Mathematical modeling and simulation analysis of hydraulic fracture propagation in three-layered poro-elastic media
- Ohio State Univ., Columbus, OH (United States)
- Lehigh Univ., Bethlehem, PA (United States)
Hydraulic fracturing plays a pivotal role in the enhancement of oil and gas production recovery from low permeability reservoirs. The process of hydraulic fracturing entails the generation of a fracture by pumping fluids blended with special chemicals and proppants into the payzone at high injection rates and pressures to extend and wedge fractures. The mathematical modeling of hydraulically induced fractures generally incorporates coupling between the formation elasticity, fracture fluid flow, and fracture mechanics equations governing the formation structural responses, fluid pressure profile, and fracture growth. Two allied unsymmetric elliptic fracture models are developed for fracture configuration evolutions in three-layered rock formations. The first approach is based on a Lagrangian formulation incorporating pertinent energy components associated with the formation structural responses and fracture fluid flow. The second model is based on a generalized variational principle, introducing an energy rate related functional. These models initially simulate a penny-shaped fracture, which becomes elliptic if the crack tips encounters (upper and/or lower) barriers with differential reservoir properties (in situ stresses, 16 elastic moduli, and fracture toughness-contrasts and fluid leak-off characteristics). The energy rate component magnitudes are determined to interpret the governing hydraulic fracture mechanisms during fracture evolution. The variational principle is extended to study the phenomenon and consequences of fluid lag in fractures. Finally, parametric sensitivity and energy rate investigations to evaluate the roles of controllable hydraulic treatment variables and uncontrollable reservoir property characterization parameters are performed. The presented field applications demonstrate the overall capabilities of the developed models. These studies provide stimulation treatment guidelines for fracture configuration design, control, and optimization.
- Research Organization:
- Lehigh Univ., Bethlehem, PA (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG21-90MC27351
- OSTI ID:
- 6371540
- Report Number(s):
- DOE/MC/27351-3335; ON: DE93000272
- Country of Publication:
- United States
- Language:
- English
Similar Records
Application of characteristic time concepts for hydraulic fracture configuration design, control, and optimization. Final report
Development of a generalized hydraulic fracture model: (Annual report) for the period November 1, 1985-October 31, 1986
Related Subjects
03 NATURAL GAS
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
HYDRAULIC FRACTURES
CRACK PROPAGATION
RESERVOIR ROCK
HYDRAULIC FRACTURING
LAGRANGIAN FUNCTION
MATHEMATICAL MODELS
OPTIMIZATION
PARAMETRIC ANALYSIS
POROUS MATERIALS
SIMULATION
FAILURES
FRACTURES
FRACTURING
FUNCTIONS
MATERIALS
020300* - Petroleum- Drilling & Production
030300 - Natural Gas- Drilling
Production
& Processing
990200 - Mathematics & Computers