This paper presents a new analytical model for pressure transient tests of water injection wells in naturally fractured reservoirs. Considering negligible flow in matrix, the dual-porosity model was assumed for formulating a mathematical model that accounts for two-phase flow and saturation changes in fracture and matrix. Water saturation distributions in fracture and matrix were calculated analytically using the Buckley-Leverett equation and the empirical transfer function to account for fracture-matrix flow. Pressure equations for two-phase flow were formulated with the multi-composite modeling approach. The system of pressure equations was solved analytically in Laplace space. Calculations were carried out stepwise as the injection or falloff time proceeds.
The model solutions were validated for such special cases as single-phase flow in the dual-porosity model, and two-phase flow in the single-porosity model. Pressure and pressure-derivative type-curves, graphed against the injection time or the dimensionless time based on well radius, exhibited features of both fractured reservoirs and two-phase flow. The parameters in the type curves are storativity ratio, interporosity two-phase flow coefficient defined as a function of shape factor, total mobilities for matrix and fracture, and exponential recovery constant Rc. Rc characterizes imbibitiondominant recovery performance of matrix, and is defined as a function of permeability, porosity and capillary pressure of matrix, and shape factor.