Paper Title
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Abstract：The paper studies mainly the inter-beds’ effect on gas storage in salt caverns building with water solution. It sets up the inter-beds mathematics model based on the little flexibility lamella curve theory. By numerical simulation, it studies the inter-beds stress distributing law caused by own load and analyses inter-beds’ effect on cavern shape and time of building gas storage in salt caverns with water solution. The research indicates that the stress changes along with inter-beds’ thickness and length, inter-beds not only can control cavern shape, but also can reduce effectively time building gas storage in salt cavern. So gas storage in salt caverns should be built in salt stratum with no or few inter-beds.
Key words：Gas storage in salt caverns, Building with water solution, Inter-beds
1 Preface
Gas storage in salt caverns building with water solution is based on the theory of mining with water solution, it builds cavity by drawing out brine, the cavity is used to storage natural gas[1][2], that is the need to the energy strategic reserve and the season change. At present, the most commonly methods to build gas storage is oil blanket’s method. Building gas storage with oil blanket’s method is a main project building storage in single well. Figure1 is the sketch map.
Gas storage in salt caverns should be built in salt deposit with better rock salt purity. But if there are continuous distribution inter-beds in the salt deposit, such as gypsum, mud shale, dolomite and limestone, it will influence cavern’s shape and effectively time in building gas storage in salt caverns. So setting up the inter-beds mathematics model, studying the inter-beds stress distributing law caused by own load by numerical simulation, analysing inter-beds’s effect on cavern shape and time of gas storage in salt caverns is important to choose site and build gas storage in salt caverns with water solution.
2 Inter-beds’s mathematics model
2.1 Basic supposition
For rock salt stratum with inter-beds, the inter-beds’s geometry characteristic and mechanics characteristic are similar with the lamella curving question in the elasticity mechanics. According to the lamella curving model with the small amount of deflection, inter-beds in the cavity is regarded as uniform thickness circular lamella (Figure2). The load is gravity G, salt water buoyancy F and pressure P (Figure 3).
(1)
—Inter beds’s cross section area, —Uniformity load, —Inter beds’s thickness, —Outer radius, —Inside radius.
2.2 Basic equation
According to the elastic curved surface basic differential equation, it may result in the axial symmetry curving fundamental equation,as in Eq. (2) [3]:
(2)
Lamella flexible rigidity,—Uniformity load,—Lamella amount of deflection.
Inter beds is looked upon circular board with a hole (Fig.1), uniformity load ,The boundary condition is as follows:
，the surrounding boundary is fixed：
， (3)
，the inside boundary is free side ,the internal force is 0：
，， (4)
2.3 Basic equation’s solution
Based on inter-beds’s basic equation and boundary condition, it can get inter-beds’s stress.
(5)
(6)
(7)
Inter-beds’s stress is as follows：
(8)
(9)
(10)
(11)
Coefficient is as follows:
(12)
(13)
(14)
(15)
，—Normal stress；—Shearing stress；，—Bending moment；—Shearing force.
3 Inter-beds’s Stress distributed law
In order to analyze the inter beds’s influence on the gas storage in salt caverns building with water solution, it is necessary to study the inter-beds’s stress distribution law and understand the inter-bed’s normal stress and shearing stress changing law along with inter-bed’s length. As follows, it gets the inter-bed’s biggest normal stress and biggest shearing stress changing curve along with inter-bed’s length and thickness, the cavity radius.
(i) Curves of the inter-bed’s biggest normal stress and biggest shearing stress along with inter-bed’s length.
Figure4 expresses curves of the biggest normal stress and biggest shearing stress along with inter-bed’s length, when the cavity radius is 10 meters, inter-beds thickness is 2 meters. It can draw the result that the biggest normal stress and biggest shearing stress increases as inter-beds length increases, inter-beds is easy to break. So there are almost not too long inter-beds in the process of building gas storage in salt caverns.
(ii) Curves of the inter-bed’s biggest normal stress and biggest shearing stress along with inter-bed’s thickness.
Figure5 expresses curves of the biggest normal stress and biggest shearing stress along with inter-bed’s thickness, when the cavity radius is 20 meters, inter-beds length is 2 meters. It can draw the result that the biggest normal stress and biggest shearing stress decreases as inter-beds thickness increases .It shows that inter-beds is not easy to break if the thickness is big. So gas storage in salt caverns should be built in salt bed with no inter-beds or much thinner inter-beds.
(iii) Curves of the inter-bed’s biggest normal stress and biggest shearing stress along with the cavern radius.
Figure6 expresses curves of the biggest normal stress and biggest shearing stress along with the cavern radius, when the cavity length is 10 meters, inter-beds thickness is 4 meters. It can draw the result that the biggest normal stress and biggest shearing stress increases as the cavern radius increases, inter-beds is easy to break. So inter-beds’s influence to the caverns is less and less as the cavern volume increases.
4 Inter-beds’s influence on gas storage in salt caverns
According to the rock salt corrosion simulation study, it establishes the mathematical model of gas storage in salt caverns building with water solution and compiles the software to simulate[[5]. According to a large of numerical simulation, as follows, it analyses inter-beds’s influence on cavity body stability and the time to building gas storage.
4.1Inter-beds influence on the cavity stability
The cavity stability is depended not only by the geologic structure characteristic and the stratum attribute, but also by the cavity geometry shape stability. According to the overseas experience of building gas storage, the cavity body with pear shape conforms to the stable requirement. Figure7 is the result of simulating and calculating gas storage in stratum with different number inter-beds based on the solving software.
It shows that inter-beds influences the gas storage cavity shape greatly. If no inter-beds, the cavity boundary continuity is very well, the shape is the pear shape, the cavity body stability is good. With the inter-beds number increasing, the cavity boundary appears not regularly any more, the cavity body shape is the cylinder shape, the cavity body stability is changing bad. The simulation study result indicates that inter-beds destroys the cavity boundary continuity in the cavity body solving process, and it unbenefits to construct the cavity and control the cavity shape. Moreover, the paper has studied the inter-beds influence of thickness and number on the cavity body stability.
4.2Inter-beds influence on the building time
In the process to build gas storage, there are the diffusing and the counter-flow phenomenon. In corrosion boundary layer, the fluid transportation performs mainly by the solution diffusion. Near the circulation tube, the fluid transportation mainly depends on the forced convection function. Between corrosion boundary layer and circulation tube, the fluid transportation mainly depends on the natural convection. The inter-beds existence delays the fluid transportation and causes the fluid in the cavity not to exchange fully. At the same time , it reduces the solution speed of salt, thus increases the time to build the gas storage in rock salt. For example, when building 200,000 m3 cavern, the relation between the inter-beds quantity and the time building gas storage can be shown from table 1.
Table 1 The Relation of Inter-beds’s Quantity and Building Time
Inter-beds number（Entries） / Building time
（Day）
0 / 605
1 / 641
2 / 668
3 / 683
5 Conclusions
(i)It sets up the inter-beds mathematics model of building gas storage in rock salt caverns based on the little flexibility lamella curve theory. By analyzing inter-beds stress distributing law, it can draw the conclusions: the biggest normal stress and biggest shearing stress increases as inter-beds length increases, and decreases as inter-beds thickness increases, and increased as the cavern radius increases. In later period of constructing the gas storage in rock salt , the inter-beds has less influence to the salt cavern.
(ii) The rock salt gas storage should be built in the stratum with no or few inter-beds and the inter-beds thickness is small. Building gas storage in the stratum with few inter-beds is in favor of controlling the cavern shape and increasing the solution speed and reducing the time to build caverns. After dissolving the cavity, there are no single inter-beds in the cavern.
References
[1]Y.Guangjie, R. Shen, ..Review of Underground Gas Storage in the Bedded Salt Deposit in China. SPE 100386，2006
[2]Gang Han，Mike Bruno.. Gas Storage and Operations in Single-Bedded Salt Caverns: Stability Analyses. SPE99520，2007（8）：368-376
[3]Wu Jia-long.Elastic Mechanics. Shanghai: Published by Tongji University,1986 :83～88 (in Chinese)
[4]Ban Fan-sheng , Gao Shu-sheng, Shan Wen-wen& Xiong Wei . The research of rock salt dissolving model of gas storage in salt caverns building with water solution. China: Journal of Liaoning Technical University, 2005, 24 (suppl):102-104 (in Chinese)
[5]Ban, Fansheng, Shan Wenwen, Gao Shusheng &Zhu Weiyao. Optimization of operating parameters for salt dome gas storages formed by water solution. China: Natural Gas Industry, 2005,25(12):108-110(in Chinese)
Authors in Brief
ZHANG Huaiyou – Dean. Professor. Mainly engaging irrigation and underground water resources research and academic activities. Email: Ph: 86 21 5444 5000
HU Li – Professor Assistant. Teacher in Agriculture Irrigation Faculty. Also focusing on irrigation and environment integration study. Email: Ph: 86 139 5448 5444