Abstract
The inter-cavern containment property assessment is one of the critical issues of the underground water-sealed oil storage facility and its result determines whether the mixing of different oil products occurs or not. In this study, an inter-cavern containment property assessment method combining discrete fracture network analysis with graph theory was proposed. In the method, the discrete fracture network analysis is adopted to obtain the distribution of the hydraulic head in the rock mass and the graph theory is used to determine the hydraulic connectivity between the two adjacent caverns. The influences of cavern spacing, liquid level differences, water curtain pressures, and geometric parameters on the inter-cavern containment property were investigated based on the assessment method. The results indicated that the inter-cavern containment property could be guaranteed by increasing cavern spacing (d), water curtain pressure (P), or decreasing liquid level differences (Δh), fracture trace length, and linear density. To compare the influence of different factors on the inter-cavern containment property, a parameter p was defined to represent the connectivity of fracture networks between caverns according to the connected relations in graph theory. By comparing changed connectivity parameter p, the influences of cavern spacing, liquid level differences, and water curtain pressures on the inter-cavern containment property were ranked as follows: Δh > d > P. Based on the Huangdao underground oil storage caverns, the inter-cavern containment properties were discussed. The result showed that the cavern spacing should be greater than 40 m, the water curtain pressure should not be greater than 130 kPa and the liquid level difference should be less than 12 m to ensure inter-cavern containment properties, which can offer good guidance for the design and operation of caverns.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- A:
-
Adjacency matrix
- C:
-
Relation matrix
- D:
-
Shortest distance matrix
- d:
-
Cavern spacing
- e:
-
Hydraulic aperture
- g:
-
Gravity
- H:
-
Piezometric head
- L:
-
Parameter to determine the connection
- M, N:
-
Number of nodes in the starting and ending boundaries, respectively
- P:
-
Water curtain pressures
- P1 :
-
Pressure in the fluid
- p:
-
Connectivity parameter
- Q:
-
Source or sink flow rate
- q:
-
Flow rate in fracture
- ux, uy, uz :
-
Flow velocities in x, y, and z directions, respectively
- W:
-
Weight matrix
- w:
-
Fracture thickness
- z:
-
Elevation head
- Δh:
-
Liquid level differences
- ρ:
-
Fluid density
- μ:
-
Fluid viscosity
- μl, μD :
-
Mean of fracture trace length and diameter, respectively
- σl, σD :
-
Standard deviation of fracture trace length and diameter, respectively
References
Aberg B (1977) Prevention of gas leakage from unlined reservoirs in rock. Pergamon, Oxford
Azarafza M, Akgün H, Asghari-Kaljahi E (2018) Stochastic geometry model of rock mass fracture network in tunnels. Q J Eng GeolHydrogeol 51:379–386. https://doi.org/10.1144/qjegh2017-136
Baghbanan A, Jing L (2007) Hydraulic properties of fractured rock masses with correlated fracture length and aperture. Int J Rock Mech Min Sci 44:704–719. https://doi.org/10.1016/j.ijrmms.2006.11.001
Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, Cambridge
Berkowitz B (1995) Analysis of fracture network connectivity using percolation theory. Math Geol 27:467–483. https://doi.org/10.1007/BF02084422
Berkowitz B, Balberg I (1993) Percolation theory and its application to groundwater hydrology. Water Resour Res 29:775–794. https://doi.org/10.1029/92WR02707
Berkowitz B, Bour O, Davy P, Odling N (2000) Scaling of fracture connectivity in geological formations. Geophys Res Lett 27:2061–2064. https://doi.org/10.1029/1999GL011241
Bour O, Davy P (1997) Connectivity of random fault networks following a power law fault length distribution. Water Resour Res 33:1567–1583. https://doi.org/10.1029/96WR00433
Bour O, Davy P (1998) On the connectivity of three-dimensional fault networks. Water Resour Res 34:2611–2622. https://doi.org/10.1029/98WR01861
Comen TH, Leiserson CE, Rivest RL, Stein C (2005) Introduction to algorithms. The MIT press, London
Dai Y, Zhou Z (2015) Steady seepage simulation of underground oil storage caverns based on Signorini type variational inequality formulation. Geosci J 19:341–355. https://doi.org/10.1007/s12303-014-0041-7
de Abreu NMM (2007) Old and new results on algebraic connectivity of graphs. Linear Algebra Appl 423:53–73. https://doi.org/10.1016/j.laa.2006.08.017
Ghotbi Ravandi E, Rahmannejad R, Karimi-Nasab S, Sarrafi A (2016) Sensitivity analysis of effective parameters on water curtain performance for crude oil storage in Iranian URC using the 2k factorial design and numerical modeling. Tunn Undergr Space Technol 58:247–256. https://doi.org/10.1016/j.tust.2016.06.001
Goodall DC, Aberg B, Brekke TL (1988) Fundamentals of gas containment in unlined rock caverns. Rock Mech Rock Eng 21:235–258. https://doi.org/10.1007/bf01020278
Hamberger U (1991) Case history: Blowout at an LPG storage cavern in Sweden. Tunn Undergr Space Technol 6:119–120. https://doi.org/10.1016/0886-7798(91)90012-S
Han X, Chen J, Wang Q, Li Y, Zhang W, Yu T (2016) A 3D fracture network model for the undisturbed rock mass at the Songta dam site based on small samples. Rock Mech Rock Eng 49:611–619. https://doi.org/10.1007/s00603-015-0747-5
Hirmand MR, Vahab M, Papoulia KD, Khalili N (2019) Robust simulation of dynamic fluid-driven fracture in naturally fractured impermeable media. Comput Methods Appl Mech Eng 357:112574. https://doi.org/10.1016/j.cma.2019.112574
Hu C, Chen H, Chen G, Liu J (2019) Detection of low-efficiency zones of water curtain system for underground LPG storage by a discrete fracture network model. Environ Earth Sci 78:11. https://doi.org/10.1007/s12665-018-8006-1
Itasca I (2016) Three-dimensional distinct element code user’s guide. Mineapolis, Minnestoa, USA
Jena R, Pradhan B (2020) A Model for visual assessment of fault plane solutions and active tectonics analysis using the global centroid moment tensor catalog. Earth Syst Environ 4:197–211. https://doi.org/10.1007/s41748-019-00142-9
Jing L, Stephansson O (2007) Fundamentals of discrete element method for engineering: theory and applications. Elsevier, Amsterdam, pp 399–444
Khisamitov I, Meschke G (2019) Configurational-force interface model for brittle fracture propagation. Comput Methods Appl Mech Eng 351:351–378. https://doi.org/10.1016/j.cma.2019.03.029
Lee E, Lim J-W, Moon HS, Lee K-K (2015) Assessment of seawater intrusion into underground oil storage cavern and prediction of its sustainability. Environ Earth Sci 73:1179–1190. https://doi.org/10.1007/s12665-014-3473-5
Li Z, Wang K, Wang A, Liu H (2009) Experimental study of water curtain performance for gas storage in an underground cavern. J Rock Mech Geotech Eng 1:89–96. https://doi.org/10.3724/SP.J.1235.2009.00089
Li S, Wang Z, Ping Y, Zhou Y, Zhang L (2014a) Discrete element analysis of hydro-mechanical behavior of a pilot underground crude oil storage facility in granite in China. Tunn Undergr Space Technol 40:75–84. https://doi.org/10.1016/j.tust.2013.09.010
Li SC, Xu ZH, Ma GW (2014b) A graph-theoretic pipe network method for water flow simulation in discrete fracture networks: GPNM. Tunn Undergr Space Technol 42:247–263. https://doi.org/10.1016/j.tust.2014.03.012
Li Z, Xue Y, Li S, Qiu D, Su M, Zhao Y, Zhou B (2019) An analytical model for surrounding rock classification during underground water-sealed caverns construction: a case study from eastern China. Environ Earth Sci 78:602. https://doi.org/10.1007/s12665-019-8606-4
Li W, Wang Z, Qiao L, Liu H, Yang J (2020a) Determination of the optimal spacing of water curtain boreholes for underground oil storage from the perspective of percolation theory. Tunn Undergr Space Technol 97:103246. https://doi.org/10.1016/j.tust.2019.103246
Li X, Li D, Xu Y, Feng X (2020b) A DFN based 3D numerical approach for modeling coupled groundwater flow and solute transport in fractured rock mass. Int J Heat Mass Transf 149:119179. https://doi.org/10.1016/j.ijheatmasstransfer.2019.119179
Li B, Bao R, Wang Y, Liu R, Zhao C (2021) Permeability evolution of two-dimensional fracture networks during shear under constant normal stiffness boundary conditions. Rock Mech Rock Eng 54:409–428. https://doi.org/10.1007/s00603-020-02273-2
Lim J-W, Lee E, Moon HS, Lee K-K (2013) Integrated investigation of seawater intrusion around oil storage caverns in a coastal fractured aquifer using hydrogeochemical and isotopic data. J Hydrol 486:202–210. https://doi.org/10.1016/j.jhydrol.2013.01.023
Liu H, Qiao L, Wang S, Li W, Liu J, Wang Z (2021) Quantifying the containment efficiency of underground water-sealed oil storage caverns: method and case study. Tunn Undergr Space Technol 110:103797. https://doi.org/10.1016/j.tust.2020.103797
Ning ZX, Xue YG, Su MX, Qiu DH, Zhang K, Li ZQ, Liu YM (2021) Deformation characteristics observed during multi-step excavation of underground oil storage caverns based on field monitoring and numerical simulation. Environ Earth Sci 80:222. https://doi.org/10.1007/s12665-021-09496-
Park JJ, Jeon S, Chung YS (2005) Design of Pyongtaek LPG storage terminal underneath Lake Namyang: a case study. Tunn Undergr Space Technol 20:463–478. https://doi.org/10.1016/j.tust.2005.03.001
Qiao L, Li S, Wang Z, Tian H, Bi L (2016) Geotechnical monitoring on the stability of a pilot underground crude-oil storage facility during the construction phase in China. Measurement 82:421–431. https://doi.org/10.1016/j.measurement.2016.01.017
Qiao L, Li C, Wang Z, Wang X, Guo J (2022) Seawater intrusion into an underground water-sealed oil storage cavern: effects of water curtain system, hydraulic conductivity and dispersivity. Tunn Undergr Space Technol 126:104542. https://doi.org/10.1016/j.tust.2022.104542
Rehbinder G, Karlsson R, Dahlkild A (1988) A study of a water curtain around a gas store in rock. Appl Sci Res 45:107–127. https://doi.org/10.1007/bf00386207
Shi L, Zhang B, Wang L, Wang H, Zhang H (2018) Functional efficiency assessment of the water curtain system in an underground water-sealed oil storage cavern based on time-series monitoring data. Eng Geol 239:79–95. https://doi.org/10.1016/j.enggeo.2018.03.015
Tonon F, Chen S (2007) Closed-form and numerical solutions for the probability distribution function of fracture diameters. Int J Rock Mech Min Sci 44:332–350. https://doi.org/10.1016/j.ijrmms.2006.07.013
Wang Z, Li S, Qiao L (2015) Assessment of hydro-mechanical behavior of a granite rock mass for a pilot underground crude oil storage facility in China. Rock Mech Rock Eng 48:2459–2472. https://doi.org/10.1007/s00603-015-0715-0
Wang Z, Li W, Bi L, Qiao L, Liu R, Liu J (2018a) Estimation of the REV size and equivalent permeability coefficient of fractured rock masses with an emphasis on comparing the radial and unidirectional flow configurations. Rock Mech Rock Eng 51:1457–1471. https://doi.org/10.1007/s00603-018-1422-4
Wang Z, Li W, Qiao L, Liu J, Yang J (2018b) Hydraulic properties of fractured rock mass with correlated fracture length and aperture in both radial and unidirectional flow configurations. Comput Geotech 104:167–184. https://doi.org/10.1016/j.compgeo.2018.08.017
Wang Z, Bi L, Kwon S, Qiao L, Li W (2020) The effects of hydro-mechanical coupling in fractured rock mass on groundwater inflow into underground openings. Tunn Undergr Space Technol 103:103489. https://doi.org/10.1016/j.tust.2020.103489
Wang B, Feng Y, Zhou X, Pieraccini S, Scialò S, Fidelibus C (2022) Discontinuous boundary elements for steady-state fluid flow problems in discrete fracture networks. Adv Water Resour 161:104125. https://doi.org/10.1016/j.advwatres.2022.104125
Warburton PM (1980) A stereological interpretation of joint trace data. Int J Rock Mech Min Sci Geomech Abstr 17:181–190. https://doi.org/10.1016/0148-9062(80)91084-0
West DB (2001) Introduction to graph theory. Pearson, New York
Wilson RJ (1996) Introduction to graph theory. Addison Wesley Longman, London
Xu ZH, Ma GW, Li SC (2014) A graph-theoretic pipe network method for water flow simulation in a porous medium: GPNM. Int J Heat Fluid Flow 45:81–97. https://doi.org/10.1016/j.ijheatfluidflow.2013.11.003
Xu ZH, Gao B, Li SC, Zhang LW, Zhao SL, Shi XS (2018) A groundwater seal evaluation method based on water inflow for underground oil storage caverns. Tunn Undergr Space Technol 82:265–277. https://doi.org/10.1016/j.tust.2018.08.030
Xu X, Wu Z, Sun H, Weng L, Chu Z, Liu Q (2021) An extended numerical manifold method for simulation of grouting reinforcement in deep rock tunnels. Tunn Undergr Space Technol 115:104020. https://doi.org/10.1016/j.tust.2021.104020
Xue Y, Ning Z, Kong F, Qiu D, Liu Y, Jiang X (2022) Water-sealing performance assessment of the water curtain system in underground water-sealed oil-storage caverns. Environ Earth Sci 81:172. https://doi.org/10.1007/s12665-022-10294-z
Yang C, Wang T, Li Y, Yang H, Li J, Da Qu XuB, Yang Y, Daemen JJK (2015) Feasibility analysis of using abandoned salt caverns for large-scale underground energy storage in China. Appl Energy 137:467–481. https://doi.org/10.1016/j.apenergy.2014.07.048
Zhang L, Einstein HH (2000) Estimating the intensity of rock discontinuities. Int J Rock Mech Min Sci 37:819–837. https://doi.org/10.1016/S1365-1609(00)00022-8
Zhao J, Bergh-Christensen J (1996) Construction and utilization of rock caverns in Singapore part D: two proposed cavern schemes. Tunn Undergr Space Technol 11:85–91. https://doi.org/10.1016/0886-7798(96)00057-0
Zhao H, Chen J (2005) Starching for seepage path of 3D network in fracture rock masses. Chin J Geotech Eng 24:622–627
Acknowledgements
This study was financially supported by the National Natural Science Foundation of China with No. 51779045 and 42177157; Liao Ning Revitalization Talents Program with No. XLYC1807029; the Fundamental Research Funds for the Central Universities with Nos. N2001025, N2001026, and N2101005; and Liaoning Natural Science Foundation with Nos. 2019-MS-114 and 2019-YQ-02.
Funding
This manuscript was supported by National Natural Science Foundation of China, 51779045, Zhechao Wang, 42177157, Liping Qiao, Liao Ning Revitalization Talents Program, XLYC1807029, Zhechao Wang, Fundamental Research Funds for the Central Universities, N2001025, Zhechao Wang, N2001026, Zhechao Wang, N2101005, Liping Qiao, Liaoning Natural Science Foundation, 2019-MS-114, Liping Qiao, 2019-YQ-02, and Zhechao Wang.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
This manuscript has not been published or presented elsewhere in part or in entirety and is not under consideration by another journal. The authors declare that there is no conflict of interest associated with this publication. All the authors read and approved the final manuscript.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Qiao, L., Li, W., Wang, Z. et al. Assessment of inter-cavern containment property of underground water-sealed oil storage caverns combining discrete fracture network analysis with graph theory. Environ Earth Sci 81, 442 (2022). https://doi.org/10.1007/s12665-022-10576-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12665-022-10576-6