A New Approach to the Modeling of a Simple Re-infiltration Gravity Drainage Process in Naturally Fractured Reservoirs

One of the most important concerns regarding prediction of production performance in naturally fractured reservoirs is the issue of re-infiltration phenomena. In this study, the modeling of a simple re-infiltration process with no effect of capillary continuity between blocks is presented by extending the gravity drainage mechanism for a single block. First, a qualitative analysis of the gravity drainage process through porous media was conducted and the role of gravity and capillary forces was investigated. Then a model for one-dimensional gravity drainage in a single block was developed in dimensionless form, a modified version of which can be found in the literature. Then, using the method of separation of variables, the corresponding partial differential equation was solved for a single block with certain boundary and initial conditions. The upper boundary is a no-feed boundary and at the lower boundary the gas saturation is always zero. At the initial condition, the gas saturation is equal to zero throughout the block. In order to model the simple re-infiltration process, the above-mentioned problem for concept was used and, based on the fact that the blocks of a stack governed by simple re-infiltration process act as single block, using a MATLAB program (The MathWorks, Inc., Natick, MA), the rate of drainage and cumulative production as function of time were obtained. The results are in very good agreement with the nature of the process in an actual case. This method can be extended to solve the problem of a stack of N blocks