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Experimental investigations of hydrodynamic characteristics of a hybrid fluidized bed airlift reactor with external liquid circulation
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Experimental investigations of hydrodynamic characteristics of a hybrid fluidized bed airlift reactor with external liquid circulation ´ Mateusz Pronczuk, Katarzyna Bizon ∗ , Robert Grzywacz Department of Chemical Engineering and Technology, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland
a r t i c l e
i n f o
a b s t r a c t
Article history:
The paper presents a simple analytical model of the hydrodynamics of a hybrid airlift appa-
Received 8 March 2017
ratus with an external liquid circulation loop. The apparatus consists of two sections: a
Received in revised form 4 August
two-phase fluidization column and a barbotage section. The advantage of such a configura-
2017
tion is that there is no contact between the gas phase and the solid phase, which is relevant
Accepted 30 August 2017
in case of processes involving a biofilm immobilization on fine carrier particles. Then, the
Available online 7 September 2017
shear stresses produced by passing bubbles do not damage the surface of a biofilm. The
Keywords:
mine basic hydrodynamic parameters of the apparatus including liquid and gas velocity,
External loop airlift
gas hold-up, and porosity and height of the fluidized bed. The model was verified exper-
proposed model was derived based on the global momentum balance. It allows to deter-
Fluidized bed
imentally and the hydrodynamics of the selected zones of the apparatus was simulated
Gas holdup
using Computational Fluid Dynamics (CFD).
Liquid circulation velocity
© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Momentum balance
1.
Introduction
the aerated and non-aerated zone acts as a driving force for the liquid circulation.
Three-phase fluidized-bed reactors; thanks to many advantages such as higher biomass concentration, better contact between liquid and solid phases and low washout of microorganisms compared to con-
However, in case of a three-phase fluidized bed, flowing gas bubbles induce a shear stress which may damage a delicate biofilm deposited on the carrier surface, which may lead to complete degradation of
ventional tank reactor (Wisecarver and Fan, 1989) are commonly used for aerobic microbiological processes (Tang et al., 1987; Wisecarver and Fan, 1989). Immobilization of the biomass on a fine carrier particles,
biofilm (Henzler, 2000). The possible solution to this problem is to separate the barbotage zone from the fluidized-bed zone. Dunn et al. (1983)
where solid particles act as a carrier for biofilm, permits to obtain a significant increase in its overall concentration in the reaction environment (Fan et al., 1987). Moreover, fluidization allows for easy bed
introduced an apparatus composed of a fluidized-bed reactor and an aerator connected by a recirculation loop. According to the authors such a configuration permits to eliminate contact of the gas bubbles with the biofilm immobilized on the solid particles. Guo et al. (1997) pro-
replacement and prevents particles agglomeration and clogging of the
posed a modification of the three-phase airlift reactor with external
pores, which is a serious issue for fixed beds (Iliuta and Larachi, 2004). Aeration of the liquid, i.e. is the process by which air is dissolved in a liquid, has two functions. Apart from providing oxygen for the reaction,
liquid circulation, in which the barbotage section is located above the fluidized-bed section, thus there is no mixing of the solid phase and gas. An additional advantage is that such a configuration does not require a
the barbotage enhances mixing. In the airlift reactor the aeration has got an additional function – supply of the air into the barbotage zone leads to the reduction of the average density of a gas–liquid mixture in
circulator pump. For an appropriate level of aeration the pressure difference enables to achieve the liquid velocity necessary to fluidize the bed.
relation to the liquid density. The difference in the average density of
Olivieri et al. (2010) introduced their own design of a hybrid airlift bioreactor. The authors proposed an apparatus with the internal liquid circulation loop having more compact design than the apparatus with the external liquid circulation. An analytical model of the
∗
Corresponding author. E-mail addresses: [email protected], [email protected] (K. Bizon). http://dx.doi.org/10.1016/j.cherd.2017.08.028 0263-8762/© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
189
Nomenclature d FV g H m n p Re S u
Diameter, m Volumetric flow rate, m3 /s Gravitational acceleration, m/s2 Height, m Mass, kg Exponent in the Richardsona and Zaki model, – Pressure drop, Pa Reynolds number, – Cross section, m2 Velocity, m/s
Greek symbols Bed porosity, – ε1 Gas holdup, – ε2 Dynamic viscosity coefficient, kg/(m s) Flow friction coefficient, – Local friction coefficient, – Density, kg/m3 Surface tension, N/m Gas bubble rise velocity, m/s
Shape factor, – Subscripts 0 Value related to the cross section of the apparatus 1–5 Zones of the apparatus (Fig. 1) Refers to local friction factor of the bend E f Refers to fluidized bed feed Refers to feed flow Gas phase g I Refers to local friction factor of the upper vessel inlet Liquid phase l Minimum fluidization conditions mf Refers to local friction factor of the mesh N O Refers to local friction factor of the upper vessel outlet s Solid phase Refers to mesh S Refers to local friction factor of the sudden SE expansion t Refers to terminal velocity of the particle
hydordynamics of the loop apparatus with the internal liquid circulation was then formulated by Tabi´s et al. (2014). Fig. 1 shows two different configurations of the apparatus, i.e. with the external (Fig. 1a) and internal (Fig. 1b) liquid circulation. Five zones can be distinguished in both configurations. As shown in Fig. 1 these zones are: fluidization zone “1”, barbotage zone “2”, downcomer “3”, degassing zone “4” and bottom zone “5”. Description of the hydrodynamics of the hybrid fluidized-bed reactor is a rather complex problem. Due to the presence of the gas phase such an apparatus may operate, like a traditional airlift reactor, in three hydrodynamic regimes characterized by: complete degassing of the liquid in the upper vessel, partial degassing of the liquid in the downcomer or gas circulation through all zones of the reactor. Depending on the liquid circulation velocity the bed of solid particles may operate as: a fixed bed resting on the bottom mesh, a fluidized bed or a fixed bed resting under the upper mesh. The combinations of operating regimes of the hybrid apparatus listed above are presented graphically in Fig. 2. Despite the variety of theoretically possible operating regimes of the hybrid apparatuses shown in Fig. 2, own experimental studies con-
Fig. 1 – Hybrid fluidized-bed apparatuses (a) with external liquid circulation, (b) with internal liquid circulation; 1 – fluidization zone, 2 – barbotage zone, 3 – downcomer, 4 – degassing zone, 5 – bottom zone. firmed complete degassing of the liquid in zone “4” (Fig. 1a). Therefore, the only possible operating modes are regimes I, IV and VII (Fig. 2) corresponding to the complete liquid degassing. On the other hand, a technologically attractive operating mode of the bed of solid particles corresponds to the regimes IV, V and VI (Fig. 2), i.e. conditions at which the bed is in a fluidized state. Thus, only the regime IV fulfils both conditions of the hybrid apparatus. The paper presents an analytical hydrodynamic model of a hybrid airlift apparatus with an external liquid circulation that provides design guidelines and allows to select optimal operating conditions. The proposed model is verified experimentally and the results obtained from the model are further compared with Computational Fluid Dynamics (CFD) simulations in order to adjust the values of local friction coefficients.
2.
Experimental setup
The experimental apparatus is shown in Fig. 3. It is equipped with an external circulation tube and is made of transparent tubes and plates made of poly methyl methacrylate (PMMA). A fluidized-bed section “1” (Fig. 1a) is located in the lower part of the riser. A wire mesh with the openings of 1 mm and made of wire having a diameter of 0.5 mm is mounted under the fluidization zone. To prevent entrainment of the particles from the fluidization zone, an identical mesh is disposed in the upper part of this section. Directly above this, a barbotage section is located. Air is supplied to the barbotage zone by means of a cross-shaped metal distributor. At the top of the gas distributor, 25 equally spaced holes (one hole in the centre and six holes on every branch) with diameter of 1 mm and at distance of 5 mm apart were drilled. The liquid leaving the barbotage section enters the upper vessel “4” and then it flows into the downcomer “3” (Fig. 1a). The design of the apparatus allows to mount circulation tubes of different diameters. The riser and the downcomer are connected in the bottom by means of a connector which creates a bottom section “5”. The air supplying the apparatus is first compressed by means of a compressor. Then it flows through a gas mass flow controller (MFC) allowing for the adjustment of the volumetric flow rate and enters the air distributor. The measurements were carried out for several values of the gas flow rate. The minimum gas flow rate coincided to the minimum fluidization conditions of the solid particles, whereas the highest corre-
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Fig. 3 – Scheme of the experimental setup: PC – personal computer, ADC – analog-to-digital converter, PS – pressure sensor, CP – conductivity probe, MFC – mass flow controller, UFM – ultrasonic flow meter, PP – peristaltic pump. Table 1 – Geometry of the apparatus, the bed properties and physical properties of the media.
Fig. 2 – Theoretically possible hydrodynamic regimes in the apparatus: (I) complete liquid degassing and fixed bed on the bottom mesh, (II) partial entrainment of gas bubbles and fixed bed on the bottom mesh, (III) circulation of gas bubbles and fixed bed on the bottom mesh, (IV) complete liquid degassing and fluidized bed, (V) partial entrainment of gas bubbles and fluidized bed, (VI) circulation of gas bubbles and fluidized bed, (VII) complete liquid degassing and fixed bed on the upper mesh, (VIII) partial entrainment of gas bubbles and fixed bed on the upper mesh, (IX) circulation of gas bubbles and fixed bed on the upper mesh. sponded to the value for which the bed height was equal to 0.9 m. Higher values of the gas flow rate led to the settlement of the particles beneath the upper mesh. The liquid supplied to the apparatus was dispensed in the lower part of the bottom zone by means of a peristaltic pump (PP). Water at the temperature of 288 K was supplied to the apparatus. The liquid circulation velocity was measured by means of the ultrasonic flow meter (UFM). Two ultrasonic transducers (UT) were mounted on the downcomer surface. They allow for non-intrusive measurement of the average flow velocity in the downcomer.
Parameter
Value
Unit
H1 H2 H3 d1 d2 d3 Hmf εmf ds
s s ut ms l l l g
1 1 2 80 × 10−3 80 × 10−3 30 × 10−3 ,50 × 10−3 ,80 × 10−3 , 105 × 10−3 0.44 3.2 × 10−3 0.976 1354 0.1204 0.4 997 11.4 × 10−4 73.2 × 10−3 1.185
m m m m m m m – m – kg m−3 m s−1 kg kg m−3 kg m−1 s−1 N m−1 kg m−3
The bed was made of polyoxymethylene (POM) polgranules. Its properties are given in Table 1. Terminal velocity of the particles was determined experimentally by measuring free fall time of the particles in the column filled with water. The pressure sensors (PS) were mounted along the barbotage zone. Measurement of the static pressure in the barbotage section permits to determine the gas holdup using the manometric method, which depending on the distance from the liquid surface in the upper zone can be calculated using the following expression: ε2 (H) =
l gH − p2 (H) l gH
(1)
The sensors were connected with a personal computer (PC) using an analog-to-digital converter (ADC). The apparatus was also equipped with five conductivity probes (CP) – before inlet and after outlet of the downcomer, under the bottom and the upper mesh, and at the barbotage zone outlet (Fig. 3). The con-
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Table 2 – Adjusted values of the local friction coefficient. Occurence of the resistance
Symbol
Value
Inlet of the upper vessel Outlet of the upper vessel Elbow Mesh
I O E N
1 0.5 1.1 12
Sudden flow expansion and collision with the bottom wall
SE
3.5
2 d 1 d3
2 −1
Fig. 4 – Liquid degassing in the upper vessel.
´ ductivity meters were used for tracer studies (Pronczuk, 2017). They consisted in the introduction of the KCl solution into downcomer, which was used as a tracer. Simultaneously measurements of a conductance were made in five points along the apparatus. Change in the liquid conductance is directly proportional to the change of the tracer concentration. All sensors and controllers were connected with the PC. The measurements and setting of the parameters were done using a Matlab script. Basic geometric parameters of the apparatus, the bed properties and physical properties of the media used in the calculations are reported in Table 1.
3.
Analytical model of the hydrodynamics
For design purposes, a hydrodynamic model should allow to determine basic hydrodynamic parameters of the apparatus, namely: liquid and gas velocities within each zone, gas holdup and a dynamic height of the fluidized bed. To prevent the settlement of the particles under the upper mesh, the superficial liquid velocity should be such that the height of the fluidized bed does not exceed 90% of the height of zone “1”. However, the superficial velocity cannot be lower than the minimum fluidization velocity. These two conditions can be written as follows: umf < u0l1 < (u0l : Hf < 0.9H1 )
Following the assumption (i) the circulation driving force can be expressed as: p = H2 ε2 l g
The hydraulic resistances in the apparatus can be divided into two groups: the friction losses and the minor losses. The terms describing pressure loss during the flow through the zones 1–3 (Fig. 1a) are calculated using Darcy–Weisbach equation (Weisbach, 1845) as follows:
p1 = 1
2 H1 ul1 d1 2 l
(4)
p2 = 2
2 H2 ul2 d2 2 l
(5)
p3 = 3
2 H3 ul3 d3 2 l
(6)
The friction coefficient in Eqs. (4)–(6) was calculated, depending on the value of the Reynolds number (7), for laminar flow (Re < 3000) using Hagen–Poiseuille (Poiseuille, 1840) Formula (8) and for turbulent flow (Re > 3000) from the Blasius (Blasius, 1913) Formula (9):
(2) Re =
The hydrodynamic model of the apparatus was formulated based on the global momentum balance. The model was developed following the earlier work of Tabi´s et al. (2014) concerning the apparatus with internal liquid circulation. Some modifications, including consideration of additional local resistances, were made to adapt this model for the apparatus with external liquid circulation. The equations reported below were derived based on the following assumptions: (i) the density difference of the medium in the barbotage zone and in the downcomer is a driving force for the liquid circulation, (ii) the driving force is completely used to overcome hydraulic resistances in the apparatus, (iii) the bed of particles is in fluidized state, (iv) complete degassing of the liquid takes place in the degassing vessel. The flow time of the gas bubbles through the liquid in the upper vessel (zone “4” in Fig. 1a) is shorter than the liquid flow time from the barbotage zone to the downcomer. Thus, the assumption of the complete degassing of the liquid in this zone may be done. For this reason, the liquid superficial velocity in the downcomer may have higher values than the slip velocity of gas bubbles. Fig. 4 shows a mechanism of degassing in the upper vessel of the apparatus. Derivation of the mathematical model requires identification of the circulation driving force and hydraulic resistances.
(3)
=
=
ul l d l
(7)
64 Re
(8)
0.3164
(9)
Re0.25
In other zones it was assumed that the pressure loss is only due to minor friction. The minor friction in the upper vessel, that is the inflow and outflow resistances (Munson et al., 2009), can be described by using the following equation:
p4 = I
u2l2 2
l + O
u2l3 2
(10)
l
Minor losses in the bottom zone, i.e. pressure loss in two elbows (Munson et al., 2009) and due to a sudden flow expansion, are expressed as follows:
p5 = 2E
u2l5 2
l + SE
u2l3 2
l
(11)
Minor loss coefficient due to sudden flow expansion was calculated using Borda–Carnot formula (Table 2).
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chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
Fig. 5 – Relationship of superficial liquid velocity in the fluidized-bed zone u0l1 and superficial gas velocity u0g2 , for two bed loadings and the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. Pressure drop across the two meshes was expressed by equation:
pN = 2N
u2l1 2
l
(12)
where minor loss coefficient N was determined experimentally Pressure drop across the fluidized bed is calculated from the following formula: pf = Hmf (1 − εmf )(s − l )g
(13)
In accordance with the assumption (ii) that the driving force is totally used to overcome the hydrodynamic resistances, the momentum balance can be written as: p = p1 + p2 + p3 + p4 + p5 + pN + pf
(14)
FVg = S2 ε2 (ul2 + )
(16)
The slip velocity of gas bubbles can be calculated from the Formula (17) proposed by Heijnen et al. (1997): = 1.53
gl (l − g ) l2
(17)
Microbiological processes which are supposed to be run in the analysed hybrid apparatus are characterised by low rates. Thus, the liquid residence time in the reactor is much higher than the time of one cycle of the liquid during its circulation. This means that the liquid flux supplying the apparatus is much lower than the circulating flux. Thus, it can be assumed that the contribution of feed flow rate is negligible. Dividing the Eqs. (15) and (16) by the area of the cross section of the zone “2” yields: u0l2 =
S3 u S2 0l3
(18)
Eq. (14) needs to be supplemented with mass balances of the liquid (15) and the gas (16) in the apparatus, that is:
u0g2 = ε2 (ul2 + )
FVl2 = FVl3 + FVlfeed
Since the liquid stream supplying the apparatus is negligible, the circulating liquid flux has the same value within all
(15)
(19)
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
193
Fig. 6 – Streamlines for the apparatus with the circulation tube with diameter of 30 mm and superficial liquid velocity u0l1 of: (a) 0.02 m/s and (b) 0.1 m/s.
Fig. 7 – Relationship of superficial liquid velocity in the fluidized-bed zone u0l1 and superficial gas velocity u0g2 for two bed loadings and the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. Results obtained after the correction of the local friction coefficients.
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chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
Fig. 8 – Gas holdup ε2 as a function of superficial gas velocity u0g2 for two bed loadings and the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. the zones of the apparatus. Therefore it is possible to relate the velocities in the apparatus and express them in terms of the superficial velocity of the liquid in the first section u0l1 and taking into account the solid holdup in section “1” the gas holdup in section “2”. In effect it yields: ul1 =
u0l1 ε1
(20)
ul2 =
u0l2 1 − ε2
(21)
ul3 =
S1 u S3 0l1
(22)
ul5 = u0l1
Fig. 9 – Fluidized-bed porosity ε1 as a function of superficial liquid velocity u0l1 .
(23)
Due to the fact that the fluidized bed occupies only a part of the section “1”, the true liquid velocity is different for the part occupied by the bed and for the freeboard. Also, the coefficient of friction is different for each of the two parts. To simplify the calculations, it was initially assumed that the true velocity in the zone “1” is equal to the superficial velocity of the liquid in this zone, that is: ul1 = u0l1
(24)
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
195
Fig. 10 – Contribution of pressure losses in fluidization section p1 , barbotage section p2 and downcomer p3 as a function of superficial gas velocity u0l1 for the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. As a result, the relationships describing the dynamic bed height do not depend on the momentum balance and the gas mass balance. The mass and momentum balances take the form of a system of two non-linear algebraic equations:
p =
5
pi + pN + pf
(25)
Eq. (27) was proposed by Richardson and Zaki (1954) based on the experimental research. They observed that the logarithm of the bed porosity ε1 and logarithm of the superficial liquid velocity in the fluidized bed u0l1 are linked by a linear relationship. In order to determine the bed porosity, it is necessary to know the value of the exponent n in Eq. (27). In this study it was determined using the formula proposed by Garside and Al-Dibouni (1977):
(26)
5.1 − n = 0.1 Re0.9 t n − 2.4
i=1
u0g2 = ε2 (ul2 + )
Eqs. (25) and (26) need to be supplemented with the formula describing the dynamic height of the bed, or alternatively the bed porosity, depending on the liquid velocity in the zone “1”. The following relationship was employed in this work: u0l1 = εn1 ut
(27)
When the bed porosity is known then its dynamic height can be calculated from the following well known formula: H = Hmf
1 − εmf 1 − ε1
(28)
(29)
where Ret the Reynolds number of the particle at terminal velocity: Ret =
4.
ut l ds l
(30)
Results and discussion
Fig. 5 shows the relationship between the superficial liquid velocity u0l1 and the superficial gas velocity u0g2 for two values of the mass of the bed material, i.e. 0.4 kg and 0.6 kg, and for three different diameters of the circulation tube d3 (Fig. 1a), that is 0.03 m, 0.05 m and 0.08 m. The symbols correspond
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Fig. 11 – Contribution of internal pressure losses in the apparatus as a function of superficial liquid velocity u0l1 for the apparatus with the circulation tube of diameter d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. to the experiential data, whereas the lines correspond to the results obtained from the proposed analytical model. It can be observed that the experimental results are in a very good qualitative agreement with the results of calculations. For the circulation tube with the diameter equal to d3 = 0.08 m (Fig. 5c) the experimental results coincide with the theoretical curves. In case of the smallest diameter of the downcomer, i.e. d3 = 0.03 m (Fig. 5a), the results obtained from the hydrodynamic model diverge from the experimental data as the superficial gas velocity u0g2 is increased. The calculated superficial liquid velocity u0l1 is higher than the measured value. This suggests that the value of one of the local resistances employed in the calculations is too low. The deterioration of the quantitative agreement of the results for the apparatus with the smallest diameter of the circulation tube implies that the resistance depends on the downcomer diameter. To confirm this hypothesis, three-dimensional CFD simulations of the downcomer “3” and of the bottom zone “5” were performed. The steady-state simulations were done using the Ansys Fluent software using the Realizable k–ε turbulence model with Enhanced Wall Treatment and energy equation enabled. Fig. 6 shows streamlines obtained from the selected simulations. The results represent the mean value of the flow velocity
without accounting for the local fluctuations of the velocity. The streamlines start at the inlet of the downcomer. However, since no significant change in the average velocity of the liquid flowing across the downcomer was observed, the figures show only a lower part of this zone. The velocity of the liquid stream flowing out from the downcomer decreases gradually when the stream flows into the bottom. However, before the complete extension of the stream in the bottom zone, it collides with the bottom wall of the apparatus. It can be observed that the kinetic energy of the flow is dissipated not only due to the formation of the vortices at the outlet of zone “3” but also due to a sudden change of the flow direction. Moreover, it can be observed that, at higher values of the liquid velocity, upon the collision with the bottom wall the stream splits into two parts. One part flows locally in the opposite direction than the direction of the liquid flow in the apparatus. Because of the presence of this additional hydrodynamic phenomena, an additional friction factor should be considered. Based on the above observations and experimental data it was assumed that the friction factor due to the sudden expansion of the cross section and due to the stream collision with the wall may be considered together and set to the value proportional to pressure drop at sudden enlargement. Thus, its value was assumed to be 3.5 times the value of the friction
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
factor at sudden enlargement. Table 2 summarizes the values of adopted local friction coefficients. The calculated values of the superficial liquid velocity in the fluidization section u0l1 as a function of the superficial gas velocity u0g2 obtained after the correction of the coefficient related to the sudden flow expansion are shown in Fig. 7. Much better quantitative agreement of the experimental data with the results determined from the proposed model is observed. The graphs in Fig. 8 show the relationship between the gas holdup ε2 and the superficial gas velocity u0g2 for different values of the diameter of the circulation tube and for two values of the solid loadings, i.e. 0.4 kg and 0.6 kg. It can be observed that with the corrected value of one of the local friction coefficient, the experimental results are in agreement with the theoretical values. Some discrepancy can be seen only for the lower bed loading and for the smallest diameter of the circulation tube. Fig. 9 shows a comparison of the measured and calculated values of the fluidized-bed porosity ε1 versus the superficial liquid velocity in the fluidization zone u0l1 . The solid line indicates the values determined from Eqs. (27) and (29). As it can be seen, the experimental values of the bed porosity do not depend on the quantity of the bed material in the zone “1”. Further tests consisted of numerical simulations aimed at determining the contribution of the friction losses in fluidization section “1”, barbotage section “2” and downcomer “3” to the total pressure drop in the apparatus depending on the superficial liquid velocity u0l1 . The results are presented in Fig. 10. It is shown that in the entire range of the liquid velocities, the contribution of the pressure loss across zones “1” and “2” does not exceed 1%. Moreover, it decreases significantly when the diameter of the downcomer is decreased. This means that the inaccuracy in the pressure drop determination caused by the adoption of the superficial liquid velocity in the fluidization section instead of the true velocity is negligible. However, the contribution of the pressure loss during the flow across the downcomer increases several times upon decreasing its diameter, and hence it becomes the main source of the pressure drop in the apparatus. In the last part of this work the evaluation of the contribution of individual pressure losses in the apparatus depending on the superficial liquid velocity u0l1 was carried out. The pressure losses were divided into three groups, namely: a contribution of losses depending on the diameter of the fluidization and barbotage column pd1 (sum of the contributions of the pressure losses during the flow across the fluidization “1” and the barbotage “2” zones and of the minor losses in the two bends, across two meshes and at the inlet of the upper vessel), a contribution of the pressure losses depending on the circulation tube pd3 (sum of the contributions of the friction loss in the downcomer “3” and minor losses at the outlet of the upper vessel and due to sudden enlargement of the cross section) and a contribution of the pressure drop across the fluidized bed pf . The mass of the bed adopted in the calculations was equal to 0.4 kg. The results obtained are shown in Fig. 11. At low values of the superficial liquid velocity, regardless of the circulation tube diameter, the dominant resistance in the apparatus is due to the presence of the fluidized bed pf . On the other hand, when decreasing the downcomer diameter, the contribution of the pressure loss p3 increases significantly. Experimental studies also confirmed that gas bubbles are practically not entrained into the circulation pipe. Even at high gas flow rates only a few gas bubbles having a diameter less than 1 mm were entrained. This phenomenon does not affect
197
the hydrodynamic characteristic of the apparatus predicted by the proposed analytical model.
5.
Conclusions
The analytical model of the hydrodynamics of a hybrid airlift apparatus proposed in this paper has shown a good qualitative and sufficient quantitative agreement with experimental results. The model permits to calculate basic hydrodynamic parameters, that are the liquid velocity in all zones of the apparatus, the gas holdup in the barbotage section, the dynamic bed height and local values of the pressure drop. It is characterised by a simple mathematical structure since it only consists of three non-linear algebraic equations that can be solved numerically employing standard numerical algorithms, such as the Newton method. The model can be used for sizing of such apparatuses and for evaluation of the intensity of aeration depending on the conditions of the fluidized bed existence, i.e. from minimum fluidization velocity up to velocity, at which the fluidized bed height expands to 0.9H1 . The assumption of complete degassing in the upper vessel was confirmed. Due to the apparatus construction, the gas bubbles do not get into the downcomer. This ensures their absence in the fluidization section, which is the basic requirement for the operation of hybrid bioreactors. Indeed, according to the literature the gas bubbles damage a biofilm immobilized on the solid particles in three-phase bioreactors. Reduction of the circulation tube diameter results in higher pressure drop. However, if we consider complete degassing of liquid in zone “4”, when diameter of the downcomer is reduced the volume of the nonaerated zone decreases, which is advantageous in case of aerobic processes. It was underlined in this work that identification of all local pressure losses is very important. As a result of the construction of the bottom zone of the apparatus used within this study, beside the resistance due to the sudden expansion of the liquid stream, another pressure drop was identified, which is due to collision of the stream exiting downcomer with the bottom wall of the zone “5”. It was assumed that this pressure drop is proportional to pressure drop at sudden enlargement. Therefore, it is necessary to adjust the local value of this friction factor experimentally.
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Henzler, H.J., 2000. Particle stress in bioreactors. Adv. Biochem. Eng. Biotechnol. 67, 35–82. Iliuta, I., Larachi, F., 2004. Biomass accumulation and clogging in trickle-bed bioreactors. AIChE J. 50, 2541–2551. Munson, B.R., Young, D.F., Okiishi, T.H., Huebsch, W.W., 2009. Fundamentals of Fluid Mechanics, 6th ed. John Wiley & Sons, Inc. Olivieri, G., Marzocchella, A., Salatino, P., 2010. A novel three-phase airlift reactor without circulation of solids. Can. J. Chem. Eng. 88, 574–578. Poiseuille, J.L.M., 1840. Recherches expérimentales sur Ie mouvement des liquides dans les tubes de trés petits diamétres; 1. Influence de la pression sur la quantité de liquide qui traverse les tubes de trés petits diametres. C. R. Acad. Sci. l1, 961–967. ´ Pronczuk, M., 2017. Experimental investigations on residence time distribution in hybrid fluidized-bed air-lift reactors. In:
Works of Departments of Chemical and Process Engineering. Cracow University of Technology. Richardson, J.F., Zaki, W.N., 1954. Sedimentation and fluidization. Part 1. Trans. Inst. Chem. Eng. 32, 35–53. ˛ ´ D., 2014. Method for Tabi´s, B., Stryjewski, W., Zareba-Boro n, designing the hydrodynamic conditions of a hybrid fluidized-bed air-lift bioreactor (in polish). Przem. Chem. 93, 1379–1382. Tang, W.-T., Wisecarver, K., Fan, L.-S., 1987. Dynamics of a draft tube gas–liquid–solid fluidized bed bioreactor for phenol degradation. Chem. Eng. Sci. 42, 2123–2134. Weisbach, J., 1845. Lehrbuch der Ingenieur und Maschinen-Mechanik. Vieweg und Sohn, Braunschweig. Wisecarver, K.D., Fan, L.-S., 1989. Biological phenol degradation in a gas–liquid–solid fluidized bed bioreactor. Biotechnol. Bioeng. 33, 1029–1038.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Experimental investigations of hydrodynamic characteristics of a hybrid fluidized bed airlift reactor with external liquid circulation ´ Mateusz Pronczuk, Katarzyna Bizon ∗ , Robert Grzywacz Department of Chemical Engineering and Technology, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland
a r t i c l e
i n f o
a b s t r a c t
Article history:
The paper presents a simple analytical model of the hydrodynamics of a hybrid airlift appa-
Received 8 March 2017
ratus with an external liquid circulation loop. The apparatus consists of two sections: a
Received in revised form 4 August
two-phase fluidization column and a barbotage section. The advantage of such a configura-
2017
tion is that there is no contact between the gas phase and the solid phase, which is relevant
Accepted 30 August 2017
in case of processes involving a biofilm immobilization on fine carrier particles. Then, the
Available online 7 September 2017
shear stresses produced by passing bubbles do not damage the surface of a biofilm. The
Keywords:
mine basic hydrodynamic parameters of the apparatus including liquid and gas velocity,
External loop airlift
gas hold-up, and porosity and height of the fluidized bed. The model was verified exper-
proposed model was derived based on the global momentum balance. It allows to deter-
Fluidized bed
imentally and the hydrodynamics of the selected zones of the apparatus was simulated
Gas holdup
using Computational Fluid Dynamics (CFD).
Liquid circulation velocity
© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Momentum balance
1.
Introduction
the aerated and non-aerated zone acts as a driving force for the liquid circulation.
Three-phase fluidized-bed reactors; thanks to many advantages such as higher biomass concentration, better contact between liquid and solid phases and low washout of microorganisms compared to con-
However, in case of a three-phase fluidized bed, flowing gas bubbles induce a shear stress which may damage a delicate biofilm deposited on the carrier surface, which may lead to complete degradation of
ventional tank reactor (Wisecarver and Fan, 1989) are commonly used for aerobic microbiological processes (Tang et al., 1987; Wisecarver and Fan, 1989). Immobilization of the biomass on a fine carrier particles,
biofilm (Henzler, 2000). The possible solution to this problem is to separate the barbotage zone from the fluidized-bed zone. Dunn et al. (1983)
where solid particles act as a carrier for biofilm, permits to obtain a significant increase in its overall concentration in the reaction environment (Fan et al., 1987). Moreover, fluidization allows for easy bed
introduced an apparatus composed of a fluidized-bed reactor and an aerator connected by a recirculation loop. According to the authors such a configuration permits to eliminate contact of the gas bubbles with the biofilm immobilized on the solid particles. Guo et al. (1997) pro-
replacement and prevents particles agglomeration and clogging of the
posed a modification of the three-phase airlift reactor with external
pores, which is a serious issue for fixed beds (Iliuta and Larachi, 2004). Aeration of the liquid, i.e. is the process by which air is dissolved in a liquid, has two functions. Apart from providing oxygen for the reaction,
liquid circulation, in which the barbotage section is located above the fluidized-bed section, thus there is no mixing of the solid phase and gas. An additional advantage is that such a configuration does not require a
the barbotage enhances mixing. In the airlift reactor the aeration has got an additional function – supply of the air into the barbotage zone leads to the reduction of the average density of a gas–liquid mixture in
circulator pump. For an appropriate level of aeration the pressure difference enables to achieve the liquid velocity necessary to fluidize the bed.
relation to the liquid density. The difference in the average density of
Olivieri et al. (2010) introduced their own design of a hybrid airlift bioreactor. The authors proposed an apparatus with the internal liquid circulation loop having more compact design than the apparatus with the external liquid circulation. An analytical model of the
∗
Corresponding author. E-mail addresses: [email protected], [email protected] (K. Bizon). http://dx.doi.org/10.1016/j.cherd.2017.08.028 0263-8762/© 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
189
Nomenclature d FV g H m n p Re S u
Diameter, m Volumetric flow rate, m3 /s Gravitational acceleration, m/s2 Height, m Mass, kg Exponent in the Richardsona and Zaki model, – Pressure drop, Pa Reynolds number, – Cross section, m2 Velocity, m/s
Greek symbols Bed porosity, – ε1 Gas holdup, – ε2 Dynamic viscosity coefficient, kg/(m s) Flow friction coefficient, – Local friction coefficient, – Density, kg/m3 Surface tension, N/m Gas bubble rise velocity, m/s
Shape factor, – Subscripts 0 Value related to the cross section of the apparatus 1–5 Zones of the apparatus (Fig. 1) Refers to local friction factor of the bend E f Refers to fluidized bed feed Refers to feed flow Gas phase g I Refers to local friction factor of the upper vessel inlet Liquid phase l Minimum fluidization conditions mf Refers to local friction factor of the mesh N O Refers to local friction factor of the upper vessel outlet s Solid phase Refers to mesh S Refers to local friction factor of the sudden SE expansion t Refers to terminal velocity of the particle
hydordynamics of the loop apparatus with the internal liquid circulation was then formulated by Tabi´s et al. (2014). Fig. 1 shows two different configurations of the apparatus, i.e. with the external (Fig. 1a) and internal (Fig. 1b) liquid circulation. Five zones can be distinguished in both configurations. As shown in Fig. 1 these zones are: fluidization zone “1”, barbotage zone “2”, downcomer “3”, degassing zone “4” and bottom zone “5”. Description of the hydrodynamics of the hybrid fluidized-bed reactor is a rather complex problem. Due to the presence of the gas phase such an apparatus may operate, like a traditional airlift reactor, in three hydrodynamic regimes characterized by: complete degassing of the liquid in the upper vessel, partial degassing of the liquid in the downcomer or gas circulation through all zones of the reactor. Depending on the liquid circulation velocity the bed of solid particles may operate as: a fixed bed resting on the bottom mesh, a fluidized bed or a fixed bed resting under the upper mesh. The combinations of operating regimes of the hybrid apparatus listed above are presented graphically in Fig. 2. Despite the variety of theoretically possible operating regimes of the hybrid apparatuses shown in Fig. 2, own experimental studies con-
Fig. 1 – Hybrid fluidized-bed apparatuses (a) with external liquid circulation, (b) with internal liquid circulation; 1 – fluidization zone, 2 – barbotage zone, 3 – downcomer, 4 – degassing zone, 5 – bottom zone. firmed complete degassing of the liquid in zone “4” (Fig. 1a). Therefore, the only possible operating modes are regimes I, IV and VII (Fig. 2) corresponding to the complete liquid degassing. On the other hand, a technologically attractive operating mode of the bed of solid particles corresponds to the regimes IV, V and VI (Fig. 2), i.e. conditions at which the bed is in a fluidized state. Thus, only the regime IV fulfils both conditions of the hybrid apparatus. The paper presents an analytical hydrodynamic model of a hybrid airlift apparatus with an external liquid circulation that provides design guidelines and allows to select optimal operating conditions. The proposed model is verified experimentally and the results obtained from the model are further compared with Computational Fluid Dynamics (CFD) simulations in order to adjust the values of local friction coefficients.
2.
Experimental setup
The experimental apparatus is shown in Fig. 3. It is equipped with an external circulation tube and is made of transparent tubes and plates made of poly methyl methacrylate (PMMA). A fluidized-bed section “1” (Fig. 1a) is located in the lower part of the riser. A wire mesh with the openings of 1 mm and made of wire having a diameter of 0.5 mm is mounted under the fluidization zone. To prevent entrainment of the particles from the fluidization zone, an identical mesh is disposed in the upper part of this section. Directly above this, a barbotage section is located. Air is supplied to the barbotage zone by means of a cross-shaped metal distributor. At the top of the gas distributor, 25 equally spaced holes (one hole in the centre and six holes on every branch) with diameter of 1 mm and at distance of 5 mm apart were drilled. The liquid leaving the barbotage section enters the upper vessel “4” and then it flows into the downcomer “3” (Fig. 1a). The design of the apparatus allows to mount circulation tubes of different diameters. The riser and the downcomer are connected in the bottom by means of a connector which creates a bottom section “5”. The air supplying the apparatus is first compressed by means of a compressor. Then it flows through a gas mass flow controller (MFC) allowing for the adjustment of the volumetric flow rate and enters the air distributor. The measurements were carried out for several values of the gas flow rate. The minimum gas flow rate coincided to the minimum fluidization conditions of the solid particles, whereas the highest corre-
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Fig. 3 – Scheme of the experimental setup: PC – personal computer, ADC – analog-to-digital converter, PS – pressure sensor, CP – conductivity probe, MFC – mass flow controller, UFM – ultrasonic flow meter, PP – peristaltic pump. Table 1 – Geometry of the apparatus, the bed properties and physical properties of the media.
Fig. 2 – Theoretically possible hydrodynamic regimes in the apparatus: (I) complete liquid degassing and fixed bed on the bottom mesh, (II) partial entrainment of gas bubbles and fixed bed on the bottom mesh, (III) circulation of gas bubbles and fixed bed on the bottom mesh, (IV) complete liquid degassing and fluidized bed, (V) partial entrainment of gas bubbles and fluidized bed, (VI) circulation of gas bubbles and fluidized bed, (VII) complete liquid degassing and fixed bed on the upper mesh, (VIII) partial entrainment of gas bubbles and fixed bed on the upper mesh, (IX) circulation of gas bubbles and fixed bed on the upper mesh. sponded to the value for which the bed height was equal to 0.9 m. Higher values of the gas flow rate led to the settlement of the particles beneath the upper mesh. The liquid supplied to the apparatus was dispensed in the lower part of the bottom zone by means of a peristaltic pump (PP). Water at the temperature of 288 K was supplied to the apparatus. The liquid circulation velocity was measured by means of the ultrasonic flow meter (UFM). Two ultrasonic transducers (UT) were mounted on the downcomer surface. They allow for non-intrusive measurement of the average flow velocity in the downcomer.
Parameter
Value
Unit
H1 H2 H3 d1 d2 d3 Hmf εmf ds
s s ut ms l l l g
1 1 2 80 × 10−3 80 × 10−3 30 × 10−3 ,50 × 10−3 ,80 × 10−3 , 105 × 10−3 0.44 3.2 × 10−3 0.976 1354 0.1204 0.4 997 11.4 × 10−4 73.2 × 10−3 1.185
m m m m m m m – m – kg m−3 m s−1 kg kg m−3 kg m−1 s−1 N m−1 kg m−3
The bed was made of polyoxymethylene (POM) polgranules. Its properties are given in Table 1. Terminal velocity of the particles was determined experimentally by measuring free fall time of the particles in the column filled with water. The pressure sensors (PS) were mounted along the barbotage zone. Measurement of the static pressure in the barbotage section permits to determine the gas holdup using the manometric method, which depending on the distance from the liquid surface in the upper zone can be calculated using the following expression: ε2 (H) =
l gH − p2 (H) l gH
(1)
The sensors were connected with a personal computer (PC) using an analog-to-digital converter (ADC). The apparatus was also equipped with five conductivity probes (CP) – before inlet and after outlet of the downcomer, under the bottom and the upper mesh, and at the barbotage zone outlet (Fig. 3). The con-
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Table 2 – Adjusted values of the local friction coefficient. Occurence of the resistance
Symbol
Value
Inlet of the upper vessel Outlet of the upper vessel Elbow Mesh
I O E N
1 0.5 1.1 12
Sudden flow expansion and collision with the bottom wall
SE
3.5
2 d 1 d3
2 −1
Fig. 4 – Liquid degassing in the upper vessel.
´ ductivity meters were used for tracer studies (Pronczuk, 2017). They consisted in the introduction of the KCl solution into downcomer, which was used as a tracer. Simultaneously measurements of a conductance were made in five points along the apparatus. Change in the liquid conductance is directly proportional to the change of the tracer concentration. All sensors and controllers were connected with the PC. The measurements and setting of the parameters were done using a Matlab script. Basic geometric parameters of the apparatus, the bed properties and physical properties of the media used in the calculations are reported in Table 1.
3.
Analytical model of the hydrodynamics
For design purposes, a hydrodynamic model should allow to determine basic hydrodynamic parameters of the apparatus, namely: liquid and gas velocities within each zone, gas holdup and a dynamic height of the fluidized bed. To prevent the settlement of the particles under the upper mesh, the superficial liquid velocity should be such that the height of the fluidized bed does not exceed 90% of the height of zone “1”. However, the superficial velocity cannot be lower than the minimum fluidization velocity. These two conditions can be written as follows: umf < u0l1 < (u0l : Hf < 0.9H1 )
Following the assumption (i) the circulation driving force can be expressed as: p = H2 ε2 l g
The hydraulic resistances in the apparatus can be divided into two groups: the friction losses and the minor losses. The terms describing pressure loss during the flow through the zones 1–3 (Fig. 1a) are calculated using Darcy–Weisbach equation (Weisbach, 1845) as follows:
p1 = 1
2 H1 ul1 d1 2 l
(4)
p2 = 2
2 H2 ul2 d2 2 l
(5)
p3 = 3
2 H3 ul3 d3 2 l
(6)
The friction coefficient in Eqs. (4)–(6) was calculated, depending on the value of the Reynolds number (7), for laminar flow (Re < 3000) using Hagen–Poiseuille (Poiseuille, 1840) Formula (8) and for turbulent flow (Re > 3000) from the Blasius (Blasius, 1913) Formula (9):
(2) Re =
The hydrodynamic model of the apparatus was formulated based on the global momentum balance. The model was developed following the earlier work of Tabi´s et al. (2014) concerning the apparatus with internal liquid circulation. Some modifications, including consideration of additional local resistances, were made to adapt this model for the apparatus with external liquid circulation. The equations reported below were derived based on the following assumptions: (i) the density difference of the medium in the barbotage zone and in the downcomer is a driving force for the liquid circulation, (ii) the driving force is completely used to overcome hydraulic resistances in the apparatus, (iii) the bed of particles is in fluidized state, (iv) complete degassing of the liquid takes place in the degassing vessel. The flow time of the gas bubbles through the liquid in the upper vessel (zone “4” in Fig. 1a) is shorter than the liquid flow time from the barbotage zone to the downcomer. Thus, the assumption of the complete degassing of the liquid in this zone may be done. For this reason, the liquid superficial velocity in the downcomer may have higher values than the slip velocity of gas bubbles. Fig. 4 shows a mechanism of degassing in the upper vessel of the apparatus. Derivation of the mathematical model requires identification of the circulation driving force and hydraulic resistances.
(3)
=
=
ul l d l
(7)
64 Re
(8)
0.3164
(9)
Re0.25
In other zones it was assumed that the pressure loss is only due to minor friction. The minor friction in the upper vessel, that is the inflow and outflow resistances (Munson et al., 2009), can be described by using the following equation:
p4 = I
u2l2 2
l + O
u2l3 2
(10)
l
Minor losses in the bottom zone, i.e. pressure loss in two elbows (Munson et al., 2009) and due to a sudden flow expansion, are expressed as follows:
p5 = 2E
u2l5 2
l + SE
u2l3 2
l
(11)
Minor loss coefficient due to sudden flow expansion was calculated using Borda–Carnot formula (Table 2).
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chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
Fig. 5 – Relationship of superficial liquid velocity in the fluidized-bed zone u0l1 and superficial gas velocity u0g2 , for two bed loadings and the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. Pressure drop across the two meshes was expressed by equation:
pN = 2N
u2l1 2
l
(12)
where minor loss coefficient N was determined experimentally Pressure drop across the fluidized bed is calculated from the following formula: pf = Hmf (1 − εmf )(s − l )g
(13)
In accordance with the assumption (ii) that the driving force is totally used to overcome the hydrodynamic resistances, the momentum balance can be written as: p = p1 + p2 + p3 + p4 + p5 + pN + pf
(14)
FVg = S2 ε2 (ul2 + )
(16)
The slip velocity of gas bubbles can be calculated from the Formula (17) proposed by Heijnen et al. (1997): = 1.53
gl (l − g ) l2
(17)
Microbiological processes which are supposed to be run in the analysed hybrid apparatus are characterised by low rates. Thus, the liquid residence time in the reactor is much higher than the time of one cycle of the liquid during its circulation. This means that the liquid flux supplying the apparatus is much lower than the circulating flux. Thus, it can be assumed that the contribution of feed flow rate is negligible. Dividing the Eqs. (15) and (16) by the area of the cross section of the zone “2” yields: u0l2 =
S3 u S2 0l3
(18)
Eq. (14) needs to be supplemented with mass balances of the liquid (15) and the gas (16) in the apparatus, that is:
u0g2 = ε2 (ul2 + )
FVl2 = FVl3 + FVlfeed
Since the liquid stream supplying the apparatus is negligible, the circulating liquid flux has the same value within all
(15)
(19)
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193
Fig. 6 – Streamlines for the apparatus with the circulation tube with diameter of 30 mm and superficial liquid velocity u0l1 of: (a) 0.02 m/s and (b) 0.1 m/s.
Fig. 7 – Relationship of superficial liquid velocity in the fluidized-bed zone u0l1 and superficial gas velocity u0g2 for two bed loadings and the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. Results obtained after the correction of the local friction coefficients.
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chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
Fig. 8 – Gas holdup ε2 as a function of superficial gas velocity u0g2 for two bed loadings and the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. the zones of the apparatus. Therefore it is possible to relate the velocities in the apparatus and express them in terms of the superficial velocity of the liquid in the first section u0l1 and taking into account the solid holdup in section “1” the gas holdup in section “2”. In effect it yields: ul1 =
u0l1 ε1
(20)
ul2 =
u0l2 1 − ε2
(21)
ul3 =
S1 u S3 0l1
(22)
ul5 = u0l1
Fig. 9 – Fluidized-bed porosity ε1 as a function of superficial liquid velocity u0l1 .
(23)
Due to the fact that the fluidized bed occupies only a part of the section “1”, the true liquid velocity is different for the part occupied by the bed and for the freeboard. Also, the coefficient of friction is different for each of the two parts. To simplify the calculations, it was initially assumed that the true velocity in the zone “1” is equal to the superficial velocity of the liquid in this zone, that is: ul1 = u0l1
(24)
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
195
Fig. 10 – Contribution of pressure losses in fluidization section p1 , barbotage section p2 and downcomer p3 as a function of superficial gas velocity u0l1 for the diameter of the circulation tube d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. As a result, the relationships describing the dynamic bed height do not depend on the momentum balance and the gas mass balance. The mass and momentum balances take the form of a system of two non-linear algebraic equations:
p =
5
pi + pN + pf
(25)
Eq. (27) was proposed by Richardson and Zaki (1954) based on the experimental research. They observed that the logarithm of the bed porosity ε1 and logarithm of the superficial liquid velocity in the fluidized bed u0l1 are linked by a linear relationship. In order to determine the bed porosity, it is necessary to know the value of the exponent n in Eq. (27). In this study it was determined using the formula proposed by Garside and Al-Dibouni (1977):
(26)
5.1 − n = 0.1 Re0.9 t n − 2.4
i=1
u0g2 = ε2 (ul2 + )
Eqs. (25) and (26) need to be supplemented with the formula describing the dynamic height of the bed, or alternatively the bed porosity, depending on the liquid velocity in the zone “1”. The following relationship was employed in this work: u0l1 = εn1 ut
(27)
When the bed porosity is known then its dynamic height can be calculated from the following well known formula: H = Hmf
1 − εmf 1 − ε1
(28)
(29)
where Ret the Reynolds number of the particle at terminal velocity: Ret =
4.
ut l ds l
(30)
Results and discussion
Fig. 5 shows the relationship between the superficial liquid velocity u0l1 and the superficial gas velocity u0g2 for two values of the mass of the bed material, i.e. 0.4 kg and 0.6 kg, and for three different diameters of the circulation tube d3 (Fig. 1a), that is 0.03 m, 0.05 m and 0.08 m. The symbols correspond
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chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
Fig. 11 – Contribution of internal pressure losses in the apparatus as a function of superficial liquid velocity u0l1 for the apparatus with the circulation tube of diameter d3 equal to: (a) 0.03 m, (b) 0.05 m and (c) 0.08 m. to the experiential data, whereas the lines correspond to the results obtained from the proposed analytical model. It can be observed that the experimental results are in a very good qualitative agreement with the results of calculations. For the circulation tube with the diameter equal to d3 = 0.08 m (Fig. 5c) the experimental results coincide with the theoretical curves. In case of the smallest diameter of the downcomer, i.e. d3 = 0.03 m (Fig. 5a), the results obtained from the hydrodynamic model diverge from the experimental data as the superficial gas velocity u0g2 is increased. The calculated superficial liquid velocity u0l1 is higher than the measured value. This suggests that the value of one of the local resistances employed in the calculations is too low. The deterioration of the quantitative agreement of the results for the apparatus with the smallest diameter of the circulation tube implies that the resistance depends on the downcomer diameter. To confirm this hypothesis, three-dimensional CFD simulations of the downcomer “3” and of the bottom zone “5” were performed. The steady-state simulations were done using the Ansys Fluent software using the Realizable k–ε turbulence model with Enhanced Wall Treatment and energy equation enabled. Fig. 6 shows streamlines obtained from the selected simulations. The results represent the mean value of the flow velocity
without accounting for the local fluctuations of the velocity. The streamlines start at the inlet of the downcomer. However, since no significant change in the average velocity of the liquid flowing across the downcomer was observed, the figures show only a lower part of this zone. The velocity of the liquid stream flowing out from the downcomer decreases gradually when the stream flows into the bottom. However, before the complete extension of the stream in the bottom zone, it collides with the bottom wall of the apparatus. It can be observed that the kinetic energy of the flow is dissipated not only due to the formation of the vortices at the outlet of zone “3” but also due to a sudden change of the flow direction. Moreover, it can be observed that, at higher values of the liquid velocity, upon the collision with the bottom wall the stream splits into two parts. One part flows locally in the opposite direction than the direction of the liquid flow in the apparatus. Because of the presence of this additional hydrodynamic phenomena, an additional friction factor should be considered. Based on the above observations and experimental data it was assumed that the friction factor due to the sudden expansion of the cross section and due to the stream collision with the wall may be considered together and set to the value proportional to pressure drop at sudden enlargement. Thus, its value was assumed to be 3.5 times the value of the friction
chemical engineering research and design 1 2 6 ( 2 0 1 7 ) 188–198
factor at sudden enlargement. Table 2 summarizes the values of adopted local friction coefficients. The calculated values of the superficial liquid velocity in the fluidization section u0l1 as a function of the superficial gas velocity u0g2 obtained after the correction of the coefficient related to the sudden flow expansion are shown in Fig. 7. Much better quantitative agreement of the experimental data with the results determined from the proposed model is observed. The graphs in Fig. 8 show the relationship between the gas holdup ε2 and the superficial gas velocity u0g2 for different values of the diameter of the circulation tube and for two values of the solid loadings, i.e. 0.4 kg and 0.6 kg. It can be observed that with the corrected value of one of the local friction coefficient, the experimental results are in agreement with the theoretical values. Some discrepancy can be seen only for the lower bed loading and for the smallest diameter of the circulation tube. Fig. 9 shows a comparison of the measured and calculated values of the fluidized-bed porosity ε1 versus the superficial liquid velocity in the fluidization zone u0l1 . The solid line indicates the values determined from Eqs. (27) and (29). As it can be seen, the experimental values of the bed porosity do not depend on the quantity of the bed material in the zone “1”. Further tests consisted of numerical simulations aimed at determining the contribution of the friction losses in fluidization section “1”, barbotage section “2” and downcomer “3” to the total pressure drop in the apparatus depending on the superficial liquid velocity u0l1 . The results are presented in Fig. 10. It is shown that in the entire range of the liquid velocities, the contribution of the pressure loss across zones “1” and “2” does not exceed 1%. Moreover, it decreases significantly when the diameter of the downcomer is decreased. This means that the inaccuracy in the pressure drop determination caused by the adoption of the superficial liquid velocity in the fluidization section instead of the true velocity is negligible. However, the contribution of the pressure loss during the flow across the downcomer increases several times upon decreasing its diameter, and hence it becomes the main source of the pressure drop in the apparatus. In the last part of this work the evaluation of the contribution of individual pressure losses in the apparatus depending on the superficial liquid velocity u0l1 was carried out. The pressure losses were divided into three groups, namely: a contribution of losses depending on the diameter of the fluidization and barbotage column pd1 (sum of the contributions of the pressure losses during the flow across the fluidization “1” and the barbotage “2” zones and of the minor losses in the two bends, across two meshes and at the inlet of the upper vessel), a contribution of the pressure losses depending on the circulation tube pd3 (sum of the contributions of the friction loss in the downcomer “3” and minor losses at the outlet of the upper vessel and due to sudden enlargement of the cross section) and a contribution of the pressure drop across the fluidized bed pf . The mass of the bed adopted in the calculations was equal to 0.4 kg. The results obtained are shown in Fig. 11. At low values of the superficial liquid velocity, regardless of the circulation tube diameter, the dominant resistance in the apparatus is due to the presence of the fluidized bed pf . On the other hand, when decreasing the downcomer diameter, the contribution of the pressure loss p3 increases significantly. Experimental studies also confirmed that gas bubbles are practically not entrained into the circulation pipe. Even at high gas flow rates only a few gas bubbles having a diameter less than 1 mm were entrained. This phenomenon does not affect
197
the hydrodynamic characteristic of the apparatus predicted by the proposed analytical model.
5.
Conclusions
The analytical model of the hydrodynamics of a hybrid airlift apparatus proposed in this paper has shown a good qualitative and sufficient quantitative agreement with experimental results. The model permits to calculate basic hydrodynamic parameters, that are the liquid velocity in all zones of the apparatus, the gas holdup in the barbotage section, the dynamic bed height and local values of the pressure drop. It is characterised by a simple mathematical structure since it only consists of three non-linear algebraic equations that can be solved numerically employing standard numerical algorithms, such as the Newton method. The model can be used for sizing of such apparatuses and for evaluation of the intensity of aeration depending on the conditions of the fluidized bed existence, i.e. from minimum fluidization velocity up to velocity, at which the fluidized bed height expands to 0.9H1 . The assumption of complete degassing in the upper vessel was confirmed. Due to the apparatus construction, the gas bubbles do not get into the downcomer. This ensures their absence in the fluidization section, which is the basic requirement for the operation of hybrid bioreactors. Indeed, according to the literature the gas bubbles damage a biofilm immobilized on the solid particles in three-phase bioreactors. Reduction of the circulation tube diameter results in higher pressure drop. However, if we consider complete degassing of liquid in zone “4”, when diameter of the downcomer is reduced the volume of the nonaerated zone decreases, which is advantageous in case of aerobic processes. It was underlined in this work that identification of all local pressure losses is very important. As a result of the construction of the bottom zone of the apparatus used within this study, beside the resistance due to the sudden expansion of the liquid stream, another pressure drop was identified, which is due to collision of the stream exiting downcomer with the bottom wall of the zone “5”. It was assumed that this pressure drop is proportional to pressure drop at sudden enlargement. Therefore, it is necessary to adjust the local value of this friction factor experimentally.
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