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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.v2.i2.50
pages 145-160

A STOCHASTIC COLLOCATION APPROACH FOR UNCERTAINTY QUANTIFICATION IN HYDRAULIC FRACTURE NUMERICAL SIMULATION

Souleymane Zio
Mechanical Engineering, COPPE, Federal University of Rio de Janeiro, P.O. Box 68503, 21941972, Rio de Janeiro, Brazil
Fernando A. Rochinha
Mechanical Engineering, COPPE, Federal University of Rio de Janeiro, P.O. Box 68503, 21941972, Rio de Janeiro, Brazil

ABSTRACT

The exploitation of oil and gas can be stimulated through hydraulic fractures (HF), which are discontinuities in the rock formation induced by the injection of high pressurized viscous fluids. Because there exists considerable variability in geologic formations, such as oil and gas reservoirs, the computational models, and, consequently, the predictions drawn from simulations, might lead to misleading conclusions, despite the use of efficient and robust numerical schemes. In order to take into account uncertainties on the numerical results due to the variability in the input data, a stochastic analysis of HF is presented here. The elasticity modulus of the rock and the confining stress are assumed to be described by random variables, and therefore, the equations governing the fracture propagation are recast as stochastic partial differential equations (SPDEs). In order to solve the resulting problem, among several alternatives available in the literature, a stochastic collocation method is adopted. The elasticity modulus probability distributions are constructed using two different approaches, both using a small amount of information. A number of numerical simulations are presented in order to illustrate the impact of the uncertainties in the data input on the fracture propagation.