Non-equilibrium upscaling of compositional transport

Abstract

Reservoir simulation is a broadly used tool in the oil and gas production industry. It can be used for production history matching, performance forecasting and field development. A common Enhanced Oil Recovery (EOR) method is the injection of miscible gases. With the injection of gas into an oil reservoir, the system has to be considered as multiphase and multicomponent. Compositional simulation gives an accurate representation of the physics of multiphase and multicomponent systems. Solving the system at a high resolution with the compositional description is computationally very intensive. Simulating at a lower resolution with a coarse grid reduces the computational loads, but it becomes less accurate. Upscaling procedures are used to convert the high resolution, fine scale simulation parameters to lower resolution, coarse scale simulation parameters.

In this research, an upscaling procedure is examined that uses a thermodynamic non-equilibrium correction to keep a high accuracy for the coarse scale compositional simulation. This non-equilibrium phenomena is represented by a source term in the thermodynamic equilibrium equation. This source term is obtained from a fine scale simulation and upscaling the phase compositions. The source terms are tabulated against the composition and are used in the coarse scale simulation. An isothermal system with number components and number of phases is considered in this research. The capillary and diffusive effects are neglected as well as the chemical reactions and adsorption. For the fine scale, a 2D grid of 102x20 is used and the coarse scale grid is 1D with 102x1 cells. The fine scale simulation is run using Automatic Differentiation General Purpose Research Simulator (AD-GPRS) and the coarse scale simulation is run with an IMPEC simulator written in Matlab.

To quantify the accuracy of the coarse scale simulation a misfit value is calculated between the coarse scale saturation distribution and the upscaled fine scale saturation distribution.
Comparing the coarse saturation distribution with the upscaled saturation distribution shows that this method allows high accuracy results to be maintained with non-equilibrium upscaling of the compositional flow.

A correlation is made between the source term and composition and used in a coarse simulation instead of the tables created from the fine scale simulation. This reduces the accuracy compared to the fine scale, but it still gives a satisfactory improvement of coarse scale results. To improve the accuracy of the simulation using the correlation, an optimization procedure is performed. The optimization improved the accuracy to the level of the accuracy of the simulation using the full source term tables. With a correlation between the source term and composition, the global fine scale compositional solution is no longer necessary for the coarse simulation.