Prediction of Breakthrough and Post Breakthrough Behavior by Percolation and Random Walk Modeling

In this work we used percolation coupling with random walk approach to model the fluid flow in porous media. In this new approach different realizations aremade based on the percolation theory and by releasing a large number of random walkers, the arrival time of each one is recorded. By analyzing the arrival times ofrandom walkers, breakthrough and post breakthrough behavior of porous media can be studied. In this study two different case studies were considered. The firstone which is ١٠th Comparative SPE Project (CSP ١٠) which is a heterogeneous reservoir and the second one is a synthesis homogeneous reservoir. In the first case study, the obtained results by random walkers for different injector well pressurewere compared by those obtained by a commercial simulator. The results show a good agreement between what predicted by random walkers and commercialsimulator in determination of breakthrough time. In the second case after analyzing breakthrough and post breakthrough behavior and correlating these behaviors together, the ability of scaling law (Scaling Ansatz) in determination most probable breakthrough time, was also verified.

Keywords:

Percolation , Random walk modeling , Breakthrough , Post breakthrough , Ansatz Scaling law