Failure analysis of thick interlayer from leaching of bedded salt caverns

International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

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Failure analysis of thick interlayer from leaching of bedded salt caverns Tongtao Wang a, Chunhe Yang a,n, Xilin Shi a, Hongling Ma a, Yinping Li a, Yun Yang b, J.J.K. Daemen c a State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, Hubei, China b McDougall School of Petroleum Engineering, University of Tulsa, OK, USA c Mackay School of Earth Sciences and Engineering, University of Nevada, Reno, NV, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 21 May 2014 Received in revised form 8 October 2014 Accepted 5 November 2014

A mathematical model is proposed to calculate the critical collapse span of a thick interlayer during the leaching of a gas storage salt cavern in bedded rock salt. In the proposed model the ratio of the height of the damaged zone to the interlayer thickness is introduced. This approach overcomes the negative effects on the calculation accuracy of the fact that the damaged rock does not fall off from the thick interlayer but is linked to it by contact forces. Brine immersion tests have been carried out to obtain the solution characteristics and the influence of brine immersion on tensile strength and on elastic modulus of interlayer samples of a salt formation from Yingcheng city, Hubei province, China. Experimental results show that these mechanical parameters decrease with immersion in brine and more so with decreasing brine density. To validate the proposed model, a 3D geomechanical model has been built of a salt cavern under construction in a bedded rock salt formation of Yingcheng city. The stresses and deformations of the thick interlayer obtained by the analytical solution and by the numerical simulation are compared, and show good agreement. The critical collapse span of the thick interlayer decreases greatly with a decrease of the ratio of damaged zone height to interlayer thickness and interlayer depth, increases with increasing tensile strength and thickness of interlayer, and is independent of the elastic modulus of the interlayer. The proposed model has been used in the planning of the leaching of the underground salt cavern gas storage of Yingcheng city, Hubei province, China. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Bedded rock salt Interlayer Failure analysis Experiment Theoretical analysis Numerical simulation

1. Introduction Rock salt caverns serve as one of the best underground methods to store energy, and can be located in a salt dome or in a bedded deposit [1–5]. According to the questionnaire results of Solution Mining Research Institute in 2009 [6], approximately 50% of the energy stored in rock salt mines (oil and gas) is stored in bedded deposits and 50% in salt domes. Rock salt in China is primarily bedded, usually composed of many salt layers and interlayers (e.g. anhydrite, mudstone, and glauberite). These interlayers are difficult to dissolve in water, and have a wide range of thicknesses [2,4,7,8]. Water solution mining with single well convection is widely used to leach salt caverns serving for underground gas storage (UGS) [9]. This method can be carried out easily in salt domes because of their large height and high mineral grade. Caverns with ideal shape can be leached, and have good

n

Corresponding author. E-mail address: [email protected] (C. Yang).

http://dx.doi.org/10.1016/j.ijrmms.2014.11.003 1365-1609/& 2014 Elsevier Ltd. All rights reserved.

stability. However, insoluble interlayers pose many challenges to this construction method in bedded rock salt formations [10–12], especially when thick interlayers may become the key factor in the cavern design and leaching. Fig. 1 presents a schematic diagram of a cavern leached by water solution mining with single well convection. Fresh water or unsaturated brine is injected into the cavity through the inner leaching tube (or through the annulus between the inner and outer leaching tubes), and high concentration brine is ejected to the surface through the annulus between the inner and outer leaching tubes (or through the inner leaching tube). Rock salt around the cavity is dissolved by the unsaturated brine, and the cavity gradually increases in size. Oil is injected into the cavity to control the solution rate of rock salt around the cavity top and to form an ideal cavern shape. However, insoluble interlayers impact the flow distribution and decrease the brine flowing speed in the areas around them. This causes the salt dissolving rate to decrease greatly, and makes the cavern shape control difficult. Moreover, a sudden collapse of an interlayer during the leaching may damage the tubing and casing and may cause other accidents. Damage of the leaching tubes

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T. Wang et al. / International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

Water in

Water in

Brine out

Brine out Oil

Oil

Production casing

Production casing

Outer leaching tubing

Mudstone

Inner leaching tubing

Mudstone

Oil blanket

Outer leaching tubing

Collapse or not?

Interlayer

Interlayer

Collapse or not?

Oil blanket Inner leaching tubing

Brine

Brine Rock salt

Rock salt

Bottom settlings

Mudstone

Bottom settlings

Mudstone

Fig. 1. Schematic diagram of cavern leaching by water solution mining with single well convection method in bedded rock salt formation. (a) Cavern intersected by thin interlayers only. (b) Cavern intersected by a thick (and thin) interlayers.

changes the depths of water outlet and brine inlet causing an irregular cavern shape. On the other hand, the interlayer may not collapse during the leaching when its thickness is relative large (44 m). This will constrain the cavern volume and will decrease the gas storage capacity. As the leaching time increases, the thick interlayer becomes a vulnerable suspended structure, as shown in Fig. 1b. Due to the solutioning of the salt above and underneath the interlayer, the entire interlayer is immersed in brine, and as a result its mechanical parameters (such as tensile strength and elastic modulus) decrease. Moreover, the forces to which the interlayer is subjected increase as the suspended span grows. Ultimately, the thick interlayer may suffer a massive collapse, and a large cavern is leached. However, how to precisely predict the critical collapse span of a suspended thick interlayer is a difficult problem. First, local damaged rock masses do not fall off from the thick interlayer immediately when the stresses reach their tensile strength but connect together, maintaining some load bearing capability as the pressure arch effect forms in the thick interlayer. Second, the forces, including in-situ stress, dead load, and brine pressure difference to which the thick interlayer is subjected compose a complicated system. Therefore, study of the failure analysis of interlayers in the leaching of underground salt caverns in bedded rock salt formation is very necessary and valuable. Many researches have been carried out on the effects of interlayers on the mechanical parameters of rock salt and on cavern

stability. Studies on the influence of interlayer collapse on the cavern leaching are still rare. Bauer et al. [13] studied the roof stability of long horizontal leached caverns in bedded rock salt formations, and built a cantilever beam model to calculate the stresses in an interlayer. They thought shear and tensile failure were the main reasons causing roof instability. The influences of horizontal in-situ stress and of interlayer thickness are not included in their model. Charnavel and Lubin [10] investigated the effects of insoluble interlayers on cavern shape. They pointed out that the insoluble interlayers caused many cavity bottle necks and that the broken insoluble interlayers fell on the center cavity floor, forming a raised bottom. As a result the brine could not be expelled from the bottom and the cavern effective working volume decreased. Roland and Wim [14] discussed the influences of brine removal on the ground subsidence and listed several failure modes of interlayers serving as the cavern roof, such as tensile failure, shear failure, crushing rupture, and plastic yield. Michael and Maurice [15] simplified the interlayer at the cavern roof as a composite beam structure to determine the minimum operating pressure, and also studied the deformation and stress of the composite beam structure. Shi et al. [11,12] proposed a mechanical model to analyze thin interlayer collapse during the cavern leaching. They discussed local and overall buckling collapse mechanics. Because of the lack of considering the failure characteristics of thick layers, above models cannot be directly used for thick interlayer collapse prediction.

T. Wang et al. / International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

suspended span (length AB), m; x1 is the horizontal coordinate value of calculating point, m; A is the origin of the coordinates, and B is the other end of the suspended span. The horizontal loads applied to the two ends of the beam are defined as P, which is equal to the product of far field in-situ stress and the beam cross sectional area. The stress produced by P is expressed as follows:

In this paper, a new mathematical model is proposed to predict the critical collapse span of a thick suspended interlayer. It includes the effects of horizontal thrust pressure and of a pressure arch. The ratio of the height of the damaged zone to interlayer thickness is introduced in the model. This can overcome the negative effects of not accounting for the fact that the damaged rock masses do not fall off from the thick interlayer immediately, but link together by the contact forces between them. Brine immersion tests are carried out to obtain the solution characteristic, tensile strength, and elastic modulus of interlayer samples from Yingcheng city. To validate the proposed model, a 3D geomechanical model has been constructed of a salt cavern under construction in bedded rock salt formations of Yingcheng city. The stresses and deformations of the thick interlayer obtained by the analytical solution and by the numerical simulation are compared. Influences of different factors on the critical collapse span of a thick interlayer are discussed. Encouraging results are obtained, which can provide fundamental data and references to the field collapse control of the thick interlayer in the process of cavern leaching.

σa ¼

0

V2 ¼

P 2

Z

l

ð4bÞ

zdx 0

Z V3 ¼ 

l 0

σ a dx

Z

l

1 2 ðz_ Þ dx x1 2

ð4cÞ

where V 1 , V 2 , and V 3 are the potential energies produced by q, P, and σ a respectively; q is the uniform load, q ¼q1 þq2, q1 is the dead load, q2 is the brine pressure difference between the upper and lower surfaces of the beam, N/m. Because the beam is in an equilibrium state, the sum of the internal and external potential energy is a constant [17]. Then, we can get ∂ðU þ VÞ ¼0 ∂δ

ð5Þ

where V ¼V1 þV2 þV3. The deflection of section C–C (Fig. 2) is calculated by

δðxÞjx ¼ 2l ¼

4

8ql

π

U

1 2EI π 4 þ 2Pl π 2  σ a l π 2 2

3

σ ¼  E UhðxÞ U δ€

ð7Þ

where h(x) is the vertical distance between the calculating point and the beam lower surface, m; δ€ is the second order derivative of δ. Fig. 3 presents a schematic diagram of the stress distribution in the section C–C obtained by Eq. (7). When the suspended span is

where z(x) is the flexural equation of the beam neutral axis; δ is the deflection of the beam middle point, m; l is the length of the z C

q

q

P

P B

A x1

Flexure axis

ð6Þ

The stresses of section C–C along the vertical direction caused by bending deformations are

ð1Þ

l

ð2Þ

where U is the energy caused by bending deformation, J; M is the bending moment at any beam section, N  m; E is the elastic modulus, Pa; I is the inertia moment of the beam, m4. Potential energy produced by the external loads is expressed as follows [17]: Z l V 1 ¼ q zdx ð4aÞ

The failure process of thick interlayers is very complicated. It is generally believed that the interlayer damage develops when the stress exceeds the tensile strength. Actually, the damaged rock masses will not fall off from the thick interlayer immediately as they can form a pressure arch to transfer dead load into horizontal loads, which allows the damaged rock masses to maintain some load bearing capability. This is rarely considered in the available literature [9–16] for the remaining load bearing capabilities are very difficult to calculate by analytical methods. This is the main reason the available models cannot be directly used to predict the critical collapse span of thick interlayers. Obert and Duvall [16] proposed a classical beam model to solve related problems. They thought the beam deforms elastically under the dead load, and the tensile stress may exceed the tensile strength, causing vertical fractures. In the model, loads applied to the two ends of the beam were not taken into account. Only the dead load was considered. Moreover, the effects of remaining load bearing capability of damaged rock masses were not considered. For these reasons the results of the Obert and Duvall beam model have a large error when compared with actual engineering monitoring data. A new mathematical model is proposed to predict the critical collapse span of a thick suspended interlayer based on the Obert and Duvall beam model. Fig. 2 presents the model for calculating the stresses and deformations of a thick interlayer intersecting a salt cavern. The origin of the Cartesian coordinate system is set at A. The flexural equation of the beam neutral axis can be assumed as follows [16]:

πx

P A

where σ a is the axial stress, Pa; A is the cross section area of the beam, m2. The beam bends under the dead load and brine pressure difference, and the energy in the beam caused by the bending deformation can be calculated by [17] Z Z 1 l M2 EI l  2 U¼ dx ¼ z€ dx ð3Þ 2 0 EI 2 0

2. Mathematical model

zðxÞ ¼ δ U sin

177

C

x

Neutral axis

Fig. 2. Model for calculating the stress and deformation of a thick interlayer in a salt cavern. Section C–C is the middle section of the beam.

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T. Wang et al. / International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

σc

σc F Neutral axis

(1-n)H

Neutral axis

H E

nH

σ t

D

Fig. 3. Stress distribution in the section C–C. (a) Before failure. (b) After failure.

relatively small, the stresses in the beam under horizontal load, dead load, and brine pressure difference are mainly compressive (Fig. 3a). As the leaching time increases, the suspended span increases, and the compressive stress in the beam bottom decreases and eventually changes into tensile stress. When the tensile stress exceeds the yield strength, rock in the bottom of the beam suffers damage, and fractures appear (Fig. 3b). The fractured rock masses do not fall off from the beam immediately, as they are linked together by the contact forces. As the height of the damaged zone increases, the fractured rock eventually falls, and the thick interlayer suffers massive collapse. To express the failure process by mathematical formulas, n is introduced, defined as follows: n¼

jDEj jDFj

ð8Þ

where n is the ratio of the height of the damaged zone |DE| to the interlayer thickness |DF|. n ranges from 0 to 1; jDEj and jDFj are the lengths of lines DE and DF (Fig. 3), m. Section C–C is subjected to the largest loads, and will fail first. The stresses at section C–C are as follows:

σ ¼ E UhðzÞ U δ€ jx ¼ 2l ;

hðzÞ ¼ nH Z

σt

ð9Þ

where H is the thickness of interlayer, m; σ t is the tensile strength of the interlayer, after brine immersion, Pa. When the beam is in the critical failure state, the collapse span of the thick interlayer can be obtained from Eq. (9). If the thick interlayer shows strong layered nonuniformity, elastic modulus (E) can be replaced by the equivalent elastic modulus (Eeqv), calculated by Eeqv ¼

E1 I 1 þ E2 I 2 þ… þ Em I m I1 þ I2 þ … þ Im

ð10Þ

where Eeqv is the equivalent elastic modulus of the thick interlayer, Pa; E1, E2, …, Em are the elastic moduli of each layer, Pa; I1, I2, …, Im are inertia moments of each layer, m4. Eq. (9) is the proposed formula to predict the critical collapse span of thick interlayers. Using the formula in actual engineering, n can be determined by any available field monitoring data to improve the calculation accuracy. If there is no field monitoring data, it is recommended to take n as about 1/3, based on the mechanical parameters of interlayers at Yingcheng city.

3. Brine immersion tests As the leaching time increases, insoluble interlayers not embedded in salt become immersed in the brine, and their tensile strength and elastic modulus decrease. According to Eq. (9), tensile strength has a significant effect on the critical collapse span of a thick interlayer. Therefore, tests have been carried out to obtain the tensile strength of interlayer samples after brine immersion.

Following are the detailed test procedures and experimental results. 3.1. Sample preparation and test device Samples used in the tests are extracted from the interlayer of the target bedded salt rock formation where the cavern is located, at a depth of about 2000 m. The formations are composed mainly of mudstone, saline mudstone and mud-bearing salt. The Brazilian splitting method is used to measure the tensile strength of the samples after brine immersion. According to the requirements of the Brazilian tests [18] and the maximum size of the salt particle (about 5 mm), the samples are prepared with a diameter of 100 mm and a thickness ranging from 60 to 65 mm. The relatively large sample size perhaps represents the rock mass realistically; samples maintain a near complete structure after immersion tests. To study the effect of brine density on the tensile strength, brine with different densities is used in the experiments. The brine is produced by mixing brine taken from the field leaching with fresh water. According to the density of field leaching and solubility at different temperatures [19], brine is classified into three levels: (i) low density (o1.100 g/mL), (ii) average density (ranging from 1.100 to 1.150 g/mL), and (iii) high density (4 1.150 g/mL). The classification is mainly to make the brine post-processing convenient and improve the economic efficiency in the actual leaching. When the density is greater than the high density, brine is economic for post-processing; whereas if the brine density is less the brine is re-injected into the cavern for leaching until its density exceeds the high density. Moreover, brine with different densities is usually used to adjust the salt dissolution rate and to control the cavern shape. To make the tests as close as possible to the actual leaching conditions, we developed equipment to test the tensile strength of the samples after immersing them in the flowing brine. The equipment consists of the holding fixture, pump, vessel, filter screen, valve, water outlet, soft pipe, etc. To allow convenient observation, one side of the vessel is made of transparent polymethyl methacrylate. The filter screen is fixed in the vessel to control the flow speed of the brine. The holding fixture can accurately apply uniform loads on samples and can fix the locations of samples during the immersion in brine. The axial displacement control mode, with a speed of 0.2 mm/min, is used in the tests. Its relative error is less than 1.0%. Because the solution rate and dissolving damage characteristics of rock salts are influenced greatly by the salt contents, samples are classified as (i) low salt content, (ii) average salt content, and (iii) high salt content according to their salt contents. The thresholds of the three levels are 0–20%, 20%–60%, and 60%–100%, respectively [11]. This classification also corresponds to the ore grade of different locations in the thick interlayer. To measure the salt contents of samples, 100 g of the interlayer rock after sample cutting are ground to powder and dissolved in 1000 ml pure water under

T. Wang et al. / International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

25 1C. After sufficient mixing, the brine density is measured by a densimeter. And then, we can obtain the salt contents of the samples. The “salt” refers to the materials easy to dissolve in the interlayer, whose main ingredient is NaCl. During the tests the temperature of the brine is kept at 25 1C. Brine density is monitored with a densimeter during the whole test. To accurately obtain the density, brine is mixed sufficiently before testing. When the density increase exceeds 5%, fresh water is added immediately to the vessel to keep the brine density constant. After immersion, a dryer is used to dry the surfaces of samples, and then their weights are measured. Usually, different degrees of dissolutioning are present at the sample surfaces after brine immersion. To carry out the Brazilian splitting tests in the flowing brine, the surfaces of samples subjected to loads need to be polished smooth, and then we measure the dimensions of the polished samples. 3.2. Experimental results and analysis Fig. 4 presents photographs of three different salt content interlayer samples after brine immersion for 8 h. Fig. 4a shows an interlayer sample with a salt content less than 5% after brine immersion. We determined the weight of the sample before and after the immersion tests, and found it decreases about 2% after immersion. Many small micro-pores are formed on the surface but the basic structure of the sample is still in good condition. Samples split along the center line diameter in the Brazilian splitting tests, showing that the experimental results are reliable. By observing the inside surfaces of split samples, there are no obvious dissolutions. Fig. 4b shows an interlayer sample with a salt content of 10% after brine immersion. The weight of the sample decreases 6% after immersion, and many obvious fractures appear on the sample surfaces. The swelling of clay minerals after soaking in brine is the main mechanism causing fractures. As shown in Fig. 4b, the basic

179

structure of the sample has deteriorated much more seriously than that shown in Fig. 4a. Many large salt particles are seen on the sample surfaces, which dissolve quickly in the water, causing the invasion of water into the sample. This makes the inside clay minerals (mainly montmorillonite, ledikite, and kaoline) soak up water, and causes them to swell, which ultimately increases the number of fractures and their size. Fig. 4c shows an interlayer sample with a salt content of 30% after brine immersion. Surface and basic structure of the sample are affected seriously, and fractures are extensive, both in the interior of the sample and on its surface. The failure mechanism is that the swelling of clay and the dissolutioning of salt take place simultaneously and promotes each other. The rate of salt dissolving is greater than that of the clay swell, which causes the water to flow into the sample and makes the clay swell further. At the same time, clay swell increases the size of the fractures, which exposes more salt to the water and accelerates the dissolutioning of the salt. This interaction aggravates the failure intensity and speed of disintegration. Fig. 5 shows the argillaceous peeling phenomenon of a sample with high salt content during a brine immersion test. The sample, with a salt content of 50%, has obvious sedimentary stratification. Its diameter and thickness are 100 and 20 mm respectively. To allow convenient observation, the tests are carried out in a transparent vessel. The brine density is 1.083 g/mL. When the immersion time reaches 30 days, the argillaceous peeling takes place. This is mainly because the clay minerals swell and soften after soaking in water. To verify the experimental collapse mechanism of interlayers during leaching, cavern shapes and brine densities are monitored by sonar and densimeter respectively during the leaching of caverns in Jintan and Yunying salt mines of China. This shows that the argillaceous peeling was also taking place on a large-scale during cavern leaching, which caused changes of the cavern bottom settlings shape and brine density. Results indicate that argillaceous peeling is the main mechanism

Fig. 4. Samples with different salt contents after immersion tests. (a) Low salt content. (b) Average salt content. (c) High salt content.

Fig. 5. Argillaceous peeling of sample with high salt content during brine immersion tests.

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T. Wang et al. / International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

Brine density (g/cm3) Parameters

High salt content

Average

Salt contents

1.12 1.15

0.51 5.12 0.61 5.45 0.58 5.59 1.45 6.53

0.38 4.22 0.97 4.74 1.03 5.12 1.46 7.16

Average salt content 0.43 5.03 0.8 5.32 0.84 5.52 1.45 6.52

Average salt content

1.5m

High salt content

Fig. 6. Locations and thicknesses of the layers with different salt contents in the vertical section of the thick interlayer.

Table 2 Material properties used in the analytical solution and numerical simulations. Property

4. Example numerical analysis and discussion of the results To validate the analytical model proposed, the collapse prediction of a thick interlayer in the cavern leaching in Yingcheng city is carried out as an example. The target formation where the cavern will be located has a depth ranging from 1900 to 2098 m, and contains 16 interlayers. The 10th interlayer has a thickness of 10 m, and its top depth is at 2024 m. Due to its large thickness, engineers do not have a clear conclusion whether the 10th interlayer will collapse during the leaching, which becomes a key difficulty in the cavern leaching. If the 10th interlayer collapses, the target formation can be used and a cavern with about 30  104 m3 will be leached, otherwise the single cavern volume will not exceed 10  104 m3. Therefore, the collapse prediction of the 10th interlayer becomes a critical issue in the cavern design and construction. According to the field sampling analysis, the 10th interlayer can be divided into five layers, based on their salt contents. Fig. 6 presents the locations of the five layers. The thicknesses of the low, average, and high salt content layers are about 4, 1.5, and 1.5 m respectively. The samples obtained from the 10th interlayer are classified into three categories according to their salt contents. Their tensile strengths and elastic modulus are listed in Table 1. By using Eq. (10) and results in Table 1, the equivalent elastic modulus is calculated as 5.85 GPa. Tensile strength is valued as 0.84 MPa according to the experimental results of samples with the highest brine density, to keep the results with some safety margin. The Poisson's ratio, cohesion and friction angle of immersed interlayer samples are not included in the experiments, and are valued as those of the interlayer samples without brine immersions. The other parameters used in the analytical solution and numerical simulation are listed in Table 2. The 3D geomechanical model of a salt cavern with thick interlayer is shown in Fig. 7. The numerical model is established by ANSYS software and introduced into FLAC3D software for calculation. Considering the model symmetry, a 1/2 geometry

1.5m

causing the collapse of thin interlayers (o4 m), and the larger scale behavior of interlayer collapse has a mechanism similar to that of the tests. The samples with good structures after the brine immersion test are polished smooth and their dimensions are measured. They are then used to test the tensile strength by Brazilian tests. To compare the test results, Brazilian tests on samples without brine immersions also are carried out. Experimental results are shown in Table 1. As shown in Table 1, the tensile strengths and elastic moduli after brine immersion are smaller than those without immersion, and increase with increasing brine density. As the brine density increases, the salt in the interlayer samples dissolves less, which is beneficial for keeping the samples stable.

Low salt content

10m

0.41 5.74 0.83 5.78 0.91 5.84 1.45 5.88

4m

Without immersion

Tensile strength /MPa Elastic modulus /GPa Tensile strength /MPa Elastic modulus /GPa Tensile strength /MPa Elastic modulus /GPa Tensile strength /MPa Elastic modulus /GPa

1.5m

Low Average High 1.1

1.5m

Table 1 Tensile strength of interlayer samples after and without brine immersion tests.

Density (kg/m3) Young's modulus (GPa) Poisson's ratio Cohesion (MPa) Friction angle (Degrees) Tensile strength (MPa)

Material Rock salt

Interlayer

Mudstone

2200 15 0.3 1.1 38.5 1.3

2400 5.85 0.3 0.7 30 0.84

2700 9.5 0.27 0.5 35 0.6

model is established to improve calculation efficiency. The model dimensions are 900  800  400 m in length, height, and width, respectively. The target rock salt formation where the salt cavern gas storage facilities are located has a depth of about 1900 m to 2098 m. The thicknesses of top and bottom mudstone layers are all about 300 m. The bottom of the model has zero displacement boundaries, i.e., the relative horizontal and vertical displacements of the bottom are all zero. The left and right sides of the model both have zero horizontal displacement boundaries. The top of the model is subjected to the overlying pressure corresponding to the overburden, which is calculated as 36.85 MPa, based on the depth and density. Considering the creep of rock salt, the initial in-situ stresses are assumed to be equal in all directions. Hexahedral, tetrahedron and pyramid transition units are used in the numerical model. The other dimensions of numerical model are shown in Fig. 7. 4.1. Comparison between analytical and numerical results Fig. 8 presents the relations between the vertical deformations of the interlayer neutral axis (line AB as shown in Fig. 2) and distance to point A obtained by using Eq. (6) and by numerical simulation. The analytical solution of the proposed model shows a good agreement with the numerical results, and the maximum deformation takes place at the middle. The maximum error between the analytical and numerical solutions is 23.25%. This is

T. Wang et al. / International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

181

Z=-1600 m

Mudstone Rock salt Interlayer Z=-1900 m

Settlings Z=-1900 m Z=-1930 m Z=-2024 m

Z=-2098 m Z=-2098 m

Z=-2400 m

Fig. 7. 3D geomechanical model of salt cavern with thick interlayer.

2.5

0

Analytical Numerical

-2

Analytical Numerical

2.0

-4

1.5

Stress/ MPa

Deformation/ cm

-6 -8 -10 -12 -14

1.0 0.5 0.0 -0.5

-16

-0.84

-1.0 -18

-1.5

-20 0

10

20

30

40

50

60

70

80

Distance/ m

0

10

20

30

40

50

60

70

80

Distance/ m

Fig. 8. Relations between the vertical deformation of the interlayer neutral axis (line AB) and distance to point A obtained by using Eq. (6) and by numerical simulation.

Fig. 9. Relations between the stresses of the interlayer (line AB as shown in Fig. 2) bottom and distance to point A obtained by using Eq. (7) and numerical simulation, where the compressive stress is defined as positive and the tensile stress is defined as negative.

because the thick interlayer is calculated as a 3D circular plate in the numerical simulation whereas it is assumed as a 2D beam in the analytical solution, causing the error to be relatively large. When the proposed model is used to predict the critical collapse span of the thick interlayer, the length of line DE (Fig. 3b) is first corrected based on available field data. This can effectively improve the calculating accuracy of the proposed model. Fig. 9 presents the relations between the stresses at the bottom of the interlayer (line AB as shown in Fig. 2) and distance from point A obtained by using Eq. (7) and by numerical simulation, where the compressive stress is defined as positive and the tensile stress is defined as negative. The stresses around the two ends are mainly compressive. With increasing distance from the ends, the compressive stresses decrease, and tensile stresses appear in the middle parts of the interlayer. This is mainly because the bending

moment caused by the dead loads and brine pressure difference in the central position of the beam is the largest, which produces a compressive stress in the beam upper portion, and the tensile stress in the beam bottom. When the tensile stress exceeds the tensile strength, rock failure takes place. With an increase of the suspended span, the height of the damaged zone increases along the thickness direction of the interlayer. When the ratio of the height of damage zone and interlayer thickness reaches 1/3, we think the entire 10th interlayer collapses. According to the testing results in Section 3, the tensile strength of the 10th interlayer is 0.84 MPa. The lengths of the beam where the bottom failure takes place by analytical and numerical solutions are 18.6 and 20.4 m. The error between them is 9.67%. Fig. 9 also shows that the results obtained by analytical and by numerical solutions are in good agreement, indicating that the proposed model is reliable.

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4.2. Influence factor analysis

130 120

n =1/4 n =1/3 n =1/2

110

Span/m

100 90 80 70 60 50

2

3

4

5

6

7

8

9

Elastic modulus/GPa 200 n =1/4 n =1/3 n =1/2

180 160

Span/m

140 120 100 80 60 40 20 0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

Tensile strength/MPa 400

n =1/4 n =1/3 n =1/2

360 320

Span/m

280 240 200 160 120 80 40 500

1000

1500

2000

2500

3000

3500

14

16

18

Depth/m 240

n =1/4 n =1/3 n =1/2

200

Span/m

160 120 80 40 0

6

8

10

12

Thickness/m Fig. 10. Effects of different variables on the critical collapse span of a thick interlayer under different n conditions. (a) Elastic modulus. (b) Tensile strength. (c) Depth of interlayer. (d) Thickness of interlayer.

According to the above analyses and theoretical derivations, many influence factors may have notable effects on the critical collapse span of a thick interlayer, such as the elastic modulus, tensile strength, depth, and thickness of the interlayer. In the examples, different values of these parameters were implemented to calculate the critical collapse span of the 10th interlayer by Eq. (9), as shown in Fig. 10. Due to the salt cavern leaching in the target formation of Yingcheng city being in its early stage, any monitoring data about the collapse span of the interlayer are lacking. The ratio of the height of damage zone and interlayer thickness (n) is the key factor to control the height of damage zone (Fig. 3b) used in Eq. (9). Therefore, n is assumed as 1/4, 1/3 and 1/2 respectively to obtain its effect on the critical collapse span of the interlayer. Fig. 10 shows the effects of different factors on the critical collapse span of an interlayer under different n conditions. The critical collapse span increases with increasing n, and is sensitive to the change of n. The value of n is a key parameter of the proposed model. Therefore, we recommend that the value of n should be determined based on field monitoring data before using the proposed model in actual engineering. Fig. 10a presents the effect of the interlayer elastic modulus on the critical collapse span when n is valued differently. In the calculations, the tensile strength is 0.84 MPa, the interlayer depth is 2024 m, the interlayer thickness is 10 m, and the equivalent elastic modulus of the interlayer is valued as 2.85, 3.85, 4.85, 5.85, 6.85, and 7.85 GPa respectively. As shown in Fig. 10a, the critical collapse span increases with the increase of n, and is not influenced by the elastic modulus. According to Eqs. (6)–(8), the elastic modulus is neutralized in the process of calculation. Therefore, it is recommended not to test the elastic modulus of interlayer after brine immersion to save time and costs. Fig. 10b presents the effect of interlayer tensile strength on the critical collapse span when n is valued differently. In these calculations, the interlayer depth is 2024 m, the interlayer thickness is 10 m, and the tensile strength of the interlayer is 0.24, 0.44, 0.64, 0.84, 1.04, and 1.24 MPa. As shown in Fig. 10b, the critical collapse span of a thick interlayer increases with increasing tensile strength. According to Eq. (9), the increase of tensile strength means the interlayer can withstand more load and collapse of the interlayer requires a larger suspended span. For example, when the tensile strength (σ t ) increases from 0.64 to 0.84 MPa, the critical collapse span increases from 63.89 to 83.86 m, a 31.26% increase, under the n ¼1/3 condition. According to the experimental results in Section 3, the tensile strength of interlayer material after brine immersion decreases greatly with a decrease of brine density. Therefore, if there is a thick interlayer in the target formation, increasing the injection rate of fresh water and decreasing the distance between water inlet and brine outlet are recommended to decrease the brine density around the thick interlayer, which will decrease its tensile strength greatly. This leaching method significantly decreases the critical collapse span and assures that the collapse of the thick interlayer takes place. The in-situ stresses originally existing in the rock mass where the cavern is located are relieved during the leaching. Due to the typical creep characteristic of rock salt, the far-field in-situ stresses gradually transfer to the cavern walls, which increases the horizontal force (P), applied to the two ends of the interlayer. Moreover, the in-situ stresses in the rock salt formation meet the hydrostatic pressure distribution [4,7,8]. Therefore, P is determined directly by the interlayer depth. Fig. 10c presents the effect of interlayer depth on the critical collapse span for different values of n. In the calculations, the tensile strength of the interlayer is 0.84 MPa, the interlayer thickness is 10 m, and the interlayer depth

T. Wang et al. / International Journal of Rock Mechanics & Mining Sciences 73 (2015) 175–183

is valued as 720, 1170, 1620, 2024, 2520 and 2970 m. As shown in Fig. 10c, the critical collapse length of the interlayer increases with a decrease of interlayer depth. This is mainly because a large depth produces large a horizontal load (P). There are always some deformations deviating from the neutral axis of the interlayer under the dead loads and brine pressure differences during the entire leaching. These two factors increase the bending moment in the interlayer causing the increasing tensile stress of the interlayer bottom. Fig. 10c also shows that when n has a larger value, the critical collapse length of the interlayer is influenced more significantly by the interlayer depth. Fig. 10d presents the effect of interlayer thickness on the critical collapse span for different values of n. In these calculations, the tensile strength of the interlayer is 0.84 MPa, the interlayer depth is 2024 m, and the interlayer thickness is 7, 8, 10, 12, 14, and 16 m respectively. As shown in Fig. 10d, the critical collapse span increases and the increase tends to accelerate more rapidly with an increase of the interlayer thickness. This is mainly because the bearing capacity of the interlayer improves with the increase of interlayer thickness. At the same time, the height of the tensile damage zone also increases accordingly. When a thick interlayer is present during the leaching, the leaching is carried out at the interlayer bottom first, to form a large volume filled with fresh water or low density brine. Then, the leaching is carried out at the interlayer top by lifting the tubes. This makes that the interlayer bottom is immersed by the fresh water or low density brine, which decreases the tensile strength greatly. This leaching method can greatly improve the collapse possibility of the thick interlayer and reduce the critical collapse span in actual engineering. 5. Conclusions (1) A mathematical model is proposed to calculate the critical collapse span of a thick interlayer during the leaching of salt caverns in bedded rock salt, which considers the effects of horizontal thrust and pressure arch. Formulas based on the proposed model are obtained by the energy method. Brine immersion tests are carried out to obtain the mechanical parameters of interlayer samples of Yingcheng city, Hubei province, China. To validate the accuracy of the proposed model, a 3D geomechanical model is established of a salt cavern under construction in the bedded rock salt formation of Yingcheng city. Results show that the proposed model can precisely predict the critical collapse length of a thick interlayer in the cavern leaching. (2) The ratio of the thickness of the damaged zone to the interlayer thickness (n) is introduced in the proposed model. It can account for the negative effect that the damaged rock will not fall off from the thick interlayer but remains linked to it by the contact forces. We propose that when parameter n reaches a certain value (1 4n 40), the entire interlayer collapses. The value of n can be adjusted based on field monitoring data. (3) The critical collapse length of a thick interlayer increases as the increase of interlayer tensile strength and thickness, and decreases as the increase of the ratio of the damaged zone height to the interlayer thickness and interlayer depth, and has

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no relation to the elastic modulus of the interlayer. Based on the results of immersion tests, the mechanical parameters (tensile strength and Young's modulus) of interlayers decrease with a decrease of brine density in which interlayer samples are immersed. Therefore, increasing the injection rate of fresh water and decreasing the distance between water inlet and brine outlet during the leaching are recommended when a thick interlayer is present in the target formation to make sure that interlayer collapse takes place.

Acknowledgments The authors wish to acknowledge the financial supports of National Natural Science Foundation of China (Grant Nos. 41272391; 41472285; 51404241; 51304187 and 51274187). References [1] Wang TT, Yan XZ, Yang HL, Jiang TT, Zhao S, Yang XJ. A new shape design method of salt cavern used as underground gas storage. Appl Energy 2013;104:50–61. [2] Yang CH, Daemen JJK, Yin JH. Experimental investigation of creep behavior of salt rock. Int J Rock Mech Min Sci 1999;36:233–42. [3] Li YP, Liu W, Yang CH, Daemen JJK. Experimental investigation of mechanical behavior of bedded rock salt containing inclined interlayer. Int J Rock Mech Min Sci 2014;69:39–49. [4] Yang CH, Jing WJ, Daemen JJK, Zhang GM, Du C. Analysis of major risks associated with hydrocarbon storage caverns in bedded salt rock. Reliab Eng Syst Saf 2013;113:94–111. [5] Bérest P, Brouard B, Hévin G. Twelve-year monitoring of the idle Etrez salt cavern. Int J Rock Mech Min Sci 2011;48:168–73. [6] Durup G. Results of the SMRI research priorities survey. In: Proceedings of the 9th world salt symposium. Beijing, China; 4–6 September; 2009. [7] Wang TT, Yang CH, Yan XZ, Li YP, Liu W, Liang C, et al. Dynamic response of underground gas storage salt cavern under seismic loads. Tunn Undergr Space Technol 2014;43:241–52. [8] Yang CH, Li YP, Chen F. Bedded salt rock mechanics and engineering. Beijing, China: Science Press; 2009 (in Chinese). [9] Brouard B, Bérest P, Couteau J. Influence of the leaching phase on the mechanical behavior of salt caverns. Int J Rock Mech Min Sci 1997;34(26): e1–15. [10] Charnavel Y, Lubin N. Insoluble deposit in salt cavern-test case. In: Proceedings of SMRI Fall Meeting. Bad Ischl, Austria; 6–9 October; 2002. [11] Shi XL, Li YP, Yang CH, Qu DA, Ma HL. Research on mechanical mechanism of interlayer collapse in solution mining for salt cavern gas storage. Rock Soil Mech 2009;30:3615–21 (in Chinese). [12] Shi XL, Li YP, Yang CH, Qu DA, Yang HJ, Ma HL. Collapse control technology for interbeds in solution mining for oil/gas storage in multi-interbedded salt formation. Chinese J Geot Eng 2011;33:1957–63 (in Chinese). [13] Bauer SJ, Ehgartner BL, Levin BL, Linn JK. Waste disposal in horizontal solution mined caverns-considerations of site location, cavern stability, and development considerations. In: Proceedings of SMRI Fall Meeting. Rome, Italy; August 4; 1998. [14] Roland RFB, Wim AP.Induction of subsidence by brine removal. In: Proceedings of SMRI Fall Meeting; Bad Ischl, Austria; 6–9 October; 2002. [15] Michael SB, Maurice BD. Geomechanical analysis of pressure limits for thin bedded salt caverns. In: Proceedings of SMRI Spring Technical Meeting; Banff, Alberta, Canada; 29–30 April; 2002. [16] Obert L, Duvall WI. Rock mechanics and the design of structures in rock. New York: John Wiley & Sons; 1967. [17] Dym CL, Shames IH. Solid mechanics. New York: Springer; 1973. [18] ISRM. Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci 1978;15:99–103. [19] KGO Group Ltd. Saturated sodium chloride brine, density & solubility at various temperatures. 2014 [accessed 14.08.01]. 〈http://www.kgogroup.com/ resources/brine/salt_saturation.pdf〉.