PKN Solution Revisit: 3-D Hydraulic Fracture Size and Stress Anisotropy Effects

Adachi J, Siebritsb E, Peirce A, Desrochesd J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44:739–757 Alberty M, McLean M (2004) A physical model for stress cages. SPE-90493 Bradley WB (1979) Failure of inclined boreholes. Trans ASME 101:232–239 Bunger AP, Zhang X, Jeffrey RG (2012) Parameters affecting the interaction among closely spaced hydraulic fractures. SPE J 17:292–306 Castonguay ST, Mear ME, Dean RH, Schmidt JH (2013) Predictions of the growth of multiple interacting hydraulic fractures in three dimensions. SPE-166259 Detournay E (2016) Mechanics of hydraulic fractures. Annu Rev Fluid Mech 48:311–339 Dohmen T, Zhang J, Li C, Blangy JP, Simon KM, Valleau DN, Ewles JD, Morton S, Checkles S (2013) A new surveillance method for delineation of depletion using microseismic and its application to development of unconventional reservoirs. Paper SPE-166274 presented at the SPE annual technology conference in New Orleans, LA Dohmen T, Blangy JP, Zhang J (2014a) Microseismic depletion delineation. Interpretation 2(3):SG1–SG13 Dohmen T, Zhang J, Blangy JP (2014) Measurement and analysis of 3D stress shadowing related to the spacing of hydraulic fracturing in unconventional reservoirs. SPE 170924 Friedrich M, Milliken M (2013) Determining the contributing reservoir volume from hydraulically fractured horizontal wells in the Wolfcamp formation in the Midland Basin. URTEC-1582170. doi:10.1190/URTEC2013-149 Geertsma J, de Klerk F (1969) A rapid method of predicting width and extent of hydraulically induced fractures. J Pet Technol 21:1571–1581 Kress O, Weng X, Gu H, Wu R (2013) Numerical modeling of hydraulic fractures interaction in complex naturally fractured formations. Rock Mech Rock Eng 46(3):555–568 Li S, Zhang D, Li X (2017) A new approach to the modeling of hydraulic-fracturing treatments in naturally fractured reservoirs. SPE J 22(4):1064–1081. doi:10.2118/181828-PA Mack MG, Warpinski NR (2000) Mechanics of hydraulic fracturing, chap. 6. In: Economides MJ, Nolte KG (eds) Reservoir stimulation, 3rd edn. Wiley, Chichester Nordgren RP (1972) Propagation of a vertical hydraulic fracture. SPE J 12(4):306–314 Perkins TK, Kern LR (1961) Widths of hydraulic fractures. In: SPE annual fall meeting, Dallas, 8–11 Oct, SPE-89-PA Roussel NP, Sharma MM (2011) Optimizing fracture spacing and sequencing in horizontal well fracturing. SPE-127986, SPE Production & Operations Sneddon IN, Elliott HA (1946) The opening of a Griffith crack under internal pressure. Q Appl Math 4:262–266 Warpinski NR, Abou-Sayed IS, Moschovidis ZA, Parker C (1993) Hydraulic fracture model comparison study: complete results. A report for Gas Research Institute Warpinski NR, Moschovidis ZA, Parker C, Abou-Sayed IS (1994) Comparison study of hydraulic fracturing models—test case: GRI staged field. Experiment No. 3. SPE-25890, SPE Production & Facilities Weng X, Kresse O, Cohen C-E, Wu R, Gu H (2011) Modeling of hydraulic-fracture-network propagation in a naturally fractured formation. SPE-140253, SPE Production & Operations Zhang J (2013) Borehole stability analysis accounting for anisotropies in drilling to weak bedding planes. Int J Rock Mech Min Sci 60:160–170 Zhang Y, Zhang J (2017) Lithology-dependent minimum horizontal stress and in situ stress estimate. Tectonophysics 703–704:1–8 Zhang J, Alberty M, Blangy JP (2016) A semi-analytical solution for estimating the fracture width in wellbore strengthening applications. Paper SPE 180296 presented at SPE deepwater drilling & completions conference held in Galveston, TX, USA