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oil storage in bedded salt
Journal Pre-proof Construction modeling and shape prediction of horizontal salt caverns for gas/oil storage in bedded salt Li Jinlong, Yang Chunhe, Shi Xilin, Xu Wenjie, Li Yinping, Jaak J.K. Daemen PII:
S0920-4105(20)30151-0
DOI:
https://doi.org/10.1016/j.petrol.2020.107058
Reference:
PETROL 107058
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 11 July 2019 Revised Date:
6 January 2020
Accepted Date: 9 February 2020
Please cite this article as: Jinlong, L., Chunhe, Y., Xilin, S., Wenjie, X., Yinping, L., Daemen, J.J.K., Construction modeling and shape prediction of horizontal salt caverns for gas/oil storage in bedded salt, Journal of Petroleum Science and Engineering (2020), doi: https://doi.org/10.1016/j.petrol.2020.107058. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Cavern shape mapped by sonar
Unknown part
Mapped cavern
Simulated cavern
HA-5
Porous Insoluble sediments
HA-5
HA-4
Suggested gas injection
Modeling Extra storage space
Unknown part
Borehole
Suggested brine discharge
A third open cavern
Through the modeling of a horizontal salt cavern (HA4-5 in China), the shape is successfully predicted to evaluate its capacity and stability before it is served as a gas storage. A third open cavern is simulated and then detected, which is suggested to be used for brine discharge to increase the storage capacity.
HA-4
1
Construction modeling and shape prediction of horizontal salt
2
caverns for gas/oil storage in bedded salt
3
Li Jinlonga, Yang Chunheb, Shi Xilinb*, Xu Wenjiea*, Li Yinpingb, Jaak J.K. Daemenc
4
a
MOE
Key
Laboratory
of
Soft
Soils
and
Geoenvironmental
Engineering,
5
Center for Hypergravity Experimental and Interdisciplinary Research, Zhejiang University,
6
Hangzhou 31005, China.
7
b State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock
8
and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, Hubei, China.
9
c Mackay School of Earth Sciences and Engineering, University of Nevada, Reno, NV, USA
10
* Correspondence and requests for materials should be addressed to Shi X.L. (email:
11
[email protected]) or Xu W.J. (email: [email protected])
12
Abstract
13
Construction modeling and shape prediction are significant for the parameters
14
optimization and capacity prediction of a horizontal salt cavern gas/oil storage.
15
However, most previous studies concentrate on the middle segment of the cavern, and
16
the insoluble substances are ignored. The actual shapes of the horizontal salt caverns
17
in bedded salt remain unknown. Here a coupled model is proposed for the
18
construction of a horizontal cavern. A composite structural mesh is presented to
19
describe the development of three segments of the cavern. The equations of the
20
salt-brine mass transfer rate and boundary movements are introduced. A simplified
21
flow and concentration field model is presented. The accumulation of the insoluble
22
substances is firstly considered in a horizontal cavern. A VC++ program using the 1
1
finite volume method is developed to obtain the numerical solution of the model and
2
as a construction design tool for the horizontal salt caverns. The reliability of the
3
model and program has been confirmed by comparisons with laboratory experiments.
4
The shape of a field horizontal cavern HA4-5 in Huai’an, China is successfully
5
simulated. The simulation results coincide well with the field data. It is found that the
6
horizontal cavern is actually U-shaped and there is an undetected open cavern in the
7
middle segment. This cavern is suggested to be used as a non-clogging de-brining
8
pool during gas/oil injection and brine discharge. The brine in the pores of the
9
insoluble sediments will be replaced by gas/oil and the storage capacity will be
10
multiplied. The finding promises a broad prospect for the horizontal salt cavern gas
11
storage in bedded salt.
12
Keywords: Bedded salt rocks; Natural gas storage; Horizontal cavern; Cavern
13
Leaching; Mathematical model; Insoluble Sediments
14
2
1
1. Introduction
2
Salt cavern underground storage is widely used for natural gas peak shaving
3
(Yang et al., 2015; Qiao et al. 2020a) and strategic petroleum reserve (Niu et al., 2015;
4
Zhang et al., 2017), for salt rock has low permeability (Liu et al., 2016, Zhang et al.
5
2016) and good rheological properties (Li et al., 2014; Fan et al., 2019). Compared
6
with other underground gas storages (Lawal et al., 2014), salt caverns have higher
7
injection-production rate and daily gas/oil output. In addition, since salt has stable
8
chemical properties, salt caverns are suitable for compressed air, H2 or CO2 storage
9
(Bai et al., 2014; Lordache et al., 2019; Qiao and Yang, 2019a; Qiao et al. 2020b) and
10
radioactive waste disposal (Shi et al., 2015) as well. Usually, a salt cavern is
11
constructed in underground salt formations by water solutioning, or ‘leaching’.
12
Usually a vertical construction method is used. A borehole is drilled and in it two
13
concentric tubes are placed (Fig. 1a), through which fresh water is injected and brines
14
are discharged (Ge et al., 2019a, 2019b). The insoluble sediments accumulate on the
15
cavern bottom during the leaching (Li et al. 2019a, 2020a). After 5-10 years of
16
dissolution, a slim and tall salt cavern develops, the volume of which can reach
17
millions of cubic meters in salt domes (Bérest et al., 2001). However, in bedded salt
18
formations (e.g. in China, Canada, and the US), it is hard to develop a tall and slim
19
vertical cavern, since there are many thick insoluble interlayers (Fig. 1b), preventing
20
the cavern from growing upward (Chen et al., 2019).
3
(a) Brines
Water
Casing Outer tube
(b)
Injection: direct well Injection: deviated well
Insoluble interlayers
Tube
Blanket pad Inner tube
Deviated segment Brines
Direct segment Middle segment
Insoluble sediments Insoluble sediments Salt dome
Bedded salt
Initial borehole
1 2
Figure 1 Schematic illustration of the construction method of salt caverns. a Vertical cavern. A
3
vertical cavern uses inner and outer tubes for water injection and brines production. b Horizontal
4
cavern.
5
Recently, a horizontal leaching method is attracting more and more attention (Liu
6
et al., 2017; Yang et al., 2016; Chen et al. 2020; Li et al. 2020b). A vertical borehole
7
name “direct well” is firstly drilled, and then a “deviated well” is drilled and
8
connected with the direct well (Fig. 1b). The distance between them can be hundreds
9
of meters. Tubes are placed in the two boreholes and are used for alternate water
10
injection and brines production (Xing et al., 2015), instead of two concentric tubes in
11
one borehole. A horizontal cavern includes three segments, a deviated segment, a
12
middle segment and a direct segment. Compared to the vertical cavern, the horizontal
13
cavern has a larger dissolution area and thus a higher leaching rate. Therefore, Liu et
14
al. (2017, 2019) and Yang et al. (2016) thought that the horizontal cavern is more
15
suitable for developing larger storage caverns in bedded salt in China.
16
There are many old horizontal caverns left by salt mining industry in China, they
17
have strong potential to be used as underground gas storages (UGSs) (Yang et al.,
4
1
2016), since they are close to the gas consumption area and the gas pipelines (Fig. 2a).
2
For example, there are about 350 mined horizontal salt caverns in Huai’an Salt, the
3
available storage space is larger than 200 million cubic meters. (a)
Pingdingshan Qianjiang
Huai’an Jintan Yunying Zhangshu
Gas consumption density Gas pipeline
Salt cavern UGS Salt cavern UGS (in construction) Salt mine (most use horizontal leaching)
(b) Detected deviated segment (HA-5) Detected direct segment（ HA-4） -1330m
270m
???
Borehole
Unknown middle segment -1490m
4 5
Figure 2 Horizontal salt caverns in mainland China. a Bedded salt mines have strong potential to
6
be used as UGSs in mainland China. b The evaluation and construction of the horizontal salt
7
cavern UGSs are delayed, since the sonar mapping cannot find the complete shape of cavern
8
HA4-5 in Huai’an Salt in June, 2017 (Shi et al., 2017).
9
Before used as a UGS, shape data is essential for the stability analysis (Wang et
10
al. 2016), airtightness analysis (Li et al. 2019b) and capacity evaluation of the salt
11
cavern. However, during the detection by sonar mapping, the horizontal salt caverns 5
1
have not been completely mapped (e.g. cavern HA4-5 (Shi et al., 2017) in Fig. 2b).
2
Only two separate caverns (HA-4 and HA-5) are mapped, while the middle segment is
3
unknown. The shape of the horizontal cavern has been assumed to be shaped like a
4
dumbbell as in salt domes (Colomé et al., 2010), but the 270 m long part in the middle
5
is “missing”. The reason is that the content of the insoluble substances reaches up to
6
45% in the bedded salt formations, these insoluble substances accumulated on the
7
cavern bottom (Li et al., 2019a) and filled the middle segment during construction.
8
The sonar cannot transverse these insoluble sediments, thus the middle segment
9
cannot be mapped. The old horizontal caverns cannot be used as UGS, since the shape
10
data is unknown.
11
A reliable construction modeling is greatly needed for the shape prediction and
12
stability/capacity evaluation of the old mined horizontal caverns. In addition, during
13
the new construction of horizontal salt caverns, modeling is needed for the design and
14
control of the caverns. Technological parameters, including injection flow rate,
15
injection position, and injection time in each leaching stages, will be optimized to
16
obtain a better shape with larger gas storage capacity and better stability.
17
However, the construction modeling of a horizontal salt cavern is much more
18
complicated than that of a vertical cavern, and the relative studies are rare. In 1995,
19
Kunstman and Urbancayk (1995) pointed out several difficulties in the modeling of
20
horizontal leaching, including the moving boundary, brines concentration/flow field
21
distribution, and mesh method of the horizontal cavern. The horizontal cavern has
22
three parts as a deviated segment, a middle segment and a direct segment (Fig. 1b). 6
1
The axisymmetric assumption of a vertical cavern (Nolen et al., 1974; Kunstman and
2
Urbanczyk, 2009; Li et al., 2018) is not suitable for a horizontal cavern. Saberian
3
(1995) firstly simulated the development of the middle segment of a horizontal cavern
4
by using a horizontal cylindrical grid. Russo (1995) presented a program named
5
HORSMIC to simulate the shape of the horizontal cavern, he concentrated on the
6
middle segment as well. Gronefeld and Saalbach (1998) used Darcy’s law to simplify
7
the complex flow field, which has greatly reduced the calculation efforts. However,
8
the shape prediction has not been verified. Liu et al. (2017, 2019) leached a horizontal
9
salt cavern in a pure salt sample, and investigated the serviceability and safety of
10
horizontal salt caverns by using mechanical stability analysis. The numerical shape
11
modeling is not involved.
12
The simulation and shape prediction of a horizontal cavern remain
13
unaccomplished in bedded salt. The reason is that the lateral developments of the
14
deviated and direct segments of a horizontal cavern are ignored in most
15
afore-mentioned studies. Considering the horizontal cavern starts from a horizontal
16
borehole, a horizontal cylindrical mesh is mostly used to trace the moving boundary
17
of the cavern (Saberian, 1995; Russo, 1995). However, the lateral developments of the
18
two ends of the cavern cannot be simulated. In addition, the insoluble substances are
19
not properly considered. Most previous studies have made assumptions that the salt is
20
pure (Kunstmann and Urbanczyk, 1995; Saberian, 1995; Russo, 1995; Gronefeld and
21
saalbach, 1998). However, there are many insoluble substances in salt formations and
22
its content can be pretty high (45% in Huai’an Salt) in bedded salt (Wang et al., 2016). 7
1
This assumption brings large deviations, e.g. the missing of the middle part of HA4-5
2
(Fig.2b) cannot be explained by current models. Without effective modeling for
3
construction design and shape prediction, the usage of horizontal caverns as gas
4
storage is seriously delayed.
5
In this study, a simulation model of horizontal salt caverns with moving
6
boundary is proposed, using theoretical methods and empirical assumptions. A novel
7
composite structural mesh is proposed to describe the development of the deviated,
8
middle and direct segments of the horizontal cavern. The empirical equations of the
9
salt-brine mass transfer rate are introduced. The coupled equations of the brines
10
flow/concentration field, the boundary movements and the accumulation of the
11
insoluble sediments in the three segments of the cavern are derived respectively. A
12
VC++ program is developed for the numerical solution of the model, using the finite
13
volume method. To verify the proposed model, a leaching experiment has been
14
conducted in the laboratory and the results are compared with the simulation. The
15
actual leaching process of HA4-5 horizontal cavern in Huai’an salt mine is simulated
16
as well. The simulated results are compared with the sonar mapping, drilling and field
17
injection-production data. At last, a new gas-injection and brine-discharge method is
18
proposed to increase the effective volume of the cavern, according to the simulated
19
shape of the horizontal salt cavern. This work will serve as a design and control tool
20
for the construction of horizontal salt caverns. It will promote the development of the
21
horizontal salt cavern gas storage in bedded salt, e.g. in China.
8
1
2. Model
2
During the construction of a salt cavern by water leaching, salt is dissolved in
3
water, and the cavern boundary develops. Since the horizontal cavern composed of
4
three segments, a composite structural mesh method is proposed to describe the
5
complex development. To predict the developing shape of the salt cavern, the
6
dissolution rate of the cavern boundary needs to be calculated, considering the
7
temperature and flow/concentration field of the brines. In addition, the insoluble
8
sediments should be considered as well.
9
2.1 Discretization by a composite structural mesh
10
In this paper, a composite structural mesh method is proposed to describe the
11
development of the horizontal salt cavern. The middle segment of the cavern is
12
described by a cylindrical mesh, whose axis is the horizontal borehole, as shown in
13
Fig. 3a. The lateral development of the two ends of the horizontal cavern are
14
described by two hemispherical grids, which turn into the deviated and the direct
15
segments. The cylindrical and hemispherical grids are composed by many vertical
16
sections, which are numbered by i from the deviated segment to the direct segment.
17
Different cavern cells on section i are numbered by j from bottom to top (Fig. 3b).
18
The control points of the cavern surface have fixed polar angles and variable radius,
19
ensuring that no negative volume will appear with the movement of the boundary. The
20
insoluble sediments are divided into columns (Fig. 3b), which share the same section
21
number i with the cavern cells. These columns are numbered by k along the radial 9
1
direction. (a)
Deviated segment
(b)
Direct segment
Middle segment
y
Cavern
il
iout
iin
z
ir
y Initial cavern shape (borehole)
2
Hemispherical grid
Cylindrical grid
x Axis of symmetry
Insoluble sediments
Hemispherical grid
3
Figure 3 A composite hemispherical-cylindrical-hemispherical mesh for the discretization of a
4
horizontal cavern. a Top view of the composite mesh. The horizontal cavern is divided into two
5
hemispherical parts and a cylindrical part. The three parts are composed by many vertical sections,
6
which are numbered by i. b Side view of section i. The cavern cells are numbered by j, and the
7
insoluble columns are numbered by k.
8
2.2 Salt dissolution and boundary movements
9
The dissolution rate of salt has a significant linear correlation with the
10
concentration of brines (Durie and Jessen, 1964). In addition, the temperature and the
11
angle of wall-brine interface play an important role as well. Wu et al. (1992) and
12
Chang et al. (1977) have proposed empirical formulae of the salt dissolution rate based
13
on laboratory experiments. On the basis of their studies, the dissolution rate of salt can
14
be calculated by,
15
T 0.44 ω (1c / c ) ln (sinα )0.25 s f e ω= 0.44 ω (1-c / c ) ln T α s f e 90
(α <90) (1)
(α >90)
16
where, ω is the dissolution rate of salt, ωf is the standard dissolution rate of a vertical
17
salt cavern wall in fresh water, which can be measured by experiments. Cs is the 10
1
concentration of the saturated brine, T is temperature, and α is the angle between the
2
normal direction of the salt cavern wall and the vertical upward direction, or the angle
3
of the salt-brine interface for short.
4
Thus, the boundary movements can be written as,
r {dx, dy, dz} = ω n
5 6
where, x, y, z are the coordinates of the curved surface of the cavern boundary,
7
the normal vector of the cavern boundary surface.
8 9
r n
is
According to the movements of the cavern boundary, the angle of the salt-brine interface can be calculated by,
∂z ∂z r n = ±{ ∂x , ∂y , 1} sin α = cos < nr ,{0, 0,1} >
10
11
(2)
(3)
2.3 Flow/concentration field
12
As described in Eq. (1), the dissolution rate of salt is mainly affected by the brine
13
concentration, temperature and salt-brine interface angle. The temperature can be
14
easily calculated by the geothermal gradient. The salt-brine interface angle can be
15
calculated from the cavern geometry. The concentration field is quite complicated
16
since it is coupled with the flow field of the brines in the cavern. It is a typical
17
convective mass transfer problem. Since the cavern size is large and the leaching last
18
for years, using traditional fluid mechanics method costs too much runtime (Misyura,
19
2018; Qiao and Yang, 2019b). To reduce the computational efforts, simplified
20
assumptions and empirical approaches are used, as in a vertical cavern.
21
Since the deviated segment and the direct segment alternate between injection 11
1
and production all the time, it is better to describe them by using “injection segment”
2
and “discharge segment” instead. The injection segment can be deviated segment or
3
direct segment, depending on where the fresh water is injected. Since the two
4
segments are expanding, their boundaries are updated according to their developing
5
radius, considering the sonar mapped shapes of the two segments are usually
6
axisymmetric (Shi et al., 2017). The brine concentration field of the injection, middle
7
and discharge segments of a horizontal cavern will be discussed in the following.
8
iin − il = rin idis − ir = rout
9
where, iin and idis are the indexes of the boundary sections between the
10
injection/discharge segments and the middle segment, il and ir are the indexes of
11
sections where the injection and discharge tubes are placed, rin and rout are the
12
maximum radii of the injection and discharge segments, which can be easily
13
calculated by using an enumeration method.
(4)
14
1) In the injection segment, fresh water or low concentration brines are injected
15
at a high flow rate (90-140 m3/h) through a tube with a diameter of 0.178 m. The
16
Reynold number is about 1e5- 2e5. The fully developed turbulent flow of fresh water
17
will flow upward with buoyancy, strongly mixing with the brines along the way.
18
While the highly saturated brines from salt dissolution flow down, the two flows will
19
be fully blended. Similar as in the direct leaching mode in a vertical cavern, the brines
20
above the injection tube can be seen as uniform (Kunstman and Urbanczyk, 2009; Li
21
et al. 2018). The salt mass conservation of this section can be written as,
12
1
∂ (Vin C in ) ∂V ∂V = QC 0 + ρ in (1 − u in ) − Q − in C in ∂t ∂t ∂t
2
where, Vin and Cin are respectively the volume and concentration of the injection
3
segment, Q and C0 are respectively the flow rate and concentration of the injected
4
liquid, ρ is the density of salt, and uin is the insolubles content.
(5)
5
QC0 is the mass of salt contained in the injected liquid, ρ∂Vin/∂t (1- uin) is the mass
6
of the dissolved salt, (Q-∂Vin/∂t)Cin is the mass of the salt contained in the outflow of
7
brines towards the middle segment. The volume of the injection segment can be
8
calculated by, iin
Vin = ∑ ∑ Vi, j
9
i =0
10
(6)
j
where, Vi,j is the volume of the cavern cell j in section i.
11
2) In the middle segment, the cavern bottom and most of the cavern wall are
12
covered by insoluble sediments, mainly the cavern top is dissolved. The dissolution of
13
the cavern top is much faster than that of the vertical cavern wall. The high
14
concentration brines from salt dissolution flow down like raindrops and are fully
15
mixed into the horizontal brine flow. The longitudinal concentration gradient of brines
16
is neglected in this paper, each section in the middle segment has the same brine
17
concentration and flow rate. Along the horizontal direction, the concentration will rise
18
due to the dissolution of salt. As shown in Fig. 4, the mass conservation of section i
19
can be written as,
20
21
C i − 1 Q i −1 − C i Q i + ρ
d Vi d( C i Q i ) (1 − u i ) = dt dt
(7)
where, Ci-1 and Qi-1 are the concentration and flow of the brines in section i-1, Ci, Qi, 13
1
Vi are the concentration, flow, and volume of the brines in section i, ui is the insoluble
2
content of the salt around section i.
3
Vi can be calculated by, Vi = ∑ Vi, j
4
(8)
j
dVi/dt
Dissolved part
Ci-1Qi-1
CiQi
Inflow
Outflow
Section i
5 6
Figure 4 Mass conservation of a section i in the middle segment of a horizontal cavern
7
Due to the incompressibility of the brines, the brine flow can be calculated by
8
volume conservation. The volume change of the brines with the concentration is
9
neglected.
10
11
dVin Qi = Q − dt Q − Q = dVi −1 i i −1 dt
( i = iin ) (9)
(iin < i ≤ iout )
where, Vi-1 and Qi-1 is the volume and flow of the brines in section i-1,
12
3) In the discharge segment, the brines are almost saturated after the salt
13
dissolution of the injection segment and a 200-400 m middle segment. Therefore, the
14
concentration can be seen as uniform. Taking the whole discharge segment as a
15
control volume, the mass of salt is conserved as,
14
1
∂ (Vout Cout ) ∂V ∂V = Qxr Cxr + ρ out (1 − uout ) − Qxr − out Cout ∂t ∂t ∂t
2
where, Vout is the volume of the discharge segment, and Cout is the concentration of the
3
brines. Qx and C x are respectively the flow rate and concentration of the brines in the r
4 5
r
last cell of the middle segment. uout is the insolubles content. The volume of the injection segment can be calculated by, Vout =
6
7
(10)
imax
∑ ∑V
i = iout
i, j
(11)
j
2.4 Insoluble sediments
8
During the leaching, the insoluble substances in bedded salt will fall down when
9
the salt to which they are attached is dissolved. The insoluble substances generated
10
from cell A on the cavern surface will settle within a distance R from its projection
11
point B on the cavern bottom, as shown in Fig. 5. According to the research of Li et al.
12
(2018), R is basically proportional to the fall height.
13
R = γ ( zA − zB )
14
where, γ is the coefficient between R and the fall height, zA and zB are the heights of
15
point A and B.
(12)
Cavern surface ∂V ub ∂t
Insoluble sediments surface
16
∂Z ∂t 15
Figure 5 The accumulation of the insoluble sediments.
1 2
Since the volume of the generated insoluble sediments from one cell is pretty
3
small, the distribution of the insolubles in the settling range can be seen as even.
4
Therefore, the height change of the insoluble sediments can be calculated by,
5
∂Z ∂V 1 = ub 2 ∂t ∂t π R
6
where, Z is the height of the insoluble sediments in the settling range, u is the
7
insolubles content, b is the bulking factor of insoluble substances in brines, and V is
8
the volume of cell A on the cavern wall.
(13)
9
After the calculation of the generated insolubles from all the cells on the cavern
10
surface, the height of the insoluble sediments needs to be adjusted according to the
11
angle of repose of the insoluble particles in brines. The unstable height of the
12
insoluble sediments can be described as, ∂Z ∂i > tan α ins ∂Z > tan α ins ∂k
13
14
(14)
where, αins is the angle of repose of the insoluble particles in brines.
15
For all the insoluble columns meeting Eq. (12), the height should be adjusted in
16
both i and k directions. Thus, the height increment of the insoluble sediments can be
17
written as,
18
∂Z = ∂t
∑
∂V 1 ub + dZ i + dZ k ∂t π R2
(15)
19
where, dZi and dZk are respectively the adjusted height in i and k directions. dZi and
20
dZk can be calculated by binary search, considering the volume conservation and 16
1
repose angle of the insoluble sediments. Detailed solving process of dZi and dZk can
2
be found in the research of Li et al. (2018).
3
3. Numerical implementation
4
According to the proposed mathematical model and mesh method, a VC++
5
program “Horizontal cavern leaching simulation program in bedded salt” (HCLS) is
6
developed by using the finite volume method, as in Fig. 6a. In HCLS, the main
7
calculating parameters include the dissolution rate of the cavern boundary, the
8
coordinates of the control points of the cavern surface, the flow and concentration
9
field of the brines, the height of the insoluble sediments, the cell volume and salt mass,
10
and the angle of the salt-brine interface. The calculation flow chart of HCLS is as
11
shown in Fig. 6b. All the calculating parameters are initialed after the input of
12
geological and technological parameters, and are updated in turn in each time step. (a)
(b) Geological parameters input and initialization Stage technological parameters input Dissolution rate Eq. (1) Boundary movements, Eq. (2, 3) Brine concentration/velocity, Eq. (4- 11) Insoluble sediments surface, Eq. (12- 15) No t=t+dt
If leaching stage ends Yes No If the whole process ends In/out alternate Yes Cavern shape export and data output
13 14
Figure 6 The developed program “Horizontal salt cavern leaching simulation (HCLS)”. a User’s
15
interface of HCLS. b Calculation flow chart of HCLS.
16
4. Experimental verification 17
1
To verify the proposed model, an experiment has been carried out in the
2
laboratory to simulate the leaching of a horizontal cavern. A 450×250×320 mm salt
3
sample from an open-pit salt mine in Pakistan is used, with insolubles content of 1.5%
4
(Chinese high-insoluble bedded salt formations are usually deep-buried, thus there are
5
no such big samples as from the open-pit salt mines). The 420×320 mm side of the
6
sample is smoothed, where a drilling channel has been carved on. A glass plate is
7
glued to this side as a plane of symmetry for the convenience of observation, as
8
shown in Fig. 7a. The left borehole is used as the injection segment, the leaching lasts
9
for 26 hours at an injection rate of 2 mL/min. The final cavern shape is as shown in
10
Fig. 7b. The cavern shows obvious nonuniformity along the horizontal direction. The
11
injection segment on the left is about 95 mm high, while the discharge segment on the
12
right barely develops. The reason is as described before: the injected fresh water flows
13
up and dissolves the salt around the injection segment first. When flowing in the
14
middle segment, the salt dissolution continues and the brine saturation rises. The brine
15
is finally saturated in the discharge segment, thus nearly no more salt is dissolved.
16
Worth to mention, the air contained in the salt sample is released and gathers on the
17
cavern top during the leaching process. The top of the injection segment of the cavern
18
is protected from being dissolved by this air pad, thus the injection segment develops
19
laterally instead.
18
a
b
c
100
50
0
95mm
Actual cavern
Insoluble sediments
Lateral development
81.0mm 77.8mm
Vertical coordinate / mm
Simulated cavern
100
1
50
0
50 150 100 Horizontal coordinate / mm
200
250
2 3
Figure 7 Experimental verification of the proposed model. a Preparation of the salt sample. b
4
Leached horizontal salt cavern with cover glass removed. c Comparison of the simulation and
5
experimental results.
6
A simulation is conducted by HCLS program, using the same parameters as the
7
experiment. According to the actual air pad position (about 95 mm height), a blanket
8
pad is also set in the simulation. As shown in Fig. 7c, the simulated cavern shape of
9
the proposed model is very close to the actual. The actual radius of the injection
10
segment is about 77.8 mm, while the simulated radius is 81.0 mm, about 4.1% larger.
11
The actual cavern volume is 386.7 mL, while the simulated cavern is 404.8 mL, about
12
4.7% larger. There is a deviation between the simulation and experiment, which has
13
been marked by a dashed line in Fig. 7c. This deviation occurs because the lateral
14
movements of the boundary of the injection segment cannot be simulated in the 19
1
proposed mesh system. This lateral development is ignored in the proposed model,
2
since there is no blanket pad in the field horizontal cavern leaching for now. In
3
general, the simulation can be seen as reliable, considering the measurement errors
4
and the lateral development of the top boundary of the injection segment.
5
5. Field application and verification
6
The construction process of HA4-5 horizontal cavern in Huai’an, China is
7
simulated by the proposed model and program. HA4-5 is a lately completed
8
horizontal salt cavern in Huai’an salt mine. The salt formations are layered, buried
9
between -1508 m and -990 m. The average content of the insoluble substances is 45%,
10
the major components of the insolubles are mudstone and gypsum. Two separate
11
caverns, HA-5 and HA-4, are mapped by sonar in June, 2017 (Shi et al., 2017). The
12
volume of HA-5 is about 121,000 m3 and HA-4 is about 52,000 m3. The total volume
13
of the injected water is about 7,019,000 m3, 3,690,000 m3 for HA-5 and 3,329,000 m3
14
for HA-4. The leaching flow rate varies from 90 to 140 m3/h. There have been 4
15
injection-production cycles. The concentration of the brine production is saturated
16
(300 g/L) or nearly saturated during the leaching. Since HA4-5 is only designed for
17
salt mining at the first place, there are no more detailed field leaching data. In the
18
simulation, the flow rate is assumed as a constant 120 m3/h, and the 4 leaching cycles
19
are assumed to be equal in time.
20
Mapped cavern
Porous insoluble sediments
-1250
Simulated cavern
Cavern HA-5 -1330
Cavern HA-4
Suggested brine discharge
Potential storage space -1410
Depth / m
Suggested gas injection
Third cavern
Simulated depth (-1468 m)
-1490
Detected depth (-1477 m)
80
0
2
80
160
240
320
400
Horizontal coordinate / m
1
Figure 8 Simulated and mapped cavern shapes of HA4-5 horizontal cavern in Huai’an, China.
3
A comparison of the simulation results and of the field data is shown in Fig. 8.
4
The simulated cavern has four parts, including porous insoluble sediments and three
5
open caverns as HA-4, HA-5 and an undected cavern in the middle. The simulation
6
results basically coincide with the field data, the details are as follows.
7 8
1) According to the previously mentioned injection and production data, the total mass of the dissolved salt can be calculated by,
9
M salt = Vinjection Cdischarge =7019000 × 300 ≈ 2.1× 109 kg
10
where, Msalt is the mass of the dissolved salt, Vinjection is the total volume of the
11
injected water, Cdischarge is the average concentration of the brine production.
12
13
(16)
Thus, the total volume of the dissolved part of the cavern can be calculated by,.
Vdissolve
M salt / ρ 2.1×109 / 2300 = = ≈ 1.66 ×106 m3 1− u 1 − 0.45
(17)
14
where, Vdissolve is the total volume of the dissolved part, including salt and insolubles.
15
u is the average content of insoluble substances in the salt formation. 21
1
The simulated volume is about 1,598,000 m3, about 3.7% smaller. Porous
2
insoluble sediments (the red part in Fig. 8) fill most of the cavern, due to the high
3
content (45%) and high bulking factor (1.6~1.8) of the insoluble substances in the salt
4
formations. This explains why only the two separate caverns HA-4 and HA-5 can be
5
mapped by sonar.
6
2) The depth range of the simulated HA-5 is between -1245.2 m and -1287.8 m,
7
the diameter is 86.2 m. According to the sonar mapping, the depth range of the actual
8
HA-5 is between -1260.7 m and -1301.0 m, the diameter is about 90.2 m. The size of
9
the simulated HA-5 is basically coincide with the actual cavern, with an error about
10
4.4%. The position of the simulated HA-5 is about 14 m higher than the actual cavern,
11
about 6% of the total height (230 m).
12
3) The depth range of the simulated HA-4 is between -1277.0 m and -1299.6 m,
13
the diameter is 84.1 m. According to the sonar mapping, the depth range of the actual
14
HA-4 is between -1292.5 m and -1314.0 m, the diameter is about 64.0 m. The position
15
of the simulated HA-5 is about 15 m higher than the actual cavern, about 6.5 % of the
16
total height (230 m). The error of the diameter of the simulated HA-4 is pretty large as
17
20 m. The diameters of the actual HA-4 (64 m) and HA-5 (90 m) are quite different as
18
well, although the volume of the injected water are almost the same. Thus, the
19
differences might result from the heterogeneity of the salt formation, which is not
20
considered in our model.
21
4) The simulation shows that there is a third cavern deep-seated in between the
22
two open caverns HA-4 and HA-5. It cannot be mapped by sonar due to the blocking 22
1
of the insoluble sediments. To confirm the existence of the third cavern, a borehole
2
was drilled to the middle in between the two caverns in September 2018. An open
3
space was successfully detected at -1477 m, confirming the reliability of the proposed
4
model. The depth of the detected cavern is 9 meters lower than the simulation (Fig. 8),
5
which is about 3.75% of the total height of HA4-5 and is acceptable for actual
6
engineering.
7
6. Discussion and suggestion
8
Through comparison, it can be said that the proposed model is reliable as a design
9
and prediction tool for the construction of horizontal salt caverns. The shape of a
10
horizontal salt cavern is firstly simulated with acceptable accuracy in bedded salt with
11
high insoluble content (45 %). It provides the critical data for the usage of hundreds of
12
old horizontal salt caverns in this area. There are some errors of the detailed shapes
13
and positions of the two open caverns, probably due to the missing of the detailed
14
field leaching data and the simplifications of our model. The accuracy of the model
15
will be further improved by trials and errors in our next work, using more detailed
16
field data and more accurate flow and concentration models.
17
The simulation shows that the whole cavern is shaped like a letter “U” in bedded
18
salt, rather than a horizontal ellipsoid or dumbbell as in the salt domes (Colomé et al.,
19
2010). There is a third open cavern in the middle of the U-shaped cavern, which
20
indicates a novel method for gas/oil injection and brine discharge. Traditionally in the
21
vertical caverns, the pore space in the insoluble sediments cannot be used for oil/gas 23
1
storage, for the de-brine tube cannot be placed below the insolubles or it will be
2
blocked (Wang et al. 2018). Now the third cavern can be used as a de-brine pool by
3
drilling and placing the de-brine tube in it. Gas or oil can be injected into HA-4 and
4
HA-5. The brines in the open caverns as well as in the pores of the insoluble
5
sediments will be extruded from the third cavern and replaced by gas/oil without
6
clogging, as shown in Fig. 8. Actually, the volume of the pores of the insoluble
7
sediments is much larger than the volume of the two open caverns. The volume of the
8
pore spaces of HA4-5 can be estimated by,
9
V pore = Vinsoluble ( b − 1)= V dissolve u ( b − 1) = 1.66 × 10 6 × 0.45 × (1.8 − 1) = 597, 600m 3 (18)
10
where, Vpore is the volume of pore space in insoluble sediments, Vinsoluble is the volume
11
of the insoluble substances contained in the dissolved salt, b is the bulking factor of
12
the insoluble substances in the brines.
13
The sum of the volumes of the two open caverns (HA-4 and HA-5) is only about
14
173,000 m3. Plus Vpore, the effective storage space of the cavern will reach about
15
770,600 m3, about 4.45 times larger than the volume of the detected spaces by sonar.
16
Under our suggestions, the field gas injection and brine discharge using the proposed
17
method has started in HA4-5 cavern in October 2018.
18
The finding shows that, in the high-insoluble bedded salt in China, the horizontal
19
salt caverns are more suitable to be used as UGSs than the vertical caverns, since the
20
U-shape and the third cavern allow the pores in the insoluble sediments to be replaced
21
by gas. Considering the quantity of the mined old horizontal salt caverns in China, as
22
shown in Fig.2, this finding promises substantial economic benefits. 24
1
7. Conclusions
2
1) In summary, a numerical model is demonstrated to predict the development of
3
horizontal
4
hemispherical-cylindrical-hemispherical mesh is proposed to describe the
5
complex boundary movements of the three segments (deviated segment, middle
6
segment and direct segment as in Fig. 1b) of a horizontal cavern. The empirical
7
equations of the dissolution rate of salt are introduced. The coupled equations of
8
the boundary movements, flow/concentration field of brines of the three segments
9
of the horizontal cavern have been derived. The accumulation of the insoluble
10
salt
caverns
during
construction.
A
composite
sediments is firstly considered in the modeling of a horizontal salt cavern.
11
2) A VC++ program “Horizontal cavern leaching simulation program in bedded salt”
12
(HCLS) is developed by using the finite volume method to implement the
13
proposed model. The reliability of the model and program have been
14
demonstrated by laboratory experiments and field applications. The proposed
15
model and program can serve as a design and control tool for the construction of
16
horizontal salt caverns.
17
3) The shape of a horizontal cavern HA4-5 (Huai’an, China) in a high-insoluble salt
18
formation has firstly been simulated by the proposed model. Confirmed by sonar
19
imaging and exploratory drilling, the simulated horizontal cavern is U-shaped
20
with a third cavern deep-seated in between HA-4 and HA-5. The third cavern is
21
suggested to be used as a non-clogging de-brine pool during gas injection and
22
brine discharge. Thus, the pore space in the insoluble sediments will be available 25
1
for gas/oil storage, the cavern capacity will be multiplied. It promises a broad
2
prospect for the horizontal salt cavern gas storage in bedded salt, e.g. in China.
3
References
4
Bai, M.X., Song, K.P., Sun, Y.X., He, M.Q., Li, Y., Sun, J.P., 2014. An overview of hydrogen
5
underground storage technology and prospects in China, J. Petrol. Sci. Eng. 124, 132–136.
6
https://doi.org/10.1016/j.petrol.2014.09.037
7
Bérest, P., Bergues, J., Brouard, B., Durup, J.G., Guerber, B., 2001. A salt cavern
8
abandonment
9
https://doi.org/10.1016/S1365-1609(01)00004-1
10 11
test.
Int.
J.
Rock
Mech.
Min.
38(3),
357-368.
Chang, C, Vliet, G C, Saberian, A., 1977. Natural Convection Mass Transfer at Salt-Brine Interfaces. Journal of Heat Transfer 99(4): 603-608. DOI: 10.1115/1.3450749
12
Chen, X.S., Li, Y.P., Liu, W., Ma, H.L., Ma, J.L., Shi, X.L., Yang, C.H., 2019. Study on
13
sealing failure of wellbore in bedded salt cavern gas storage. Rock Mech. Rock Eng. 52(1),
14
215-228. https://doi.org/10.1007/s00603-018-1571-5
15
Chen, J., Lu, D., Liu, W., Fan, J.Y., Jiang, D.Y., Yi, L., 2020. Stability study and optimization
16
design of small-spacing two-well (SSTW) salt caverns for natural gas storages. J. Energ. Storage.
17
27, 101131. https://doi.org/10.1016/j.est.2019.101131.
18
Colomé, J.D., Preti, L., Carbajal, R., Wood, M.G., 2010. Improving dual well horizontal
19
cavern volume and shape predictions by post-processing single well sonar data. In: Solution
20
Mining Research Institute Fall Technical Conference, Leipzig Germany.
21 22 23
Durie, R.W., Jessen, F.W., 1964. Mechanism of the dissolution of salt in the formation of underground salt cavities. SPE J. 4(2), 183-190. DOI: 10.2118/678-PA Fan, J.Y., Jiang, D.Y., Liu, W., Wu, F., Chen, J., Daemen, J.J.K., 2019. Discontinuous fatigue
24
of salt rock with low-stress intervals. Int. J. Rock Mech. Min. 115(3), 77-86.
25
https://doi.org/10.1016/j.ijrmms.2019.01.013
26
Ge, X.B., Li, Y.P., Shi, X.L., Chen, X.S., Ma, H.L., Yang, C.H., Shu, C., Liu, Y.X., 2019a. 26
1
Experimental Device for the Study of Liquid–Solid Coupled Flutter Instability of Salt Cavern
2
Leaching Tubing. J. Nat. Gas Sci. Eng. 66, 168-179. https://doi.org/10.1016/j.jngse.2019.03.026
3
Ge, X.B., Li, Y.P., Chen, X.S., Shi, X.L., Ma, H.L., Yin, H.W., Zhang, N., Yang, C.H., 2019b.
4
Dynamics of a partially confined, vertical upward-fluid-conveying, cantilever pipe with reverse
5
external flow. Applied Sciences, 9(7), 1425. https://doi.org/10.3390/app9071425
6 7
Gronefeld, P., Saalbach, B., 1998. Numerical 3D simulation of horizontal leaching processes. In: Solution Mining Research Institute Fall Meeting, Rome, Italy.
8
Kunstman, A., Urbanczyk, K., 1995. Modelling of horizontal cavern leaching: Main aspects
9
and perspectives. In: Solution Mining Research Institute Fall Meeting, San Antonio, Texas, U.S.A.
10
Kunstman, A., Urbanczyk, K., 2009. Application of winubro program to modelling of carven
11
development in trona deposit. In: Solution Mining Research Institute Spring Technical Conference,
12
Krakow, Poland.
13
Lawal, K.A., Ovuru, M.I., Eyitayo, S.I., Matemilola, S. Adeniyi, A.T., 2016. Underground
14
storage as a solution for stranded associated gas in oil fields. J. Petrol. Sci. Eng. 150, 366–375.
15
https://doi.org/10.1016/j.petrol.2016.12.020
16
Li, J.L. Shi, X.L., Yang, C.H., Li, Y.P., Wang, T.T., Ma, H.L., 2018. Mathematical model of
17
salt cavern leaching for gas storage in high-insoluble salt formations. Sci. Rep. 8(1), 372.
18
DOI: 10.1038/s41598-017-18546-w
19
Li, J.L., Tang, Y., Shi, X.L., Xu, W.J., Yang, C.H., 2019a. Modeling the construction of
20
energy
storage
salt
caverns
in
bedded
21
https://doi.org/10.1016/j.apenergy.2019.113866
salt.
Applied
Energy
255,
113866.
22
Li, J.L., Xu, W.J., Zheng, J.J., Liu, W., Shi, X.L., Yang, C.H., 2020a. Modeling the mining of
23
energy storage salt caverns using a structural dynamic mesh. Energy 193, 116730.
24
https://doi.org/10.1016/j.energy.2019.116730
25 26
Li, J.L., Shi, X.L., Zhang, S., 2020b. Construction modeling and parameter optimization of multi-step horizontal energy storage salt caverns. Energy, In Press.
27
Li, Y.P., Liu, W., Yang, C.H., Daemen, J.J.K., 2014. Experimental investigation of mechanical
28
behavior of bedded rock salt containing inclined interlayer. Int. J. Rock Mech. Min. 69, 39-49.
29
DOI: 10.1016/j.ijrmms.2014.03.006 27
1
Li, Y.P., Chen, X.S., Shi, X.L., Zhang, N., Ma, C.K., Yang, C.H. 2019b. Analysis of the
2
plugging process of the leaking interlayer in a thin interbedded salt cavern gas storage of Jintan
3
(China) by high-pressure grouting and potential applications. J. Nat. Gas Sci. Eng. 68, 102918.
4
https://doi.org/10.1016/j.jngse.2019.102918
5
Liu, W., Chen, J., Jiang, D.Y., Shi, X.L., Li, Y., Daemen, J.J.K., Yang C.H., 2016. Tightness
6
and suitability evaluation of abandoned salt caverns served as hydrocarbon energies storage under
7
adverse
8
http://dx.doi.org/10.1016/j.apenergy.2016.06.086
geological
conditions
(AGC).
Appl.
Energ.
178,
703-720.
9
Liu, W., Jiang, D.Y., Chen, J., Daemen, J.J.K., Wu, F., 2017 Comprehensive feasibility study
10
of two-well-horizontal caverns for natural gas storage in thinly-bedded salt rocks in china. Energy
11
143(15), 1006-1019. https://doi.org/10.1016/j.energy.2017.10.126
12
Liu, W., Zhang Z.X., Chen J., Fan J.Y., Jiang, D.Y., Daemen, J.J.K., 2019. Physical
13
simulation of construction and control of two butted-well horizontal cavern energy storage using
14
large
15
https://doi.org/10.1016/j.energy.2019.07.014
molded
rock
salt
specimens.
Energy
185,
682-694.
16
Lordache, M., Schitea, D., Deveci, M., Akyurt, I.Z., Lordache, L., 2019. An integrated ARAS
17
and interval type-2 hesitant fuzzy sets method for underground site selection: Seasonal hydrogen
18
storage
19
https://doi.org/10.1016/j.petrol.2019.01.051.
20 21
in
salt
caverns,
J.
Petrol.
Sci.
Eng.
175.
1088-1098.
Misyura, S.Y., 2018. The influence of characteristic scales of convection on non-isothermal evaporation of a thin liquid layer. Sci. Rep. 8, 11512. DOI: 10.1038/s41598-018-29015-3
22
Niu, C.K., Tan, Y.F., Li, J.N., Song, C.L., 2015. Model validation and stability analysis for
23
operation projects in Jintan Salt Cavern for strategic oil storage of China, J. Petrol. Sci. Eng. 127:
24
44-52. https://doi.org/10.1016/j.petrol.2015.01.029
25
Nolen, J.S., von Hantlemann, O., Meister, S., Kleinitz, W., Heiblinger, J., 1974. Numerical
26
simulation of the solution mining process. In: SPE European Spring Meeting, Amsterdam,
27
Netherlands. http://dx.doi.org/10.2118/4850-MS
28
Qiao, W., Yang, Z., 2019a. Forecast the electricity price of U.S. using a wavelet
29
transform-based hybrid model. Energy 193, 116704. https://doi.org/10.1016/j.energy.2019.116704 28
1
Qiao, W., Yang, Z., 2019b. An improved dolphin swarm algorithm based on Kernel Fuzzy
2
C-means in the application of solving the optimal problems of large-scale function. IEEE Access.
3
In Press. Doi:10.1109/ACCESS.2019.2958456.
4
Qiao, W., Yang, Z., Kang, Z., Pan, Z., 2020a. Short-term natural gas consumption prediction
5
based on Volterra adaptive filter and improved whale optimization algorithm. Eng. Appl. Artif.
6
Intel. 87, 103323.
7
Qiao, W., Lu, H., Zhou, G., Azimi, M., Yang, Q., Tian, W., 2020b. A hybrid algorithm for
8
carbon dioxide emissions forecasting based on improved lion swarm optimizer. J. Clean. Prod.
9
244, 118612.
10 11 12 13 14
Russo, A.J., 1995. HORSMIC Solution Mining Code for Horizontal Caverns. In: Solution Mining Research Institute Fall Meeting, San Antonio, Texas, USA. Saberian, A., 1995. A preliminary model for horizontal well leaching. In: Solution Mining Research Institute Fall Meeting, San Antonio, Texas, USA. Scott, V., Gilfillan, S., Markusson, N., Chalmers, H., Haszeldine, R.S., 2012. Last chance for
15
carbon capture and storage. Nature Clim. Change 3(2), 105-111. DOI: 10.1038/NCLIMATE1695
16
Shi, X.L., Li, Y.P., Yang, C.H., Xu, Y.L., Ma, H.L., Liu, W., Ji, G.D., 2015. Influences of
17
filling abandoned salt caverns with alkali wastes on surface subsidence. Environmental Earth
18
Sciences 73, 6939-6950. DOI: 10.1007/s12665-015-4135-y
19
Shi, X. L. Li, J. L. Chen, T., 2017. Detection and evaluation of Huai’an horizontal cavern (in
20
Chinese). (Technical report of Institute of Wuhan Rock and Soil Mechanics, Chinese Academy of
21
Science).
22
Soubeyran, A., Rouabhi, A., Coquelet, C., 2019. Thermodynamic analysis of carbon dioxide
23
storage in salt caverns to improve the Power-to-Gas process. Appl. Energ. 242, 1090–1107.
24
https://doi.org/10.1016/j.apenergy.2019.03.102
25
Wang, T.T., Yang, C.H., Li, J.J., Li, J.L., Shi, X.L., Ma, H.L., 2016. Failure analysis of
26
overhanging blocks in the walls of a gas storage salt cavern: a case study. Rock Mechanics &
27
Rock Engineering 1-13. doi:10.1007/s00603-016-1102-1
28 29
Wang, T.T. Yang, C.H., Wang, H.M., Ding, S.L., Daemen, J.J.K., 2018. Debrining prediction of a salt cavern used for compressed air energy storage. Energy 147, 464-476. 29
1 2 3
https://doi.org/10.1016/j.energy.2018.01.071 Wu, G., Xiao, C. F., Qiu, X. D. Study on the dissolution rate of rock salt (in Chinese). Chem. Min. Tech. 01, 19-22 (1992).
4
Xing, W., Zhao, J., Hou, Z.M., Were, P., Li, M.Y., Wang, G., 2015. Horizontal natural gas
5
caverns in thin-bedded rock salt formations. Environ. Earth Sci. 73, 6973-6985. DOI:
6
10.1007/s12665-015-4410-y
7
Yang, C.H., Wang, T.T., Li, Y.P., Yang, H.J., Li, J.J., Qu, D.A., Xu, B.C., Yang, Y., Daemen,
8
J.J.K., 2015. Feasibility analysis of using abandoned salt caverns for large-scale underground
9
energy
10
storage
in
China.
Applied
Energy
137
(1),
467-481.
http://dx.doi.org/10.1016/j.apenergy.2014.07.048
11
Yang, C.H., Wang, T.T., Qu, D.A., Ma, H.L., Li, Y.P., Shi, X.L., Daemen, J.J.K., 2016.
12
Feasibility analysis of using horizontal caverns for underground gas storage: a case study of
13
yunying
14
http://dx.doi.org/10.1016/j.jngse.2016.10.009
salt
district.
J.
Nat.
Gas
Sci.
Eng.
36,
252-266.
15
Zhang, N., Ma, L.J., Wang, M.Y., Zhang, Q.Y., Li, J., Fan, P.X., 2016. Comprehensive risk
16
evaluation of underground energy storage caverns in bedded rock salt. J. Loss Prevent Proc. 45,
17
264-276. https://doi.org/10.1016/j.jlp.2016.10.016
18
Zhang, N., Shi, X.L., Wang, T.T., Yang, C.H., Liu, W., Ma, H.L., Daemen J. K., 2017.
19
Stability and availability evaluation of underground strategic petroleum reserve (SPR) caverns in
20
bedded
21
https://doi.org/10.1016/j.energy.2017.06.073
rock
salt
of
Jintan,
China.
Energy
134,
504-514.
22
23
Acknowledgements
24
The authors wish to acknowledge the financial supports of Basic Science Center
25
Program for Multiphase Evolution in Hypergravity of the National Natural Science
26
Foundation of China (No. 51988101), China Postdoctoral Science Foundation (Grant
27
No. 2018M642433), National Natural Science Foundation of China (Grant No. 30
1
51774266), Open Research Fund of State Key Laboratory of Geomechanics and
2
Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of
3
Sciences(Grant No. Z018021), Fundamental Research Funds for the Central
4
Universities (No. 2019QNA4034, 2019QNA4035), Natural Science Foundation for
5
Innovation Group of Hubei Province, China (Grant No. 2016CFA014). The authors
6
are sincerely grateful to Jiangsu Suyan Jingshen Co., Ltd and PetroChina for their
7
help in the field.
8 9
Author Contributions
10
J.L. wrote the main manuscript text and are responsible for the mathematical model
11
and the program implementation; C.Y., X.S. and W.X. have made contributions to the
12
conception and design of the work. Y.L. and J.D. have made contributions to the
13
improvements of the model and the analysis of the results. All authors discussed the
14
results and critically reviewed the manuscript.
31
Highlights A model and a C++ program are presented for the construction simulation and shape prediction of a horizontal salt cavern. A composite structural mesh and a simplified flow/concentration field model are proposed. The high-content of insoluble substances in bedded salt are considered. The reliability of the model has been verified by laboratorial and field tests. A third cavern is simulated and detected, using which a gas injection method is proposed to increase the effective storage capacity.
Li Jinlong: Methodology, Software, Writing - Original Draft, Visualization, Data Curation Yang Chunhe: Conceptualization, Resources, Supervision Shi Xilin: Investigation, Validation, Project administration Xu Wenjie: Validation, Funding acquisition Li Yinping: Conceptualization, Validation Jaak J.K. Daemen: Writing - Review & Editing
Declaration of interests √The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0920-4105(20)30151-0
DOI:
https://doi.org/10.1016/j.petrol.2020.107058
Reference:
PETROL 107058
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 11 July 2019 Revised Date:
6 January 2020
Accepted Date: 9 February 2020
Please cite this article as: Jinlong, L., Chunhe, Y., Xilin, S., Wenjie, X., Yinping, L., Daemen, J.J.K., Construction modeling and shape prediction of horizontal salt caverns for gas/oil storage in bedded salt, Journal of Petroleum Science and Engineering (2020), doi: https://doi.org/10.1016/j.petrol.2020.107058. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Cavern shape mapped by sonar
Unknown part
Mapped cavern
Simulated cavern
HA-5
Porous Insoluble sediments
HA-5
HA-4
Suggested gas injection
Modeling Extra storage space
Unknown part
Borehole
Suggested brine discharge
A third open cavern
Through the modeling of a horizontal salt cavern (HA4-5 in China), the shape is successfully predicted to evaluate its capacity and stability before it is served as a gas storage. A third open cavern is simulated and then detected, which is suggested to be used for brine discharge to increase the storage capacity.
HA-4
1
Construction modeling and shape prediction of horizontal salt
2
caverns for gas/oil storage in bedded salt
3
Li Jinlonga, Yang Chunheb, Shi Xilinb*, Xu Wenjiea*, Li Yinpingb, Jaak J.K. Daemenc
4
a
MOE
Key
Laboratory
of
Soft
Soils
and
Geoenvironmental
Engineering,
5
Center for Hypergravity Experimental and Interdisciplinary Research, Zhejiang University,
6
Hangzhou 31005, China.
7
b State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock
8
and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, Hubei, China.
9
c Mackay School of Earth Sciences and Engineering, University of Nevada, Reno, NV, USA
10
* Correspondence and requests for materials should be addressed to Shi X.L. (email:
11
[email protected]) or Xu W.J. (email: [email protected])
12
Abstract
13
Construction modeling and shape prediction are significant for the parameters
14
optimization and capacity prediction of a horizontal salt cavern gas/oil storage.
15
However, most previous studies concentrate on the middle segment of the cavern, and
16
the insoluble substances are ignored. The actual shapes of the horizontal salt caverns
17
in bedded salt remain unknown. Here a coupled model is proposed for the
18
construction of a horizontal cavern. A composite structural mesh is presented to
19
describe the development of three segments of the cavern. The equations of the
20
salt-brine mass transfer rate and boundary movements are introduced. A simplified
21
flow and concentration field model is presented. The accumulation of the insoluble
22
substances is firstly considered in a horizontal cavern. A VC++ program using the 1
1
finite volume method is developed to obtain the numerical solution of the model and
2
as a construction design tool for the horizontal salt caverns. The reliability of the
3
model and program has been confirmed by comparisons with laboratory experiments.
4
The shape of a field horizontal cavern HA4-5 in Huai’an, China is successfully
5
simulated. The simulation results coincide well with the field data. It is found that the
6
horizontal cavern is actually U-shaped and there is an undetected open cavern in the
7
middle segment. This cavern is suggested to be used as a non-clogging de-brining
8
pool during gas/oil injection and brine discharge. The brine in the pores of the
9
insoluble sediments will be replaced by gas/oil and the storage capacity will be
10
multiplied. The finding promises a broad prospect for the horizontal salt cavern gas
11
storage in bedded salt.
12
Keywords: Bedded salt rocks; Natural gas storage; Horizontal cavern; Cavern
13
Leaching; Mathematical model; Insoluble Sediments
14
2
1
1. Introduction
2
Salt cavern underground storage is widely used for natural gas peak shaving
3
(Yang et al., 2015; Qiao et al. 2020a) and strategic petroleum reserve (Niu et al., 2015;
4
Zhang et al., 2017), for salt rock has low permeability (Liu et al., 2016, Zhang et al.
5
2016) and good rheological properties (Li et al., 2014; Fan et al., 2019). Compared
6
with other underground gas storages (Lawal et al., 2014), salt caverns have higher
7
injection-production rate and daily gas/oil output. In addition, since salt has stable
8
chemical properties, salt caverns are suitable for compressed air, H2 or CO2 storage
9
(Bai et al., 2014; Lordache et al., 2019; Qiao and Yang, 2019a; Qiao et al. 2020b) and
10
radioactive waste disposal (Shi et al., 2015) as well. Usually, a salt cavern is
11
constructed in underground salt formations by water solutioning, or ‘leaching’.
12
Usually a vertical construction method is used. A borehole is drilled and in it two
13
concentric tubes are placed (Fig. 1a), through which fresh water is injected and brines
14
are discharged (Ge et al., 2019a, 2019b). The insoluble sediments accumulate on the
15
cavern bottom during the leaching (Li et al. 2019a, 2020a). After 5-10 years of
16
dissolution, a slim and tall salt cavern develops, the volume of which can reach
17
millions of cubic meters in salt domes (Bérest et al., 2001). However, in bedded salt
18
formations (e.g. in China, Canada, and the US), it is hard to develop a tall and slim
19
vertical cavern, since there are many thick insoluble interlayers (Fig. 1b), preventing
20
the cavern from growing upward (Chen et al., 2019).
3
(a) Brines
Water
Casing Outer tube
(b)
Injection: direct well Injection: deviated well
Insoluble interlayers
Tube
Blanket pad Inner tube
Deviated segment Brines
Direct segment Middle segment
Insoluble sediments Insoluble sediments Salt dome
Bedded salt
Initial borehole
1 2
Figure 1 Schematic illustration of the construction method of salt caverns. a Vertical cavern. A
3
vertical cavern uses inner and outer tubes for water injection and brines production. b Horizontal
4
cavern.
5
Recently, a horizontal leaching method is attracting more and more attention (Liu
6
et al., 2017; Yang et al., 2016; Chen et al. 2020; Li et al. 2020b). A vertical borehole
7
name “direct well” is firstly drilled, and then a “deviated well” is drilled and
8
connected with the direct well (Fig. 1b). The distance between them can be hundreds
9
of meters. Tubes are placed in the two boreholes and are used for alternate water
10
injection and brines production (Xing et al., 2015), instead of two concentric tubes in
11
one borehole. A horizontal cavern includes three segments, a deviated segment, a
12
middle segment and a direct segment. Compared to the vertical cavern, the horizontal
13
cavern has a larger dissolution area and thus a higher leaching rate. Therefore, Liu et
14
al. (2017, 2019) and Yang et al. (2016) thought that the horizontal cavern is more
15
suitable for developing larger storage caverns in bedded salt in China.
16
There are many old horizontal caverns left by salt mining industry in China, they
17
have strong potential to be used as underground gas storages (UGSs) (Yang et al.,
4
1
2016), since they are close to the gas consumption area and the gas pipelines (Fig. 2a).
2
For example, there are about 350 mined horizontal salt caverns in Huai’an Salt, the
3
available storage space is larger than 200 million cubic meters. (a)
Pingdingshan Qianjiang
Huai’an Jintan Yunying Zhangshu
Gas consumption density Gas pipeline
Salt cavern UGS Salt cavern UGS (in construction) Salt mine (most use horizontal leaching)
(b) Detected deviated segment (HA-5) Detected direct segment（ HA-4） -1330m
270m
???
Borehole
Unknown middle segment -1490m
4 5
Figure 2 Horizontal salt caverns in mainland China. a Bedded salt mines have strong potential to
6
be used as UGSs in mainland China. b The evaluation and construction of the horizontal salt
7
cavern UGSs are delayed, since the sonar mapping cannot find the complete shape of cavern
8
HA4-5 in Huai’an Salt in June, 2017 (Shi et al., 2017).
9
Before used as a UGS, shape data is essential for the stability analysis (Wang et
10
al. 2016), airtightness analysis (Li et al. 2019b) and capacity evaluation of the salt
11
cavern. However, during the detection by sonar mapping, the horizontal salt caverns 5
1
have not been completely mapped (e.g. cavern HA4-5 (Shi et al., 2017) in Fig. 2b).
2
Only two separate caverns (HA-4 and HA-5) are mapped, while the middle segment is
3
unknown. The shape of the horizontal cavern has been assumed to be shaped like a
4
dumbbell as in salt domes (Colomé et al., 2010), but the 270 m long part in the middle
5
is “missing”. The reason is that the content of the insoluble substances reaches up to
6
45% in the bedded salt formations, these insoluble substances accumulated on the
7
cavern bottom (Li et al., 2019a) and filled the middle segment during construction.
8
The sonar cannot transverse these insoluble sediments, thus the middle segment
9
cannot be mapped. The old horizontal caverns cannot be used as UGS, since the shape
10
data is unknown.
11
A reliable construction modeling is greatly needed for the shape prediction and
12
stability/capacity evaluation of the old mined horizontal caverns. In addition, during
13
the new construction of horizontal salt caverns, modeling is needed for the design and
14
control of the caverns. Technological parameters, including injection flow rate,
15
injection position, and injection time in each leaching stages, will be optimized to
16
obtain a better shape with larger gas storage capacity and better stability.
17
However, the construction modeling of a horizontal salt cavern is much more
18
complicated than that of a vertical cavern, and the relative studies are rare. In 1995,
19
Kunstman and Urbancayk (1995) pointed out several difficulties in the modeling of
20
horizontal leaching, including the moving boundary, brines concentration/flow field
21
distribution, and mesh method of the horizontal cavern. The horizontal cavern has
22
three parts as a deviated segment, a middle segment and a direct segment (Fig. 1b). 6
1
The axisymmetric assumption of a vertical cavern (Nolen et al., 1974; Kunstman and
2
Urbanczyk, 2009; Li et al., 2018) is not suitable for a horizontal cavern. Saberian
3
(1995) firstly simulated the development of the middle segment of a horizontal cavern
4
by using a horizontal cylindrical grid. Russo (1995) presented a program named
5
HORSMIC to simulate the shape of the horizontal cavern, he concentrated on the
6
middle segment as well. Gronefeld and Saalbach (1998) used Darcy’s law to simplify
7
the complex flow field, which has greatly reduced the calculation efforts. However,
8
the shape prediction has not been verified. Liu et al. (2017, 2019) leached a horizontal
9
salt cavern in a pure salt sample, and investigated the serviceability and safety of
10
horizontal salt caverns by using mechanical stability analysis. The numerical shape
11
modeling is not involved.
12
The simulation and shape prediction of a horizontal cavern remain
13
unaccomplished in bedded salt. The reason is that the lateral developments of the
14
deviated and direct segments of a horizontal cavern are ignored in most
15
afore-mentioned studies. Considering the horizontal cavern starts from a horizontal
16
borehole, a horizontal cylindrical mesh is mostly used to trace the moving boundary
17
of the cavern (Saberian, 1995; Russo, 1995). However, the lateral developments of the
18
two ends of the cavern cannot be simulated. In addition, the insoluble substances are
19
not properly considered. Most previous studies have made assumptions that the salt is
20
pure (Kunstmann and Urbanczyk, 1995; Saberian, 1995; Russo, 1995; Gronefeld and
21
saalbach, 1998). However, there are many insoluble substances in salt formations and
22
its content can be pretty high (45% in Huai’an Salt) in bedded salt (Wang et al., 2016). 7
1
This assumption brings large deviations, e.g. the missing of the middle part of HA4-5
2
(Fig.2b) cannot be explained by current models. Without effective modeling for
3
construction design and shape prediction, the usage of horizontal caverns as gas
4
storage is seriously delayed.
5
In this study, a simulation model of horizontal salt caverns with moving
6
boundary is proposed, using theoretical methods and empirical assumptions. A novel
7
composite structural mesh is proposed to describe the development of the deviated,
8
middle and direct segments of the horizontal cavern. The empirical equations of the
9
salt-brine mass transfer rate are introduced. The coupled equations of the brines
10
flow/concentration field, the boundary movements and the accumulation of the
11
insoluble sediments in the three segments of the cavern are derived respectively. A
12
VC++ program is developed for the numerical solution of the model, using the finite
13
volume method. To verify the proposed model, a leaching experiment has been
14
conducted in the laboratory and the results are compared with the simulation. The
15
actual leaching process of HA4-5 horizontal cavern in Huai’an salt mine is simulated
16
as well. The simulated results are compared with the sonar mapping, drilling and field
17
injection-production data. At last, a new gas-injection and brine-discharge method is
18
proposed to increase the effective volume of the cavern, according to the simulated
19
shape of the horizontal salt cavern. This work will serve as a design and control tool
20
for the construction of horizontal salt caverns. It will promote the development of the
21
horizontal salt cavern gas storage in bedded salt, e.g. in China.
8
1
2. Model
2
During the construction of a salt cavern by water leaching, salt is dissolved in
3
water, and the cavern boundary develops. Since the horizontal cavern composed of
4
three segments, a composite structural mesh method is proposed to describe the
5
complex development. To predict the developing shape of the salt cavern, the
6
dissolution rate of the cavern boundary needs to be calculated, considering the
7
temperature and flow/concentration field of the brines. In addition, the insoluble
8
sediments should be considered as well.
9
2.1 Discretization by a composite structural mesh
10
In this paper, a composite structural mesh method is proposed to describe the
11
development of the horizontal salt cavern. The middle segment of the cavern is
12
described by a cylindrical mesh, whose axis is the horizontal borehole, as shown in
13
Fig. 3a. The lateral development of the two ends of the horizontal cavern are
14
described by two hemispherical grids, which turn into the deviated and the direct
15
segments. The cylindrical and hemispherical grids are composed by many vertical
16
sections, which are numbered by i from the deviated segment to the direct segment.
17
Different cavern cells on section i are numbered by j from bottom to top (Fig. 3b).
18
The control points of the cavern surface have fixed polar angles and variable radius,
19
ensuring that no negative volume will appear with the movement of the boundary. The
20
insoluble sediments are divided into columns (Fig. 3b), which share the same section
21
number i with the cavern cells. These columns are numbered by k along the radial 9
1
direction. (a)
Deviated segment
(b)
Direct segment
Middle segment
y
Cavern
il
iout
iin
z
ir
y Initial cavern shape (borehole)
2
Hemispherical grid
Cylindrical grid
x Axis of symmetry
Insoluble sediments
Hemispherical grid
3
Figure 3 A composite hemispherical-cylindrical-hemispherical mesh for the discretization of a
4
horizontal cavern. a Top view of the composite mesh. The horizontal cavern is divided into two
5
hemispherical parts and a cylindrical part. The three parts are composed by many vertical sections,
6
which are numbered by i. b Side view of section i. The cavern cells are numbered by j, and the
7
insoluble columns are numbered by k.
8
2.2 Salt dissolution and boundary movements
9
The dissolution rate of salt has a significant linear correlation with the
10
concentration of brines (Durie and Jessen, 1964). In addition, the temperature and the
11
angle of wall-brine interface play an important role as well. Wu et al. (1992) and
12
Chang et al. (1977) have proposed empirical formulae of the salt dissolution rate based
13
on laboratory experiments. On the basis of their studies, the dissolution rate of salt can
14
be calculated by,
15
T 0.44 ω (1c / c ) ln (sinα )0.25 s f e ω= 0.44 ω (1-c / c ) ln T α s f e 90
(α <90) (1)
(α >90)
16
where, ω is the dissolution rate of salt, ωf is the standard dissolution rate of a vertical
17
salt cavern wall in fresh water, which can be measured by experiments. Cs is the 10
1
concentration of the saturated brine, T is temperature, and α is the angle between the
2
normal direction of the salt cavern wall and the vertical upward direction, or the angle
3
of the salt-brine interface for short.
4
Thus, the boundary movements can be written as,
r {dx, dy, dz} = ω n
5 6
where, x, y, z are the coordinates of the curved surface of the cavern boundary,
7
the normal vector of the cavern boundary surface.
8 9
r n
is
According to the movements of the cavern boundary, the angle of the salt-brine interface can be calculated by,
∂z ∂z r n = ±{ ∂x , ∂y , 1} sin α = cos < nr ,{0, 0,1} >
10
11
(2)
(3)
2.3 Flow/concentration field
12
As described in Eq. (1), the dissolution rate of salt is mainly affected by the brine
13
concentration, temperature and salt-brine interface angle. The temperature can be
14
easily calculated by the geothermal gradient. The salt-brine interface angle can be
15
calculated from the cavern geometry. The concentration field is quite complicated
16
since it is coupled with the flow field of the brines in the cavern. It is a typical
17
convective mass transfer problem. Since the cavern size is large and the leaching last
18
for years, using traditional fluid mechanics method costs too much runtime (Misyura,
19
2018; Qiao and Yang, 2019b). To reduce the computational efforts, simplified
20
assumptions and empirical approaches are used, as in a vertical cavern.
21
Since the deviated segment and the direct segment alternate between injection 11
1
and production all the time, it is better to describe them by using “injection segment”
2
and “discharge segment” instead. The injection segment can be deviated segment or
3
direct segment, depending on where the fresh water is injected. Since the two
4
segments are expanding, their boundaries are updated according to their developing
5
radius, considering the sonar mapped shapes of the two segments are usually
6
axisymmetric (Shi et al., 2017). The brine concentration field of the injection, middle
7
and discharge segments of a horizontal cavern will be discussed in the following.
8
iin − il = rin idis − ir = rout
9
where, iin and idis are the indexes of the boundary sections between the
10
injection/discharge segments and the middle segment, il and ir are the indexes of
11
sections where the injection and discharge tubes are placed, rin and rout are the
12
maximum radii of the injection and discharge segments, which can be easily
13
calculated by using an enumeration method.
(4)
14
1) In the injection segment, fresh water or low concentration brines are injected
15
at a high flow rate (90-140 m3/h) through a tube with a diameter of 0.178 m. The
16
Reynold number is about 1e5- 2e5. The fully developed turbulent flow of fresh water
17
will flow upward with buoyancy, strongly mixing with the brines along the way.
18
While the highly saturated brines from salt dissolution flow down, the two flows will
19
be fully blended. Similar as in the direct leaching mode in a vertical cavern, the brines
20
above the injection tube can be seen as uniform (Kunstman and Urbanczyk, 2009; Li
21
et al. 2018). The salt mass conservation of this section can be written as,
12
1
∂ (Vin C in ) ∂V ∂V = QC 0 + ρ in (1 − u in ) − Q − in C in ∂t ∂t ∂t
2
where, Vin and Cin are respectively the volume and concentration of the injection
3
segment, Q and C0 are respectively the flow rate and concentration of the injected
4
liquid, ρ is the density of salt, and uin is the insolubles content.
(5)
5
QC0 is the mass of salt contained in the injected liquid, ρ∂Vin/∂t (1- uin) is the mass
6
of the dissolved salt, (Q-∂Vin/∂t)Cin is the mass of the salt contained in the outflow of
7
brines towards the middle segment. The volume of the injection segment can be
8
calculated by, iin
Vin = ∑ ∑ Vi, j
9
i =0
10
(6)
j
where, Vi,j is the volume of the cavern cell j in section i.
11
2) In the middle segment, the cavern bottom and most of the cavern wall are
12
covered by insoluble sediments, mainly the cavern top is dissolved. The dissolution of
13
the cavern top is much faster than that of the vertical cavern wall. The high
14
concentration brines from salt dissolution flow down like raindrops and are fully
15
mixed into the horizontal brine flow. The longitudinal concentration gradient of brines
16
is neglected in this paper, each section in the middle segment has the same brine
17
concentration and flow rate. Along the horizontal direction, the concentration will rise
18
due to the dissolution of salt. As shown in Fig. 4, the mass conservation of section i
19
can be written as,
20
21
C i − 1 Q i −1 − C i Q i + ρ
d Vi d( C i Q i ) (1 − u i ) = dt dt
(7)
where, Ci-1 and Qi-1 are the concentration and flow of the brines in section i-1, Ci, Qi, 13
1
Vi are the concentration, flow, and volume of the brines in section i, ui is the insoluble
2
content of the salt around section i.
3
Vi can be calculated by, Vi = ∑ Vi, j
4
(8)
j
dVi/dt
Dissolved part
Ci-1Qi-1
CiQi
Inflow
Outflow
Section i
5 6
Figure 4 Mass conservation of a section i in the middle segment of a horizontal cavern
7
Due to the incompressibility of the brines, the brine flow can be calculated by
8
volume conservation. The volume change of the brines with the concentration is
9
neglected.
10
11
dVin Qi = Q − dt Q − Q = dVi −1 i i −1 dt
( i = iin ) (9)
(iin < i ≤ iout )
where, Vi-1 and Qi-1 is the volume and flow of the brines in section i-1,
12
3) In the discharge segment, the brines are almost saturated after the salt
13
dissolution of the injection segment and a 200-400 m middle segment. Therefore, the
14
concentration can be seen as uniform. Taking the whole discharge segment as a
15
control volume, the mass of salt is conserved as,
14
1
∂ (Vout Cout ) ∂V ∂V = Qxr Cxr + ρ out (1 − uout ) − Qxr − out Cout ∂t ∂t ∂t
2
where, Vout is the volume of the discharge segment, and Cout is the concentration of the
3
brines. Qx and C x are respectively the flow rate and concentration of the brines in the r
4 5
r
last cell of the middle segment. uout is the insolubles content. The volume of the injection segment can be calculated by, Vout =
6
7
(10)
imax
∑ ∑V
i = iout
i, j
(11)
j
2.4 Insoluble sediments
8
During the leaching, the insoluble substances in bedded salt will fall down when
9
the salt to which they are attached is dissolved. The insoluble substances generated
10
from cell A on the cavern surface will settle within a distance R from its projection
11
point B on the cavern bottom, as shown in Fig. 5. According to the research of Li et al.
12
(2018), R is basically proportional to the fall height.
13
R = γ ( zA − zB )
14
where, γ is the coefficient between R and the fall height, zA and zB are the heights of
15
point A and B.
(12)
Cavern surface ∂V ub ∂t
Insoluble sediments surface
16
∂Z ∂t 15
Figure 5 The accumulation of the insoluble sediments.
1 2
Since the volume of the generated insoluble sediments from one cell is pretty
3
small, the distribution of the insolubles in the settling range can be seen as even.
4
Therefore, the height change of the insoluble sediments can be calculated by,
5
∂Z ∂V 1 = ub 2 ∂t ∂t π R
6
where, Z is the height of the insoluble sediments in the settling range, u is the
7
insolubles content, b is the bulking factor of insoluble substances in brines, and V is
8
the volume of cell A on the cavern wall.
(13)
9
After the calculation of the generated insolubles from all the cells on the cavern
10
surface, the height of the insoluble sediments needs to be adjusted according to the
11
angle of repose of the insoluble particles in brines. The unstable height of the
12
insoluble sediments can be described as, ∂Z ∂i > tan α ins ∂Z > tan α ins ∂k
13
14
(14)
where, αins is the angle of repose of the insoluble particles in brines.
15
For all the insoluble columns meeting Eq. (12), the height should be adjusted in
16
both i and k directions. Thus, the height increment of the insoluble sediments can be
17
written as,
18
∂Z = ∂t
∑
∂V 1 ub + dZ i + dZ k ∂t π R2
(15)
19
where, dZi and dZk are respectively the adjusted height in i and k directions. dZi and
20
dZk can be calculated by binary search, considering the volume conservation and 16
1
repose angle of the insoluble sediments. Detailed solving process of dZi and dZk can
2
be found in the research of Li et al. (2018).
3
3. Numerical implementation
4
According to the proposed mathematical model and mesh method, a VC++
5
program “Horizontal cavern leaching simulation program in bedded salt” (HCLS) is
6
developed by using the finite volume method, as in Fig. 6a. In HCLS, the main
7
calculating parameters include the dissolution rate of the cavern boundary, the
8
coordinates of the control points of the cavern surface, the flow and concentration
9
field of the brines, the height of the insoluble sediments, the cell volume and salt mass,
10
and the angle of the salt-brine interface. The calculation flow chart of HCLS is as
11
shown in Fig. 6b. All the calculating parameters are initialed after the input of
12
geological and technological parameters, and are updated in turn in each time step. (a)
(b) Geological parameters input and initialization Stage technological parameters input Dissolution rate Eq. (1) Boundary movements, Eq. (2, 3) Brine concentration/velocity, Eq. (4- 11) Insoluble sediments surface, Eq. (12- 15) No t=t+dt
If leaching stage ends Yes No If the whole process ends In/out alternate Yes Cavern shape export and data output
13 14
Figure 6 The developed program “Horizontal salt cavern leaching simulation (HCLS)”. a User’s
15
interface of HCLS. b Calculation flow chart of HCLS.
16
4. Experimental verification 17
1
To verify the proposed model, an experiment has been carried out in the
2
laboratory to simulate the leaching of a horizontal cavern. A 450×250×320 mm salt
3
sample from an open-pit salt mine in Pakistan is used, with insolubles content of 1.5%
4
(Chinese high-insoluble bedded salt formations are usually deep-buried, thus there are
5
no such big samples as from the open-pit salt mines). The 420×320 mm side of the
6
sample is smoothed, where a drilling channel has been carved on. A glass plate is
7
glued to this side as a plane of symmetry for the convenience of observation, as
8
shown in Fig. 7a. The left borehole is used as the injection segment, the leaching lasts
9
for 26 hours at an injection rate of 2 mL/min. The final cavern shape is as shown in
10
Fig. 7b. The cavern shows obvious nonuniformity along the horizontal direction. The
11
injection segment on the left is about 95 mm high, while the discharge segment on the
12
right barely develops. The reason is as described before: the injected fresh water flows
13
up and dissolves the salt around the injection segment first. When flowing in the
14
middle segment, the salt dissolution continues and the brine saturation rises. The brine
15
is finally saturated in the discharge segment, thus nearly no more salt is dissolved.
16
Worth to mention, the air contained in the salt sample is released and gathers on the
17
cavern top during the leaching process. The top of the injection segment of the cavern
18
is protected from being dissolved by this air pad, thus the injection segment develops
19
laterally instead.
18
a
b
c
100
50
0
95mm
Actual cavern
Insoluble sediments
Lateral development
81.0mm 77.8mm
Vertical coordinate / mm
Simulated cavern
100
1
50
0
50 150 100 Horizontal coordinate / mm
200
250
2 3
Figure 7 Experimental verification of the proposed model. a Preparation of the salt sample. b
4
Leached horizontal salt cavern with cover glass removed. c Comparison of the simulation and
5
experimental results.
6
A simulation is conducted by HCLS program, using the same parameters as the
7
experiment. According to the actual air pad position (about 95 mm height), a blanket
8
pad is also set in the simulation. As shown in Fig. 7c, the simulated cavern shape of
9
the proposed model is very close to the actual. The actual radius of the injection
10
segment is about 77.8 mm, while the simulated radius is 81.0 mm, about 4.1% larger.
11
The actual cavern volume is 386.7 mL, while the simulated cavern is 404.8 mL, about
12
4.7% larger. There is a deviation between the simulation and experiment, which has
13
been marked by a dashed line in Fig. 7c. This deviation occurs because the lateral
14
movements of the boundary of the injection segment cannot be simulated in the 19
1
proposed mesh system. This lateral development is ignored in the proposed model,
2
since there is no blanket pad in the field horizontal cavern leaching for now. In
3
general, the simulation can be seen as reliable, considering the measurement errors
4
and the lateral development of the top boundary of the injection segment.
5
5. Field application and verification
6
The construction process of HA4-5 horizontal cavern in Huai’an, China is
7
simulated by the proposed model and program. HA4-5 is a lately completed
8
horizontal salt cavern in Huai’an salt mine. The salt formations are layered, buried
9
between -1508 m and -990 m. The average content of the insoluble substances is 45%,
10
the major components of the insolubles are mudstone and gypsum. Two separate
11
caverns, HA-5 and HA-4, are mapped by sonar in June, 2017 (Shi et al., 2017). The
12
volume of HA-5 is about 121,000 m3 and HA-4 is about 52,000 m3. The total volume
13
of the injected water is about 7,019,000 m3, 3,690,000 m3 for HA-5 and 3,329,000 m3
14
for HA-4. The leaching flow rate varies from 90 to 140 m3/h. There have been 4
15
injection-production cycles. The concentration of the brine production is saturated
16
(300 g/L) or nearly saturated during the leaching. Since HA4-5 is only designed for
17
salt mining at the first place, there are no more detailed field leaching data. In the
18
simulation, the flow rate is assumed as a constant 120 m3/h, and the 4 leaching cycles
19
are assumed to be equal in time.
20
Mapped cavern
Porous insoluble sediments
-1250
Simulated cavern
Cavern HA-5 -1330
Cavern HA-4
Suggested brine discharge
Potential storage space -1410
Depth / m
Suggested gas injection
Third cavern
Simulated depth (-1468 m)
-1490
Detected depth (-1477 m)
80
0
2
80
160
240
320
400
Horizontal coordinate / m
1
Figure 8 Simulated and mapped cavern shapes of HA4-5 horizontal cavern in Huai’an, China.
3
A comparison of the simulation results and of the field data is shown in Fig. 8.
4
The simulated cavern has four parts, including porous insoluble sediments and three
5
open caverns as HA-4, HA-5 and an undected cavern in the middle. The simulation
6
results basically coincide with the field data, the details are as follows.
7 8
1) According to the previously mentioned injection and production data, the total mass of the dissolved salt can be calculated by,
9
M salt = Vinjection Cdischarge =7019000 × 300 ≈ 2.1× 109 kg
10
where, Msalt is the mass of the dissolved salt, Vinjection is the total volume of the
11
injected water, Cdischarge is the average concentration of the brine production.
12
13
(16)
Thus, the total volume of the dissolved part of the cavern can be calculated by,.
Vdissolve
M salt / ρ 2.1×109 / 2300 = = ≈ 1.66 ×106 m3 1− u 1 − 0.45
(17)
14
where, Vdissolve is the total volume of the dissolved part, including salt and insolubles.
15
u is the average content of insoluble substances in the salt formation. 21
1
The simulated volume is about 1,598,000 m3, about 3.7% smaller. Porous
2
insoluble sediments (the red part in Fig. 8) fill most of the cavern, due to the high
3
content (45%) and high bulking factor (1.6~1.8) of the insoluble substances in the salt
4
formations. This explains why only the two separate caverns HA-4 and HA-5 can be
5
mapped by sonar.
6
2) The depth range of the simulated HA-5 is between -1245.2 m and -1287.8 m,
7
the diameter is 86.2 m. According to the sonar mapping, the depth range of the actual
8
HA-5 is between -1260.7 m and -1301.0 m, the diameter is about 90.2 m. The size of
9
the simulated HA-5 is basically coincide with the actual cavern, with an error about
10
4.4%. The position of the simulated HA-5 is about 14 m higher than the actual cavern,
11
about 6% of the total height (230 m).
12
3) The depth range of the simulated HA-4 is between -1277.0 m and -1299.6 m,
13
the diameter is 84.1 m. According to the sonar mapping, the depth range of the actual
14
HA-4 is between -1292.5 m and -1314.0 m, the diameter is about 64.0 m. The position
15
of the simulated HA-5 is about 15 m higher than the actual cavern, about 6.5 % of the
16
total height (230 m). The error of the diameter of the simulated HA-4 is pretty large as
17
20 m. The diameters of the actual HA-4 (64 m) and HA-5 (90 m) are quite different as
18
well, although the volume of the injected water are almost the same. Thus, the
19
differences might result from the heterogeneity of the salt formation, which is not
20
considered in our model.
21
4) The simulation shows that there is a third cavern deep-seated in between the
22
two open caverns HA-4 and HA-5. It cannot be mapped by sonar due to the blocking 22
1
of the insoluble sediments. To confirm the existence of the third cavern, a borehole
2
was drilled to the middle in between the two caverns in September 2018. An open
3
space was successfully detected at -1477 m, confirming the reliability of the proposed
4
model. The depth of the detected cavern is 9 meters lower than the simulation (Fig. 8),
5
which is about 3.75% of the total height of HA4-5 and is acceptable for actual
6
engineering.
7
6. Discussion and suggestion
8
Through comparison, it can be said that the proposed model is reliable as a design
9
and prediction tool for the construction of horizontal salt caverns. The shape of a
10
horizontal salt cavern is firstly simulated with acceptable accuracy in bedded salt with
11
high insoluble content (45 %). It provides the critical data for the usage of hundreds of
12
old horizontal salt caverns in this area. There are some errors of the detailed shapes
13
and positions of the two open caverns, probably due to the missing of the detailed
14
field leaching data and the simplifications of our model. The accuracy of the model
15
will be further improved by trials and errors in our next work, using more detailed
16
field data and more accurate flow and concentration models.
17
The simulation shows that the whole cavern is shaped like a letter “U” in bedded
18
salt, rather than a horizontal ellipsoid or dumbbell as in the salt domes (Colomé et al.,
19
2010). There is a third open cavern in the middle of the U-shaped cavern, which
20
indicates a novel method for gas/oil injection and brine discharge. Traditionally in the
21
vertical caverns, the pore space in the insoluble sediments cannot be used for oil/gas 23
1
storage, for the de-brine tube cannot be placed below the insolubles or it will be
2
blocked (Wang et al. 2018). Now the third cavern can be used as a de-brine pool by
3
drilling and placing the de-brine tube in it. Gas or oil can be injected into HA-4 and
4
HA-5. The brines in the open caverns as well as in the pores of the insoluble
5
sediments will be extruded from the third cavern and replaced by gas/oil without
6
clogging, as shown in Fig. 8. Actually, the volume of the pores of the insoluble
7
sediments is much larger than the volume of the two open caverns. The volume of the
8
pore spaces of HA4-5 can be estimated by,
9
V pore = Vinsoluble ( b − 1)= V dissolve u ( b − 1) = 1.66 × 10 6 × 0.45 × (1.8 − 1) = 597, 600m 3 (18)
10
where, Vpore is the volume of pore space in insoluble sediments, Vinsoluble is the volume
11
of the insoluble substances contained in the dissolved salt, b is the bulking factor of
12
the insoluble substances in the brines.
13
The sum of the volumes of the two open caverns (HA-4 and HA-5) is only about
14
173,000 m3. Plus Vpore, the effective storage space of the cavern will reach about
15
770,600 m3, about 4.45 times larger than the volume of the detected spaces by sonar.
16
Under our suggestions, the field gas injection and brine discharge using the proposed
17
method has started in HA4-5 cavern in October 2018.
18
The finding shows that, in the high-insoluble bedded salt in China, the horizontal
19
salt caverns are more suitable to be used as UGSs than the vertical caverns, since the
20
U-shape and the third cavern allow the pores in the insoluble sediments to be replaced
21
by gas. Considering the quantity of the mined old horizontal salt caverns in China, as
22
shown in Fig.2, this finding promises substantial economic benefits. 24
1
7. Conclusions
2
1) In summary, a numerical model is demonstrated to predict the development of
3
horizontal
4
hemispherical-cylindrical-hemispherical mesh is proposed to describe the
5
complex boundary movements of the three segments (deviated segment, middle
6
segment and direct segment as in Fig. 1b) of a horizontal cavern. The empirical
7
equations of the dissolution rate of salt are introduced. The coupled equations of
8
the boundary movements, flow/concentration field of brines of the three segments
9
of the horizontal cavern have been derived. The accumulation of the insoluble
10
salt
caverns
during
construction.
A
composite
sediments is firstly considered in the modeling of a horizontal salt cavern.
11
2) A VC++ program “Horizontal cavern leaching simulation program in bedded salt”
12
(HCLS) is developed by using the finite volume method to implement the
13
proposed model. The reliability of the model and program have been
14
demonstrated by laboratory experiments and field applications. The proposed
15
model and program can serve as a design and control tool for the construction of
16
horizontal salt caverns.
17
3) The shape of a horizontal cavern HA4-5 (Huai’an, China) in a high-insoluble salt
18
formation has firstly been simulated by the proposed model. Confirmed by sonar
19
imaging and exploratory drilling, the simulated horizontal cavern is U-shaped
20
with a third cavern deep-seated in between HA-4 and HA-5. The third cavern is
21
suggested to be used as a non-clogging de-brine pool during gas injection and
22
brine discharge. Thus, the pore space in the insoluble sediments will be available 25
1
for gas/oil storage, the cavern capacity will be multiplied. It promises a broad
2
prospect for the horizontal salt cavern gas storage in bedded salt, e.g. in China.
3
References
4
Bai, M.X., Song, K.P., Sun, Y.X., He, M.Q., Li, Y., Sun, J.P., 2014. An overview of hydrogen
5
underground storage technology and prospects in China, J. Petrol. Sci. Eng. 124, 132–136.
6
https://doi.org/10.1016/j.petrol.2014.09.037
7
Bérest, P., Bergues, J., Brouard, B., Durup, J.G., Guerber, B., 2001. A salt cavern
8
abandonment
9
https://doi.org/10.1016/S1365-1609(01)00004-1
10 11
test.
Int.
J.
Rock
Mech.
Min.
38(3),
357-368.
Chang, C, Vliet, G C, Saberian, A., 1977. Natural Convection Mass Transfer at Salt-Brine Interfaces. Journal of Heat Transfer 99(4): 603-608. DOI: 10.1115/1.3450749
12
Chen, X.S., Li, Y.P., Liu, W., Ma, H.L., Ma, J.L., Shi, X.L., Yang, C.H., 2019. Study on
13
sealing failure of wellbore in bedded salt cavern gas storage. Rock Mech. Rock Eng. 52(1),
14
215-228. https://doi.org/10.1007/s00603-018-1571-5
15
Chen, J., Lu, D., Liu, W., Fan, J.Y., Jiang, D.Y., Yi, L., 2020. Stability study and optimization
16
design of small-spacing two-well (SSTW) salt caverns for natural gas storages. J. Energ. Storage.
17
27, 101131. https://doi.org/10.1016/j.est.2019.101131.
18
Colomé, J.D., Preti, L., Carbajal, R., Wood, M.G., 2010. Improving dual well horizontal
19
cavern volume and shape predictions by post-processing single well sonar data. In: Solution
20
Mining Research Institute Fall Technical Conference, Leipzig Germany.
21 22 23
Durie, R.W., Jessen, F.W., 1964. Mechanism of the dissolution of salt in the formation of underground salt cavities. SPE J. 4(2), 183-190. DOI: 10.2118/678-PA Fan, J.Y., Jiang, D.Y., Liu, W., Wu, F., Chen, J., Daemen, J.J.K., 2019. Discontinuous fatigue
24
of salt rock with low-stress intervals. Int. J. Rock Mech. Min. 115(3), 77-86.
25
https://doi.org/10.1016/j.ijrmms.2019.01.013
26
Ge, X.B., Li, Y.P., Shi, X.L., Chen, X.S., Ma, H.L., Yang, C.H., Shu, C., Liu, Y.X., 2019a. 26
1
Experimental Device for the Study of Liquid–Solid Coupled Flutter Instability of Salt Cavern
2
Leaching Tubing. J. Nat. Gas Sci. Eng. 66, 168-179. https://doi.org/10.1016/j.jngse.2019.03.026
3
Ge, X.B., Li, Y.P., Chen, X.S., Shi, X.L., Ma, H.L., Yin, H.W., Zhang, N., Yang, C.H., 2019b.
4
Dynamics of a partially confined, vertical upward-fluid-conveying, cantilever pipe with reverse
5
external flow. Applied Sciences, 9(7), 1425. https://doi.org/10.3390/app9071425
6 7
Gronefeld, P., Saalbach, B., 1998. Numerical 3D simulation of horizontal leaching processes. In: Solution Mining Research Institute Fall Meeting, Rome, Italy.
8
Kunstman, A., Urbanczyk, K., 1995. Modelling of horizontal cavern leaching: Main aspects
9
and perspectives. In: Solution Mining Research Institute Fall Meeting, San Antonio, Texas, U.S.A.
10
Kunstman, A., Urbanczyk, K., 2009. Application of winubro program to modelling of carven
11
development in trona deposit. In: Solution Mining Research Institute Spring Technical Conference,
12
Krakow, Poland.
13
Lawal, K.A., Ovuru, M.I., Eyitayo, S.I., Matemilola, S. Adeniyi, A.T., 2016. Underground
14
storage as a solution for stranded associated gas in oil fields. J. Petrol. Sci. Eng. 150, 366–375.
15
https://doi.org/10.1016/j.petrol.2016.12.020
16
Li, J.L. Shi, X.L., Yang, C.H., Li, Y.P., Wang, T.T., Ma, H.L., 2018. Mathematical model of
17
salt cavern leaching for gas storage in high-insoluble salt formations. Sci. Rep. 8(1), 372.
18
DOI: 10.1038/s41598-017-18546-w
19
Li, J.L., Tang, Y., Shi, X.L., Xu, W.J., Yang, C.H., 2019a. Modeling the construction of
20
energy
storage
salt
caverns
in
bedded
21
https://doi.org/10.1016/j.apenergy.2019.113866
salt.
Applied
Energy
255,
113866.
22
Li, J.L., Xu, W.J., Zheng, J.J., Liu, W., Shi, X.L., Yang, C.H., 2020a. Modeling the mining of
23
energy storage salt caverns using a structural dynamic mesh. Energy 193, 116730.
24
https://doi.org/10.1016/j.energy.2019.116730
25 26
Li, J.L., Shi, X.L., Zhang, S., 2020b. Construction modeling and parameter optimization of multi-step horizontal energy storage salt caverns. Energy, In Press.
27
Li, Y.P., Liu, W., Yang, C.H., Daemen, J.J.K., 2014. Experimental investigation of mechanical
28
behavior of bedded rock salt containing inclined interlayer. Int. J. Rock Mech. Min. 69, 39-49.
29
DOI: 10.1016/j.ijrmms.2014.03.006 27
1
Li, Y.P., Chen, X.S., Shi, X.L., Zhang, N., Ma, C.K., Yang, C.H. 2019b. Analysis of the
2
plugging process of the leaking interlayer in a thin interbedded salt cavern gas storage of Jintan
3
(China) by high-pressure grouting and potential applications. J. Nat. Gas Sci. Eng. 68, 102918.
4
https://doi.org/10.1016/j.jngse.2019.102918
5
Liu, W., Chen, J., Jiang, D.Y., Shi, X.L., Li, Y., Daemen, J.J.K., Yang C.H., 2016. Tightness
6
and suitability evaluation of abandoned salt caverns served as hydrocarbon energies storage under
7
adverse
8
http://dx.doi.org/10.1016/j.apenergy.2016.06.086
geological
conditions
(AGC).
Appl.
Energ.
178,
703-720.
9
Liu, W., Jiang, D.Y., Chen, J., Daemen, J.J.K., Wu, F., 2017 Comprehensive feasibility study
10
of two-well-horizontal caverns for natural gas storage in thinly-bedded salt rocks in china. Energy
11
143(15), 1006-1019. https://doi.org/10.1016/j.energy.2017.10.126
12
Liu, W., Zhang Z.X., Chen J., Fan J.Y., Jiang, D.Y., Daemen, J.J.K., 2019. Physical
13
simulation of construction and control of two butted-well horizontal cavern energy storage using
14
large
15
https://doi.org/10.1016/j.energy.2019.07.014
molded
rock
salt
specimens.
Energy
185,
682-694.
16
Lordache, M., Schitea, D., Deveci, M., Akyurt, I.Z., Lordache, L., 2019. An integrated ARAS
17
and interval type-2 hesitant fuzzy sets method for underground site selection: Seasonal hydrogen
18
storage
19
https://doi.org/10.1016/j.petrol.2019.01.051.
20 21
in
salt
caverns,
J.
Petrol.
Sci.
Eng.
175.
1088-1098.
Misyura, S.Y., 2018. The influence of characteristic scales of convection on non-isothermal evaporation of a thin liquid layer. Sci. Rep. 8, 11512. DOI: 10.1038/s41598-018-29015-3
22
Niu, C.K., Tan, Y.F., Li, J.N., Song, C.L., 2015. Model validation and stability analysis for
23
operation projects in Jintan Salt Cavern for strategic oil storage of China, J. Petrol. Sci. Eng. 127:
24
44-52. https://doi.org/10.1016/j.petrol.2015.01.029
25
Nolen, J.S., von Hantlemann, O., Meister, S., Kleinitz, W., Heiblinger, J., 1974. Numerical
26
simulation of the solution mining process. In: SPE European Spring Meeting, Amsterdam,
27
Netherlands. http://dx.doi.org/10.2118/4850-MS
28
Qiao, W., Yang, Z., 2019a. Forecast the electricity price of U.S. using a wavelet
29
transform-based hybrid model. Energy 193, 116704. https://doi.org/10.1016/j.energy.2019.116704 28
1
Qiao, W., Yang, Z., 2019b. An improved dolphin swarm algorithm based on Kernel Fuzzy
2
C-means in the application of solving the optimal problems of large-scale function. IEEE Access.
3
In Press. Doi:10.1109/ACCESS.2019.2958456.
4
Qiao, W., Yang, Z., Kang, Z., Pan, Z., 2020a. Short-term natural gas consumption prediction
5
based on Volterra adaptive filter and improved whale optimization algorithm. Eng. Appl. Artif.
6
Intel. 87, 103323.
7
Qiao, W., Lu, H., Zhou, G., Azimi, M., Yang, Q., Tian, W., 2020b. A hybrid algorithm for
8
carbon dioxide emissions forecasting based on improved lion swarm optimizer. J. Clean. Prod.
9
244, 118612.
10 11 12 13 14
Russo, A.J., 1995. HORSMIC Solution Mining Code for Horizontal Caverns. In: Solution Mining Research Institute Fall Meeting, San Antonio, Texas, USA. Saberian, A., 1995. A preliminary model for horizontal well leaching. In: Solution Mining Research Institute Fall Meeting, San Antonio, Texas, USA. Scott, V., Gilfillan, S., Markusson, N., Chalmers, H., Haszeldine, R.S., 2012. Last chance for
15
carbon capture and storage. Nature Clim. Change 3(2), 105-111. DOI: 10.1038/NCLIMATE1695
16
Shi, X.L., Li, Y.P., Yang, C.H., Xu, Y.L., Ma, H.L., Liu, W., Ji, G.D., 2015. Influences of
17
filling abandoned salt caverns with alkali wastes on surface subsidence. Environmental Earth
18
Sciences 73, 6939-6950. DOI: 10.1007/s12665-015-4135-y
19
Shi, X. L. Li, J. L. Chen, T., 2017. Detection and evaluation of Huai’an horizontal cavern (in
20
Chinese). (Technical report of Institute of Wuhan Rock and Soil Mechanics, Chinese Academy of
21
Science).
22
Soubeyran, A., Rouabhi, A., Coquelet, C., 2019. Thermodynamic analysis of carbon dioxide
23
storage in salt caverns to improve the Power-to-Gas process. Appl. Energ. 242, 1090–1107.
24
https://doi.org/10.1016/j.apenergy.2019.03.102
25
Wang, T.T., Yang, C.H., Li, J.J., Li, J.L., Shi, X.L., Ma, H.L., 2016. Failure analysis of
26
overhanging blocks in the walls of a gas storage salt cavern: a case study. Rock Mechanics &
27
Rock Engineering 1-13. doi:10.1007/s00603-016-1102-1
28 29
Wang, T.T. Yang, C.H., Wang, H.M., Ding, S.L., Daemen, J.J.K., 2018. Debrining prediction of a salt cavern used for compressed air energy storage. Energy 147, 464-476. 29
1 2 3
https://doi.org/10.1016/j.energy.2018.01.071 Wu, G., Xiao, C. F., Qiu, X. D. Study on the dissolution rate of rock salt (in Chinese). Chem. Min. Tech. 01, 19-22 (1992).
4
Xing, W., Zhao, J., Hou, Z.M., Were, P., Li, M.Y., Wang, G., 2015. Horizontal natural gas
5
caverns in thin-bedded rock salt formations. Environ. Earth Sci. 73, 6973-6985. DOI:
6
10.1007/s12665-015-4410-y
7
Yang, C.H., Wang, T.T., Li, Y.P., Yang, H.J., Li, J.J., Qu, D.A., Xu, B.C., Yang, Y., Daemen,
8
J.J.K., 2015. Feasibility analysis of using abandoned salt caverns for large-scale underground
9
energy
10
storage
in
China.
Applied
Energy
137
(1),
467-481.
http://dx.doi.org/10.1016/j.apenergy.2014.07.048
11
Yang, C.H., Wang, T.T., Qu, D.A., Ma, H.L., Li, Y.P., Shi, X.L., Daemen, J.J.K., 2016.
12
Feasibility analysis of using horizontal caverns for underground gas storage: a case study of
13
yunying
14
http://dx.doi.org/10.1016/j.jngse.2016.10.009
salt
district.
J.
Nat.
Gas
Sci.
Eng.
36,
252-266.
15
Zhang, N., Ma, L.J., Wang, M.Y., Zhang, Q.Y., Li, J., Fan, P.X., 2016. Comprehensive risk
16
evaluation of underground energy storage caverns in bedded rock salt. J. Loss Prevent Proc. 45,
17
264-276. https://doi.org/10.1016/j.jlp.2016.10.016
18
Zhang, N., Shi, X.L., Wang, T.T., Yang, C.H., Liu, W., Ma, H.L., Daemen J. K., 2017.
19
Stability and availability evaluation of underground strategic petroleum reserve (SPR) caverns in
20
bedded
21
https://doi.org/10.1016/j.energy.2017.06.073
rock
salt
of
Jintan,
China.
Energy
134,
504-514.
22
23
Acknowledgements
24
The authors wish to acknowledge the financial supports of Basic Science Center
25
Program for Multiphase Evolution in Hypergravity of the National Natural Science
26
Foundation of China (No. 51988101), China Postdoctoral Science Foundation (Grant
27
No. 2018M642433), National Natural Science Foundation of China (Grant No. 30
1
51774266), Open Research Fund of State Key Laboratory of Geomechanics and
2
Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of
3
Sciences(Grant No. Z018021), Fundamental Research Funds for the Central
4
Universities (No. 2019QNA4034, 2019QNA4035), Natural Science Foundation for
5
Innovation Group of Hubei Province, China (Grant No. 2016CFA014). The authors
6
are sincerely grateful to Jiangsu Suyan Jingshen Co., Ltd and PetroChina for their
7
help in the field.
8 9
Author Contributions
10
J.L. wrote the main manuscript text and are responsible for the mathematical model
11
and the program implementation; C.Y., X.S. and W.X. have made contributions to the
12
conception and design of the work. Y.L. and J.D. have made contributions to the
13
improvements of the model and the analysis of the results. All authors discussed the
14
results and critically reviewed the manuscript.
31
Highlights A model and a C++ program are presented for the construction simulation and shape prediction of a horizontal salt cavern. A composite structural mesh and a simplified flow/concentration field model are proposed. The high-content of insoluble substances in bedded salt are considered. The reliability of the model has been verified by laboratorial and field tests. A third cavern is simulated and detected, using which a gas injection method is proposed to increase the effective storage capacity.
Li Jinlong: Methodology, Software, Writing - Original Draft, Visualization, Data Curation Yang Chunhe: Conceptualization, Resources, Supervision Shi Xilin: Investigation, Validation, Project administration Xu Wenjie: Validation, Funding acquisition Li Yinping: Conceptualization, Validation Jaak J.K. Daemen: Writing - Review & Editing
Declaration of interests √The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: