Acceleration of Gas Reservoir Simulation Using Proper Orthogonal Decomposition

Yi Wang,Bo Yu,Ye Wang

doi:10.1155/2018/8482352

Abstract

High-precision and high-speed reservoir simulation is important in engineering. Proper orthogonal decomposition (POD) is introduced to accelerate the reservoir simulation of gas flow in single-continuum porous media via establishing a reduced-order model by POD combined with Galerkin projection. Determination of the optimal mode number in the reduced-order model is discussed to ensure high-precision reconstruction with large acceleration. The typical POD model can achieve high precision for both ideal gas and real gas using only 10 POD modes. However, acceleration of computation can only be achieved for ideal gas. The obstacle of POD acceleration for real gas is that the computational time is mainly occupied by the equation of state (EOS). An approximation method is proposed to largely promote the computational speed of the POD model for real gas flow without decreasing the precision. The improved POD model shows much higher acceleration of computation with high precision for different reservoirs and different pressures. It is confirmed that the acceleration of the real gas reservoir simulation should use the approximation method instead of the computation of EOS.

Highlights

Reservoir simulation, utilizing mathematical models to predict fluid flow in petroleum reservoirs, has been developed since the 1800s [1]
The Proper orthogonal decomposition (POD) model is examined in the case of ideal gas (Z ≡ 1), where a and b in the Van der Waals equation (see (4)) are all zero
Proper orthogonal decomposition is utilized in gas reservoir simulation to accelerate the simulation speed of gas flow in single-continuum porous media

Summary

Introduction

Reservoir simulation, utilizing mathematical models to predict fluid flow in petroleum reservoirs, has been developed since the 1800s [1]. The computational cost of the oil reservoir simulations is huge because a very dense mesh should be used causing long-time iterations to achieve enough resolution. Ghommem et al [22, 23] and Efendiev et al [24] discussed the POD and dynamic mode decomposition method for time-dependent incompressible single-phase flow in highcontrast heterogeneous porous media. They proved that the POD model can achieve good precision in an appropriate range. The compressibility of the gas leads to a POD model with stronger nonlinearity than oil flow.

Numerical Methods

Results and Discussions

Conclusions