ARMA 13-432 The behavior of Carthage Marble and Terratek Sandstone during high pressure, high temperature compression tests Zhang, P., Mishra, B. and Heasley, K.A. National Energy Technology Laboratory-Regional University Alliance (NETL-RUA), West Virginia University, Morgantown, WV, USA Copyright 213 ARMA, American Mechanics Association This paper was prepared for presentation at the 47 th US Mechanics / Geomechanics Symposium held in San Francisco, CA, USA, 23-26 June 213. This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented. ABSTRACT: A suite of high pressure, high temperature (HPHT) triaxial compression tests were performed on Carthage Marble and Terratek Sandstone in order to provide accurate input properties for numerical models in support of the Extreme Drilling Laboratory (XDL) of DOE-NETL. Both rock types were tested in a servo-controlled triaxial test frame at temperatures that ranged from 25 C (77 F) to 18 C (356 F) and at confining pressure that varied from 34.5 MPa (5 ksi) to MPa (29 ksi). Results from the tests showed that the strength of both rock types increased with increasing confining pressure; however, there was a reduction in the confining stress induced strength increase with increase in temperature. Further the failure behavior was seen to transition from brittle to ductile as the confining pressure increased from 13 MPa (15 ksi) to MPa (29 ksi). Ultimately, a multi-variable linear regression analysis of the test data was used to develop empirical formulae which define the relationship between the rock properties (failure strength, elastic modulus, Poisson s ratio, friction angle, cohesion and dilation angle) and the confining pressure and temperature. 1. INTRODUCTION The Department of Energy (DOE) National Energy Technology Laboratory (NETL) developed the Extreme Drilling Laboratory (XDL) with the Ultra-Deep Drilling Simulator (UDS) in order to optimize drilling operations in deep High Pressure and High Temperature (HPHT) environments where much of our nation s future supply of oil and natural gas are located [1]. To best leverage the valuable data from experiments in the UDS, a 3D finite-difference model of the cutter-rock interaction in the UDS was developed [2]. In developing this finitedifference model, it became clear that there was a lack of knowledge and associated lack of modeling input parameters for the mechanical response and failure of rock at high pressures and/or high temperatures. Very little fundamental research had been done in the past to understanding the changes that occur in rock due to HPHT conditions, especially with regard to rock cutting at the bottom of a deep borehole. This research strives to address this lack of HPHT rock mechanics data by performing a suite of HPHT triaxial compression tests to investigate the changes in rock properties and failure characteristics associated with changes in pressure and/or temperature. 2. EXPERIMENTAL METHODOLOGY 2.1. Triaxial Test Systems The RTX-1 triaxial rock testing system from GCTS (which meets the specifications of the International Society for Mechanics (ISRM) for triaxial testing of rock samples) was used for the experiments (see Fig. 1). This testing system is equipped with a servocontrolled vertical loading capacity of 1 kn (33 kips), and a servo-controlled confining pressure capacity of MPa (3 ksi). The axial load is applied direct from a hydraulic pump while the confining pressure is obtained through a pressure intensifier system. This testing frame also has an optional high temperature control system for consistently maintaining test temperatures up to C (392 F). Axial and lateral strains of the specimen are measured through special HPHT LVDTs (linear variable differential transformers) located inside the high pressure triaxial cell. Two LVDTs are used to measure axial displacement, and one LVDT is used to measure circumferential/lateral strain (see Fig. 2). During the triaxial tests, an axial load rate of.1% axial strain per minute was applied to the specimens while maintaining a constant confining pressure.
standard [4], and are summarized in Table 1. The Carthage Marble specimens had an average elastic modulus of 18.81 ± 1.61 GPa (2727 ± 234 ksi) and an average Poisson s ratio of.36 ±.3. For the Terratek Sandstone, the elastic modulus averaged 18.58 ± 3.4 GPa (2694 ± 441 ksi) and the Poisson s ratio averaged.27 ±.2. Table 1. Specimen information Fig. 1. GCTS RTX-1 Triaxial Test System. Axial HPHT LVDTs C.M. T.S. Items Specimen Size D, cm L, cm Density, kg/m 3 Sonic Velocity E, v GPa Avg. 5.4 1.417 265 18.81.36 St. Dev..1.338 66 1.61.3 St. Dev. / Avg..2% 3.2% 2.5% 8.6% 8.3% Ave. 5.34 1.353 2483 18.58.27 St. Dev..5.18 54 3.4.2 St. Dev. / Avg..1% 1.7% 2.2% 16.4% 7.4% Circumferential HPHT LVDT Fig 2. Specimen inside triaxial cell 2.2. Specimen Preparation Using the ASTM standard [3], forty rock specimens of NX size were prepared as detailed in Table 1. Twenty specimens where cored from Carthage Marble blocks with an average diameter of 5.4 ±.1 cm (1.984 ±.4 in), an average length of 1.417 ±.338 cm (4.11 ±.133 in) and an average density of 265 ± 66 kg/m 3 (162.6 ± 4.1 lb/ft 3 ). Another twenty specimens were cored from Terratek Sandstone blocks with an average diameter of 5.34 ±.5 cm (1.982 ±.2 in), an average length of 1.353 ±.18 cm (4.76 ±.71 in), and an average density of 2483 ± 54 kg/m 3 (155. ± 3.4 lb/ft 3 ). 2.3. Determination of Dynamic Elastic Modulus and Poisson s Ratio Ultrasonic wave velocity tests were performed for both rock types. Specifically, the compressional wave (Pwave) and shear wave (S-wave) velocities were measured using the OYO Model-5217 ultrasonic wave velocity measurement system. The elastic modulus (E) and Poisson s ratio (v) were calculated using the ASTM 2.4. Triaxial test plan For the triaxial tests, two specimens of each rock type were tested at confining pressures of 34.5, 69, 13, 137, 172 and MPa (5, 1, 15, 2, 25 and 29 ksi), and at ambient temperature of 25 C (77 F). Then, one specimen of each rock type was tested at the confining pressures of 34.5, 69, 137 and MPa (5, 1, 2 and 29 ksi), and at elevated temperatures of 1 C (212 F) and 18 C (356 F). Therefore, a total number of forty triaxial tests were performed with twenty tests for each rock type. The triaxial compression test plan is summarized in Table 2. Table 2. Triaxial compression test plan C.M. T.S. Temp., C Confining pressure, MPa 34.5 69 13 137 172 Total 25 2 2 2 2 2 2 12 1 1 1 NA 1 NA 1 4 18 1 1 NA 1 NA 1 4 Total 4 4 2 4 2 4 2 25 2 2 2 2 2 2 12 1 1 1 NA 1 NA 1 4 18 1 1 NA 1 NA 1 4 Total 4 4 2 4 2 4 2
2.5. property determination During the analysis of the rock specimens, the mechanical properties of: strength (σ), elastic modulus (E), Poisson s ratio (v), dilation angle (ψ), friction angle (φ) and cohesion (c) were determined. For a typical unconfined compressive test, determining the strength of a brittle rock is fairly straight forward. The stress-strain curve is typically linear and increases to the failure point where the rock breaks and the stress rapidly falls. In the elastic brittle case, the rock strength (σ) is equal to the peak stress (σ p ), which is denoted on the stress-strain curve (σ = σ p ). However, when the confining pressure and/or temperature is increased, a rock specimen can start to exhibit ductile behavior where the rock no longer behaves linear elastically and the stress-strain curve rolls over with a decreasing modulus with increasing strain, as shown in Fig. 3a. In ductile case, the strength (σ) of the rock is a bit harder to determine. Instead of the peak strength, the yield point of the rock is considered to be the failure point. This point of yield stress designates the point of transition from the pre-failure linear elastic behavior to the post-failure plastic behavior. The point on the stressstrain curve (Fig. 3a) at the yield is designate by the yield stress (σ y ) and the yield strain (ԑ y ) [5]. (c) 2nd derivative of stress vs. strain Fig. 3. Yield stress determination (after Christensen[5]). Following the process outlined by Christensen [5], the yield stress (σ y ) and yield strain (ԑ y ) can be determined by the maximum absolute value of the second derivative of the axial stress versus the axial strain ( d 2 σ/dɛ 2 max ) (see Fig 3c). This is the point of greatest change, or inflection point, in the plot of the elastic modulus versus the axial strain (see Fig. 3b). Therefore, for ductile behavior, the rock strength (σ) value is represented by the yield stress (σ y ), i.e. σ = σ y. Furthermore, according to the study performed by Christensen [5], the strain level which delineates the limit of the linear elastic range (the linear elastic range strain, ԑ L ) is 95% of the yield strain (ԑ y ) (see Eq. (1) and Fig. 4). Thus, the ultimate linear elastic stress (σ L ) is the stress at ԑ L. ε =.95 (1) L ε y (a) Axial stress vs. strain Fig. 4. Yield point and linear elastic range point (b) 1st derivative of stress vs. strain Using the ASTM standard [6], the elastic modulus (E) was determined as the tangent modulus of the stressstrain curve at 5% of the compressive strength [6]. For brittle behavior, the peak failure strength of the rock was used as the compressive strength. For ductile behavior, the stress at the limit of the linear elastic range of the specimen was used as the compressive strength. Similarly, the Poisson s ratio (v) was calculated by dividing the slope of axial stress-strain curve by the
slope of lateral stress-strain curve at 5% of the compressive strength/linear elastic limit. The dilation angle (ψ) was determined using the bilinear idealization concept proposed by Vermeer and Borst [7]. Using this method, the calculated dilation angle was essentially equal to the average value of the dilation angle in the post-failure range of the specimen. For the determination of the friction angle (φ) and cohesion (c), the triaxial test results were input into the RocLab software [8]. The software then provided the least square fit of the laboratory data to the Mohr- Coulomb failure criteria and the associated friction angle and cohesion. 3. TRIAXIAL TEST RESULTS 3.1. Introduction Among the forty triaxial tests (twenty tests for each rock type), eight specimens from the Terratek Sandstone (1 @ 25 C, 13 MPa; 1 @ 25 C, 137 MPa; 2 @ 25 C, 172 MPa; 2 @ 25 C, MPa; 1 @ 1 C, MPa and 1 @ 18 C, MPa) were not able to be tested to rock failure due to the axial load limitation of the loading frame. However, for each of the other 32 specimens, the failure/yield strength, elastic modulus, Poisson s ratio, dilation angle, friction angle and cohesion were determined (as described above). In order to further explore the influence of the confining pressure and temperature on the rock properties and to develop formulas suitable for input to a numerical model, a multi-variable linear regression was applied to the rock test parameters and resulting rock properties. As a result of this regression analysis, for each different rock property, an equation was developed that provides the best-fit value of that rock property as a function of the given temperature and confining stress. The generic form of the regression equations is presented as Eq. (2). In this generic equation; the a regression coefficient is the value of the rock property at C and MPa, the a 1 regression coefficient specifies the change in the value of the rock property as a result of a 1 C change in temperature, and the a 2 regression coefficient specifies the change in the value of the rock property as a result of a 1 MPa change in confining pressure. = a + a T + a P (2) R 1 2 where: R = the value of the chosen rock property; T = the temperature of the rock, C; P = the confining pressure on the rock, MPa; a, a 1, a 2 = regression coefficients. Since the statistical analysis was based on the triaxial test data, the resulting regression equations are only truly valid within the limits of temperature and pressure tested, 25 to 18 C and to MPa. 3.2. Carthage Marble Test Results A sample of the Carthage Marble testing results is shown in Fig. 5. Fig. 5a presents the stress-strain curves for the twelve specimens tested at ambient temperature (25 C) and various confining pressures (34.5, 69, 13, 137, 172 and MPa), and Fig. 5b presents the stressstrain curves for four specimens tested at a constant confining pressure (69 MPa) and various temperatures (25, 1 and 18 C) (see Fig. 6). Clearly, Fig. 5 shows that the rock deformation characteristics during load test are directly related to the confining pressure and temperature. Fig. 5a shows that the yield strength consistently increases as confining pressures increases; however, Fig 5b, also clearly shows that the yield strength decreases as the temperature increases. Maybe not so readily apparent, but Fig 5a also shows that the elastic modulus for the Carthage Marble steadily increases as the confining pressure increases, and that the tests with elevated confining pressure show ductile failure behavior. 1 (a) Axial strain vs. stress at 25 C (77 F) 1 MPa 25 C 1 C 18 C (b) Axial strain vs. stress at 69 MPa (1 ksi) Fig. 5. Carthage Marble axial stress-strain curve 172 MPa 137 MPa 13 MPa 69 MPa 34.5 MPa
Fig. 6. Specimens of Carthage Marble after triaxial compressive tests at 69 MPa (1 ksi) The results of the regression analysis on the Carthage Marble test specimens are shown in Table 3. As seen previously in Fig. 5, the results of the testing with Carthage Marble were very consistent and repeatable. The quality of the test results is further verified with very high correlation coefficients for the regression analysis of the rock properties, especially for the strength (R 2 =.95), friction angle (R 2 =.86) and dilation angle (R 2 =.88). Table 3. Multi-variable, linear regression analysis of the Carthage Marble properties Property 25 C 1 C 18 C Multi-linear Regression Influence Coefficient Intercept T, C P, MPa σ, MPa 224.16 -.61.87.95 E, MPa 4,627 87 42.4 v.271.1.2.3 φ,.35 -.13 -.5.86 c, MPa 23.16 -.2.9.44 ψ, 54.1.9 -.33.88 As an example of how to use the testing results presented in Table 3, the coefficients from the table specify that the relationship between the yield strength of Carthage Marble, and the temperature and confining pressure can be expressed as shown Eq. (3), where σ CM is the specimen yield strength in MPa. σ CM = 224.16.61 T +.87 P (3) This equation specifies that if the temperature is increased by 1 C, the specimen yield strength should, on average, decrease by.61 MPa. Similarly, the equation specifies that if the confining pressure increases by 1 MPa, the specimen yield strength will increase by.87 MPa. So, for a specimen at 1 C and 69 MPa, the testing data estimates that the specimen should yield at 223 MPa as shown below: R 2 3.3. Terratek Sandstone The Terratek Sandstone was tested and analyzed in the same manner as the Carthage Marble, except that eight of the Terratek Sandstone specimens were not able to be tested to rock failure due to the axial load limitation of the loading frame. A sample of the Terratek Sandstone testing results is shown in Fig.7. Similar to the Carthage Marble results in Fig. 5, Fig. 7 a presents the stressstrain curves for the twelve Terratek Sandstone specimens tested at ambient temperature (25 C) and various confining pressures (34.5, 69, 13, 137, 172 and MPa), and Fig. 7b presents the stress-strain curves for four Terratek Sandstone specimens tested at a constant confining pressure (69 MPa) and various temperatures (25, 1 and 18 C) (see Fig. 8). (a) Axial strain vs. stress at 25 C (77 F) 8 7 1 8 7 1 MPa 172 MPa 18 C (b) Axial strain vs. stress at 69 MPa (1 ksi) 137 MPa 69 MPa 34.5 MPa 25 C 1 C 13 MPa Fig. 7. Terratek Sandstone axial stress-strain curve σ CM = 224.16.61 1 +.87 69 = 223 MPa (4)
Table 4. Multi-variable, linear regression analysis of the Terratek Sandstone properties 25 C 1 C 18 C Fig. 8. Specimens of Terratek Sandstone after triaxial compressive tests at 69 MPa (1 ksi) Fig. 7a shows that the yield strength of the Terratek Sandstone tends to increases as confining pressures increases, but not necessarily as consistently as the Carthage Marble. Fig. 7b shows that the yield strength decreases as the temperature increases similar to the Carthage Marble, but the effect is not as pronounced until the higher temperatures. Not very apparent at all in Fig 7a, but the regression analysis below does show that the elastic modulus of the Terratek Sandstone increases as the confining pressure increases, very similar to the Carthage Marble. A couple of very distinct differences between the two different rock types are presented in Fig 7a. First, the failure strength of the Terratek Sandstone is noticeable higher than the Carthage Marble. Second, the failure behavior of the sandstone stays very brittle until a confining pressures of 13 MPa (15 ksi) or greater, where the failure becomes ductile, as opposed to the Carthage Marble which was ductile for all elevated confining pressures. The results of the multi-variable linear regression analysis for the Terratek Sandstone are presented in Table 4. (Since the dilation angle determination is based on plastic deformation, the dilation angle regression analysis was limited to one independent variable due to the brittle deformation behavior of the Terratek Sandstone.) Although a number of the Terratek Sandstone specimens were not able to be tested to failure, the remaining specimens still provided fairly consistent results with high correlation coefficients for the regression analysis of the rock the elastic modulus (R 2 =.88), friction angle (R 2 =.87) and cohesion (R 2 =.96). Property Multi-linear Regression Influence Coefficient Intercept T, C P, MPa σ, MPa 369.93-1.3 2.4.75 E, MPa 32,73 23 46.88 v.262 -.1 -.4.51 φ,.35 -.4 -.1.87 c, MPa 31.43 -.5.44.96 ψ, 51.36 N/A -.13.23 4. SUMMARY AND CONCLUSIONS In the research presented in this paper, a suite of high pressure, high temperature triaxial compression tests were performed on Carthage Marble and Terratek Sandstone (2 samples each). In these tests, the temperatures ranged from 25 to 18 C (77 to 356 F) and the confining pressures ranged from 34.5 to MPa (5 to 29 ksi). The results from these tests were analyzed using multiple variable regression analysis to produce equations which provide the best-fit value of six rock properties (strength, elastic modulus, Poisson s ratio, dilation angle, friction angle and cohesion) as a function of the given temperature and confining stress. These regression equations are suitable for determining the rock properties in a numerical model, and the individual regression coefficients in the equations provide insight into the specific effect of changing temperature and/or pressure on the given rock property. The results from the tests on both rock types showed that the failure/yield strength of the rock specimen increases with increasing confining pressure, but decreases with increasing temperature. Further, the elastic modulus of both rock types was seen to increase with increasing confining pressure. During the testing, it was noted that the failure strength of the Terratek Sandstone was noticeable higher than that of the Carthage Marble. Further, it was seen that Carthage Marble behaved in a ductile manner for all elevated confining pressures, while the Terratek Sandstone behaved in a very brittle manner until confining pressures of 13 MPa (15 ksi) or greater, where the failure then became ductile. 5. ACKNOWLEDGEMENT As part of the National Energy Technology Laboratory s Regional University Alliance (NETL-RUA), a collaborative initiative of the NETL, this technical effort was performed under the RES contract DE-FE. R 2
6. DISCLAIMER This project was funded by the Department of Energy, National Energy Technology Laboratory, an agency of the United States Government, through a support contract with URS Energy & Construction, Inc. Neither the United States Government nor any agency thereof, nor any of their employees, nor URS Energy & Construction, Inc., nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 8. Rocscience Inc. 2. RocLab User Manual. p.27. Toronto. REFERENCES 1. Lyons, K.D., S. Honeygan, and T. Mroz. 8. NETL extreme drilling laboratory studies high pressure high temperature drilling phenomena. J. Energy Resour. Technol. 13(4): 4312-1 43112-4. 2. Tulu, I. B., K. A. Heasley, I. Bilgesu, and O. Sunal. 8. Modeling rock and drill cutter behavior. In Proceedings of the 42nd US Mechanics Symposium and 2nd US-Canada Mechanics Symposium, San Francisco, CA, June 29 July 2, 8, eds. P. Smeallie et al., p.6. Red Hook: Curran Associates, Inc. 3. ASTM Standard D4543-1. 1. Standard practices for preparing rock core specimens and determining dimensional and shape tolerances. ASTM International, West Conshohocken, PA, 1, DOI: 1.152/D4543-1, www.astm.org. 4. ASTM Standard C1419-99a. 9. Standard test method for sonic velocity in refractory materials at room temperature and its use in obtaining an approximate Young's modulus. ASTM International, West Conshohocken, PA, 9, DOI: 1.152/C1419-99AR9, www.astm.org. 5. Christensen, R. M. 8. Observations on the definition of yield stress. Acta Mech. 196(3-4): 239 244. 6. ASTM Standard D712-1. 21. Standard test method for compressive strength and elastic moduli of intact rock core specimens under varying states of stress and temperatures. ASTM International, West Conshohocken, PA, 21, DOI: 1.152/D712-1, www.astm.org. 7. Vermeer, P.A. and R. De Borst. 1984. Non-associated plasticity for soils. Concrete and. 29(3): 1 64.