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Pumping characteristics of a large-scale gas-lift system
Experimental Thermal and Fluid Science 28 (2004) 479–488 www.elsevier.com/locate/etfs
Pumping characteristics of a large-scale gas-lift system T. Saito
a,*
, T. Kajishima b, K. Tsuchiya
c
a
c
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, Shizuoka 432-8561, Japan b Department of Mechanical Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Miyakodani, Tatara, Kyotanabe, Kyoto 610-0321, Japan
Abstract In this study the hydrodynamics of a gas-lift system for CO2 sequestration at deep sea (so-called ‘‘GLAD System: Gas Lift Advanced Dissolution System’’) are investigated. Experimental results are presented for both laboratory and pilot scale gas-lift pumps, ranging from 47 to 151 mm in diameter and 7.7 to 196.6 m in height. It was found that for each pump geometry a maximum liquid flowrate was achieved for the range of gas injection rates studied. Moreover, the liquid-phase hold-up was adequately modeled based on a gas-phase Froude number and applying 1-D Drift-Flux analysis. The axial pressure distribution for both scale systems exhibited similar properties when normalized with respect to overall pipe length and outlet absolute pressure. A simple hydrodynamic numerical model was found to adequately predict the induced liquid flowrate for a given gas injection rate. Closer agreement is expected when frictional losses for non-smooth pipe surface are taken into account as well as dissolution of gas from the rising bubbles. Further work in this area is currently in progress. Ó 2003 Elsevier Inc. All rights reserved. Keywords: CO2 sequestration; Gas Lift Advanced Dissolution System; Gas-lift pumping; Two phase flow
1. Introduction Recently, global environmental problems, such as global warming, acid rain, forest destruction and so on, are getting more and more obvious. Consequently, all nations have been discussing a cutback in the discharge amount of CO2 for the purpose of mitigating global warming [1]. Humankind faces an enormous task to find effective solutions to the problem. The inherent difficulties of the problem stem from the fact that the total amount of CO2 emitted from human activities is just enormous (23 GtC/year) [2], and is directly related to the consumption of fossil fuels used to support our daily lifestyles [3]. Although changing our lifestyle and saving energy are essential, and the most effective way to reduce the CO2 emission, they are insufficient for completely solving the global warming problem. Isolation of CO2 from the atmosphere will still be needed to mitigate the expected peak of CO2 concentration in the atmosphere in the near future. Ocean sequestration of CO2 is a hopeful option [4] because the CO2 -absorption capacity *
Corresponding author. Tel./fax: +81-53-478-1601. E-mail address: [email protected] (T. Saito).
0894-1777/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2003.07.005
of the ocean is huge [5], and is capable of isolating CO2 for more than several hundred years [6]. A method of ocean sequestration necessitates isolating a huge amount of CO2 from the atmosphere for long term (several hundred or thousand years) with low cost, low energy consumption and a low secondary-environmental impact. To realize these difficult demands simultaneously, we have developed a gas-lift system for CO2 sequestration in seawater at depths on the order of 1000 m. The system is a bundle of inverse-J pipelines set in the ocean of 200–3000 m depth, as illustrated in Fig. 1 [7–9], the so-called GLAD (Gas Lift Advanced Dissolution) System. The CO2 -containing gas is pumped using a compressor (3) and transported through an underwater gas pipeline (4). The gas is injected into a riser (5) at a depth between 200 and 400 m. Gas-lift effect will occur in the riser, while CO2 gas inside the bubbles dissolves into the liquid phase (seawater). The resulting CO2 solution is forced to flow into a downcomer (6) and transported through a drainpipe (8) to be released from the bottom of the drainpipe. The successful operation of the system relies on the gas-lift pumping capability of the riser as well as reliable dissolution of CO2 gas into the liquid phase. So far we
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Nomenclature A a b C0 D Fl Frg fl G g J L0 L1 L2 Pz p pa pout Q q R Re
cross-sectional area of a pipe [m] factor [–] index number [–] qffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =ql [–] pipe diameter [m] average liquid holdup [–] gas-phase Froude number [–] liquid holdup [–] momentum of mixture ¼ aqg vg þ ð1 aÞql vl [kg/m2 s] gravity acceleration [m/s2 ] superficial velocity [m/s] pipe length between an inlet and a gas injection point [m] pipe length between a gas injection point and the water surface [m] pipe length between a gas injection point and an outlet [m] dimensionless pressure [–] static pressure [MPa] or [Pa] atmospheric pressure [MPa] or [Pa] external pressure [MPa] or [Pa] volumetric flow rate [m3 /min] or [m3 /s] volumetric flow rate at z [m3 /s] gas constant [J/(kg K)] Reynolds number [–]
T t U V Vg2 v Z z a C k l n q r s
temperature [K] time [s] drift velocity [m/s] velocity [m/s] pffiffiffiffiffiffi 1:2½Jl þ Jg ðzÞ þ 0:35 or pffiffiffiffiffiffigD 1:2½Jl þ Jg þ 0:35 gD [m/s] velocity [m/s] normalized length elevation [–] vertical distance from a gas injection point [m] void fraction [–] gas injection rate per unit volume the gas– liquid mixture [kg/m3 s] friction factor [–] viscosity [Pa s] loss factor at an inlet [–] density [kg/m3 ] surface tension of liquid [N/m] wall-friction stress of the liquid phase [Pa]
Subscripts 1 inlet 2 gas injection point 3 outlet g gas phase l liquid phase m mixture
have studied extensively the mass transfer between bubble swarms and the liquid phase [10], and turbulence structure of bubbly flows in a large-diameter pipe [11]. Those characteristics are essential to fully understand
the dissolution process of CO2 gas in the GLAD system. For its optimal design and operation, an understanding of overall pumping characteristics of the system is also needed since the proposed system will be of a massive
(5) Gas including CO2
(6)
Gas including CO2 (3) (2)
Ambient seawater
CO2-rich seawater
1000 – 3000m
(7) 200 – 400m
(4) (6)
(5) Continental shelf
(8) Continental slope
(1) Fired power plant, (2) CO2 separation/capture system, (3) Compressor, (4) Underwater gas pipeline, (5) Riser of GLAD, (6) Downcomer of GLAD, (7) Float, (8) Drainpipe Fig. 1. Conceptual diagram of GLAD System.
(1)
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
large-scale (of 200-m height) setup is shown in Fig. 2. A shaft (1) of 1.5 m in diameter and 200 m in depth is placed under the ground and filled with tap water. A gas-lift pipe (2), made of steel, 151 mm in diameter and 212.6 m in total height, is connected to a gas–water separator (9) via a smooth bend. Compressed air (temperature of 30–35 °C), supplied from a compressor (3), is controlled with a mass flow controller (5) and injected into the gas-lift pipe at a depth of 71, 100, 131 or 184 m through an annular-type gas injector. The water level in the shaft kept constant using a water-supply tank (6) and pump (7). The flow rate of lifted water (tap water; temperature of 20–23 °C) is measured with an electromagnetic flow meter (8), being registered as the superficial liquid velocity. The gas–water mixture is separated into each phase in the separator (9) with the gas being discharged into the atmosphere while the liquid is returned to the shaft through a swing pipe (10) and a return pipe (11). A measure tank (12) and load cells (13) are used to weigh the mass of the discharged water. The pressure difference in the gas-lift pump was measured via a strain-gauge type differential pressure transducer (14); where the distance between the pressure taps at the measured section was 4 m. The static pressure inside the gas-lift pipe was measured via a strain-gauge type pressure transducer (15) at several depths. A check of the sensitivity of the pressure tapping measurements (locations shown in Fig. 3) was obtained by recording the single (liquid) phase pressure drop at various flow rates to determine the Moody friction
scale, where the dissolution section is of the order of 200-m height. Few papers, however, have been published regarding this kind of large-scale gas-lift pump [12,13]. To obtain the necessary data on large-scale gaslift pump, we have systematically performed a wide range of experiments using pipes of 46.7–151 mm in diameter and 7.7–196.6 m in height. In this paper the characteristics of a gas-lift pump are modeled using a Froude number represented by the length of the gas-lift pipe, the superficial velocity of the gas phase, and the average void fraction in the pipe. The lifting characteristics of water via a gas-lift pump are investigated experimentally for a wide range of geometries and experimental conditions. In particular, the flow pattern near the outlet for both large- and laboratory-scale measurements is examined based on a waveform analysis of differential pressure. Comparison is also made between the axial pressure profiles for the two systems. Finally, a computational method for analyzing the pumping characteristics is discussed and the numerical results are compared with experimental measurements.
2. Experimental 2.1. Large-scale apparatus The study involves both large-scale and laboratoryscale experimental setups. A schematic diagram of the
(9) (5)
(3)
(14) (11)
(7) (6)
71m
100m
(12) (13)
(15) (1)
200m
184m
131m
(2)
(10)
12.6m
(4)
481
(8)
(1) Shaft, (2) Gas-lift pipe, (3) Compressor, (4) Cooling tower, (5) Mass flow controller, (6) Water supply tank, (7) Pump, (8) Electromagnetic flow meter, (9) Gas-water separator, (10) Swing pipe, (11) Return pipe, (12) Measure tank, (13) Load cell, (14) Differential pressure transducer, (15) Pressure transducer
Fig. 2. Schematic diagram of 200-m gas-lift pump.
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
Outlet
Pressure gauge 5 Air injection: 131m
190.1 m
Air injection: 100m
200 m
212.6 m
Pressure gauge 4
166.5 m
Air injection: 71m
133.5 m
Pressure gauge 3
111.5 m
Pressure gauge 2
78.7 m
Water level
45.7 m
Differential pressure gauge Pressure gauge 1 3.0 m 23.7 m
482
Pressure gauge 6
Pressure gauge 7 Air injection: 184m
Electromagnetic flow meter
Inlet: 200m Fig. 3. Location of static and differential pressure taps.
4 e /D = 0.00042
λ [–]
3
2
10-2
4
6
8 105 Re [–]
2
4
6
Fig. 4. Relationship between friction factor and the Reynolds number. ( ) Friction factor actually measured in water flow; (––) calculated from Moody’s diagram. Relative roughness of pipe wall e=D ¼ 0:00042.
factor [14]. The comparison of the measured values with the calculated (reported) values, in terms of the friction factor vs. the Reynolds number relationship, is shown in Fig. 4 which indicates a good agreement.
a control valve (10), it was injected into a selected gaslift pipe through an annular-type gas injector (3). The flow rate of lifted water (tap water; temperature of 21– 23 °C) was measured via an electromagnetic flow meter (5). The lifted water was discharged from the gas-lift pipe into the gas–liquid separator (2) via a smooth pipe bend. The water level in the head tank (4) is automatically controlled in each run to be constant using the water supply system (13–16). The pressure difference in the gas-lift pump was measured via a strain-gauge type differential pressure transducer (11); where the distance between the pressure taps at the measuring section is 1 m. The static pressure inside the gas-lift pipe is measured via strain-gauge type pressure transducers (12) at several heights. A validity check similar to that for the large-scale apparatus is carried out.
3. Theoretical modeling 2.2. Laboratory-scale apparatus Fig. 5 shows a schematic diagram of the laboratoryscale experimental apparatus. It consists of three acrylic gas-lift pipes (1) of diameters 130, 75.7 and 46.7 mm, with corresponding heights of 11.8, 11.6 and 11.6 m, respectively. For the 46.7-mm pipe, different gas injector (3) positions at 0, 1.7 and 3.9 m could be selected. Gas (air) was supplied from an oil-free air compressor (6). After carefully controlling the mass flow rate of the air (temperature of 31–34 °C) via a mass flow meter (8) and
We will consider the momentum balance between the bottom and top of a gas-lift pump as shown in Fig. 6. Given that z is the vertical distance from the gas injector, L0 the pipe length between the inlet and the gas injector, L1 the length between the gas injector and the surface of the water in the shaft or the vertical water tank, L2 the length between the gas injector and the outlet, L3 the total length of the gas-lift pipe, and D the inner diameter of the gas-lift pipe, the flowing equation for the momentum balance is obtained:
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
483
(2) (12) (11)
(4)
(1)
(1)
(1)
(3)
(3) (16)
(10) (9) (8)
(3) (3)
(15) (13)
(5)
(14)
(7)
(3) (5)
(5)
(6)
(1) Gas-lift pipes, (2) Air-water separator, (3) Gas injectors, (4) Head tank, (5) Electromagnetic flow meters, (6) Compressor, (7) Cooling tower, (8) Gas Mass flow meters, (9) Thermocouple, (10) Automatic control valve, (11) Differential pressure transducer, (12) Pressure transducers, (13) Water tank, (14) Pump, (15) Electromagnetic flow meter, (16) Automatic control valve
Fig. 5. Schematic diagram of laboratory-scale gas-lift pump.
where A is the cross-sectional area of the gas-lift pipe, g the gravitational acceleration, V the velocity of a given phase, a and b are the factor and index number, respectively, k the friction factor of the pipe wall, q the density, n the loss factor at the inlet, subscripts g and l denote the gas and liquid phases, respectively, subscripts 1 and 3 denote the inlet and outlet of the gas-lift pipe, respectively, and fl ðzÞ is the hold-up of liquid at z or fl ðzÞ ¼ 1 aðzÞ with aðzÞ being void fraction at z. The second term on the right-hand side of Eq. (1) signifies a loss at the inlet and is negligible because it is usually very small. The integrals in the fourth and fifth terms in Eq. (1) can be expressed as Z L2 fl ðzÞ dz ¼ L2 Fl ; ð2Þ
(C) Surface of the water
L2 L3
L1
z (B)
0
L0
Z
(A)
0
b
a½fl ðzÞ dz ¼ LaFlb ;
ð3Þ
0
Fig. 6. Gas-lift pump model. (A) Inlet, (B) air injection and (C) outlet.
q AV 2 L0 ql AVl12 ql AVl1 ðVl3 Vl1 Þ ¼ L1 ql gA n l l1 k 2 D 2 Z L2 1 Vl12 ql gA fl ðzÞ dz k D 2 0 Z L2 a½fl ðzÞb dz;
L2
where Fl represents the average liquid hold-up in the section between the gas injector and the outlet. From Eqs. (2) and (3), and denoting Vl1 ¼ Jl , Eq. (1) can be rearranged to give Jl Jg L1 L0 Jl2 L2 Jl2 k 2 pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi ¼ Fl k aF b ; L2 2gD D 2gL2 l 2gL2 2gL2 L2 ð4Þ
ð1Þ
where J is the superficial velocity of each phase. From Eq. (4), the pumping performance of a gas-lift pump is
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T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
found to be expressed in terms of the average hold-up (or void fraction) in the pump, three kinds of Froude number and the dimensionless numbers representing pump size. In summary, the pumping performance of a gas-lift pump depends on the average gas holdup in the gas-lift pipe and the Froude number characterized by the superficial velocity of the gas phase and the length of the gas-lift pipe. On this basis it is assumed that a onedimensional numerical simulation can be used to analyze the pumping performance of a gas-lift pump.
4. Numerical simulation Based on the above theoretical analysis the gas–water two-phase flow in the vertical pipe section in the GLAD system can be simulated one-dimensionally. Assuming that the density of the liquid phase ql and the temperature T are constant, the conservation laws of mass and momentum can be considered using a drift-flux model. The mass conservation of the gas phase is expressed as
C0 ¼ 1:2 0:2
qffiffiffiffiffiffiffiffiffiffiffi qg =ql ;
8 1=4 > g < 1:41 rg ql q 2 ql Ug ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > : 0:35 gD ql qg ql
ð11Þ a 6 0:25
ðbubbly flowÞ
a P 0:3
ðslug flowÞ
; ð12Þ
where r is the surface tension of liquid. In the present computation, the drift velocity Ug is linearly interpolated with a in the range 0:25 < a < 0:30 which marks the transition from bubbly to slug flow. The wall friction is estimated from the model [17]: sw ¼
kqJl2 8ð1 aÞ1:75
ð13Þ
;
where 64 Re1 l k¼ 0:3164 Re0:25 l
Rl < 2300 ; Rl < 2300
ð14Þ
where a is the void fraction, v the velocity, and Cg the gas injection rate per unit volume of the gas–liquid mixture. By defining the density and momentum of the mixture by qm ¼ aqg þ ð1 aÞql and G ¼ aqg vg þ ð1 aÞql vl , respectively, the conservation of mass and momentum of the mixture can be represented by the following basic equations:
where Rel is the Reynolds number, Rel ¼ Dql Jl =ll , with ll being the viscosity of liquid. The finite difference method has been applied to discretize the basic equations. Specifically, the non-linear (convection) terms in the conservation laws are discretized based on the upstream finite difference method [18,19]. The implicit time marching scheme for the density and pressure was employed to deal with the high compressibility of the gas phase [20]. The formal accuracy is 4th-order in space and 1st-order in time.
oðqm Þ oG þ ¼ Cg ; ot oz
ð6Þ 5. Results and discussion
oG oðaqg v2g Þ o½ð1 aÞql v2l op 4sw þ ¼ qg þ ; ot oz oz oz D
ð7Þ
oðaqg Þ oðaqg vg Þ þ ¼ Cg ; ot oz
ð5Þ
5.1. Effect of gas injection rate on liquid pumping rate
where p represents the static pressure; sw the wall-friction stress of the liquid phase. The third basic equation is the gas equation (for an ideal gas): p ; ð8Þ qg ¼ RT where R is the gas constant. It is noted that four parametric variables q, G (or the velocity of the mixture vm ¼ G=qm ), p and a are involved in the basic equations. A drift-flux model is employed to close the above set of basic equations, Eqs. (5)–(8), where vg , vl and sw are to be expressed in terms of vm and a. Consequently, the velocity components of each phase are given as:
The volumetric liquid (water) flow rate, Qw , vs. the volumetric gas injection rate, Qg , is plotted in Fig. 7 for different pipe diameters, D, pipe lengths, L2 and submergence ratios, L1 =L2 . It can be seen that for each experimental geometry there is a maximum in the liquid pumping rate for the given range of gas injection rates. It is also found that Qw or its maximum value increases with D, and that Qw tends to increase with L2 as well when Qg and D are kept constant. From the theory of an air-lift pump by Nicklin [21], the liquid hold-up at z, fl ðzÞ, can be expressed by the following equations:
vg ¼ C0 Jm þ Ug ;
fl ðzÞ ¼ 1 Jg ðzÞ=Vg2 ðzÞ;
vl ¼
ð1 aC0 ÞJm aUg ; 1a
ð9Þ
ð15Þ
where ð10Þ
where Jm ¼ Jg þ Jl ; Jg ¼ avg and Jl ¼ ð1 aÞvl . C0 and Ug are given as follows [15,16]:
Jg ðzÞ ¼ qg ðzÞ=A; Vg2 ðzÞ ¼ 1:2½Jl þ Jg ðzÞ þ 0:35
ð16Þ pffiffiffiffiffiffi gD:
ð17Þ
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
10
Qw [m3/min]
1
D (mm) 151 151 151 151 130
L2 (m) L1 / L2 (-) 196.6 0.936 143.6 0.912 112.6 0.888 83.6 0.849 11.8 0.700
L2 (m) L1 / L2 (-) 11.6 0.850 11.6 0.800 11.6 0.700 11.6 0.850 11.6 0.800 11.6 0.700 9.90 0.700 7.70 0.700
D (mm) 75.7 75.7 75.7 46.7 46.7 46.7 46.7 46.7
0.1
0.01 0.01
485
0.1
1 Qg [Nm3/min]
10
100
Fig. 7. Liquid volumetric flow rate vs. gas injection rate.
100 8
Fl [–]
6 4
2
10-1 10-2
L2 (m)
D (mm)
L2 (m)
D (mm)
L2 (m)
D (mm)
83.6 112.6 142.6 196.6
151 151 151 151
11.6 11.6 11.6
47 47 47
75.7 75.7 75.7
7.7 9.9
47 47
11.6 11.6 11.6 11.8
2
4
6
8 10-1 FRg [–]
130
2
4
6
8 100
Fig. 8. Liquid phase holdup vs. gas-phase Froude number.
Since the static pressure inside the pipe, pðzÞ, is approximated by pðzÞ ¼ rql gðL1 zÞ þ pa , the gas volumetric flow rate at z, qg ðzÞ, is calculated from L1 z 1þr qg ðzÞ ¼ pa Qg =pðzÞ ¼ Qg : ð18Þ 10 From Eqs. (15) and (18), the average liquid hold-up in the pipe, Fl , is calculated as follows: Z L1 1 Fl ¼ fl ðzÞ dz L1 0 1 Jg L1 Jg 1 1:2 ¼1þ Vg2 10 Vg2
L1 Jg 1 1:2 ln 1 þ1 ; ð19Þ 10 Vg2 where pffiffiffiffiffiffi Vg2 ¼ 1:2ðJl þ Jg Þ þ 0:35 gD;
ð20Þ
Fl against the gas-phase Froude number, Frg , is plotted in Fig. 8 for different pipe diameters, pipe lengths and submergence ratios. pffiffiffiffiffiffiffiffiffiffi ð21Þ Frg ¼ Jg = 2gL2 : The pumping performance of gas-lift pumps is considered to be a function of Fl and Frg as shown in Fig. 8 with dimensionless parameters of L1 =L2 , L0 =L2 and D=L2 Thus, one can find that the theoretical analysis presented in Section 3 is valid. Moreover, this indicates that one-dimensional numerical simulation can be used to analyze the pumping performance of gas-lift pumps. 5.2. Axial pressure and waveform analysis The differential pressure fluctuation for both the laboratory- and large-scale systems was examined in accordance with [22] in order to gain a clear understanding
486
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488 1.0
Normalized mag squared [-]
0.8 1.0
Normalized mag squared [-]
0.8
0.6
0.6
0.4
(b)
0.2
0.4 (a)
0
0.2
0
5
10
15
Frequency [Hz] 0 0
5
10
of the flow patterns occurring inside the gas-lift pumps. Fast Fourier Transform analysis was used to obtain the normalized (magnitude)2 vs. frequency spectrum shown in Fig. 9. It can be seen that the frequency plots for both systems are similar with a shift to higher frequencies occurring for the large-scale gas-lift pump. The reason for this is that the frequency of void fluctuation in the large-scale gas-lift pump is increased with increases in the velocities of liquid and gas phases. Regrettably, the frequency plots do not specifically identify the type of flow, although it is expected that the flow is either churnturbulent or slugging. The axial pressure profile, p, in the gas-lift pipe has been plotted in Fig. 10 for both the laboratory- and large-scale systems. Also shown in the figure is the external fluid pressure (ambient plus hydrostatic) as a function of pipe elevation. For the laboratory scale
15
Frequency [Hz]
1.8
Fig. 9. Normalized pressure fluctuation spectra. (a) D ¼ 75:7 mm, L2 ¼ 11:6 m, Qg ¼ 1:47 N m3 /min. (b) D ¼ 151 mm, L2 ¼ 196:6 m, Qg ¼ 38:4 N m3 /min.
Qg(Nm3/min) 0.491 0.962 1.47 1.93
1.6
Qg (Nm3/min) 0.491 0.962 1.47 1.93
Outlet
0
L2 –z [m]
2 Water level
4
Pz [–]
1.4
1.2
p out
6
1.0
8
10
0.8
Air injection Inlet
12
0
0.2
0.1
Outlet Water level
50
0.8
1.0
1.8
p [MPa]
0
Qg(Nm3/min) Qg (Nm3/min) 2.29 10.8 38.4
2.29 10.8 38.4
1.6
1.4 Pz [–]
L2 –z [m]
0.20
0.15
0.6
Z (= 1 – z / L2) [–]
(a) 14 0.05 (a)
0.4
100
1.2 150
1.0 Air injection Inlet
200
0.8 0 (b)
0.5
1 1.5 p [MPa]
0
2
Fig. 10. Axial pressure profiles. (a) D ¼ 75:7 mm, L2 ¼ 11:6 m. (b) D ¼ 151 mm, L2 ¼ 196:6 m.
(b)
0.2
0.4
0.6
0.8
1.0
Z (= 1 –z / L2) [–]
Fig. 11. Dimensionless pressure vs. normalized axial position. (a) D ¼ 75:7 mm, L2 ¼ 11:6 m. (b) D ¼ 151 mm, L2 ¼ 142:6 m.
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
system, in the region above the gas injection point, up to approximately 0.3L2 the axial pipe pressure is similar to the external fluid pressure. However, beyond this distance there is a marked difference between the internal and external pressure, whereby the internal pressure is significantly greater than the external pressure. In order to better compare the axial pressure profiles between the two systems, the length elevation and pressure measurements have been normalized as follows: Z ¼ 1 z=L2 ;
ð22Þ
Pz ¼ p=pout ;
ð23Þ
where Z is the normalized length elevation, Pz the normalized pressure, and pout the external pressure. The pressure ratio is shown in Fig. 11(a) and (b). The ratio Pz sharply increases with an increase in Z before reaching the maximum; the ratio takes the maximum at the water surface. After the maximum, it decreases with an increase in Z. Although the maximum value in the large-scale gas-lift pump is larger than that in the laboratory-scale, their profiles are very similar. Thus, these experimental results on the pressure profiles in the gas-lift pipes also indicate that the theoretical analysis presented in Section 3 is valid and that
one-dimensional numerical simulation can be used to analyze the pumping performance of gas-lift pumps. 5.3. Numerical model predictions The numerical model, based on the equations described in Section 4, was used to predict the induced water volumetric flow rate for the large-scale gas-lift pump. The comparison between the steady state and measured values is given in Fig. 12. Numerical results show satisfactory agreement with the measured. Generally, the numerical model predicted slightly larger liquid volumetric flowrates for any given gas injection rate. This was due to the underestimation of the wall friction losses resulting from the assumption of a hydrodynamically-smooth inside pipe surface. As a result, the numerical model and computational method proposed in the present study can be used to analyze the pumping capability of GLAD system. In the present numerical model, mass transfer from the bubbles has not been included, which would in practice reduce the bubble size resulting in a lower gas void fraction and thereby reducing the buoyancy driving force among the liquid flow. A model describing dissolution of CO2 from bubbles to a liquid phase should be linked with the present study.
6
4
4
Qw [m3/min]
Qw [m3/min]
6
: Experimental : Numerical prediction
2
: Experimental : Numerical prediction
2 1.5
1.5 1
10 Qg
(a)
1
100
[Nm3/min]
10 Qg
(b) 6
4
4
100
[Nm3/min]
Qw [m3/min]
Qw [m3/min]
6
: Experimental : Numerical prediction
2
: Experimental : Numerical prediction
2 1.5
1.5 1 (c)
487
10 Qg [Nm3/min]
1
100 (d)
10 Qg [Nm3/min]
Fig. 12. Predicted vs. measured liquid volumetric flow rate for large-scale gas-lift pump.
100
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T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
6. Conclusions In this study a comparison was made between the lifted liquid volumetric flow rate for both laboratoryand large-scale gas-lift pumps. It was found that for each pump geometry a maximum liquid flowrate was achieved for the range of gas injection rates studied. Moreover, the liquid-phase hold-up was adequately modeled based on a gas-phase Froude number and applying 1-D Drift-Flux analysis. The axial pressure distribution for both scale systems exhibited similar properties when normalized with respect to overall pipe length and outlet absolute pressure. A simple hydrodynamic numerical model was found to adequately predict the induced liquid flowrate for a given gas injection rate. Closer agreement is expected when frictional losses for non-smooth pipe surface are taken into account as well as dissolution of gas from the rising bubbles. Further work in this area is currently in progress. Acknowledgements The present study was carried out with the financial support of Scientific Research A No. 13355008, Grantsin-Aid for Scientific Research, JSPF (Japan Society for the Promotion of Science). The authors would like to gratefully acknowledge the support of the society. References [1] Intergovernmental Panel on Climate Change (IPCC), Summary for Policymakers: The Economic and Social Dimensions of Climate Change, IPCC Working Group III, 2000. [2] International Energy Agency (IEA), World Energy Outlook 1998 Edition, 1998, pp. 34–36. [3] IEA, World Energy Outlook 1998 Edition, 1998, pp. 53–55. [4] P.M. Haugan, H. Drange, Sequestration of CO2 in the deep ocean by shallow injection, Nature 357 (1992) 318–320. [5] C. Marchetti, On geoengineering and the CO2 problem, Climatic Change 1 (1977) 59–68. [6] M.I. Hoffert, Y.C. Wey, A.J. Callegari, W.S. Broecker, Atmospheric response to deep-sea injections of fossil-fuel carbon dioxide, Climatic Change 2 (1979) 53–68.
[7] T. Saito, T. Kajishima, Method and Apparatus for Dissolving and Isolating Carbon Dioxide Gas under the Sea, US Patent No. 5662837, 1997. [8] T. Saito, T. Kajishima, R. Nagaosa, CO2 sequestration at sea by gas-lift system of shallow injection and deep releasing, Environmental Science and Technology 34 (2000) 4140–4145. [9] T. Saito, S. Kosugi, T. Kajishima, K. Tsuchiya, Characteristics and performance of a deep ocean disposal system for low-purity CO2 gas via a gas lift effect, Energy and Fuels 15 (2001) 285–292. [10] T. Saito, T. Kajishima, K. Tsuchiya, S. Kosugi, Mass transfer and structure of bubbly flows in a system of CO2 disposal into the ocean by gas-lift column, Chemical Engineering Science 54 (1999) 4945–4951. [11] R.F. Mudde, T. Saito, Hydrodynamical similarities between bubble column and bubbly pipe flow, Journal of Fluid Mechanics 437 (2001) 203–228. [12] M. Weber, Y. Dedegil, Transport of solids according to the air-lift principle, in: Proceedings of Hydrotransport 4 H1, 1976, pp. 1–23. [13] Y. Shimizu, C. Tojyo, M. Suzuki, T. Saito, T. Usami, An experimental study on the steady and unsteady characteristics of air-lift pumping system, in: Proceedings of the International Conference on Multiphase Flows ’91––Tsukuba, 1991, pp. 367– 369. [14] L.F. Moody, Friction factors for pipe flow, Transactions of the ASME 66 (1944) 671–684. [15] N. Zuber, J.A. Findlay, Average volumetric concentration in twophase flow systems, Transactions of the ASME Series C Heat Transfer 87 (1965) 453–468. [16] M. Ishii, One dimensional Drift-flux Model and Constitutive Equations for relative motion between phases in various two phase flow regimes, Argonne National Laboratory, ANL-77-47, 1977. [17] T. Tomiyama, N. Furutani, H. Minagawa, T. Sakaguchi, Numerical analyses of air-lift pumps based on the multi-fluid model, Japanese Journal of Multiphase Flow 2 (1992) 173–188. [18] T. Kajishima, Conservation properties of finite difference method for convection, Transactions of the Japanese Society of Mechanical Engineers Series B 60 (1994) 2058–2063. [19] T. Kajishim, Upstream-shifted interpolation method for numerical simulation of incompressible flows, Transactions of the Japanese Society of Mechanical Engineers Series B 60 (1994) 3319–3326. [20] T. Kajishima, T. Saito, Numerical simulation of unsteady flow in air-lift pump, JSEM International Journal, Series B 39 (1996) 525– 532. [21] D.J. Nicklin, The air-lift pump: theory and optimisation, Transactions of the IChemE 41 (1963) 29–39. [22] O.C. Jones, N. Zuber, Interrelation between void fraction and fluctuations and flow patterns in two-phase flow, International Journal of Multiphase Flow 2 (1975) 273–306.
Pumping characteristics of a large-scale gas-lift system T. Saito
a,*
, T. Kajishima b, K. Tsuchiya
c
a
c
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, Shizuoka 432-8561, Japan b Department of Mechanical Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Miyakodani, Tatara, Kyotanabe, Kyoto 610-0321, Japan
Abstract In this study the hydrodynamics of a gas-lift system for CO2 sequestration at deep sea (so-called ‘‘GLAD System: Gas Lift Advanced Dissolution System’’) are investigated. Experimental results are presented for both laboratory and pilot scale gas-lift pumps, ranging from 47 to 151 mm in diameter and 7.7 to 196.6 m in height. It was found that for each pump geometry a maximum liquid flowrate was achieved for the range of gas injection rates studied. Moreover, the liquid-phase hold-up was adequately modeled based on a gas-phase Froude number and applying 1-D Drift-Flux analysis. The axial pressure distribution for both scale systems exhibited similar properties when normalized with respect to overall pipe length and outlet absolute pressure. A simple hydrodynamic numerical model was found to adequately predict the induced liquid flowrate for a given gas injection rate. Closer agreement is expected when frictional losses for non-smooth pipe surface are taken into account as well as dissolution of gas from the rising bubbles. Further work in this area is currently in progress. Ó 2003 Elsevier Inc. All rights reserved. Keywords: CO2 sequestration; Gas Lift Advanced Dissolution System; Gas-lift pumping; Two phase flow
1. Introduction Recently, global environmental problems, such as global warming, acid rain, forest destruction and so on, are getting more and more obvious. Consequently, all nations have been discussing a cutback in the discharge amount of CO2 for the purpose of mitigating global warming [1]. Humankind faces an enormous task to find effective solutions to the problem. The inherent difficulties of the problem stem from the fact that the total amount of CO2 emitted from human activities is just enormous (23 GtC/year) [2], and is directly related to the consumption of fossil fuels used to support our daily lifestyles [3]. Although changing our lifestyle and saving energy are essential, and the most effective way to reduce the CO2 emission, they are insufficient for completely solving the global warming problem. Isolation of CO2 from the atmosphere will still be needed to mitigate the expected peak of CO2 concentration in the atmosphere in the near future. Ocean sequestration of CO2 is a hopeful option [4] because the CO2 -absorption capacity *
Corresponding author. Tel./fax: +81-53-478-1601. E-mail address: [email protected] (T. Saito).
0894-1777/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2003.07.005
of the ocean is huge [5], and is capable of isolating CO2 for more than several hundred years [6]. A method of ocean sequestration necessitates isolating a huge amount of CO2 from the atmosphere for long term (several hundred or thousand years) with low cost, low energy consumption and a low secondary-environmental impact. To realize these difficult demands simultaneously, we have developed a gas-lift system for CO2 sequestration in seawater at depths on the order of 1000 m. The system is a bundle of inverse-J pipelines set in the ocean of 200–3000 m depth, as illustrated in Fig. 1 [7–9], the so-called GLAD (Gas Lift Advanced Dissolution) System. The CO2 -containing gas is pumped using a compressor (3) and transported through an underwater gas pipeline (4). The gas is injected into a riser (5) at a depth between 200 and 400 m. Gas-lift effect will occur in the riser, while CO2 gas inside the bubbles dissolves into the liquid phase (seawater). The resulting CO2 solution is forced to flow into a downcomer (6) and transported through a drainpipe (8) to be released from the bottom of the drainpipe. The successful operation of the system relies on the gas-lift pumping capability of the riser as well as reliable dissolution of CO2 gas into the liquid phase. So far we
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Nomenclature A a b C0 D Fl Frg fl G g J L0 L1 L2 Pz p pa pout Q q R Re
cross-sectional area of a pipe [m] factor [–] index number [–] qffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =ql [–] pipe diameter [m] average liquid holdup [–] gas-phase Froude number [–] liquid holdup [–] momentum of mixture ¼ aqg vg þ ð1 aÞql vl [kg/m2 s] gravity acceleration [m/s2 ] superficial velocity [m/s] pipe length between an inlet and a gas injection point [m] pipe length between a gas injection point and the water surface [m] pipe length between a gas injection point and an outlet [m] dimensionless pressure [–] static pressure [MPa] or [Pa] atmospheric pressure [MPa] or [Pa] external pressure [MPa] or [Pa] volumetric flow rate [m3 /min] or [m3 /s] volumetric flow rate at z [m3 /s] gas constant [J/(kg K)] Reynolds number [–]
T t U V Vg2 v Z z a C k l n q r s
temperature [K] time [s] drift velocity [m/s] velocity [m/s] pffiffiffiffiffiffi 1:2½Jl þ Jg ðzÞ þ 0:35 or pffiffiffiffiffiffigD 1:2½Jl þ Jg þ 0:35 gD [m/s] velocity [m/s] normalized length elevation [–] vertical distance from a gas injection point [m] void fraction [–] gas injection rate per unit volume the gas– liquid mixture [kg/m3 s] friction factor [–] viscosity [Pa s] loss factor at an inlet [–] density [kg/m3 ] surface tension of liquid [N/m] wall-friction stress of the liquid phase [Pa]
Subscripts 1 inlet 2 gas injection point 3 outlet g gas phase l liquid phase m mixture
have studied extensively the mass transfer between bubble swarms and the liquid phase [10], and turbulence structure of bubbly flows in a large-diameter pipe [11]. Those characteristics are essential to fully understand
the dissolution process of CO2 gas in the GLAD system. For its optimal design and operation, an understanding of overall pumping characteristics of the system is also needed since the proposed system will be of a massive
(5) Gas including CO2
(6)
Gas including CO2 (3) (2)
Ambient seawater
CO2-rich seawater
1000 – 3000m
(7) 200 – 400m
(4) (6)
(5) Continental shelf
(8) Continental slope
(1) Fired power plant, (2) CO2 separation/capture system, (3) Compressor, (4) Underwater gas pipeline, (5) Riser of GLAD, (6) Downcomer of GLAD, (7) Float, (8) Drainpipe Fig. 1. Conceptual diagram of GLAD System.
(1)
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
large-scale (of 200-m height) setup is shown in Fig. 2. A shaft (1) of 1.5 m in diameter and 200 m in depth is placed under the ground and filled with tap water. A gas-lift pipe (2), made of steel, 151 mm in diameter and 212.6 m in total height, is connected to a gas–water separator (9) via a smooth bend. Compressed air (temperature of 30–35 °C), supplied from a compressor (3), is controlled with a mass flow controller (5) and injected into the gas-lift pipe at a depth of 71, 100, 131 or 184 m through an annular-type gas injector. The water level in the shaft kept constant using a water-supply tank (6) and pump (7). The flow rate of lifted water (tap water; temperature of 20–23 °C) is measured with an electromagnetic flow meter (8), being registered as the superficial liquid velocity. The gas–water mixture is separated into each phase in the separator (9) with the gas being discharged into the atmosphere while the liquid is returned to the shaft through a swing pipe (10) and a return pipe (11). A measure tank (12) and load cells (13) are used to weigh the mass of the discharged water. The pressure difference in the gas-lift pump was measured via a strain-gauge type differential pressure transducer (14); where the distance between the pressure taps at the measured section was 4 m. The static pressure inside the gas-lift pipe was measured via a strain-gauge type pressure transducer (15) at several depths. A check of the sensitivity of the pressure tapping measurements (locations shown in Fig. 3) was obtained by recording the single (liquid) phase pressure drop at various flow rates to determine the Moody friction
scale, where the dissolution section is of the order of 200-m height. Few papers, however, have been published regarding this kind of large-scale gas-lift pump [12,13]. To obtain the necessary data on large-scale gaslift pump, we have systematically performed a wide range of experiments using pipes of 46.7–151 mm in diameter and 7.7–196.6 m in height. In this paper the characteristics of a gas-lift pump are modeled using a Froude number represented by the length of the gas-lift pipe, the superficial velocity of the gas phase, and the average void fraction in the pipe. The lifting characteristics of water via a gas-lift pump are investigated experimentally for a wide range of geometries and experimental conditions. In particular, the flow pattern near the outlet for both large- and laboratory-scale measurements is examined based on a waveform analysis of differential pressure. Comparison is also made between the axial pressure profiles for the two systems. Finally, a computational method for analyzing the pumping characteristics is discussed and the numerical results are compared with experimental measurements.
2. Experimental 2.1. Large-scale apparatus The study involves both large-scale and laboratoryscale experimental setups. A schematic diagram of the
(9) (5)
(3)
(14) (11)
(7) (6)
71m
100m
(12) (13)
(15) (1)
200m
184m
131m
(2)
(10)
12.6m
(4)
481
(8)
(1) Shaft, (2) Gas-lift pipe, (3) Compressor, (4) Cooling tower, (5) Mass flow controller, (6) Water supply tank, (7) Pump, (8) Electromagnetic flow meter, (9) Gas-water separator, (10) Swing pipe, (11) Return pipe, (12) Measure tank, (13) Load cell, (14) Differential pressure transducer, (15) Pressure transducer
Fig. 2. Schematic diagram of 200-m gas-lift pump.
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
Outlet
Pressure gauge 5 Air injection: 131m
190.1 m
Air injection: 100m
200 m
212.6 m
Pressure gauge 4
166.5 m
Air injection: 71m
133.5 m
Pressure gauge 3
111.5 m
Pressure gauge 2
78.7 m
Water level
45.7 m
Differential pressure gauge Pressure gauge 1 3.0 m 23.7 m
482
Pressure gauge 6
Pressure gauge 7 Air injection: 184m
Electromagnetic flow meter
Inlet: 200m Fig. 3. Location of static and differential pressure taps.
4 e /D = 0.00042
λ [–]
3
2
10-2
4
6
8 105 Re [–]
2
4
6
Fig. 4. Relationship between friction factor and the Reynolds number. ( ) Friction factor actually measured in water flow; (––) calculated from Moody’s diagram. Relative roughness of pipe wall e=D ¼ 0:00042.
factor [14]. The comparison of the measured values with the calculated (reported) values, in terms of the friction factor vs. the Reynolds number relationship, is shown in Fig. 4 which indicates a good agreement.
a control valve (10), it was injected into a selected gaslift pipe through an annular-type gas injector (3). The flow rate of lifted water (tap water; temperature of 21– 23 °C) was measured via an electromagnetic flow meter (5). The lifted water was discharged from the gas-lift pipe into the gas–liquid separator (2) via a smooth pipe bend. The water level in the head tank (4) is automatically controlled in each run to be constant using the water supply system (13–16). The pressure difference in the gas-lift pump was measured via a strain-gauge type differential pressure transducer (11); where the distance between the pressure taps at the measuring section is 1 m. The static pressure inside the gas-lift pipe is measured via strain-gauge type pressure transducers (12) at several heights. A validity check similar to that for the large-scale apparatus is carried out.
3. Theoretical modeling 2.2. Laboratory-scale apparatus Fig. 5 shows a schematic diagram of the laboratoryscale experimental apparatus. It consists of three acrylic gas-lift pipes (1) of diameters 130, 75.7 and 46.7 mm, with corresponding heights of 11.8, 11.6 and 11.6 m, respectively. For the 46.7-mm pipe, different gas injector (3) positions at 0, 1.7 and 3.9 m could be selected. Gas (air) was supplied from an oil-free air compressor (6). After carefully controlling the mass flow rate of the air (temperature of 31–34 °C) via a mass flow meter (8) and
We will consider the momentum balance between the bottom and top of a gas-lift pump as shown in Fig. 6. Given that z is the vertical distance from the gas injector, L0 the pipe length between the inlet and the gas injector, L1 the length between the gas injector and the surface of the water in the shaft or the vertical water tank, L2 the length between the gas injector and the outlet, L3 the total length of the gas-lift pipe, and D the inner diameter of the gas-lift pipe, the flowing equation for the momentum balance is obtained:
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
483
(2) (12) (11)
(4)
(1)
(1)
(1)
(3)
(3) (16)
(10) (9) (8)
(3) (3)
(15) (13)
(5)
(14)
(7)
(3) (5)
(5)
(6)
(1) Gas-lift pipes, (2) Air-water separator, (3) Gas injectors, (4) Head tank, (5) Electromagnetic flow meters, (6) Compressor, (7) Cooling tower, (8) Gas Mass flow meters, (9) Thermocouple, (10) Automatic control valve, (11) Differential pressure transducer, (12) Pressure transducers, (13) Water tank, (14) Pump, (15) Electromagnetic flow meter, (16) Automatic control valve
Fig. 5. Schematic diagram of laboratory-scale gas-lift pump.
where A is the cross-sectional area of the gas-lift pipe, g the gravitational acceleration, V the velocity of a given phase, a and b are the factor and index number, respectively, k the friction factor of the pipe wall, q the density, n the loss factor at the inlet, subscripts g and l denote the gas and liquid phases, respectively, subscripts 1 and 3 denote the inlet and outlet of the gas-lift pipe, respectively, and fl ðzÞ is the hold-up of liquid at z or fl ðzÞ ¼ 1 aðzÞ with aðzÞ being void fraction at z. The second term on the right-hand side of Eq. (1) signifies a loss at the inlet and is negligible because it is usually very small. The integrals in the fourth and fifth terms in Eq. (1) can be expressed as Z L2 fl ðzÞ dz ¼ L2 Fl ; ð2Þ
(C) Surface of the water
L2 L3
L1
z (B)
0
L0
Z
(A)
0
b
a½fl ðzÞ dz ¼ LaFlb ;
ð3Þ
0
Fig. 6. Gas-lift pump model. (A) Inlet, (B) air injection and (C) outlet.
q AV 2 L0 ql AVl12 ql AVl1 ðVl3 Vl1 Þ ¼ L1 ql gA n l l1 k 2 D 2 Z L2 1 Vl12 ql gA fl ðzÞ dz k D 2 0 Z L2 a½fl ðzÞb dz;
L2
where Fl represents the average liquid hold-up in the section between the gas injector and the outlet. From Eqs. (2) and (3), and denoting Vl1 ¼ Jl , Eq. (1) can be rearranged to give Jl Jg L1 L0 Jl2 L2 Jl2 k 2 pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi ¼ Fl k aF b ; L2 2gD D 2gL2 l 2gL2 2gL2 L2 ð4Þ
ð1Þ
where J is the superficial velocity of each phase. From Eq. (4), the pumping performance of a gas-lift pump is
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T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
found to be expressed in terms of the average hold-up (or void fraction) in the pump, three kinds of Froude number and the dimensionless numbers representing pump size. In summary, the pumping performance of a gas-lift pump depends on the average gas holdup in the gas-lift pipe and the Froude number characterized by the superficial velocity of the gas phase and the length of the gas-lift pipe. On this basis it is assumed that a onedimensional numerical simulation can be used to analyze the pumping performance of a gas-lift pump.
4. Numerical simulation Based on the above theoretical analysis the gas–water two-phase flow in the vertical pipe section in the GLAD system can be simulated one-dimensionally. Assuming that the density of the liquid phase ql and the temperature T are constant, the conservation laws of mass and momentum can be considered using a drift-flux model. The mass conservation of the gas phase is expressed as
C0 ¼ 1:2 0:2
qffiffiffiffiffiffiffiffiffiffiffi qg =ql ;
8 1=4 > g < 1:41 rg ql q 2 ql Ug ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > : 0:35 gD ql qg ql
ð11Þ a 6 0:25
ðbubbly flowÞ
a P 0:3
ðslug flowÞ
; ð12Þ
where r is the surface tension of liquid. In the present computation, the drift velocity Ug is linearly interpolated with a in the range 0:25 < a < 0:30 which marks the transition from bubbly to slug flow. The wall friction is estimated from the model [17]: sw ¼
kqJl2 8ð1 aÞ1:75
ð13Þ
;
where 64 Re1 l k¼ 0:3164 Re0:25 l
Rl < 2300 ; Rl < 2300
ð14Þ
where a is the void fraction, v the velocity, and Cg the gas injection rate per unit volume of the gas–liquid mixture. By defining the density and momentum of the mixture by qm ¼ aqg þ ð1 aÞql and G ¼ aqg vg þ ð1 aÞql vl , respectively, the conservation of mass and momentum of the mixture can be represented by the following basic equations:
where Rel is the Reynolds number, Rel ¼ Dql Jl =ll , with ll being the viscosity of liquid. The finite difference method has been applied to discretize the basic equations. Specifically, the non-linear (convection) terms in the conservation laws are discretized based on the upstream finite difference method [18,19]. The implicit time marching scheme for the density and pressure was employed to deal with the high compressibility of the gas phase [20]. The formal accuracy is 4th-order in space and 1st-order in time.
oðqm Þ oG þ ¼ Cg ; ot oz
ð6Þ 5. Results and discussion
oG oðaqg v2g Þ o½ð1 aÞql v2l op 4sw þ ¼ qg þ ; ot oz oz oz D
ð7Þ
oðaqg Þ oðaqg vg Þ þ ¼ Cg ; ot oz
ð5Þ
5.1. Effect of gas injection rate on liquid pumping rate
where p represents the static pressure; sw the wall-friction stress of the liquid phase. The third basic equation is the gas equation (for an ideal gas): p ; ð8Þ qg ¼ RT where R is the gas constant. It is noted that four parametric variables q, G (or the velocity of the mixture vm ¼ G=qm ), p and a are involved in the basic equations. A drift-flux model is employed to close the above set of basic equations, Eqs. (5)–(8), where vg , vl and sw are to be expressed in terms of vm and a. Consequently, the velocity components of each phase are given as:
The volumetric liquid (water) flow rate, Qw , vs. the volumetric gas injection rate, Qg , is plotted in Fig. 7 for different pipe diameters, D, pipe lengths, L2 and submergence ratios, L1 =L2 . It can be seen that for each experimental geometry there is a maximum in the liquid pumping rate for the given range of gas injection rates. It is also found that Qw or its maximum value increases with D, and that Qw tends to increase with L2 as well when Qg and D are kept constant. From the theory of an air-lift pump by Nicklin [21], the liquid hold-up at z, fl ðzÞ, can be expressed by the following equations:
vg ¼ C0 Jm þ Ug ;
fl ðzÞ ¼ 1 Jg ðzÞ=Vg2 ðzÞ;
vl ¼
ð1 aC0 ÞJm aUg ; 1a
ð9Þ
ð15Þ
where ð10Þ
where Jm ¼ Jg þ Jl ; Jg ¼ avg and Jl ¼ ð1 aÞvl . C0 and Ug are given as follows [15,16]:
Jg ðzÞ ¼ qg ðzÞ=A; Vg2 ðzÞ ¼ 1:2½Jl þ Jg ðzÞ þ 0:35
ð16Þ pffiffiffiffiffiffi gD:
ð17Þ
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
10
Qw [m3/min]
1
D (mm) 151 151 151 151 130
L2 (m) L1 / L2 (-) 196.6 0.936 143.6 0.912 112.6 0.888 83.6 0.849 11.8 0.700
L2 (m) L1 / L2 (-) 11.6 0.850 11.6 0.800 11.6 0.700 11.6 0.850 11.6 0.800 11.6 0.700 9.90 0.700 7.70 0.700
D (mm) 75.7 75.7 75.7 46.7 46.7 46.7 46.7 46.7
0.1
0.01 0.01
485
0.1
1 Qg [Nm3/min]
10
100
Fig. 7. Liquid volumetric flow rate vs. gas injection rate.
100 8
Fl [–]
6 4
2
10-1 10-2
L2 (m)
D (mm)
L2 (m)
D (mm)
L2 (m)
D (mm)
83.6 112.6 142.6 196.6
151 151 151 151
11.6 11.6 11.6
47 47 47
75.7 75.7 75.7
7.7 9.9
47 47
11.6 11.6 11.6 11.8
2
4
6
8 10-1 FRg [–]
130
2
4
6
8 100
Fig. 8. Liquid phase holdup vs. gas-phase Froude number.
Since the static pressure inside the pipe, pðzÞ, is approximated by pðzÞ ¼ rql gðL1 zÞ þ pa , the gas volumetric flow rate at z, qg ðzÞ, is calculated from L1 z 1þr qg ðzÞ ¼ pa Qg =pðzÞ ¼ Qg : ð18Þ 10 From Eqs. (15) and (18), the average liquid hold-up in the pipe, Fl , is calculated as follows: Z L1 1 Fl ¼ fl ðzÞ dz L1 0 1 Jg L1 Jg 1 1:2 ¼1þ Vg2 10 Vg2
L1 Jg 1 1:2 ln 1 þ1 ; ð19Þ 10 Vg2 where pffiffiffiffiffiffi Vg2 ¼ 1:2ðJl þ Jg Þ þ 0:35 gD;
ð20Þ
Fl against the gas-phase Froude number, Frg , is plotted in Fig. 8 for different pipe diameters, pipe lengths and submergence ratios. pffiffiffiffiffiffiffiffiffiffi ð21Þ Frg ¼ Jg = 2gL2 : The pumping performance of gas-lift pumps is considered to be a function of Fl and Frg as shown in Fig. 8 with dimensionless parameters of L1 =L2 , L0 =L2 and D=L2 Thus, one can find that the theoretical analysis presented in Section 3 is valid. Moreover, this indicates that one-dimensional numerical simulation can be used to analyze the pumping performance of gas-lift pumps. 5.2. Axial pressure and waveform analysis The differential pressure fluctuation for both the laboratory- and large-scale systems was examined in accordance with [22] in order to gain a clear understanding
486
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488 1.0
Normalized mag squared [-]
0.8 1.0
Normalized mag squared [-]
0.8
0.6
0.6
0.4
(b)
0.2
0.4 (a)
0
0.2
0
5
10
15
Frequency [Hz] 0 0
5
10
of the flow patterns occurring inside the gas-lift pumps. Fast Fourier Transform analysis was used to obtain the normalized (magnitude)2 vs. frequency spectrum shown in Fig. 9. It can be seen that the frequency plots for both systems are similar with a shift to higher frequencies occurring for the large-scale gas-lift pump. The reason for this is that the frequency of void fluctuation in the large-scale gas-lift pump is increased with increases in the velocities of liquid and gas phases. Regrettably, the frequency plots do not specifically identify the type of flow, although it is expected that the flow is either churnturbulent or slugging. The axial pressure profile, p, in the gas-lift pipe has been plotted in Fig. 10 for both the laboratory- and large-scale systems. Also shown in the figure is the external fluid pressure (ambient plus hydrostatic) as a function of pipe elevation. For the laboratory scale
15
Frequency [Hz]
1.8
Fig. 9. Normalized pressure fluctuation spectra. (a) D ¼ 75:7 mm, L2 ¼ 11:6 m, Qg ¼ 1:47 N m3 /min. (b) D ¼ 151 mm, L2 ¼ 196:6 m, Qg ¼ 38:4 N m3 /min.
Qg(Nm3/min) 0.491 0.962 1.47 1.93
1.6
Qg (Nm3/min) 0.491 0.962 1.47 1.93
Outlet
0
L2 –z [m]
2 Water level
4
Pz [–]
1.4
1.2
p out
6
1.0
8
10
0.8
Air injection Inlet
12
0
0.2
0.1
Outlet Water level
50
0.8
1.0
1.8
p [MPa]
0
Qg(Nm3/min) Qg (Nm3/min) 2.29 10.8 38.4
2.29 10.8 38.4
1.6
1.4 Pz [–]
L2 –z [m]
0.20
0.15
0.6
Z (= 1 – z / L2) [–]
(a) 14 0.05 (a)
0.4
100
1.2 150
1.0 Air injection Inlet
200
0.8 0 (b)
0.5
1 1.5 p [MPa]
0
2
Fig. 10. Axial pressure profiles. (a) D ¼ 75:7 mm, L2 ¼ 11:6 m. (b) D ¼ 151 mm, L2 ¼ 196:6 m.
(b)
0.2
0.4
0.6
0.8
1.0
Z (= 1 –z / L2) [–]
Fig. 11. Dimensionless pressure vs. normalized axial position. (a) D ¼ 75:7 mm, L2 ¼ 11:6 m. (b) D ¼ 151 mm, L2 ¼ 142:6 m.
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
system, in the region above the gas injection point, up to approximately 0.3L2 the axial pipe pressure is similar to the external fluid pressure. However, beyond this distance there is a marked difference between the internal and external pressure, whereby the internal pressure is significantly greater than the external pressure. In order to better compare the axial pressure profiles between the two systems, the length elevation and pressure measurements have been normalized as follows: Z ¼ 1 z=L2 ;
ð22Þ
Pz ¼ p=pout ;
ð23Þ
where Z is the normalized length elevation, Pz the normalized pressure, and pout the external pressure. The pressure ratio is shown in Fig. 11(a) and (b). The ratio Pz sharply increases with an increase in Z before reaching the maximum; the ratio takes the maximum at the water surface. After the maximum, it decreases with an increase in Z. Although the maximum value in the large-scale gas-lift pump is larger than that in the laboratory-scale, their profiles are very similar. Thus, these experimental results on the pressure profiles in the gas-lift pipes also indicate that the theoretical analysis presented in Section 3 is valid and that
one-dimensional numerical simulation can be used to analyze the pumping performance of gas-lift pumps. 5.3. Numerical model predictions The numerical model, based on the equations described in Section 4, was used to predict the induced water volumetric flow rate for the large-scale gas-lift pump. The comparison between the steady state and measured values is given in Fig. 12. Numerical results show satisfactory agreement with the measured. Generally, the numerical model predicted slightly larger liquid volumetric flowrates for any given gas injection rate. This was due to the underestimation of the wall friction losses resulting from the assumption of a hydrodynamically-smooth inside pipe surface. As a result, the numerical model and computational method proposed in the present study can be used to analyze the pumping capability of GLAD system. In the present numerical model, mass transfer from the bubbles has not been included, which would in practice reduce the bubble size resulting in a lower gas void fraction and thereby reducing the buoyancy driving force among the liquid flow. A model describing dissolution of CO2 from bubbles to a liquid phase should be linked with the present study.
6
4
4
Qw [m3/min]
Qw [m3/min]
6
: Experimental : Numerical prediction
2
: Experimental : Numerical prediction
2 1.5
1.5 1
10 Qg
(a)
1
100
[Nm3/min]
10 Qg
(b) 6
4
4
100
[Nm3/min]
Qw [m3/min]
Qw [m3/min]
6
: Experimental : Numerical prediction
2
: Experimental : Numerical prediction
2 1.5
1.5 1 (c)
487
10 Qg [Nm3/min]
1
100 (d)
10 Qg [Nm3/min]
Fig. 12. Predicted vs. measured liquid volumetric flow rate for large-scale gas-lift pump.
100
488
T. Saito et al. / Experimental Thermal and Fluid Science 28 (2004) 479–488
6. Conclusions In this study a comparison was made between the lifted liquid volumetric flow rate for both laboratoryand large-scale gas-lift pumps. It was found that for each pump geometry a maximum liquid flowrate was achieved for the range of gas injection rates studied. Moreover, the liquid-phase hold-up was adequately modeled based on a gas-phase Froude number and applying 1-D Drift-Flux analysis. The axial pressure distribution for both scale systems exhibited similar properties when normalized with respect to overall pipe length and outlet absolute pressure. A simple hydrodynamic numerical model was found to adequately predict the induced liquid flowrate for a given gas injection rate. Closer agreement is expected when frictional losses for non-smooth pipe surface are taken into account as well as dissolution of gas from the rising bubbles. Further work in this area is currently in progress. Acknowledgements The present study was carried out with the financial support of Scientific Research A No. 13355008, Grantsin-Aid for Scientific Research, JSPF (Japan Society for the Promotion of Science). The authors would like to gratefully acknowledge the support of the society. References [1] Intergovernmental Panel on Climate Change (IPCC), Summary for Policymakers: The Economic and Social Dimensions of Climate Change, IPCC Working Group III, 2000. [2] International Energy Agency (IEA), World Energy Outlook 1998 Edition, 1998, pp. 34–36. [3] IEA, World Energy Outlook 1998 Edition, 1998, pp. 53–55. [4] P.M. Haugan, H. Drange, Sequestration of CO2 in the deep ocean by shallow injection, Nature 357 (1992) 318–320. [5] C. Marchetti, On geoengineering and the CO2 problem, Climatic Change 1 (1977) 59–68. [6] M.I. Hoffert, Y.C. Wey, A.J. Callegari, W.S. Broecker, Atmospheric response to deep-sea injections of fossil-fuel carbon dioxide, Climatic Change 2 (1979) 53–68.
[7] T. Saito, T. Kajishima, Method and Apparatus for Dissolving and Isolating Carbon Dioxide Gas under the Sea, US Patent No. 5662837, 1997. [8] T. Saito, T. Kajishima, R. Nagaosa, CO2 sequestration at sea by gas-lift system of shallow injection and deep releasing, Environmental Science and Technology 34 (2000) 4140–4145. [9] T. Saito, S. Kosugi, T. Kajishima, K. Tsuchiya, Characteristics and performance of a deep ocean disposal system for low-purity CO2 gas via a gas lift effect, Energy and Fuels 15 (2001) 285–292. [10] T. Saito, T. Kajishima, K. Tsuchiya, S. Kosugi, Mass transfer and structure of bubbly flows in a system of CO2 disposal into the ocean by gas-lift column, Chemical Engineering Science 54 (1999) 4945–4951. [11] R.F. Mudde, T. Saito, Hydrodynamical similarities between bubble column and bubbly pipe flow, Journal of Fluid Mechanics 437 (2001) 203–228. [12] M. Weber, Y. Dedegil, Transport of solids according to the air-lift principle, in: Proceedings of Hydrotransport 4 H1, 1976, pp. 1–23. [13] Y. Shimizu, C. Tojyo, M. Suzuki, T. Saito, T. Usami, An experimental study on the steady and unsteady characteristics of air-lift pumping system, in: Proceedings of the International Conference on Multiphase Flows ’91––Tsukuba, 1991, pp. 367– 369. [14] L.F. Moody, Friction factors for pipe flow, Transactions of the ASME 66 (1944) 671–684. [15] N. Zuber, J.A. Findlay, Average volumetric concentration in twophase flow systems, Transactions of the ASME Series C Heat Transfer 87 (1965) 453–468. [16] M. Ishii, One dimensional Drift-flux Model and Constitutive Equations for relative motion between phases in various two phase flow regimes, Argonne National Laboratory, ANL-77-47, 1977. [17] T. Tomiyama, N. Furutani, H. Minagawa, T. Sakaguchi, Numerical analyses of air-lift pumps based on the multi-fluid model, Japanese Journal of Multiphase Flow 2 (1992) 173–188. [18] T. Kajishima, Conservation properties of finite difference method for convection, Transactions of the Japanese Society of Mechanical Engineers Series B 60 (1994) 2058–2063. [19] T. Kajishim, Upstream-shifted interpolation method for numerical simulation of incompressible flows, Transactions of the Japanese Society of Mechanical Engineers Series B 60 (1994) 3319–3326. [20] T. Kajishima, T. Saito, Numerical simulation of unsteady flow in air-lift pump, JSEM International Journal, Series B 39 (1996) 525– 532. [21] D.J. Nicklin, The air-lift pump: theory and optimisation, Transactions of the IChemE 41 (1963) 29–39. [22] O.C. Jones, N. Zuber, Interrelation between void fraction and fluctuations and flow patterns in two-phase flow, International Journal of Multiphase Flow 2 (1975) 273–306.