@Article{cmes.2020.08033,
AUTHOR = {Daobing Wang, Sergio Zlotnik, Pedro Díez, Hongkui Ge, Fujian Zhou, Bo Yu},
TITLE = {A Numerical Study on Hydraulic Fracturing Problems via the Proper Generalized Decomposition Method},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {122},
YEAR = {2020},
NUMBER = {2},
PAGES = {703--720},
URL = {http://www.techscience.com/CMES/v122n2/38327},
ISSN = {1526-1506},
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. },
DOI = {10.32604/cmes.2020.08033}
}