Parameterized Local Reduced Order Model of Stimulated Volume Evolution in Reservoirs

Abstract

Real‐time simulation of large‐scale geomechanics problems, such as hydraulic dilation stimulation, is computationally expensive as they must span multiple spatial and temporal length scales, often including nonlinearities and thermo‐hydromechanical processes. This paper introduces a novel local reduced order model (LROM) to enhance computational efficiency for nonlinear and fully‐coupled hydromechanical simulations. The model employs finite element analysis of a two‐dimensional deformable porous media with Drucker–Prager plasticity and stress‐induced permeability enhancement models to describe behavior of sandstone. LROM combines various reduced order models (ROMs), including proper orthogonal decomposition‐Galerkin (POD‐G) to reduce number of degrees of freedom (DoFs), discrete empirical interpolation method (DEIM) to accelerate computation of nonlinear terms, and local POD and local DEIM (LPOD/LDEIM) for further performance enhancements. LPOD and LDEIM classify parameterized training data, obtained from offline coupled full order model (CFOM) runs, into multiple subspaces with similar dynamic features. A new strategy for clustering and classification techniques that align with coupled formulation framework is proposed. The advantages of LROM are demonstrated in a large‐scale application: hydraulic dilation stimulation. LROM exhibits stable, accurate, and efficient online phase, while ROM built with classical POD/DEIM lacks efficiency and stability in Newton–Raphson solver. First, performance of LROM, parameterized by hardening modulus and initial permeability, is evaluated for inputs within training domain. Under CFOMs with DoFs, LROM speed‐up is 400 times. LROM is then parameterized by three inputs, including injection rate and two material properties. Results show that LROM maintains efficiency even for injection rates that extend beyond the training regime.