Analytical Modeling of Re-Infiltration Process between Matrix Blocks in Gas Invaded Zone in Gravity Drainage Process

Fractured carbonate reservoirs constitute considerable number of hydrocarbon reservoirs in Iran. In the fractured reservoirs, the gravity drainage is one of the dominating oil producing mechanisms, which controls oil production depending on the interaction between upper and lower blocks. However, in few theoretical studies have investigated the modelling of re-infiltration process between stack of matrix blocks. In this study, at first the gravity drainage process is modelled for a 1-D single matrix block by consideration of gravity and capillary forces, then Laplace transform is used to solve the governing partial differential equation related to matrix blocks, with the appropriate initial and boundary conditions. Moreover, the obtained equations are extended to a stack of matrix blocks and the effect of re-infiltration process in investigated. The inlet oil from the upper boundary of the blocks is a function of time, and the lower boundary of the blocks is fully saturated with oil. At the initial condition, the matrix block is saturated with oil. Finally, based on the determined saturation equations, oil production rate, cumulative production, the gravity drainage mechanism and the effect of re-infiltration process are studied. It is worth mentioning that proposed solution for re-infiltration problem in this study is fully analytical, while previous proposed solutions from other researchers (Firoozabadi and Ishimoto [1]) have been numerical or semi-analytical.