Experimental study on the gas tightness of a mined cavern with groundwater

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1 Experimental study on the gas tightness of a mined cavern with groundwater Yoshinobu Nishimoto a *, Noboru Hasegawa a, and Makoto Nishigaki b a Electric Power Development Co. Ltd., Japan b Okayama University, Okayama, Japan * yos_nishi@jpower.co.jp Abstract The gas tightness of underground rock cavern tanks installed for the storage of gas and oil is preserved by sealing the rock joints around the cavern tanks with groundwater. This storage system is efficient and cost effective, because utilizing groundwater around the rock cavern tanks negates the need for expensive steel liner plates. However, the mechanisms and principles of this gas sealing method are not entirely clear. Two conditions are important for a groundwater sealing system. The first condition is that gas does not exude into the rock joints from the cavern surface. The second condition is that gas bubbles must be retained in the rock joints, even if exuding into the joints. Ensuring higher water pressure than gas pressure satisfies the first condition. The second condition is thought to be governed by bubble buoyancy, capillary pressure, and drag force, however the effect of these factors on the second condition is not clearly understood. Therefore, we performed laboratory experiments to elucidate the mechanisms of securing gas tightness in rock joints with groundwater. The experimental model was comprised parallel glass plates imitating an actual underground rock joint, and we observed the behavior of air bubbles injected into the gap filled with water. The width of the gap between the parallel glass plates and the hydraulic gradient were varied parametrically. This paper shows the methods and results of the experiments and theoretical speculations of the reliance of gas tightness on the buoyancy, surface tension, and drag force. Keywords: Cavern tank, Gas tightness, Hydraulic gradient, Buoyancy, Capillary pressure, Drag force. Introduction. General Overview The cavern tank gas-tight system sealed with groundwater, hereafter referred to as the water sealing system, is applied for water insoluble liquid, oil, and gas storage. It is a very efficient and economical system because it consists primarily of a mined cavern and groundwater without expensive construction materials. In securing gas tightness, it is important to manage the distribution of the groundwater level and the groundwater pressure around cavern tanks. Fig shows the schematic design of the cavern tank used in the water sealing system. To secure gas tightness in the cavern tank, it is very important to maintain natural and artificial groundwater conditions. Presently, the general design method to ensure gas tightness is not always quantitatively proven to be gas-tight. The existing parameters have been developed on the basis of reviewing previous research and design criteria elucidated therein..2 Gas tightness in a rock cavern tank A great deal of research on gas tightness in a rock cavern tank has already been conducted, both experimentally and theoretically. The existing research focuses on two aspects of gas leakage: gas leaking into the rock joints from the cavern surface and gas bubble behavior inside the rock joints filled with groundwater. Fig. 2 shows the two points where gas leakage can occur. The blue circles show gas tightness at the cavern surface, and the red circles show gas tightness in the rock joints. Much of the existing research shows gas tightness as a hydraulic gradient (Aberg, 977; Komada et

al., 980; Nakagawa et al., 986). For gas tightness at the cavern surface, the hydraulic gradient should be close to 0.

Because the latter condition can easily become critical, gas tightness inside rock joints is more important than at the cavern surface. Gas-tightness in rock joint Gas-tightness on cavern surface Fig.

.3 Design criteria of gas-tightness in Japan In Japan, three crude oil storage bases and two liquefied petroleum gas (LPG) storage bases are already safely in operation.

The designed hydraulic gradient was determined primarily by referring to the estimated hydraulic gradient on the basis of the information on the existing underground crude oil and LPG bases, such as

2 al., 980; Nakagawa et al., 986). For gas tightness at the cavern surface, the hydraulic gradient should be close to 0. For gas tightness inside the rock joints, the hydraulic gradient should be at least.0. Because the latter condition can easily become critical, gas tightness inside rock joints is more important than at the cavern surface. Gas-tightness in rock joint Gas-tightness on cavern surface Fig. -. Schematic design of cavern tank. Fig. -2. Outline of gas leakage points through cavern surface and inside rock joints..3 Design criteria of gas-tightness in Japan In Japan, three crude oil storage bases and two liquefied petroleum gas (LPG) storage bases are already safely in operation. All airtightness design criteria were based on the hydraulic gradient. The designed hydraulic gradient was determined primarily by referring to the estimated hydraulic gradient on the basis of the information on the existing underground crude oil and LPG bases, such as storage pressure, groundwater level, water curtain pressure, and installation depth. For the crude oil storage base, the designed hydraulic gradient was estimated considering internal pressure and installation depth from the operating groundwater level. The value was calculated as in Eq. (). This estimation yielded a hydraulic gradient of 0.8 for crude oil. = ( ) () I: hydraulic gradient h: top of cavern tank depth from groundwater level (m) P: inner pressure head (m) In the case of the LPG storage base, the designed hydraulic gradient was determined on the basis of the results of FEM analysis with similar conditions of internal pressure and installation depth from groundwater level as in the existing storage base. According to this analysis, the designed hydraulic gradient was defined Experimental study 2.Theoretical approach In the theoretical methods of studying gas tightness, three forces buoyancy Fb, capillary pressure Fc, and drag force Fd are considered, as in a previous study (A. Tomiyama et al., 996). The buoyant force occurs because of density differences between water and gas. This is the driving force of gas leakage. Capillary pressure occurs because of surface tension in air bubbles in groundwater that is in contact with joint surfaces of the rock. Drag force that acts on bubbles is a result of the water flow along the hydraulic gradient. Capillary pressure and drag force are forces that resist gas leakage. When the

buoyant force is greater than the combined effects of capillary pressure and drag, gas bubbles move upward. When the buoyant force is less, gas bubbles are retained or move downward.

Through this experiment, we confirmed the occurrence of air leakage and evaluated the relationship between buoyancy, capillary pressure, and drag on the basis of the observed conditions.

3 buoyant force is greater than the combined effects of capillary pressure and drag, gas bubbles move upward. When the buoyant force is less, gas bubbles are retained or move downward. In laboratory experiments, air bubbles were injected between parallel glass plates with varying gap widths. Through this experiment, we confirmed the occurrence of air leakage and evaluated the relationship between buoyancy, capillary pressure, and drag on the basis of the observed conditions. = ( ) (2) = = 2 2 (3) = (4) ρ w : specific gravity of water F cp : passive capillary pressure (N/m) ρ a : specific gravity of gas F ca : active capillary pressure (N/m) g: acceleration due to gravity (m/s 2 ) θ p : meniscus angle of F cp (deg) r: diameter of bubble (m) θ a : meniscus angle of F ca (deg) t: gap width(m) V: floating speed of bubble (m/s) C d : drag coefficient S: projected area of bubble in floating direction (m 2 ) Fig. -3. Forces acting on a bubble in parallel glass plates. 2.2 Test equipment As mentioned above, there several results have been reported in previous gas tightness studies. Referring to these previous results, we performed a gas tightness study in order to determine a method to ensure gas tightness in a narrow gap by using a parallel glass plate model. Actual rock joint conditions are complicated and their width, orientation, roughness, and filling materials vary greatly. It is difficult to consider and monitor these factors for the test model. Therefore, we designed a simple test model using flat parallel grass plates, considering only the basic factors. The test model shown in Fig. 4 comprises two glass plates, two head tanks, connecting pipes, and a pin hole located at the center of one of the glass plates. The gap width of the parallel glass plates, which varied between 50 and,000 µm, was set by inserting thin stainless steel gauge plates within the gap. The water pipes are connected at both ends of test model, with each pipe connected to its respective head tank. The setting of the hydraulic gradient depended on changing the relative head tank height. Three experiments were implemented according to the following procedures.

The parallel glass plate size (h) 60 cm (w) 20 cm 3. Experiments and results 3. Capillary pressure test Fig. -4. Schematic of parallel glass plates test model.

The value of the surface tension of water is known but the meniscus angle is not, and capillary pressure is also unknown.

As the surface tension is constant but the angle of the meniscus varies, the capillary pressure acts along both the passive and active directions during bubble movement.

0728N/m (20 ) : Meniscus angle h: Capillary height : Gap width of parallel glass plates Upward process Active case Downward process Passive case t t t t = 2 a = ha = 2 p = hp = p a = 2 ( p a) ha hp

4 The parallel glass plate size (h) 60 cm (w) 20 cm 3. Experiments and results 3. Capillary pressure test Fig. -4. Schematic of parallel glass plates test model. Capillary pressure is caused by surface tension when a bubble is in contact with the surface of a wall in the narrow gap. Capillary pressure is estimated surface tension and meniscus angle. The value of the surface tension of water is known but the meniscus angle is not, and capillary pressure is also unknown. This test is executed to determine the actual capillary pressure in this model. The capillary pressure is usually calculated from the capillary height of water inside the gap as shown in Eq. (5). As the surface tension is constant but the angle of the meniscus varies, the capillary pressure acts along both the passive and active directions during bubble movement. The difference between the passive and active direction becomes the suppressive force of the capillary pressure. = 2 = h (5) : Capillary raise force N/m [Remark 4] : Surface tension N/m (20 ) : Meniscus angle h: Capillary height : Gap width of parallel glass plates Upward process Active case Downward process Passive case t t t t = 2 a = ha = 2 p = hp = p a = 2 ( p a) ha hp Fig. -5. Capillary pressure test. To ensure the presence of both passive and active capillary pressures in this test, both upward and downward process tests were implemented. The upward process demonstrates the active capillary pressure, and the downward process demonstrates the passive capillary pressure. Fig. 6 shows the relation between the capillary height and the gap width. They are roughly inversely

5 proportional. For the passive (downward) process, capillary height (hp) is larger than that for the active (upward) process (ha); this difference is larger for narrow gaps. Fig. 7 shows the relation between the gap width and the calculated meniscus angle. It was assumed that the meniscus angles would be constant, but the calculated angles are not constant. The constant values, when the surface tension T = N/m, are θa = 65 and θp = 55. The total capillary pressure Fc, which is the difference of Pca and Pcp (3), is estimated to be 0.022N/m. capillary height : mm Upward process Downward process Gap width μm Fig. -6. Relationship between gap width and capillary height. Calculated Meniscuc angle θ deg Upward process Downward process Gap width μm Fig. -7. Relationship between gap width and meniscus angle. 3.2 Bubble behavior test in static water A purpose of the bubble behavior test in static water is to confirm the critical condition of bubbles floating when buoyancy and capillary pressure are equal in magnitude. Bubbles float upward if buoyancy is greater than capillary pressure. The width of the gap and the size of the air bubbles changed parametrically. Air bubbles were injected through the pin hole in the center of one glass plate. Floating speed cm/s Gap width μm Force N.E+00.E-0.E-02.E-03.E-04.E-05 Fc Fb 50μm Fb 0μm Fb 200μm Fb 500μm 0.5.E Bubble diameter mm Fig. -8. Bubble floating velocity in static water test..e-07 Bubble diameter mm Fig. -9. Theoretical equilibrium values of buoyancy Fb and capillary pressure Fc for different bubble diameters. Fig. 8 shows the relation between bubble size and floating speed. When the gap width was 500 μm,

6 air bubbles of 3 9 mm diameter floated, and when the gap width was 200 μm, air bubbles of 20 mm diameter did not move, but air bubbles of 30 mm diameter floated. Fig. 9 shows the theoretical equilibrium values of buoyancy and capillary pressure for the static water test. The actual bubble shape is not perfectly circular, but the buoyancy and capillary pressure are calculated assuming that the bubbles are circular disks. The red line shows the capillary pressure, and the blue line shows the buoyancy for each gap width. The buoyancy is proportional to the square of the bubble diameter, and the capillary pressure is proportional to the bubble diameter. Therefore, buoyancy increases more rapidly for larger bubble diameters. For a 200 μm gap width, bubbles of 30 mm diameter floated upward. This is consistent with the theoretical result. 3.3 Bubble behavior test in flowing water A purpose of the flowing water test is to confirm the relation between the buoyancy, the capillary pressure, and the drag force occurring in flowing water. This test is the final test for confirming gas tightness. Water flow was generated by changing the height of both head tanks. The hydraulic gradient was estimated by dividing the height difference of the head tanks by the gap width. At first, we injected the air bubble into the gap using an injector, but the injection disturbed the water flow. Therefore, in this test, hydrogen bubbles were introduced to the system by electrolysis. Fig. shows the relation between gap width and the hydraulic gradient at the critical condition when the air bubble begins to move. In case of a narrow gap, bubbles cannot move easily and seem to be caught in the narrow gap because of the large surface tension. For a gap width of 300 μm, a minimum hydraulic gradient of I > 2 was needed to move the bubbles. When the gap was wider, bubbles can move more easily, and the influence of the drag force was larger. For a gap width of 500 μm, bubbles could move in a hydraulic gradient of I <. For a bubble diameter of 8 mm, the hydraulic gradient in the upward and downward direction were equal, and the capillary effect was very small. Concerning bubble size, smaller bubbles cannot move easily. 5.E+08 Hydrauric gradient 4 Dmm Down 3 Dmm Up 2 D3mm Down 0 D3mm Up - D8mm Down -2 D8mm Up Gap width μm Cd.E+07.E+06.E+05.E+04.E+03.E+02.E+0.E+00.E-05 y = 89.77x E-04.E-03.E-02.E-0 Reynolds Number.E+00.E+0 Fig. -. Relationship between gap width and hydraulic gradient in water flowing test. Fig. -. Relationship between Reynolds number and drag coefficient. Referring to this result, for gas tightness, large bubbles and wide gap width are critical. At a 500 μm gap width, the largest bubble 8 mm in diameter does not float when the hydraulic gradient is around 0.3. This might suggest that the critical hydraulic gradient would be around 0.5, or at least smaller than.0. The following is the theoretical approach of determining gas tightness when considering buoyancy, capillary pressure, and drag. Buoyancy and capillary pressure were already evaluated by previous tests.

7 It is necessary to evaluate drag force, and drag force is estimated by Eq. (4). Cd in the narrow gap is special as the shape of bubble is flat. Cd is estimated according to the method used in a previous study on the water flow between parallel glass plates (S. Onishi et al., 200). Cd is determined using the following force balance equation as Eqs. (6), (7), and (8). = + (6) ( ) = (7) = ( ) (8) The Reynolds number is defined as in Eq. (9), referring to a previous study. Re : Reynolds number V : Bubble floating velocity in static water d : Equivalent diameter of bubble ν : Coefficient of kinematic viscosity t : Gap width = = (9) On the basis of the bubble behavior test in static water, the relationship between Cd and Re is as shown in Fig., and the equation of regression is as in Eq. () = () Fig. 2 shows gas tightness in relation to Fb and Fc + Fd. Fd is determined from the abovementioned equations. The vertical axis represents Fb/(Fc + Fd), and it shows a safety factor of gas tightness because Fb is the driving force of gas leakage and Fc + Fd is the suppressing force. The graphs show that gas tightness is more severe when the gap is wider. In the case of I = 0.5, gas tightness is kept at a gap width of at least mm. 4. Conclusions Through the above series of tests, the following were concluded. ) Though the model was simplified, it confirmed that gas tightness was secured in affection of hydraulic gradient. 2) The drag force from the flow of the groundwater and the capillary pressure, resulting from the surface tension, are contributing factors to the force resisting gas leakage in narrow gaps. 3) The capillary pressure of bubbles is roughly consistent with the results that the capillary pressure test of the parallel flat board provided. 4) The binding force by the theoretical capillary pressure matches with a limit state of bubble rise in static water test. 5) In the test with flowing water acting as a hydraulic gradient, drag force contributed to the degree of gas tightness, but in this study the value of drag itself was not evaluated but was calculated by inverse estimation through the Reynolds number. 6) Gas tightness is generalized on the basis of the assumption of inverse estimated drag force. 7) When the hydraulic gradient is greater than 0.5, gas tightness is maintained for a gap width of less than mm in a smooth parallel glass plate gap.

8 00 0 Slit width 2.0E E-04.0E-04.0E E Slit width 2.0E E-04.0E-04.0E E-04 Fb/(Fc+Fd) I=0 Fb/(Fc+Fd) I= Diameter of bubble mm 0. Diameter of bubble mm 00 0 Slit width 2.0E E-04.0E-04.0E E Slit width 2.0E E-04.0E-04.0E E-04 Fb/(Fc+Fd) Fb/(Fc+Fd) I=.0 I= Diameter of bubble mm Diameter of bubble mm Fig. 2. Gas tightness in parallel glass plate model. Acknowledgements Experimental data in this report were obtained in 998 and 999 as in-house R&D in order to clarify and understand gas tightness prior to the design of an LPG underground storage facility. The experimental data were not studied theoretically at the time; therefore, they were reviewed more theoretically under the instruction of Prof. Nishigaki of Okayama University. We thank the member who performed the original experiment to gather the data used in this study. References Aberg, B., 977, Prevention of Gas Leakage from Unlined Reservation in Rock: Storage in Excavated Rock Caverns, Proc. of Rock Store 77, Stockholm, Sweden Komada H., Nakagawa K., Kitahara., Hayashi M., 980, Study on Seepage Flow Through Surrounding Rock Mass of Unlined Underground Cavern For Petroleum Storage, Proceedings of JSCE No.300, Nakagawa K., Komada H., Miyashita K., Murata M., 986, Prevention of Leakage of Compressed Air Storage in Unlined Rock Caverns, Proceedings of JSCE No.370, Onishi S., Ebara M., Mori R., Sema K., 200, Hydraulic study bubbles rising through in water in narrow slit, Proceedings of JSCE No.69/Ⅱ-57, Tomiyama A., Hosokawa S., Ebara M., Miyanaga Y., Kawakubo Y., Kinoto H., 996, Terminal Velocity and Drag Coefficient of Single Air Bubbles in Stagnant Water Filling in Narrow Parallel Walls, Japanese J. Multiphase Flow Vol. No

Irrigation &Hydraulics Department lb / ft to kg/lit.

CAIRO UNIVERSITY FLUID MECHANICS Faculty of Engineering nd Year CIVIL ENG. Irrigation &Hydraulics Department 010-011 1. FLUID PROPERTIES 1. Identify the dimensions and units for the following engineering