700 rpm, the flow regime is defined as internal only because the entire gas phase passes up through the perforated rotor discs (Figure 11c). This characterization of gas/liquid flow in the TCDC is valid for gas flow rates up to 3 L min_STP⁻¹ and a moderate liquid flow rate of 0.18 L min⁻¹ up to 0.42 L min⁻¹ as applied in this study. The general trend of dispersed gas phase holdup φ_g in the TCDC column is shown in Figure 12. The area of linearly decreasing dispersed phase holdup is used during neutralization experiments. Increasing rotational speed increases the centrifugal forces on the gaseous and liquid phase. The light gaseous phase is pressed towards the rotor shaft, forcing the gas phase to pass up through the perforated rotor discs. This unique flow behavior is used to establish constant dispersed gas phase holdup in the TCDC. Videos of Figure 11 (a) S1, (b) S2 and (c) S3 can be downloaded from Supplementary Material.

The dispersed gas phase holdup was measured using a differential pressure transducer. For all experiments, an IDM 331 (Schneider Messtechnik, 0 mbar to 20 mbar, ≤±1% FSO) was used. According to the static pressure equilibrium (Equation (7)), $\mathsf{\Delta }\mathrm{P}$ is the measured pressure difference between the bypass line filled with continuous phase (water) and the aerated column. Figure 2 illustrates the connection ports of the differential pressure transducer (PDT). In order to indicate the dynamic pressure caused by the rotation of the rotor shaft, reference measurements were performed without gas flow at the respective rotational speed and water flow rate. The measured pressure difference without aeration was subtracted from the differential pressure measured at aerated conditions. Holdup measurements were performed at 25 °C. The results are shown in Figure 13. The dispersed gas phase holdup φ_g in the TCDC setup under experimental conditions was between 2% and 16% depending on the rotational speed and gas flow rate.

3.2.2. Residence Time Distribution

Concentration gradients are affected by unavoidable axial back mixing. For modelling, the CSTR cascade model [1,19] was applied. Pulse experiments were performed at 25 °C for all operating points given in Table 6. The recorded data in normalized form, as described in Section 2.4, were (for convenience) fitted with a four-parameter log-normal distribution (Equation (35)). a, b, c and d are the fit parameters and ϴ is the dimensionless residence time.

$${\mathrm{E}}_{{\mathsf{\theta }}_{\mathrm{i},\mathrm{model}}}=\mathrm{a}+\mathrm{b}·\exp \left(-\frac{1}{2}·{\left(\frac{\ln \left(\frac{\mathsf{\theta }}{\mathrm{c}}\right)}{\mathrm{d}}\right)}^2\right)$$

(35)

Figure 14 shows the applied evaluation algorithm for the number of continuously stirred tanks in the cascade. The number of CSTRs (Equation (12)) is compared to the outcome of the log normal fit. The CSTR cascade model describes the measured data well. The mean residence time $\mathrm{t} ¯$ (Equation (9)), the number of CSTRs in the cascade, the Bodenstein number Bo (Equation (13)) and the axial dispersion coefficient D_ax (Equation (14)) are compared in the following section.

Figure 15a shows the measured mean residence times ${\mathrm{t}}_{\exp }=\overline{\mathrm{t}}$ for the three flow rate parameter sets (lines). The hydraulic residence time t_hydro was calculated using Equation (36). The average increase in the residence time compared to the hydraulic residence time was 43%. The influence of rotational speed is small compared to the influence of the flow rate.

$${\mathrm{t}}_{\mathrm{hydro}}=\frac{{\mathrm{V}}_{\mathrm{C}}}{\dot{{\mathrm{V}}_{\mathrm{l}}}}$$

(36)

Increasing rotational speed decreases axial back mixing, as shown in Figure 15b, with Bo increasing with increasing rotational speed, increasing N_CSTR (Figure 15c) and decreasing axial dispersion coefficient D_ax (Figure 15d). Increasing rotational speed in countercurrent gas/liquid contact changes the flow regime, as shown in Figure 4. When the gas flow rate through the perforated rotor discs exceeds the maximum (at about 2 L min_STP⁻¹), the excess amount of gas is forced to rise in the gap between the rotor discs and the column wall (for example at 3 L min_STP⁻¹) with a negative effect on back mixing, as shown with the Bo number in Figure 15b, N_CSTR in Figure 15c and D_ax in Figure 15d.

3.2.3. Liquid Phase Volumetric Mass Transfer Coefficient k_La

The liquid side volume-based mass transfer coefficient is determined for steady-state operation conditions with the air (oxygen from air) and water test system as described in Section 2.4. Figure 16 shows little influence of rotational speed on the k_La value. The influence of rotational speed is small and shows no characteristic trend. However, it confirms the outcome of the RTD measurements. At low gas load (1 L min_STP⁻¹), k_La slightly increases with rotational speed. At 2 L min_STP⁻¹, we registered a change in the flow regime. In operation state 3 L min_STP⁻¹, the effect of rotational speed on “bypass gas flow” no longer affected the mass transfer area. Similar results were found by Ramezani et al. who investigated the oxygen mass transfer in an air-water Taylor-Couette reactor [2]. The k_La value is highly sensitive to the air flow rate (Figure 16) and temperature (Figure 17). k_La values are in the range of between 0.005 s⁻¹ for 25 °C and 1 L min_STP⁻¹ air flow rate and 0.02 s⁻¹ for 60 °C and 3 L min_STP⁻¹ air flow rate, which agrees well with the literature [2,3].

Temperature dependency of the k_La can be described by Equation (37) with the temperature T in °C, measured k_La at 25 °C and the temperature correction factor β fitted for the experimental data [33]. Figure 18 shows the increasing k_La with increasing temperature for specific operation conditions and β = 0.019.

$${\mathrm{k}}_{\mathrm{L}}\mathrm{a}={\mathrm{k}}_{\mathrm{L}}{\mathrm{a}}_{25}·{\mathsf{\beta }}^{\left(\mathrm{T}-25\right)}$$

(37)

3.3. Reactor Modelling

The steady-state experimental data from the neutralization experiments, as discussed in Section 3.1, were used to develop the reactor mass balance. Depending on the consumed ${\mathrm{CO}}_2$ amount in the reactor, the ratio between hydrogen carbonate ${\mathrm{HCO}}_3^{-}$ and carbonate ${\mathrm{CO}}_3^{2-}$ ions can be calculated by fitting the pKa value of the Henderson–Hasselbach equation (Equation (4)). The measured outlet concentrations of CO₂ in the gas phase and ${\mathrm{OH}}^{-}$ in the aqueous phase are used for the mass balance. Due to the temperature dependency, the pKa value was fitted for the three different reaction temperatures. The literature reports a pKa value of 10.22 at 38 °C [15], which compares well to the fitted value of 10.29 for the neutralization experiments at 40 °C. For 25 °C, a pKa of 10.14 was obtained and for 60 °C, a pKa of 10.36 was obtained. Figure 19 shows a parity plot of the measured and calculated CO₂ consumption in the reactor. The fitted pKa values also compare well with thermodynamic pKa values, confirming the quality of the experiments.

The evaluation of residence time distribution in Section 3.2.2 resulted in at least four continuously stirred tanks in cascade over a length of 0.87 m. According to Levenspiel [17], the concentration over reactor volume may be approximated using plug-flow reactor behavior. Therefore, the evaluation of the overall reaction rate in respect to CO₂ was modelled using an ideal plug-flow reactor approach (Equation (38)) by plotting the overall CO₂ conversion X [-] over ${\mathrm{V}}_{\mathrm{C}}/{\dot{\mathrm{n}}}_{{\mathrm{CO}}_2}$. The overall reaction rate is indicated by the slope of the connecting line between 0 and the steady-state operational point, as shown in Figure 20 for a temperature of 25 °C, resulting in reaction rates of 0.17 mol m⁻³ s⁻¹ for 1 L min_STP⁻¹ gas flow, 0.36 mol m⁻³ s⁻¹ for 2 L min_STP⁻¹ and 0.56 mol m⁻³ s⁻¹ for 3 L min_STP⁻¹.

$$\mathrm{V}={\dot{\mathrm{n}}}_{{\mathrm{CO}}_2,0}·{{\displaystyle \int }}_0^{\mathrm{X}}\frac{\mathrm{dX}}{-{\mathrm{r}}_{\mathrm{A}}}$$

(38)

It was not possible to investigate the influence of temperature because at these high conversion rates, no significant difference in CO₂ consumption was registered for the chosen parameters. Steady-state CO₂ concentration at the column outlet is shown in Figure 12. The observed trend in CO₂ outlet concentration in a range from 0 to 500 ppm does not affect the CO₂ transfer at such a high feed concentration of 30 vol%. The average reaction rate is slightly influenced by the rotational speed. Figure 21 shows the decreasing reaction rate with increasing rotational speed, which agrees well with the decreasing dispersed phase holdup for increasing rotational speed (Figure 13). The reaction rate increases linearly with increasing gas flow rate. It must be mentioned that the feed rate of 0.1 molar NaOH solution also increased with the gas flow rate, as shown in Table 6.

The experimental data from the neutralization experiments at steady-state operation (Section 3.1.4) and hydrodynamic characterization (Section 3.2) were used to model the TCDC as a countercurrent CSTR cascade. The algorithm used for the evaluation of the reaction rate −r_A is explained in Section 2.5. The gas-side mass transfer resistance is not concerned in order of high gas flow rate and intense mixing. The volume-based liquid-side mass transfer coefficient was measured for oxygen in water. According to the film theory, Equation (39) is used for the calculation of ${\mathrm{k}}_{\mathrm{L}}{\mathrm{a}}_{{\mathrm{CO}}_2}$ [34]. The diffusion coefficient ${\mathrm{D}}_{{\mathrm{CO}}_2}$ is calculated by Equation (31). The diffusion coefficient for oxygen ${\mathrm{D}}_{\mathrm{O}}{}_2$ at 25°C is 2.22·10⁻⁹ m² s⁻¹ [35].

$$\frac{{\mathrm{k}}_{\mathrm{L}}{\mathrm{a}}_{{\mathrm{O}}_2}}{{\mathrm{k}}_{\mathrm{L}}{\mathrm{a}}_{{\mathrm{CO}}_2}}=\frac{{\mathrm{D}}_{{\mathrm{O}}_2}}{{\mathrm{D}}_{{\mathrm{CO}}_2}}$$

(39)

The model principle is shown in Figure 22. The number of continuously stirred tanks is obtained from residence time distribution measurements (Figure 15c). The neutralization process was modelled exemplarily for the neutralization experiment at 25 °C with a gas flow rate of 3 L min_STP⁻¹ of 30 vol% CO₂ and 70 vol% N₂. The corresponding feed rate of 0.1 molar NaOH was 0.42 L min⁻¹. The pH value at the column outlet was pH 9.05. Because of the double jacket, it was not possible to measure the pH trajectory over the column height. Therefore, the pH trajectory was iteratively solved for the reactor model. The evaluation of the pH over column height could be significantly improved by using 2-tracer laser-induced fluorescence (2T-LIF), as suggested by Hlawitschka et al. [10] for non-invasive pH measurement in reactive bubble columns.

The modelled molar CO₂ flux over column height is shown in Figure 23 for five continuously stirred tanks in cascade (dashed line). The dots indicate the molar CO₂ flow according to the pH in the individual CSTR, as calculated using the CSTR design equation. For reactor modelling, the volume-specific mass transfer area a [m² m⁻³] is calculated from the Sauter mean diameter d₃₂ and dispersed gas holdup (Equation (40)). It was found that a Sauter mean diameter of 9 mm can represent the CO₂ chemisorption in the CSTR cascade approach. This outcome agrees well with visual investigation of slow-motion videos recorded by a high-speed camera. Detailed investigation of bubble size distribution would contribute to the modelling approach.

$$\mathrm{a}=\frac{6·\mathsf{\phi }}{{\mathrm{d}}_{32}}$$

(40)

The result of the iterative solution for the pH trajectory over column height is shown in Figure 24a. A major pH change is located halfway up the TCDC column. The enhancement factor E was evaluated in every single CSTR using Equation (32). Optical view by pH color indicator (Figure 22) agrees with these results. The pH-specific ion species were calculated using the Henderson–Hasselbach equation (Equation (4)) and are shown in Figure 24b.

4. Conclusions

The hydraulic performance of continuous countercurrent gas/liquid flow in a Taylor Couette disc contactor was investigated using a non-reactive air-water test system. The rotor disc design for gas/liquid flow was adjusted to the needs of gas/liquid flow by installing perforated rotor discs. Due to the increasing centrifugal force over increasing rotational speed, the volumetric gas phase holdup decreases with increasing rotational speed. Dispersed gas phase holdup between 2.6% at 700 rpm and 1 L min_STP⁻¹ air and 17.4% at 300 rpm and 3 L min_STP⁻¹ air was obtained. The residence time distribution of continuous countercurrent flow was modelled using a CSTR cascade model. With the active reactor height of 0.87 m and 24 compartments N_CSTR of four to six continuously stirred tanks in series, depending on the flow rate and rotational speed, was deduced from residence time distribution measurements. It was observed that the number of continuously stirred tanks in the cascade increases with increasing rotational speed. This can be explained by the decreasing dispersed phase holdup at higher rotational speed. Characterization of gas/liquid mass transfer was performed by physical absorption of oxygen at steady-state operation. The observed k_La values are in the range between 0.05 s⁻¹ at 25 °C and 1 L min _STP⁻¹ air and 0.2 s⁻¹ at 60 °C and 3 L min_STP⁻¹ of air. The measured hydraulic data were used to model the chemisorption of CO₂ in 0.1 molar sodium hydroxide solution. The outlet pH at steady-state operation was set to nine by NaOH feed adjustment. A gas mixture of 30 vol% CO₂ and 70 vol% N₂ was used for neutralization. The outlet CO₂ concentration on top of the column and the pH at the bottom of the column were continuously monitored. CO₂ conversions in the reactor were found to be almost 100% for the chosen experimental parameters. The neutralization process was modelled according to the film theory, considsering the reactor height as a cascade of ideal continuously stirred tanks. This study presents the characterization of continuous countercurrent gas/liquid contact in a multiphase Taylor-Couette disc contactor with continuous chemisorption of CO₂ in 0.1 molar sodium hydroxide solution. The outcome of the study demonstrates the successful implementation of a continuous gas/liquid reaction system in the column-type Taylor-Couette disc contactor.