Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Uncertainty Quantification
IF: 4.911 5-Year IF: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

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; 1Institut du Génie des Systèmes Industriels et Textiles, École Polytechnique de Ouagadougou, 18 BP 234 Ouagadougou, Burkina Faso, West Africa
Fernando A. Rochinha
Mechanical Engineering Department, Federal University of Rio de Janeiro, RJ 21945-970, 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.


Articles with similar content:

DATA-DRIVEN CALIBRATION OF P3D HYDRAULIC FRACTURING MODELS
International Journal for Uncertainty Quantification, Vol.10, 2020, issue 4
Souleymane Zio , Fernando A. Rochinha
DATA-CONSISTENT SOLUTIONS TO STOCHASTIC INVERSE PROBLEMS USING A PROBABILISTIC MULTI-FIDELITY METHOD BASED ON CONDITIONAL DENSITIES
International Journal for Uncertainty Quantification, Vol.10, 2020, issue 5
L. Bruder, Timothy Wildey, M. W. Gee
OPTIMAL SENSOR PLACEMENT FOR THE ESTIMATION OF TURBULENCE MODEL PARAMETERS IN CFD
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 6
Costas Papadimitriou, Dimitrios I. Papadimitriou
GRID-BASED INVERSION OF PRESSURE TRANSIENT TEST DATA WITH STOCHASTIC GRADIENT TECHNIQUES
International Journal for Uncertainty Quantification, Vol.2, 2012, issue 4
Fikri Kuchuk, Richard Booth, Kirsty Morton, Mustafa Onur
A MIXED UNCERTAINTY QUANTIFICATION APPROACH USING EVIDENCE THEORY AND STOCHASTIC EXPANSIONS
International Journal for Uncertainty Quantification, Vol.5, 2015, issue 1
Tyler Winter, Serhat Hosder, Harsheel Shah