دانلود رایگان مقاله راه حل عددی معادلات جابجایی تراکم ناپذیر در واسطه ناهمگون

1. Introduction

CO2 enhanced oil recovery has received a lot of attention from industry, government and environmental organizations for both its potential to increase US oil production and its potential for permanently storing CO2. In this paper, we study the miscible displacement of one fluid by another in a porous medium. The mathematical model is a system of coupled elliptic and convection-dominated parabolic equations. While there is an extensive mathematical analysis for the coupling of elliptic and parabolic equations, there is a need for developing efficient and accurate numerical methods for solving the miscible displacement problem in realistic porous media. One numerical difficulty is the approximation of intricate velocity fields resulting from highly varying permeabilities. Ideal numerical methods should yield negligible artificial diffusion as the accurate front tracking of the fluid mixture has direct economical consequences.

5.2.3. Heterogeneous permeabilities

In the last two examples, we consider the permeability fields from the SPE 10 benchmark problem [17]. The first permeability field is from a Tarbert formation while the second is from an Upper Ness formation. Fig. 8 shows the permeability values in a logarithmic scale. The Upper Ness formation is a more challenging field as there are intricate fractures in the medium and the range of the permeability values is larger than for the Tarbert case. We apply the second order in space RT2-NIPG2 with the second order Gauss I method in time. Snapshots of the concentration at different times for the Tarbert case are shown in Fig. 9 whereas the solutions for the Upper Ness formation are shown in Fig. 10. We observe in both cases, that the solvent fluid reaches the production well by sweeping the regions with highest permeability values. As expected, the boundary of these regions is less smooth for the porous mediumof Upper Ness type. Our method captures the very small regions of lower permeability and the concentration fronts remain sharp.