skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Mathematical modeling and simulation analysis of hydraulic fracture propagation in three-layered poro-elastic media

Abstract

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 studymore » 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.« less

Authors:
 [1]; ;  [2]
  1. Ohio State Univ., Columbus, OH (United States)
  2. Lehigh Univ., Bethlehem, PA (United States)
Publication Date:
Research Org.:
Lehigh Univ., Bethlehem, PA (United States)
Sponsoring Org.:
USDOE; USDOE, Washington, DC (United States)
OSTI Identifier:
6371540
Report Number(s):
DOE/MC/27351-3335
ON: DE93000272
DOE Contract Number:  
FG21-90MC27351
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
02 PETROLEUM; 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

Citation Formats

Moon, H. Y., Advani, S. H., and Lee, T. S. Mathematical modeling and simulation analysis of hydraulic fracture propagation in three-layered poro-elastic media. United States: N. p., 1992. Web. doi:10.2172/6371540.
Moon, H. Y., Advani, S. H., & Lee, T. S. Mathematical modeling and simulation analysis of hydraulic fracture propagation in three-layered poro-elastic media. United States. https://doi.org/10.2172/6371540
Moon, H. Y., Advani, S. H., and Lee, T. S. Sun . "Mathematical modeling and simulation analysis of hydraulic fracture propagation in three-layered poro-elastic media". United States. https://doi.org/10.2172/6371540. https://www.osti.gov/servlets/purl/6371540.
@article{osti_6371540,
title = {Mathematical modeling and simulation analysis of hydraulic fracture propagation in three-layered poro-elastic media},
author = {Moon, H. Y. and Advani, S. H. and Lee, T. S.},
abstractNote = {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.},
doi = {10.2172/6371540},
url = {https://www.osti.gov/biblio/6371540}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1992},
month = {11}
}