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The growth rate of gas hydrate from refrigerant R12
Experimental Thermal and Fluid Science 30 (2006) 643–651 www.elsevier.com/locate/etfs
The growth rate of gas hydrate from refrigerant R12 Abdullah Abbas Kendoush a
a,*
, Khalid A. Joudi b, Najim Abid Jassim
a
Centre of Engineering Physics, Ministry of Sciences and Technology, P.O. Box 765, Baghdad, Iraq b Al-Nahrain University, Baghdad, Iraq
Received 9 November 2005; received in revised form 30 December 2005; accepted 15 January 2006
Abstract Experimental and theoretical investigations were presented dealing with three phase direct-contact heat transfer by evaporation of refrigerant drops in an immiscible liquid. Refrigerant R12 was used as the dispersed phase, while water and brine were the immiscible continuous phase. A numerical solution is presented to predict the formation rate of gas hydrates in test column. The solution provided an acceptable agreement when compared with experimental results. The gas hydrate growth rate increased with time. It increased with increasing dispersed phase flow rate. The presence of surface-active sodium chloride in water had a strong inhibiting effect on the gas hydrate formation rate. 2006 Elsevier Inc. All rights reserved. Keywords: Gas hydrate formation; R12 host molecules; Direct-contact heat transfer; Clathrate hydrate
1. Introduction Gas hydrates have been increasingly involved in the development of various energy and environment-related technologies in recent years. In addition to the well known problem of plugging of natural gas pipelines by hydrate formation, various hydrate-related scientific and technological problems such as, exploration and recovery of in situ hydrate as an energy resource, thermodynamics of hydrate-forming systems, kinetics of hydrate formation, mass and heat transfer during hydrate formation and dissociation, and utilization of hydrates in energy storage and transportation need to be investigated. Direct-contact heat transfer plays a major role in the formation of the gas hydrate. Gas hydrates are ice-like solids that form when a sufficient amount of water (host phase), and a hydrate former (guest phase) are present at the right combination of temperature and pressure. Hydrate formation is favored by low temperature and high
*
Corresponding author. Tel.: +964 79 0215 8251. E-mail address: [email protected] (A.A. Kendoush).
0894-1777/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.01.009
pressure. The utilization of gas hydrates for desalination offers great advantages as the formation of hydrate crystals consumes less power than the classical processes. To form an R12 hydrate crystal, one molecule of R12 combines with 15.6 molecules of H2O. The R12 single molecule would be enclosed in a cagelike crystalline water structure. Maini and Bishoni [1] studied experimentally the hydrate formation at constant pressure. They found that a bubble of natural gas in 3 C saline water formed a hydrate when the pressure was 4826 kPa, but when the pressure was 8963 kPa, the rate of formation was extremely fast causing the collapse of the injected bubble into large flakes of hydrates. Carbajo [2] performed experiments to produce R12 hydrates for cool storage purposes. He injected R12 in either liquid or vapor form into an agitating column to produce R12 hydrates. Ternes [3] described results of an experimental work with an open-loop R12 hydrate storage facility. He discussed in some detail the effectiveness of mechanical agitation and the addition of surfactants for the reduction of supercooling of fluid contents in a crystallizer. Ternes [3] stated that crusts of hydrates were formed at the phase
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Nomenclature Cp d D0 H0 h hfg k n Nu3 Pe3 Pr Re R0 r T TB T2i t uc u x
specific heat at constant pressure (J/kg K) equivalent diameter of the two-phase bubble (m) diameter of the column (m) initial water level in the column (m) instantaneous heat transfer coefficient (W/m2 K) latent heat (kJ/kg) thermal conductivity (W/m K) total number of R12 drops in column (–) Nusselt number (h3d/k) (–) Peclet number [ud/a] (–) Prandtl number [Cpl/k] (–) Reynolds number [qud/l] (–) radius of column (m) radial coordinate (m) temperature (K) continuous phase bulk temperature (K) dispersed phase inlet temperature (K) time (s) continuous phase velocity (m/s) average velocity of continuous phase (m/s) vaporization ratio within the drop
boundaries, while R12 and water both in liquid states and the mixtures of their vapors constituted three phases superposed on top of one another in the crystallizer and that the crusts acted as barriers separating otherwise neighboring phases, thus preventing further hydrate formation. In a series of papers, Gudmundsson and his colleagues [4–6] developed the technique of using natural gas hydrate (NGH) for storing and transporting natural gas as an alternative to the established technology of liquefied natural gas (LNG). NGH is produced in a high pressure columns operated at 50–70 bar and 2–10 C. Typically the natural gas-bubbling column are charged with water. Hydrate formation starts when a magnetic stirrer is operated for about 1 h. Takaoki et al. [7] described the processes of production, pelletization, transportation, storage and re-gasification of NGH. It can be concluded from the literature survey that there were no reported systematic and detailed heat transfer analyses of the process of using gas-bubbling technique for the formation of gas hydrates. In this paper, an experimental investigation was conducted to study the thermal effects of the formation rate of R12 hydrate in a glass column. A numerical solution predicted the experimental Z-growth rate of the hydrate in the column. The choice of R12 as a hydrate former was because of the relatively low system pressure required to be applied. The experimental glass system, necessary for visualizing the growth rate cannot withstand excessive pressures of gas hydrate formation needed for other types of gases.
z ZG
axial coordinate along column (m) gas hydrate growth rate (cm/s)
Greek letters a thermal diffusivity [k/qCp] (m2/s) DT temperature difference (K) l absolute viscosity (kg/m s) m kinematic viscosity (m2/s) q density (kg/m3) s dimensionless time (–) " volume of continuous phase (m3) Subscripts cr critical h hydrate w column wall 0 initial value [t = 0] 1 vapor R12 phase in two-phase bubble 2 liquid R12 phase in two-phase bubble 3 continuous phase (water)
2. Experimental apparatus The experimental system is shown schematically in Fig. 1. It consists of a test column (crystallizer), cold water
Fig. 1. Schematic of experimental system: X = rotameter, Y = refrigeration unit.
A.A. Kendoush et al. / Experimental Thermal and Fluid Science 30 (2006) 643–651
supply system, dispersed phase supply system, and closedloop vapor compression refrigerator. The test column is illustrated schematically in Fig. 2. It consists of a cylindrical Pyrex glass column of 80 mm diameter and 1.20 m long, in which the test fluid, water was confined. A rectangular Perspex water jacket was made concentrically around the inner cylindrical column. The jacket served as a constant-temperature water bath and also contributed to minimizing the distortion of the images of the bubbles or drops inside the test column. A digital video camera (Sony CCD48X) with 30 frames/ s is used. The pictures are recorded on a rotary magnetic disk and projected on a screen. Thus the growth rate of the hydrate is monitored. Sixteen calibrated sheathed T-type thermocouples were distributed along the column in different positions to measure the temperature of the water axially and radially within the column. An auxiliary water cooling circuit is provided to cool the water in the test column at the start of experiments and to cool the water of the jacket surrounding the test column during the experimental tests as shown in Fig. 1. The experiments were conducted at a pressure of 4 bar and by varying the following conditions: dispersed phase flow rate of 0.8–2 cc/s, initial temperature difference between R12 and water from 3 to 8 K, water height in column (0.25–0.5 m), initial drop diameter of 2–4 mm, and brine concentration of 0–8 wt.%.
645
Fig. 3. Distributor orifice configurations. All dimensions are in millimeter.
The dispersed phase is injected into the test column from a Teflon manifold located at the bottom of the test column. The Teflon manifold consisted of a main and an interchangeable perforated plate or distributor. The diameter of the distributor is 60 mm and its thickness is 4 mm. Three different types of configurations are used for the arrangement of orifices as shown in Fig. 3. The number of orifices are 7, 19 and 36. In each configuration, three different orifice diameters of 0.7, 1 and 1.5 mm are employed. Bubble size, void fraction and bubble velocity were measured by the electroresistivity probes [10]. The probe utilizes the difference in electrical conductivity between the liquid and gas phases. The output from all of the probes are passed through an interface circuit to analyze the signals. The signals are monitored continuously by a personal computer. In the present experiment, the column contained the three phases of H2O (liquid), R12 (liquid), R12 hydrate (solid) and R12 (vapor). 3. Experimental procedure and observations Typical experiments are conducted as follows:
Fig. 2. Assembly drawing of test column (crystallizer).
1. Water was cooled in test column by the auxiliary cooling system to the desired temperature in the range of 10– 20 C. When water in the test column attained the desired temperature above the R12 saturation temperature of 12 C, the test column was filled with water to the desired level and the circulation stopped. 2. The refrigerant loop was evacuated from air by the use of a vacuum pump (not shown in Fig. 1) and R12 was supplied from the high pressure bomb to the loop till a sufficient volume of R12 in the liquid state was stored in the reservoir. 3. As the compressor began to work, the R12 was not added from the bomb to the loop. The needle valve
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was then adjusted to give the required flow and the required pressure of R12. Measurements of temperature and pressure in the test column, as well as the flow rate of R12 were immediately started. The R12 drops started to evaporate as they entered the test column due to its contact with water at higher temperature than its saturation temperature. Then the superheated R12 vapor left the test column. The evaporation was allowed to proceed and the R12 drops rose as two-phase bubbles, then as pure vapor bubbles and eventually part of it reacted with the water molecules to form gas hydrate. The other part of R12 vapor condensed and recirculated. Gas hydrate in the form of slurry accumulated at the top of the column, above the water surface as shown in Fig. 13. The hydrate layer advanced downward with time until the whole column becomes full of hydrate.
r z ; Z¼ dimensionless radial and R0 D0 vertical coordinates uz U¼ dimensionless axial velocity uc
R¼
Using the dimensionless groups: Pe3 ¼
uc D0 a3
Rec ¼
uc D0 ; m3
Ec ¼
u2c C p3 ðT w T 2 Þ
and
l3 C p3 ; k3 nh3 d 2 M2 ¼ k3L Pr ¼
The governing energy equation in dimensionless form becomes: oh oh 1 þU ¼ os oZ Pe3
(
2 ) 4 o oh o2 h oU 2 R þ 2 M h þ 4EcPr R oR oR oR oZ
ð2Þ
4. Mathematical model 4.1. Formulations and assumptions The water flow in the column is induced by the rise of R12 drops/bubbles. The column height is L and its radius is R0. Thermal energy needed for the evaporation of R12 drops are extracted from the bulk of the flowing water. Once R12 bubbles are formed, they become guest molecules in the hydrate crystals. The following assumptions were adopted:
where h is the dependent variable R, Z and s are independent variables. Eq. (2) is subject to the following initial condition and boundary conditions: The initial condition is L h ¼ 1:0 s ¼ 0; 0 6 R 6 1; 0 6 Z 6 ð3aÞ D0 The boundary conditions are • Cylinder wall condition:
(1) The heat flow across the hydrate layer (Fig. 13) and the water–R12 solution are two dimensional (r, z) in the cylindrical coordinates. (2) The physical properties (Appendix B) are constant throughout each of the hydrate and water–R12 solution irrespective of the temperature distribution inside them. The governing energy equation for the water–R12 solution is the following: oT oT 1 o oT o2 T þ uz ¼ a3 r þ 2 ot oz r or or oz 2 nh3 A2 l3 ouZ ðT T 2 Þ þ ð1Þ q3 C p3 8 q3 C p3 or The first term on the right side of this equation is the heat conduction contribution, the second term represents the heat sink and the third term is the viscous dissipation. We introduce the following dimensionless quantities: h ¼ ðT T 2 Þ=ðT w T 2 Þ dimensionless temperature uc t s¼ dimensionless time D0 Here uc is the velocity of the continuous phase at the center of the column.
h¼1
for R ¼ 0;
06Z6
L D0
ð3bÞ
• Cylinder center line condition: oh ¼0 oR
for R ¼ 0;
06Z6
L D0
ð3cÞ
Here U of Eq. (2) is the axial velocity profile of a modular flow in a bubble column. It was developed by Walter and Blanch [9] as follows: U ¼ 1 6R2 þ 5R3
ð4Þ
This velocity distribution is shown schematically in Fig. 11A. The original equation of Walter and Blanch [9] has a parameter N in it. It was considered equal to unity here. Gas hydrate growth rate can be calculated by applying the energy balance through out the system, therefore the gas hydrate growth rate (Z-growth) is q3 uC p3 ðT B T 2i Þ ZG ¼ ð5Þ qh hfgh Here T2i is the temperature of R12 drops at inlet to the test column and hfgh is the latent heat of gas hydrate. Appendix A gives the derivation of this equation. The energy equation was solved numerically by applying the explicit finite difference method. The derivatives in this
A.A. Kendoush et al. / Experimental Thermal and Fluid Science 30 (2006) 643–651
, DT21 is the temperature difference bewhere f ðxÞ ¼ 0:5þx 1x tween the R12 drop2 and the bubble1 inside it and DT32 is the temperature difference between the continuous liquid3 (water) and R12 drops2. Eq. (6) was derived for a single two-phase bubble, so it was multiplied by n number of bubbles in the column. 4.2. Numerical solution The present solution resembles to a certain extent the Gratz–Nusselt problem of finding the temperature profile and heat convection rate in a fully developed laminar flow inside circular pipes. This type of solution allows the temperature profile to be calculated from substituting the parabolic velocity profile into the energy equation [13]. The numerical solution of Eq. (2) is obtained by establishing a finite number of rectangular grid points having coordinates: R = iDR and Z = jDZ at discrete time sn where i, j and n are integer numbers of grid points in the R, Z and s dimensions. The explicit finite difference method was employed for the present numerical solution. The stability of the numerical solution imposed the following restrictions on the size of the time step Ds " #1 4 2 2 Ds 6 þ þM ð7Þ 2 2 ðDRÞ ðDZÞ The outline of the present model is to calculate the bulk temperature distribution numerically from the following: Z rcr =R0 Z rcr =R0 hB ¼ hUR dR UR dR ð8Þ
0.09 ΔT=3 k ΔT=5 k ΔT=8 k
0.08
0.07
0.06
0.05
0.04
0.03 12
5. Results and discussion The inception of gas hydrate occurred when the temperature and pressure in the crystallizer column reached the conditions of the triple point (that is, 12 C and 4 bar). The hydrate layer continued to be accumulated upwards while the water level continued to decrease downward. In studying the effect of the initial temperature difference and water column height on gas hydrate growth rate, a sig-
20
24
28
32
36
40
44
Fig. 4. Variation of gas hydrate growth rate with time at different initial temperature difference. H0 = 0.4 m, flow rate of R12 = 1.2 cc/s.
0.095
0
where rcr is the critical radius at which uz = 0, i.e., the radius bordering the upward-flow region and the outer downward-flow region. According to Eq. (4), rcr/R0 0.56. The bulk temperature was defined in the core region of the flow (0 6 R 6 rcr/R0). Finally applying Eq. (5) to get the growth rate of the hydrate.
16
Time (min)
Gas hydrate layer thickness (m)
0
nificant dependence was found. At lower temperature difference or column height results in a rapid hydrate formation but after the gas hydrate was started the growth rate increases with increasing the temperature driving force, which is controlling the crystal growth process as shown in Figs. 4 and 5. Fig. 5 shows that at a constant flow rate of R12 drops, the low water level would have a high number of R12 molecules per unit volume. These molecules are acting as guest species for hydrate formation, whereas the high water level would contain smaller number of R12 molecules per unit volume, thus lower growth rate is encountered here. The relation between gas hydrate growth rate with the presence of sodium chloride in water is shown in Fig. 6. It was seen that the existence of sodium chloride has a strong inhibiting effect on gas hydrate formation growth rate. This result has an important bearing on the process
Gas hydrate layer thickness (m)
equation could be replaced by the finite difference approximations [11]. The instantaneous heat transfer coefficient h3 of the sink term of Eq. (1) was calculated by using the derived equation of Kendoush [12] as follows: 1=2 DT 21 k 2 q2 Cp2 Nu3 ¼ 0:921 Pe3 xf ðxÞ ð6Þ DT 32 k 3 q3 C p 3
647
0.085
Ho =0.25 m Ho =0.4 m Ho =0.5 m
0.075 0.065 0.055 0.045 0.035 0.025 12
18
24 30 Time (min)
36
42
Fig. 5. Change of hydrate growth rate with time at different initial column height. Flow rate of R12 = 1.2 cc/s, DT32 = 5 K.
648
A.A. Kendoush et al. / Experimental Thermal and Fluid Science 30 (2006) 643–651 0.090
0.09
Gas hydrate layer thickness (m)
0.08
Gas hydrate layer thickness (m)
Distilled water Distilled water with 4 wt% NaCl Distilled water with 8 wt% NaCl
0.07 0.06 0.05 0.04 0.03 0.02
0.075
do =0.2 cm do =0.27 cm do =0.4 cm
0.060
0.045
0.030
0.015 12
18
0.00 15
24
30
36
42
Time (min)
0.01
20
25
30
35
40
45
50
55
Fig. 8. Change of hydrate growth rate with time at different initial R12 drop diameter. H0 = 40 cm, flow rate of R12 = 1.2 cc/s.
Time (min) Fig. 6. Variation of gas hydrate growth rate with time at different continuous phase solutions. H0 = 40 cm, flow rate of R12 = 1.2 cc/s.
Gas hydrate layer thickness (m)
Gas hydrate layer thickness (m)
0.13
Vd = 2 cc/s Vd = 1.2 cc/s Vd = 0.8 cc/s
0.11
0.11
0.09
0.07
0.05
0.10
Present Experimental Work Present Theoretical Work
0.09 0.08 0.07 0.06 0.05 0.04
0.03
0.03
16 0.01 5
15
25
35
45
55
Time (min) Fig. 7. Change of hydrate growth rate with time at different R12 flow rates. H0 = 40 cm, DT32 = 5 K.
of the utilization of gas hydrate for the desalination of saline water. Fig. 7 shows the effect of the R12 flow rate on the rate of hydrate growth at a constant water level in the column and a constant subcooling. The same argument, that was discussed before, of the availability of R12 molecules per unit volume, is applied here and is responsible for the increase of the hydrate growth rate. Fig. 8 shows a higher growth rate for lower droplet diameter of R12. Physically, the smaller the diameter of the droplet, the lower the velocity of its rise. This slow motion allows ample time for the reaction rate to take place for the formation of the R12 hydrate. Fig. 9 shows a comparison between experimental and theoretical values of gas hydrate growth rate in this work.
20
24 28 Time (min)
32
36
Fig. 9. Comparison between the experimental data and the numerical solution.
It clear from this figure that the predicted value of gas hydrate growth rate, during the middle of experiment is in the better agreement with the experimental results than those at the early or later stages of the experiments. Fig. 10 shows a comparison between the experimental data of Mori and Mori [8] and the present work regarding the amount of supercooling achieved by both experiments. Clearly higher crystallizer bulk temperatures were obtained by Mori and Mori [8] due to the use of a mechanical stirrer in their crystallizer. Vortical flow is generated by these stirrers as shown in Fig. 11. Parabolic temperature distributions were obtained in the present work as shown in Fig. 12. This temperature distribution was changed dramatically in the work of Mori and Mori [8] due to the vortical flow caused by the mechanical stirrers. This difference may explain the formation of two
A.A. Kendoush et al. / Experimental Thermal and Fluid Science 30 (2006) 643–651
649
Fig. 12. The temperature distribution in the crystallizer of the present experiment at z = 5D.
Fig. 10. Comparison between the present experiment (–s–) and that of Mori and Mori [8] (—).
(A)
Fig. 13. Schematic illustration of R12 drops and their hydrate formation in the crystallizers of the following: (A) Mori and Mori [8]: column with an agitating stirrer. (B) Present experiment without stirrer.
to a scheme of thermal design of gas-bubbling hydrate reactors for various hydrate-based technologies (e.g. natural gas storage, biogas treatment, water desalination, etc.). Some of the present experimental results are given in Tables 1–6.
Table 1 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.27 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C
(B) Fig. 11. Flow patterns in the crystallizers. (A) Present experiment: Eq. (4), (B) Mori and Mori [8]: vortical flow.
layers of hydrates by Mori and Mori [8]; one on the upper part of the crystallizer (at the water surface) and the other at the bottom of the crystallizer as shown in Fig. 13A. In the present work, only the upper layer formed and progressed in growth downward as shown in Fig. 13B. The model analysis of the multiphase heat transfer inside the column of the present work may be extended
Time (min)
TB (C)
H3a (m)
HGb (m)
0 3 6 9 18 21 24 27 30 33
18.0 16.5 15.0 13.9 12.0 11.0 10.3 9.7 9.2 7.8
0.400 0.420 0.435 0.447 0.448 0.432 0.410 0.386 0.362 0.337
0 0 0 0 0.037 0.053 0.061 0.075 0.080 0.082
a b
H3 = water level in column. HG = thickness of R12 hydrate layer.
650
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Table 2 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.34 cm, volume flow rate of R12 = 2 cm3/s, DTi = 5 C
Table 5 Experimental results of R12 gas hydrate: orifice diameter = 1.5 mm, number of drops = 7, initial drop diameter = 0.4 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C
Time (min)
TB (C)
H3a (m)
HGb (m)
Time (min)
TB (C)
H3a (m)
HGb (m)
0 3 6 9 12 15 18 21 24 27
18.0 16.1 14.4 13.0 11.8 10.0 9.7 8.6 7.7 6.8
0.400 0.436 0.458 0.474 0.451 0.429 0.402 0.367 0.336 0.302
0 0 0 0 0.048 0.063 0.081 0.090 0.098 0.107
0 5 10 15 20 24 27 30 33 36 39
18.0 16.3 15.0 13.8 12.8 12.0 11.4 10.6 10.0 9.6 9.3
0.400 0.417 0.430 0.441 0.450 0.447 0.435 0.418 0.400 0.382 0.363
0 0 0 0 0 0.024 0.039 0.050 0.062 0.071 0.073
a b
H3 = water level in column. HG = thickness of R12 hydrate layer.
a b
Table 3 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.22 cm, volume flow rate of R12 = 0.8 cm3/s, DTi = 5 C Time (min)
TB (C)
H3a
0 5 10 15 20 25 30 33 36 39 42 45 48 51
18.0 16.5 15.0 13.9 12.0 11.0 10.3 9.7 9.2 7.8 10.7 10.4 10.0 9.7
0.400 0.420 0.435 0.447 0.448 0.432 0.410 0.386 0.362 0.337 0.393 0.378 0.362 0.345
a b
(m)
HGb
(m)
0 0 0 0 0.037 0.053 0.061 0.075 0.080 0.082 0.044 0.051 0.052 0.054
Time (min)
TB (C)
H3a (m)
HGb (m)
0 3 6 9 12 15 18 21 24 27 30
18.0 16.6 15.4 14.1 12.5 11.9 10.5 9.3 8.3 7.8 7.0
0.400 0.428 0.444 0.458 0.471 0.456 0.435 0.413 0.387 0.362 0.335
0 0 0 0 0 0.050 0.065 0.072 0.078 0.081 0.083
a
H3 = water level in column. HG = thickness of R12 hydrate layer.
Table 6 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.3 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C, NaCl wt.% = 4 Time (min)
TB (C)
H3a (m)
HGb (m)
0 5 10 15 20 24 27 30 33 36 39
18.0 15.3 12.9 10.6 8.00 7.00 6.50 6.00 5.70 5.80 5.40
0.400 0.422 0.436 0.449 0.460 0.453 0.443 0.428 0.412 0.393 0.375
0 0 0 0 0 0.023 0.034 0.050 0.054 0.059 0.065
a b
H3 = water level in column. HG = thickness of R12 hydrate layer.
6. Conclusions
H3 = water level in column. HG = thickness of R12 hydrate layer.
Table 4 Experimental results of R12 gas hydrate: orifice diameter = 0.7 mm, number of drops = 36, initial drop diameter = 0.27 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C
b
H3 = water level in column. HG = thickness of R12 hydrate layer.
Experimental and theoretical investigations of two-component (R12 and water), three-phase (vapor, liquid and solid) in direct-contact in an unagitating column for the formation of gas hydrate has been carried out. The following are conclusions abstracted from the results of the present work. The growth rate of R12 hydrates was increasing with time and with the variations of the following parameters: (1) The decrease in the initial temperature difference between the continuous phase and R12 drops. (2) The decrease in the initial water level in the column. (3) The purity of the continuous phase. Saline solutions gave lower rates of growth. (4) The increase in the flow rate of R12 drops. (5) The decrease in the initial R12 drop diameter. Acknowledgements We are indebted to Professor Y.H. Mori of the University of Keio in Yokohama, Japan for encouraging us to
A.A. Kendoush et al. / Experimental Thermal and Fluid Science 30 (2006) 643–651
work in the field of gas hydrate and for his kind offer of his pioneer publications. Appendix A. Gas hydrate growth rate The rate of heat loss of the continuous phase (water) due to the evaporation and rise of R12 droplets is given as follows: q ¼ q3 C p3 uAðT B T 2i Þ
ðA:1Þ
Here A is the cross sectional area of the column, T2i is the initial temperature of R12 drop as it enters the column and u is the average velocity of the continuous phase in the test column. It is given by the following: Z rcr =R0 1 u¼ U 2pR dR ðA:2Þ 2 pðrcr =R0 Þ 0 The expression for U is given by Eq. (4). The heat of formation of the hydrate is given by the following: ðA:3Þ
q ¼ qh Z G Ahfgh
Equating Eqs. (A.1)–(A.3) yields the gas hydrate growth rate as given by Eq. (5) of the text. Appendix B. Physical properties of water and R12 at 15 C Property
Substance Value
Unit
Density of liquid Density of liquid Density of vapor Thermal conductivity Thermal conductivity Specific heat Specific heat Viscosity Viscosity Latent heat of ice Latent heat of evaporation Surface tension Surface tension Density with 4 wt.% NaCl Density with 8 wt.% NaCl Specific heat with 4 wt.% NaCl Specific heat with 8 wt.% NaCl
H 2O R12 R12 H 2O R12 H 2O R12 H 2O R12 H 2O R12 H 2O R12 H 2O
1000 1350 27 0.6 0.073 4184 950 0.00125 0.00037 2470 145 0.073 0.01 1028
kg/m3 kg/m3 kg/m3 W/m K W/m K J/kg K J/kg K kg/m s kg/m s kJ/kg kJ/kg N/m N/m kg/m3
H 2O
1057
kg/m3
H 2O
4000
J/kg K
H 2O
3800
J/kg K
651
References [1] B.B. Maini, P.R. Bishoni, Experimental investigation of hydrate formation behavior of natural gas bubbles in a simulated deep environment, Chem. Eng. Sci. 35 (1981) 183–189. [2] J.J. Carbajo, A direct-contact charged direct-contact discharged cool storage system using gas hydrate, ASHRAE Trans. 91 (1985) 258– 266. [3] M.P. Ternes, Characterization of refrigerant-12 gas hydrate formation for heat pump cool storage application, ASME paper 84-AES12, American Society of Mechanical Engineers, New York, 1984. [4] J.J. Gudmundsson, A.B. Brrehaug, Frozen hydrate for transport of natural gas, in: 2nd Int. Conf. on Natural Gas Hydrate, June 2–6, 1996, Toulouse, France. [5] V. Andersson, J.J. Gudmundsson, Flow experiments on concentrated hydrate slurries, SPE 56567, in: SPE Annual Conf. and Exhibition, Houston, October 3–6, 1999. [6] J.J. Gudmundsson, M. Parlktuna, O.I. Levik, V. Andersson, Laboratory for continuous production of natural gas hydrate, Ann. N.Y. Acad. Sci. 912 (2000) 851–858. [7] T. Takaoki, T. Iwasaki, Y. Katoh, T. Arai, K. Horiguchi, Use of hydrate pellets for transportation of natural gas—I. Advantage of pellet form of natural gas hydrate in sea transportation, in: Proc. of the 4th Int. Conf. on Gas Hydrates, Yokohama, May 19–23, 2002. [8] T. Mori, Y.H. Mori, Characterization of gas hydrate formation in direct contact cool storage process, Int. J. Refrig. 12 (1989) 259–265. [9] J.F. Walter, H.W. Blanch, Liquid circulation patterns and their effect on gas hold-up and axial mixing in bubble columns, Chem. Eng. Commun. 19 (1983) 243–262. [10] A.A. Kendoush, T.J. Mohammed, B.A. Abid, M.S. Hameed, Experimental investigation of the hydrodynamic interaction in bubbly two-phase flow, Chem. Eng. Process. 43 (2004) 23–33. [11] P.R. Turner, Guide to Numerical Analysis, Macmillan Education Ltd., New York, 1989. [12] A.A. Kendoush, Theory of convective drop evaporation in direct contact with an immiscible liquid, Desalination 169 (2004) 33–41. [13] N.A. Poirer, A.S. Mujumdar, Numerical solution to the Gratz problem: achieving accuracy in the entrance region, Int. Commun. Heat Mass Transfer 16 (1989) 205–214.
The growth rate of gas hydrate from refrigerant R12 Abdullah Abbas Kendoush a
a,*
, Khalid A. Joudi b, Najim Abid Jassim
a
Centre of Engineering Physics, Ministry of Sciences and Technology, P.O. Box 765, Baghdad, Iraq b Al-Nahrain University, Baghdad, Iraq
Received 9 November 2005; received in revised form 30 December 2005; accepted 15 January 2006
Abstract Experimental and theoretical investigations were presented dealing with three phase direct-contact heat transfer by evaporation of refrigerant drops in an immiscible liquid. Refrigerant R12 was used as the dispersed phase, while water and brine were the immiscible continuous phase. A numerical solution is presented to predict the formation rate of gas hydrates in test column. The solution provided an acceptable agreement when compared with experimental results. The gas hydrate growth rate increased with time. It increased with increasing dispersed phase flow rate. The presence of surface-active sodium chloride in water had a strong inhibiting effect on the gas hydrate formation rate. 2006 Elsevier Inc. All rights reserved. Keywords: Gas hydrate formation; R12 host molecules; Direct-contact heat transfer; Clathrate hydrate
1. Introduction Gas hydrates have been increasingly involved in the development of various energy and environment-related technologies in recent years. In addition to the well known problem of plugging of natural gas pipelines by hydrate formation, various hydrate-related scientific and technological problems such as, exploration and recovery of in situ hydrate as an energy resource, thermodynamics of hydrate-forming systems, kinetics of hydrate formation, mass and heat transfer during hydrate formation and dissociation, and utilization of hydrates in energy storage and transportation need to be investigated. Direct-contact heat transfer plays a major role in the formation of the gas hydrate. Gas hydrates are ice-like solids that form when a sufficient amount of water (host phase), and a hydrate former (guest phase) are present at the right combination of temperature and pressure. Hydrate formation is favored by low temperature and high
*
Corresponding author. Tel.: +964 79 0215 8251. E-mail address: [email protected] (A.A. Kendoush).
0894-1777/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.01.009
pressure. The utilization of gas hydrates for desalination offers great advantages as the formation of hydrate crystals consumes less power than the classical processes. To form an R12 hydrate crystal, one molecule of R12 combines with 15.6 molecules of H2O. The R12 single molecule would be enclosed in a cagelike crystalline water structure. Maini and Bishoni [1] studied experimentally the hydrate formation at constant pressure. They found that a bubble of natural gas in 3 C saline water formed a hydrate when the pressure was 4826 kPa, but when the pressure was 8963 kPa, the rate of formation was extremely fast causing the collapse of the injected bubble into large flakes of hydrates. Carbajo [2] performed experiments to produce R12 hydrates for cool storage purposes. He injected R12 in either liquid or vapor form into an agitating column to produce R12 hydrates. Ternes [3] described results of an experimental work with an open-loop R12 hydrate storage facility. He discussed in some detail the effectiveness of mechanical agitation and the addition of surfactants for the reduction of supercooling of fluid contents in a crystallizer. Ternes [3] stated that crusts of hydrates were formed at the phase
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Nomenclature Cp d D0 H0 h hfg k n Nu3 Pe3 Pr Re R0 r T TB T2i t uc u x
specific heat at constant pressure (J/kg K) equivalent diameter of the two-phase bubble (m) diameter of the column (m) initial water level in the column (m) instantaneous heat transfer coefficient (W/m2 K) latent heat (kJ/kg) thermal conductivity (W/m K) total number of R12 drops in column (–) Nusselt number (h3d/k) (–) Peclet number [ud/a] (–) Prandtl number [Cpl/k] (–) Reynolds number [qud/l] (–) radius of column (m) radial coordinate (m) temperature (K) continuous phase bulk temperature (K) dispersed phase inlet temperature (K) time (s) continuous phase velocity (m/s) average velocity of continuous phase (m/s) vaporization ratio within the drop
boundaries, while R12 and water both in liquid states and the mixtures of their vapors constituted three phases superposed on top of one another in the crystallizer and that the crusts acted as barriers separating otherwise neighboring phases, thus preventing further hydrate formation. In a series of papers, Gudmundsson and his colleagues [4–6] developed the technique of using natural gas hydrate (NGH) for storing and transporting natural gas as an alternative to the established technology of liquefied natural gas (LNG). NGH is produced in a high pressure columns operated at 50–70 bar and 2–10 C. Typically the natural gas-bubbling column are charged with water. Hydrate formation starts when a magnetic stirrer is operated for about 1 h. Takaoki et al. [7] described the processes of production, pelletization, transportation, storage and re-gasification of NGH. It can be concluded from the literature survey that there were no reported systematic and detailed heat transfer analyses of the process of using gas-bubbling technique for the formation of gas hydrates. In this paper, an experimental investigation was conducted to study the thermal effects of the formation rate of R12 hydrate in a glass column. A numerical solution predicted the experimental Z-growth rate of the hydrate in the column. The choice of R12 as a hydrate former was because of the relatively low system pressure required to be applied. The experimental glass system, necessary for visualizing the growth rate cannot withstand excessive pressures of gas hydrate formation needed for other types of gases.
z ZG
axial coordinate along column (m) gas hydrate growth rate (cm/s)
Greek letters a thermal diffusivity [k/qCp] (m2/s) DT temperature difference (K) l absolute viscosity (kg/m s) m kinematic viscosity (m2/s) q density (kg/m3) s dimensionless time (–) " volume of continuous phase (m3) Subscripts cr critical h hydrate w column wall 0 initial value [t = 0] 1 vapor R12 phase in two-phase bubble 2 liquid R12 phase in two-phase bubble 3 continuous phase (water)
2. Experimental apparatus The experimental system is shown schematically in Fig. 1. It consists of a test column (crystallizer), cold water
Fig. 1. Schematic of experimental system: X = rotameter, Y = refrigeration unit.
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supply system, dispersed phase supply system, and closedloop vapor compression refrigerator. The test column is illustrated schematically in Fig. 2. It consists of a cylindrical Pyrex glass column of 80 mm diameter and 1.20 m long, in which the test fluid, water was confined. A rectangular Perspex water jacket was made concentrically around the inner cylindrical column. The jacket served as a constant-temperature water bath and also contributed to minimizing the distortion of the images of the bubbles or drops inside the test column. A digital video camera (Sony CCD48X) with 30 frames/ s is used. The pictures are recorded on a rotary magnetic disk and projected on a screen. Thus the growth rate of the hydrate is monitored. Sixteen calibrated sheathed T-type thermocouples were distributed along the column in different positions to measure the temperature of the water axially and radially within the column. An auxiliary water cooling circuit is provided to cool the water in the test column at the start of experiments and to cool the water of the jacket surrounding the test column during the experimental tests as shown in Fig. 1. The experiments were conducted at a pressure of 4 bar and by varying the following conditions: dispersed phase flow rate of 0.8–2 cc/s, initial temperature difference between R12 and water from 3 to 8 K, water height in column (0.25–0.5 m), initial drop diameter of 2–4 mm, and brine concentration of 0–8 wt.%.
645
Fig. 3. Distributor orifice configurations. All dimensions are in millimeter.
The dispersed phase is injected into the test column from a Teflon manifold located at the bottom of the test column. The Teflon manifold consisted of a main and an interchangeable perforated plate or distributor. The diameter of the distributor is 60 mm and its thickness is 4 mm. Three different types of configurations are used for the arrangement of orifices as shown in Fig. 3. The number of orifices are 7, 19 and 36. In each configuration, three different orifice diameters of 0.7, 1 and 1.5 mm are employed. Bubble size, void fraction and bubble velocity were measured by the electroresistivity probes [10]. The probe utilizes the difference in electrical conductivity between the liquid and gas phases. The output from all of the probes are passed through an interface circuit to analyze the signals. The signals are monitored continuously by a personal computer. In the present experiment, the column contained the three phases of H2O (liquid), R12 (liquid), R12 hydrate (solid) and R12 (vapor). 3. Experimental procedure and observations Typical experiments are conducted as follows:
Fig. 2. Assembly drawing of test column (crystallizer).
1. Water was cooled in test column by the auxiliary cooling system to the desired temperature in the range of 10– 20 C. When water in the test column attained the desired temperature above the R12 saturation temperature of 12 C, the test column was filled with water to the desired level and the circulation stopped. 2. The refrigerant loop was evacuated from air by the use of a vacuum pump (not shown in Fig. 1) and R12 was supplied from the high pressure bomb to the loop till a sufficient volume of R12 in the liquid state was stored in the reservoir. 3. As the compressor began to work, the R12 was not added from the bomb to the loop. The needle valve
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was then adjusted to give the required flow and the required pressure of R12. Measurements of temperature and pressure in the test column, as well as the flow rate of R12 were immediately started. The R12 drops started to evaporate as they entered the test column due to its contact with water at higher temperature than its saturation temperature. Then the superheated R12 vapor left the test column. The evaporation was allowed to proceed and the R12 drops rose as two-phase bubbles, then as pure vapor bubbles and eventually part of it reacted with the water molecules to form gas hydrate. The other part of R12 vapor condensed and recirculated. Gas hydrate in the form of slurry accumulated at the top of the column, above the water surface as shown in Fig. 13. The hydrate layer advanced downward with time until the whole column becomes full of hydrate.
r z ; Z¼ dimensionless radial and R0 D0 vertical coordinates uz U¼ dimensionless axial velocity uc
R¼
Using the dimensionless groups: Pe3 ¼
uc D0 a3
Rec ¼
uc D0 ; m3
Ec ¼
u2c C p3 ðT w T 2 Þ
and
l3 C p3 ; k3 nh3 d 2 M2 ¼ k3L Pr ¼
The governing energy equation in dimensionless form becomes: oh oh 1 þU ¼ os oZ Pe3
(
2 ) 4 o oh o2 h oU 2 R þ 2 M h þ 4EcPr R oR oR oR oZ
ð2Þ
4. Mathematical model 4.1. Formulations and assumptions The water flow in the column is induced by the rise of R12 drops/bubbles. The column height is L and its radius is R0. Thermal energy needed for the evaporation of R12 drops are extracted from the bulk of the flowing water. Once R12 bubbles are formed, they become guest molecules in the hydrate crystals. The following assumptions were adopted:
where h is the dependent variable R, Z and s are independent variables. Eq. (2) is subject to the following initial condition and boundary conditions: The initial condition is L h ¼ 1:0 s ¼ 0; 0 6 R 6 1; 0 6 Z 6 ð3aÞ D0 The boundary conditions are • Cylinder wall condition:
(1) The heat flow across the hydrate layer (Fig. 13) and the water–R12 solution are two dimensional (r, z) in the cylindrical coordinates. (2) The physical properties (Appendix B) are constant throughout each of the hydrate and water–R12 solution irrespective of the temperature distribution inside them. The governing energy equation for the water–R12 solution is the following: oT oT 1 o oT o2 T þ uz ¼ a3 r þ 2 ot oz r or or oz 2 nh3 A2 l3 ouZ ðT T 2 Þ þ ð1Þ q3 C p3 8 q3 C p3 or The first term on the right side of this equation is the heat conduction contribution, the second term represents the heat sink and the third term is the viscous dissipation. We introduce the following dimensionless quantities: h ¼ ðT T 2 Þ=ðT w T 2 Þ dimensionless temperature uc t s¼ dimensionless time D0 Here uc is the velocity of the continuous phase at the center of the column.
h¼1
for R ¼ 0;
06Z6
L D0
ð3bÞ
• Cylinder center line condition: oh ¼0 oR
for R ¼ 0;
06Z6
L D0
ð3cÞ
Here U of Eq. (2) is the axial velocity profile of a modular flow in a bubble column. It was developed by Walter and Blanch [9] as follows: U ¼ 1 6R2 þ 5R3
ð4Þ
This velocity distribution is shown schematically in Fig. 11A. The original equation of Walter and Blanch [9] has a parameter N in it. It was considered equal to unity here. Gas hydrate growth rate can be calculated by applying the energy balance through out the system, therefore the gas hydrate growth rate (Z-growth) is q3 uC p3 ðT B T 2i Þ ZG ¼ ð5Þ qh hfgh Here T2i is the temperature of R12 drops at inlet to the test column and hfgh is the latent heat of gas hydrate. Appendix A gives the derivation of this equation. The energy equation was solved numerically by applying the explicit finite difference method. The derivatives in this
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, DT21 is the temperature difference bewhere f ðxÞ ¼ 0:5þx 1x tween the R12 drop2 and the bubble1 inside it and DT32 is the temperature difference between the continuous liquid3 (water) and R12 drops2. Eq. (6) was derived for a single two-phase bubble, so it was multiplied by n number of bubbles in the column. 4.2. Numerical solution The present solution resembles to a certain extent the Gratz–Nusselt problem of finding the temperature profile and heat convection rate in a fully developed laminar flow inside circular pipes. This type of solution allows the temperature profile to be calculated from substituting the parabolic velocity profile into the energy equation [13]. The numerical solution of Eq. (2) is obtained by establishing a finite number of rectangular grid points having coordinates: R = iDR and Z = jDZ at discrete time sn where i, j and n are integer numbers of grid points in the R, Z and s dimensions. The explicit finite difference method was employed for the present numerical solution. The stability of the numerical solution imposed the following restrictions on the size of the time step Ds " #1 4 2 2 Ds 6 þ þM ð7Þ 2 2 ðDRÞ ðDZÞ The outline of the present model is to calculate the bulk temperature distribution numerically from the following: Z rcr =R0 Z rcr =R0 hB ¼ hUR dR UR dR ð8Þ
0.09 ΔT=3 k ΔT=5 k ΔT=8 k
0.08
0.07
0.06
0.05
0.04
0.03 12
5. Results and discussion The inception of gas hydrate occurred when the temperature and pressure in the crystallizer column reached the conditions of the triple point (that is, 12 C and 4 bar). The hydrate layer continued to be accumulated upwards while the water level continued to decrease downward. In studying the effect of the initial temperature difference and water column height on gas hydrate growth rate, a sig-
20
24
28
32
36
40
44
Fig. 4. Variation of gas hydrate growth rate with time at different initial temperature difference. H0 = 0.4 m, flow rate of R12 = 1.2 cc/s.
0.095
0
where rcr is the critical radius at which uz = 0, i.e., the radius bordering the upward-flow region and the outer downward-flow region. According to Eq. (4), rcr/R0 0.56. The bulk temperature was defined in the core region of the flow (0 6 R 6 rcr/R0). Finally applying Eq. (5) to get the growth rate of the hydrate.
16
Time (min)
Gas hydrate layer thickness (m)
0
nificant dependence was found. At lower temperature difference or column height results in a rapid hydrate formation but after the gas hydrate was started the growth rate increases with increasing the temperature driving force, which is controlling the crystal growth process as shown in Figs. 4 and 5. Fig. 5 shows that at a constant flow rate of R12 drops, the low water level would have a high number of R12 molecules per unit volume. These molecules are acting as guest species for hydrate formation, whereas the high water level would contain smaller number of R12 molecules per unit volume, thus lower growth rate is encountered here. The relation between gas hydrate growth rate with the presence of sodium chloride in water is shown in Fig. 6. It was seen that the existence of sodium chloride has a strong inhibiting effect on gas hydrate formation growth rate. This result has an important bearing on the process
Gas hydrate layer thickness (m)
equation could be replaced by the finite difference approximations [11]. The instantaneous heat transfer coefficient h3 of the sink term of Eq. (1) was calculated by using the derived equation of Kendoush [12] as follows: 1=2 DT 21 k 2 q2 Cp2 Nu3 ¼ 0:921 Pe3 xf ðxÞ ð6Þ DT 32 k 3 q3 C p 3
647
0.085
Ho =0.25 m Ho =0.4 m Ho =0.5 m
0.075 0.065 0.055 0.045 0.035 0.025 12
18
24 30 Time (min)
36
42
Fig. 5. Change of hydrate growth rate with time at different initial column height. Flow rate of R12 = 1.2 cc/s, DT32 = 5 K.
648
A.A. Kendoush et al. / Experimental Thermal and Fluid Science 30 (2006) 643–651 0.090
0.09
Gas hydrate layer thickness (m)
0.08
Gas hydrate layer thickness (m)
Distilled water Distilled water with 4 wt% NaCl Distilled water with 8 wt% NaCl
0.07 0.06 0.05 0.04 0.03 0.02
0.075
do =0.2 cm do =0.27 cm do =0.4 cm
0.060
0.045
0.030
0.015 12
18
0.00 15
24
30
36
42
Time (min)
0.01
20
25
30
35
40
45
50
55
Fig. 8. Change of hydrate growth rate with time at different initial R12 drop diameter. H0 = 40 cm, flow rate of R12 = 1.2 cc/s.
Time (min) Fig. 6. Variation of gas hydrate growth rate with time at different continuous phase solutions. H0 = 40 cm, flow rate of R12 = 1.2 cc/s.
Gas hydrate layer thickness (m)
Gas hydrate layer thickness (m)
0.13
Vd = 2 cc/s Vd = 1.2 cc/s Vd = 0.8 cc/s
0.11
0.11
0.09
0.07
0.05
0.10
Present Experimental Work Present Theoretical Work
0.09 0.08 0.07 0.06 0.05 0.04
0.03
0.03
16 0.01 5
15
25
35
45
55
Time (min) Fig. 7. Change of hydrate growth rate with time at different R12 flow rates. H0 = 40 cm, DT32 = 5 K.
of the utilization of gas hydrate for the desalination of saline water. Fig. 7 shows the effect of the R12 flow rate on the rate of hydrate growth at a constant water level in the column and a constant subcooling. The same argument, that was discussed before, of the availability of R12 molecules per unit volume, is applied here and is responsible for the increase of the hydrate growth rate. Fig. 8 shows a higher growth rate for lower droplet diameter of R12. Physically, the smaller the diameter of the droplet, the lower the velocity of its rise. This slow motion allows ample time for the reaction rate to take place for the formation of the R12 hydrate. Fig. 9 shows a comparison between experimental and theoretical values of gas hydrate growth rate in this work.
20
24 28 Time (min)
32
36
Fig. 9. Comparison between the experimental data and the numerical solution.
It clear from this figure that the predicted value of gas hydrate growth rate, during the middle of experiment is in the better agreement with the experimental results than those at the early or later stages of the experiments. Fig. 10 shows a comparison between the experimental data of Mori and Mori [8] and the present work regarding the amount of supercooling achieved by both experiments. Clearly higher crystallizer bulk temperatures were obtained by Mori and Mori [8] due to the use of a mechanical stirrer in their crystallizer. Vortical flow is generated by these stirrers as shown in Fig. 11. Parabolic temperature distributions were obtained in the present work as shown in Fig. 12. This temperature distribution was changed dramatically in the work of Mori and Mori [8] due to the vortical flow caused by the mechanical stirrers. This difference may explain the formation of two
A.A. Kendoush et al. / Experimental Thermal and Fluid Science 30 (2006) 643–651
649
Fig. 12. The temperature distribution in the crystallizer of the present experiment at z = 5D.
Fig. 10. Comparison between the present experiment (–s–) and that of Mori and Mori [8] (—).
(A)
Fig. 13. Schematic illustration of R12 drops and their hydrate formation in the crystallizers of the following: (A) Mori and Mori [8]: column with an agitating stirrer. (B) Present experiment without stirrer.
to a scheme of thermal design of gas-bubbling hydrate reactors for various hydrate-based technologies (e.g. natural gas storage, biogas treatment, water desalination, etc.). Some of the present experimental results are given in Tables 1–6.
Table 1 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.27 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C
(B) Fig. 11. Flow patterns in the crystallizers. (A) Present experiment: Eq. (4), (B) Mori and Mori [8]: vortical flow.
layers of hydrates by Mori and Mori [8]; one on the upper part of the crystallizer (at the water surface) and the other at the bottom of the crystallizer as shown in Fig. 13A. In the present work, only the upper layer formed and progressed in growth downward as shown in Fig. 13B. The model analysis of the multiphase heat transfer inside the column of the present work may be extended
Time (min)
TB (C)
H3a (m)
HGb (m)
0 3 6 9 18 21 24 27 30 33
18.0 16.5 15.0 13.9 12.0 11.0 10.3 9.7 9.2 7.8
0.400 0.420 0.435 0.447 0.448 0.432 0.410 0.386 0.362 0.337
0 0 0 0 0.037 0.053 0.061 0.075 0.080 0.082
a b
H3 = water level in column. HG = thickness of R12 hydrate layer.
650
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Table 2 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.34 cm, volume flow rate of R12 = 2 cm3/s, DTi = 5 C
Table 5 Experimental results of R12 gas hydrate: orifice diameter = 1.5 mm, number of drops = 7, initial drop diameter = 0.4 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C
Time (min)
TB (C)
H3a (m)
HGb (m)
Time (min)
TB (C)
H3a (m)
HGb (m)
0 3 6 9 12 15 18 21 24 27
18.0 16.1 14.4 13.0 11.8 10.0 9.7 8.6 7.7 6.8
0.400 0.436 0.458 0.474 0.451 0.429 0.402 0.367 0.336 0.302
0 0 0 0 0.048 0.063 0.081 0.090 0.098 0.107
0 5 10 15 20 24 27 30 33 36 39
18.0 16.3 15.0 13.8 12.8 12.0 11.4 10.6 10.0 9.6 9.3
0.400 0.417 0.430 0.441 0.450 0.447 0.435 0.418 0.400 0.382 0.363
0 0 0 0 0 0.024 0.039 0.050 0.062 0.071 0.073
a b
H3 = water level in column. HG = thickness of R12 hydrate layer.
a b
Table 3 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.22 cm, volume flow rate of R12 = 0.8 cm3/s, DTi = 5 C Time (min)
TB (C)
H3a
0 5 10 15 20 25 30 33 36 39 42 45 48 51
18.0 16.5 15.0 13.9 12.0 11.0 10.3 9.7 9.2 7.8 10.7 10.4 10.0 9.7
0.400 0.420 0.435 0.447 0.448 0.432 0.410 0.386 0.362 0.337 0.393 0.378 0.362 0.345
a b
(m)
HGb
(m)
0 0 0 0 0.037 0.053 0.061 0.075 0.080 0.082 0.044 0.051 0.052 0.054
Time (min)
TB (C)
H3a (m)
HGb (m)
0 3 6 9 12 15 18 21 24 27 30
18.0 16.6 15.4 14.1 12.5 11.9 10.5 9.3 8.3 7.8 7.0
0.400 0.428 0.444 0.458 0.471 0.456 0.435 0.413 0.387 0.362 0.335
0 0 0 0 0 0.050 0.065 0.072 0.078 0.081 0.083
a
H3 = water level in column. HG = thickness of R12 hydrate layer.
Table 6 Experimental results of R12 gas hydrate: orifice diameter = 1.0 mm, number of drops = 19, initial drop diameter = 0.3 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C, NaCl wt.% = 4 Time (min)
TB (C)
H3a (m)
HGb (m)
0 5 10 15 20 24 27 30 33 36 39
18.0 15.3 12.9 10.6 8.00 7.00 6.50 6.00 5.70 5.80 5.40
0.400 0.422 0.436 0.449 0.460 0.453 0.443 0.428 0.412 0.393 0.375
0 0 0 0 0 0.023 0.034 0.050 0.054 0.059 0.065
a b
H3 = water level in column. HG = thickness of R12 hydrate layer.
6. Conclusions
H3 = water level in column. HG = thickness of R12 hydrate layer.
Table 4 Experimental results of R12 gas hydrate: orifice diameter = 0.7 mm, number of drops = 36, initial drop diameter = 0.27 cm, volume flow rate of R12 = 1.2 cm3/s, DTi = 5 C
b
H3 = water level in column. HG = thickness of R12 hydrate layer.
Experimental and theoretical investigations of two-component (R12 and water), three-phase (vapor, liquid and solid) in direct-contact in an unagitating column for the formation of gas hydrate has been carried out. The following are conclusions abstracted from the results of the present work. The growth rate of R12 hydrates was increasing with time and with the variations of the following parameters: (1) The decrease in the initial temperature difference between the continuous phase and R12 drops. (2) The decrease in the initial water level in the column. (3) The purity of the continuous phase. Saline solutions gave lower rates of growth. (4) The increase in the flow rate of R12 drops. (5) The decrease in the initial R12 drop diameter. Acknowledgements We are indebted to Professor Y.H. Mori of the University of Keio in Yokohama, Japan for encouraging us to
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work in the field of gas hydrate and for his kind offer of his pioneer publications. Appendix A. Gas hydrate growth rate The rate of heat loss of the continuous phase (water) due to the evaporation and rise of R12 droplets is given as follows: q ¼ q3 C p3 uAðT B T 2i Þ
ðA:1Þ
Here A is the cross sectional area of the column, T2i is the initial temperature of R12 drop as it enters the column and u is the average velocity of the continuous phase in the test column. It is given by the following: Z rcr =R0 1 u¼ U 2pR dR ðA:2Þ 2 pðrcr =R0 Þ 0 The expression for U is given by Eq. (4). The heat of formation of the hydrate is given by the following: ðA:3Þ
q ¼ qh Z G Ahfgh
Equating Eqs. (A.1)–(A.3) yields the gas hydrate growth rate as given by Eq. (5) of the text. Appendix B. Physical properties of water and R12 at 15 C Property
Substance Value
Unit
Density of liquid Density of liquid Density of vapor Thermal conductivity Thermal conductivity Specific heat Specific heat Viscosity Viscosity Latent heat of ice Latent heat of evaporation Surface tension Surface tension Density with 4 wt.% NaCl Density with 8 wt.% NaCl Specific heat with 4 wt.% NaCl Specific heat with 8 wt.% NaCl
H 2O R12 R12 H 2O R12 H 2O R12 H 2O R12 H 2O R12 H 2O R12 H 2O
1000 1350 27 0.6 0.073 4184 950 0.00125 0.00037 2470 145 0.073 0.01 1028
kg/m3 kg/m3 kg/m3 W/m K W/m K J/kg K J/kg K kg/m s kg/m s kJ/kg kJ/kg N/m N/m kg/m3
H 2O
1057
kg/m3
H 2O
4000
J/kg K
H 2O
3800
J/kg K
651
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