Hydrodynamics and Mass Transfer in a Concentric Internal Jet-Loop Airlift Bioreactor Equipped with a Deflector
Abstract
:1. Introduction
1.1. Algae Potential
1.2. Microalgae Cultivation
1.3. Internal-Loop Airlift Reactor
1.4. Main Operational Parameters
1.4.1. Total Gas Holdup
1.4.2. Homogenization Time
1.4.3. Overall Volumetric Mass Transfer Coefficient kLa
1.4.4. Effect of Solid Phase
1.5. Motivation
2. Materials and Methods
2.1. Experimental Apparatus
2.2. Experimental Conditions
2.3. Experimental Methods
2.3.1. Total Gas Holdup
2.3.2. Homogenization Time
2.3.3. Overall Volumetric Liquid-Phase Mass Transfer Coefficient kLa
2.3.4. Statistical Analysis
- (i)
- average absolute error (AAE):
- (ii)
- average biased error (ABE):
- (iii)
- coefficient of determination (R2):
3. Results
3.1. Total Gas Holdup
3.2. Homogenization Time tH
3.3. Overall Volumetric Liquid-Phase Mass Transfer Coefficient kLa
4. Conclusions
- 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–liquid–solid 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].
Author Contributions
Funding
Conflicts of Interest
Nomenclature
AAE | average absolute error | % |
ABE | average bias error | % |
AC | column cross-section area | m2 |
AD | downcomer cross-section area | m2 |
AR | riser cross-section area | m2 |
Bo | Bond number; Bo = g⋅ρL⋅Dchar2/σ | - |
BR | bottom spatial ratio; B = CRB/DR | - |
cL | mass concentration of liquid dissolved oxygen | kg/m3 |
mass concentration of dissolved oxygen in liquid at saturation | kg/m3 | |
C | temperature correction factor in Equation (11) | - |
C | constant of proportionality in Equation (4) | (m/s)-α |
C | constant of proportionality in Equation (6) | s⋅(m/s)-α |
C | constant of proportionality in Equation (7) | s |
C | constant of proportionality in Equation (12) | h−1⋅(m/s)-α |
C | constant of proportionality in Equation (13) | h−1 |
CD | deflector clearance | m |
CRB | riser bottom clearance | m |
CRU | riser upper clearance | m |
dh | hole diameter (in gas distributor) | m |
DC | column inner diameter | m |
Dchar | characteristic diameter (DR or DC) | m |
DD | downcomer inner diameter | m |
DL | diffusivity coefficient of gas in liquid | m2/s |
DR | riser inner diameter | m |
DS | gas separator inner diameter | m |
DT | draft tube inner diameter | m |
Fr | Froude number; Fr = uSG/(g⋅Dchar)0.5 | - |
g | gravity acceleration | m/s2 |
Ga | Galilei number; Ga = g⋅ρL2⋅Dchar3/μL2 | - |
HL0 | liquid filling height | m |
HG+L | height of gas–liquid dispersion | m |
HG+L+S | height of gas–liquid–solid dispersion | m |
HR | riser height | m |
kLa | overall volumetric liquid-phase mass transfer coefficient | s−1 |
Mo | Morton number; Mo = g⋅μL4/(ρL⋅σL3) | - |
OTR | oxygen transfer rate | kg/(m3.s) |
R | downcomer resistance flow ratio; R = AD/AR | - |
R2 | coefficient of determination | - |
SG | gas-to-liquid interfacial area | m2 |
Sc | Schmidt number; Sc = μL/(ρL⋅DL) | - |
Sh | Sherwood number; Sh = kLa⋅Dchar2/DL | - |
t | time | s |
T | temperature | °C |
TR | top spatial ratio; T = CRU/DR + 1 | - |
uSG | superficial gas velocity (for riser or column) | m/s |
uSGC | column superficial gas velocity (based on the column cross-section); /AC | m/s |
uSGR | riser superficial gas velocity (based on the riser cross-section); /AR | m/s |
V | volume | m3 |
gas volumetric flowrate | m3/s | |
Y | gas separator ratio; Y = (CRU + DR)/DS | - |
Greek Letters
α | power-law exponent in Equations (4), (6), and (12) | - |
α | power-law exponent in Equations (7) and (13) | s/m |
α | significance level | - |
β | power-law exponent in Equations (4), (6), (7), (12), and (13) | - |
ε | gas hold up | - |
φS | volumetric solid fraction | - |
μL | dynamic viscosity of liquid | Pa.s |
υ | kinematic viscosity | m2/s |
ρ | density | kg/m3 |
σ | surface tension | N/m |
τ | response time of oxygen probe | s |
Indexes
B | bottom |
C | column |
calc | calculated |
D | downcomer |
G | gas phase |
L | liquid phase |
pred | predicted |
R | riser |
S | gas separator |
S | solid phase |
T | draft tube |
T | total |
U | upper |
Abbreviation
ALR | airlift reactor |
References
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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. |
Source | Correlation |
---|---|
Lu et al. [29] | Concentric tube ALR. DD = 0.188 m, AR/AD = 0.695 and 1.38. Gas distribution: Single nozzle. Air–water system. |
εGT = 0.035 × uSGC0.647 × (AR/AD)−0.085 | |
0.02 < uSGC (m/s) < 0.1 | |
Square airlift with concentric tube; W = 0.167 m; AR/AD = 0.695 and 1.38. Gas distribution: Single nozzle. Air–water system. | |
εGT = 0.046 × uSGC0.58 × (AR/AD)−0.072 | |
0.02 < uSGC (m/s) < 0.1 | |
Chisti [31] | Concentric tube ALR Gas distribution: Perforated plate (40 holes, dh = 1 mm) Air–liquid system. Liquids: Water, salt solution. |
ε = 1.488 × uSGC0.892; bubble flow, perforated plate. | |
ε = 0.371 × uSGC0.430; coalesced bubble flow, perforated plate. | |
Juraščík et al. [32] | Concentric tube ALR. Gas distribution: Perforated plate. Air–water system. ALR1: V = 12 dm3, DC = 0.108 m, AD/AR = 1.23; ALR2: V = 40 dm3, DC = 0.157 m, AD/AR = 0.95; ALR3: V = 195 dm3, DC = 0.294 m, AD/AR = 1.01; |
εGT = 0.999 × uSGR2/3 × (1+AD/AR)−1; V = 12 dm3 | |
εGT = 0.946 × uSGR2/3 × (1+AD/AR)−1; V = 40 dm3 | |
εGT = 1.060 × uSGR2/3 × (1+AD/AR)−1; V = 195 dm3 | |
uSGC ≤ 0.065 m/s | |
Albijanić et al. [33] | Concentric-tube ALR with spherical bottom, DD = DC = 106 mm, DR/DC = 0.51. Gas distribution: Single orifice (dh = 4 mm). Air–liquid system; Liquids: Water, an aqueous solution of methanol, ethanol, n-propanol, isopropanol, and n-butanol (1 wt %). |
0.0025 < uSGC (m/s) < 0.05 | |
εGT = 1.65 × uSGC0.97 × [1 + (−dσ/dcA)0.20]1.52 | |
cA—alcohol concentration (wt %) (dσ/dcA)—surface tension gradient | |
Gavrilescu and Tudose [34] | Concentric tube airlift; DR = 0.1 ÷ 0.6 m. Dchar = DR. Gas distribution: Perforated plate sparger (100 × dh = 2 mm), multiring sparger (dh = 3.5 mm). Air–water system. |
εGT = 3 × FrR1.2 × B−0.13 × Y−0.2 × T−0.6 × R−0.16 | |
5⋅10−3 < FrR < 110·10−3, 0.5 < B < 3.8, 0.333 < Y < 1.267, 1 < T < 3.8, 0.1 < R < 0.9, AD/AR ≥ 1, uSGR ≤ 0.11 m/s | |
B—bottom spatial ratio (B = CRB/DR) R—downcomer resistance flow ratio (R = AD/AR) T—top spatial ratio (T = CRU/DR + 1) Y—gas separator ratio (Y = (CRU + DR)/DS) | |
Gouveia et al. [35] | Concentric-draft tube ALR, annulus-sparged ALR; AD/AR = 0.63. DC = 0.100 m; DD = DT = 0.080 m, Dchar = DRekv (riser equivalent diameter). Gas distribution: Ring with 35 holes (dh = 0.7 mm). Air–water system. |
εGT = 1.32 × FrR0.77 × B0.39 × T0.08 | |
0.0126 < uSGR (m/s) < 0.0440 |
Source | Correlation |
---|---|
Lu et al. [29] | Concentric tube ALR; DD = 0.188 m, AR/AD = 0.695 and 1.38. Gas distribution: Single nozzle. Air–water system. |
tH (s) = 45.70 × uSGC−0.377 × (AR/AD)−0.319 | |
0.02 < uSGC (m/s) < 0.1 | |
Square airlift with concentric tube; W = 0.167 m; AR/AD = 0.695 and 1.38. Gas distribution: Single nozzle. Air–water system. | |
tH (s) = 53.15 × uSGC−0.377 × (AR/AD)−0.269 | |
0.02 < uSGC (m/s) < 0.1 | |
Bando et al. [37] | Concentric tube airlift; DC(m)/DT(m) = 0.164/0.094; 0.300/0.164; 0.500/0.300. Gas distribution: perforated plate (dh = 3 mm). Air–water system. |
tH (s) = C × uSGC−0.5 × DC1.4 × (HG+L/DC)1.2 × (DT/DC)−1.4 × (1 − DT/DC)−1.1 | |
C = 2.2 for draft tube sparged ALR or C = 2.6 for annulus sparged ALR; 0.114 ≤ DC ≤ 0.50 m; 5 ≤ HG+L/DC ≤ 40; 0.4 ≤ DT/DC ≤ 0.8. | |
Gavrilescu and Tudose [38] | Concentric draft tube ALR; DR = 0.1 ÷ 0.6 m. Dchar = DR. Gas distribution: Perforated plate sparger (100 × dh = 2 mm), multiring sparger (dh = 3.5 mm). Air–water system. |
a) bubble and transition flow regime (uSGR < 0.08 m/s) | |
tH (s) = 4.6 × R−0.47 × B−1.10 × T−0.64 × FrR −1.11 | |
b) churn-turbulent regime (uSGR > 0.08 m/s) | |
tH (s) = 4.6 × R−0.47 × B0.8T × FrR −1.11 | |
Petrović et al. [39] | Concentric tube ALR; DC = 0.2 m, DT = 0.080, 0.1, and 0.15 m. Air–water system. |
tH (s) = 53.5 × uSGC−0.31 × (HT/DC)0.12 × VR0.19 × VD0.50 × VS−0.26 | |
uSGC (m/s) < 0.08 |
Source | Correlation |
---|---|
Juraščík et al. [32] | Concentric tube ALR. ALR1: V = 12 dm3, DC = 0.108 m, AD/AR = 1.23; ALR2: V = 40 dm3, DC = 0.157 m, AD/AR = 0.95; ALR3: V = 195 dm3, DC = 0.294 m, AD/AR = 1.01; Gas distribution: Perforated plate. Air–water system. |
kLa (s−1) = 0.473εGT1.2; V = 12 dm3 | |
kLa (s−1) = 0.524εGT1.2; V = 40 dm3 | |
kLa (s−1) = 0.541εGT1.2; V = 195 dm3 | |
kLa (s−1) = 0.401uSGR0.8 × (1 + AD/AR)−1; V = 12 dm3 | |
kLa (s−1) = 0.428uSGR0.8 × (1 + AD/AR)−1; V = 40 dm3 | |
kLa (s−1) = 0.506uSGR0.8 × (1 + AD/AR)−1; V = 195 dm3 | |
uSGC ≤ 0.065 m/s | |
Albijanić et al. [33] | Concentric- tube ALR with spherical bottom, DD = DC = 106 mm, DR = DT, DR/DC = 0.51; Dchar = DC. Gas distribution: Single orifice (dh = 4 mm). Air–liquid system; Liquids: Water, an aqueous solution of methanol, ethanol, n-propanol, isopropanol, and n-butanol (1 wt. %). |
0.0025 < uSGC (m/s) < 0.05 | |
kLa (s−1) = 0.028 × uSGC0.77 × [1 + (−dσ/dcA)0.15]0.71 | |
cA—alcohol concentration (wt %) (dσ/dcA)—surface tension gradient | |
Sanchez Miron et al. [36] | Concentric draft tube ALR; DC = DD = 193 mm, DR = DT = 144 mm. Gas distribution: Cross-piece type sparger (13 holes, dh = 0.5 mm). Air–liquid system. Liquids: Tap water, seawater. uSGC (m/s) < 0.03 |
kLa (s−1) = 0.641/(uSGC−0.935 − 1) for tap water | |
kLa (s−1) = 0.865/(uSGC−0.964 − 1) for sea water | |
Luo et al. [44] | Concentric tube ALR; DR = DC = 0.284 m, DD = DT = 0.07 m, CTB = 0.040 m. Annulus sparged ALR. Gas distribution: Two-orifice nozzle (dh = 2.6 mm), 4-orifice nozzle (1.84 mm), O-ring distributor (63 holes, dh = 1 mm). Air–water system. |
kLa (s−1) = 0.2557uSGC0.8496; 2-orifice nozzle | |
kLa (s−1) = 0.4661uSGC0.8496; 4-orifice nozzle | |
kLa (s−1) = 0.2557uSGC0.8496; O-ring nozzle | |
0.0007 ≤ uSGC (m/s) ≤ 0.00281 | |
Gouveia et al. [35] | Concentric-draft tube ALR, annulus-sparged ALR; AD/AR = 0.63. DC = 0.100 m; DD = DT = 0.080 m, Dchar = DRekv (riser equivalent diameter). Gas distribution: Ring with 35 holes (dh = 0.7 mm). Air–water system. |
ShR = 7.16 × 106 × FrR1.121 × B0.201 × T0.410 | |
0.0126 < uSGR (m/s) < 0.0440; 40 < kLa (h−1) < 250 | |
Koide et al. [40] | Concentric draft tube ALR with flat bottom, DD = DC, DR = DT, Dchar = DC. Gas distributors: Single nozzle, perforated plate, porous glass plate Air–liquid system, liquid: Water, an aqueous solution of glycerol, glycol, BaCl2, NaSO4, Na2SO3. |
0.021 ≤ uSGC (m/s) ≤ 0.15; 0.1 ≤ DD ≤ 0.3 m; 0.06 ≤ DR ≤ 0.19 m | |
ShC = 0.477⋅× εGT1.36 × Sc0.5 × GaC0.257 × BoC0.873 × (DT/DC)−0.542 | |
369 ≤ Sc ≤ 56,800; 1,360 ≤ BoC ≤ 12,200; 2.27⋅108 ≤ GaC ≤ 3.32⋅1011; 0.471 ≤ DT/DC ≤ 0.743; 0.037 ≤ εGT ≤ 0.21 | |
Gavrilescu and Tudose [41] | Concentric-draught tube ALR. DR = 0.1 ÷ 0.6 m. Gas distribution: Perforated plate sparger (100 × dh = 2 mm), multiring sparger (dh = 3.5 mm). Air-water system. |
ShR = 1.204⋅106 × FrR0.9 × GaR0.01 × T−0.18 × B−0.1 × Y−1.70 × R−0.18 | |
5⋅10−3 < FrR < 110⋅10−3, 9⋅106 < GaR < 3⋅109, 0.5 < B < 3.8, 0.333 < Y < 1.267, 1 < T < 3.8, 0.1 < R < 0.9, AD/AR ≥ 1, uSGR ≤ 0.11 m/s | |
Cerri et al. [42] | Concentric tube airlift with flat bottom, DD = DC, DR = DT, Dchar = DR. DR/DC = 0.6; 1.68 ≤ AD/AR ≤ 1.84; V = 2, 5, and 10 dm3. Gas distribution: Cross-piece type sparger (dh = 0.5 mm) Air–liquid system. Liquids: Newtonian fluids (water, aqueous solutions of glycerol) and non-Newtonian fluids (aqueous solutions of xanthan gum). |
ShR = 4.6 × 10−5 × FrR0.642 × Sc0.779 × GaR0.673 × BoR0.245 × εGT0.2 | |
4.921 < ShR < 256,768; 0.011 < FrR < 0.143; 297 < Sc < 27,544; 410 < BoR < 1.510; 1.4⋅107 < GaR < 1.8⋅1010; 0.009 < εGT < 0.170 | |
Koide et al. [45] | Concentric draft tube ALR with conical bottom, DD = DC, DR = DT, Dchar = DC. Gas distributor: Perforated plate. Air–liquid system, liquid: Water, an aqueous solution of glycerol, glycol, BaCl2, NaSO4. |
0.021 ≤ uSGC (m/s) ≤ 0.15; 0.1 ≤ DD ≤ 0.3 m; 0.06 ≤ DR ≤ 0.19 m; | |
ShC = 4.04⋅× εGT1.34 × Sc0.5 × GaC0.260 × BoC0.670⋅× (DT/DC)−0.047 × (1 + 2.00φS1.30)−1 | |
371 ≤ Sc ≤ 55,200; 2,660 ≤ BoC ≤ 12,200; 2.35⋅108 ≤ GaC ≤ 3.29⋅1011; 1.69⋅10−11 ≤ Mo ≤ 6.67⋅10−7; 0.471 ≤ DT/DC ≤ 0.743; 0.0379 ≤ εGT ≤ 0.224; 0 ≤ φS (v/v) ≤ 0.20 |
Parameter | Symbol | This Work |
---|---|---|
downcomer diameter | DD (mm) | 300 |
riser diameter | DR (mm) | 66 |
gas separator diameter | DS (mm) | 300 |
riser height | HR (mm) | 720 |
riser bottom clearance | CRB (mm) | 70 |
riser upper clearance | CRU (mm) | 200 |
deflector clearance | CD (mm) | 30, 70, 110, 150 |
unaerated liquid height | HL (mm) | 960 |
unaerated liquid volume | VL (m3) | 0.0625 |
Phase | Properties |
---|---|
Gas phase | air (T = 25 ± 2 °C); uSGR = 0.011; 0.023; 0.034; 0.045 m/s |
Liquid phase | tap water (T = 25 ± 2 °C) |
Solid phase | extruded PVC rods (Ø 4 mm × L = (2.5 ÷ 4) mm; ρ = 1 287 kg/m3); 1% v/v |
Gas–Liquid System | Gas–Liquid–Solid System | |||
---|---|---|---|---|
Hypothesis Testing | Relation: εGT = BR·(uSGR)α αcalc (-) | Hypothesis 1: εGT = BH·(uSGR)0.8 t-Characteristics | Relation: εGT = BR·(uSGR)α αcalc (-) | Hypothesis 1: εGT = BH·(uSGR)0.8 t-Characteristics |
= 0.75 | 0.621 | 9.7 (not acceptable) | 1.616 | 1.2 (acceptable) |
= 0.55 | 0.567 | 4.1 (acceptable) | 1.085 | 2 (acceptable) |
= 0.35 | 0.850 | 2.9 (acceptable) | 1.188 | 0.1 (acceptable) |
= 0.15 | 1.032 | 4 (acceptable) | 0.861 | 3.5 (acceptable) |
Overall data analysis | 0.802 | --- | 1.187 | --- |
Gas–Liquid System | Gas–Liquid–Solid System | |||
---|---|---|---|---|
Hypothesis Testing | Relation: εGT = BR·()β βcalc (-) | Hypothesis 1: εGT = BH·()0 t-Characteristics | Relation: εGT = BR·()β βcalc (-) | Hypothesis 1: εGT = BH·()0 t-Characteristics |
uSGR = 0.011 m/s | 0.468 | 5.5 (not acceptable) | --- | --- |
uSGR = 0.023 m/s | 0.246 | 8.2 (not acceptable) | −0.275 | 3.3 (acceptable) |
uSGR = 0.034 m/s | 0.107 | 2.3 (acceptable) | −0.083 | 1.1 (acceptable) |
uSGR = 0.045 m/s | 0.085 | 4.1 (acceptable) | −0.017 | 0.6 (acceptable) |
Overall data analysis | 0.205 | --- | −0.125 | --- |
System | C 1 ((m/s)-α) | α (-) | β (-) | R2 (-) | AAE (%) | ABE (%) |
---|---|---|---|---|---|---|
Gas–liquid | 0.098 ± 0.002 | 0.8 | 0.2 | 0.948 | 7.81 | −1 |
Gas–liquid–solid | 0.351 ± 0.008 | 1.2 | −0.1 | 0.930 | 7.74 | −0.1 |
Gas–Liquid System | Gas–Liquid–Solid System | |||
---|---|---|---|---|
Hypothesis Testing | Relation: tH = BR·(uSGR)α αcalc (-) | Hypothesis 1: tH = BH·(uSGR)0.8 t-Characteristics | Relation: tH = BR·(uSGR)α αcalc (-) | Hypothesis 1: tH = BH·(uSGR)0.8 t-Characteristics |
= 0.75 | −0.595 | 1.4 (acceptable) | −0.306 | 16 (not acceptable) |
= 0.55 | −0.589 | 0.5 (acceptable) | −0.303 | 0.1 (acceptable) |
= 0.35 | −0.537 | 0.3 (acceptable) | −0.318 | 0.4 (acceptable) |
= 0.15 | −0.579 | 0.9 (acceptable) | −0.296 | 0.04 (acceptable) |
Overall data analysis | −0.575 | --- | −0.306 | --- |
Gas–Liquid System | Gas–Liquid–Solid System | |||
---|---|---|---|---|
Hypothesis Testing | Relation: tH = BR·()β βcalc (-) | Hypothesis 1: tH = BH·()0 t-Characteristics | Relation: tH = BR·()β βcalc (-) | Hypothesis 1: tH = BH·()0 t-Characteristics |
uSGR = 0.011 m/s | −0.404 | 4.2 (acceptable) | --- | --- |
uSGR = 0.023 m/s | −0.427 | 3 (acceptable) | −0.132 | 5.1 (not acceptable) |
uSGR = 0.034 m/s | −0.382 | 2.2 (acceptable) | −0.160 | 7.9 (not acceptable) |
uSGR = 0.045 m/s | −0.442 | 5.1 (not acceptable) | −0.132 | 6.6 (not acceptable) |
Overall data analysis | −0.414 | --- | −0.141 | --- |
System | C 1 (s⋅(m/s)-α) | α (-) | β (-) | R2 (-) | AAE (%) | ABE (%) |
---|---|---|---|---|---|---|
Gas–liquid | 3.640 ± 0.105 | −0.5 | −0.4 | 0.91 | 13 | 2.72 |
Gas–liquid–solid | 8.746 ± 0.094 | −0.3 | −0.1 | 0.917 | 3 | 0.44 |
System | C 1 (s) | α (s/m) | β (-) | R2 (-) | AAE (%) | ABE (%) |
---|---|---|---|---|---|---|
Gas–liquid | 99.3 ± 1.3 | −24 | 0.6 | 0.981 | 4.13 | 0.1 |
Gas–liquid–solid | 41.8 ± 0.4 | −9 | 0.2 | 0.952 | 2.4 | 0.15 |
Gas–Liquid System | Gas–Liquid–Solid System | |||
---|---|---|---|---|
Hypothesis Testing | Relation: kLa = BR·(uSGR)α αcalc (-) | Hypothesis 1: kLa = BH·(uSGR)0.8 t-Characteristics | Relation: kLa = BR·(uSGR)α αcalc (-) | Hypothesis 1: kLa = BH·(uSGR)0.8 t-Characteristics |
= 0.75 | 0.973 | 0.2 (acceptable) | 1.045 | 0.7 (acceptable) |
= 0.55 | 1.069 | 0.4 (acceptable) | 1.027 | 0.1 (acceptable) |
= 0.35 | 1.075 | 0.4 (acceptable) | 1.064 | 4.4 (not acceptable) |
= 0.15 | 0.917 | 0.7 (acceptable) | 0.941 | 0.4 (acceptable) |
Overall data analysis | 1.009 | --- | 1.019 | --- |
Gas–Liquid System | Gas–Liquid–Solid System | |||
---|---|---|---|---|
Hypothesis Testing | Relation: kLa = BR·()β βcalc (-) | Hypothesis 1: kLa = BH·()0 t-Characteristics | Relation: kLa = BR·()β βcalc (-) | Hypothesis 1: kLa = BH·()0 t-Characteristics |
uSGR = 0.011 m/s | −0.108 | 6.3 (not acceptable) | --- | --- |
uSGR = 0.023 m/s | −0.091 | 1.3 (acceptable) | −0.159 | 3.1 (acceptable) |
uSGR = 0.034 m/s | −0.049 | 1 (acceptable) | −0.125 | 4 (acceptable) |
uSGR = 0.045 m/s | −0.039 | 0.5 (acceptable) | −0.118 | 3.7 (acceptable) |
Overall data analysis | −0.072 | --- | −0.134 | --- |
System | C 1 (h−1⋅(m/s)-α) | α (-) | β (-) | R2 (-) | AAE (%) | ABE (%) |
---|---|---|---|---|---|---|
Gas–liquid | 246 ± 8.3 | 1 | −0.1 | 0.923 | 11.2 | 4.7 |
Gas–liquid–solid | 166.6 ± 2.4 | 1 | −0.1 | 0.974 | 4.14 | 1 |
System | C 1 (h−1) | α (s/m) | β (-) | R2 (-) | AAE (%) | ABE (%) |
---|---|---|---|---|---|---|
Gas–liquid | 1.81 ± 0.03 | 42 | −0.1 | 0.979 | 4.5 | 0.4 |
Gas–liquid–solid | 1.89 ± 0.02 | 31 | −0.1 | 0.984 | 3.2 | 0.6 |
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Šulc, R.; Dymák, J. Hydrodynamics and Mass Transfer in a Concentric Internal Jet-Loop Airlift Bioreactor Equipped with a Deflector. Energies 2021, 14, 4329. https://doi.org/10.3390/en14144329
Šulc R, Dymák J. Hydrodynamics and Mass Transfer in a Concentric Internal Jet-Loop Airlift Bioreactor Equipped with a Deflector. Energies. 2021; 14(14):4329. https://doi.org/10.3390/en14144329
Chicago/Turabian StyleŠulc, Radek, and Jan Dymák. 2021. "Hydrodynamics and Mass Transfer in a Concentric Internal Jet-Loop Airlift Bioreactor Equipped with a Deflector" Energies 14, no. 14: 4329. https://doi.org/10.3390/en14144329