Hydrodynamics and Axial Dispersion in a Gas−Liquid−(Solid) EL-ALR

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Ind. Eng. Chem. Res. 2008, 47, 4008–4017

Hydrodynamics and Axial Dispersion in a Gas-Liquid-(Solid) EL-ALR with Different Sparger Designs Changqing Cao,† Shuqin Dong,† Qijin Geng,†,‡ and Qingjie Guo*,† College of Chemical Engineering, Qingdao UniVersity of Science and Technology, Qingdao 266042, People’s Republic of China, and Department of Chemistry and Chemical Engineering, Weifang UniVersity, Weifang 261061, People’s Republic of China

The gas-liquid-(solid) three-phase hydrodynamics in an external-loop airlift reactor (EL-ALR) with an upward pipe 0.47 m in diameter and 2.5 m in height, two external loop downward pipes 0.08 m in diameter and 2.5 m in height, were investigated using four different gas sparger designs. The microconductivity probe and the three-dimensional (3-D) laser Doppler anemometry (LDA) techniques were, respectively, implemented to measure the local gas holdup in the riser (RGr) and liquid phase velocity in the downcomer (ULd) using air as the gas phase, water as the liquid phase, and alginate gel beads as the solid phase, over a wide range of operation conditions. The tracer age distribution was measured using the pulse-pursuit response technology. Axial dispersion model (ADM) was used to estimate the model parameter Peclet number (Pe) values as a fitted parameter with the measured data, using the gold partition method for nonlinear programming strategy inequation restrict conditions. The ADM gave better fits to the experimental data at high axial locations and lower superficial gas velocity (UG) for an EL-ALR used with a large L/DR ratio. A synergistic effect of ULd, RGr, Pe, solids loading (SL), and sparger designs on the performance of an EL-ALR was observed in our experiments. The sparger designs were determined to have a noticeable effect on the RGr and Pe in the lower gas velocity and lower solid loading ranges (UG < 0.025 m/s and SL < 2%), but only a slight effect in the high gas velocity and high solid loading ranges (UG > 0.030 m/s and SL > 3%). However, the effect of sparger designs on the ULd is greater in the gas velocity from 0.025 m/s to 0.045 m/s. For the lower solids loading, the increase of orifice diameter leads to a decrease in RGr. This is in accordance with what was presented in the gas-liquid two-phase system. Moreover, the influence of orifice diameters of the spargers is negligible for solids loading of >3%. Although the Pe values decreased with the operating gas velocity, the gas velocity change from 0.03 m/s to 0.04 m/s yielded lower Pe values, as a result of the reduced bubble size. As the gas velocity further increased to 0.06 m/s, the RGr and the ULd values increased, while the Pe values negligibly increased. For a gas-liquid two-phase system, Pe decreases with the orifice diameter and, for 1% of solids, Pe is also lower for sparger P-2 (φ 0.6 mm) than for sparger P-1 (φ 0.3 mm). For higher amounts of solids (3%), Pe does not have a defined trend. In addition to the gas velocity and sparger design effects, the solids loading had the effect of decreasing the ULd values, while such effect became small and flattened at high solid loadings. The ULd values, especially with VO ) 100%, are 20% lower in three-phase flow than that in two-phase flow. In addition, the ULd profiles in three-phase flow are flatter than that in two-phase flow with VO ) 50%-100%, actually showing a parabolic shape rather than the almost linear one encountered in two-phase flow. This is very important for design and optimum operation that are used to systemically investigate the synergistic effect of ULd, RGr, Pe, solid loading (SL), and sparger designs on hydrodynamic performance of an EL-ALR. Introduction Bubble columns are reactors in which a continuous liquid phase and a gas flow in the form of bubbles are brought into contact. They are widely employed in chemical, biochemical, and petrochemical industrial processes, because of their advantages as simple construction and excellent heat and mass transfer, as mixing is induced only by gas aeration.1 Their main drawback is a severe degree of backmixing in the liquid phase, which is due to the low liquid flow rate. Backmixing is known to increase drastically when local liquid circulation develops. To reduce backmixing, modified bubble columns have been designed. external loop airlift reactors (EL-ALRs) constitute an important class of such modified bubble columns in which an * To whom correspondence should be addressed. Tel.: 0086-53284022757. E-mail: [email protected]. † College of Chemical Engineering, Qingdao University of Science and Technology. ‡ Department of Chemistry and Chemical Engineering, Weifang University.

overall circulation of the continuous phase is induced by a differential aeration between the riser and the downcomer. Such reactors give flatter liquid velocity profiles, thereby reducing shear, which improves life preservation of microorganisms in biological applications.2 External-loop fermenters have frequently been used in investigations of reactor behavior in laboratory, bench-scale, and pilot-plant installations, apparently because of the welldefined conditions in the system. However, the amount of generalized information available is small. This is due to the fact that, for a given superficial gas velocity value, any variation of gas or liquid physical properties, downcomer and riser crosssection ratio, top and bottom riser and downcomer connecting sections geometry, phase separation conditions, liquid volume, reactor height or gas distributing plate generates a modification in liquid velocity and gas holdup.3 The complexity increases when a third phase (solid) is added to the system. The majority of data have been obtained for air-water systems that are not necessarily representing the fermentation processes, which are

10.1021/ie0715254 CCC: $40.75  2008 American Chemical Society Published on Web 05/10/2008

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 4009

characterized by the presence of a solid phase that is slightly denser than water and where high concentrations of solids may occur. Kochbeck et al.4 observed that liquid velocity in an ELALR was drastically reduced by the presence of high-density solid particles. Working with low-density solids and with high amounts of solids (up to 30% v/v), Freitas et al.5 found that solids loading and density had considerable influence on gas holdup, liquid velocity, and mixing time of an internal-loop airlift reactor with a degassing zone. Parameters of the gas distributing system–in particular, free plate area and orifice diameter–had been shown to influence strongly the gas hold-up values in bubble columns,6 because the bubble size is affected. Gas holdup in an airlift reactor is a parameter of great importance, not only for its effect on the circulation rate of the liquid but also for its consequence on gas residence time and liquid mixing. However, relatively little attention has been paid to the effect of gas distribution in airlift reactors, and there are no data published about its influence on the performance of three-phase EL-ALRs. Merchuk7 reported that there was no difference in the gas holdup and liquid velocity for different holes diameters of the distributing plate for gas-liquid systems in an EL-ALR. Also, for a two-phase system and an EL-ALR, different results were obtained by Snape et al.8 when investigating the effect of the distributing plate geometry on gas holdup and liquid velocity. They found that the plate with 0.5- mm orifices had a markedly different behavior than the plates with larger orifices diameters, while only a slight increase of gas holdup and liquid velocity with decreasing orifice diameter was observed for orifice diameters in the range of 1.0-3.0 mm. However, reports on the effect of gas distributor (sparger) designs on the gas-liquid mass transfer are limited. Abraham and Sawant9 used a single-orifice distributor and a ladder-type multiorifice distributor, and Han et al.10 used a metal sinter distributor and a six-hole perforated plate in their study of k1a in bubble column, where they found difference in the measured k1a using these spargers. The gas distributor is important in reactor design and has been proved to directly affect the hydrodynamics and phase mixing in bubble column reactors at certain conditions.11–14 Hence, the sparger effect on gas-liquid mass transfer must be further characterized. However, ALRs have been far less studied than conventional bubble columns in the literature and their geometry is more complex, which makes their design trickier: specific phenomena may occur in each section and, thus, the sections do not scale necessarily in proportion! Indeed, the present design practice of these reactors is still closer to an art than a science.15 Standard design procedures are still based on a one-dimensional hydrodynamic analysis that combines empirical correlations to either tank-in-series or axial dispersion models to take backmixing into account. For ALRs, experimental evidence is generally more recent, but less abundant, and it seems often contradictory (compare, for example, the results of Gavrilescu and Tudose16 with those of Merchuk et al.17). This stems first from the fact that the role of many geometrical parameters, such as the sparger, has been often ignored, as shown by Merchuk and Yunger18 for internal-loop reactors or Snape et al.19 for externalloop ALRs. The differences also are derived from the method used for the estimation of axial dispersion coefficient (Dax). Most contributions are indeed based on the Blenke model, which considers an axial dispersion coefficient for the entire reactor.20 Even more difficulties arise from the introduction of a solid phase, because the influence of the solids–which may change quantity, density, and/or size–on the energy loss and, hence, on hydrodynamics is very difficult to predict. Thus, only a few

Figure 1. Mass balance scheme of the axial dispersion model.

of the models in the literature describe the hydrodynamics of three-phase airlift reactors being developed for only one type or amount of solids. As a result, no specific model for the Peclet number (Pe) prediction is available in an EL-ALR in the literature up to now. Therefore, it seems necessary to revisit our knowledge on mixing in an EL-ALR. To obtain further information about the behavior of threephase external-loop reactors working with low-density particles, the effect of airflow rate, solids loading, and different sparger designs on the riser gas holdup and downcomer liquid velocity is systematically studied. The axial dispersion model for Pe prediction is validated based on the recent experimental data obtained in an EL-ALR, to improve the prediction of mixing in EL-ALRs. The result will be used to obtain a better theoretical understanding of the mechanisms of mixing in EL-ALRs and, particularly, to evaluate the respective roles of sparger structure as well as gas holdup and liquid velocity profiles. Axial Dispersion Models (ADMs) Consider the plug flow of a fluid, on top of which is superimposed some degree of backmixing or intermixing, the magnitude of which is independent of the position within the reactor. This condition implies that no stagnant pockets exist and no gross bypassing or short-circulating of fluid in the reactors occurs. This is called the dispersion model. Figure 1 shows a general scheme, which is common for axial dispersion models adopted to predict the mixing in the riser and the downcomer, respectively. ADM Establishment. The mass balance equation for the tracer is

[

uc + EZ

2 πD2R ∂ ∂c πDR ∂c ∂c ) u c+ dl + EZ + c + dl ∂l ∂l 4 ∂l ∂l 4 2 ∂c πDR dl (1) ∂t 4

(

)]

[(

)

]

( )

where u is the fluid velocity, c the tracer concentration, l the distance from the inlet, DR the diameter of the reactor, and EZ the axial dispersion coefficient. The aforementioned equation is also given by ∂2c ∂c ∂c ) EZ 2 - u ∂t ∂l ∂l

(2)

In dimensionless form, where θ ) t/tj ) tu/L, ψ ) c/c0, Z ) l/L, and Pe ) uL/EZ, the basic differential equation that represents this axial dispersion model becomes 1 ∂2ψ ∂ψ ∂ψ ) ∂θ Pe ∂Z2 ∂Z

(3)

The model can be solved using the following assumptions: (1) The liquid phase passes through the reactor under the constant fluid velocity and EZ is constant along the axial direction.

4010 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008

(2) The radial concentration profiles in any cross section are uniform. (3) EZ is independent of the resident time and the axial positions in the reactor. It is a function of the reactor structure, operation conditions, and fluid physical properties. (4) The tracer concentration is a continuous function of axial distance. The fluid concentration of the aforementioned model is given using Laplace integral transform.21 (i) The liquid phase is at batch operation mode; therefore, the liquid concentration is given by ∞ c(Zu, θu) ) c0 j)-∞

∑




[

B0 B0 exp (j + Zu - θu)2 4πθu 4θu

]

(4)

(ii) When the liquid is at continuous operation mode, the liquid concentration is given by ∞ c(Zu, θu) n-1 ) c0 n j)-∞

∑(

)
4πθ exp[- 4θ (j + Z - θ ) ] B0

B0

θu

2

u

u

u

u

(5a)

where B0 )

PeL EZ

(5b)

Initial and Boundary Conditions. For the axial dispersion model, there are commonly three steady solution conditions: open-type condition, semi-open-type condition, and closed-type condition. In this work, the open-type steady solution condition is adopted to simulate the local hydrodynamics of an EL-ALR. The initial conditions are given in dimensional and dimensionless format, respectively. c(t, 0) ) c0δ(l)

(6)

ψ(Z, 0) ) δ(Z)

(7)

The boundary conditions that correspond to the aforementioned initial conditions are given by c(0, t) ) c(L, t)

(8)

∂c(0, t) ∂c(L, t) ) ∂l ∂l

(9)

ψ(0, θ) ) ψ(1, θ)

(10)

∂ψ(0, θ) ∂ψ(1, θ) ) ∂Z ∂Z

(11)

Numerical Methods The aforementioned partial differential equations are transformed to an algebraic equation group, using the six-point difference format. The equation solution, ψ(θn,Zn), is solved using the pursuit method. To optimize the model parameter (Pe), the nonlinear programming strategy is obtained with minimum square error fits between the model prediction value ψcat and the experimental value ψexp at different times and axial distances in an EL-ALR. M

minF(Pe) )

∑ (ψ

(12)

Pe g 0

(13)

2 cat,i - ψexp,i)

i)1

The exclusive model parameter is optimized using the gold partition method for nonlinear programming strategy, given the aforementioned equation restriction conditions. The flowcharts

of the program of the model parameter simulation using the gold partition method and of the detailed procedure of calculating ψ(θn,Zn) using the pursuit method are shown in Figures 2 and 3, respectively. Experimental Setup The experimental apparatus was the same as that once used by Cao et al.22 in our laboratory. The column had a riser (with a diameter of 0.47 m and a height of 2.5 m) and two downcomers (with a diameter of 0.08 m and a height of 2.5 m). The measurements of the local gas holdups, using the microconductivity probe, and liquid circulation velocity, using the 3D laser Doppler anemometry (LDA) system, all followed the same strategies.23 Filtered tap water was used as the liquid phase in batch operation mode. Compressed and filtered air was supplied as the gas-phase flow. The gas flow rate was controlled by calibrated rotameters, in various reading ranges, that were connected in parallel. Superficial gas velocity was set to be 0-0.06 m/s, to ensure that the measured local time-average gas holdups were 0.8 m/s, the flux becomes more uniform and the Pe values become flatter with increasing SL. In agreement with the results obtained for RGr in Figure 12, the Pe parameter is only significantly affected by the sparger orifice diameter for low SL values. For a gas-liquid two-phase system, Pe decreases with the orifice diameter and, for 1% of solids, the Pe value is also lower for sparger P-2 (φ ) 0.6 mm) than for sparger P-1 (φ ) 0.3 mm). For higher amounts of solids (3%), Pe does not have a defined trend. In this case, as RGr decreases with the increasing orifice diameter of the sparger, the driving force for liquid circulation becomes smaller and, hence, the value of Pe becomes smaller. For high SL, because of the different amounts of bubbles entered into the downcomer for the four spargers, the difference between the riser and the downcomer gas holdup is affected in different ways, which could explain the uncertainty time in these cases. However, the differences observed are very small, which leads us to conclude that the sparger orifice diameter has a small influence on Pe for high SL values. Model Validation. Using the model developed in this work, one can estimate the value of Pe after RGr, UGr, and ULd are known from the experiments. Experimental results have been used here. Form eqs 3, 4, 5b, and 8–13, one can estimate Pe by optimization, using eqs 6 and 7 as the objective. The results are presented in Figure 15, and they confirm the validity of the model, which seems superior to the conventional correlations for the bubble columns36,37 or airlift reactors.17 The model developed for the prediction of Pe has also been compared to Pe estimations, based on computional fluid dynamics (CFD). Using the results from Vial26 for the calculation of the flow field in an EL-ALR, one can estimate the Pe value by recording the calculated concentration of the tracer versus the time at different heights in the riser. Figure 15 shows good agreement between the predictions and experimental data for this work. The root-mean square (rms) of the local bubble velocity and interstitial liquid velocity in the axial direction and bubble diameter have been postulated to be almost constant over the riser diameter; therefore, the result seems realistic, from a physical point of view. This takes into account the fact that the role of turbulence on mixing at the local scale is almost constant all over the cross-sectional area of the riser, despite the presence of velocity and gas holdup profiles, because they result mainly from bubble properties and sparger structures. The data of Baird and Rice,37 to some extent, confirm the model predictions. However, it is clear that such conventional correlations from Baird and Rice37 for the bubble column are only able to describe the effect of EZ between the

4016 Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 Table 3. Comparison between Pe Values from RTD Experiments, the Model Developed in This Work, and CFD Calculations Peclet Number, Pe via residence time via axial dispersion via computational fluid model, ADM dynamics, CFD UG (m/s) distribution, RTD 0.011 0.023 0.037

1.25 2.50 3.70

1.19 2.30 3.30

1.15 1.98 2.89

homogeneous regime and the transition region quantitatively. However, the prediction values for EZ of Merchuk17 and Deckwer36 are higher than experimental data. These big differences between the predictions and the experimental values stem, first, from the fact that the role of many geometrical parameters, such as the sparger, has been often ignored. The differences also are derived from the methods used for the estimation of EZ. The conventional correlations of Merchuk17 and Deckwer36 are indeed based on the Blenke method. This method is suitable for internal-loop airlift reactors, for which deaeration is seldom complete; however, this point is more doubtful in EL-ALRs, as shown by Verlaan et al.,38 Lu et al.,39 and Dhaouadi et al.40 These authors have suggested an analysis of mixing in each individual section, arguing that their respective role on mixing could be very different. A model similar to that applied to experimental results for residence time distribution (RTD) can then be used with CFD data. The calculations have been conducted using a commercially available CFD package (Fluent 6.0) on the twodimensional (2-D) geometry of Vial,26 along with a two-fluid model and a classical k- model for turbulence modeling. For the mathematical modeling of the tracer injection in the CFD code, the procedure proposed by Cockx41 has been used. Finally, Pe values based on RTD measurements, those predicted by the one-dimensional (1-D) model developed in this paper, and those from 2-D CFD calculations have been compared in Table 3, but only in the homogeneous regime, because a simple twofluid model is not able to predict the flow field in the churnturbulent regime.42 The agreement is quite acceptable, which shows that the model developed in this work is based on first principles. Conclusions (1) A detailed description of the local hydrodynamic parameters of both liquid and gas phases has been obtained in an external-loop airlift reactor (EL-ALR) with four different sparger designs and solids loadings, using the microconductivity probe and laser Doppler anemometry (LDA) measurement techniques. This may be useful for the purpose of computational fluid dynamics (CFD) validation. (2) All the experimental data for the Peclet number (Pe) have been compared with prediction values obtained using the axial dispersion model (ADM), literature values, and CFD values. A reasonable agreement is achieved in the homogeneous regime. The inaccuracy of the prediction values at high gas flow rate is shown to be due to the poor estimation of turbulent parameters. (3) The sparger designs were determined to have a noticeable effect on the local gas holdup (RGr) and Pe in the lower gas velocity and lower solid loading ranges (UG < 0.025 m/s and SL < 2%), but only a slight effect in the high gas velocity and high solid loadings ranges (UG > 0.030 m/s and SL > 3%). However, the effect of sparger design on ULd is greater in the gas velocity range of 0.025-0.045 m/s. For the smaller SL values, the increase in orifice diameter leads to a decrease in RGr. This is in accordance with that presented in the gas-liquid

two-phase system. Moreover, the influence of orifice diameters of the spargers is negligible for SL > 3%. The magnitude of ULd with a downward-pores sparger (R-1) is smaller than that observed with an upward-pores sparger (P-1). Although the Pe values decreased as the operating gas velocity decreased, the gas velocity change from 0.03 m/s to 0.04 m/s yielded lower Pe values, as a result of the reduced bubble size. As the gas velocity further increased to 0.06 m/s, the RGr and ULd values increased, whereas the Pe values increased negligibly. For a gas-liquid two-phase system, Pe decreases as the orifice diameter decreases and, for SL ) 1%, Pe is also lower for sparger P-2 (φ ) 0.6 mm) than for sparger P-1 (φ ) 0.3 mm). For higher amounts of solids (SL ) 3%), Pe does not have a defined trend. (4) In addition to the gas velocity and sparger design effects, the solids loading had the effect of decreasing the ULd values, while such effect became small and flattened at high solid loadings. The ULd values, especially with VO ) 100%, are 20% lower in three-phase flow than that in two-phase flow. In addition, the ULd profiles in a three-phase flow are flatter than that in a two-phase flow with VO ) 50%-100%, which actually shows a parabolic shape rather than the almost-linear one encountered in two-phase flow. It is very important for design and optimum operation that one systemically investigate the synergistic effect of ULd, RGr, Pe, SL, and sparger design on the hydrodynamic performance of an EL-ALR. Acknowledgment The financial support of this research by Taishan Mountain Scholar Constructive Engineering Foundation of China (No. Js200510036), by National Natural Science Foundation of China (No. 20676064), and by Young Scientist Awarding Foundation of Shandong Province (No. 2006BS08002) is gratefully acknowledged. Nomenclature B0 ) Bodenstein number (dimensionless) c ) tracer concentration (kmol/m3) c0 ) initial tracer concentration (kmol/m3) dp ) particle diameter (m) DR ) column diameter (m) Ez ) axial dispersion coefficient (m2/s) l ) reactor axial position (m) L ) reactor axial length (m) Pe ) Peclet number (dimensionless) Re ) Reynolds number (dimensionless) t ) time (s) U ) superficial velocity (m/s) UG ) superficial gas velocity (m/s) UGr ) superficial gas velocity in the riser (m/s) UL ) superficial liquid velocity (m/s) ULd ) superficial liquid velocity in the downcomer (m/s) RGr ) local gas holdup (dimensionless) ψ ) dimensionless concentration (dimensionless) θ ) dimensionless time (dimensionless) Z ) dimensionless distance (dimensionless) F ) density (kg/m3) φ ) sparger hole diameter (mm) AbbreViations ADM ) axial dispersion model C-1 ) cross sparger CFD ) computational fluid dynamics

Ind. Eng. Chem. Res., Vol. 47, No. 11, 2008 4017 EL-ALR ) external-loop airlift reactor IL-ALR ) internal-loop airlift reactor LD ) solids loading LDA ) laser Doppler anemometer P-1, P-2 ) perforated plate RTD ) residence time distribution R-1 ) ring sparger VO ) valve opening

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ReceiVed for reView November 8, 2007 ReVised manuscript receiVed March 14, 2008 Accepted March 20, 2008 IE0715254