The previous studies incorporating the matrix-fracture transfer functions in the naturally fractured reservoir models overlooked the effect of the fracture surface conditions on primary petroleum recovery by pressure depletion and secondary oil recovery by waterflooding and capillary imbibition. This paper presents an improved matrix-fracture transfer model and analytical solutions for rectangular shape matrix blocks in naturally fractured petroleum reservoirs by hindered interface flow between matrix blocks and surrounding fractures. The rectangular shapes are considered to represent the matrix blocks formed by intersecting fractures. The restricted and hindered matrix-fracture interface flow phenomenon is considered in order to account for the effect of the skin due to damaged matrix block surfaces by various processes, including deposition of mineral matter and other debris. The matrix fluid flow equations are formulated for multi-dimensional media, and linearized and solved analytically. The formulation is carried out in dimensionless form, leading to the same dimensionless equations and results based on the analogy between the single and two-phase flow situations involving pressure depletion and capillary-imbibition induced petroleum recovery processes. Then, full scale, and short and long-term analytical solutions are presented and validated by experimental data.
By means of these analytical models, various laboratory experimental data are analyzed, and it is demonstrated that the condition of the matrix block surface is an important factor in determining the rate of fluid flow between matrix blocks and fractures, and the skin effect may reduce the petroleum recovery factor. Comparison with previous simplified models shows that the present model can accurately predict the matrix-fracture interface fluid transfer rate over the full range of the petroleum recovery period, while the previous models can only represent either the early or the late time behavior with limited accuracy. In addition, the effect of the reservoir rock properties on the rate of petroleum recovery by hindered-flow is investigated by means of the hydraulic diffusivity coefficient, determined by correlating the experimental data by means of the new models. This study reveals that there is a strong relationship between the petroleum recovery factor and the diffusion coefficient.
The analytical models developed here can be utilized for rapid and accurate prediction of gas recovery from naturally fractured reservoirs undergoing a pressure depletion or waterflooding process.