Paper Title
First author, Second author
Address and e-mail
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
Wate
Wate
Brine
water solution is based on the theory of
Oil
r
r
mining with water solution, it builds cavity by
Protective
drawing out brine, the cavity is used to
Protective
Central
casing
Central
casing
storage natural gas[1][2], that is the need to
tube
tube
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
Inner
Inner
storage in single well. Figure1 is the sketch
tube
tube
map.
Gas storage in salt caverns should be
built in salt deposit with better rock salt
a. Direct circulation
b. Reverse circulation
Figure 1 Building gas storage with oil blanket
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).
PG  F
q
(1)
s
s —Inter beds’s cross section area, q —Uniformity load, t —Inter beds’s thickness, a —Outer
radius, b —Inside radius.
z
F
r
a
o b
t
G
P
Figure 2 Inter-beds sketch map in the cavern
Figure 3 Inter-beds sketch map under the force
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]:
d 2 1 d d 2 w 1 dw
q
(2)
( 2
)( 2 
)
r dr dr
r dr
D
dr
Lamella flexible rigidity D 
Et 3
, q —Uniformity load, w —Lamella amount of deflection.
12(1   2 )
Inter beds is looked upon circular board with a hole (Fig.1), uniformity load q  q0 ,The boundary
condition is as follows:
r  a ，the surrounding boundary is fixed：
dw
(3)
( w) r  a  0 ， ( ) r  a  0
dr
r  b ，the inside boundary is free side ,the internal force is 0：
M r r b  0 ， M r b  0 ， Qr r b  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.
r 
12 M r
z
t3
(5)
 
12M 
z
t3
(6)
 rz 
6Qr t 2
(  z2 )
t3 4
(7)
Inter-beds’s stress is as follows：
Mr 
C1
3 
(1   ) D  (3   )C2 D  (1  2  )C2 D ln r  2(1   )C3 D 
q0 r 2
2
16
r
M  
C1
1  3
(1   ) D  (1  3 )C2 D  (2   )C2 D ln r  2(1   )C3 D 
q0 r 2
16
r2
(8)
(9)
4C2 D q0 r

r
2
 Q  0
Qr  
(10)
M r
(11)
Coefficient is as follows:
q0 b 4
16 D
q b2
C2   0
8D
q b2
C3  0 (1  2ln b)
16D
C1  
C4 
(12)
(13)
(14)
q0
[4b 4 ln a  8a 2b 2 ln a  a 4  4a 2b 2 (1  2 ln b)]
64 D
(15)
3 Inter-beds’s Stress distributed
law
Stress(Mpa)
 r ，   —Normal stress；  rz —Shearing stress； M r ， M  —Bending moment； Qr —Shearing force.
10
8
6
4
2
0
Normal stress
Shearing stress
Stress(Mpa)
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
0 1 2 3 4 5 6 7 8 9 10 11
stress and shearing stress changing law
Inter-beds length(m)
along with inter-bed’s length. As follows, it
gets the inter-bed’s biggest normal stress
Fig.4
biggest
and stress
stress
FigureThe
4 The
biggestshearing
shearing strength
strength and
and biggest shearing stress changing curve
distributingcurve
curvealong
along the inter-beds
distributing
inter-bedslength
length
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
70
Normal stress
is 10 meters, inter-beds thickness is 2
60
meters. It can draw the result that the
Shearing stress
50
biggest normal stress and biggest
40
shearing stress increases as inter-beds
30
length increases, inter-beds is easy to
20
break. So there are almost not too long
10
inter-beds in the process of building gas
0
storage in salt caverns.
0
0.5
1
1.5
2
2.5
3
3.5
4
(ii) Curves of the inter-bed’s
Inter-beds thickness(m)
biggest normal stress and biggest
Fig.5 The
biggest
strengthstrength
and stress
Figure
5 Theshearing
biggest shearing
anddistributing
stress
shearing stress along with inter-bed’s
curve along
inter-beds
thickness
distributing
curvethe
along
the inter-beds
thickness
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
Stress(Mpa)
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
70
Normal stress
biggest normal stress and biggest
60
Shearing stress
shearing stress along with the cavern
50
radius, when the cavity length is 10
40
meters, inter-beds thickness is 4 meters.
30
It can draw the result that the biggest
20
10
normal stress and biggest shearing
0
stress increases as the cavern radius
increases, inter-beds is easy to break.
0
0.5
1
1.5
2
2.5
3
3.5
4
So inter-beds’s influence to the caverns
Inter-beds thickness(m)
is less and less as the cavern volume
Fig.6Figure
The biggest
shearing
strengthstrength
and stress
6 The biggest
shearing
anddistributing
stress
increases.
distributing
curve
along
the
cavern
radius
curve along the cavern radius
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
a.0
b.1
c.2
d.3
Figure7 The salt cavern configuration in different inter-beds
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）
0
1
2
3
Building time
（Day）
605
641
668
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: Huanyuai@ubt.edu.cn Ph: 86 21 5444 5000
HU Li – Professor Assistant. Teacher in Agriculture Irrigation Faculty. Also focusing on irrigation and
environment integration study. Email: Huli2009@ubt.edu.cn Ph: 86 139 5448 5444