Proper Orthogonal Decomposition-Based Method for Predicting Flow and Heat Transfer of Oil and Water in Reservoir

Abstract

Calculation process of some reservoir engineering problems involves several passes of full-order numerical reservoir simulations, and this makes it a time-consuming process. In this study, a fast method based on proper orthogonal decomposition (POD) was developed to predict flow and heat transfer of oil and water in a reservoir. The reduced order model for flow and heat transfer of oil and water in the hot water-drive reservoir was generated. Then, POD was used to extract a reduced set of POD basis functions from a series of “snapshots” obtained by a finite difference method (FDM), and these POD basis functions most efficiently represent the dynamic characteristics of the original physical system. After injection and production parameters are changed constantly, the POD basis functions combined with the reduced order model were used to predict the new physical fields. The POD-based method was approved on a two-dimensional hot water-drive reservoir model. For the example of this paper, compared with FDM, the prediction error of water saturation and temperature fields were less than 1.3% and 1.5%, respectively; what is more, it was quite fast, where the increase in calculation speed was more than 70 times.

Physics-informed reduced-order learning from the first principles for simulation of quantum nanostructures

“…To thoroughly account for the influences among different heights of the pyramid potentials, if five different heights are selected for each pyramid, a combination of all different heights for the five pyramids should be included in the DNSs to collect the WF data. This would lead to an enormous number of additional samples, i.e., 5 5 = 3125, which requires an immense computational effort to collect the WF data from DNSs and evaluate the POD Hamiltonian elements in ( 11)-( 13). To minimize the training effort, five pyramids varying together with the same (five) heights from 0.07 to 0.35 eV in DNS are used to collect just one additional sample of WF data with the hope that the physical principles enforced by the Galerkin projection would intelligently predict the influences among different heights of pyramids.…”

“…An accurate prediction beyond the training conditions, including higher external field and larger internal potential in untrained quantum states, is also achieved. Comparison is also carried out between the physics-based learning and Fourier-based plane-wave approaches for a periodic case.In recent years, reduced order modeling techniques have been widely adopted to decrease the computational complexity in scientific and engineering problems [1][2][3][4][5][6][7][8][9][10][11][12] . Many of these techniques involve projecting the problem of interest onto a set of orthogonal basis functions to reduce the degrees of freedom (DoF) using the basis functions that are optimal for the problem.…”

“…Many of these techniques involve projecting the problem of interest onto a set of orthogonal basis functions to reduce the degrees of freedom (DoF) using the basis functions that are optimal for the problem. Proper orthogonal decomposition (POD) 13,14 is one of the such modeling techniques, where its basis functions (hereafter referred to as POD modes) are generated by maximizing the mean square inner product of each mode with the solution data for the problem [2][3][4][5][6][7] . The solution data used in the decomposition should incorporate as much as possible a realistic range of parametric variations for the problem.…”

“…In recent years, reduced order modeling techniques have been widely adopted to decrease the computational complexity in scientific and engineering problems [1][2][3][4][5][6][7][8][9][10][11][12] . Many of these techniques involve projecting the problem of interest onto a set of orthogonal basis functions to reduce the degrees of freedom (DoF) using the basis functions that are optimal for the problem.…”