Salman Ghorbani Zadeh - PhD Student, Institute of Petroleum Engineering, Tehran University
Muhammad Shojaadini - PhD Student, Institute of Petroleum Engineering, Tehran University
Mahdi Matin - PhD Student, Institute of Petroleum Engineering, Tehran University
Mohammad Hossein Ghazanfari - Chemical and Petroleum Engineering Department, Sharif University of Technology

Free fall gravity drainage is one of the most effective mechanisms of producing the oil from the matrix blocks in the gas invaded zone of thenaturally fractured reservoirs. Although several analytical models havebeen proposed to characterize this mechanism in a matrix block, butthese models suffer from the practical or theoretical viewpoints. In thisstudy, a new analytical model was presented to predict the oil productionrate versus time from a homogeneous matrix block under free fall gravitydrainage mechanism. The model was developed by considering the balance between involved forces in the gas-oil gravity drainage process. By simplifying the equation derived from the momentum balance, adifferential equation was obtained. To develop new analytical model, theobtained differential equation was analytically solved by using the Lambert W function. The prediction of derived model was tested againstthe results of numerical analysis and conventional simulation as well asexperimental data in the core and micromodel scale. The validation results show that the model predictions match with the data sets excellently.

Matrix Block, Free Fall Gravity Drainage, Analytical Modeling, Gas Invaded Zone, Naturally Fractured Reservoir