Evaluation of breakthrough and post breakthrough behavior using percolation theory at early stage of reservoir life

The knowledge of the breakthrough time which accounts for the first passage time (i.e. transport) between the injector and the producer has many important applications. The conventional simulation approach to predict the breakthrough and post breakthrough behavior is to build a detailed geological model, upscale it, and then perform flow simulations. To evaluate the uncertainty in breakthrough time, this procedure has to be repeated for many realizations of the geological model which takes many hours of CPU time. Moreover, during the early stage of reservoir life when data is scare, breakthrough time prediction and post breakthrough time behaviour are usually based on analogues or rules of thumb and not detailed reservoir simulation. Here we use a statisticaly based approach called percolation approach to predict breakthrough and post breakthrough bahavior. The previously proposed scaling law of the breakthrough time by Andrade et al. (2000) is been compared with the results obtained from the conventional numerical simulations on the Burgan formation dataset of Norouz offshore oil field in the south of Iran. In addition, we set out to find a new scaling law for the post breakthrough behavior. There is a good agreement between the prediction from the percolation based expressions and the numerical simulation results. Moreover, the prediction from the scaling law took a fraction of a second of CPU times (as it only needs some algebraic calculations) compared with many hours required for the conventional numerical simulations.