Improved mathematical model for mass transfer in fractured reservoirs during the gas injection process

In fractured reservoirs with relatively low matrix permeability, i.e. small matrix block size with respect to capillary threshold height, diusion becomes an important recovery mechanism. In this work, we have attempted to model the mass transfer between the matrix and fracture by considering a fractured porous media as a single matrix block with an adjacent fracture. An appropriate model should be applicable in the case of the matrix being saturated with both saturated and undersaturated oils. The proposed model presents such versatility. The model is a modication for the formulation of Jamili et al. [Jamili, A., Whillhite, G.P. and Green, D.W., Modeling Gas-Phase Mass Transfer Between Fracture and Matrix in Naturally Fractured Reservoir, SPE132622 (2011)], which suered from several drawbacks such as the use of the classical Fickʹs law, and of Hua and Whitson [Hua Hu, Whitson, C.H. and Yuanchang, Q.i., A Study of Recovery Mechanism in a Nitrogen Diusion Experiment, SPE21893 (1991)] to calculate diusion mass transfer coecients between the fracture and matrix, and the use of Darcyʹs law to model convection mass transfer between the fracture and matrix. In this work, these drawbacks were surveyed and amended. Subsequently, the improved model has been validated through a gas injection experiment. Following model validation, the eects on the recovery rate of matrix permeability, initial gas saturation and injection rate are investigated. The numerical analysis showed that the eect of gas injection rate on the recovery rate is considerable.