Hydrodynamics and Mass Transfer in a Concentric Internal Jet-Loop Airlift Bioreactor Equipped with a Deflector

The gas–liquid hydrodynamics and mass transfer were studied in a concentric tube internal jet-loop airlift reactor with a conical bottom. Comparing with a standard design, the gas separator was equipped with an adjustable deflector placed above the riser. The effect of riser superficial gas velocity uSGR on the total gas holdup εGT, homogenization time tH, and overall volumetric liquid-phase mass transfer coefficient kLa was investigated in a laboratory bioreactor, of 300 mm in inner diameter, in a two-phase air–water system and three-phase air–water–PVC–particle system with the volumetric solid fraction of 1% for various deflector clearances. The airlift was operated in the range of riser superficial gas velocity from 0.011 to 0.045 m/s. For the gas–liquid system, when reducing the deflector clearance, the total gas holdup decreased, the homogenization time increased twice compared to the highest deflector clearance tested, and the overall volumetric mass transfer coefficient slightly increased by 10–17%. The presence of a solid phase shortened the homogenization time, especially for lower uSGR and deflector clearance, and reduced the mass transfer coefficient by 15–35%. Compared to the gas–liquid system, the noticeable effect of deflector clearance was found for the kLa coefficient, which was found approx. 20–29% higher for the lowest tested deflector clearance.


Algae Potential
Algae represent a wide group of aquatic photosynthetic organisms ranging from a single cell to multicellular structures. Two main groups called microalgae and macroalgae; therefore, are distinguished. The details regarding the bioactive compounds produced by macroalgae are presented by Lafarga et al. [1], and cultivation systems are discussed by Papacek et al. [2].
To produce 1 kg of biomass, the microalgae consumes 1.8 to 2 kg of CO 2 [3]. Therefore, microalgae is a highly efficient system for CO 2 fixation compared with agricultural crops or forests, due to much higher growth rates and a very short harvesting cycle [7]. The potential of microalgal CO 2 sequestration was discussed for fuel gases generated by the power industry [8] or car vehicles [9]. Thanks to the high content of lipids and polysaccharides and high biomass yield connected with fast growth, microalgae have been considered as the third generation feedstock for biodiesel and bioethanol production [10]. by freeze-drying. They reported a productivity of 90 t/(ha.year) and a production cost of 69 €/kg. Labor and depreciation were found to be the major items. The centrifugal pumps recirculating the microalgae culture consume over 53% approx. of the total electricity consumption. The air blowers are the second highest consumer, consuming 21% of electricity.

Internal-Loop Airlift Reactor
The advantages and limitations of airlift reactors adapted from the literature [8,15,17,18,21] are presented in Table 1. The simple design, no moving parts, and relatively low shear stress are the biggest advantages of airlift reactors. In general, increasing the aeration rate improves mixing and mass transfer, but on the other side, shear stress increases what can be a problem for some cells sensitive to stress [22]. Table 1. Advantages and limitations of airlift reactors; adapted from [8,15,17,18,21].

Advantages Limitations
Simple design. Compressed gas required. No moving parts.
Small illumination surface area. Good mixing due to circular mixing pattern.
Scale-up process is difficult.
Intensive mass transfer.
Decrease of illumination surface during scale-up.
Low shear stress. Increasing light path with increasing column diameter.
Efficient light penetration and utilization. Insufficient turbulence creation through airlift operation. Exposure to light/dark cycles.
Risk of high shear stress on an algae culture.
High biomass concentration. Restricted working volume by oxygen removal capability of airlift process. Good photosynthetic efficiency.
Photo-inhibition problems. Low built area −→ High areal production. Low fouling.
Gas injected into the riser zone induces a highly turbulent flow and high gas holdup. The hydrodynamics is similar to bubble columns. The liquid is returned to the riser inlet through the downcomer. The downcomer hydrodynamics can be approximated by the plug flow model. Zhang et al. [21] note that the novel ideas in downcomer design enabling to control flow may allow utilizing the potential of airlift reactors. The riser and the downcomer are connected at the upper part by the degassing section and by the bottom section at the lower part. The flow regimes in these sections can be modeled as continuously stirred reactors. In the degassing zone, depending on the geometry and operating conditions, the gas or its part escapes from the circulating liquid. Heijnen et al. [27] defined three typical flow regimes in downcomers of internal-loop ALRs depending on the increasing superficial velocity: (i) No bubbles enter the downcomer and gas escapes from the free liquid surface (regime I); (ii) part of the bubbles, mainly small bubbles, is entrained into the downcomer by the down-flowing liquid (regime II); and (iii) complete gas recirculation into the riser (regime III). The role of the bottom section is often mispriced. Koide et al. [28] reported increasing circulating liquid flow with increasing bottom clearance with riser diameter within the range C B /D R ≤ 1 2 . For a higher ratio, the flow was unchanged. Lu et al. [29] studied the hydrodynamics and mass transfer characteristics in concentric tube airlift, modified square airlift reactor, and square bubble column. They reported larger ε, slightly longer homogenization time, and larger k L a for the square airlift reactor compared to standard airlift. Zhang et al. [30] investigated the effect of conical bottom and funnel-shaped internal above the tubular riser on hydrodynamics experimentally and by CFD. Installing the internals, the gas holdup was enhanced by a maximum of 15%, and the turbulent kinetic energy can be reduced by a maximum of 7.8%, which can be promising for stress-sensitive biological processes. The published data on the measurement methods, hydrodynamic characteristics, and modeling of flow dynamics in airlift reactors were summarized by Zhang et al. [21].

Total Gas Holdup
The gas holdup represents the gas volume fraction occupied in the gassed batch: where V G is the volume of the gas phase, V bed is the total volume of a gassed batch. When the gas holdup is investigated in the gas-liquid-solid dispersion, the V bed represents the sum of the volumes of the present phases. The effect of superficial gas velocity u SG on gas holdup ε G has been usually described by the power-law function [31]: where u SG is the superficial gas velocity related to the column diameter (u SGC ) or riser diameter (u SGR ), and C and α are empirical constants depending on gas and liquid physical properties, hydrodynamic regime, and column geometry. The selected published correlations adapted from the literature [19,[31][32][33][34][35] are presented in Table 2.

Homogenization Time
The homogenization time is one of the important parameters for the design of photobioreactors. Shorter homogenization time indicates intensive mixing and enables to reach a faster homogeneous concentration distribution. The homogenization time is defined as the time required to achieve a homogenous mixture after the injection of a tracer solution [15]. Sanchéz Mirón et al. [36] tested the correlation proposed by Bando et al. [37] in the draft tube airlift reactor of 0.193 m in reactor diameter. They found the tested correlation overpredicted the time for the column superficial gas velocity u SGC in the range from 0 to 0.01 m/s, where the mixing is most sensitive to aeration velocity. The selected published correlations for homogenization time adapted from the literature [29,[37][38][39] are presented in Table 3. Table 3. Homogenization time t H -selected published correlations; adapted from [29,[37][38][39].

Source Correlation
Lu et al. [29] Concentric tube ALR; D D = 0.188 m, A R /A D = 0.695 and 1.38. Gas distribution: Single nozzle. Air-water system. The mass transfer is most frequently described by the overall volumetric mass transfer coefficient k L a. Koide et al. [40] investigated k L a coefficients in internal-loop ALRs and bubble columns of different sizes and gas distributor types for demineralized water and five Newtonian solutions and air as a gaseous phase. The k L a coefficient was found to be larger in ALR compared to the bubble column. Increasing D R /D D ratio, the k L a coefficient decreases. Gavrilescu and Tudose [41] investigated the effect of top and bottom clearance and A D /A R ratio on k L a coefficient in three concentric-tube ALRs of different scales (0.07, 2.50, and 5.20 m 3 ) in non-coalescent Newtonian fluid (sodium sulfite solution). Gouveia et al. [35] investigated the effects of riser superficial gas velocity, bottom clearance, and top clearance on k L a coefficient in the air-water system using sulfite oxidation method in an internal-loop ALR of 6 dm 3 volume with A D /A R = 0.63. Juraščík et al. [32] investigated k L a coefficients in three airlift reactors of different sizes (12 dm 3 , 40 dm 3 , and 195 dm 3 ). Cerri et al. [42] investigated the effects of riser superficial gas velocity and physical properties (D L , υ, ρ, and σ) in three concentric tube ALRs of different sizes (2, 5, and 10 dm 3 ) with cross-piece type sparger. The experimental data obtained for eight Newtonian fluids and five non-Newtonian fluids were fitted using a correlation type originally proposed by Akita and Yoshida [43] for bubble columns. The effect of superficial gas velocity u SG on the overall volumetric mass transfer coefficient k L a has been usually also described by the power-law function. The selected published correlations for k L a adapted from the literature [32,33,35,36,[40][41][42]44,45] are presented in Table 4. Table 4. Overall volumetric mass transfer coefficient k L a-selected published correlations; adapted from [32,33,35,36,[40][41][42]44,45].

Source Correlation
Koide et al. [40] Concentric draft tube ALR with flat bottom, D D = D C , D R = D T , D char = D C. Gas distributors: Single nozzle, perforated plate, porous glass plate Air-liquid system, liquid: Water, an aqueous solution of glycerol, glycol, BaCl 2 , NaSO 4 , Na 2 SO 3 .

Effect of Solid Phase
Koide et al. [45] investigated the effect of column diameter, gas velocity, liquid properties, and size and concentration of gel particles in a conical draft tube ALR with a conical bottom. The solid phase concentration was varied in the range from 0 to 20 vol.%. They found the presence of gel particles reduced the values of the gas holdup and the overall volumetric mass transfer coefficient. The degree of reduction increased with increasing solid concentration and was independent of gel particle diameter in the range from 1.88 to 3.98 mm. Yang et al. [46] investigated the effect of superficial gas velocity and top clearance on hydrodynamics and mass transfer in the gas-liquid and gas-slurry system in internal loop airlift with draft tube (D D /D R = 140/280 mm) and perimeter aeration. The aluminum oxide particles with a diameter of 98.67 µm were used as the solid phase. The experiments were carried out at a volumetric solid loading of 0.5%. The effect of top clearance on the k L a coefficient was found when the superficial gas velocity was higher than 0.034 m/s. The increase of k L a coefficient in the gas-slurry system was approx. 8% for the superficial gas velocity higher than 0.034 m/s. Sastaravet et al. [47] investigated the effect of polypropylene particles of different shapes and solid loading on the bubble hydrodynamics and mass transfer in a bubble column and internal-loop airlift reactor with a splitting baffle. The enhancement of the k L a coefficient up to 38.5% was achieved in the airlift reactor when the solid particles were added. The solid particles shaped like cylinders and rings were found to be most effective for k L a enhancement.

Motivation
Based on the standard design, we designed a novel configuration of an internal jetloop airlift reactor. The gas separator was equipped with an adjustable deflector placed above the riser. Installing the deflector, the fluctuation of the dispersion level should be stabilized in the gas separator and the contact time between liquid and gas bubbles should be prolonged. The conical airlift bottom was used for better flow direction in the bottom section and elimination of particle accumulation in a dead zone when the flat bottom is used. The preliminary results were presented in our previous work [48].
This work aims to study the effects of riser superficial gas velocity u SGR and deflector clearance C D above a riser on total gas holdup ε GT , homogenization time t H, and overall volumetric liquid-phase mass transfer coefficient k L a in the two-phase gas-liquid system and three-phase gas-liquid-solid system in the range of riser superficial gas velocity up to 0.045 m/s.

Experimental Apparatus
The experiments were carried out in a laboratory conical jet-loop airlift bioreactor of 300 mm inner diameter and volume of 62.5 dm 3 . The geometrical parameters are presented in Table 5. The tap water was used as a model liquid and the air was fed into the airlift reactor via a single nozzle having three orifices of 1 mm in hole diameter. The scheme of the experimental apparatus is depicted in Figure 1.

Experimental Conditions
The air-water system was used as a tested two-phase gas-liquid system. The extruded PVC rods of diameter 4 mm and length ranging from 2.5 to 4 mm were used as the model solid phase. The solid phase fraction used was 1% v/v. The air flow rate was in the range of riser superficial gas velocity u SGR from 0.011 to 0.045 m/s. The airlift was operated in regime I according to the classification given by Heijnen et al. [27]. The experimental conditions are summarized in Table 6. The gas holdup was determined visually by the measurement of the difference between the non-aerated liquid level and the aerated liquid level. The overall gas holdup ε GT was determined by measuring the bed height at a given superficial gas velocity as: where H G+L+S is the gassed bed height, H L+S is the height of the liquid/suspension before aeration.
The effects of riser superficial gas velocity u SGR and deflector clearance C D on the measured total gas holdup ε GT were correlated using the power-law function: where C * D is the dimensionless deflector clearance; C RU is the riser upper clearance; C, α and β are model parameters.

Homogenization Time
The homogenization time was measured by the decolorization technique [49] using 1M NaOH and 10% wt. H 2 SO 4 . Phenolphthalein was used as an indicator.
The effects of riser superficial gas velocity u SGR and deflector clearance C D on the measured homogenization time t H were correlated using the power-law function: Alternatively, the experimental data were successfully correlated using a combined exponential-and power-law function:

Overall Volumetric Liquid-Phase Mass Transfer Coefficient k L a
The overall volumetric mass transfer coefficient k L a was determined using the unsteady dynamic method from the oxygen probe response curve [50]. The water was deoxygenated by nitrogen N 2 . Then the water was re-oxygenated by air. The time evolution of dissolved oxygen concentration was measured by an oxygen probe. Applying film theory, the oxygen transfer rate (OTR) between gas and liquid can be expressed in a given spot as follows: where k L is the overall mass transfer coefficient related to liquid-phase side, S G is the gas-to-liquid interfacial area, c L is the mass concentration of dissolved oxygen in the liquid, c * L is the mass concentration of dissolved oxygen in the liquid at saturation, a is the specific gas to liquid interfacial area. In practice, the product of k L and a, called volumetric mass transfer coefficient, has been evaluated due to the experimental difficulties of determination of k L and separately. Assuming that c * L = const. in a given spot (i.e., the oxygen fraction in air bubbles in a given spot is practically stable during absorption), the following relation can be obtained by integration of Equation (3): where t is the time, c L (t) is the dissolved oxygen concentration at time t, and c L (t = 0) is the initial dissolved oxygen concentration.
In this work, the response time of the oxygen probe was taken into account. The k L a coefficient was determined using the following relation [51]: where τ is the response time of the oxygen probe. The dissolved oxygen concentration in the liquid was measured by an oxygen optiluminiscence probe FDO 925 (WTW Germany). The response time of this probe is 30 s. The oxygen probe was placed in the middle of the annulus and the measuring part was immersed 25 mm below the liquid level.
The k L a coefficient was obtained using Equation (5) by the fitting of the time course of dissolved oxygen concentration using nonlinear regression. For k L a determination, only part of the data record of c L (t) was used. The time dependence of dissolved oxygen was transformed into the time dependence of the relation ln(c * L − c L (t)). The part of the record having a linear course of the time dependence of the relation ln(c * L − c L (t)) was identified as relevant for k L a determination.
For k L a data correlation, the k L a value obtained at experimental temperature T has to be corrected to the reference temperature T ref [52]. The k L a value obtained at temperature T was corrected to the reference temperature T = 20 • C as follows [52]: where (k L a) T is the mass transfer coefficient measured at temperature T, (k L a) 20 is the mass transfer coefficient at reference temperature 20 • C, and C is the empirical temperature correction factor. Bewtra et al. [52] present factor C as 1.0192 and Nogaj and Hurwitz [53] presented the value 1.024 as the factor. It should be noted that this approach has been critically discussed [54]. Nevertheless, in this work, the measured values of the overall volumetric mass transfer coefficient were corrected onto 20 • C using this approach and the factor of 1.024. The effects of riser superficial gas velocity u SGR and deflector clearance C D on the temperature corrected overall volumetric mass transfer coefficient k L a were correlated using the power-law function: Alternatively, the experimental data were successfully correlated using a combined exponential-and power-law function:

Statistical Analysis
The effects of riser superficial gas velocity u SGR and deflector clearance C D on the properties investigated were analyzed statistically using hypothesis testing [55]. For this analysis, the power-law dependence is assumed. The statistical method of hypothesis testing can estimate whether the differences between the predicted power-law exponent α pred and the evaluated power-law exponent α calc from the measured data are negligible. The testing characteristics t is calculated: where y exp,i is the experimental value of an investigated property for the independent variable x i , C is the constant of proportionality of power-law function, s α is the standard deviation of a power-law exponent α, m is the number of experimental data items. If the absolute value of the calculated testing characteristics |t| is less than the critical value of the t-distribution for (m − 2) degrees of freedom and significance level α, the difference between α calc and α pred can be assumed statistically negligible. The significance level α = 0.05 [56] was used for the determination of the critical t-value. The t-distribution coefficient t (m−2),α is 4.3027 for four riser superficial gas velocities, and the significance level α = 0.05. Three statistical parameters were used as evaluating parameters of the proposed correlations, which are computed as follows [57]: (i) average absolute error (AAE): (ii) average biased error (ABE): (iii) coefficient of determination (R 2 ): where y pred,i is the property value predicted by proposed correlation, y exp is the average of experimental property values. These three statistical criteria are employed to assess the applicability of proposed or tested correlations [58]. The average absolute error (AAE) measures the degree of closeness between the predicted and measured results [57]. A smaller value of AAE indicates higher accuracy of the proposed correlation [58]. The average biased error (ABE) indicates the degree of overestimation and underestimation of proposed or tested correlation [57]. The positive value of ABE indicates an overall overestimation, whereas a negative value of ABE indicates an overall underestimation [58]. The coefficient of determination (R 2 -value) is used to determine the degree of goodness and accuracy of proposed or tested correlation [57]. A higher R 2 -value indicates a better fitting quality of correlation used [58]. The proposed or tested correlation is considered the best fitting model if the AAE and ABE values tend to zero and R 2 -value is close to 1 [57].

Total Gas Holdup
The measured values of total gas holdup are shown in Figure 2 as a function of dimensionless deflector clearance for the gas-liquid and gas-liquid-solid systems. For comparison, the values calculated using the proposed correlation (4) are shown also. For the gas-liquid-solid system, the riser superficial velocity of 0.011 m/s was insufficient to suspend all solid particles.
As was expected, reducing the deflector clearance, the total gas holdup decreases for the gas-liquid system. Unlike this, the weak effect of deflector clearance was observed for the gas-liquid-solid system, especially for higher u SGR . The higher gas holdup was observed for the lowest u SGR and the smallest deflector clearance. Competitive impingement between aeration, particle suspension, and flow restriction due to changing deflector clearance may result in this dissimilar behavior. It can be indicated by unconsolidated values of α-exponent and β-exponent (Tables 7 and 8 in detail). The values of the power law exponent for superficial gas velocity reported in the literature range usually in the range from 0.647 to 1.2 for the gas-liquid system. Analyzing overall data, the α-values of 0.802 and 1.187 were obtained for the gas-liquid system and gas-liquid-solid system, respectively. The applicability of the α-values of 0.8 and 1.2 for gas-liquid system and gas-liquid-solid system, respectively, was tested using the hypothesis test for each deflector clearance separately. The hypothesis testing was done for both the gas-liquid system and the gas-liquid-solid system. The hypothesis test results are presented in Table 7. For illustration, the average values of the calculated t values are presented here also. Except for C * D = 0.75 in the gas-liquid system, the proposed α-values were statistically confirmed for both systems.
The effect of deflector clearance on total gas holdup was tested for each riser superficial gas velocity. In this case, the independence of total gas holdup of the deflector clearance was tested as the hypothesis, that is, ε GT = B.(C * D ) 0 = const. (i.e., β pred = 0). The hypothesis test results are presented in Table 8. Statistically, the effect of deflector clearance can be neglected for the gas-liquid-solid system, and at higher u SGR in the gas-liquid system. Analyzing the overall data, the β-values of 0.205 and −0.125 were obtained for the gasliquid system and gas-liquid-solid system, respectively. For the data correlation, the β-values of 0.2 and −0.1 were assumed for the gas-liquid system and gas-liquid-solid system, respectively. Table 7. Total gas holdup ε GT : Results of the hypothesis testing-effect of riser superficial velocity u SGR for deflector clearance C * D = const.

Hypothesis Testing
Relation: The evaluated parameters of the power-law correlation (4), coefficient of determination (R 2 ), average absolute error (AAE), and average bias error (ABE) are presented in Table 9 for the gas-liquid and gas-liquid-solid system. The low negative ABE value indicates only a low overall underestimation of total gas holdup by the proposed correlation (4). The comparison of experimental data and the correlation given by Equation (4) is presented in Figure 3 for both systems. The lines representing the relative error of ±15% are shown also in Figure 3 for illustration. Table 9. Total gas holdup ε GT : Evaluated parameters of correlation (4).

Homogenization Time t H
The measured values of homogenization time are shown in Figure 4 as a function of dimensionless deflector clearance for the gas-liquid and gas-liquid-solid systems. For comparison, the values calculated using the proposed correlation (6) are shown also. For gas-liquid system, reducing the deflector clearance, the homogenization time increases significantly. Homogenization time for C * D = 0.15 is approx. two times higher compared to C * D = 0.75. For lower u SGR and lower C D , the presence of solid phase shortened the homogenization time. For the gas-liquid-solid system, the effect of deflector clearance is weaker compared to the gas-liquid system.
The values of the power law exponent for superficial gas velocity reported in the literature range usually in the range from −0.31 to −1.11 for the gas-liquid system. Analyzing overall data, the α-values of −0.575 and −0.306 were obtained for the gas-liquid system and gas-liquid-solid system, respectively. The applicability of the α-values of −0.5 and −0.3 for gas-liquid system and gas-liquid-solid system, respectively, was tested using the hypothesis test for each deflector clearance separately. The hypothesis test results are presented in Table 10. Except for C * D = 0.75 in the gas-liquid-solid system, the proposed α-values were statistically confirmed for both systems.
Furthermore, the independence of homogenization time of the deflector clearance was tested as the hypothesis, that is, t H = B.(C * D ) 0 = const. (i.e., β pred = 0). The hypothesis test results are presented in Table 11. Statistically, the deflector clearance plays a role in the gas-liquid-solid system. Unlike this, the effect of deflector clearance can be neglected at lower u SGR in the gas-liquid system. However, the parity analysis shows that the deflector clearance should be taken into account. Analyzing the overall data, the β-values of −0.414 and −0.141 were obtained for the gas-liquid system and gas-liquid-solid system, respectively. For the data correlation, the β-values of −0.4 and −0.1 were assumed for the gas-liquid system and gas-liquid-solid system, respectively. Table 10. Homogenization time t H : Results of the hypothesis testing for effect of riser superficial velocity u SGR for deflector clearance C * D = const.  Table 11. Homogenization time t H : Results of the hypothesis testing for effect of deflector clearance C D on superficial gas velocity u SGR = const. The evaluated parameters of the power-law correlation (6) and values of AAE, ABE, and R 2 are presented in Table 12 for the gas-liquid and gas-liquid-solid systems. The positive ABE value, higher compared to the AAE value, indicates an overall overestimation of the experimental homogenization time by the proposed correlation (6), especially for the gas-liquid system. The comparison of experimental data and the correlation given by Equation (6) is presented in Figure 5 for both systems. The lines representing ±15% of the relative error are shown also in Figure 5 for illustration.   Alternatively, the experimental data were successfully correlated using a combined exponential and power-law function (7). The evaluated parameters of the power-law correlation (7), and values of AAE, ABE, and R 2 are presented in Table 13 for the gasliquid and gas-liquid-solid system. The three times lower AAE value indicates better predictability of homogenization time by correlation (7) compared to correlation (6) for the gas-liquid system. The slightly positive ABE value indicates a practically uniform estimation of the homogenization time by the proposed correlation (7). The comparison of measured values and values calculated using the proposed correlation (7) is shown in Figure 6 as a function of the riser superficial gas velocity for the gas-liquid and gas-liquidsolid systems.   (7) for gas-liquid system (dotted line), correlation (7) for gas-liquid-solid system (full line).

Gas-Liquid System
The comparison of experimental data and the correlation given by Equation (7) is presented in Figure 7 for both systems. The lines representing the relative error of ±15% are shown also in Figure 7 for illustration.

Overall Volumetric Liquid-Phase Mass Transfer Coefficient k L a
The values of the overall volumetric mass transfer coefficient corrected onto 20 • C are shown in Figure 8 as a function of dimensionless deflector clearance for the gas-liquid and gas-liquid-solid systems. For comparison, the values calculated using the proposed correlation (12) are shown also. For the gas-liquid system, reducing the deflector clearance, the overall volumetric mass transfer coefficient slightly increases. Mass transfer coefficient for C * D = 0.15 is approx. 10-17% higher than for C * D = 0.75. The presence of solid phase reduced the mass transfer coefficient by 15-35%. In the gas-liquid-solid system, the effect of deflector clearance is more accentuated compared to the gas-liquid system. Mass transfer coefficient for C * D = 0.15 is approx. 20-29% higher than for C * D = 0.75. The values of the power law exponent for superficial gas velocity reported in the literature range usually in the range from 0.642 to 1.12 for the gas-liquid system. Analyzing overall data, the α-values of 1.009 and 1.019 were obtained for the gas-liquid system and gas-liquid-solid system, respectively. The applicability of the α-values of 1 for the gas-liquid system and the gas-liquid-solid system was tested using a hypothesis test for each deflector clearance separately. The hypothesis test results are presented in Table 14. Except for C * D = 0.35 in the gas-liquid-solid system, the proposed α-value was statistically confirmed for both systems.
The independence of the overall volumetric mass transfer coefficient of the deflector clearance was tested as the hypothesis, that is, k L a = B.(C * D )0 = const. (i.e., β pred = 0). The hypothesis test results are presented in Table 15. Statistically, the independence of deflector clearance was confirmed practically for all u SGR except the lowest u SGR of 0.011 m/s in the gas-liquid system. However, the parity analysis shows that the deflector clearance should be taken into account for both systems. Analyzing the overall data, the β-values of −0.072 and −0.134 were obtained for the gas-liquid system and gas-liquid-solid system, respectively. For the data correlation, the β-value of −0.1 was assumed for the gas-liquid system and the gas-liquid-solid system. Table 14. Overall volumetric mass transfer coefficient k L a: Results of the hypothesis testing-effect of riser superficial velocity u SGR for deflector clearance C * D = const.

Hypothesis Testing
Relation: k L a = B R ·(u SGR ) α α calc (-) Hypothesis 1 : k L a = B H ·(u SGR ) 0.8 t-Characteristics |t| Relation: k L a = B R ·(u SGR ) α α calc (-)   The evaluated parameters of the power-law correlation (12) and values of AAE, ABE, and R 2 are presented in Table 16 for the gas-liquid and gas-liquid-solid systems. The positive ABE value, higher compared to the AAE value, indicates an overall overestimation of the experimental k L a coefficient by the proposed correlation (12), especially for the gas-liquid system. The comparison of experimental data and the correlation given by Equation (12) is presented in Figure 9 for both systems. The lines representing the relative error of ±15% are shown also in Figure 9 for illustration. Table 16. Overall volumetric mass transfer coefficient k L a: Evaluated parameters of correlation (12).  Alternatively, the experimental data were successfully correlated using a combined exponential and power-law function (13). The evaluated parameters of the power-law correlation (13) and values of AAE, ABE, and R 2 are presented in Table 17 for the gas-liquid and gas-liquid-solid system. The approx. three times lower AAE value indicates better predictability of k L a coefficient by correlation (13) compared to correlation (12) for the gasliquid system. The slightly positive ABE value indicates a practically uniform estimation of the k L a coefficient by the proposed correlation (13). The comparison of measured values and values calculated using the proposed correlation (13) is shown in Figure 10 as a function of the riser superficial gas velocity for the gas-liquid and gas-liquid-solid systems. The comparison of experimental data and the correlation given by Equation (13) is presented in Figure 11 for both systems. The lines representing ±15% of the relative error are shown also in Figure 11 for illustration Figure 10. Overall volumetric mass transfer coefficient k L a: Effect of riser superficial gas velocity: Gas-liquid system (empty symbols), gas-liquid-solid system (full symbols), correlation (13) for gas-liquid system (dotted line), correlation (13) for gas-liquid-solid system (full line).

Conclusions
The experiments were carried out in a laboratory conical jet-loop airlift bioreactor of 300 mm in inner diameter and volume of 62.5 dm 3 . As a novelty, the gas separator was equipped with an adjustable deflector placed above the riser compared with a standard design. The effects of riser superficial gas velocity u SGR on total gas holdup ε GT , homogenization time t H , and overall volumetric liquid-phase mass transfer coefficient k L a were investigated in the two-phase air-water system and three-phase air-water-PVC particle system with the volumetric solid fraction of 1%. The airlift was operated in regime I according to the classification given by Heijnen et al. [27]. The experimental data were successfully correlated using a power-law function or using a combined exponential-and power-law function. The evaluated values of the power law exponent for superficial gas velocity were compared with the values reported in the literature for the gas-liquid system using the hypothesis testing method.
The following results were gained: • Reducing the deflector clearance, the total gas holdup decreases for the gas-liquid system. Unlike this, the weak effect of deflector clearance was observed for the gas-liquid-solid system, especially for higher values of riser superficial gas velocity; • For the gas-liquid system, when reducing deflector clearance, homogenization time increased twice compared to the highest deflector clearance tested. For the gas-liquidsolid system, the effect of deflector clearance is weaker compared to the gas-liquid system and the presence of solid phase shortens the homogenization time, especially for lower riser superficial gas velocity and deflector clearance; • For the gas-liquid system, when reducing the deflector clearance, the overall volumetric mass transfer coefficient slightly increases by 10-17%. The presence of solid phase reduced the mass transfer coefficient by 15-35%. In the gas-liquid-solid system, the effect of deflector clearance is more accentuated compared to the gas-liquid system. The mass transfer coefficient for the lowest tested deflector clearance was approx. 20-29% higher than for the highest tested deflector clearance.

•
The airlift reactors equipped with internals placed in the gas separation section may be a promising novel airlift reactor design, as reported by Zhang et al. [30].