Abstract

FLUID DYNAMICS; HEAT AND MASS TRANSFER; AND OTHER TOPICS

Experimental investigation of the liquid volumetric mass transfer coefficient for upward gas-liquid two-phase flow in rectangular microchannels

X. Y. Ji; Y. G. Ma^* * To whom correspondence should be addressed ; T. T. Fu; CH. Y. Zhu; D. J. Wang

School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China E-mail: ygma@tju.edu.cn

ABSTRACT

The gas-liquid two-phase mass transfer process in microchannels is complicated due to the special dynamical characteristics. In this work, a novel method was explored to measure the liquid side volumetric mass transfer coefficient k_La. Pressure transducers were utilized to measure the pressure variation of upward gas-liquid two-phase flow in three vertical rectangular microchannels and the liquid side volumetric mass transfer coefficient k_La was calculated through the Pressure-Volume-Temperature correlation of the gas phase. Carbon dioxide-water, carbon dioxide-ethanol and carbon dioxide-n-propanol were used as working fluids, respectively. The dimensions of the microchannels were 40 µm×240 µm (depth×width), 100 µm×800 µm and 100 µm×2000 µm, respectively. Results showed that the channel diameter and the capillary number influence k_La remarkably and that the maximum value of k_La occurs in the annular flow regime. A new correlation of k_La was proposed based on the Sherwood number, Schmidt number and the capillary number. The predicted values of k_La agreed well with the experimental data.

Keywords: Microchannels; Gas-liquid upward two-phase flow; Mass transfer; Pressure variation.

INTRODUCTION

The gas-liquid two-phase micro-contactor is a very important part of micro-chemical systems. The interfacial area - to - volume ratio of gas-liquid two-phase flow in microchannels was demonstrated to be much higher than that in conventional tubes (Haverkamp et al., 2001; Yue et al., 2006; Fu et al., 2010) and the mass transfer process was greatly enhanced. Therefore, microchannels could be used efficiently and safely in gas absorption, desorption, direct fluorination, hydrogenation and other processes (Tegrotenhuis et al., 2000; Jǎhnisch et al., 2000; Demas et al.; 2003; Yeong et al., 2004; Kobayashi et al., 2004). There are many reports (Jepsen, 1970; Irandoust and Andersson, 1988; Irandoust et al., 1992; Tortopidis and Bontozoglou, 1997; Bercic and Pintar, 1997; Kreutzer, 2003; Van Baten and Krishna, 2004; Vandu et al., 2005; Yue et al., 2009) on the gas-liquid two-phase mass transfer process. Because of the significant effect of surface tension on gas-liquid two-phase flow in microchannels, the characteristics of gas-liquid two-phase flow in microchannels are quite different from those in conventional channels. Consequently, a fundamental understanding of the gas-liquid mass transfer process in microchannels is very necessary.

Although titration methods show good accuracy in determining the concentration of solute in solutions, their disadvantage is also obvious. For instance, a large amount of solution is required and the determination of the endpoint often depends on artificial factors. In microchannels 100µm in magnitude, the titration method is quite limited by the small volumetric flow rates of gas and liquid phases. Moreover, trace absorption and real-time observation and measurement are very difficult. In this paper, a high-speed camera and pressure transducers were utilized, respectively, to directly observe the flow pattern and measure the pressure change for upward gas-liquid two-phase flow in real-time in three vertical rectangular microchannels. The liquid volumetric mass transfer coefficient k_La was calculated based on the Pressure-Volume-Temperature correlation of the gas phase. The experimental results at high flow rates were verified by the titration method and the capillary number Ca was introduced to correlate the liquid volumetric mass transfer coefficient k_La.

EXPERIMENTAL SETUP

The microchannel chips were fabricated first by the etching technique on transparent glass and then the mechanical method was applied to produce and polish the microchannels with rectangular cross-section. Dimensions of the microchannels were 40 µm×240 µm (depth×width), 100 µm×800 µm and 100 µm×2000 µm, respectively, referred to as microchannels 1, 2 and 3 for short. The length of the two-phase inlets and mixing section were 1.5 and 4cm, respectively, as shown in Figure 1 (a). The hydraulic diameters d_h of the microchannels were 68.57µm, 177.78µm and 190.48 µm, respectively, and all the experiments were carried out at atmospheric pressure and 298.15K.

To eliminate the effect of outlet connecting tubes and two-phase collectors on the mass transfer of two-phase mixing sections, absorption in non-mixing section microchannels was conducted under the same conditions (named blank experiments), but, as shown in Figure 1(b), the T-junction was connected directly to the outlet connecting tubes without the mixing section.

The flow chart of experiments is shown in Figure 2. Pure carbon dioxide was driven and the flow rates were set by a micro-infusion pump. After flowing through a filter and a valve, it was then injected into the vertical microchannels. The pressure transducer installed on the gas inlet connecting pipe determines the inlet pressure of the microchannels. Water was boiled to remove the dissolved carbon dioxide and then cooled to room temperature. Water, ethanol and n-propanol (physical properties are listed in Table 1) were driven by the micro-infusion pump and the actual flow rates of the liquid phases were determined by using an electronic balance. Liquid phase and carbon dioxide flowed in the mixing section of microchannels and then into the two-phase collector through an outlet connecting tube of 0.5mm diameter. The two-phase collector was enclosed to isolate it from the outside environment. The pressure transducer installed on the outlet connecting tube measured the outlet pressure of the microchannels and two thermocouple thermometers installed on the inlet and outlet connecting tubes were employed to determine the temperature of the system. A high-speed camera (2500fps) was used for the observation of the flow patterns. The mass transfer of carbon dioxide into the liquid phases was determined by the Pressure-Volume-Temperature correlation of the gas phase based on the pressure variation before and after the absorption. The titration method was used to verify the pressure method at large flow rates. For this purpose, 10mL of 0.1mol·L^-1 NaOH solution were added to 10mL of the two-phase mixture and then 0.1mol·L^-1 HCl solution was used for titration; phenolphthalein and helianthine were used as the first and second endpoint indicators (light pink and orange), respectively. The results showed that the relative deviation of the two methods at large flow rates was 1~2.5%, which confirmed the credibility of the pressure variation method.

To eliminate the effect of the frictional pressure drop on the experimental results, the frictional pressure drop of nitrogen-water, without absorption, was measured experimentally. The frictional pressure drop for nitrogen-ethanol and nitrogen-n-propanol without absorption were calculated based on the model of Lockhart and Martinelli (1949) and the method of Chisholm (1967).

The Lockhart and Martinelli model could be expressed via Eqs. (1) and (2):

where (ΔP_F/L)_t is the total two-phase frictional pressure drop in the microchannels, kPa·m^-1; (ΔP_F/L)_t is the liquid single-phase frictional pressure drop in the microchannels, kPa·m^-1; (ΔP_F/L)_t is the gas single-phase frictional pressure drop in the microchannels, kPa·m^-1. is the two-phase multiplier and X is the Martinelli parameter.

Chisholm related to X by introducing another parameter, the Chisholm factor C:

A new correlation of the Chisholm factor C that takes into account the different physical properties of the liquid phases was proposed in our previous work and was employed to calculate the frictional pressure drop of nitrogen-ethanol and nitrogen-n-propanol without absorption. The correlation expressed as follows:

where Ca_L=µ_LJ_L/σ, a=7.59-0.4237×A^-0.9485+0.0023×Re_L and b=0.223+0.2×A^0.9778. A is the aspect ratio of the rectangular cross-section of the microchannels. Thus, the practical pressure change resulting from absorption could be derived by subtracting the frictional pressure drop from the total pressure change.

RESULTS AND DISCUSSION

Flow Patterns of Upward Two-Phase Flow in Vertical Microchannels

The gas-liquid two-phase flow patterns captured by the high-speed camera in the experiments are shown in Figure 3. The flow patterns varied from Taylor bubble flow to annular flow with increasing gas and liquid flow rates. The length of the gas bubbles L_B and liquid slugs L_S in Taylor bubble flow were obtained from an analysis of flow pattern images. Figure 4 shows the experimental results for Taylor bubble length and slug length. As can be seen from Figure 4, the distribution of the length of Taylor bubbles and liquid slugs became gradually uniform from water to ethanol and to n-propanol as the continuous phase, which indicated that there was a better mixing effect and mass transfer performance in the carbon dioxide-n-propanol system than in the other two systems.

Calculation of the Liquid Volumetric Mass Transfer Coefficient k_La

The mass transfer of carbon dioxide into water, ethanol and n-propanol is mainly governed by the liquid phase and k_La is obtained from the equation of mass balance (Yue et al. (2006)):

where C₀ and C₁ are concentrations of carbon dioxide in the liquid phase at the inlet and outlet of the microchannels and C_e is the equilibrium concentration of carbon dioxide in the liquid phase (Zhang, 1986; Liu et al., 2002), J_L is the liquid phase superficial velocity and L_C is the length of the mixing section of the microchannel. The value of k_La in the outlet connecting tube of the experiments is the same as that of the blank experiments, expressed as follow:

Yue et al. (2006) demonstrated that Eq. (6) could reasonably eliminate the outlet effect. Combination of Eq. (5) and Eq. (6) results in the following expression:

where C₂ and are the concentrations of carbon dioxide in the liquid phases in the two-phase collector of the microchannel flow experiments and the blank experiments, respectively, and are calculated from the following correlations:

where P_in is the inlet pressure of the absorption processes and is that of the blank experiments; P_ob is the outlet pressure before absorption in the experiments and is that of the blank experiments; P_oa is the outlet pressure after absorption in the experiments and is that of the blank experiments; T is the temperature of system in the experiments and T' is that of the blank experiments; is the total CO₂ volume injected into the system in the experiments and is that of the blank experiments; V_liquid is the total liquid phase volume injected into the system in the experiments and is that of the blank experiments; and V is the total volume of the system.

A large amount of experimental data has been measured for calculating k_La. Table 2 lists typical measured values for the quantities on the r.h.s. of Eqs. (8) and (9) of the three systems in microchannel 1 at J_L=0.05m·s^-1 and J_G=1.8 m·s^-1.

Liquid Volumetric Mass Transfer Coefficient k_La

Figure 5 and Figure 6 illustrate the influences of channel diameter and capillary number on k_La, respectively, with the liquid phase superficial velocities J_L=0.03, 0.05 and 0.07 m·s^-1 from bottom to top, respectively; the transition from Taylor bubble flow to an annular flow pattern is marked by black lines.

It can be seen from Figures 5 and 6 that the value of k_La in microchannel 1 was much larger than that in microchannels 2 and 3. The values of k_La also presented remarkable differences between the different liquid phases used, which demonstrated the great influence of both channel diameter and liquid phase capillary number on k_La. The value of k_La increased with gas and liquid superficial velocities, because, in Taylor bubble flow, the number of gas bubbles increased with increasing the gas flow rate. As a consequence, the interfacial area for mass transfer was enhanced, resulting in the increase of k_La. The value of k_La achieved the maximum in the annular flow, in accord with the literature (Haverkamp et al., 2001; Kobayashi et al., 2004).

There are many reports on the investigation of the liquid mass transfer coefficient k_La in Taylor bubble flow. Jepsen (1970) proposed an energy dissipation model to correlate the value of k_La and the pressure drop of the system is required to use this model. Bercic and Pintar (1997) studied the absorption of methane into water in a circular tube and proposed a model of k_La that did not consider the influence of tube diameter and diffusion coefficient. Subsequently, researchers divided the mass transfer of the Taylor bubble to the surrounding liquid into three parts, the cap and tail of bubbles into the liquid slug, and the cylindrical part of bubble into the liquid film between the gas bubble and the tube wall. On the basis of this, Van Baten and Krishna (2004) simulated the mass transfer process of a Taylor bubble rising into the surrounding liquid in vertical circular tubes with CFD and proposed a model of k_La that introduced the tube diameter and diffusion coefficient, as follows:

where J_B is the rising velocity of the Taylor bubble, approximately given by J_B≈ J_L+J_G , as validated by analyzing the variation of flow pattern images, D is the liquid phase diffusivity, and the Taylor bubble length and liquid slug length were obtained by visualization and measurement of flow pattern images captured with a high speed camera. Van Baten and Krishna (2004) regarded the mass transfer of the cylindrical part of the bubble into the liquid film as the dominant part of the total mass transfer process. Based on this, Vandu et al. (2005) investigated the mass transfer process of oxygen into water in circular and square channels of 1mm, 2mm and 3mm diameters and proposed a model of k_La that approximated the total mass transfer as being only that of the cylindrical part transferring into the film. Yue et al.(2009) also investigated the absorption of oxygen into water experimentally in an air-water system and proposed a correlation of k_La according to Eq. (10).

The precise length of the Taylor bubbles and liquid slugs is required to apply the above models, which results in great limitations in application. Yue et al. (2006) utilized the Sherwood number and Schmidt number to correlate k_La in a rectangular microchannel with a hydraulic diameter of 667µm, as follows:

where the Sherwood number is Sh _L=k_Ld_h/D, the Schmidt number Sc_L=µ_L/ρ_LD, the gas phase Reynolds number Re_G=ρ_GJ_Gd_h/µ_G and liquid phase Reynolds number Re_L=p_LJ_Ld_h/µ_L, with µ_L,µ_G and ρ_L,ρ_G as the viscosities and densities of the liquid and gas phases, respectively.

Figure 7 shows the comparison of experimental results for carbon dioxide-water with values predicted by Eqs. (10) and (11). Because the results of carbon dioxide-ethanol and carbon dioxide-n-propanol showed the same trends as that of carbon dioxide-water, they are not displayed here. It can be seen from Figure 6 that there exists a remarkable deviation between the experimental results and values predicted by Eqs. (10) and (11). This may be explained as follows: Eq. (10) considers that the mass transfer of the cylindrical part into the liquid film dominates the total mass transfer; the mass transfer into the liquid film is thus mainly controlled by the length of the liquid slugs surrounding the Taylor bubbles. The longer the liquid slugs, the easier the absorbed gas phase is transferred into the liquid slugs from the liquid film. As a consequence, the liquid film could absorb more gas phase, which results in the high value of k_La (Van Baten and Krishna, 2004; Vandu et al., 2005; Yue et al., 2009). However, the hydraulic diameters of the microchannels used in our experiments were 100 µm in magnitude, such that the lengths of the liquid slugs were much shorter than those (L_S>3L_B) in large tubes. Consequently, the gas phase absorbed by the liquid film could not be transferred into the liquid slugs efficiently. Therefore, the liquid film achieved saturation and could not absorb any more gas phase; in this case, the experimental results for k_La were much lower than those of the literature. The predictive performance of Eq. (11) is better than that of Eq. (10) and appears to be quite well consistent with experimental results in the range of Re_L=59.4~700.6 and Re_G=62.1~1088.3. However, it is worth noting that the ranges of gas and liquid Reynolds numbers in the present experiments were Re_L=1.1~13.07 and Re_G=0.87~61.9, respectively. The hydraulic diameters of microchannels were also much smaller than the 667µm used by Yue et al. (2006), resulting in the large deviation of more than 20% of the predictions of by Eq. (11) from the experimental data in this work, as shown in Fig.6.

The hydraulic diameters of the microchannels used here were all less than 200µm. On such a micro-scale, the capillary number Ca has an important influence on gas-liquid two-phase flow, which was demonstrated by the remarkable difference of the experimental results between water, ethanol and n-propanol as the working liquid phase. Thus, in this paper, a new correlation is proposed based on Eq. (11) but introducing the liquid phase capillary number Ca_L:

where Ca_L=µ_LJ_L/σ, with σ being the surface tension. The values of the parameters were obtained by using the least square fitting method. The comparison between experimental results and values predicted by Eq. (12) is shown in Figure 8. The mean deviations are 10.5%, 13.75% and 15.06% for carbon dioxide-water, 11.65%, 8.05% and 6.93% for carbon dioxide-ethanol and 12.16%, 10.27% and 12.13% for carbon dioxide-n-propanol in the three microchannels, respectively. Figure 9 shows the comparison of predictions of Eq. (12) with experimental data in the circular channels of Van Baten and Krishna (2004) and in the rectangular channel of Yue et al. (2006); the mean deviations are 4.82% and 4.19%, respectively, indicating that Eq. (12) has good predictive performance in both circular and rectangular microchannels.

CONCLUSIONS

The liquid volumetric mass transfer coefficient k_La of carbon dioxide-water, carbon dioxide-ethanol and carbon dioxide-n-propanol two-phase upward flow in vertical microchannels were obtained by measuring the pressure variation before and after the absorption processes. The experimental results were checked by titration under large flow rates and the following conclusions could be obtained:

1) Determination of the liquid volumetric mass transfer coefficient k_La via measuring the pressure variation of the system before and after the absorption process has the advantage of a non-interferencing, real-time determination, high credibility, and good accuracy for trace absorption and requires very little solution, being suitable for the micro-scale;

2) Both the channel diameter and the liquid phase capillary number influence the liquid volumetric mass transfer coefficient remarkably, and k_La achieves its maximum in the annular flow pattern;

3) A new dimensionless correlation of k_La was proposed by introducing the liquid phase capillary number, which showed good predictive performance under micro-scale conditions.

ACKNOWLEDGEMENTS

This work was supported by the National Nature Science Foundation of China (No. 20876107) and the Opening Project of State Key Laboratory of Chemical Engineering (No. SKL-ChE-08B06).

NOMENCLATURE

a

P_in

P_ob

P_oa

T

T'

V_liquid

V

Greek Letters

Dimensionless Group

Sh_L

Sc_L

Re_G

Re_L

Ca_L

(Submitted: June 30, 2010 ; Revised: August 2, 2010 ; Accepted: August 26, 2010)

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