Generalized analytical solution for gravity drainage phenomena in finite matrix block with arbitrary time dependent inlet boundary condition and variable matrix block size

Traditional gravity drainage models do not consider the effect of matrix block size distribution on oil recovery. In this study, a gravity drainage model is proposed to evaluate the oil recovery factor that considers this factor. The solution to the uniform distribution can be extended to more general distributions. Regarding the fact that the strength of gravity drainage mechanism is related to block size, higher fracture intensity (smaller grid blocks) leads to a fairly small decrease in gravity drainage forces such that most of oil within the matrix block stays unchanged. The obtained results from this study show that higher fracture intensity (smaller block height) causes lower oil recovery from matrix in gas invaded zone. The results of analytical model were compared with previous analytical model and experimental data and reasonable match was obtained for predicting final oil recovery.