Dual-Porosity Dual-Permeability Rate Transient Analysis for Horizontal Wells with Nonuniform and Asymmetric Hydraulic Fractures

• Published in: Rock mechanics and rock engineering 2022-02, Vol.55 (2), p.541-563
• Main Authors: Liu, Chao, Phan, Dung T., Abousleiman, Younane N.
• Format: Article
• Language: English
• Subjects: Analysis; Asymmetry; Civil Engineering; Earth and Environmental Science; Earth Sciences; Exact solutions; Fluid dynamics; Fluid flow; Gas wells; Geophysics/Geodesy; Horizontal wells; Hydraulic fracturing; Hydraulics; Microseisms; Nonuniformity; Oil wells; Original Paper; Permeability; Porosity; Rocks; Transient analysis
• ISSN: 0723-2632; 1434-453X
• DOI: 10.1007/s00603-021-02692-9

Microseismic monitoring in the field has widely shown nonuniformity and asymmetry of hydraulic fractures resulted from multi-stage hydraulic fracturing operations. Considering these influential features of the hydraulic fractures, this paper presents semi-analytical solutions for the wellbore pressure (oil well) and pseudo-pressure (gas well) during production from multi-fractured horizontal wells (MFHW). The solutions further account for bounded and naturally fractured rock formations, recovering existing dual-porosity dual-permeability solutions for a vertical wellbore with one single hydraulic fracture and single-porosity solutions for MFHW. Instead of using the common and simple Warren and Root model, which neglects fluid flow in rock matrix, we adopt the Barenblatt model, which considers fluid flow in both rock matrix and natural fractures. We introduce a permeability ratio,  k D , and show that Warren and Root model becomes problematic when  k D  is larger than 0.05. Comparison analysis shows that the nonuniformity of the hydraulic fracture length distributed along the horizontal wellbore, the nonuniformity of the fracture height, and their asymmetry could have a bigger role than the spacing in the rate transient analysis. For the cases with symmetric and uniform hydraulic fractures, analytical expressions are derived for the classical + 1/2, 0, and + 1 slopes with six characteristic times related to the flow regimes. The application of the semi-analytical solutions to rate transient analysis is demonstrated through five field case studies, consisting of two horizontal and three vertical wells.