Effect of Mass Transport by Convective Flow on the Distribution of Dissolved Carbon Monoxide in a Stirred Tank

Abstract

The dissolved gas concentration in a stirred tank has significant importance in the chemical and biological processing industries as mass transfer from the injected gas to an aqueous solution must occur for the gas to be usable. As the solubility of the gas in the solution is low and there are no probes for measuring dissolved gas concentration, a volumetric mass transfer coefficient is selected as a criterion of design for the scale-up of stirred reactors. However, it is difficult to accurately predict the non-equilibrium state dissolved gas distribution using only the volumetric mass transfer coefficient. In this study, computational fluid dynamics (CFD)-based numerical analysis was conducted to systematically evaluated the effects of mass transport by convective flow on the distribution of dissolved carbon monoxide in a stirred tank. The dissolved carbon monoxide distribution and the volumetric mass transfer coefficient were compared at various rotational speeds of the impellers. At a rotational speed of 900 RPM, the Pearson correlation coefficient was about 0.52, which denotes a moderate correlation. In contrast, Pearson correlation coefficients less than 0.20 were obtained for speeds less than 700 RPM, indicating a weak correlation. By considering the dissolved carbon monoxide transport that occurs during convective flow in stirred tanks, we can provide more accurate information about the dissolved carbon monoxide distribution.

1. Introduction

In the chemical and biological processing industries, absorption/dissolution of a gas in a liquid has been considered as one of the most important reactions in various processes, such as the Fisher–Tropch process, wastewater treatment, and fermentations. In these processes, mass transfer from the gas to the aqueous solution must occur for the target material to be usable. For instance, gaseous carbon monoxide should be dissolved in an aqueous solution while it is converted into liquid hydrocarbon during syngas fermentation. Furthermore, the dissolution of oxygen in an aqueous solution should take place for the oxygen to be available for aerobic microbial growth, during which biomass is produced. For these processes, vessels with mechanical stirring by means of multiple impellers are widely used [1,2].

Over the past few decades, many aspects have been considered to examine the hydrodynamics of stirred tanks. Lee and Dudukovic [3] utilized an optical probe to determine the flow regime of a laboratory-scale stirred tank. Khopkar et al. [4] measured the local gas hold-up in a stirred tank reactor and compared this with CFD simulation results. Tamburini et al. [5] carried out numerical simulations to understand the different fluid flow features of baffled and unbaffled vessels, and Wang et al. [6] discussed gas hold-up and liquid velocity in a stirred tank under varied operating conditions. Although many studies have been conducted to determine the hydrodynamic characteristics in stirred tanks, they have focused on gas–liquid mass transfer, which is affected by these characteristics. The rate of mass transfer has been determined as the product of a volumetric mass transfer coefficient ($k_{\mathrm{L}}a)$ and the difference between the saturation concentration and dissolved concentration of the transferred material in the liquid. The volumetric mass transfer coefficient is a function of the interfacial area ($a$) between a gas and liquid, and the liquid phase mass transfer coefficient ($k_{\mathrm{L}})$ [7].

Many studies have been carried out to experimentally determine the volumetric mass transfer coefficient, such as chemical methods using absorption of carbon dioxide or sulfite oxidation [8], and a dynamic method based on the measurement of dissolved gas concentration with time [2,9]. Several models have been proposed to determine $k_{\mathrm{L}}$ and $a$. Among them, the Higbie penetration model [10] and the Danckwert surface renewal model [11] have been widely accepted for gas-liquid mass transfer description. Computational fluid dynamics (CFD) coupled with the population balance model (PBM) has been introduced to simulate the complex hydrodynamic modeling of bubble distribution in stirred tanks to predict the gas-liquid interfacial area [12].

Because of the low solubility of the gas phase in the aqueous phase, the mass transfer rate usually dominates the overall rate of processes and determines the productivity of the systems. Therefore, the volumetric mass transfer coefficient ($k_{\mathrm{L}}a)$ is selected as a criterion of scale-up and design of the reactors. However, by only considering the $k_{\mathrm{L}}a$, it is difficult to estimate possible dead spots for microbial growth in such a syngas fermentation process. This is because, at all times, the dissolved gas is substantially transported by fluid flow, which means a low volumetric mass transfer coefficient does not directly imply a low dissolved gas concentration [13]. There are few studies showing the distribution of dissolved gas concentration in stirred tanks. Ranganathan and Sivaraman [7] showed the distribution of dissolved oxygen using several different types of mass transfer coefficient model. Nauha et al. [13] found a correlation between the dissolved oxygen concentration in a large-scale bioreactor and the possible dead zone for oxygen transfer.

Although, there have been improvements in detection methods [14] and the development of investigations into hydrodynamic characteristics [15], to the best of our knowledge, there is a lack of systematic studies on the distribution of dissolved gases considering mass transport by convective flow. In this study, the hydrodynamic behavior of dissolved carbon monoxide in a stirred tank was investigated using multi-phase three-dimensional CFD simulations. An investigation of the effect of mass transport by convective flow on dissolved gas concentration was performed by considering mechanisms involving turbulence flow, bubble evolution, and mass transfer from the injected gas to the liquid. The volumetric mass transfer coefficient was calculated with a theoretical model based on Higbie’s penetration theory, and its correlation with dissolved gas concentration was examined using the Pearson correlation coefficient as a representative value.

2. Model Description and Methods

2.1. Eulerian Multiphase Modelling

In this study, a three-dimensional Eulerian-Eulerian model was adopted to describe the fluid flows. The equations for conservation of mass and momentum were solved for each phase as follows:

$$\frac{\partial }{\partial t}\left({\alpha }_i{\rho }_i\right)+\nabla ·\left({\alpha }_i{\rho }_i{\overrightarrow{u}}_i\right)=0$$

(1)

$$\frac{\partial }{\partial t}\left({\alpha }_i{\rho }_i{\overrightarrow{u}}_i\right)+\nabla ·\left({\alpha }_i{\rho }_i{\overrightarrow{u}}_i{\overrightarrow{u}}_i\right)=-{\alpha }_i\nabla P+\nabla ·\left({\mu }_{ i}{\alpha }_i\left[\left(\nabla {\overrightarrow{u}}_i+\nabla {\overrightarrow{u}}_i{}^T\right)-\frac{2}{3}\nabla ·{\overrightarrow{u}}_i\right]\right)+\overrightarrow{F_I}+{\alpha }_i{\rho }_i\overrightarrow{g}$$

(2)

where ${\alpha }_i$, ${\rho }_i$, $u_i$, $g$, ${\mu }_{ i}$, $P$, and $F_I$ are the volume fraction, density, velocity, gravity acceleration, molecular viscosity, pressure, and interfacial momentum exchange term, respectively. Three interfacial forces, referred to as the drag, virtual mass, and lift force were considered in the interfacial momentum exchange term. The drag force was accounted for using the Schiller–Naumann drag model [16,17,18,19], whereas the virtual mass and lift force was accounted for using a virtual mass coefficient of 0.5 and a lift coefficient with the Legendre–Magnaudet model [20].

2.2. Turbulence Modeling

The k$–\epsilon$ model was utilized to depict turbulence flow as previous investigations [21,22,23] have confirmed that it is appropriate for describing gas-liquid hydrodynamic characteristics and is not computationally intensive. As the volume fraction of the secondary phase (gas phase) is dilute in the stirred tank, the dispersed k$–\epsilon$ turbulence model was used here. In this dispersed k$–\epsilon$ model, the turbulence quantities for the dispersed phase (gas phase) are not obtained from the transport equations. Even though the turbulence quantities for dispersed phase were significant only around the impellers, their effect on the predicted results is quantitatively negligible [4]. Therefore, the governing equations to solve k and $\epsilon$ transport equations were used only for the continuous liquid phase.

Among three different k$–\epsilon$ models (i.e., the standard, RNG, and realizable model), the realizable k–ε model was utilized as follows [24]:

$$\frac{\partial }{\partial t}\left({\rho }_{l}k\right)+\nabla ·\left({\rho }_l{\overrightarrow{u}}_{l}k\right)=\nabla \left(\mu +\frac{{\mu }_{t,l}}{{\sigma }_k}\nabla k\right)+{\mu }_{t,l}{S}^2-{\rho }_l\epsilon$$

(3)

$$\frac{\partial }{\partial t}\left({\rho }_l\epsilon \right)+\nabla ·\left({\rho }_l{\overrightarrow{u}}_l\epsilon \right)=\nabla \left(\mu +\frac{{\mu }_{t,l}}{{\sigma }_{\epsilon }}\nabla \epsilon \right)+{\rho }_l{C}_{1}S\epsilon -C_2\frac{{\rho }_l{\epsilon }^2}{k+\sqrt{\nu \epsilon }}$$

(4)

where

$${\mu }_{t,l}={\rho }_l{C}_{\mu }\frac{k^2}{\epsilon }$$

(5)

$$S=\sqrt{2S_{mn}{S}_{mn}}$$

(6)

$$S_{mn}=\frac{1}{2}\left(\frac{\partial u_m}{\partial x_n}+\frac{\partial u_n}{\partial x_m}\right)$$

(7)

$$C_1=\max \left[0.43,\frac{\eta }{\eta +5}\right]$$

(8)

$$\eta =S\frac{k}{\epsilon }$$

(9)

The difference between the realizable k$–\epsilon$ model and the other, standard and RNG k$–\epsilon$, models, is that $C_{\mu }$, which is used for obtaining the turbulence viscosity, is a function dependent on the mean strain, rotation, and turbulence flows rather than a constant [25].

2.3. Bubble Population Balance Model (PBM)

The size of the bubbles distributed in the reactor varies depending on the location. This inhomogeneity is the key reason why the population balance model should be applied to describe the system.

Let $n\left(V,t\right)$ represent the number density of bubbles of volume V at time t. The population balance equation is:

$$\frac{\partial }{\partial t}\left[n\left(V,t\right)\right]+\nabla ·\left[\overrightarrow{u_g}n\left(V,t\right)\right]=B_{ag}-D_{ag}+B_{br}-D_{br}$$

(10)

where $D_{ag}$, $B_{ag}$ and $D_{br}$, $B_{br}$ are the death, birth rate of bubbles by reason of aggregation and death, birth rate of bubbles by reason of breakage, respectively. These rates can be expressed as:

$$B_{ag}=\frac{1}{2}{{\displaystyle \int }}_0^{V_p}Q\left(V_p-V_q,V_q\right)n\left(V_p-V_q,t\right)n\left(V_q,t\right)d{V}_q$$

(11)

$$D_{ag}={{\displaystyle \int }}_0^{\infty }Q\left(V_p,V_q\right)n\left(V_p,t\right)n\left(V_q,t\right)d{V}_q$$

(12)

$$B_{br}={{\displaystyle \int }}_{V_p}^{\infty }g\left(V_p,V_q\right)n\left(V_q,t\right)d{V}_q$$

(13)

$$D_{br}=n\left(V_p,t\right)\frac{1}{2}{{\displaystyle \int }}_0^{V_p}g\left(V_p,V_q\right)d{V}_q$$

(14)

where $Q\left(V_p,V_q\right)$ is the specific aggregation rate and $g\left(V_p,V_q\right)$ is the specific breakage rate. In this study, the Luo and Svendsen model [26] was adopted to express the specific breakage rate as:

$$g\left(V_p,V_q\right)=0.9238\left(1-{\alpha }_g\right){\left(\frac{\epsilon }{d_p^2}\right)}^{\frac{1}{3}}{{\displaystyle \int }}_{{\xi }_{min} }^1\frac{{\left(1+\xi \right)}^2}{{\xi }^{11/3}}\exp \left(-\frac{12\left(f^{\frac{2}{3}}+{\left(1-f\right)}^{\frac{2}{3}}-1\right)\sigma }{\beta {\rho }_l{\epsilon }^{\frac{2}{3}}{d}_p{ }^{\frac{5}{3}}{\xi }^{\frac{11}{3}}}\right)d\xi$$

(15)

This model considers the integral over the size of eddies $\mathsf{\lambda }$ hitting the bubble with a diameter of $d$. $\xi$ is the dimensionless size of eddies $\xi =\mathsf{\lambda }/d_p$. $f=V_q/V_p$, ${\alpha }_g$, $\sigma$, and $\beta =$ 2.047 are the size fractions of the bubbles, gas volume fraction, interfacial tension, and constant, respectively.

The general aggregation kernel, using the Luo aggregation model [26], is defined as the formation rate of a particle in consequence of the collision of two particles having a volume of $V_p$ and $V_q$ each:

$$Q\left(V_p,V_q\right)=\omega \left(V_p,V_q\right)P\left(V_p,V_q\right)$$

(16)

$$\omega \left(V_p,V_q\right)=\frac{\pi }{4}{\left(d_p+d_q\right)}^2{n}_p{n}_q{\overline{u}}_{pq}$$

(17)

$$P\left(V_p,V_q\right)=\exp \left(-c_1\frac{{\left[0.75\left(1+x_{pq}^2\right)\left(1+x_{pq}^3\right)\right]}^{\frac{1}{2}}}{{\left(\frac{{\rho }_l}{{\rho }_g}+0.5\right)}^{\frac{1}{2}}{\left(1+x_{pq}\right)}^3}W{e}_{pq}^{0.5} \right)$$

(18)

where $\omega \left(V_p,V_q\right)$ is the frequency of collision and $P\left(V_p,V_q\right)$ is the probability that the collision results in coalescence. ${\overline{u}}_{pq}$ is the characteristic velocity of collision of two bubbles with diameters $d_p$ and $d_q$ and number density $n_p$ and $n_q$, respectively.

$${\overline{u}}_{pq}={\left({\overline{u}}_p^2+{\overline{u}}_q^2\right)}^{0.5}$$

(19)

$${\overline{u}}_p=1.43{\left(\epsilon d_p\right)}^{1/3}$$

(20)

$c_1$ is a constant of order unity, $x_{pq}=d_p/d_q$, and the Weber number is defined as follows:

$$W{e}_{pq}=\frac{{\rho }_l{d}_p{\left({\overline{u}}_{pq}\right)}^2}{\sigma }$$

(21)

2.4. Mass Transfer Model

For the mass transfer, the two-resistance model based on the two-film theory was utilized [27], Mass transport equations were solved as follows:

$$\frac{\partial }{\partial t}\left({\alpha }_i{\rho }_i{Y}_i\right)+\nabla ·\left({\alpha }_i{\rho }_i{\overrightarrow{u}}_i{Y}_i\right)=-\nabla ·\left({\alpha }_i{\overrightarrow{J}}_i\right)+\dot{m}$$

(22)

where $Y_i$ is the local mass fraction of species i, and ${\overrightarrow{J}}_i$ is the flux due to molecular diffusion. The gas–liquid mass transfer rate $\dot{m}$ was determined by:

$$\dot{m}=k_{L}a\left[\left({\varphi }_l{}^{*}\right)-\left({\varphi }_l\right)\right]$$

(23)

where ${\varphi }_l$, and ${\varphi }_l{}^{*}$ are the concentration of gas in the liquid phase, and saturation concentration of gas in the liquid phase, which is calculated according to Henry’s law, respectively. In this equation, $k_L$ and $a$ are determined as:

$$k_L=2\sqrt{\frac{D_L}{\pi }}{\left(\frac{\epsilon }{v}\right)}^{0.25}$$

(24)

$$a=6{\alpha }_g/d_B$$

(25)

where $D_L$ is the diffusion coefficient, $\epsilon$ is the turbulent dissipation rate, $v$ is the kinematic viscosity of liquid, and $d_B$ is the Sauter bubble mean diameter.

The model for $k_L$ is based on Higbie’s penetration theory which is frequently used in numerical simulations of bubbly flows [28,29]. The specific interfacial area $\left(a\right)$ is determined using the Sauter mean diameter known from the population balance model [7].

3. Simulation Configuration

In this study, all the simulations were carried out using CFD software ANSYS Fluent-19.0. The details of the tank configurations corresponding to the computational domain is shown in Figure 1.

Around 350,000 total computational nodes were created to ensure grid independency. The fluid motion produced by the stirring was modeled with the multiple reference frame model, a widely used method for simulating the fluid flows of stirred tank reactors [7,30]. The inlet boundary condition was specified as an inlet velocity of 0.1 m/s for bubbles located along the circumference of a round shape sparger of 0.01 m diameter. A total of 11 groups of bubbles with diameters from 0.3 to 9.6 mm were taken into account. The diameters of each of the 11 groups were 0.3, 0.4, 0.6, 0.8, 1.2, 1.6, 2.4, 3.3, 4.8, 6.7, and 9.6 mm, respectively. The bubble group with diameter 2.4 mm was set for inlet size. In this study, carbon monoxide was used as an inlet gas. Therefore, the diffusion coefficient for the liquid phase carbon monoxide was used as 2.03 $\times$ 10⁻⁹ m²s⁻¹ [31]. The saturation concentration of the dissolved carbon monoxide was calculated by Henry’s law:

$${\varphi }_l{}^{*}=y_g{P}_g/K_H$$

(26)

where $y_g$, $P_g$, and $K_H$ are the molar fraction of carbon monoxide in the gas phase, total pressure of the gas phase, and Henry’s constant, respectively. Henry’s constant was determined by the Van’t Hoff correlation:

$$K_H=K_H^0\exp \left(-\frac{{∆}_{soln}H}{R}\left(\frac{1}{T}-\frac{1}{T_{ref}}\right)\right)$$

(27)

where ${∆}_{soln}H$ is the enthalpy of the solution and $K_H^0$ is Henry’s constant at the reference temperature, $T_{ref}$. The values 9.5 $\times$ 10⁻⁴ M/atm and 1300 K were used for $K_H^0$ and $T_{ref}$, respectively for carbon monoxide in water at 298.15 K [32]. For the other conditions, the tank walls were set as no-slip conditions. The tank was filled with water and the top free surface was defined to have a degassing boundary condition which allows the gas phase to escape but not the liquid phase

The second-order upwind spatial discretization was applied for convection terms in equations for the turbulent kinetic energy, turbulence dissipation rate, momentum, volume fraction, and pressure. A pressure-velocity-coupled algorithm was used to solve the equations of momentum and continuity [24]. The convergence criteria used in all the simulations was 10⁻⁴.

4. Results and Discussion

Figure 2a shows the predicted liquid velocity profile in the y = 0 m plane at a rotational speed of 500 RPM and an inlet velocity of 0.1 m/s. The loop circulation is generated in the region below the bottom impeller, which is consistent with previous observations [17]. Figure 2b shows the contour of the gas hold-up distribution. Bubbles mostly accumulate near the shaft and the impellers. Near the impellers, the bubbles move slightly to the radial direction as the impeller rotates. Although a number of bubbles are observed just above the sparger owing to the gas injection, there are only a few bubbles far away from the sparger in the region below the bottom impeller. Figure 2c shows the distribution of the dissolved carbon monoxide concentration. Although the gas hold-up is extremely low in the bottom region near the tank wall, a high concentration of dissolved carbon monoxide is observed in the entire region below the bottom impeller. The volume averaged gas hold-up and dissolved carbon monoxide concentration in each region (i.e., above the upper impeller, between two impellers and below the bottom impeller) are shown in Figure 2d,e. The gas hold-up in the region below the bottom impeller is approximately 20% lower than that above the upper impeller, while the volume-averaged dissolved carbon monoxide concentration in the region below the bottom impeller is approximately 70% higher than that above the upper impeller.

Figure 3a shows the axial distribution of the turbulent dissipation rate at x = 0.03 m with a rotational speed of 500 RPM and an inlet velocity of 0.1 m/s. Note that x is the radial distance away from a center point of the stirred tank. A high turbulent dissipation rate is observed near the impellers. The turbulent dissipation rate at the tip of the impellers is about 10 times higher than those at other regions. Figure 3b shows the axial distribution of the gas hold-up which was high around impellers as the bubbles were dispersed from the shaft, where bubbles were continuously supplied from inlet sparger, by the impellers. Figure 3c shows the axial distribution of the volumetric mass transfer coefficient that was calculated with the turbulent dissipation rate and the gas hold-up. Figure 3d shows the axial distribution of the dissolved carbon monoxide concentration at x = 0.03 m. Although the volumetric mass transfer coefficient is extremely low, except near the impellers, dissolved carbon monoxide still accumulates in this region. As the density of dissolved carbon monoxide is comparable with that of the liquid, the dissolved gas near the impellers was transported by the convective flow generated in a radial direction at the tip of the impellers and downward near the tank wall.

The simulations were also conducted with various rotational speeds of the impellers. As shown in Figure 4a,b, with a rotational speed of 300 RPM and an inlet velocity of 0.1 m/s, both a high volumetric mass transfer coefficient and a high concentration of dissolved carbon monoxide are observed near the shaft and the impellers, similar to the case with a rotational speed of 500 RPM. In Figure 4b, the dissolved carbon monoxide concentration in the region below the bottom impeller is about two times higher than that in the region above the upper impeller. Figure 4c shows the axial distribution and volumetric mass transfer coefficient profiles with a rotation speed of 900 RPM and an inlet velocity of 0.1 m/s. Unlike in the case with a rotational speed of 300 RPM, the volumetric mass transfer coefficient is high in the region above the upper impeller due to the wide dispersion of bubbles in the radial direction by convective flow. From Figure 4d, it can also be seen that the dissolved carbon monoxide concentration in the region above the upper impeller is higher than that in the region below the bottom of the impeller because the high mass transfer rate is affected by the high turbulent dissipation rate and high gas hold-up in the region above the upper impeller.

Figure 5a shows the axial distribution of the turbulent dissipation rate at x = 0.03 m with rotational speeds of 300 and 900 RPM. The turbulent dissipation rate at peak points near the impeller with a rotational speed of 900 RPM is about 40 times higher than that with a rotational speed of 300 RPM. The high turbulent dissipation rate leads to a rapid increase in the number density of bubbles due to the breakage of bubbles as shown in Figure 5b. The gas hold-up at 900 RPM is higher and more widely dispersed than that at 300 RPM in the upper region (A) as shown in Figure 5c. The high gas hold-up near the impeller can be verified by previous experimental data that depicted the axial distribution of the gas hold-up at different rotational speeds [33].

The Pearson correlation coefficient ($r$) was used to obtain the linear relationship between the volumetric mass transfer coefficient and the dissolved carbon monoxide concentration [34,35]. Figure 5d shows the calculated Pearson correlation coefficient on the y = 0 m plane at various rotational speeds. The Pearson correlation coefficient takes a range of values from $-$1 to +1. The closer the Pearson correlation coefficient is to +1 or $-$1, the higher the positive or negative linear correlation. The Pearson correlation coefficient was determined as follows [35]:

$$r=\frac{{{\displaystyle \sum }}_{i=1}^n\left[\left(x_i-\overline{x}\right)·\left(y_i-\overline{y}\right)\right]}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-\overline{x}\right)}^2}·\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(28)

Here, the variables $x_i$ and $y_i$ relate to the volumetric mass transfer coefficient and the dissolved carbon monoxide concentration, respectively. $\overline{x}$ and $\overline{y}$ denote the means of the two variables, and $n$ is the sample number. Evans [36] stated that $r\le$ 0.39 represents a weak correlation, $r$ between 0.40 to 0.69 represents a moderate correlation, $r$ between 0.70 to 1 represents a strong or high correlation, and $r\ge$ 0.9 represents a very high correlation [35,37]. As the rotational speeds of the impellers increase, the Pearson correlation coefficient also increases. It can be seen that when the rotational speed of the impellers is 900 RPM, the Pearson correlation coefficient is approximately 0.52, indicating a moderate correlation between the volumetric mass transfer coefficient and the dissolved carbon monoxide concentration. On the other hand, in the cases of rotational speeds under approximately 700 RPM, a Pearson correlation coefficient less than 0.20 is obtained, indicating a weak correlation.

5. Validation

5.1. Validation of Grid Independence

For the CFD simulations, we checked grid independence by calculating skewness of mesh elements and the velocity of the fluid flow. Figure 6 shows the normalized liquid velocity with different grid size at 500 RPM and an inlet velocity of 0.1 m/s. $u_l$ is the velocity of the liquid phase, $u_{l, tip}$ is the velocity of the liquid phase at the tip of the impeller, and $H$ is the height of the tank, respectively. When the number of mesh elements increased from 353,020 to 488,239, the change in the average velocity of the fluid flow at x = 0.03 m was less than 3%. The results with medium and dense meshes were similar, hence the grid independence was achieved with the number of mesh elements of 353,020 as shown in

Table 1. The average velocity of the fluid flow and the average skewness depending on the number of mesh elements.

Numbers of Mesh Elements	Average Velocity (m/s)	Average Skewness
488,239	0.117	0.227
353,020 (This work)	0.120	0.228
107,173	0.135	0.244

.

5.2. Validation of Drag Models

For the simulations, the Schiller–Naumann and Brucato drag models were considered. Both drag models are acceptable for general use in gas-liquid bioreactors [17,18,19]. As shown in Figure 7, the highest gas hold-up was observed near the impellers in both drag models. This is because of the gas accumulation in the recirculating flow region formed near the impellers. The lowest gas hold-up was observed in the bottom of the tank under the lower impeller since the rise of the bubbles by the buoyancy forces overcomes the recirculation flow of the fluid. These trends were comparable to the experimental data [38], except in the upper part close to the free surface of the reactor. The difference in gas-holdup can be attributed to the difference in scale of the actual reactors used in the experiment and the simulation. Although the gassing rates per unit volume were similar, the volume of the reactor used in the experiment was about hundred times larger than the volume of the reactor used in the simulation. Intuitively, as the scale of the reactor increases, the gas-holdup may increase due to the increase in the travel distance and residence time of the bubbles. This can be seen in the results of a study [39] which compared the gas hold-up distribution in stirred tank reactors with the same configurations but different scales. Additionally, a mismatch of gas hold-up in the upper part of the reactor has been reported previously [17]. In this study, we used the Schiller–Naumann drag model because of its simplicity and as it is less time-consuming than the Brucato drag model, while maintaining the equivalent gas distribution trends [40].

6. Conclusions

In this study, the distribution of dissolved carbon monoxide at various rotational speeds of the impellers was investigated. Owing to the mass transport that occurs during convective flow, a mismatch between the distribution of a volumetric mass transfer coefficient and dissolved carbon monoxide was observed. The trends of change in the distribution of the gas hold-up derived from the simulations were comparable to previous experiments. The distribution between local dissolved carbon monoxide concentration and the volumetric mass transfer coefficient were more similar at 900 RPM than at values less than 700 RPM. For further comparison, the Pearson’s correlation coefficient was calculated. At 900 RPM, the Pearson’s correlation coefficient was about 0.52, which denotes a moderate correlation. In contrast, a Pearson correlation coefficient less than 0.20 was obtained for rotational speeds less than 700 RPM, indicating a weak correlation. These results suggest that optimization of the reactor design and improvement in productivity are possible by examining how the substrates are distributed under the influence of convective flow, rather than by modifying the part in the reactor where the mass transfer coefficient is expected to be low. Future studies should focus on investigation of the dissolved gas concentration under more varied operating conditions in order to have the strongest Pearson’s correlation and highest efficiency for dissolving gas in a stirred tank. In addition, using other base fluids with syngas fermentation modeling can enable application to a specific biochemical field.