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Journal of Information & Computational Science 10:12 (2013) 38153823 August 10, 2013Available at http://www.joics.com

Creep Model Analysis of Rock Salt Cavern UnderNormal Operations

Xinrong Liu a ,b, Jianqiang Guo a , b ,, Junbao Wang a , b, Liang Zhang a , b

a College of Civil Engineering, Chongqing University, Chongqing 400045, China b Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing

University), Ministry of Education, Chongqing 400045, China

Abstract

The quality of numerical simulation results depends on the availability of creep parameters, based onthe characteristic of the creep parameters in engineering applications, put a great deal of emphasis onthe choice of the creep model under injection and production, and propose that it is more meaningfulto make the coefficient of determination (R 2 ) of creep parameters be to 1 under normal operations (inthe range of inside pressure from 5 to 30 MPa) than complete stress (so called [0, + )). So, Oneside, to formulate the linear creep constitutive mode is one of the bases of the testing results and insidepressure standard under normal operations; For another, to evaluate the variability of the creep velocityin different creep parameters, which are linear and power function creep constitutive. The results showthat linear creep constitutive mode has less parameters and is simple, but also variation of the creep rate

is little in a relatively wide range. Linear creep model can be applied to research such as the predictionof the long-term volume shrinkage in the operation process of salt rock storage.

Keywords : Rock Salt; Salt Cavern Storage; Critical Conning Pressure; Creep Constitutive Model

1 Introduction

Rock salt is a worldwide-recognized ideal medium for underground storage of hydrocarbons orothers (e.g. toxic or radioactive). The results have showed in developed countries that it is nowpossible to store billions of normal cubic meters of hydrocarbons safely and economically in saltcaverns [1]. The storage caverns in China, which were building in Jiang Su Jin-tan and planningHu Bei Yun-ying, Chong Qing Wan-zhou, He Nan Ping-ding-shan, have to meet the criterianecessary to assure stable and tight high-pressure.

The effects of rock salt creep on cavern shrinkage, several models for rock salt creep havebeen formulated. A common goal of the previous investigations is to determine the creep con-stitutive model. It has been found that some of them have not a remarkable success because

Graduate Creative Fund (0218005204101); Science Fund for Creative Research Groups (No. 50921063) Corresponding author.Email address: [email protected] (Jianqiang Guo).

15487741 / Copyright 2013 Binary Information PressDOI: 10.12733/jics20102020

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of multitudinous parameters in engineering applications [2]-[4]; other models (e. g. power andexponential function) are well received [5]-[14]. Rare investigation has, however, made to identify

the parameters effect on the time-dependent properties and creep rate.The quality of numerical simulation results depends on the availability of creep parameters [13,

14]. In the present paper we start from a complete and accurate set of triaxial creep data onJiang Su Hong-ze rock salt. One side, a new constitutive equation for normal operated cavernis proposed; For another, evaluate the variability of the creep rate in different creep parameters,which derive from linear and power creep constitutive. Linear creep constitutive mode have lessparameters and is simple, but also variation of the creep rate is little in a relatively wide range,so it can be applied to research such as the prediction of the long-term volume shrinkage in theoperation process of salt rock storage.

2 Rock Salt Creep Test Design

2.1 Testing Condition

Rock salt creep test have been performed in an MTS system-RLW2000 by the Laboratory for CoalMine Disaster Dynamic and Control Chongqing University, Fig. 1. The axial stress is controlledby the MTS control system. Data acquisition system is high desirable to regulate the testingparameters, and to record the stress, temperature, displacement and pore water pressure. The

maximum stress, axial and lateral, are 2000 kN and 80 MP. The measurement precision of theaxial and lateral load is 200 N and an accuracy of 0.01%. The system is suitable for rock saltcreep testing.

Fig. 1: RLW-2000 electric-uid serving compression machine

The specimens tested here were obtained from Hongze mining area Jiangsu province. The spec-imens were kept tightly wrapped in cellophane to preclude moisture loss or gain. The samples arecylinders with length 100 mm and diameter 50 mm. The samples, which meets the requirementsof Code for Rock Tests of Hydroelectric and Water Conservancy Engineering (SL 264-2001) thatrequires without obvious fractures and cracks.

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Table 1: Experiment results of rock salt creep

Stress/MPaTime/h Creep Rate/10 4 h 1 Note

3 1

1520 47 0.4

Rock salt

25 45 1.030 46 2.0

2530 48 1.735 50 2.840 50 4.2

deviatoric stress and temperature, the equation is:

s = f c (3 )D (1 3 )H (T ) (1)

where s is steady state creep strain rate; f c (3 ) is a function representing the effects of conningpressure; D (1 3 ) represents the effects of deviatoric stress; H (T ) is a function of temperature.

For constant room temperature Eq. (1) can be written as:

s = D (1 3 )f c (3 ) (2)

Both reference 5 and 7 paid attention to the analysis of the conning pressure and emphasizedthe critical conning pressure ( 30 ). 30 is 3.0 and 5.0 MPa respectively for Yang et al. inreference 7 and Liu et al. in reference 5. The critical conning pressure ( 30 ) is that valueconning pressure 3 beyond which the steady state creep strain rate is effectively independentof the conning pressure and is only a function of deviatoric stress; When 3 < 30 the steadystate creep strain rate decreases steeply in the range of the conning pressure ( 3 ) from 0 to 30 .The critical conning pressure ( 30 ) is different, however, one is not beyond 5 MPa.

Yang et al. [12] based on the basis of the optimization of cavern, stability and long-termstability, proposed the change laws of the inside pressure in operation from 5.5 to 22 MPa; Ma[16] that considering results of stability and creep analysis, 17 MPa is advised to be the long-term

minimum pressure for the formation of over 1800 m which is called ultra-deep formation.Based on research achievements obtained Yang et al. [12] and Ma [16], it is reasonable to thinkoperating of the rock salt cavern is in the range of inside pressure from about 5 to 30 MPa, thatis, operating inside pressure is greater than the critical conning pressure ( 30 ) under normaloperation.

We can see that deviatoric stress has good linear with the steady state creep strain rate byevaluating the results, which conning pressure is in the range of inside pressure from about 5 to30 MPa. Based on the study achievement for rock salt, the following assumptions can be drawn:

(1) Rock salt creep is absent under mean stress (so called static hydraulic stress), that is,initial creep rate is close to zero;

(2) The R 2 is the coefficient of determination that falls be in the range from 0 to 1; thecloser R2 value is to 1, the better the regression t. Based on the characteristics of cavernunder injection and production to propose that it is more meaningful to make the coefficient of

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determination (R 2 ) of creep parameters be to 1 under normal operations than complete stress (socalled [0, + )).

(3) It is desirable that steady state strain rate appears not to be sensitive to creep parametersfor constitutive model.

Based on the above assumptions and creep investigation results, constitutive equation in therange of conning pressure from about 5 to 30 MPa can be represented by:

s = D (1 3 ) =a + b(1 3 ) q q 0

(aq 0 + b (1 3 ) q < q 0 (3)where a and b are material constants, which are obtained by tting the experiment data; 10 is the

minimum axial for stepwise creep testing; 3 is the conning pressure; q = 1 3 ; q 0 = 10 3 .Based on the Eqs. (1), (2) and (3), one obtain:

s =[a + b(1 3 )]f c (3 ) 3 30D (1 3 ) 3 > 30

(4)

From the data of Table 1, the parameters in Eq. (4) are as follows: a = 0.4088, b = 0 .1402for conning pressure 3 = 15 MPa:

s =

0.4088 + 0.1402(1 3 ) q 5

(0.1402 0.40885 (1 3 ) q < 5For conning pressure 3 = 25 MPa, a = 0 .3504, b = 0 .2190:

s =0.3504 + 0.219(1 3 ) q 5

(0.219 + 0.35045 (1 3 ) q < 54 Study on Parameters of Power Function Creep Consti-

tutive Mode

Norton-Power creep strain rate is assumed to be an power function of deviatoric stress (q) alone,as given by:

s = Aq n (5)

Eq. (5) can be t to almost all experimental data of creep strain rate versus time; Both A andn are material constant, the parameters are get by tting.

Chen et al. [11], the parameters in Eq. (5) are as follows: A = 5 .86E-6, n = 3 .5. Fig. 4 show aset of creep strain rate at different parameters ( A and n) for Eq. (5), the unit of creep stain rateis yr 1 and the unit of stress q shall be in MPa.

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30Deviatoric stress/MPa

C r e e p r a t e

/ y r

1

A =3.0E 6; n =3.6A =3.0E 6; n =3.8A =3.0E 6; n =3.3A =3.0E 6; n =3.4A =3.0E 6; n =3.5A =5.86E 6; n =3.5

Cited References [11]

Fig. 4: s under different creep parameters

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20 25 30Deviatoric dtress/MPa

Caluated valuesfrom experiments

C r e e p r a t e

/ y r

1

A =0.25; n =0.7500A =0.25; n =0.8121A =0.25; n =0.9000A =0.3961; n =0.7500A =0.3961; n =0.8121A =0.3961; n =0.9000

Fig. 5: s under different creep parameters

From the data of Table 1, the parameters in Eq. (5) for conning pressure 25 MPa with leastsquare method are as follows: A = 0 .3961, n = 0 .8121. Fig. 5 show a set of creep strain rate atdifferent parameters ( A and n) for Eq. (5), the unit of creep stain rate is yr 1 and the unit of stress q shall be in MPa.

As shown in Fig. 4 and Fig. 5 creep strain rate appears to be sensitive to parameters A and n,creep strain rate increases or decreases with either or both increasing or decreasing, the divergenceof the creep strain rate are more obvious with increasing deviatoric stress, especially. Accordingto some research results (Wu et al. [14]; Zhao et al. [13]) the quality of numerical simulationresults of power function creep equation s = Aq n depends on the variability of creep parametersA and n .

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5 Study on Parameters of Linear Creep ConstitutiveMode

Fig. 6 show a set of creep strain rate at different parameters ( a and b) for Eq. (4), the unit of creep stain rate is yr 1 and the unit of stress q shall be in MPa.

0 5 10 15 20 25 30Deviatoric stress/MPa

0

2

4

68

10

12

14

C r e e p r a t e

/ y r

1

a =0.15; b =0.10a =0.35; b =0.22a =0.70; b =0.40a =0.15; b =0.10a =0.35; b =0.22a =0.70; b =0.22

Caluated valuesfrom experiments

Fig. 6: s under different linear creep parameters

Fig. 6 presents the results for Eq. (3). It is possible for the creep rate of the linear creep modelto change signicantly, as a result just both parameter a and b increase or decrease obviously,but creep rate change negligibly because of b stability for conning pressure in the range from 5to 30 MPa.

Based on above test results and analysis, the following conclusion may be drawn, it is reasonableto make use of the linear constitutive equation to estimate the volume shrinkage in the operationprocess of salt rock storage by identifying the creep parameters both s = Aq n and linear creepformulation

6 Conclusions

(1) The quality of numerical simulation results of power function creep equation s = Aq n dependson the variability of creep parameters A and n, the same conclusions are gained in cited reference13 and 14;

(2) Based on the characteristics of cavern under injection and production to propose that it ismore meaningful to make the coefficient of determination (R 2 ) of creep parameters be to 1 undernormal operations than complete stress (so called [0, + ));

(3) By evaluating the creep data conning pressure from 5 to 30 MPa, the results show thatdeviatoric stress has good linear with the steady state creep strain rate, so the creep constitutive

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equation is expressed as:

s = D (1 3 ) =a + b(1 3 ) q q 0

(aq 0 + b (1 3 ) q < q 0 ;(4) It is possible for the creep rate of the linear creep model to change signicantly, as a result

just both parameter a and b increase or decrease obviously, but creep rate change negligiblybecause of b stability;

(5) It is reasonable to make use of the linear constitutive equation to estimate the volumeshrinkage in the operation process of salt rock storage by identifying the creep parameters both s = Aq n and linear creep formulation.

References

[1] R. L. Thoms, R. M. Gehle, A brief history of salt cavern use [C], Proc. 8 th World Salt Symposium,Elsevier, 2000, 207-214

[2] D. E. Munson, K. L. DeVries, A. F. Fossum et al., Extension of the M-D model for treatingstress drops in salt [C], In: Proceedings of the 3rd Conference on the Mechanical Behavior of Salt,Palaiseau, France: [s.n.], 1993, 31-44

[3] K. S. Chan, S. R. Bodner, A. F. Fossum et al., A damage mechanics treatment of creep failure inrock salt [J], International Journal of Damage Mechanics, 6(1), 1997, 121-152

[4] Z. M. Hou, W. Wu, A damage and creep model for rock salt as well its validation [J], ChineseJournal of Rock Mechanics and Engineering, 21(12), 2002, 1797-1804

[5] Jiang Liu, Chunhe Yang, Wen Wu et al., Study on creep characteristics and constitutive relationof rock salt [J], Rock and Soil Mechanics, 27(8), 2006, 1267-1271 (in Chinese)

[6] Xiaoping Gao, Chunhe Yang, Wen Wu et al., Eperimental studies on temperature dependentproperties of creep of rock salt [J], Chinese Journal of Rock Mechanics and Engineering, 24(12),2005, 2054-2059 (in Chinese)

[7] Chunhe Yang, Shiwei Bai, Yimin Wu, Stress level and loading path effect on time dependentproperties of salt rock [J], Chinese Journal of Rock Mechanics and Engineering, 19(3), 2000, 270-275 (in Chinese)

[8] Feng Chen, Yingpin Li, Chunhe Yang et al., Experimental study on creep behavior of rock saltin YU Ying salt mine [J], Chinese Journal of Rock Mechanics and Engineering, 25(s1), 2006,3022-3027 (in Chinese)

[9] Chunhe Yang, Yijun Zeng, Wen Wu et al., Constitutive relationship of deep salt rock and its appli-cation to petroleum drilling engineering [J], Chinese Journal of Rock Mechanics and Engineering,22(10), 2003, 1678-1682 (in Chinese)

[10] Feng Chen, Chunhe Yang, Shiwei Bai, Investigation on creep damage of natural gas storage in saltrock layer [J], Rock and Soil Mechanics, 27(6), 2006, 945-949 (in Chinese)

[11] Feng Chen, Chunhe Yang, Shiwei Bai, Investigation on optimized gas recovery velocity of naturalgas storage in salt rock layer by numerical simulation [J], Rock and Soil Mechanics, 28(1), 2007,

57-62 (in Chinese)[12] Chunhe Yang, Weiguo Liang, Donghou Wei et al., Investigation on possibility of energy storage insalt rock in China [J], Chinese Journal of Rock Mechanics and Engineering, 24(24), 2005, 4409-4417(in Chinese)

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[13] Kelie Zhao, Haijun Yang, Feng Chen, Chunhe Yang, Research on creep parameters optimizationof salt bed in deep gas storage group [J], Chinese Journal of Rock Mechanics and Engineering,28(s2), 2009, 3550-3555 (in Chinese)

[14] Wen Wu, Zhengmeng Hou, Chunhe Yang, Investigations on evaluating criteria of stabilities forenergy (petroleum and natural gas) storage caverns in rock salt [J], Chinese Journal of RockMechanics and Engineering, 24(14), 2005, 2497-2505 (in Chinese)

[15] Chunhe Yang, Yinping Li, Feng Chen, Mechanics Theory and Engineering of Bedded Rock Salt[M], Beijing: Science Press: 2009

[16] Hongling Ma, Study on Feasibility of Rock Salt Underground Storage in Ultra-deep Formation[D], Ph.D. Thesis, Wuhan: Institute of Rock & Soil Mechanics, Chinese Academy of Sciences, WuHan, China, 2010

[17] K. S. Chan, A damage mechanics treatment of creep failure in rock salt [J], International Journalof Damage Mechanics, 6, 1997, 122-152

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