Tiltmeter Mapping of Measured Nonsymmetric Hydraulic-Fracture Growth in a Conglomerate/Sandstone Formation Using the Implicit Level-Set Algorithm and the Extended Kalman Filter
- Venkataraman Pandurangan (CSIRO Energy) | Anthony Peirce (University of British Columbia) | Zuorong R. Chen (CSIRO Energy) | Robert G. Jeffrey (SCT Operations)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- February 2018
- Document Type
- Journal Paper
- 172 - 185
- 2018.Society of Petroleum Engineers
- Hydraulic fracture, tiltmeter mapping, asymmetry, extended Kalman filter, level set
- 1 in the last 30 days
- 172 since 2007
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A novel method to map asymmetric hydraulic-fracture propagation using tiltmeter measurements is presented. Hydraulic fracturing is primarily used for oil-and-gas well stimulation, and is also applied to precondition rock before mining. The geometry of the developing fracture is often remotely monitored with tiltmeters—instruments that are able to remotely measure the fracture-induced deformations. However, conventional analysis of tiltmeter data is limited to determining the fracture orientation and volume. The objective of this work is to detect asymmetric fracture growth during a hydraulic-fracturing treatment, which will yield height-growth information for vertical fracture growth and horizontal asymmetry for lateral fracture growth or detect low preconditioning-treatment efficiency in mining. The technique proposed here uses the extended Kalman filter (EKF) to assimilate tilt data into a hydraulic-fracture model to track the geometry of the fracture front. The EKF uses the implicit level set algorithm (ILSA) as the dynamic model to locate the boundary of the fracture by solving the coupled fluid-flow/fracture-propagation equations, and uses the Okada half-space solution as the observation model (forward model) to relate the fracture geometry to the measured tilts. The 3D fracture model uses the Okada analytical expressions for the displacements and tilts caused by piecewise constant-displacement discontinuity elements to discretize the fracture area. The proposed technique is first validated by a numerical example in which synthetic tilt data are generated by assuming a confining-stress gradient to generate asymmetric fracture growth. The inversion is carried in a two-step process in which the fracture dip and dip direction are first obtained with an elliptical fracture-forward model, and then the ILSA-EKF model is used to obtain the fracture footprint by fixing the dip and dip direction to the values obtained in the first step. Finally, the ILSA-EKF scheme is used to predict the fracture width and geometry evolution from real field data, which are compared with intersection data obtained by temperature and pressure monitoring in offset boreholes. The results show that the procedure is able to satisfactorily capture fracture growth and asymmetry even though the field data contain significant noise, the tiltmeters are relatively far from the fracture, and the dynamic model contains significant “unmodeled dynamics” such as stress anisotropy, material heterogeneity, fluid leakoff into the formation, and other physical processes that have not been explicitly accounted for in the dynamic ILSA model. However, all the physical processes that affect the tilt signal are incorporated by the EKF when the tilt measurements are used to obtain the maximum likelihood estimates of the fracture widths and geometry.
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Adachi, J., Siebrits, E., Peirce, A. et al. 2007. Computer Simulation of Hydraulic Fractures. International Journal of Rock Mechanics and Mining Sciences 44: 739–757. https://doi.org/10.1016/j.ijrmms.2006.11.006.
Bennett, C. O., Rosato, N. D., Reynolds, A. C. et al. 1983. Influence of Fracture Heterogeneity and Wing Length on the Response of Vertically Fractured Wells. SPE J. 23: 219–230. SPE-9886-PA. https://doi.org/10.2118/9886-PA.
Cipolla, C. L. and Wright, C. A. 2000. State-of-the-Art in Hydraulic Fracture Diagnostics. Presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane, Australia. SPE-64434-MS. https://doi.org/10.2118/64434-MS.
Davis, P. M. 1983. Surface Deformation Associated With a Dipping Hydrofracture. J. Geophys. Res. 88: 5826–5834. https://doi.org/10.1029/JB088iB07p05826.
Gelb, A. (ed.). 1974. Applied Optimal Estimation. MIT Press.
Jeffrey, R. G. 1996. Asymmetrically Propped Hydraulic Fractures. SPE Prod & Fac 11. SPE-28079-PA. https://doi.org/10.2118/28079-PA.
Jeffrey, R. G., Chen, Z. R., Mills, K. W. et al. 2013. Monitoring and Measuring Hydraulic Fracturing Growth During Preconditioning of a Roof Rock Over a Coal Longwall Panel. In Effective and Sustainable Hydraulic Fracturing, ed. R. Jeffrey. InTech.
Lecampion, B., Jeffrey, R., and Detournay, E. 2005a. Resolving the Geometry of Hydraulic Fractures From Tilt Measurements. Pure Appl. Geophys. 162: 2433–2452. https://doi.org/10.1007/s00024-005-2786-4.
Lecampion, B., Jeffrey, R., and Detournay, E. 2005b. Resolving the Geometry of Hydraulic Fractures From Tilt Measurements. Pure Appl. Geophys. 162: 2433–2452. https://doi.org/10.1007/s00024-005-2786-4.
Lecampion, B. and Gunning, J. 2007. Model Selection in Fracture Mapping From Elastostatic Data. International Journal of Solids and Structures 44: 1391–1408. https://doi.org/10.1016/j.ijsolstr.2006.06.022.
Montgomery, C. T. and Smith, M. B. 2010. Hydraulic Fracturing: History of an Enduring Technology. J Pet Technol 62 (12): 26–40. SPE-1210-0026-JPT. https://doi.org/10.2118/1210-0026-JPT.
Okada, Y. 1992. Internal Deformation Due to Shear and Tensile Faults in a Half-Space. Bull. of the Seismological Society of America 82 (2): 1018–1040. https://doi.org/10.1016/0148-9062(86)90674-1.
Olson, J. E., Du, Y., and Du, J. 1997. Tiltmeter Data Inversion With Continuous, Non-Uniform Opening Distributions: A New Method for Detecting Hydraulic Fracture Geometry. International Journal of Rock Mechanics and Mining Sciences 34 (3–4): 236.e1–236.e10. https://doi.org/10.1016/S1365-1609(97)00120-2.
Pandurangan, V., Chen, Z., and Jeffrey, R. G. 2015. Mapping Hydraulic Fractures From Tiltmeter Data Using the Ensemble Kalman Filter. Int. J. Numer. Anal. Meth. Geomech. 40 (4): 546–567. https://doi.org/10.1002/nag.2415.
Peirce, A. P. and Siebrits, E. 2001. Uniform Asymptotic Approximations for Accurate Modeling of Cracks in Layered Elastic Media. International Journal of Fracture 110: 205–239. https://doi.org/10.1023/A:1010861821959.
Peirce, A. and Detournay, E. 2008. An Implicit Level Set Method for Modeling Hydraulically Driven Fractures. Computer Methods in Applied Mechanics and Engineering 197: 2858–2885. https://doi.org/10.1016/j.cma.2008.01.013.
Peirce, A. and Rochinha, F. 2012. An Integrated Extended Kalman Filter–Implicit Level Set Algorithm for Monitoring Planar Hydraulic Fractures. Inverse Problems 28: 15009. https://doi.org/10.1088/0266-5611/28/1/015009.
Peirce, A. 2015. Modeling Multi-Scale Processes in Hydraulic Fracture Propagation Using the Implicit Level Set Algorithm. Computer Methods in Applied Mechanics and Engineering 283: 881–908. https://doi.org/10.1016/j.cma.2014.08.024.
Rochinha, F. A. and Peirce, A. 2010. Monitoring Hydraulic Fractures: State Estimation Using an Extended Kalman Filter. Inverse Problems 26: 25009. https://doi.org/10.1088/0266-5611/26/2/025009.
Siebrits, E. and Peirce, A. P. 2002. An Efficient Multi-Layer Planar 3D Fracture Growth Algorithm Using a Fixed Mesh Approach. Int. J. Numer. Meth. Engng. 53: 691–717. https://doi.org/10.1002/nme.308.
Valkó, P. and Michael, J. E. 1995. Hydraulic Fracture Mechanics. New York: Wiley.
Warpinski, N. R., Griffin, L. G., Davis, E. J. et al. 2006. Improving Hydraulic Fracture Diagnostics by Joint Inversion of Downhole Microseismic and Tiltmeter Data. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24–27 September. SPE-102690-MS. https://doi.org/10.2118/102690-MS.
Wright, C. A., Davis, E. J., Minner, W. A. et al. 1998. Surface Tiltmeter Fracture Mapping Reaches New Depths—10,000 Feet and Beyond? Presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, 5–8 April. SPE-39919-MS. https://doi.org/10.2118/39919-MS.
Wu, R., Bunger, A. P., Jeffrey, R. G. et al. 2008. A Comparison of Numerical and Experimental Results of Hydraulic Fracture Growth Into a Zone of Lower Confining Stress. Presented at the the 42nd US Rock Mechanics Symposium (USRMS), San Francisco, 29 June–2 July. ARMA-08-267.
Yang, X.-M. and Davis, P. M. 1986. Deformation Due to a Rectangular Tension Crack in an Elastic Half-Space. Bull. of the Seismological Society of America 76 (3): 865–881.
Zhang, X., Detournay, E., and Jeffrey, R. 2002. Propagation of a Penny-Shaped Hydraulic Fracture Parallel to the Free-Surface of an Elastic Half-Space. International Journal of Fracture 115: 125–158. https://doi.org/10.1023/A:1016345906315.