Energy & Fuels 2001, 15, 147-150
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Mass Transfer from CO2 Drops Traveling in High-Pressure and Low-Temperature Water Keiichi Ogasawara, Akihiro Yamasaki,* and Ho Teng National Institute of Materials and Chemical Research, 1-1 Higashi, Tsukuba 305-8656, Japan Received July 11, 2000. Revised Manuscript Received October 24, 2000
Mass transfer from CO2 drops traveling in high-pressure and low-temperature water, simulating the process of CO2 ocean disposal, was investigated in a water tunnel. This investigation covered cases for CO2 drops with and without a hydrate shell. In both cases, the CO2 drops dissolved in water, indicating that the crystal hydrate shell did not stop mass transfer. Influence of the water flow on mass transfer was studied. The drop-shrinkage rate was noticed to increase with increase in the water velocity; and, the rate of mass transfer from CO2 drops with a hydrate shell was found to be much smaller than that from CO2 drops without a hydrate shell under the same flow condition. Coefficients for mass transfer from CO2 drops with and without a hydrate shell were analyzed. In the former case, the mass-transfer coefficient was evaluated on the basis of a seriesmass-transfer model; in the latter case, a conventional-type correlation for the mass-transfer coefficient was developed.
Introduction Several ocean-disposal scenarios to mitigate global warming have been proposed.1,2 The majority of them are concerning the discharge of liquid CO2 into the ocean at intermediate depths (500∼1500 m). In these cases, the CO2 discharged is believed to dissolve in seawater, and hence to be sequestrated in the ocean. To minimize the impact of the CO2 disposal on the ocean environment, the process of CO2 dissolution/dilution must be carefully controlled. Therefore, an understanding of the mass transfer of CO2 into seawater is of great importance. Under pressures and temperatures of intermediate-depth waters (p > 45 bar and T < 283 K), the thermodynamic conditions for hydrate formation are satisfied; thus, stable hydrate may form at the CO2seawater interface,3 which has been confirmed in laboratory simulations.4-13 Although the hydrate shell formed on the CO2 drops is thin,4-13 this crystal inter* Corresponding author. e-mail:
[email protected] (1) Halmann, M. M.; Steinberg, M. Greenhouse Gas Carbon Dioxide Mitigation; Lewis: Boca Raton, FL, 1999. (2) Handa N.; Ohsumi, T. Direct Ocean Disposal of Carbon Dioxide; Terra Scientific Publishing Company: Tokyo, 1995. (3) Song, K. Y.; Kobayashi, R. SPE Formation Evaluation; Society of Petroleum Engineers: 1987; pp 500-508. (4) Aya, I.; Yamane, K.; Yamada, N. ASME- HTD 1992, 215, 17. (5) Aya, I.; Yamane, K.; Yamada, N. Trans. Jpn. Soc. Mech. Eng. 1993, 59B, 1210-1215. (6) Aya, I.; Yamane, K.; Yamada, N. Energy Convs. Mgmnt. 1995, 36, 485-488. (7) Shindo, Y.; Lund, P. C.; Fujioka, Y.; Komiyama, H. Energy Convs. Mgmnt. 1993, 34, 1073-1079. (8) Shindo, Y.; Lund, P. C.; Fujioka, Y.; Komiyama, H. Int. J. Chem. Kinet. 1993, 25, 777-782. (9) Shindo, Y.; Fujioka, Y.; Takenouchi, K.; Komiyama, H. Int. J. Chem. Kinet. 1995, 27, 569-575. (10) Nishikawa, N.; Ishibashi, M.; Ohta, H.; Akutsu, N.; Tajika, M.; Sugitani, T.; Hiraoka, R.; Kimuro, H.; Shiota, T. Energy Convers. Manage. 1995, 36, 489-492. (11) Hirai, S.; Okazaki, K.; Araki, N.; Yazawa, H.; Ito, H.; Hijikata, K. Energy Convers. Manage. 1996, 37, 1073-1078.
phase may affect the mass transfer of CO2 into seawater significantly. Several kinetic models have been proposed for the mass-transfer process9,14-17 and these models have been reviewed by Mori18 recently. Despite these intensive studies, the mechanism for this interfacial mass transfer is still not clear and the role played by the hydrate interface in the overall mass transfer is still not fully understood. Behavior of CO2 drops in suspension in a tube-type reactor was discussed in our previous report.19 Since a stable suspension suggests that the buoyancy of and the drag on the drops be balanced, our previous tests actually simulated drops moving in their terminal velocities. Due to the limitation of experimental conditions, in those tests the drop sizes and corresponding Reynolds number were relatively small. In reality, the drops in the ocean may move with a finite acceleration (i.e., the buoyancy and drag are not in balance) and the drop Reynolds number also could be large. Under these conditions, behavior of drop dissolution may differ from that reported previously. Taking this into consideration, we extended our mass-transfer investigation to cases where CO2 drops move in high-pressure and lowtemperature water with Reynolds numbers up to 800. (12) Hirai, S.; Okazaki, K.; Tabe, Y.; Hijikata, K.; Mori, Y. Energy 1997, 22, 285-293. (13) Warzinski, R. P.; Cugini, A. V.; Holder, G. D. Coal Science; Pajares, J. A., Tascon, J. M. D., Eds.; Elsevier: Amsterdam, 1995; pp 1931-1935. (14) Fujioka, Y.; Takeuchi, K.; Shindo, Y.; Komiyama, H. Int. J. Energy Res. 1994, 18, 765-769. (15) Lund, P. C.; Shindo, Y.; Fujioka, Y.; Komiyama, H. Int. J. Chem. Kinet. 1994, 26, 289-297. (16) Holder, G. D.; Cugini, A. V.; Warzinski, R. P. Environ. Sci. Technol. 1995, 29, 276-278. (17) Holder, G. D.; Warzinski, R. ACS Division of Fuel Chemistry Reprints 1996, 41, 1452-1457. (18) Mori, Y. H. Energy Convers. Manage. 1998, 39, 1537-1557. (19) Teng, H.; Yamasaki, A. Energy Convers. Manage. 2000, 41, 929-937.
10.1021/ef000151n CCC: $20.00 © 2001 American Chemical Society Published on Web 12/12/2000
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Figure 2. An image of liquid CO2 drop in a polycarbonate tube test section.
Figure 1. Schematic diagram for the experimental apparatus.
Experimental Section Figure 1 shows a schematic diagram of the experimental system. Since details of the system have been reported in our previous work,19 the system is only briefed here. The test section of the system was a tapered polycarbonate tube that could stand pressures up to 300 bar. Through the test section, the pressurized water was circulated and the volume rate of water flow could be controlled at any value in the range 0-9 L/min by a high-pressure pump that drove the circulation. A piston-type pressure controller governed the system pressure at an accuracy of 0.2 bar. The system temperature was controlled by a heat exchanger with an accuracy of 0.5 K. Formation of the hydrate film on the surface of the CO2 drops could be controlled by changing the initial pressure of the system before injecting CO2 into the system. The CO2 injection process was as follows. The system was first filled with water at the atmospheric pressure and then it was pressurized to a certain pressure (referred to as the initial water pressure hereafter), under which liquid CO2 was introduced to the system through a 2-mm-diameter nozzle at the bottom of the test section. After the injection, the entire system (water plus CO2) was pressurized to a specified pressure (55 bar in most cases), under which the dissolution investigation was conducted. A stainless steel net mounted at the top of the test section kept the buoyant CO2 drops to be within the test section. When the drops reached the net, water flow was started immediately in the direction opposite that of the CO2drop buoyancy. Because the test section was transparent, behavior of the CO2 drops could be observed directly and the phenomena were recorded by a digital video camera connected to a PC where the captured phenomena were viewed and analyzed. Figure 2 shows an image of an in-suspension CO2 drop in the test section in a typical dissolution test.
Results and Discussion Hydrate Formation. We found that the initial water pressure under which the CO2 was injected into the system affected hydrate formation on CO2 drops. In cases where the initial water pressure was higher than 31 bar, no hydrate was noticed to form either at the injection stage (at 31 bar) or in the drop-dissolution process (at 55 bar). However, in cases where the initial water pressure was lower than 19 bar, the hydrate was
Figure 3. Time course for the dissolution of CO2 drop with hydrate film (temperature ) 278 K, pressure ) 55 bar).
found to form on the drops immediately when the drops entered the water and the hydrate shell remained on the drop surface throughout the entire dissolution process (at 55 bar). This may be due to the fact that the initial water pressure affected the injection speed of CO2 through the nozzle. Because the CO2 injection pressure was constant, a lower initial water pressure resulted in a higher injection speed, which enhanced the rate of mass transfer of the CO2 drop into water and, thus, caused a higher level of the CO2 concentration in the immediate neighborhood water around the drop. Note that a high concentration is crucial to hydrate crystallization. Drop Shrinkage. Figure 3 shows the drop-size vs time relationship for CO2 drops covered with a hydrate shell during the course of dissolution in various flow conditions. The initial drop diameters were about 18 mm, and the pressure and temperature under which the dissolution took place were 55 bar and 278 K. It is seen in Figure 3 that the drop-shrinkage rate increases with increase in the water-flow rate. The shrinkage of a CO2 drop may be characterized by the following relationship for mass transfer from the drop into water:
Mass Transfer from CO2 Drops Traveling in Water
d 4 3 πr C0 ) -4πr2kT(C0 - Cw) dt 3
(
)
Energy & Fuels, Vol. 15, No. 1, 2001 149
(1)
where r is the drop radius (in m), C0 and Cw are the CO2 concentrations in the drop and in the ambient water (in mol/m3), kT is an overall mass-transfer coefficient. Equation 1 may be rearranged as
|dr/dt| ) kT(C0 - CW)/C0
(2a)
Because Cw is much smaller than C0, eq 2a may be simplified to
|dr/dt| ≈ kT
(2b)
Equation 2b suggests that the overall mass-transfer coefficient kT may be calculated on the basis of the dropsize vs time relationship (such as those given in Figure 3) in drop dissolution. Figure 4 shows the dependence of the mass-transfer coefficient on Reynolds number. In this study, the characteristic dimension was the drop size and the characteristic velocity was taken to be the mean velocity for the flow at the top of the observation part. Since Reynolds number varies with drop size, the Reynolds numbers given in Figure 4 were values timeaveraged in every three minutes. It is seen in Figure 4 that the mass-transfer coefficient increased with Reynolds number. For a given Reynolds number, the masstransfer coefficient for drops with a hydrate shell was much smaller than that without a hydrate shell. Mass Transfer from Drops without a Hydrate Shell. In cases where hydrate is not involved, mass transfer is governed by a concentration boundary layer on the water side through which the major resistance to mass transfer is formed. It is reasonable to assume that at the inner surface of the boundary-layer water is in equilibrium with the liquid CO2 (the corresponding CO2 concentration being C*). Under this assumption, the flux of mass transfer through the boundary layer is
J ) kL(C* - CW) ) kT(C0 - Cw)
(3)
where kL is a coefficient for mass transfer through the boundary layer. Noting that the CO2 concentration is negligibly low in the ambient water, eq 3 may be simplified to
kT ) (C*/C0)kL
(4)
C0 and C* are constants at given pressure and temperature; thus, the coefficient for mass transfer through the boundary layer is proportional to the overall masstransfer coefficient. In Figure 5, kL was plotted as a function of Reynolds number and the values for C0 and C* are taken to be C0 ) 20.5 kg/m3 () FCO2/MCO2) and C* ) 1.67 kg/m3.21 Dependence of the mass-transfer coefficient on Reynolds number is given in analogy to the Ranz-Marshall’s relationship21 as follows:
kL ) a + bRen
(5)
where a, b, and n are experimentally determined (20) Cussler, E. L. Diffusion Mass Transfer in Fluid Systems; Cambridge University Press: New York, 1997. (21) Teng, H.; Yamasaki, A.; Shindo, Y. Chem. Eng. Sci. 1996, 51, 4979-4986.
Figure 4. Overall mass transfer coefficient as a function of Reynolds number. (temperature ) 278 K, pressure ) 55 bar).
Figure 5. Fitting of the overall mass transfer coefficient data by eq 5. (temperature ) 278 K, pressure ) 55 bar).
parameters. On the basis of our test data, it is determined that a ) 2.1 × 10-8 m/s, b ) 5.1 × 10-8 m/s, and n ) 0.33. Comparison of test data with predictions from eq 5 is given in Figure 5. It is seen that eq 5 reasonably presents the test data. Mass Transfer from Drops with a Hydrate Shell. A comprehensive model is proposed for mass transfer from CO2 drops with a hydrate shell here. The model is illustrated in Figure 6. In this model, the resistance to mass transfer from a CO2 drop into water consists of three links in series: (1) a sublayer of stable hydrate on the CO2-rich side, (2) a sublayer of quasi-stable hydrate on the water-rich side, which always undergoes formation and dissociation during the process of drop dissolution, and (3) a diffusion boundary layer. Note that the inner and outer hydrate layers form the hydrate shell. It is reasonable to assume that equilibrium is realized in the stable inner hydrate layer. Since the kinetic process for hydrate formation or dissociation is very rapid, it may be assumed that hydrate formation and dissociation are in equilibrium in the outer hydrate layer in a kinetic sense. This assumption agrees with our experimental observation. Thus, both inner and outer hydrate layers are in equilibrium, although the outer layer is only in quasi-equilibrium. It is further assumed that the CO2 concentration in the inner layer
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Figure 7. Mass transfer coefficient of the hydrate film. (temperature ) 278 K, pressure ) 55 bar).
Figure 6. Mass transfer model for CO2 from liquid CO2 drop.
of the hydrate shell is Ch1, which is corresponding to the maximum CO2 occupancy in the hydrate lattice (Ch1 ) 7.69 kmol/m3),21 and that the CO2 concentration in the outer layer of the hydrate shell is Ch2, which is corresponding to the minimum CO2 occupancy for hydrate lattice stability (Ch2 ) 4.80 kmol/m3).21 Because it is adjacent to the hydrate surface, the inner surface of the boundary layer is supersaturated with CO2 and its concentration is Ci. Ci is a function of Ch2. For simplicity, we take Ci ) sCh2, where s is a constant. Therefore, the flux for mass transfer from a CO2 drop with a hydrate shell may be given as
J ) kH(Ch1 - Ch2) ) kL(sCh2 - CW) ) kT(C0 - Cw)
(6)
Figure 7. The increase in the mass-transfer coefficient with Reynolds number suggests that the hydrate-shell thickness may decrease with increase in the flow rate. It is seen in Figure 7 that orders of magnitude of the coefficient for mass transfer from CO2 drops with a hydrate shell are in 10-7 to 10-6 m/s. Although the diffusion coefficient in the hydrate shell is not known, its value should be close to those in zeolites because crystalline structures of some zeolites are almost identical to that of CO2 hydrate. Typical values of diffusion coefficients of CO2 molecules in zeolite crystalline structures are reported falling in the range of 10-11 to 10-12 m2/s.22 If we assume that the diffusion coefficient of CO2 molecule in the hydrate structure is in the same range, then the thickness of the hydrate film would be given in the range of 10-5 to 10-6 m based on the mass transfer coefficient obtained in this study. The above value for the hydrate-shell thickness agrees with those reported in the literature14,21 (obtained either experimentally or analytically) in order of magnitude.
which leads to
(
C0 1 1 1 ) + kT Ch1 kH skL
)
Conclusions
(7)
where kH is a coefficient for mass transfer through the hydrate shell. It is seen in eq 7 that the overall masstransfer coefficient kT is composed by two sub-coefficients kH and kL. The coefficient for mass transfer through the boundary layer may be assumed to be same as that without a hydrate shell under the same flow condition (thus, a same Reynolds number); hence, kL may also be determined by eq 5. Considering that the CO2 concentration in supersaturated water is close to that in the hydrate with minimum lattice stability, s may be taken as unity. The coefficient for mass transfer through the hydrate shell can be given alternatively as
kH ) DH/δ
Influence of the ambient flow on mass transfer from CO2 drops was investigated experimentally. In cases where hydrate was not involved, the overall masstransfer coefficient was found to increase linearly with Re0.33. In cases where CO2 drops were covered with a hydrate shell, the mass-transfer coefficient became much smaller although with a same Reynolds number. The resistance to mass transfer due to the hydrate shell was analyzed employing a series mass-transfer model. It was found that the mass-transfer coefficient through the hydrate shell was in orders of 10-7-10-6 m/s. In both cases for drops with and without a hydrate shell, the mass-transfer coefficients were noticed to increase with Reynolds number.
(8)
where DH is an effective diffusion coefficient of CO2 in the hydrate shell and δ is the hydrate-shell thickness. kH also is Reynolds number dependent, as is shown in
EF000151N (22) Ka¨rger, J.; Ruthven, D. M. Diffusion in Zeolites; John Wiley: New York, 1992.
