Rate Decline Analysis for Modeling Volume Fractured Well Production in Naturally Fractured Reservoirs

Based on the property discontinuity in the radial direction, this paper develops a new composite model to simulate the productivity of volume fractured wells in naturally fractured reservoirs. The analytical solution of this model is derived in detail and its accuracy is verified by the same model's numerical solution. Detailed analyses of the traditional transient and cumulative rate are provided for the composite model. Results show that volume fracturing mainly contributes to the early-flow period's production rate. As interregional diffusivity ratio increases or interregional conductivity ratio decreases, the transient rate at the same wellbore pressure increases. Three characteristic decline stages may be observed on transient rate curves and the shape of traditional rate curves in the middle- and late-flow periods depends on naturally fractured medium and boundary condition. By introducing a new pseudo-steady constant, new Blasingame type curves are also established and their features are more salient than those of traditional rate curves. Five typical flow regimes can be observed on these new type curves. Sensitivity analysis indicates that new Blasingame type curves for varied interregional diffusivity ratio, interregional conductivity ratio, interporosity coefficient and dimensionless reservoir radius, except storativity ratio, will normalize in the late-flow period.