Stability analysis of complex behavior of salt cavern subjected to cyclic loading by laboratory measurement and numerical modeling using LOCAS (case study: Nasrabad gas storage salt cavern)

Abstract

Stability analysis of salt caverns is a very complicated subject due to the coupled time-dependent thermo-mechanical behavior of salt during leaching and operational phase of the gas storage subjected to the cyclic loading. Because of purely plastic behavior of salt and the relevant convergence during injection and withdrawal, investigation of the salt cavern stability becomes more challenging. The objective of this study is stability analysis of Nasrabad salt cavern by numerical method using a comprehensive software entitled LOCAS having capability to model the complex time-dependent thermo-mechanical behavior of salt under cyclic loading of natural gas pressure. Measurement of geomechanical properties of salt is also the important requirement for modelling. First, geomechanical properties of Nasrabad salt including uniaxial and tri-axial compressive strength, tensile strength, uniaxial and tri-axial creep under different temperatures were measured. Thereafter, time-dependent behaviors and parameters of dilatancy criterion of the test results were analyzed by the advanced constitutive models for rock salt to obtain accurate parameters for modeling. Then, long-term stability was analyzed for Nasrabad salt cavern having different shapes, sizes, and depths under cyclic loading 3–8 MPa as minimum and maximum gas pressures. The results showed that an ellipsoidal cavern having initial volume of 100,000 m³ at 450 m depth by 0.3% creep closure rate per year and volume loss of 0.8% of the initial volume per year as ideal conditions can store 8,000,000 m³ natural gas with working capacity of about 6,000,000 m³.

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Environmental Earth Sciences (2021) 80:317
https://doi.org/10.1007/s12665-021-09620-8
ORIGINAL ARTICLE
Stability analysis ofcomplex behavior ofsalt cavern subjected tocyclic
loading bylaboratory measurement andnumerical modeling using
LOCAS (case study: Nasrabad gas storage salt cavern)
RahimHabibi1· HassanMoomivand1· MortezAhmadi2· AminAsgari3
Received: 4 May 2020 / Accepted: 17 November 2020
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
Abstract
Stability analysis of salt caverns is a very complicated subject due to the coupled time-dependent thermo-mechanical
behavior of salt during leaching and operational phase of the gas storage subjected to the cyclic loading. Because of purely
plastic behavior of salt and the relevant convergence during injection and withdrawal, investigation of the salt cavern stabil-
ity becomes more challenging. The objective of this study is stability analysis of Nasrabad salt cavern by numerical method
using a comprehensive software entitled LOCAS having capability to model the complex time-dependent thermo-mechanical
behavior of salt under cyclic loading of natural gas pressure. Measurement of geomechanical properties of salt is also the
important requirement for modelling. First, geomechanical properties of Nasrabad salt including uniaxial and tri-axial
compressive strength, tensile strength, uniaxial and tri-axial creep under different temperatures were measured. Thereafter,
time-dependent behaviors and parameters of dilatancy criterion of the test results were analyzed by the advanced constitutive
models for rock salt to obtain accurate parameters for modeling. Then, long-term stability was analyzed for Nasrabad salt
cavern having different shapes, sizes, and depths under cyclic loading 3–8MPa as minimum and maximum gas pressures.
The results showed that an ellipsoidal cavern having initial volume of 100,000 m3 at 450m depth by 0.3% creep closure rate
per year and volume loss of 0.8% of the initial volume per year as ideal conditions can store 8,000,000 m3 natural gas with
working capacity of about 6,000,000 m3.
Keywords Salt cavern· Natural gas· Time dependent· Thermo-mechanical· Underground storage· LOCAS
Introduction
Natural gas storage has an important role in regulation of
gas distribution as it can provide the possibility by which
the gas pipelines work at their maximum capacity. To meet
this demand, storing natural gas in underground spaces as
well as salt caverns is a way to provide the proper energy
management. Numerous cavern storage facilities have been
developed worldwide in salt formations due to safety issues
which are triggered with low permeability and healing salt
strata (Horváth etal. 2018). The complex time-dependent
thermo-mechanical behavior of salt considerably affects the
salt cavern behavior during leaching, debrining, and opera-
tional phase under cyclic loading.
Nasrabad salt dome is one of the largest salt formations
in central Iran, northwest of Kashan, 240km from Tehran.
It has extensions of 6.12km in northwest and 11.5km in
southeast directions. Nasrabad gas storage project is the first
salt cavern gas storage being constructed in Iran Nasrabad
* Hassan Moomivand
h.moomivand@Urmia.ac.ir
Rahim Habibi
R.Habibi12@yahoo.com
Mortez Ahmadi
moahmadi@modares.ac.ir
Amin Asgari
AminAsgari2010@gmail.com
1 Mining Engineering Department, Urmia University, Urmia,
Iran
2 Mining Engineering Department, University ofTarbiat
Modares, Tehran, Iran
3 Faculty ofMining, Petroleum andGeophysics Engineering,
Shahrood University ofTechnology, Shahrood, Iran
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Environmental Earth Sciences (2021) 80:317
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salt cavern project is conducted by National Iranian Gas
Company (NIGC) to ensure energy demand of Tehran at
peak points of energy consummation. In summer, when the
gas consummation is low, the natural gas would be stored
in the cavern, in winter it would flow through the network
of distribution pipelines. So, it experiences one injection/
production cycle per year. However, in most cases, salt cav-
erns experience daily cycles. Nasrabad rock salt has low
strength and high creep deformation and such behaviors
of salt cause many challenges for cavern construction and
operation (Wang etal. 2018; Li etal. 2019).
The stresses around a storage cavern are induced by the
difference between the gas pressure acting on the cavern
walls and the insitu stresses in the surrounding salt forma-
tion. The creep deformation, in turn, is influenced by the
time-dependent thermo-mechanical behavior of salt rock
under cyclic loading around the cavern. Damage evolution
with the creep progress causes micro-fracturing and spalling
of the cavern roof and finally failure of the casing shoe.
Therefore, on the one hand, time-dependent thermo-mechan-
ical behavior of salt cavern needs to be investigated in design
step and, on the other hand, the geometrical and operational
parameters of the cavern are required to be developed by
modeling (Ghasemloonia and Butt 2015). To reach a desir-
able stability and a suitable serviceability of caverns, various
design methods have been proposed by researchers during
decades so as to operational pressures were limited between
a range in which no or less micro-fracturing was permit-
ted (Habibi 2019). However, recently, DeCosta etal. (2020)
proposed a new conceptual design method through which
a parametric study is performed to select the best relation
between flow rate, leaching time, structural stability, and
the volume of gas. Finally, a geomechanical design will be
conducted by means of these parameters.
The creep behavior of a salt rock can be divided into
three major stages: transient, steady state, and tertiary. The
steady-state creep behavior is supposed to the dominant
type of behavior in the underground salt cavern, and sev-
eral empirical models have been developed to describe this
behavior. Passaris (1979) proposed a relatively simple con-
stitutive model for rock salt by a spring element, a sticky and
a Kelvin model. Munson (1997) and Hunsche and Hampel
(1999) presented constitutive models in which the creep rate
of the secondary creep stage (steady creep) is expressed as a
power function with deviatotic stress and exponential rela-
tionship with temperature. Qiu etal. (2003) also developed
a creep model by the comparative analysis for the reasons
why creep damage of two kinds of rock salt is different.
Some researches have also been carried out to describe
the constitutive equation relevant to steady creep rate with
respect to the influences of temperature, confining pressure,
deviatotic stress for the creep of rock salt (Ling etal. 2007;
Tijani 2009; Jiang etal. 2012, Thoraval etal. 2015). The
nonlinear relation between steady-state creep rate (second-
ary creep stage) and stress which is sensitive to temperature
and activation energy of salt, has been accepted by several
researchers (Brouard etal. 2002; Djizanne etal. 2014). Such
models have been defined in the finite element software
entitled LOCAS developed by Brouard Consulting (2014)
for salt caverns which was used in this research. Brouard
etal. (2002) applied LOCAS for better understanding of the
long-term behavior, especially abandonment of salt cavern.
Elasto-visco-plastic behaviors of cement and casing and salt
can also be taken into account numerically using LOCAS
(Brouard etal. 2006). The effect of a rapid pressure build-up
which leads to onset of tensile effective stresses at the cavern
wall, as it is observed in a gas-filled salt cavern experiencing
large yearly pressure cycles has been considered in LOCAS
(Brouard etal. 2007a, b). Some thermo-mechanical simula-
tions of the salt cavern behavior under different gas opera-
tion scenarios have also been discussed using LOCAS and
ABAQUS in which the stresses, strain states, and stability
can be analyzed (Karimi-Jafari etal. 2011). The generated
effective tensile stresses at the cavern wall by rapid pressure
changes can lead to micro-fracturing and increasing perme-
ability. Djizanne etal. (2012) studied the state of stresses
under different scenarios by different stability criteria using
LOCAS. Djizanne etal. (2014) applied LOCAS to explain
falling overhanging blocks under different temperatures and
stresses which are commonly created when salt is leached.
Caverns progressively close in salt are because salt
deforms continuously and permanently when subject to a
stress exceeding the yield. The stresses increase as the cav-
ern gas pressure decreases. In turn, the rate of creep closure
increases as a power function of the shear stress. The shear
stresses can exceed the strength and create the micro-frac-
ture in the salt surrounding a cavern when the gas pressure
inside the cavern decreases considerably. The micro-fracture
or dilatancy creates additional porosity in the salt and cavern
volume decreases during creep deformation.
Some stability criteria have been proposed for rock
salt (Spirs etal. 1990; Van Sambeek etal. 1993; De Vries
etal. 2005; Rokhar etal. 2003; Nieland and Ratigan 2006;
Hampel 2012). The power function relation between second
invariant of the deviatoric stress (
√
J
2
) and the first invariant
of the stress (I1) with a nonzero intercept has been developed
for salt caverns (De Vries etal. 2005) as its parameters have
been defined in LOCAS software.
Apart from these, various numerical modellings have
been performed to investigate the stability of salt caverns due
to the operational pressure, volume loss rate, displacements
of cavern’s roof (Chan etal. 1997; Adams 1997; DeVries
etal. 2002, 2005; Heusermann etal. 2003; Sobolik and
Ehgartner 2006; Wang etal. 2019; Ma etal. 2012; Nazary-
Moghadam etal. 2015; Yang etal. 2016). These authors have
provided important guidance for the study and evaluation of
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the stability of salt caverns from geomechanical prospective.
Yet, regarding to the thermally induced stresses, recently,
Böttcher and Görke (2017) applied OpenGeoSys as a cou-
pled simulator using a visco-elastic constitutive law to inves-
tigate the effect of thermal loads on stability of the cavern.
The results proved that thermally induced loads can induce
tensile stress around the cavern. Initiation tensile fracture
was proved through insitu experiments by Blanco-Martin
etal. (2018) at Varangéville salt mine in North-Eastern
France. Ngo and Pellet (2018) used fracture mechanics in
the extended finite element code to address fracture location
and fracture geometry due to thermal loading. Thereafter,
Labaune and Rouabhi (2019) investigated the behavior of
a spherical cavern thermo-mechanically through numerical
simulations in the form of the new design methodology. Li
etal. (2019) analyzed the stability of a cavern thermally
during injection and withdrawal using mathematical model.
The results of the models agreed well with withdrawal test
results. Berest (2019) discussed the heat transfer in salt
caverns to clarify thermodynamic behavior of salt caverns
containing different material including brine, oil, natural
gas, air or hydrogen was featured. Through thermodynamic
equations, he emphasized that the heat transfer and ther-
mal perturbation must be taken into account for stability
analysis. However, it should be noted that the induced ther-
mal stresses were not considered during leaching in these
researches. Brouard etal. (2007a, b) showed that leaching
phase has major role in stress distribution around cavern due
to endothermic dissolution process leading to temperature
decline around the cavern which, in turn, decreases creep
rate.
Dissolution of salt can also affect the thermo-mechanical
behavior of salt cavern considerably. However, less atten-
tion has been paid to the dissolution process of salt and the
complex time-dependent thermo-mechanical behavior for
modelling salt cavern under cyclic loading. Variation of gas
temperature during injection and withdrawal as well as stor-
ing time need also be investigated for each site especifically
due to specific injection and withdrawal rate. To control
the shape of the cavern for achieving the ideal case is also
complicated, because many parameters affect the shape of
the cavern particularly during the leaching. Leaching expe-
rience of salt caverns shows that a complicated irregular
shape such as shape of Etzel EZ 53 salt cavern in France
may be obtained (Brouard Consulting 2014). Both labora-
tory experiments and numerical modelling are needed to
better understand the mechanical behavior of salt forma-
tions surrounding salt caverns (Zhang etal. 2017). Stability
of salt cavern has theoretically been discussed without any
measurement recently by Asgari etal. (2020). However, the
stability analysis of salt caverns is a very complicated sub-
ject due to the coupled time-dependent thermo-mechanical
behavior of salt, and the proper measurement and assessment
of time-dependent thermo-mechanical properties are the
important parts of a project. Nasrabad salt cavern is the
first underground gas storage in Iran and less studies have
been performed on salt cavern technology in general and
Nasrabad formation in particular. Time-dependent thermo-
mechanical behavior of surrounding rock cavern has been a
critical issue for researchers and practical engineers. Thus,
to address the complex behavior of the cavern under thermal
and mechanical loading as well as investigate availability of
the cavern, authors have studied the creep behavior and sta-
bility criterion of Nasrabad salt rock by measuring geome-
chanical properties such as uniaxial and trixial compression
strengths. The coupled time-dependent thermo-mechanical
behavior of rock salt can be modelled by LOCAS software.
Thus, in this paper, first, the creep behavior and stability
criterion of Nasrabad rock salt dome have been determined.
Then, stability of the salt cavern has been analyzed under
the gas storage cyclic loading considering time-dependent
thermo-mechanical behavior by numerical modelling using
LOCAS software.
Laboratory experiments
Preparation ofrock specimens
Cylindrical specimens for testing physical and mechani-
cal properties of salt were provided from the central part
of the Nasrabad salt dome, the place where the cavern will
be constructed. Salt cores were cut by core cutting machine
in the rock mechanics laboratory for testing the unit weight,
porosity, tensile strength, modulus of elasticity, Poison’s
ratio, uniaxial and tri-axial strength, time-dependent (creep)
behavior under uniaxial and tri-axial loading at different
temperatures. Specimens were prepared according to ISRM
standards (ISRM 1981a, b). Diameter of the cylindrical salt
specimens was 54.5mm. The height-to-diameter (H/D) ratio
of cylindrical specimens was from 0.55 to 0.97 for Brazilian
tensile strength test and the H/D ratio of all other specimens
was about 2. Based on the petro-physical characteristics of
the core salt, the specimens have been classified as pure rock
salt (halite > 95%). The measured grain sizes of Nasrabad
rock salt are shown in Fig.1.
Mechanical andphysical measurements
To model the cavern behavior numerically, the mechanical
properties such as modulus of elasticity (E), Poisson’s ratio
(
𝜈
), uniaxial compressive strength (σci), and tensile strength
(σt) are required. Uniaxial compression tests were carried
out for specimens having diameter of 54mm and H/D of
2 according to ISRM standard (1981a, b). Tensile strength
was also carried out using Brazilian test. All measurements
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were performed at room temperature. The porosity (p) and
unit weight (γ) of Nasrabad’s salt rock were determined
according to ISRM standard (ISRM 1981b). The number
of test results (N), the average unit weight (γ), porosity (p),
uniaxial compressive strength (σci), tensile strength (σt),
modulus of elasticity, and (E) Poisson’s ratio (
𝜈
) are shown
in Table1. The tensile strength of Nasrabad’s salt rock has
been compared with that of other types of rock salt. The
tensile strength of Nasrabad’s salt rock is lower than the
average values of the others (Fig.2).
Creep tests underdifferent stresses
andtemperatures
Three types of creep tests including constant stress, constant
strain rate, and relaxation tests are commonly carried out to
study time-dependent behavior of salt rocks. The constant
stress test is ideal for determining the steady-state creep
behavior of the salt which is useful for the numerical mod-
eling of the salt rock cavern over a long period (Hudson
1993; ASTM 2008). Creep test of cylindrical rock salt speci-
mens was performed under uniaxial and tri-axial stresses for
different temperatures according to ISRM standard (Aydan
etal. 2014). The relationships between strain and time for
rock salt specimens under constant uniaxial stresses for
temperatures of 25, 50, and 70°C are shown in Fig.3. The
temperatures are chosen based on the temperature of cavern
which varies from 37 to 50°C when depth varies 400–800m
by taking the geothermal gradient of salt formation which
equals
0.03oC/m
. The relations between strain and elapsed
time for rock salt specimens under tri-axial stresses with
confining pressure of 0–2.5MPa and temperatures of 25°C
are also shown in Fig.4. The strain rate (
̇𝜀
) at steady state
(secondary creep) was determined under uniaxial and tri-
axial stresses for different temperatures (Table2).
Assessment of the nonlinear and time-dependent thermo-
mechanical behavior of salt caverns requires advanced con-
stitutive models which can describe the material behavior
of the rock salt under different thermo-hydro-mechanical
conditions at different time scales. Various advanced con-
stitutive models on the basis of different assumptions and
concepts have been developed and proposed to describe the
thermo-hydro-mechanical behavior of rock salt by taking
into account various phenomena and parameters. The fol-
lowing comprehensive and the most recommended model
based on Norton–Hoff law can represent the time-dependent
behavior of the rock salt considering temperature and activa-
tion energy to analyze the stability of a salt cavern (Thoraval
etal. 2015).
where,
̇𝜀
is the steady-state strain rate, σ is the deviatoric
stresses (σ1–σ3) in MPa, σ1 is the axial strength in MPa,
σ3 = confining pressure in MPa, T is the absolute tempera-
ture in oK, R is the universal gas constant in kJ mol−1 K−1,
Q = activation energy in kJ mol−1, n is the stress exponent.
The relationship between strain rate (
̇𝜀
) at steady state
and deviatoric stresses (σ) of creep test results was analyzed
to determine constant A, n and Q under different tempera-
tures and stresses. A, n and Q were obtained equal to 2.928,
1.9696 and 38,025.89 respectively.
Determination ofparameters ofstability criterion
Cavern stability is a crucial consideration for the design and
development of storage caverns constrained by cavern size,
spacing and operating pressure range in salt formations.
An acceptable operating pressure range for a salt cavern is
generally determined by a geo-mechanics evaluation that
typically requires that the cavern response satisfies various
design constraints. These constraints are intended to ensure
containment of the gas, cavern stability and safe operation
(1)
̇𝜀 =Ae
−
(
Q
RT
)𝜎
n
,
Fig. 1 The grains of rock salt under microscope
Table 1 Average values of unit weight (γ), porosity (n) uniaxial compression strength (σci), Brazilian tensile strength (σt), modulus of elasticity
(E) and Poisson’s ratio (
𝜈
) with their standard deviation (Std)
Unit weight Porosity Uniaxial compression
strength
Brazilian tensile
strength
Modulus of elasticity Poisons ’s ratio
γ (gr/cm3)Std n (%) Std σci (MPa) Std σt (MPa) Std E (GPa) Std
𝜈
Std
2.1 0.075 0.746 0.02 13.15 1.425 1.57 0.3 9.30841 1.564 0.284 0.01
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of the storage cavern. The cavern experiences hydraulic frac-
turing when pressure in the cavern is larger than a certain
amount. However, if the pressure in a cavern considerably
decreases, the shear stresses in the surrounding salt can
exceed the strength of the salt. Then micro-fracture, dilation,
and additional porosity will develop as salt permeability will
increase during creep deformation. Hence, stored material
Fig. 2 Comparison between Brazilian tensile strength of Nasrabad rock salt with that of the other salts (1Hansen 1984; 2Phueakphum 2003;
3Fuenkajorn etal. 2003; 4Wetchasat 2002; 5Kensakoo 2006; 6De Vries 2002; 7Boontongloan 2000)
Fig. 3 Relationship between strain (
𝜀
) and time for uniaxial creep test
results under three different temperatures (T)Fig. 4 Relationship between strain (
𝜀
) and time (t) for tri-axial creep
test results under different axial stresses (AS) and confining pressures
(CP) at temperature of 25°C
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would be leaked when the permeability increases. Various
criteria such as small tensile stress zone, low dilatant, low
volume loss rate, subsidence and RD criterion have been
proposed for stability analysis of salt caverns (Karimi-Jafari
etal. 2011; Brouard etal. 2007a, b). The low volume loss
and subsidence are almost the same and have less appli-
cability. Since cavern experiences tension state at certain
condition especially at very fast cycles, small tensile stress
is not applicable in stability analysis as well. RD criterion
(DeVries etal. 2005) that considers both the stress state and
the effect of Lode angle can be reliable to assess the dilation
boundary of the salt caverns. Therefore, RD criterion is used
in this research: the power function relationship between
√
J
2
and I1 has been also recommended as a failure criterion
for salt cavern particularly when LOCAS software is applied
for stability analysis as follows (DeVries etal. 2005):
where, I1 is the first invariant of stress in MPa, J2 is the sec-
ond invariant of deviatoric stresses in MPa, σt is the tensile
strength in MPa,
Ψ
is the Lode angle, σ0 is the a dimen-
sional constant with the same units as I1 and it is equal to 1,
sgn(I1) is the term identify the plus or minus sign, n is the a
constant power less than or equal to one, D1 is the material
constant, D2 is the material constant.
sgn(I1) is positive for axial stress greater than the lateral
stresses and it is negative for axial stress lower than the lat-
eral stresses. In this research, sgn(I1) is positive. Lode angle
(
Ψ
) is also 30° for axial stress greater than the lateral stresses
and it is −30° for axial stress lower than the lateral stresses.
Therefore, in this research, the power function relationship
between
√
J
2
and I1 is simplified a little as follows:
(2)

J2=D1

I1
sgn(I1)𝜎0
n
+𝜎t

3 cos Ψ−D2sin Ψ
,
(3)

J2=





D1
(sgn(I1)𝜎0)n3 cos 𝜓−D2sin 𝜓





I
n
1
+𝜎t

3 cos 𝜓−D2sin 𝜓

,
The tensile strength (σt) was determined by testing rock
salt specimens in laboratory and the average value of tensile
strength is 1.57MPa (Table1). The power function rela-
tionship between second invariant of the deviatoric stress
(
√
J
2
) and the first invariant of the stress (I1) having f factor
[f=D1∕(1.5 −0.5D2)]
and exponent n with a nonzero inter-
cept
[c=
𝜎
t∕(1.5 −0.5D2)]
of the test results were analyzed
by DataFit to determine D1, D2 and n as follows (Fig.5):
D1, D2, and n were obtained 0.97, 0.818, and 0.9 based on
tri-axial compression tests, respectively. Parameters of A, Q,
D1, and D2 are used for stability analysis of salt cavern by
LOCAS software.
(4)

J2=

D1
1.5 −0.5D
2
In
1+
𝜎t
1.5 −0.5D
2
.
(5)

J2=
D
1
1.5 −0.5D2

In
1+
𝜎t
1.5 −0.5D
2
=fIn
1
+c=0.818I0.83
1
+1.27,
(6)
𝜎
t
1.5 −0.5D2
=
1.27,
(7)
D
1
1.5
−0.5D
2
=
0.818.
Table 2 The strain rate (
̇𝜀
) at
steady state under uniaxial and
tri-axial stresses for different
temperatures
Parameter Sample
UC1 UC2 TC1 TC2 TCT1 TCT2
σ1, MPa 11 12.5 12.5 13.5 12.5 12.5
σ3, MPa 0 0 1.5 2 0 0
T, oC 25 25 25 25 50 70
̇𝜀
, s−1 0.021797 0.0236175 0.03062 0.034103 0.06531 0.07351
Fig. 5 The relationship between second invariant of the deviatoric
stress (
√
J2 ) and the first invariant of the stress (I1) of Nasrabad salt
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Stability analysis ofNasrabad’s salt cavern
bynumerical modeling
Simulation oftime‑dependent thermo‑mechanical
behavior ofsalt cavern undercyclic loading using
LOCAS software
An adequate and accurate numerical computation requires to
apply coupled time-dependent thermo-mechanical behavior
for modeling salt caverns under cyclic loading. Special pro-
cedures are required to analyze the behavior of salt cavern
due to the excavation stages by rock salt dissolution method.
The complexity of time-dependent thermo-mechanical
behavior under cyclic loading and leaching stage of a salt
cavern can be modeled by LOCAS software (Brouard Con-
sulting 2014). LOCAS is a finite element software especially
dedicated to salt caverns. Various time-dependent thermo-
mechanical effective parameters can be applied to simulate
for understanding and designing complicated behavior of
gas-filled salt caverns. Numerous calculations and post-
processing features allow to analyze various aspects from
short-term mechanical stability to long-term subsidence.
The LOCAS post-processor can also displays graphical fea-
tures for all hydro-thermo-mechanical changes of rock salt
and natural gas in 30 outputs either as contours or distribu-
tional curves.
Generally, it is complicated to control the shape of the
cavern insitu during leaching. Because of many parameters
including at leaching process, the shape of cavern comes
different in compared with the ideal case. In this study, based
on the salt cavern leaching’s experience in whole of world,
shape of the Nasrabad’s cavern hypothetically is considered
as the shape of Etzel EZ 53 (France) (Fig.6) as a starting
point to understanding general behavior such as temperature
changes of cavern by which, so, the size, depth etc. would
be optimized.
A complicated irregular shape such as shape of Etzel EZ
53 salt cavern in France may be obtained according to the
leaching’s experience (Brouard Consulting 2014). First, the
shape of Nasrabad’s cavern is taken as the shape of Etzel
EZ53 for modelling. Its extension in X and Y direction are
350m and about 720m, respectively. The height of cavern
is 151m (Fig.6). Geometric parameters, temperature. and
pressures of salt cavern are shown in Table3. The physical
and mechanical and thermal properties including density,
Young’s modulus, Poisson ratio, permeability, thermal con-
ductivity, geothermal gradient, specific heat, thermal expan-
sion factor of salt and non-salt are shown in Table4. There
are three layers at Nasrabad salt dome field (Table4).
The assessed time-dependent and thermo-mechanical
properties and geometry of salt cavern were used in the
LOCAS software as input parameters according to the
defined procedure. The stability analysis of cavern was
performed for 12years including 2years for leaching and
10years for operation phase, respectively. A wide range
of element’s size between 0.001 and 100m can be used
in LOCAS software that is as an important advantage to
control the size of elements. Also, the element’s size of the
model can be divided in to small, medium, and large zones
Fig. 6 Assumed shape of Nas-
rabad cavern (left) and cavern’s
mesh element sizes (right)
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by which cavern entire include the smaller elements of 0.5m
(Fig.6). This model includes 50,296 nodes and 99,810 ele-
ments (Fig.6).
At the end of the leaching phase, the cavern’s debrining
was started at time the first gas injection started into the cav-
ern. After that, the seasonal operation was carried out under
cyclic loading for minimum and maximum gas pressure of 3
and 8MPa, respectively (Fig.7).
Volume change of the salt caverns is an important cri-
terion to evaluate the stability and capability of gas stor-
age. Stability analysis of the irregular assumed shape of
Nasrabad cavern (Etzel EZ 53 shape in Fig.6) shows that
its volume continuously decreases with an increase of time
under cyclic loading (Fig.8). The compressive tangential
stresses decrease with an increase of gas pressure by gas
injection. The creep plastic deformations of salt cavern can-
not be recovered by decreasing the tangential stresses due to
the increase of loading by gas pressure. Convergence of the
cavern continuously increases with increasing time under
cyclic loading (Fig.8). The volume loss of 15,000 m3 per
year (6% of overall volume per year) occurs during seasonal
operations. The considerable cavern volume loss is related to
the low strength of Nasrabad salt, great depth of casing shoe
of 649m and irregular shape of cavern that makes higher
stress concentration hence higher dilation.
As, on the one hand, it is not possible to increase the
injection pressure more than vague, on the other hand, it
is not possible to increase the maximum internal pressure
because it induces hydraulic fracturing. So, the following
four solutions are proposed to decrease the salt cavern vol-
ume loss:
Table 3 Geometric parameters, conditions of temperature and pres-
sures of Nasrabad salt cavern
Parameters Unit
Depth of casing shoe 649m
Depth of cavern bottom 800m
Average depth 724.5m
Height 151m
Average radius 65m
Volume 250,192 m3
Surface area 38,229 m2
Ratio of volume to surface area 6.51m
Geothermal temperature at average depth 35.2 °C
Geothermal pressure at average depth 13.32MPa
Minimum pressure at casing shoe 3.24MPa
Minimum pressure gradient at casing shoe 0.5MPa/m
Maximum pressure at casing shoe 11.68MPa
Maximum pressure gradient at casing shoe 1.8MPa/m
Gas volume 25,000,000 m3
Table 4 The physical, mechanical and thermal properties of salt and non-salt layers
Layer Thickness (m) Depth Density (kg/m3) Young’s
modulus
(MPa)
Poisson’s ratio Permeability (m2) Thermal
conductivity
(W/mk)
Geothermal
gradient
(°C/m)
Specific
heat (kg/
kJ°C)
Thermal
expansion
factor
Constitutive law
Sandstone 100 < 100 2100 10,000 0.3 1 × E−5 2.6 0.038 0.921 – Elastic
Shale 200 100–300 1800 24,000 0.24 1 × E−5 1.73 0.028 0.921 – Elastic
Rock salt > 1000 > 300 1840 9310 0.284 1 × E−20 5.2 0.016 0.921 4 × E−5/C) N–H
Brine – – 1200 – – – 0.57 – 3.768 4.39 –
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Fig. 7 Operation program of Nasrabad’s salt cavern
Fig. 8 Volume loss and volume loss rate of assumed irregular cavern shape at depth of 649 m for seasonal operations under cyclic loading
between 3 and 8MPa of Nasrabad salt cavern
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1. changing the shape of cavern;
2. leaving brine in cavern;
3. reducing the size of cavern;
4. reducing the depth of cavern.
Changing theshape ofcavern
Wang etal. (2012) introduced slope instability and arch pres-
sure concepts by which an optimum shape for cavern in view
of stability could be proposed. They concluded that a shape
with arched roof has less potential of collapse. Zhang etal.
(2017) also investigated Jintan salt formation for construct-
ing underground gas storage salt cavern via a semi ellipti-
cal shape. The maximum radial deformation occurs at mid
height of a vertical ellipsoid cavern. The diameter of the
ellipsoid decreases during the operations of the seasonal
cyclic loading, as the elliptical shape of a cavern deforms
and gradually approaches a cylindrical shape. Hence, the
Fig. 9 Volume loss and volume loss rate of an ellipsoid-shape cavern at depth of 649m for seasonal operations under cyclic loading of 3 and
8MPa
Fig. 10 Volume loss and volume loss rate of an ellipsoid-shape cavern having 100,000 m3 at 649m depth for seasonal operations
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vertical ellipsoid cavern having diameter of 25m and height-
to-diameter ratio (H/D) of 3 was chosen. Regarding this
change, the stability analysis of creep closure shows that
the volume loss is 10,000 m3 per year (4% of total volume
per year) during seasonal operations (Fig.9). The volume
loss and the range of volume loss rate are lower than for
the irregular shape (Etzel EZ 53). Considering the change
of cavern’s shape, the volume loss (Fig.9) decreases with
respect to first condition (Fig.8).
Leaving some brine inthecavern
To decrease the creep closure, the second solution of leaving
pre-determined brine inside the cavern was investigated. A
part of cavern, filled by brine, will be under Halmostatic
pressure in this case, as inside pressure of this part of cavern
is greater than the other parts of cavern during withdrawal.
It needs more time to reach this part of cavern to its critical
creep closure and this method extend the time of cavern
operation. But leaving brine into cavern needs more surface
construction, water supply, and extra expenses. So, this solu-
tion needs to be discarded.
Reducing thesize ofcavern
According to the third solution, if the size of cavern is
reduced, the reaction of rock would be a little bit limited.
Therefore, the size of cavern was decreased from 250,000
to 100,000 m3. The volume loss and volume loss rate of an
ellipsoid-shape cavern (achieved from the first solution) hav-
ing initial volume of 100,000 m3 versus elapsed time under
cyclic loading is shown in Fig.10. The cavern’s volume
loss reduces to 2050 m3 per year (%2.05 of initial volume
per year) during seasonal operations. The size also greatly
affects the salt cavern volume loss. However, the volume
loss is not sufficient, so, it needs to be decreased more by
applying the 4th solution (Section“Leaving some brine in
the cavern”).
Fig. 11 Volume loss and volume loss rate of an ellipsoid-shape cavern with 100,000 m3 at depth of 450m on seasonal operations
Fig.12 Optimized conditions of Nasrabad salt cavern having ellipsoid
shape, 100,000 m3 volume and depth of 450m
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Fig.13 Distribution of tangen-
tial stress under minimum (a)
and maximum (b) cyclic load-
ing (gas pressure 3 and 8MPa)
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Reducing thedepth ofcavern The induced stresses of cav-
ern can be minimized by an increase of the depth. To opti-
mize the design, the depth of cavern was decreased from
650 to 450 m. So, stability analysis of the Nasrabad salt
cavern was performed for an ellipsoid shape with 100,000
m3 at the depth of 450m. Volume loss and volume loss rate
of an ellipsoid-shape cavern having 100,000m at 465 m
depth verses elapsed time for seasonal operations is shown
in Fig.11. The results show that depth considerably affects
the volume loss and convergence of the cavern. In this case,
the volume loss of the cavern is 800 m3 per year (%0.8 of
initial volume per year) during the seasonal operations, and
Fig. 14 Tangential stress at radial direction of casing shoe under minimum (a) and maximum (b) gas pressure (cyclic loading of 3 and 8MPa)
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the volume loss percentage of the cavern is considerably
smaller than the cases 1 and 3. The percentage of yearly
volume loss under this condition is smaller than the accept-
able limit value of %1 suggested by Berest and Brouard
(1998).
Tangential stress, dilation, andtemperature
changes aroundsalt cavern undercyclic loading
foroptimized conditions
The tangential stress, dilation, and temperature changes were
analyzed for the ellipsoid-shape cavern having 100,000 m3
at depth of 465m under cyclic loading (Fig.12). The dis-
tribution of tangential stress of the surrounding salt rock
for minimum and maximum gas pressure in the cavern is
shown in Fig.13. Tangential stress in the radial direction
of casing shoe of the cavern under minimum and maximum
gas pressure (cyclic loading of 3 and 8MPa) is shown in
Fig.14. Tangential stress has greater value in vicinity of the
cavern boundary and it has also greater value under mini-
mum gas pressure inside the cavern. Tangential stress could
be decreased by increasing the internal gas pressure and,
in turn, volume loss would be decreased due to the time-
dependent and thermo-mechanical behavior of salt under
lower tangential stress.
Dilatancy decreases with an increase of the distance from
the cavern boundary and it has lower value under maximum
pressure. According to the RD criterion (De Vries etal.
2005), the resulted stress condition proposes a boundary in
and space below which the dilation is not took place, yet
above the boundary the dilation has been already occurred.
Considering safety factor proposed by Van Smabeek etal.
(1993) for their dilation boundary, which has been proved
by actual engineering applications (Sobolik and Ehgartner
2006), the safety factor is determined using RD criterion as
follows:
The related factor of safety (FOS) also increases with an
increase of the distance from the cavern boundary and it
(8)
FOS
=
D1

I1
sgn(I1)𝜎0
n
+𝜎t
3 cos 𝜓−D2sin 𝜓

J
2
.
Fig. 15 Dilatancy and related factor of safety (FOS) around cavern
under minimum cyclic pressure (a) and maximum cyclic pressure (b)
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Fig. 16 Factor of safety (FOS) under minimum (a) and maximum (b) gas pressure (cyclic loading of 3 and 8MPa at radial direction of casing
shoe
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has higher value under maximum cyclic loading of 8MPa
(Figs.15 and 16).
The radial displacements around cavern wall after 880
and 3880days are shown in Fig.17. The displacement of
the cavern wall increases up to 850mm as larger wall con-
vergence of 850mm occurs towards cavern center after
10.6years (3880days). The ellipsoid shape of salt cavern
deforms to the cylindrical shape with increase of wall con-
vergence in long-term operation. The displacements in hori-
zontal (Ux) and vertical (Uz) directions of the cavern roof
are shown in Fig.18. The radial displacement at 462.58 (at
cavern roof) increases up to about 600mm after 10.6years
(3880days) operations.
Fig. 17 Vertical distribution of radial displacements along cavern wall for 880days (a) and 3880days (b), respectively, after leaching
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Temperature changes around cavern at minimum and
maximum gas pressure of cavern are given in Fig.19. Tem-
perature inside the cavern increased from 30.97 to 37.76°C
(6.79°C) for increasing gas pressure from 3 to 8MPa.
Increase of gas temperature inside the cavern affects the
surrounding salt rock. Radial distribution of temperature
during leaching and operation period is shown in Fig.20.
Temperature of salt rock surrounded cavern due to the gas
pressure is greater than the geothermal temperature.
Fig. 18 Radial distribution of vertical displacement (Uz) and horizontal displacement (Ux) at 462.58 (at cavern roof) for 880 days (a) and
3880days (b) operations, respectively, after leaching
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Conclusions
Laboratory measurements of the mechanical and time-
dependent properties have been conducted for the first time
on rock salt of Nasrabad (Central Iran). Based on the labora-
tory results, the thermo-mechanical behavior of a natural gas
cavern in this salt formation was numerically simulated (in
different shapes, sizes, and depths) using LOCAS to evalu-
ate the safety factor of the cavern. The conclusions from this
study are presented as follows:
1. Based on the measured data, it can be concluded that the
salt rock of Nasrabad formation is weak due to its low
values of compressive strength and tensile strength, and
high value of strain rate.
2. Stability analysis of the irregular assumed shape of
Nasrabad cavern (Etzel EZ 53 shape of Fig.3) shows
that its volume continuously decreases 15,000 m3/year
(6% of initial volume per year) with an increase of time
under cyclic loading of 3 and 8MPa of gas pressure. The
considerable cavern volume loss is related to the low
strength of Nasrabad salt, great depth of casing shoe of
649m and the irregular shape and large size of cavern.
3. The volume loss decreased up to 10,000 m3/year (4% per
year) when cavern shape changed to the vertical ellip-
soid. The depth also greatly affects the creep behavior
hence volume loss of the salt cavern. When the initial
volume the cavern having ellipsoid shape was reduced
to 1,000,000 m3 and its depth was situated at 450m, the
volume loss was 0.8% of initial volume per year.
4. The temperature changes (about 7°C) were consider-
ably observed during injection which has capability to
induce thermal stresses around the cavern. Hence, the
importance of the thermo-mechanical analysis against
mechanical analysis is proved.
5. Through sensitive analysis of the design parameters such
as depth, an optimized condition of Nasrabad cavern
was obtained to be at depth of 450m, initial volume of
1,000,000 m3 with vertical ellipsoid shape.
Fig. 19 Temperature around the cavern during injection (a) and pro-
duction (b)
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Acknowledgments The authors would like to thank National Iranian
Gas Company for cooperation in using salt cores and geological infor-
mation of Nasrabad’s salt dome. The authors would like to extend their
sincere thanks to Dr Benoit Brouard (Brouard Consulting) for using
LOCAS software program that can simulate complex time-dependent
thermo-mechanical behavior of gas-filled salt cavern under cyclic
loading.
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