# Investigation and Modeling of Gas-Liquid Mass Transfer in a Sparged and Non-Sparged Continuous Stirred Tank Reactor with Potential Application in Syngas Fermentation

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## Abstract

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_{2}and CO

_{2}) fermentation suffers from mass transfer limitation due to low solubility of CO and H

_{2}in the liquid medium. Therefore, it is critical to characterize the mass transfer in syngas fermentation reactors to guide in delivery of syngas to the microorganisms. The objective of this study is to measure and predict the overall volumetric mass transfer coefficient, k

_{L}a for O

_{2}at various operating conditions in a 7-L sparged and non-sparged continuous stirred-tank reactor (CSTR). Measurements indicated that the k

_{L}a for O

_{2}increased with an increase in air flow rate and agitation speed. However, k

_{L}a for O

_{2}decreased with the increase in the headspace pressure. The highest k

_{L}a for O

_{2}with air sparged in the CSTR was 116 h

^{−1}at 600 sccm, 900 rpm, 101 kPa, and 3 L working volume. Backmixing of the headspace N

_{2}in the sparged CSTR reduced the observed k

_{L}a. The mass transfer model predicted the k

_{L}a for O

_{2}within 10% of the experimental values. The model was extended to predict the k

_{L}a for syngas components CO, CO

_{2}and H

_{2}, which will guide in selecting operating conditions that minimize power input to the bioreactor and maximize the syngas conversion efficiency.

## 1. Introduction

_{2}and CO

_{2}) regardless of biomass composition and origin, followed by fermentation of syngas to biofuel [4]. Based on a process simulation model, the hybrid process has the potential to produce biofuels with higher yield from same amount of biomass compared to biochemical platform [5]. This process can achieve 440 L ethanol/Mg biomass compared to 340 L ethanol/Mg biomass in the biochemical platform due to utilization of all components of the biomass, including lignin, to make ethanol [6].

_{2}in the liquid medium [11]. Mass transfer limitations occur when cells have the capacity to process more gas than the bioreactor can supply. The resistance of gaseous substrate diffusion at the gas-liquid interface was recognized as the limiting step in syngas fermentation [12,13]. Gaseous substrate mass transfer limitation results in low cell concentration and low productivity, making the process not economically feasible [14]. Therefore, it is necessary to characterize and model the mass transfer in the bioreactor used for syngas fermentation to understand how to overcome mass transfer limitation of the gaseous substrates, CO and H

_{2}. In addition, modeling improves understanding of the process behavior and assists in bioreactor design, process control and optimization of operating conditions to maximize productivity and reduce costs to meet the requirements for commercial fermentation [5].

_{L}a) than the CSTR. Besides, the effect of internal pressure and gas/liquid interface area on the CO mass transfer rate in an HFR was investigated and an increase in CO mass transfer rate was observed [20]. Another study reported that for syngas fermentation in an external HFR, the membrane surface area was found to be the most significant factor in the enhancement of CO mass transfer rates [21].

_{L}a of CO and H

_{2}in a HFR had also been developed [22]. However, when considered for syngas fermentation, each reactor has its own advantages and disadvantages in terms of operation and scale up [15]. The CSTR, as a conventional reactor, has been more extensively studied and applied in industrial fermentation processes than the HFR and TBR [11,15]. In addition, the CSTR operation is simpler than other types of reactors and can provide good mixing capability and high mass transfer rates, but requires high power consumption, which becomes an issue for large reactors due to high power cost. Moreover, the HFR operation can suffer from membrane fouling, and the pump for liquid recirculation requires external power input [15,23,24]. The TBR increases gas and liquid contact by forming a thin liquid film on the packing; however, an external pump is required to circulate the liquid to the TBR [15,17]. Issues related to scale up and operation parameters of various bioreactors for syngas fermentation have been recently addressed [13,15,25,26,27].

_{2}mass transfer rate in a stirred bioreactor was studied and a correlation has been presented [30,31]. CO and H

_{2}solubility and the driving force for mass transfer increase with elevated CO and H

_{2}partial pressures in the headspace [12]. The incorporation of various liquid working volumes and pressures will provide a more accurate description of mass transfer characteristics of the CSTR for syngas fermentation. For large-scale syngas fermentation, the headspace pressure, gas flow rate, the power consumption, and reactor working volume are critical parameters for estimating the feasibility of fermentation process. The incorporation of these parameters into one model will help determine the operational parameters and meet the microbial kinetics requirement for syngas fermentation. No such models have been reported in the literature. In addition, backmixing of syngas components (CO and H

_{2}) from the headspace into the fermentation medium can increase the gas substrate’s retention time and improve gas conversion efficiency. The increase in the headspace pressure in the bioreactor at high agitation can increase the headspace gas backmixing. However, no reports were found on the effect of headspace gas backmixing on mass transfer for syngas fermentation reactors.

_{L}a for O

_{2}in an air-water system at various gas flow rates, headspace pressures, agitation speeds, and working volumes using a 7-L CSTR. In addition, the effect of backmixing of headspace gas on k

_{L}a was studied in non-sparged and sparged conditions. Moreover, a correlation of k

_{L}a with power consumption and gas flow rate was developed. Finally, the k

_{L}a for syngas components CO, CO

_{2}and H

_{2}were estimated from k

_{L}a for O

_{2}based on the penetration or surface renewal theory [33,34].

## 2. Materials and Methods

#### 2.1. CSTR Configuration and Operating Conditions

_{2}or air (UHP/Zero grade, Stillwater Steel Co., Stillwater, OK, USA) was fed to the CSTR using a microsparger with 10–15 µm pore size (New Brunswick Scientific Co.). The inlet N

_{2}and air flow rates were controlled by two separate thermal mass flow controllers (MFC) (Burkert, Charlotte, NC, USA). Two 0.2 µm pore size gas filters (New Brunswick Scientific Co.) were used in the inlet and outlet gas lines. The CSTR temperature was controlled at 37 °C by a water heating jacket. A dissolved oxygen (DO) probe (InPro 6830, Mettler Toledo, Columbus, OH, USA) was used to measure % DO saturation.

_{2}was then sparged into the CSTR at 1000 sccm (standard cubic centimeters per minute, 20 °C and 101 kPa) to remove dissolved O

_{2}from the DI water with the agitation speed set at 900 rpm and headspace pressure of 101 kPa. The high N

_{2}flow rate and agitation speed were used to shorten the O

_{2}stripping time. Three headspace pressures (101, 150 and 240 kPa) were studied. When % DO in the DI water was less than 0.2%, the headspace pressure was set at the desired pressure using a backpressure regulator. Then, N

_{2}flow rate and agitation speed were adjusted to the desired conditions. When the headspace pressure was stable at the required set point, N

_{2}flow was stopped and air flow was started at the desired flow rate. Three air flow rates of 90, 150, and 600 sccm were tested. The agitation speeds examined were 150, 300, 450, 600, 750, and 900 rpm. The DO probe was calibrated at each tested pressure to 100% DO by saturating the DI water with sparging air at 1000 sccm and 900 rpm. This eliminates the differences in the saturated % DO at various headspace pressures. The % DO values did not exceed 100% saturation. The changes in the % DO in the DI water during aeration were recorded every 12 s by the Biocommand software (New Brunswick Scientific Co.) for the estimation of k

_{L}a. When the % DO in the water reached saturation, air flow was stopped. Experiments were performed in duplicates.

_{L}a in a non-sparged and sparged CSTR was also examined. Backmixing experiments started by first calibrating the DO probe as mentioned earlier. The O

_{2}in the DI water in the bioreactor was stripped by flowing 1000 sccm N

_{2}at 101 kPa until the % DO was near 0%. Then, N

_{2}flow and agitation were stopped. To replace the N

_{2}in the CSTR headspace, the headspace was flushed with air at 1000 sccm for 2 min at 101 kPa by inserting a needle into the headplate septum as shown in Figure 2. After 2 min, the pressure inside the CSTR was set at the test value of 101, 150 or 240 kPa by closing the backpressure regulator valve. Two agitation speeds (150 and 900 rpm) and two working volumes (3 and 5.6 L) were examined in the non-sparged CSTR. Agitation was started immediately when the headspace pressure reached the required value. During the backmixing experiment with non-sparged CSTR, no air was sparged in the DI water and the CSTR exhaust was completely closed by the backpressure regulator valve (Figure 2). The backmixing experiment with the sparged CSTR was performed with the 3 L working volume and air sparged in the DI water at 600 sccm and 900 rpm. The backpressure regulator valve was adjusted to keep the pressure in the headspace at the desired value.

#### 2.2. Calculations

#### 2.2.1. Overall Volumetric Mass Transfer Coefficient

_{L}a, was estimated by the following equation [15,32]:

_{L}is liquid film mass transfer coefficient (m h

^{−1}), a is gas-liquid interfacial area per unit volume (a=A/V

_{L}) (m

^{−1}), A is the mass transfer area (m

^{2}), V

_{L}is the liquid working volume in the CSTR (m

^{3}), k

_{L}a is overall volumetric mass transfer coefficient (h

^{−1}), C

_{S}is the saturated DO concentration in the liquid (mol m

^{−3}), C

_{L}is the DO concentration in the bulk liquid (mol m

^{−3}), and t is time (h). C

_{L}/C

_{S}is replaced by % DO/100 [15]. For calculating the k

_{L}a in non-sparged CSTR at various pressures, C

_{S}in Equation (1) was replaced by equilibrium saturated % DO at the examined pressure. The k

_{L}a value for O

_{2}was estimated from the linear slope of ln(1- C

_{L}/C

_{S}) versus t when % DO was between 20% and 80% of saturation level.

#### 2.2.2. Volumetric Flow Rate at Various Headspace Pressures

_{a}is air density at 20 °C (kg m

^{−3}), M

_{a}is air molecular weight (g mol

^{−1}), V

_{NIST}is air flow rate (m

^{3}min

^{−1}) at standard National Institute of Science and Technology (NIST) conditions (20 °C, 101.3 kPa) set using the thermal mass flow controller (MFC), n

_{a}is air molar flow rate from MFC (mol min

^{−1}), P

_{HP}is the hydraulic pressure above the microsparger (kPa), ρ

_{w}is water density (kg m

^{−3}), g is gravitational acceleration (m s

^{−2}), h is the distance between the microsparger and liquid surface (m), P

_{HS}is the headspace pressure (kPa), P

_{total}is the total pressure in the CSTR (kPa), Q

_{g}is the air volumetric flow rate (mL min

^{−1}), R is the ideal gas constant (L kPa mol

^{−1}K

^{−1}), T

_{310K}is the temperature used (310 K).

#### 2.2.3. Power Consumption

_{p}) of a single six-blade Rushton impeller was reported to be 5.5 [35]. Thus, the calculated power number for the marine impeller of 2.2 was chosen. The power consumption of all impellers above a microsparger was calculated using Equations (6) to (10) as suggested [35]

_{A}is aeration number (dimensionless), N

_{Fr}is Froude number (dimensionless), Q

_{g}is the air volumetric flow rate (mL min

^{−1}), g is gravity acceleration (m·s

^{−2}), P

_{u}is the ungassed power consumption of a single impeller (W), N

_{p}is power number of a single Rushton impeller or marine impeller (dimensionless), N is the impeller rotational speed (s

^{−1}), D is the diameter of impeller (m), P

_{g,lower}is gassed power consumption of the single impeller mounted directly above the microsparger (W), µ is water dynamic viscosity (Pa·s), P

_{g,upper}is the power consumption of upper impellers not mounted directly above the gas sparger (W), A = 5.3 exp[−5.4(D/T)]; B = 0.47(D/T)

^{1.3}; C = 0.64−1.1(D/T); E = 0.25. D is the impeller diameter (m) and T is the tank diameter (m).

_{g}, is the additive power consumption from all impellers mounted on the shaft. For the 3 L working volume, P

_{g}equals to the power consumption of one Rushton impeller directly above the microsparger calculated using Equation (9) plus the power consumption of the second Rushton impeller calculated using Equation (10). However, for the 5.6 L working volume, the total power consumption, P

_{g}, equals the power consumed by one Rushton impeller directly above the microsparger calculated using Equation (9) plus the power consumed by the second Rushton and third marine impellers calculated using Equation (10).

#### 2.2.4. Mass Transfer Model of a 7-L CSTR

_{L}a, at different operating parameters. However, the most used correlation for k

_{L}a is expressed in terms of power input per unit volume and superficial gas velocity [32,35,37,38]. The overall volumetric mass transfer coefficient typically follows the model below [35]:

_{g}is the total impeller power consumption under gassed condition (W), α, β and c are model parameters, V

_{L}is the liquid working volume (m

^{3}), v

_{g}is superficial gas velocity (m s

^{−1}). The model parameters α, β and c in Equation (11) were estimated based on the volumetric flow rates at 37 °C, agitation speeds, and working volumes used in the present study. The least square approach and SOLVER function in EXCEL (Microsoft, Redmond, WA, USA) were used to estimate the model parameters α, β and c.

_{L}a for CO, CO

_{2}and H

_{2}, were calculated from the measured k

_{L}a for O

_{2}using the penetration or surface renewal theory based on their diffusivities in the fermentation broth. The k

_{L}a for gas species i can be calculated from k

_{L}a for gas species j, using the following equation [33,34]:

_{i}and D

_{j}are the diffusivities of gas species i and j (O

_{2}). In water, the diffusivities of CO, CO

_{2}and H

_{2}were 107%, 90%, and 212%, respectively, of the O

_{2}diffusivity at 37 °C [15]. Thus, the ratios of (k

_{L}a)

_{i}/(k

_{L}a)

_{O2}for CO, CO

_{2}and H

_{2}based on their diffusivities are 1.03, 0.95 and 1.46, respectively.

#### 2.2.5. Statistical Analysis

_{L}a for O

_{2}between when the headspace was flushed with air for 2 and 12 min in the non-sparged CSTR during the backmixing experiment at 95% confidence level. Also, the statistical differences of the k

_{L}a for O

_{2}in the backmixing study in the sparged CSTR with and without air flushing of the headspace were also determined by T-TEST procedure using SAS.

## 3. Results and Discussion

#### 3.1. Effect of Agitation Speed, Pressure and Gas Flow Rate on k_{L}a

_{L}a for O

_{2}with the 3 L and 5.6 L working volumes in the air-water system are shown in Figure 3. The k

_{L}a for O

_{2}increased as agitation speed increased at fixed air flow rate, headspace pressure and working volume. Also, the mass transfer of O

_{2}into the DI water was improved with increasing air flow rate. The highest measured k

_{L}a for O

_{2}was 116.2 h

^{−1}at 600 sccm, 900 rpm and 101 kPa with 3 L working volume (Figure 3). The measured k

_{L}a values for O

_{2}in 3 L working volume were generally 6% to 50% higher than with 5.6 L working volume at similar standard air flow rates, headspace pressures and all agitation speeds except at 900 rpm. At 900 rpm, the measured k

_{L}a for O

_{2}was generally 10% to 50% lower in the 3 L working volume than in the 5.6 L working volume at headspace pressures of 150 and 240 kPa and flow rates 90 and 150 sccm. The decrease in the measured k

_{L}a for O

_{2}at these conditions was due to the backmixing of N

_{2}and O

_{2}depleted air from the headspace into the water.

_{2}in the fermentation medium. Mass transfer can be increased by increasing the agitation speed and gas flow rate. In addition, the increase in headspace pressure improves molar mass transfer by increasing the driving force. Thus, it is important to determine the effect of headspace pressure on k

_{L}a in sparged and non-sparged CSTRs to guide in reactor operation. The k

_{L}a for O

_{2}was the highest at the lowest headspace pressure of 101 kPa compared to 150 and 240 kPa at the same agitation speed, working volume and standard air flow rate in sccm. This decrease in k

_{L}a is caused by lower volumetric gas flow at higher pressure. Estimated air flow rates at 37 °C and headspace pressures of 150 and 240 kPa were 32% and 57%, respectively, lower than at 101 kPa. Thus, the actual volumetric gas flow rate that results from elevated headspace pressure should be considered in k

_{L}a estimation. The hydraulic head above the microsparger should also be considered in the estimation of k

_{L}a values in large fermentor. The decrease in volumetric air flow rate reduces the air superficial velocity, vg (m s

^{−1}), as calculated from Equation (13), resulting in reduced k

_{L}a in Equation (11).

_{L}a for O

_{2}in the sparged CSTR with 3 L working volume decreased from 10% to 50% when the agitation speed increased from 750 to 900 rpm and air flow rate was below 600 sccm (Figure 3). However, the measured k

_{L}a for O

_{2}with the 3 L working volume increased when the agitation speed was increased from 750 to 900 rpm at air flow rate of 600 sccm. The phenomenon of decreasing k

_{L}a for O

_{2}was not observed with the 5.6 L working volume even at 900 rpm. The decrease in measured k

_{L}a in the 3 L working volume was attributed to severe backmixing of N

_{2}in the headspace into water and O

_{2}stripping from water, which increased the time for DO concentration reaching saturation values. There was 2.9 times more N

_{2}initially present in the headspace in the sparged CSTR with the 3 L working volume compared to the 5.6 L working volume, which caused higher effect of backmixing on k

_{L}a in the 3 L working volume. In addition, the amounts of N

_{2}in the headspace at 150 and 250 kPa were 1.5 times and 2.4 times, respectively, higher than at 101 kPa. The measured k

_{L}a for O

_{2}at air flow rate of 600 sccm, 900 rpm and 101 kPa in the 3 L working volume increased from the k

_{L}a measurement at 750 rpm because the high air flow rate increased the O

_{2}content in the headspace over four times faster than at 90 and 150 sccm. The measured k

_{L}a for O

_{2}remained almost constant at 600 sccm with the headspace pressures of 150 and 240 kPa when the agitation speed was increased from 750 to 900 rpm with the 3 L working volume (Figure 3). This was due to lower volumetric air flow rates at 150 and 240 kPa, which could not flush N

_{2}from headspace as fast as at 101 kPa.

#### 3.2. Effect of Headspace Backmixing on k_{L}a

_{L}a for O

_{2}in non-sparged CSTR and 3 L and 5.6 L working volumes was evaluated at agitation speeds of 150 and 900 rpm and headspace pressures of 101, 150 and 240 kPa (Table 1). In this set of experiments, the headspace was purged with air at 1000 sccm for 2 min and pressure was set at the desired value. During the test at each condition, the inlet and outlet CSTR gas lines were completely closed. Results showed that the effect of backmixing of air from the headspace on the k

_{L}a for O

_{2}in the 5.6 L working volume was negligible compared to 3 L working volume (Table 1). For the CSTR with 3 L working volume at 150 rpm and headspace pressures between 101 and 240 kPa, the backmixing of air from the headspace was low, resulting in k

_{L}a values for O

_{2}below 1.3 h

^{−1}. However, the k

_{L}a for O

_{2}increased from 0.7 h

^{−1}to 67.3 h

^{−1}due to backmixing of air from the headspace when the agitation speed was increased from 150 rpm to 900 rpm at 101 kPa. Moreover, the k

_{L}a for O

_{2}in the non-sparged CSTR at 900 rpm increased by 77% with the increase in the air pressure in the headspace from 101 to 240 kPa in the 3 L working volume. This explains the decrease in the k

_{L}a for O

_{2}when air was sparged into the water with initial N

_{2}headspace was due to backmixing of N

_{2}from the headspace at 900 rpm with pressures of 150 and 240 kPa at air flow rates of 90 and 150 sccm (Figure 3).

_{L}a from backmixing at 900 rpm was attributed to the impeller arrangement in the CSTR. The distance from the top impeller to the liquid surface was 6.4 cm in the 3 L working volume (Figure 1). However, there was 16.7 cm between the top impeller and the liquid surface in the 5.6 L working volume. No vortex was observed in the 5.6 L working volume at 900 rpm. However, a vortex formed between the water surface and the top impeller in the 3 L working volume, drawing gas from the headspace to circulate in the liquid.

_{L}a for O

_{2}, the headspace in the CSTR with 3 L working volume was flushed with air for 2 and 12 min at 1000 sccm. Flushing the CSTR headspace for 2 min at 1000 sccm represented about 50% of the headspace volume with the 3 L working volume. However, using O

_{2}saturation when each run reached equilibrium as % DO for Cs in Eq. 1 corrected for the lower initial concentration of O

_{2}in the headspace that resulted from low purging time. In addition, the results showed that there was no statistical difference (p > 0.05) between the headspace flushing times (Table 1). Thus, 2 min was sufficient to flush the headspace with air to evaluate the backmixing effect on the k

_{L}a for O

_{2}.

_{L}a from Equation (1) assumes a constant O

_{2}concentration at the gas/liquid interface, Cs. However, O

_{2}transferred into the water is removed from the headspace gas lowering the O

_{2}concentration at the interface. The change of O

_{2}concentration in the headspace was estimated by the O

_{2}mass balance and the equilibrium O

_{2}saturation (% DO) to be 2% and 9% for the 3 and 5.6 L working volumes, respectively. The mass transfer driving force for O

_{2}transfer was estimated by the logarithmic mean of the initial difference of partial pressure in the gas and 0 kPa in the water, and a low terminal partial pressure difference of 0.2 kPa between the gas and the near equilibrium saturation of the water. This estimation shows the average driving force increases with pressure. This suggests that the increase in observed k

_{L}a for O

_{2}in the non-sparged CSTR due to backmixing with increased pressure resulted from increased driving force.

^{−1}. Therefore, the subsequent experiments on effect of backmixing were done with the 3 L working volume. In this set of experiments, the headspace was flushed with air before air was sparged in water through the CSTR inlet sparger to evaluate if the backmixing of air affects the k

_{L}a for O

_{2}in the 3 L working volume at 600 sccm and 900 rpm and various headspace pressures.

_{L}a for O

_{2}increased between 20% and 48% when the headspace was flushed with air before flowing air into the CSTR compared to no air flushing (i.e., only N

_{2}in the headspace) (Table 2). The k

_{L}a for O

_{2}were 32% and 50% lower at 150 kPa and 240 kPa, respectively, compared to 101 kPa when the headspace was not initially flushed with air (Table 2). However, when the headspace was flushed with air, the k

_{L}a values for O

_{2}were 16% and 41% lower at 150 kPa and 240 kPa, respectively, than at 101 kPa. This was due to 32% and 57% lower superficial gas velocities at 150 and 240 kPa, respectively, compared to 101 kPa. In addition, the differences in k

_{L}a values for O

_{2}were lower when the headspace was flushed with air at 150 and 240 kPa compared to 101 kPa since higher initial O

_{2}content in the headspace added to the rate of O

_{2}saturation compared to stripping of O

_{2}by the N

_{2}headspace.

_{2}into products. However, if conversion of CO and H

_{2}was high, the inert gas such as N

_{2}from the producer gas derived from biomass [39] in the headspace can reduce the k

_{L}a for CO or H

_{2}at high agitation speed due to backmixing. Thus, it would be beneficial to operate the syngas fermentation at low agitation speed, and high working volume to alleviate the backmixing effect when the syngas conversion efficiency is high. However, other factors such as gas flow rate, gas uptake rate, and agitation speed should be considered in evaluating the benefits of backmixing on syngas fermentation.

#### 3.3. Model Predictions of k_{L}a for O_{2}

_{L}a for O

_{2}at air flow rates (90, 150 and 600 sccm), various agitation speeds (150 to 900 rpm), working volumes (3 and 5.6 L) and headspace pressures (101, 150 and 240 kPa). Based on the experimental data, the air flow rates at standard condition in sccm were converted using Equations (2) to (5) into the corresponding volumetric flow rates in mL min

^{−1}at 37 °C and the various hydraulic heads and headspace pressures used. The power consumption per unit volume (P

_{g}/V

_{L}) and superficial velocity were calculated using Equations (6) to (10) and (13). Using the experimental data, the constants α, β and c in Equation (11) were determined and the k

_{L}a for O

_{2}can be estimated using Equation (14).

_{L}a for O

_{2}in the CSTR with 5.6 L working volume. When agitation speeds were low, mainly 150 to 600 rpm in 3 L working volume, less than 10% variation between the experimental and predicted k

_{L}a values for O

_{2}were observed. However, there were 30% to 60% variation between the experimental and predicted k

_{L}a values for O

_{2}in the 3 L working volume at low standard flow rate 90 and 150 sccm and agitation speed above 750 rpm. This was due to the backmixing of N

_{2}that lowered the observed k

_{L}a deviating from model predictions. The superficial gas velocity v

_{g}in Equation (11) was determined using the volumetric flow rate at 37 °C as shown in Equation (13). Higher headspace pressures for the same standard flow rate in sccm resulted in lower volumetric flow rates in mL min

^{−1}at 37 °C and lower v

_{g}and k

_{L}a. The model predictions of k

_{L}a for O

_{2}were compared with the experimental results at various agitation speeds and volumetric flow rates (Figure 4). In addition, the model predictions of the k

_{L}a for O

_{2}were plotted versus experimental data, which were mostly within 10% of variance (Figure 5). The R

^{2}value for model predictions of the experimental data was 0.97, indicating a very good fit.

_{g}/V

_{L}, was calculated using Equations (6) to (10). Increasing the agitation speed from 150 to 900 rpm increased power consumption from 33 to 8181 W m

^{−3}and from 21 to 5216 W m

^{−3}in the 3 L and 5.6 L working volumes, respectively. The P

_{g}/V

_{L}slightly decreased (no more than 8%) when air flow rate was increased from 90 to 600 sccm and headspace pressure was increased from 101 to 240 kPa. This showed that the increase in flow rate and headspace pressure within the tested ranges had small effects on P

_{g}/V

_{L}.

_{L}a for O

_{2}in 3 L working volume was from 6% to 50% higher than in 5.6 L working volume at similar operating conditions, the P

_{g}/V

_{L}consumed in 5.6 L working volume was about 37% lower than in 3 L working volume indicating the advantage of using higher working volumes in terms of power consumption. In addition, when high conversion efficiencies of CO, CO

_{2}and H

_{2}in 3 L working volume were to be attained, the backmixing of N

_{2}from producer gas [39] would diminish the advantage of using this working volume with higher k

_{L}a than the 5.6 L working volume.

#### 3.4. Model Predictions of k_{L}a for CO, CO_{2} and H_{2}

_{2}in the process. It is more convenient to measure the k

_{L}a for O

_{2}using an air-water system for the simplicity of the method and then predict the k

_{L}a for CO, CO

_{2}and H

_{2}. The k

_{L}a for CO, CO

_{2}and H

_{2}were calculated from the model prediction of k

_{L}a for O

_{2}(Equation (14)) based on the penetration or surface renewal theory [33,34] as shown in Equations (15) to (17).

_{L}a for CO was 6% higher and 30% lower than the k

_{L}a for CO

_{2}and H

_{2}, respectively, at all similar operating conditions. For syngas fermentation in a CSTR, the k

_{L}a for CO, CO

_{2}and H

_{2}can be estimated if the bioreactor size, number and type of impellers, working volume, agitation speeds, headspace and hydraulic pressures and gas flow rates are known.

_{L}a. [11,15] Therefore, CSTR operating conditions should be carefully selected to reduce the power input to make the process more economically feasible. As shown in Figure 6, the predicted k

_{L}a for O

_{2}increased with the increase in the P

_{g}/V

_{L}. The trends of k

_{L}a for O

_{2}were similar in 3 and 5.6 L working volumes at the same standard flow rate and headspace pressure. The k

_{L}a values for O

_{2}increased by over four times when the flow rate was increased from 90 to 600 sccm at the same headspace pressure and P

_{g}/V

_{L}. Therefore, higher k

_{L}a for O

_{2}can be realized by increasing the air flow rate without increasing the P

_{g}/V

_{L}. However, while increasing gas flow rate during syngas fermentation increases k

_{L}a, this can reduce syngas conversion efficiency when gas transfer rate exceeds the kinetic capacity of the cells. High cell concentrations are required to increase the gas conversion efficiency at high gas flow rates. Increased cell concentration in the fermentor was successfully demonstrated using membrane module for cell recycle [41,42]. Moreover, the increase in the headspace pressure from 101 to 240 kPa decreased the k

_{L}a for O

_{2}by 48% at similar P

_{g}/V

_{L}. This means that higher P

_{g}/V

_{L}is required to achieve the same k

_{L}a for O

_{2}at higher pressure, offsetting the higher driving force gained at high pressure. The change of k

_{L}a for O

_{2}as a function of P

_{g}/V

_{L}would be similar to k

_{L}a for CO, CO

_{2}and H

_{2}during syngas fermentation. When operating syngas fermentation bioreactors, Equations (15) to (17) are useful to predict the mass transfer capacity for CO, CO

_{2}and H

_{2}based on the uptake ability of the culture used, and therefore can guide in setting the operating conditions to minimize P

_{g}/V

_{L}and maximize gas conversion efficiency.

_{L}a values for different reactors using air and syngas components were reported by various research groups (Table 3). Based on Equation (12), k

_{L}a for CO is 1.03 the k

_{L}a for O

_{2}. However, it is difficult to compare k

_{L}a values based on the same gas accurately because of the different reactors and operating parameters used and unreported data about reactor volume, gas and liquid flow rates, pressure and agitation (Table 3). However, a comparison of the data from the literature showed that the k

_{L}a values of the HFR and TBR reactors were greatly higher than in various reported CSTRs [15,20,43,44]. HFR reactors showed remarkably high k

_{L}a values (about 1000 h

^{−1}), which depended on the type of the membrane, surface area to unit volume, gas flow rate and pressure [15,24,43]. An increase in the gas pressure in the HFR increased the k

_{L}a [20,43]. However, an increase in the gas pressure in the CSTR decreased k

_{L}a due to lower volumetric gas flow rate at high pressure (Table 3). The k

_{L}a values reported for CSTRs in Table 3 were below 160 h

^{−1}[18,45,46]. However, the k

_{L}a values for the TBR, air-lift and MBR coupled with CSTR were 421, 130 and 450 h

^{−1}, respectively [15,16,47].

_{L}a values in the CSTR increased by increasing the gas flow rate and agitation speed (Figure 3). In addition, the k

_{L}a values in sparged CSTR increased with a decrease in the headspace pressure. However, the k

_{L}a values in non-sparged CSTR increased with an increase in the headspace pressure and agitation due to increased backmixing (Table 1). These results provide guidance in design, operation, and scale up of syngas fermentation reactors.

## 4. Conclusions

_{L}a for O

_{2}was increased by increasing the air flow rates and agitation speeds in the 7-L Bioflo 415 CSTR with the 3 and 5.6 L working volumes. The increase in headspace pressure decreased the k

_{L}a for O

_{2}due to lower volumetric gas flow rate at high pressure. The highest k

_{L}a for O

_{2}was 116 h

^{−1}, which was obtained at 600 sccm, 900 rpm and 101 kPa with the 3 L working volume. Backmixing from the headspace in the non-sparged CSTR at 900 rpm with the 3 L working volume increased k

_{L}a. The highest k

_{L}a for O

_{2}due to backmixing in the non-sparged CSTR was 119 h-1, attained at 900 rpm and headspace air pressure of 240 kPa. A mass transfer model was developed and the model predicted the experimental k

_{L}a values for O

_{2}within 10%. Also, the model predicts an increase in k

_{L}a for O

_{2}with an increase in the gas flow rate without increasing the power consumption per unit volume (P

_{g}/V

_{L}). The model was extended to predict the k

_{L}a values for syngas components CO, CO

_{2}, and H

_{2}, which can provide crucial insights for setting operating conditions in the CSTR to minimize P

_{g}/V

_{L}and increase gas conversion efficiency.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

a | Gas-liquid interfacial area per unit volume (m^{−1}) |

A, B, C and E Parameters in Equations (9) and (10) | |

C_{L} | Bulk dissolved oxygen (DO) concentration in the liquid (mol m^{−3}) |

C_{S} | Saturated dissolved oxygen (DO) concentration (mol m^{−3}) |

D | Impeller diameter (m) |

D_{i} and D_{j} | Diffusivities of gas species i and j in water (cm^{2} s^{−1}) |

DO | Dissolved oxygen (%) |

g | Gravitational acceleration (m s^{−2}) |

h | Distance of microsparger from the surface of liquid (m) |

k_{L} | Liquid film mass transfer coefficient (m h^{−1}) |

k_{L}a | Overall volumetric mass transfer coefficient (h^{−1}) |

M_{a} | Molecular weight of air (g mol^{−1}) |

MFC | Mass flow controller |

n_{a} | Molar air flow rate (mol min^{−1}) |

N | Rotation speed of impeller (s^{−1}) |

N_{A} | Aeration number (dimensionless) |

N_{Fr} | Froude number (dimensionless) |

NIST | National Institute of Science and Technology |

N_{p} | Power number of single Rushton impeller or marine impeller (dimensionless) |

P_{HS} | Headspace pressure (kPa) |

P_{HP} | Liquid pressure above the microsparger (kPa) |

P_{total} | Total pressure in the CSTR (kPa) |

P_{g} | Total impeller power consumption at gassed condition (W) |

P_{g,lower} | Gassed power consumption of single impeller mounted directly above microsparger (W) |

P_{g,upper} | Gassed power consumption for impellers not directly installed above microsparger (W) |

P_{g}/V_{L} | Power consumption per unit volume (W m^{−3}) |

P_{u} | Ungassed power consumption of single impeller (W) |

Q_{g} | Volumetric air flow rate at the applied pressure and 37 °C (mL min^{−1}) |

R | Ideal gas law constant (L kPa mol^{−1} K^{−1}) |

t | Time (h) |

T | Tank diameter (m) |

T_{NIST} | NIST standard temperature of 293.15 K |

v_{g} | Superficial gas velocity (m s^{−1}) |

V_{L} | Liquid working volume in CSTR (m^{3}) |

V_{NIST} | Volumetric flow rate of air at standard NIST conditions (m^{3} min^{−1}) |

α, β and c | Model parameters in Equation (11) |

ρ_{a} | Air density (kg m^{−3}) |

ρ_{w} | Water density (kg m^{−3}) |

µ | Dynamic viscosity of water (Pa s) |

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**Figure 1.**7-L Bioflo 415 continuous stirred-tank reactor (CSTR) with the 3 and 5.6 L working volumes and impellers configuration.

**Figure 2.**Bioflo 415 CSTR setup. (1) Rushton impellers, (2) marine impeller, (3) microsparger, (4) dissolved oxygen (DO) probe, (5) 0.2 µm gas filters, (6) condenser, (7) backpressure regulator valve, (8) rotameter, (9) two-way valve, and (10) headspace septum used with purging the headspace.

**Figure 3.**k

_{L}a for O

_{2}in air water system at standard flow rates in standard cubic centimeters per minute, sccm, (

**A**) 90 sccm, (

**B**) 150 sccm and (

**C**) 600 sccm and headspace pressures of 101 kPa (■), 150 kPa (♦) and 240 kPa (●) in 3 L (experimental data in solid symbols, model predictions in solid lines) and 5.6 L (experimental data in open symbols, model predictions in dash lines) working volumes. Error bars not visible are smaller than the symbols.

**Figure 4.**Experimental and predicted k

_{L}a for O

_{2}in (

**A**) 3 L and (

**B**) 5.6 L working volumes in the 7 L Bioflo 415 CSTR at volumetric flow rates between 40 mL min

^{−1}to 630 mL min

^{−1}and 37 °C and various agitation speeds: 150 rpm (♦), 300 rpm (▲), 450 rpm (●), 600 rpm (×), 750 rpm (■) and 900 rpm (+); model prediction (dash lines). Error bars not visible are smaller than the symbols.

**Figure 5.**Predicted versus experimental k

_{L}a for O

_{2}at volumetric flow rates between 40 mL min

^{−1}to 630 mL min

^{−1}and 37 °C, agitation speeds range from 150 rpm to 900 rpm in the 3 L and 5.6 L working volumes.

**Figure 6.**Profiles of predicted k

_{L}a for O

_{2}with P

_{g}/V

_{L}at various headspace pressures (

**A**) 101 kPa (

**B**) 150 kPa (

**C**) 240 kPa and 90 sccm (▲), 150 sccm (♦) and 600 sccm (■) in 3 L working volume (solid symbol and solid line) and 5.6 L working volume (open symbol and dash line).

**Table 1.**Effect of headspace pressure and backmixing at 150 and 900 rpm on k

_{L}a for O

_{2}in a non-sparged CSTR with 3 and 5.6 L working volumes.

Parameters | ||||||
---|---|---|---|---|---|---|

Headspace pressure (kPa) | 101 | 101 | 150 | 150 | 240 | 240 |

Agitation speed (rpm) | 150 | 900 | 150 | 900 | 150 | 900 |

k_{L}a for O_{2} (h^{−1}) ^{a} | 0.7 ± 0.0 | 67.3 ± 1.0 ^{†} | 0.8 ± 0.0 | 92.0 ± 3.5 ^{†} | 1.3 ± 0.4 | 119.3 ± 2.1 ^{†} |

k_{L}a for O_{2} (h^{−1}) ^{b} | — ^{‡} | 67.0 ± 0.2 ^{†} | — | 88.2 ± 0.3 ^{†} | — | 122.3 ± 1.4 ^{†} |

k_{L}a for O_{2} (h^{−1}) ^{c} | 0.2 ± 0.0 | 1.5 ± 0.0 | 0.2 ± 0.0 | 1.8 ± 0.0 | 0.3 ± 0.0 | 1.8 ± 0.0 |

^{a}3 L working volume and headspace flushed with air for 2 min.

^{b}3 L working volume headspace flushed with air for 12 min.

^{c}5.6 L working volume and headspace flushed with air for 2 min.

^{†}No statistical differences between headspace flushed with air for 2 min and 12 min at 95% confidence level (p > 0.05).

^{‡}Not determined.

**Table 2.**Effect of headspace pressure and backmixing on k

_{L}a for O

_{2}in a sparged CSTR with 3 L working volume at standard air flow rate of 600 sccm and 900 rpm.

Parameters | |||
---|---|---|---|

Headspace pressure (kPa) ^{a} | 101 | 150 | 240 |

Volumetric flow rate at 37 °C (mL min^{−1}) | 628 | 428 | 270 |

k_{L}a without flushing headspace with air (h^{−1}) | 116.2 ± 6.4 | 79.0 ± 0.1 ^{†} | 57.7 ± 0.5 ^{†} |

k_{L}a with flushing headspace with aira (h^{−1}) | 139.8 ± 5.4 | 116.8 ± 5.7 ^{†} | 82.6 ± 1.4 ^{†} |

k_{L}a increase due to backmixing (%) | 20.3 | 47.9 | 43.2 |

^{a}Headspace flushed at 1000 sccm with air for 2 min before sparging air in water.

^{†}Statistical difference between with and without flushing the headspace with air at 95% confidence level (p < 0.05).

Reactor^{a} | Physical (Working) Volumes (L) | Gas | Medium | Gas Flow (mL min^{−1}) | Gas Pressure (kPa) | Agitation (rpm) | Liquid Flow (mL min^{−1}) | k_{L}a (h^{−1}) | References |
---|---|---|---|---|---|---|---|---|---|

CSTR | 7.0 (3.0) | Air | Water | 600 | 101 | 900 | --- | 116 | This study |

600 | 101 | 900 | --- | 140^{b} | |||||

600 | 240 | 900 | --- | 58 | |||||

600 | 240 | 900 | --- | 83^{b} | |||||

0 | 240 | 150 | --- | 1 | |||||

0 | 240 | 900 | --- | 119 | |||||

7.0 (5.6) | 600 | 101 | 900 | --- | 79 | ||||

600 | 240 | 900 | --- | 51 | |||||

CSTR | 14 (7.0) | CO | Water | 6000 | NA | 600 | --- | 155 | [45] |

CSTR | 14 (7.0) | CO | Water | 5000 | NA | 400 | --- | 100 | [46] |

15,000 | NA | 400 | --- | 153 | |||||

CSTR | 3 (2.5) | Air | Water | 400 | 101 | 900 | --- | 114 | [15] |

TBR | 0.5 (0.2) | Air | Water | 106 | 101 | --- | 50 | 421 | |

HFR | NA (0.025) | Air+21%O_{2} | Water | 2000 | 106 | --- | 400 | 1062 | |

CSTR | 3.3 (1.5) | CO | Water | 375 | NA | 600 | --- | 88 | [18] |

1050 | NA | 600 | --- | 160 | |||||

h-RPB | 3.3 (1.5) | CO | Water | 1500 | 115 | 100 | --- | 70 | |

HFR | NA (3.0) | CO | Water | NA | 136 | --- | 1500 | 205 | [43] |

NA | 308 | --- | 1500 | 947 | |||||

HFR | 4.0 (2.0) | CO | Water | 2000 | 138 | --- | NA | 137 | [44] |

HFR | 0.5 (0.4) | CO | Water | NA | 139^{c} | --- | NA | 155 | [20] |

NA | 170^{d} | --- | NA | 92 | |||||

NA | 195^{d} | --- | NA | 136 | |||||

Air-lift | NA^{a} (3.0) | CO | Water | 5000 | 170 | --- | --- | 91 | [48] |

Air-lift | NA (3.0) | CO | Water | 5000 | 170 | --- | 500 | 130 | [47] |

H2 | Water | 5000 | 170 | --- | 500 | 97 | |||

HFR cw CSTR | NA (2.5^{e}) | CO:H2:CO_{2}^{f} | Water | 139 | NA | 90 | --- | 385^{g} | [21] |

HFR cw CSTR | NA (8.0^{h}) | CO | Water | 5000 | 205 | 200 | 1000 | 1096 | [24] |

MBR cw CSTR | NA (8.0 ^{h}) | CO | Water | 500 | NA | NA | 500 | 450 | [16] |

^{a}CSTR: continuous stirred tank reactor; HFR: hollow fiber membrane reactor; cw: coupled with; TRB: trickle bed reactor; BCR: bubble column reactor; MBR: monolithic biofilm reactor; h-RPB: horizontal rotating pack bed; NA: not available;

^{b}Headspace flushed with 1000 sccm air for 2 min before sparging air in water in CSTR;

^{c}&

^{d}membrane surface area per unit working volume = 62.5 & 27.5 m

^{−1}, respectively;

^{e}STR: 2.4 L and HFR: 0.13 L;

^{f}CO:H

_{2}:CO

_{2}(50:30:20);

^{g}For CO;

^{h}total volume of both reactors.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, K.; Phillips, J.R.; Sun, X.; Mohammad, S.; Huhnke, R.L.; Atiyeh, H.K.
Investigation and Modeling of Gas-Liquid Mass Transfer in a Sparged and Non-Sparged Continuous Stirred Tank Reactor with Potential Application in Syngas Fermentation. *Fermentation* **2019**, *5*, 75.
https://doi.org/10.3390/fermentation5030075

**AMA Style**

Liu K, Phillips JR, Sun X, Mohammad S, Huhnke RL, Atiyeh HK.
Investigation and Modeling of Gas-Liquid Mass Transfer in a Sparged and Non-Sparged Continuous Stirred Tank Reactor with Potential Application in Syngas Fermentation. *Fermentation*. 2019; 5(3):75.
https://doi.org/10.3390/fermentation5030075

**Chicago/Turabian Style**

Liu, Kan, John R. Phillips, Xiao Sun, Sayeed Mohammad, Raymond L. Huhnke, and Hasan K. Atiyeh.
2019. "Investigation and Modeling of Gas-Liquid Mass Transfer in a Sparged and Non-Sparged Continuous Stirred Tank Reactor with Potential Application in Syngas Fermentation" *Fermentation* 5, no. 3: 75.
https://doi.org/10.3390/fermentation5030075