Estimation of Fracture Stiffness, In Situ Stresses, and Elastic Parameters of Naturally Fractured Geothermal Reservoirs
Shike Zhang1; Shunde Yin, M.ASCE2; and Yanguang Yuan3
Abstract: Knowledge of fracture stiffness, in situ stresses, and elastic parameters is essential to the development of efficient well patterns and enhanced geothermal systems. In this paper, an artificial neural network (ANN)–genetic algorithm (GA)-based displacement back analysis is presented for estimation of these parameters. Firstly, the ANN model is developed to map the nonlinear relationship between the fracture stiffness, in situ stresses, elastic parameters, and borehole displacements. A two-dimensional discrete element model is used to conduct borehole stability analysis and provide training samples for the ANN model. The GA is used to estimate the fracture stiffness (kn, Ks), horizontal in situ stresses(sH,sh),andelasticparameters(E,v)basedontheobjectivefunctionthatisestablishedbycombiningtheANNmodelwithmonitoring displacements. Preliminary results of a numerical experiment show that the ANN-GA-based displacement back analysis method can effectively estimate the fracture stiffness, horizontal in situ stresses, and elastic parameters from borehole displacements during drilling in naturally fractured geothermal reservoirs. DOI: 10.1061/(ASCE)GM.1943-5622.0000380. © 2014 American Society of Civil Engineers.
Author keywords: Enhanced geothermal systems; Fracture stiffness; In situ stresses; Elastic parameters; Borehole displacements; Artificial neural network (ANN)–genetic algorithm (GA) model.
In the geothermal energy industry, information on fracture stiffness, in situ stresses, and elastic parameters of naturally fractured geo- thermal reservoirs is vital for safe massive extraction of fluids, wellbore stability analysis, hydraulic fracturing design, and coupled geomechanics-reservoir simulation. Fracture stiffness describes the stress-deformation characteristics of fracture, in situ stresses de- scribe the state that the formation is subject to by initial compressive stresses prior to any artificial activity, and elastic parameters reflect the stress-strain characteristics of rock. Accurate and low-cost in- formation on these parameters is crucial for economic drilling and production of heat from an enhanced geothermal system (EGS) (Rutqvist and Stephansson 2003; Häring et al. 2008).
In naturally fractured geothermal reservoirs, natural fracture characterization is essential for recovery strategy design and borehole- design optimization (Magnusdottir and Horne 2011). The natural fracture pattern and its initial aperture are relatively straightforward to be obtained by using direct methods (e.g., cores and cuttings) and/ or indirect methods (e.g., borehole images, geophysical logs, flow logs, and temperature logs) (Kubik and Lowry 1993; Dezayes et al. 2010). Recently, Magnusdottir and Horne (2011) investigated subsurface electrical resistivity to infer the dimensions and topology of a fracture network in geothermal fields. Juliusson (2012) studied
1Assistant Professor, School of Civil Engineering and Architecture, Anyang Normal Univ., Anyang, Henan 455000, China. E-mail: [email protected] gmail.com
2Assistant Professor, Dept. of Chemical and Petroleum Engineering, Univ. of Wyoming, Laramie, WY 82071 (corresponding author). E-mail: [email protected]
3Professor, BitCan Geosciences and Engineering Inc., Suite 217-2770, 3 Ave. NE, Calgary, AB, Canada T2A 2L5. E-mail: [email protected]
Note. This manuscript was submitted on August 15, 2013; approved on December 11, 2013; published online on December 13, 2013. Discussion period open until September 3, 2014; separate discussions must be submitted for individual papers. This paper is part of the International Journal of Geomechanics, © ASCE, ISSN 1532-3641/04014033(9)/$25.00.
heat production data to characterize the fracture network layout of geothermal reservoirs. The works of Main et al. (1990) and Watanabe and Takahashi (1995) have shown that fracture patterns of naturally fractured geothermal reservoirs are commonly fractal.
However, estimation of normal and shear stiffness of a natural fracture is difficult or even impossible, especially for normal stiff- ness of a fracture (Hesler et al. 1990; Alber and Hauptfleisch 1999; Gokceoglu et al. 2004). The two parameters are indispensable in designing a borehole recovery strategy and modeling fractured geothermal reservoirs (McDermott and Kolditz 2006; Sharifzadeh and Karegar 2007; Koh et al. 2011). Some researchers used labo- ratory methods to estimate these parameters. Huang et al. (1993) investigated fracture shear stiffness using a direct shear apparatus under a boundary condition of constant normal load. This method, however, is not suitable for deep underground rock formations. To overcome this limitation, Jiang et al. (2004) developed an automated servocontrolled direct shear apparatus to determine fracture shear stiffness by assuming a constant normal stiffness condition. In practice, it is more difficult to obtain information on normal stiffness than shear stiffness of a fracture. Because of various limitations of laboratory methods, some researchers choose to perform a back analysis to estimate these parameters by using different numerical models (Alber and Hauptfleisch 1999; Nassir et al. 2010; Morris 2012; Jing and Stephansson 2007; Noorzad and Aminpoor 2008). Jiang et al. (2009) investigated the relationship between fracture transmissivity and depth, and used information of depth-dependent transmissivity to estimate fracture normal stiffness. A limitation of these approaches is that they require precise knowledge of in situ stresses and rock elastic parameters.
In general, the orientations of the in situ stresses are assumed to coincide with the vertical and horizontal directions. Bell and Gough (1979) reduced the stress tensor to three components: (1) the vertical stress magnitude, sv ; (2) the maximum horizontal stress, sH ; and (3) the minimum horizontal stress, sh. By integration of rock densities from the surface to the depth of interest, the vertical stress magnitude can be easily calculated (Haftani et al. 2008). For the two hor- izontal in situ stresses, however, it is generally difficult to determine
© ASCE 04014033-1 Int. J. Geomech.
Int. J. Geomech.
Downloaded from ascelibrary.org by UNIVERSITE LAVAL on 06/28/14. Copyright ASCE. For personal use only; all rights reserved.
by simple calculation. Hydraulic fracturing methods (Haimson and Fairhurst 1969; White et al. 2002; Sheridan and Hickman 2004; Haftani et al. 2008) and an inversion method based on wellbore deformation (Moos and Zoback 1990; Valley and Evans 2007; Zoback 2007) are popular methods for the determination of maximum and minimum horizontal in situ stresses (Sheridan and Hickman 2004).
However, investigations (Rutqvist and Stephansson 1996; Yang et al. 1997; Hossain et al. 2002) have shown that hydraulic fracturing methods are difficult to conduct or are ineffective for the estimation of horizontal in situ stresses of naturally fractured geothermal reser- voirs at a great depth because of the higher horizontal in situ stresses and preexisting natural fractures. Other methods, such as laboratory rock strength tests, in situ pore pressure measurements, wireline logging data, and the acoustic emission method (Amadei and Ste- phansson 1997), can also be used to obtain the horizontal in situ stresses under the assumption that rock elastic parameters are known constants. However, these may only serve as a complement to hydraulic fracturing or borehole deformation methods and are less accurate (Ljunggren et al. 2003; Sheridan and Hickman 2004). Estimating natural fracture stiffness, in situ stresses, and elastic parameters of naturally fractured geothermal reservoirs simulta- neously, therefore, still remains challenging as a geomechanics problem (Gokceoglu et al. 2004; Jiang et al. 2009).
In this paper, a novel method that can simultaneously identify the fracture stiffness, horizontal in situ stresses, and elastic parameters using field monitoring data is presented. This proposed method is the artificial neural network (ANN)–genetic algorithm (GA)-based dis- placement back analysis method, which has been successfully used in rock mechanics and engineering for parameter identification and optimum design (Feng et al. 2000, 2004; Pichler et al. 2003; Zhang and Yin 2013). This paper takes advantage of monitoring borehole displacements at multiple points of location during drilling to identify the previously mentioned parameters because the wellbore dis- placements are easily measured by International Society for Rock Mechanics–suggested methods (Li et al. 2013a, b). The remainder of the paper is structured as follows. First, the two-dimensional numerical model for sample generation and validation of iden- tified parameters is described. Then, the hybrid ANN-GA model for back analysis is presented. Finally, the results of a numerical experiment study are presented and discussed.
Discrete Element Method Model Based on a Thermoporoelastoplasticity Framework
Subsurface drilling in oil and gas development involves a strong coupling among fluid flow, heat transfer, and rock deformation (Yuan et al. 1995; Yin et al. 2010). The coupling effect is also significant in drilling through fractured geothermal reservoirs (Koh et al. 2011). The deformation of a fractured rock formation is composed of both the elastic and plastic deformation of intact rock and displacements along and across fracture (Barton et al. 1985). Universal Distinct Element Code (UDEC) 5.0 has been successfully used in the numerical modeling of borehole behavior in fractured rock masses (Chen et al. 2003; Nicolson and Hunt 2004), and therefore is used in this paper to conduct the coupled thermal- hydraulic-mechanical (THM) analysis in which fracture conductiv- ity is dependent on the fracture properties. Elastoplastic deformation of intact rock is represented by the Mohr-Coulomb criterion and nonassociated flow rule in a thermoporoelastoplasticity framework. The deformation of the fractures follows the Coulomb slip model.
Stress and Strain of Intact Rock
The constitutive relation for the nonisothermal single phase fluid flow through deformable fractured media incorporating the con- cept of effective stress can be expressed as (Lewis and Schrefler 1998)
Abdallah, G., Thoraval, A., Steir, A., and Piguet, J. P. (1995). “Thermal convection of fluid in fractured media.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 32(5), 481–490.
Alber, M., and Hauptfleisch, U. (1999). “Generation and visualization of microfractures in Carrara marble for estimating fracture toughness, fracture shear and fracture normal stiffness.” Int. J. Rock Mech. Min. Sci., 36(8), 1065–1071.
Amadei, B., and Stephansson, O. (1997). Rock stress and its measurement, Chapman & Hall, London.
Barton, N., Bandis, S., and Bakhtar, K. (1985). “Strength, deformation and conductivity coupling of rock joints.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 22(3), 121–140.
Bell, J. S., and Gough, D. I. (1979). “Northeast-southwest compressive stress in Alberta evidence from oil wells.” Earth Planet. Sci. Lett., 45(2), 475–482.
Brittenham, T. L., Neudecker, J. W., Rowley, J. C., and William, R. E. (1982). “Directional drilling equipment and techniques for deep, hot granite wells.” J. Pet. Technol., 34(7), 1421–1430.
Chen, X., Tan, C. P., and Detournay, C. (2003). “A study on wellbore stability in fracture rock masses with impact of mud infiltration.” J. Petrol. Sci. Eng., 38(3–4), 145–154.
Dezayes, C., Genter, A., and Valley, B. (2010). “Structure of the low permeable naturally fractured geothermal reservoir at Soultz.” C. R. Geosci., 342(7–8), 517–530.
Feng, X., Zhang, Z., and Sheng, Q. (2000). “Estimating mechanical rock mass parameters relating to the Three Gorges Project permanent shiplock using an intelligent displacement back analysis method.” Int. J. Rock Mech. Min. Sci., 37(7), 1039–1054.
Feng, X., Zhao, H., and Li, S. (2004). “A new displacement back analysis to identify mechanical geomaterial parameters based on hybrid intelligent methodology.” Int. J. Numer. Anal. Methods Geomech., 28(11), 1141–1165.
Gen, M., and Cheng, R. (1997). Genetic algorithms and engineering design, Wiley, New York.
Gokceoglu, C., Yesilnacar, E., Sonmez, H., and Kayabasi, A. (2004). “A neuro-fuzzy model for modulus of deformation of jointed rock masses.” Comput. Geotech., 31(5), 375–383.
Goldberg, D. E. (1989). Genetic algorithm in search, optimization and machine learning, 1st Ed., Addison-Wesley, Boston.
Goodman, R. E. (1970). “Deformability of joints.” Proc., Determination of the In Situ Modulus of Deformation of Rock, ASTM, West Conshohoken, PA, 174–196.
Haftani, M., and Bohloli, B., Ellassi, M., and Talebi, B. (2008). “In-situ stress determination in Sabalan geothermal reservoir.” 2nd IASME/ WSEAS Int. Conf. on Geology and Seismology, World Scientific and Engineering Academy and Society, Cambridge, U.K., 88–93.
Haimson, B., and Fairhurst, C. (1969). “In-situ stress determination at great depth by means of hydraulic fracturing.” 11th U.S. Symp. on Rock Mechanics (USRMS), American Rock Mechanics Association, Alex- andria, VA, 559–584.
Häring, M. O., Schanz, U., Ladner, F., and Dyer, B. C. (2008). “Charac- terization of the Basel 1 enhanced geothermal system.” Geothermics, 37(5), 469–495.
Hossain, M. M., Rahman, M. K., and Rahman, S. S. (2002). “A shear dilation stimulation model for production enhancement from naturally fractured reservoirs.” SPE J., 7(2), 183–195.
Hesler, G. J., Zheng, Z., and Myer, L. R. (1990). “In-situ fracture stiffness determination.” Rock mechanics contribution and challenges, W. Hustrulid and G. A. Johnson, eds., Balkema, Rotterdam, 405–411.
Huang, X., Haimson, B. C., Plesha, M. E., and Qiu, X. (1993). “An in- vestigation of the mechanics of rock joints–Part 1. Laboratory inves- tigation.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30(3), 257–269.
Jiang, X. W., Wan, L., Wang, X. S., Liang, S. H., and Hu, B. X. (2009). “Estimation of fracture normal stiffness using as transmissivity-depth correlation.” Int. J. Rock Mech. Min. Sci., 46(1), 51–58.
Jiang, Y., Xiao, J., Tanabashi, Y., and Mizokami, T. (2004). “Development of an automated servo-controlled direct shear apparatus applying a constant normal stiffness condition.” Int. J. Rock Mech. Min. Sci., 41(2), 275–286.
Jing, L., and Stephansson, O. (2007). Fundamentals of discrete element methods for rock engineering: Theory and application, Developments in geotechnical engineering, 1st Ed., Vol. 85, Elsevier, London.
Juliusson, E. (2012). “Characterization of fractured geothermal reservoirs based on production data.” SGP-TR-195, Ph.D. thesis, Stanford Univ., Stanford, CA.
Koh, J., Roshan, H., and Rahman, S. S. (2011). “A numerical study on the long term thermo-poroelastic effects of cold water injection into naturally fractured geothermal reservoirs.” Comput. Geotech., 38(5), 669–682.
Kubik, W., and Lowry, P. (1993). “Fracture identification and characterization using cores, FMS, CAST, and Borehole camera: Devonian shale, Pike County, Kentucky.” SPE 25897, SPE Rocky Mountain/Low Permeability Reservoirs Symp. Proc., Society of Petroleum Engineers, Richardson, TX, 543–555.
Lewis, R. W., and Schrefler, B. A. (1998). The finite element method in the static and dynamic deformation and consolidation of porous media, Wiley, New York.
Li, S., Feng, X., and Hudson, J. A. (2013a). “ISRM suggested method for measuring rock mass displacement using a sliding micrometer.” Rock Mech. Rock Eng., 46(3), 645–653.
Li, S., Feng, X., Wang, C. Y., and Hudson, J. A. (2013b). “ISRM suggested method for rock fractures observations using a borehole digital optical televiewer.” Rock Mech. Rock Eng., 46(3), 635–644.
Ljunggren, C., Chang, Y., Janson, T., and Christiansson, R. (2003). “An overview of rock stress measurement methods.” Int. J. Rock Mech. Min. Sci., 40(7–8), 975–989.
Magnusdottir, L., and Horne, R. N. (2011). “Characterization of fractures in geothermal reservoirs using resistivity.” Proc., 36th Workshop on Geo- thermal Reservoir Engineering, Stanford Univ., Stanford, CA, 1–7.
Main, I. G., Meredith, P. G., Sammonds, P. R., and Jones, C. (1990). “Influence of fractal flaw distributions on rock deformation in the brittle field in deformation mechanisms.” Deformation mechanisms, rheology and tectonics, Geological Society of London special publication No. 54, R. J. Knipe and E. H. Rutter, eds., 81–96.
McCulloch, W. S., and Pitts, W. H. (1943). “A logical calculus of the ideas immanent in nervous activity.” Bull. Math. Biol., 5(4), 115–133.
McDermott, C., and Kolditz, O. (2006). “Geomechanical model for fracture deformation under hydraulic, mechanical and thermal loads.” Hydro- geol. J., 14(4), 485–498.