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Investigation of rock salt layer creep and its effects on casing collapse
International Journal of Mining Science and Technology xxx (xxxx) xxx
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International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Investigation of rock salt layer creep and its effects on casing collapse S. Reza Taheri a,b, Ali Pak a,b,⇑, Saeed Shad b,c, Behzad Mehrgini d, Meisam Razifar e a
Civil Engineering Department, Sharif University of Technology, Tehran, Iran Upstream Petroleum Research Institute, Sharif University of Technology, Tehran, Iran c Chemical & Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran d Kish Petroleum Engineering Company, Tehran, Iran e Folowrd Industrial Projects Company, Tehran, Iran b
a r t i c l e
i n f o
Article history: Received 8 December 2018 Received in revised form 13 May 2019 Accepted 2 February 2020 Available online xxxx Keywords: Rock salt Gachsaran formation Creep Power law Casing collapse Numerical simulation
a b s t r a c t Casing collapse is one of the costly incidents in the oil industry. In the oil fields of southwest Iran, most casing collapses have occurred in Gachsaran formation, and the halite rock salt layer in this formation may be the main cause for these incidents because of its peculiar creep behavior. In this research, triaxial creep experiments have been conducted on Gachsaran salt samples under various temperatures and differential stresses. The main purpose was to determine the creep characteristics of Gachsaran rock salt, and to examine the role of creep in several casing collapses that occurred in this formation. Results indicated that the halite rock salt of Gachsaran formation basically obeys the power law; however, its creep parameters are quite different from other halite rocks elsewhere. The time-dependent creep of Gachsaran rock salt exhibits strong sensitivity to temperature change; however, its sensitivity to variation of differential stress is rather low. The numerical simulation of the rock salt creep in a real oil well demonstrated the importance of creep and reservoir conditions on the safety factor of the tubing related to casing collapse. Ó 2020 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Casing collapse is a major problem in the oil industry. Delay in oil production, and sometimes total loss of the well make casing collapse an event that imposes heavy cost on oil companies. Several factors can be responsible for casing collapse in oil wells, including the reservoir depletion effects, effects of natural faults and fractures, well completion problems and cementing imperfections, time-dependent creep of the surrounding rock layers, and chemical effects. A large number of casing collapse incidents have been reported within the rock salt layers that are attributed to creep of rock salt, especially under high pressure and high temperature condition [1–5]. Creep, depicted as the gradual deformation of material under constant stress, generally has three stages: First, a period in which the rate of time-dependent deformation decreases with time, called transient creep. If stresses are reduced to zero at this stage, the deformation will also become zero. In the secondary stage, the creep rate remains constant. By removing the load at this stage, the creep deformation will not be completely eliminated. In the ter⇑ Corresponding author at: Civil Engineering Department, Sharif University of Technology, Tehran, Iran. E-mail address: [email protected] (A. Pak).
tiary stage, the strain rate increases with time, so it may quickly lead to failure, sometimes accompanied by rapid expansion of unstable fissures. Fig. 1a shows these three stages schematically [6]. Also, a sigmoidal stress-strain curve is shown in Fig. 1b, indicating three different stages of strain hardening corresponding to Fig. 1a obtained by deformation experiments on single crystals of rock salt [7]. In oil wells, an initial creep occurs shortly after drilling, followed by steady-state creep. The third stage is not usually important in oil wells because the casing installation and cementing do not allow further deformations. For rock types such as salt, the steady-state deformation may lead to structural collapse of the casing tube, therefore the steady-state creep rate should be evaluated [5]. Many studies have been carried out to investigate the creep behavior of rock salts and several researchers have tried to formulate this peculiar type of deformation mentioned above [8–14]. In rheological models, different compositions of idealized spring and dashpot elements are used to define the creep behavior (e.g. theoretical models of Maxwell, Kelvin-Voigt, and Burgers). On the other hand, some empirical laws have been proposed based on curve-fitting of the creep tests on different rock salt types. Among these empirical models, the power, exponential, and logarithmic
https://doi.org/10.1016/j.ijmst.2020.02.001 2095-2686/Ó 2020 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 1. Various stages of creep and three different stages of strain hardening for single crystals of rock salt (after [6,7]).
laws are most widely used depending on the rock salt type and the conditions that have been applied during the experiments [15]. Two main deformation mechanisms are important in rock salt: (1) dislocation creep that covers the creep properties of rock salt over a wide range of physical conditions; and (2) pressure solution (in wet and relatively fine grained rock salt) [16,17]. It will be shown later herein that the microstructural analysis indicates that the rock salt under study is typically dry coarse grained, so it is expected that dislocation creep is the dominant deformation mechanism. Although complexity exists within exact definitions of rock salt creep, there are two common main features in this regard that holds for dislocation creep: (1) the rock salt creep strain rate; and (2) temperature. The rock salt creep strain rate is proportional to the applied differential stress (Dr) to the power n (n > 1) [18]. The general creep relationship between the strain rate and differential stress can be written as follows [19]:
ðDrÞn ¼ Ae_
ð1Þ
where Dr = r1 r3 is the differential stress defined in conventional triaxial test where r1 and r3 is axial and confining stress, respectively; n the power coefficient; A the material constant; and e_ the strain rate. Fig. 2 shows the linear and double logarithmic curves drawn based on Eq. (1). In ordinary linear space, two different behaviors of linear and non-linear (power function) are visible (Fig. 2a). However, in logarithmic scale (Fig. 2b), a line with a slope equal to cot1n exists for each state. Therefore, n value can specify the governing creep behavior. The creep behavior follows Newtonian pattern only when n is close to 1, and the line slope in Fig. 2b is around 45°. However, rock salt usually does not follow the viscous behavior proposed by Newton, as n is more than 1 which demonstrate itself in the form of a straight line with a milder slope in the loglog plot of differential stress versus strain rate [19]. Temperature affects the creep strain rate of the rock salt such that the strain rate rises due to temperature increase [6]. This feature combined with Eq. (1) can be written as [20,21]:
e_ ¼ A0 ðDrÞn exp
Q RT
where A0 is the viscosity coefficient; Q the activation energy; n the non-unit power of the differential stress (usually 3 n 6); R the universal constant of gases; and T the absolute temperature of rock [18]. In this study, the creep behavior of Gachsaran rock salt layer in southwest Iran and its effects on casing collapse are of concern, because most of the casing collapse incidents in this area have reported to occur in this layer [22]. To the best of our knowledge, no comprehensive study is yet carried out to investigate the Gachsaran rock salt creep behavior, or to predict its effects on the casing collapse by an integrated numerical model. The only study about creep in Gachsaran rock salt consists of uniaxial experiments at various temperatures carried out by Gorjian, the results of which are used in this study [23]. In the following, after a brief review of the Gachsaran formation characteristics, and description of the experimental set up built for conducting creep tests at elevated temperature and stress, the laboratory results are explained and discussed. Then, a comparison between Gachsaran rock salt and other rock salts is carried out using the power law to highlight their differences. Next, attempts have been made to evaluate the change of deformation characteristics of rock salt due to its viscous behavior over time. A numerical simulation is then presented to show how creep in this type of rock can lower the safety factor against casing collapse for one of the oil wells in southwest Iran. Finally, some conclusions are drawn. 2. Formation overview and sample preparation As noted before, the highest number of casing collapse incidents in southwest Iran has been reported to occur in the Gachsaran formation. Fig. 3 shows the general stratigraphy of the area in which Gachsaran formation is highlighted. Below the Gachsaran formation, there is a giant limestone reservoir called Asmari which is one of the largest oil-rich reservoirs in the world. The Gachsaran formation consists of seven members (M1-M7 in Fig. 3) deposited in the geological periods of the lower to middle Miocene. The dominant rock types in Gachsaran formation are rock salt, marl, and anhydrite. These salty sections are bulky, and their thickness reaches 200 m in some places, and red violet layers (M2 and M4) are salt-rich [24]. The in-situ temperature of these salty layers at depths of 2900– 3200 m is around 90 °C. According to X-ray diffraction (XRD) tests, Gachsaran salt contains around 95% halite [23]. Halite is the mineral form of sodium chloride (NaCl) which is commonly called rock salt. Halite has specific properties including high ductility and low creep strength [25,26]. The Gachsaran halite has been formed by
Fig. 2. Differential stress versus strain rate (after [19]).
ð2Þ
Fig. 3. General stratigraphy of Gachsaran formation.
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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ion binding with 39.4% sodium and 60.6% chlorine and its impurities are often in the forms of brine drops, gas bubbles, clay, and organic content. The transparent minerals of Gachsaran halite have white streaks [27]. The rock salt specimens for creep testing were taken from the Ambal ridge area, 12 km northeast of Gotvand city, Khuzestan Province, Iran. Based on CT-scan images, all selected specimens were visually homogeneous. There were no obvious fractures and cracks on the specimens. Results of the microstructural analyses for the experimental samples showed that the Gachsaran rock salt is typically dry and coarse grained and as mentioned before, pressure solution is unlikely to have taken place and dislocation creep is the dominant deformation mechanism (Fig. 4). As shown in Fig. 4, undeformed microstructure has an average grain size of 2.3 mm. The micrographs show experimentally undeformed halite-dominated Gachsaran rock salt with small amount of disseminated fluid inclusions.
3. Experimental apparatus and testing procedure The irregular-shaped rock salt blocks were carefully cut and used in the experimental apparatus. All samples were trimmed into cylinders with a height (73 mm) to diameter (37 mm) ratio of about 2. Fig. 5a shows some rock salt samples being prepared for testing. A triaxial test set up for studying the creep behavior of Gachsaran rock salt under various stresses and temperatures up to the in-situ temperature of 90 °C was designed and built in the course of this study (Fig. 5b). The apparatus can operate either in constant stress or in constant strain modes. In this case, the creep tests were conducted under constant stress mode in both axial and lateral directions. The test apparatus (Fig. 5b) has a servo-controlled loading system which is capable of applying the desired confining and axial stresses. It was equipped with data acquisition and online control systems for continuous monitoring of the test results during the rock salt sample creep. The triaxial structure of the test set up provided the possibility to examine the differences between the rock salt creep parameters under uniaxial stress condition and the triaxial one. Fig. 6 schematically depicts different parts of the testing apparatus. All tests were conducted under stress-controlled mode with the accuracy of 10 KPa. One linear variable differential transducer (LVDT) was used to measure the axial deformation of the sample, and three lateral sensors equally spaced in mid-height of the sample were used for measuring lateral deformations. The accuracy of LVDTs for strain measurement was 1 106. Lateral LVDTs were designed to have a hydraulically balanced internal housing, so any change in the pressure was distributed uniformly inside the chamber. Application of the different axial and lateral stresses in the triaxial cell induces shear stresses in the sample. Multistage creep tests were carried out to measure the creep parameters under a range of increasing shear stresses. Table 1 summarizes the tests conditions. The apparatus and the measurement devices were calibrated before and after the creep test. Calibration for the lateral pressure
Fig. 4. Transmitted light micrograph of one Gachsaran rock salt sample.
3
Fig. 5. Rock salt samples in the lab and the testing apparatus.
and axial stress was performed with a reference pressure gage, and a reference load cell, respectively; and calibration of the volumetric measurement element was conducted with reference blocks and measuring tools. The effect of temperature and stress on calibration factors were then verified with reference materials with known properties under no stress and no temperature conditions. To conduct the tests at the reservoir temperature, samples were kept in the oven to reach a certain temperature before placement in the cell for creep experiment. During the test, the temperature was held constant using thermal jackets and an insulation system equipped with monitoring sensors with an accuracy of 0.1 °C. All sensors were placed out of the zone affected by heat, so displacement measuring sensors are located behind a firewall to eliminate the temperature effect on the measurements. The temperature sensor is located inside the cell and insulated from environmental effect. It is connected to a proportional integral differential (PID) controller and indicators in the data acquisition system. The thermal jacket is a heating and insulation jacket with a 5 kw electrical heating element embedded in the insulation jacket and a PID control unit. The power of the heating element is controlled continuously to keep the temperature constant and avoid fluctuation in temperature.
4. Experimental results 4.1. Direct findings Figs. 7 and 8 show the axial strain versus time for two multistage triaxial creep tests. These tests were conducted under constant confining stress of 15.0 MPa at constant temperatures of 23 °C and 90 °C, respectively. For the first stage (Dr = 17.6 MPa), the creep rate was high at the beginning of applying the differential stress and gradually decreased in a nonlinear manner, and then remained almost constant with a fixed slope. After assuring that the strain rate was constant at steady-state condition, the next loading stage was started. For the second stage (Dr = 22.4 MPa), again the initial strain rate was high and it decreased gradually until it remained constant. The differential stress (Dr) of the third stage was 25.6 MPa. The differential stresses were selected to reach maximum 70% of the ultimate shear strength of the rock salt specimens which was 46.0 MPa [22]. Fig. 8 shows the tests results in the same manner of that of Fig. 7. Comparison between Fig. 7 at 23 °C and Fig. 8 at 90 °C points out the importance of temperature, as the strain rate at a high temperature is around ten times greater than that at a low temperature. Fig. 9 shows a rock salt sample before and after the creep test. The specimen has deformed in a barrel shape without any visible crack. The Gachsaran salt has flowed under nearly constant volumetric conditions.
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 6. A schematic view of testing apparatus.
4.2. Model parameters determination
Table 1 Creep tests conditions. Test condition
Value
Differential stress, Dr (MPa) Temperature, T (°C)
17.6–32.2 23.0–90.0
Fig. 7. Axial strain over time (T = 23 °C).
Fig. 8. Axial strain over time (T = 90 °C).
Fig. 9. Rock salt sample before and after the creep test.
In order to determine the power law representation parameters, variation of the logarithm of the axial strain rates at the steadystate condition is plotted versus the logarithm of the differential stresses in Fig. 10 for two temperature levels (23 °C and 90 °C). The slopes of the lines fitted to the experimental results show the power n of the stress term in Eq. (2). As shown in Fig. 10, the slopes of both lines are 3.0. It is notable that the data depicted by hollow circle in Fig. 10 comes from [23]. For obtaining the activation energy (Q) in Eq. (2), variation of the logarithm of axial strain rate at the steady-state condition is plotted against 1000/RT for four different confining stress levels (Dr = 13.2, 15.4, 17.6 and 25.6 MPa), as shown in Fig. 11. The values in the horizontal axis vary according to the temperatures in the range of 23 °C to 90 °C. The average slope of the fitted lines equals Q, which is 22.6 kJmol1. After specifying n and Q, A0 can be calculated using Eq. (2). Based on the obtained results, the power law model parameters for Gachsaran rock salt are summarized in Table 2. For the sake of comparison between the characteristics of Gachsaran rock salt and other halite rock salts, the parameters reported by a number of investigators are added into Table 2. The parameters differ from each other due to variation of the mineral composition, halite grain size, and impurities. As can be seen in Table 2, the activation energy Q of Gachsaran rock salt is much lower than that of the other halite rock salts, indicating its high sensitivity to temperature. On the other hand, Gachsaran rock salt has little sensitivity to differential stress, as its n value is minimum. Also, the A0 value of Gachsaran rock salt is among the lowest values.
Fig. 10. Variation of strain rate versus differential stress in log-log coordinates (after [23]).
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 11. Variation of logarithm of strain rate versus 1000/RT. Fig. 12. Applied differential stress versus strain rate (after [23]).
4.3. Model parameters verification Variation of the applied differential stress versus the strain rate is illustrated in Fig. 12 in two types of coordinates (arithmetic and log-log) to be compared with Fig. 2. Based on Fig. 12, one can conclude that the power law representation is an appropriate mean for formulating the creep behavior of Gachsaran rock salt. The results of the previous study by Gorjian are also included in Fig. 12. In order to examine the accuracy of the obtained creep parameters of Gachsaran rock salt, a comparison between the measured and predicted creep rates according to the obtained power law parameters introduced in Eq. (2) is shown in Fig. 13 for different temperatures and applied stresses. Many points are located close to the 1:1 line (diagonal line) and the obtained power law relationship shows a very good accuracy level. There is a good agreement between the measured and predicted creep rates based on Eq. (2), despite of one point located far from the 1:1 line.
end of mode 3 in Fig. 14b, gets around 6 times greater than the axial strain at the end of mode 1 in Fig. 14a, considering that both modes 1 and 3 have the same differential stress. The time specific stiffnesses that correspond to the deformation moduli during creep tests are shown in Fig. 15. The modulus of deformation (Md) values are calculated as the ratio of the differential stress to the corresponding axial strain over time. The modulus of volumetric change (Mv) is defined as the ratio of confining stress to the corresponding volumetric strain. Both Md and Mv values are determined directly from the test results as follows:
Md ¼
ðr1 r3 Þt ð r3 Þt ; Mv ¼ ðe1 Þt ðev Þt
ð3Þ
5. Discussions 5.1. Variation of deformation characteristics of the rock salt In the following, variation of Gachsaran rock salt deformation characteristics is studied based on the experimental observations. Table 3 specifies four considered experimental modes. Time variations of the axial and volumetric strains are shown in Fig. 14a for modes 1 and 2, and in Fig. 14b for modes 3 and 4. The solid vertical lines with arrows specify the times when the mode changes from 1 to 2 in Fig. 14a, and from 3 to 4 in Fig. 14b, respectively. Modes 1 and 2 indicate different loading stages for one sample and the same situation is established for modes 3 and 4. The volumetric strains became nearly constant over time showing that the creep process did not induce significant volume changes. However, increasing the differential stress caused a jump in the axial strain. Comparing the axial strains in Fig. 14a and b indicates the temperature effect on the rock salt creep. The axial strain at the
Fig. 13. Comparison of the predicted and measured creep rates of Gachsaran rock salt.
Table 3 Different modes of experiments. No.
Temperature, T (°C)
Differential stress, Dr (MPa)
1 2 3 4
23 23 90 90
17.6 22.4 17.6 25.6
Table 2 Power law model parameters of several halite rock salts. Halite type Salado Salado Asse West Hackbr. Bryan Mound Bryan Mound Bayou Choctaw Synthetic Avery Island Avery Island Synthetic wet salt Ara Salt GOM Gachsaran
A0 (MPans1) 8.82 2.71 7.26 3.15 8.93 7.78 3.94 4.70 1.60 8.10 2.75 1.82 5.19 2.88
6
10 103 106 105 105 103 106 104 104 105 102 109 108 108
Q (Jmol1)
n
Reference
50,160 69,180 53,920 54,840 63,290 74,530 49,450 24,530 68,100 51,600 80,000 32,400 41,868 22,600
4.9 5.1 5 4.7 4.5 5.2 4.1 3 5.3 3.4 5.6 5 4.9 3
[28] [28] [28] [28] [28] [28] [28] [29] [30] [30] [31] [32] [4] This study
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 16. Variation of strain rate with differential stress based on two series of creep tests results (after [23]). Fig. 14. Variations of axial and volumetric strains over time at different temperatures and modes.
where e1 is the axial strain; ev the volumetric strain; and t the time. Md value drops considerably with time at lower temperature for modes 1 and 2; however, at high temperatures, Md does not change much under higher differential stress (mode 4). For example, as shown in Fig. 15a for the case of 90 °C, Md declined sharply and reached around 10.0% of its initial value in one day. This reduction was about 50% at 23 °C for the similar time period. Therefore, a significant reduction of Md occurs at the reservoir temperature conditions. As a result, it seems that the sharp softening behavior of Gachsaran rock salt can cause high stress transmission to the cement and the casing in the wellbore. Therefore, the timedependent behavior of rock salt can be a key factor when studying the effects of Gachsaran rock salt on casing collapse incidents. As shown in Fig. 15b, Mv reveals a mild decreasing pattern for the case of 23 °C and in case of 90 °C it remains approximately constant. Meanwhile, increasing the differential stress (depicted by solid vertical lines with arrows in Fig. 15a and b) changes the trend of variations for both parameters (Md and Mv) to some extent.
Fig. 16 indicates that when the applied differential stress and the temperature are the same, the strain rate is also the same, despite of the difference between the confining stresses, as depicted by the two blue circles in Fig. 16. Therefore, Fig. 16 reveals the fact that the creep strain rate is not affected by the confining stress neither at the ambient temperature (23 °C) nor at the reservoir temperature (90 °C). In other words, for studying the creep behavior of Gachsaran rock salt, uniaxial tests yield satisfactory results. However, the effect of temperature on the creep parameters of Gachsaran rock salt is remarkable, as higher temperature causes higher axial strain in the sample under sustained load. The small value of the activation energy (Q) which is lowest in Table 2 confirms this finding. 6. Numerical simulation of creep effects on the well casing Numerical simulation with the finite element method (FEM) is performed using the commercial code ABAQUS to examine the effects of the rock salt creep with experimentally-obtained parameters on a real casing collapse incident in an Iranian oil well [33]. 6.1. Simulation description
5.2. Sensitivity of creep parameters to temperature and confining stress In order to evaluate the effect of the confining stress and temperature on Gachsaran rock salt behavior, results of the current study along with the previous study results reported by Gorjian are shown in Fig. 16 [23]. The results of two studies are in good agreement. Both results indicate that the strain rate increases with the differential stress almost linearly and the slopes of the two lines are almost identical. Although Gorjian conducted creep tests using uniaxial apparatus, the results (depicted by hollow circle, hollow triangle and hollow rectangle in Fig. 16) match well with the current study results (depicted by solid rhombus and solid rectangle in Fig. 16) that was conducted using triaxial apparatus under rather high (15.0 MPa) confining stress [23].
Fig. 17a presents the simulated area including the borehole and its surrounding formations over the underlain reservoir layer, up to the ground surface (±0.0 m). The borehole diameter is 0.311 m. The casing and the cement are included in the simulation (Fig. 17b). In view of that, the wellbore area is completed with 86.9 kg/m V150 casing with the outside diameter of 0.244 m and thickness of 15.1 103 m. The annulus between the casing and the wellbore is filled with cement. Fig. 17c shows the FE mesh of the salt layer as a separate part of the simulated area to show the meshing detail. A similar mesh pattern is used for other rock layers. The salt layer is approximately 114 m thick; its top elevation is 3198 m and the bottom elevation is –3312 m. The overall height of the simulated area is 3712 m and the quadratic element size is around 6.5 m. The other dimensions of the elements range from 6.5 m at the outer boundary to around
Fig. 15. Effect of creep behavior on modulus of deformation and modulus of volumetric change.
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 18. External pressure on the casing versus production time based on numerical simulation.
Fig. 17. Benchmark model.
3 cm at the wellbore area adjacent to cement. The FE mesh of the simulated area includes 350,923 nodes and 196,912 elements. The 8-node quadratic elements integrated with a full quadrature scheme were used in the numerical simulations. The material properties used in the numerical modeling are tabulated in Table 4. All materials other than the rock salt including rock layers, casing, and cement are simulated using a linear elastic model. The creep properties of the rock salt are based on the obtained experimental values and the power law model introduced in Table 2 and mentioned again in Table 4. In order to estimate the in-situ stress state, it needs at first to define the vertical effective stresses at each specified depth which is equal to total pressure exerted by the weight of overburden layers minus the fluid pressure, as defined following:
S0 v ¼ Sv aP p
ð4Þ
where S’v is the vertical effective stress; Sv the vertical stress integrated from the surface at each depth according to density of the overlying layers; a the Biot coefficient which can be assumed equal to 1.0; and Pp the pore pressure. The hydrostatic pore pressure regime is assumed from the ground surface to the model base and the initial geostatic stress field is considered based on the densities of rock layers integrated over the simulated depth. According to the results of the Leak-off tests (LOTs), stress analysis report and drilling evidences in the area under study [22]; one can assume that both horizontal effective stresses are the same. Assuming the theory of linear elasticity for the rock layers, the horizontal effective stress equals to:
S0H ¼ S0h ¼
v
S0 1v v
ð5Þ
where S0 H is the maximum horizontal effective stress; S0 h the minimum horizontal effective stress; and v the Poisson’s ratio.
Fig. 19. Safety factor versus the production time.
Boundary conditions are such that the model base is constrained against any displacement, the lateral boundaries are fixed in the radial direction only, and the model top at the ground surface is free. The interaction between various rock layers are defined in such a way that they cannot slip relative to each other. The casing and cement are also tied together. The simulation covers the whole pre-production process, including various stages of in-situ stress conditions, drilling, completion, and production. The first step of the simulation is about the geostatic condition to equilibrate the in-situ stress state of the model. This step also establishes the initial distribution of pore pressure. Afterwards, instantaneous drilling is considered, i.e. all the elements corresponding to the borehole are removed. At the same time, the pressure exerted by the drilling mud is imposed on the inner surface of the borehole which equals 2.0 MPa more than the pore pressure at each depth. Then, the cement and the casing are introduced to the model. At the end, the production stage is simulated in which the pressure draw-down from the reservoir area for 24 years of production is considered by coupled displacement/diffusion analysis to simulate the outflow from the reservoir (Fig. 17a).
6.2. Simulation results Fig. 18 shows the variation of the maximum external pressure on the casing during 24 years of oil production from this well. The arrows drawn inside the right hand image of Fig. 17 indicate the external pressure on the casing. As shown in Fig. 18, the external pressure on the casing due to Gachsaran rock salt creep behavior develops over time and reaches
Table 4 Material parameters [22]. Casing Outside diameter (m) Wall thickness (m) Young’s modulus (GPa) Poisson’s ratio
Cement 0.244 0.0151 207 0.27
Thickness (m) Young’s modulus (GPa) Poisson’s ratio
Salt 0.0333 10 0.25
Initial Young’s modulus(GPa) Initial Poisson’s ratio Activation energy (kJmol1) Viscosity coefficient (MPans1) Stress power
6 0.16 22.6 2.88 108 3
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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a constant amount after around 7 years. The possibility of casing failure gradually increases due to the higher applied external pressure. At the reservoir conditions, the external pressure is almost doubled before its value becomes constant compared to its initial value at the end of completion stage. Creep causes salt to flow toward the adjacent materials to relieve the induced stress perturbations. This viscous flow creates high contact pressures on the cement sheath and then on the casing which can be beyond the casing strength. The outcome of the numerical simulation indicates that the location of the maximum external pressure shown in Fig. 18 is at the interface between salt and non-salt rock layers (at elevation of –3312.0 m in Fig. 17a). This result indicates that the exit section from a salt layer is the critical part of the oil wells considering the rock salt creep. As depicted in Fig. 18, considering the reservoir conditions, the external pressure on the casing becomes 104 MPa after 7 years of production which is around 16 MPa greater than the external pressure on the casing at the ambient conditions. It is notable that these results are for the ideal conditions in which the cement quality is good, and the casing is centralized, so the external pressure on the casing is uniform for the whole wellbore section. However, this state may be wrecked because of cementing imperfections that can cause non-uniform loading on the casing which may increase the risk of the casing collapse. Fig. 19 shows the variation of the safety factor against casing collapse over the 24 years of production history. The safety factor is defined as the ratio of the collapse strength based on the technical specification data, divided by the value equal to the difference between the external pressure on the casing and the inside flowing pressure:
Saftey factor ¼
Collapse strength External pressure inside flowing pressure
ð6Þ
effects of creep and in-situ stresses on the casing. Based on the results, the following conclusions can be drawn: (1) The halite rock salt of Gachsaran formation obeys the power law creep model; however, its parameters differ from those of other halite rock salts around the world. The Gachsaran rock salt exhibits strong sensitivity to the temperature but its sensitivity towards differential stress is low. (2) The 3D nature of the triaxial creep tests showed that the creep behavior of this rock salt is independent of the confining stress. (3) Variation of deformation characteristics confirm that creep causes the rock salt to become significantly softer, at the time when no volume change occurs. The obtained results are instrumental in studying the effect of rock salt creep on casing collapse incidents. (4) The numerical simulation of one well in southwest oil field of Iran supported this theory that creep of the rock salt can be a major cause of casing collapse in the Gachsaran formation. At the reservoir conditions, the external pressure on the casing almost doubled compared to the pressure when the production starts before reaching the constant value. This additional pressure reduced the safety factor against the collapse to a value close to unity. (5) Numerical modeling indicated that ignoring the reservoir conditions affecting the creep behavior of the salt layer could be misleading for the casing design since adequate measures may not be provided to correctly evaluate the possibility of the casing collapse.
Declaration of Competing Interest
The collapse strength of the casing is 80 MPa, and the internal pressure determined from the flowing pressure data at elevation of 3712 m (Fig. 17a) is 26 MPa. Considering all items, it is possible to calculate the safety factor against the collapse and its variation over time. Based on what is shown in Fig. 19, two main observations can be made:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(1) The creep in rock salt layer reduces the safety factor against casing collapse from 3.30 to 1.02 under the reservoir conditions and to 1.27 under the ambient conditions. These findings confirm that the creep of Gachsaran rock salt can be a major cause of casing collapse, as it lowers the safety factor against casing collapse considerably. (2) Consideration of the reservoir condition for casing design in the rock salt layer is crucial for wellbore stability analysis, as there is a minimum difference of around 0.25 between the safety factors under the reservoir conditions and ambient conditions. Therefore, considering the safety factor based on the parameters obtained at the ambient conditions can be misleading.
This work is funded by Iran National Science Foundation (Grant No. 96001589 and contract No. 96002219). This support is gratefully acknowledged. Also, authors would like to show their gratitude to Firouz Ardeshirian, and Reza Sanajian for their cooperation in the experimental part of this research.
7. Conclusions This paper investigated the time-dependent creep of the rock salt layer of Gachsaran formation which is believed to be one of the causes of casing collapses in southwest Iranian oil fields. Some creep tests were carried out at various temperatures and stresses on Gachsaran rock salt to study the effects of temperature and stress on the creep behavior. Also, the appropriate constitutive model for creep, and its parameters were determined and verified. Then, numerical simulation was conducted to specify the possible
Acknowledgements
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Contents lists available at ScienceDirect
International Journal of Mining Science and Technology journal homepage: www.elsevier.com/locate/ijmst
Investigation of rock salt layer creep and its effects on casing collapse S. Reza Taheri a,b, Ali Pak a,b,⇑, Saeed Shad b,c, Behzad Mehrgini d, Meisam Razifar e a
Civil Engineering Department, Sharif University of Technology, Tehran, Iran Upstream Petroleum Research Institute, Sharif University of Technology, Tehran, Iran c Chemical & Petroleum Engineering Department, Sharif University of Technology, Tehran, Iran d Kish Petroleum Engineering Company, Tehran, Iran e Folowrd Industrial Projects Company, Tehran, Iran b
a r t i c l e
i n f o
Article history: Received 8 December 2018 Received in revised form 13 May 2019 Accepted 2 February 2020 Available online xxxx Keywords: Rock salt Gachsaran formation Creep Power law Casing collapse Numerical simulation
a b s t r a c t Casing collapse is one of the costly incidents in the oil industry. In the oil fields of southwest Iran, most casing collapses have occurred in Gachsaran formation, and the halite rock salt layer in this formation may be the main cause for these incidents because of its peculiar creep behavior. In this research, triaxial creep experiments have been conducted on Gachsaran salt samples under various temperatures and differential stresses. The main purpose was to determine the creep characteristics of Gachsaran rock salt, and to examine the role of creep in several casing collapses that occurred in this formation. Results indicated that the halite rock salt of Gachsaran formation basically obeys the power law; however, its creep parameters are quite different from other halite rocks elsewhere. The time-dependent creep of Gachsaran rock salt exhibits strong sensitivity to temperature change; however, its sensitivity to variation of differential stress is rather low. The numerical simulation of the rock salt creep in a real oil well demonstrated the importance of creep and reservoir conditions on the safety factor of the tubing related to casing collapse. Ó 2020 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Casing collapse is a major problem in the oil industry. Delay in oil production, and sometimes total loss of the well make casing collapse an event that imposes heavy cost on oil companies. Several factors can be responsible for casing collapse in oil wells, including the reservoir depletion effects, effects of natural faults and fractures, well completion problems and cementing imperfections, time-dependent creep of the surrounding rock layers, and chemical effects. A large number of casing collapse incidents have been reported within the rock salt layers that are attributed to creep of rock salt, especially under high pressure and high temperature condition [1–5]. Creep, depicted as the gradual deformation of material under constant stress, generally has three stages: First, a period in which the rate of time-dependent deformation decreases with time, called transient creep. If stresses are reduced to zero at this stage, the deformation will also become zero. In the secondary stage, the creep rate remains constant. By removing the load at this stage, the creep deformation will not be completely eliminated. In the ter⇑ Corresponding author at: Civil Engineering Department, Sharif University of Technology, Tehran, Iran. E-mail address: [email protected] (A. Pak).
tiary stage, the strain rate increases with time, so it may quickly lead to failure, sometimes accompanied by rapid expansion of unstable fissures. Fig. 1a shows these three stages schematically [6]. Also, a sigmoidal stress-strain curve is shown in Fig. 1b, indicating three different stages of strain hardening corresponding to Fig. 1a obtained by deformation experiments on single crystals of rock salt [7]. In oil wells, an initial creep occurs shortly after drilling, followed by steady-state creep. The third stage is not usually important in oil wells because the casing installation and cementing do not allow further deformations. For rock types such as salt, the steady-state deformation may lead to structural collapse of the casing tube, therefore the steady-state creep rate should be evaluated [5]. Many studies have been carried out to investigate the creep behavior of rock salts and several researchers have tried to formulate this peculiar type of deformation mentioned above [8–14]. In rheological models, different compositions of idealized spring and dashpot elements are used to define the creep behavior (e.g. theoretical models of Maxwell, Kelvin-Voigt, and Burgers). On the other hand, some empirical laws have been proposed based on curve-fitting of the creep tests on different rock salt types. Among these empirical models, the power, exponential, and logarithmic
https://doi.org/10.1016/j.ijmst.2020.02.001 2095-2686/Ó 2020 Published by Elsevier B.V. on behalf of China University of Mining & Technology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 1. Various stages of creep and three different stages of strain hardening for single crystals of rock salt (after [6,7]).
laws are most widely used depending on the rock salt type and the conditions that have been applied during the experiments [15]. Two main deformation mechanisms are important in rock salt: (1) dislocation creep that covers the creep properties of rock salt over a wide range of physical conditions; and (2) pressure solution (in wet and relatively fine grained rock salt) [16,17]. It will be shown later herein that the microstructural analysis indicates that the rock salt under study is typically dry coarse grained, so it is expected that dislocation creep is the dominant deformation mechanism. Although complexity exists within exact definitions of rock salt creep, there are two common main features in this regard that holds for dislocation creep: (1) the rock salt creep strain rate; and (2) temperature. The rock salt creep strain rate is proportional to the applied differential stress (Dr) to the power n (n > 1) [18]. The general creep relationship between the strain rate and differential stress can be written as follows [19]:
ðDrÞn ¼ Ae_
ð1Þ
where Dr = r1 r3 is the differential stress defined in conventional triaxial test where r1 and r3 is axial and confining stress, respectively; n the power coefficient; A the material constant; and e_ the strain rate. Fig. 2 shows the linear and double logarithmic curves drawn based on Eq. (1). In ordinary linear space, two different behaviors of linear and non-linear (power function) are visible (Fig. 2a). However, in logarithmic scale (Fig. 2b), a line with a slope equal to cot1n exists for each state. Therefore, n value can specify the governing creep behavior. The creep behavior follows Newtonian pattern only when n is close to 1, and the line slope in Fig. 2b is around 45°. However, rock salt usually does not follow the viscous behavior proposed by Newton, as n is more than 1 which demonstrate itself in the form of a straight line with a milder slope in the loglog plot of differential stress versus strain rate [19]. Temperature affects the creep strain rate of the rock salt such that the strain rate rises due to temperature increase [6]. This feature combined with Eq. (1) can be written as [20,21]:
e_ ¼ A0 ðDrÞn exp
Q RT
where A0 is the viscosity coefficient; Q the activation energy; n the non-unit power of the differential stress (usually 3 n 6); R the universal constant of gases; and T the absolute temperature of rock [18]. In this study, the creep behavior of Gachsaran rock salt layer in southwest Iran and its effects on casing collapse are of concern, because most of the casing collapse incidents in this area have reported to occur in this layer [22]. To the best of our knowledge, no comprehensive study is yet carried out to investigate the Gachsaran rock salt creep behavior, or to predict its effects on the casing collapse by an integrated numerical model. The only study about creep in Gachsaran rock salt consists of uniaxial experiments at various temperatures carried out by Gorjian, the results of which are used in this study [23]. In the following, after a brief review of the Gachsaran formation characteristics, and description of the experimental set up built for conducting creep tests at elevated temperature and stress, the laboratory results are explained and discussed. Then, a comparison between Gachsaran rock salt and other rock salts is carried out using the power law to highlight their differences. Next, attempts have been made to evaluate the change of deformation characteristics of rock salt due to its viscous behavior over time. A numerical simulation is then presented to show how creep in this type of rock can lower the safety factor against casing collapse for one of the oil wells in southwest Iran. Finally, some conclusions are drawn. 2. Formation overview and sample preparation As noted before, the highest number of casing collapse incidents in southwest Iran has been reported to occur in the Gachsaran formation. Fig. 3 shows the general stratigraphy of the area in which Gachsaran formation is highlighted. Below the Gachsaran formation, there is a giant limestone reservoir called Asmari which is one of the largest oil-rich reservoirs in the world. The Gachsaran formation consists of seven members (M1-M7 in Fig. 3) deposited in the geological periods of the lower to middle Miocene. The dominant rock types in Gachsaran formation are rock salt, marl, and anhydrite. These salty sections are bulky, and their thickness reaches 200 m in some places, and red violet layers (M2 and M4) are salt-rich [24]. The in-situ temperature of these salty layers at depths of 2900– 3200 m is around 90 °C. According to X-ray diffraction (XRD) tests, Gachsaran salt contains around 95% halite [23]. Halite is the mineral form of sodium chloride (NaCl) which is commonly called rock salt. Halite has specific properties including high ductility and low creep strength [25,26]. The Gachsaran halite has been formed by
Fig. 2. Differential stress versus strain rate (after [19]).
ð2Þ
Fig. 3. General stratigraphy of Gachsaran formation.
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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ion binding with 39.4% sodium and 60.6% chlorine and its impurities are often in the forms of brine drops, gas bubbles, clay, and organic content. The transparent minerals of Gachsaran halite have white streaks [27]. The rock salt specimens for creep testing were taken from the Ambal ridge area, 12 km northeast of Gotvand city, Khuzestan Province, Iran. Based on CT-scan images, all selected specimens were visually homogeneous. There were no obvious fractures and cracks on the specimens. Results of the microstructural analyses for the experimental samples showed that the Gachsaran rock salt is typically dry and coarse grained and as mentioned before, pressure solution is unlikely to have taken place and dislocation creep is the dominant deformation mechanism (Fig. 4). As shown in Fig. 4, undeformed microstructure has an average grain size of 2.3 mm. The micrographs show experimentally undeformed halite-dominated Gachsaran rock salt with small amount of disseminated fluid inclusions.
3. Experimental apparatus and testing procedure The irregular-shaped rock salt blocks were carefully cut and used in the experimental apparatus. All samples were trimmed into cylinders with a height (73 mm) to diameter (37 mm) ratio of about 2. Fig. 5a shows some rock salt samples being prepared for testing. A triaxial test set up for studying the creep behavior of Gachsaran rock salt under various stresses and temperatures up to the in-situ temperature of 90 °C was designed and built in the course of this study (Fig. 5b). The apparatus can operate either in constant stress or in constant strain modes. In this case, the creep tests were conducted under constant stress mode in both axial and lateral directions. The test apparatus (Fig. 5b) has a servo-controlled loading system which is capable of applying the desired confining and axial stresses. It was equipped with data acquisition and online control systems for continuous monitoring of the test results during the rock salt sample creep. The triaxial structure of the test set up provided the possibility to examine the differences between the rock salt creep parameters under uniaxial stress condition and the triaxial one. Fig. 6 schematically depicts different parts of the testing apparatus. All tests were conducted under stress-controlled mode with the accuracy of 10 KPa. One linear variable differential transducer (LVDT) was used to measure the axial deformation of the sample, and three lateral sensors equally spaced in mid-height of the sample were used for measuring lateral deformations. The accuracy of LVDTs for strain measurement was 1 106. Lateral LVDTs were designed to have a hydraulically balanced internal housing, so any change in the pressure was distributed uniformly inside the chamber. Application of the different axial and lateral stresses in the triaxial cell induces shear stresses in the sample. Multistage creep tests were carried out to measure the creep parameters under a range of increasing shear stresses. Table 1 summarizes the tests conditions. The apparatus and the measurement devices were calibrated before and after the creep test. Calibration for the lateral pressure
Fig. 4. Transmitted light micrograph of one Gachsaran rock salt sample.
3
Fig. 5. Rock salt samples in the lab and the testing apparatus.
and axial stress was performed with a reference pressure gage, and a reference load cell, respectively; and calibration of the volumetric measurement element was conducted with reference blocks and measuring tools. The effect of temperature and stress on calibration factors were then verified with reference materials with known properties under no stress and no temperature conditions. To conduct the tests at the reservoir temperature, samples were kept in the oven to reach a certain temperature before placement in the cell for creep experiment. During the test, the temperature was held constant using thermal jackets and an insulation system equipped with monitoring sensors with an accuracy of 0.1 °C. All sensors were placed out of the zone affected by heat, so displacement measuring sensors are located behind a firewall to eliminate the temperature effect on the measurements. The temperature sensor is located inside the cell and insulated from environmental effect. It is connected to a proportional integral differential (PID) controller and indicators in the data acquisition system. The thermal jacket is a heating and insulation jacket with a 5 kw electrical heating element embedded in the insulation jacket and a PID control unit. The power of the heating element is controlled continuously to keep the temperature constant and avoid fluctuation in temperature.
4. Experimental results 4.1. Direct findings Figs. 7 and 8 show the axial strain versus time for two multistage triaxial creep tests. These tests were conducted under constant confining stress of 15.0 MPa at constant temperatures of 23 °C and 90 °C, respectively. For the first stage (Dr = 17.6 MPa), the creep rate was high at the beginning of applying the differential stress and gradually decreased in a nonlinear manner, and then remained almost constant with a fixed slope. After assuring that the strain rate was constant at steady-state condition, the next loading stage was started. For the second stage (Dr = 22.4 MPa), again the initial strain rate was high and it decreased gradually until it remained constant. The differential stress (Dr) of the third stage was 25.6 MPa. The differential stresses were selected to reach maximum 70% of the ultimate shear strength of the rock salt specimens which was 46.0 MPa [22]. Fig. 8 shows the tests results in the same manner of that of Fig. 7. Comparison between Fig. 7 at 23 °C and Fig. 8 at 90 °C points out the importance of temperature, as the strain rate at a high temperature is around ten times greater than that at a low temperature. Fig. 9 shows a rock salt sample before and after the creep test. The specimen has deformed in a barrel shape without any visible crack. The Gachsaran salt has flowed under nearly constant volumetric conditions.
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 6. A schematic view of testing apparatus.
4.2. Model parameters determination
Table 1 Creep tests conditions. Test condition
Value
Differential stress, Dr (MPa) Temperature, T (°C)
17.6–32.2 23.0–90.0
Fig. 7. Axial strain over time (T = 23 °C).
Fig. 8. Axial strain over time (T = 90 °C).
Fig. 9. Rock salt sample before and after the creep test.
In order to determine the power law representation parameters, variation of the logarithm of the axial strain rates at the steadystate condition is plotted versus the logarithm of the differential stresses in Fig. 10 for two temperature levels (23 °C and 90 °C). The slopes of the lines fitted to the experimental results show the power n of the stress term in Eq. (2). As shown in Fig. 10, the slopes of both lines are 3.0. It is notable that the data depicted by hollow circle in Fig. 10 comes from [23]. For obtaining the activation energy (Q) in Eq. (2), variation of the logarithm of axial strain rate at the steady-state condition is plotted against 1000/RT for four different confining stress levels (Dr = 13.2, 15.4, 17.6 and 25.6 MPa), as shown in Fig. 11. The values in the horizontal axis vary according to the temperatures in the range of 23 °C to 90 °C. The average slope of the fitted lines equals Q, which is 22.6 kJmol1. After specifying n and Q, A0 can be calculated using Eq. (2). Based on the obtained results, the power law model parameters for Gachsaran rock salt are summarized in Table 2. For the sake of comparison between the characteristics of Gachsaran rock salt and other halite rock salts, the parameters reported by a number of investigators are added into Table 2. The parameters differ from each other due to variation of the mineral composition, halite grain size, and impurities. As can be seen in Table 2, the activation energy Q of Gachsaran rock salt is much lower than that of the other halite rock salts, indicating its high sensitivity to temperature. On the other hand, Gachsaran rock salt has little sensitivity to differential stress, as its n value is minimum. Also, the A0 value of Gachsaran rock salt is among the lowest values.
Fig. 10. Variation of strain rate versus differential stress in log-log coordinates (after [23]).
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 11. Variation of logarithm of strain rate versus 1000/RT. Fig. 12. Applied differential stress versus strain rate (after [23]).
4.3. Model parameters verification Variation of the applied differential stress versus the strain rate is illustrated in Fig. 12 in two types of coordinates (arithmetic and log-log) to be compared with Fig. 2. Based on Fig. 12, one can conclude that the power law representation is an appropriate mean for formulating the creep behavior of Gachsaran rock salt. The results of the previous study by Gorjian are also included in Fig. 12. In order to examine the accuracy of the obtained creep parameters of Gachsaran rock salt, a comparison between the measured and predicted creep rates according to the obtained power law parameters introduced in Eq. (2) is shown in Fig. 13 for different temperatures and applied stresses. Many points are located close to the 1:1 line (diagonal line) and the obtained power law relationship shows a very good accuracy level. There is a good agreement between the measured and predicted creep rates based on Eq. (2), despite of one point located far from the 1:1 line.
end of mode 3 in Fig. 14b, gets around 6 times greater than the axial strain at the end of mode 1 in Fig. 14a, considering that both modes 1 and 3 have the same differential stress. The time specific stiffnesses that correspond to the deformation moduli during creep tests are shown in Fig. 15. The modulus of deformation (Md) values are calculated as the ratio of the differential stress to the corresponding axial strain over time. The modulus of volumetric change (Mv) is defined as the ratio of confining stress to the corresponding volumetric strain. Both Md and Mv values are determined directly from the test results as follows:
Md ¼
ðr1 r3 Þt ð r3 Þt ; Mv ¼ ðe1 Þt ðev Þt
ð3Þ
5. Discussions 5.1. Variation of deformation characteristics of the rock salt In the following, variation of Gachsaran rock salt deformation characteristics is studied based on the experimental observations. Table 3 specifies four considered experimental modes. Time variations of the axial and volumetric strains are shown in Fig. 14a for modes 1 and 2, and in Fig. 14b for modes 3 and 4. The solid vertical lines with arrows specify the times when the mode changes from 1 to 2 in Fig. 14a, and from 3 to 4 in Fig. 14b, respectively. Modes 1 and 2 indicate different loading stages for one sample and the same situation is established for modes 3 and 4. The volumetric strains became nearly constant over time showing that the creep process did not induce significant volume changes. However, increasing the differential stress caused a jump in the axial strain. Comparing the axial strains in Fig. 14a and b indicates the temperature effect on the rock salt creep. The axial strain at the
Fig. 13. Comparison of the predicted and measured creep rates of Gachsaran rock salt.
Table 3 Different modes of experiments. No.
Temperature, T (°C)
Differential stress, Dr (MPa)
1 2 3 4
23 23 90 90
17.6 22.4 17.6 25.6
Table 2 Power law model parameters of several halite rock salts. Halite type Salado Salado Asse West Hackbr. Bryan Mound Bryan Mound Bayou Choctaw Synthetic Avery Island Avery Island Synthetic wet salt Ara Salt GOM Gachsaran
A0 (MPans1) 8.82 2.71 7.26 3.15 8.93 7.78 3.94 4.70 1.60 8.10 2.75 1.82 5.19 2.88
6
10 103 106 105 105 103 106 104 104 105 102 109 108 108
Q (Jmol1)
n
Reference
50,160 69,180 53,920 54,840 63,290 74,530 49,450 24,530 68,100 51,600 80,000 32,400 41,868 22,600
4.9 5.1 5 4.7 4.5 5.2 4.1 3 5.3 3.4 5.6 5 4.9 3
[28] [28] [28] [28] [28] [28] [28] [29] [30] [30] [31] [32] [4] This study
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Fig. 16. Variation of strain rate with differential stress based on two series of creep tests results (after [23]). Fig. 14. Variations of axial and volumetric strains over time at different temperatures and modes.
where e1 is the axial strain; ev the volumetric strain; and t the time. Md value drops considerably with time at lower temperature for modes 1 and 2; however, at high temperatures, Md does not change much under higher differential stress (mode 4). For example, as shown in Fig. 15a for the case of 90 °C, Md declined sharply and reached around 10.0% of its initial value in one day. This reduction was about 50% at 23 °C for the similar time period. Therefore, a significant reduction of Md occurs at the reservoir temperature conditions. As a result, it seems that the sharp softening behavior of Gachsaran rock salt can cause high stress transmission to the cement and the casing in the wellbore. Therefore, the timedependent behavior of rock salt can be a key factor when studying the effects of Gachsaran rock salt on casing collapse incidents. As shown in Fig. 15b, Mv reveals a mild decreasing pattern for the case of 23 °C and in case of 90 °C it remains approximately constant. Meanwhile, increasing the differential stress (depicted by solid vertical lines with arrows in Fig. 15a and b) changes the trend of variations for both parameters (Md and Mv) to some extent.
Fig. 16 indicates that when the applied differential stress and the temperature are the same, the strain rate is also the same, despite of the difference between the confining stresses, as depicted by the two blue circles in Fig. 16. Therefore, Fig. 16 reveals the fact that the creep strain rate is not affected by the confining stress neither at the ambient temperature (23 °C) nor at the reservoir temperature (90 °C). In other words, for studying the creep behavior of Gachsaran rock salt, uniaxial tests yield satisfactory results. However, the effect of temperature on the creep parameters of Gachsaran rock salt is remarkable, as higher temperature causes higher axial strain in the sample under sustained load. The small value of the activation energy (Q) which is lowest in Table 2 confirms this finding. 6. Numerical simulation of creep effects on the well casing Numerical simulation with the finite element method (FEM) is performed using the commercial code ABAQUS to examine the effects of the rock salt creep with experimentally-obtained parameters on a real casing collapse incident in an Iranian oil well [33]. 6.1. Simulation description
5.2. Sensitivity of creep parameters to temperature and confining stress In order to evaluate the effect of the confining stress and temperature on Gachsaran rock salt behavior, results of the current study along with the previous study results reported by Gorjian are shown in Fig. 16 [23]. The results of two studies are in good agreement. Both results indicate that the strain rate increases with the differential stress almost linearly and the slopes of the two lines are almost identical. Although Gorjian conducted creep tests using uniaxial apparatus, the results (depicted by hollow circle, hollow triangle and hollow rectangle in Fig. 16) match well with the current study results (depicted by solid rhombus and solid rectangle in Fig. 16) that was conducted using triaxial apparatus under rather high (15.0 MPa) confining stress [23].
Fig. 17a presents the simulated area including the borehole and its surrounding formations over the underlain reservoir layer, up to the ground surface (±0.0 m). The borehole diameter is 0.311 m. The casing and the cement are included in the simulation (Fig. 17b). In view of that, the wellbore area is completed with 86.9 kg/m V150 casing with the outside diameter of 0.244 m and thickness of 15.1 103 m. The annulus between the casing and the wellbore is filled with cement. Fig. 17c shows the FE mesh of the salt layer as a separate part of the simulated area to show the meshing detail. A similar mesh pattern is used for other rock layers. The salt layer is approximately 114 m thick; its top elevation is 3198 m and the bottom elevation is –3312 m. The overall height of the simulated area is 3712 m and the quadratic element size is around 6.5 m. The other dimensions of the elements range from 6.5 m at the outer boundary to around
Fig. 15. Effect of creep behavior on modulus of deformation and modulus of volumetric change.
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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Fig. 18. External pressure on the casing versus production time based on numerical simulation.
Fig. 17. Benchmark model.
3 cm at the wellbore area adjacent to cement. The FE mesh of the simulated area includes 350,923 nodes and 196,912 elements. The 8-node quadratic elements integrated with a full quadrature scheme were used in the numerical simulations. The material properties used in the numerical modeling are tabulated in Table 4. All materials other than the rock salt including rock layers, casing, and cement are simulated using a linear elastic model. The creep properties of the rock salt are based on the obtained experimental values and the power law model introduced in Table 2 and mentioned again in Table 4. In order to estimate the in-situ stress state, it needs at first to define the vertical effective stresses at each specified depth which is equal to total pressure exerted by the weight of overburden layers minus the fluid pressure, as defined following:
S0 v ¼ Sv aP p
ð4Þ
where S’v is the vertical effective stress; Sv the vertical stress integrated from the surface at each depth according to density of the overlying layers; a the Biot coefficient which can be assumed equal to 1.0; and Pp the pore pressure. The hydrostatic pore pressure regime is assumed from the ground surface to the model base and the initial geostatic stress field is considered based on the densities of rock layers integrated over the simulated depth. According to the results of the Leak-off tests (LOTs), stress analysis report and drilling evidences in the area under study [22]; one can assume that both horizontal effective stresses are the same. Assuming the theory of linear elasticity for the rock layers, the horizontal effective stress equals to:
S0H ¼ S0h ¼
v
S0 1v v
ð5Þ
where S0 H is the maximum horizontal effective stress; S0 h the minimum horizontal effective stress; and v the Poisson’s ratio.
Fig. 19. Safety factor versus the production time.
Boundary conditions are such that the model base is constrained against any displacement, the lateral boundaries are fixed in the radial direction only, and the model top at the ground surface is free. The interaction between various rock layers are defined in such a way that they cannot slip relative to each other. The casing and cement are also tied together. The simulation covers the whole pre-production process, including various stages of in-situ stress conditions, drilling, completion, and production. The first step of the simulation is about the geostatic condition to equilibrate the in-situ stress state of the model. This step also establishes the initial distribution of pore pressure. Afterwards, instantaneous drilling is considered, i.e. all the elements corresponding to the borehole are removed. At the same time, the pressure exerted by the drilling mud is imposed on the inner surface of the borehole which equals 2.0 MPa more than the pore pressure at each depth. Then, the cement and the casing are introduced to the model. At the end, the production stage is simulated in which the pressure draw-down from the reservoir area for 24 years of production is considered by coupled displacement/diffusion analysis to simulate the outflow from the reservoir (Fig. 17a).
6.2. Simulation results Fig. 18 shows the variation of the maximum external pressure on the casing during 24 years of oil production from this well. The arrows drawn inside the right hand image of Fig. 17 indicate the external pressure on the casing. As shown in Fig. 18, the external pressure on the casing due to Gachsaran rock salt creep behavior develops over time and reaches
Table 4 Material parameters [22]. Casing Outside diameter (m) Wall thickness (m) Young’s modulus (GPa) Poisson’s ratio
Cement 0.244 0.0151 207 0.27
Thickness (m) Young’s modulus (GPa) Poisson’s ratio
Salt 0.0333 10 0.25
Initial Young’s modulus(GPa) Initial Poisson’s ratio Activation energy (kJmol1) Viscosity coefficient (MPans1) Stress power
6 0.16 22.6 2.88 108 3
Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001
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a constant amount after around 7 years. The possibility of casing failure gradually increases due to the higher applied external pressure. At the reservoir conditions, the external pressure is almost doubled before its value becomes constant compared to its initial value at the end of completion stage. Creep causes salt to flow toward the adjacent materials to relieve the induced stress perturbations. This viscous flow creates high contact pressures on the cement sheath and then on the casing which can be beyond the casing strength. The outcome of the numerical simulation indicates that the location of the maximum external pressure shown in Fig. 18 is at the interface between salt and non-salt rock layers (at elevation of –3312.0 m in Fig. 17a). This result indicates that the exit section from a salt layer is the critical part of the oil wells considering the rock salt creep. As depicted in Fig. 18, considering the reservoir conditions, the external pressure on the casing becomes 104 MPa after 7 years of production which is around 16 MPa greater than the external pressure on the casing at the ambient conditions. It is notable that these results are for the ideal conditions in which the cement quality is good, and the casing is centralized, so the external pressure on the casing is uniform for the whole wellbore section. However, this state may be wrecked because of cementing imperfections that can cause non-uniform loading on the casing which may increase the risk of the casing collapse. Fig. 19 shows the variation of the safety factor against casing collapse over the 24 years of production history. The safety factor is defined as the ratio of the collapse strength based on the technical specification data, divided by the value equal to the difference between the external pressure on the casing and the inside flowing pressure:
Saftey factor ¼
Collapse strength External pressure inside flowing pressure
ð6Þ
effects of creep and in-situ stresses on the casing. Based on the results, the following conclusions can be drawn: (1) The halite rock salt of Gachsaran formation obeys the power law creep model; however, its parameters differ from those of other halite rock salts around the world. The Gachsaran rock salt exhibits strong sensitivity to the temperature but its sensitivity towards differential stress is low. (2) The 3D nature of the triaxial creep tests showed that the creep behavior of this rock salt is independent of the confining stress. (3) Variation of deformation characteristics confirm that creep causes the rock salt to become significantly softer, at the time when no volume change occurs. The obtained results are instrumental in studying the effect of rock salt creep on casing collapse incidents. (4) The numerical simulation of one well in southwest oil field of Iran supported this theory that creep of the rock salt can be a major cause of casing collapse in the Gachsaran formation. At the reservoir conditions, the external pressure on the casing almost doubled compared to the pressure when the production starts before reaching the constant value. This additional pressure reduced the safety factor against the collapse to a value close to unity. (5) Numerical modeling indicated that ignoring the reservoir conditions affecting the creep behavior of the salt layer could be misleading for the casing design since adequate measures may not be provided to correctly evaluate the possibility of the casing collapse.
Declaration of Competing Interest
The collapse strength of the casing is 80 MPa, and the internal pressure determined from the flowing pressure data at elevation of 3712 m (Fig. 17a) is 26 MPa. Considering all items, it is possible to calculate the safety factor against the collapse and its variation over time. Based on what is shown in Fig. 19, two main observations can be made:
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(1) The creep in rock salt layer reduces the safety factor against casing collapse from 3.30 to 1.02 under the reservoir conditions and to 1.27 under the ambient conditions. These findings confirm that the creep of Gachsaran rock salt can be a major cause of casing collapse, as it lowers the safety factor against casing collapse considerably. (2) Consideration of the reservoir condition for casing design in the rock salt layer is crucial for wellbore stability analysis, as there is a minimum difference of around 0.25 between the safety factors under the reservoir conditions and ambient conditions. Therefore, considering the safety factor based on the parameters obtained at the ambient conditions can be misleading.
This work is funded by Iran National Science Foundation (Grant No. 96001589 and contract No. 96002219). This support is gratefully acknowledged. Also, authors would like to show their gratitude to Firouz Ardeshirian, and Reza Sanajian for their cooperation in the experimental part of this research.
7. Conclusions This paper investigated the time-dependent creep of the rock salt layer of Gachsaran formation which is believed to be one of the causes of casing collapses in southwest Iranian oil fields. Some creep tests were carried out at various temperatures and stresses on Gachsaran rock salt to study the effects of temperature and stress on the creep behavior. Also, the appropriate constitutive model for creep, and its parameters were determined and verified. Then, numerical simulation was conducted to specify the possible
Acknowledgements
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Please cite this article as: S. R. Taheri, A. Pak, S. Shad et al., Investigation of rock salt layer creep and its effects on casing collapse, International Journal of Mining Science and Technology, https://doi.org/10.1016/j.ijmst.2020.02.001