Open Access

ARTICLE

A Numerical Study on Hydraulic Fracturing Problems via the Proper Generalized Decomposition Method

Daobing Wang^{1, *}, Sergio Zlotnik^{2, *}, Pedro Díez², Hongkui Ge³, Fujian Zhou³, Bo Yu⁴

1 School of Mechanical Engineering, Beijing Key Laboratory of Pipeline Critical Technology and Equipment for Deepwater Oil & Gas Development, Beijing Institute of Petrochemical Technology, Beijing, 102617, China.
2 Laboratori de Càlcul Numèric (LaCàN), ETS de Ingeniero de Caminos, Canales y Puertos, Universitat Politècnica de Catalunya, Barcelona, E-08034, Spain.
3 Research Institute of Unconventional Oil and Gas Science and Technology, China University of Petroleum, Beijing, 102249, China.
4 Department of Oil & Gas Transportation and Engineering, Beijing Institute of Petrochemical Technology, Beijing, 102617, China.
∗ Corresponding Authors: Daobing Wang. Email: upcwdb@bipt.edu.cn;
   Sergio Zlotnik. Email: sergio.zlotnik@upc.edu.

(This article belongs to the Special Issue: Advances in Modeling and Simulation of Complex Heat Transfer and Fluid Flow)

Computer Modeling in Engineering & Sciences 2020, 122(2), 703-720. https://doi.org/10.32604/cmes.2020.08033

Received 22 July 2019; Accepted 08 October 2019; Issue published 01 February 2020

Abstract

The hydraulic fracturing is a nonlinear, fluid-solid coupling and transient problem, in most cases it is always time-consuming to simulate this process numerically. In recent years, although many numerical methods were proposed to settle this problem, most of them still require a large amount of computer resources. Thus it is a high demand to develop more effificient numerical approaches to achieve the real-time monitoring of the fracture geometry during the hydraulic fracturing treatment. In this study, a reduced order modeling technique namely Proper Generalized Decomposition (PGD), is applied to accelerate the simulations of the transient, non-linear coupled system of hydraulic fracturing problem, to match this extremely tight response time constraint. The separability of the solution in space and time dimensions is studied for a simplifified model problem. The solid and flfluid equations are coupled explicitly by inverting the solid discrete problem, and a simple iterative procedure to handle the non-linear characteristic of the hydraulic fracturing problem is proposed in this work. Numeral validation illustrates that the results of PGD match well with these of standard fifinite element method in terms of fracture opening and fluid pressure in the hydro-fracture. Moreover, after the off-line calculations, the numerical results can be obtained in real time.

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