...-order model. These runs are performed over a wide range of operating conditions (rates and bottom-hole pressures) to cover most of the test-time predictions. Results from the training runs are saved in the form of snapshots of state variables at each grid block at each timestep. There are three...

... & Gas reservoir simulation koopman operator approximation dynamic mode decomposition neural network Fluid Dynamics production data dynamical system production profile prediction Florez equation gildin edmd decomposition society of petroleum engineers autoencoder snapshot fracture...

... iteration Upstream Oil & Gas tensor speedup Florez equation algorithm reduction model-order reduction society of petroleum engineers matrix subspace gildin snapshot fracture mechanics Introduction Coupled flow and geomechanics simulations are highly elaborate and require solving...

... Simulation snapshot Modeling & Simulation Fluid Dynamics accuracy water saturation computational cost reduction matrix Durlofsky reservoir model Introduction Model reduction in the context of reservoir simulation and optimization has been evolving in recent years to become a practical...

... by updating the POD subspace and the DEIM approximation of the nonlinear functions. These global online basis function updates improve the accuracy of snapshot approximation. Since the adaption is performed infrequently, the new methodology does not add a significant computational overhead due...

... the optimization process TPWL/POD model must be retrained to incorporate new state snapshots corresponding to those controls. This work proposes TPWL/POD retraining criteria based on the trust region accuracy parameter and an error indicator that represents the average distance between stored snapshots...

... achieving the computational cost that is independent of the fine grid dimension. POD snapshots are inexpensively computed using local model reduction techniques based on Generalized Multiscale Finite Element Method (GMsFEM) which provides (1) a hierarchical approximation of snapshot vectors (2) adaptive...

.... machine learning proper orthogonal decomposition surrogate model snapshot Artificial Intelligence approximation representation Radial basis Function neural network empirical interpolation method reduction decomposition order model RBF network formulation interpolation method dynamical...

... and informative of the entire spatial field being interpolated. To reduce the dimensions involved in evaluating the nonlinear term, DEIM approximates F in a subspace of ℝ n via POD. Suppose we have some snapshots { F 1 , …, F m } of F , which are obtained by some training simulations, we then apply POD...

...-dimensional subspace. The basis of this subspace is obtained by performing singular value decomposition (SVD) of a matrix containing, as its columns, the solution states (or ‘snapshots’) computed from previous simulations. The simulations used to provide these snapshots are referred to as ‘training’ runs; new...

... upstream oil & gas eigenvector pressure equation basis function snapshot covariance matrix validation simulation solver time pressure field training simulation decomposition reservoir simulation injector linear solver time application matrix equation reduced-order model Introduction...

.../pressure fields based on local proper orthogonal decompositions (PODs) glued together using the Multiscale Mixed FEM (MsMFEM) framework on a coarse grid. Based on snapshots from one or more simulation run, we perform singular value decompositions (SVDs) for the flux distribution over coarse grid...