This study presents analytical models for naturally fractured tectonic reservoirs (NFTRs), which essentially correspond to type I fractured reservoirs, including the effects of the nonlinear gradient term for radial flow, single phase (oil), for constant rate in an infinite reservoir. Using an exact solution of Navier-Stokes equation and Cole-Hopf transform, NFTRs have been modeled. Our models are applied for fissured formations with extensive fractures. Smooth and rough extension fractures were analyzed using single and slab flow geometries. The motivation for this study was to develop a real and representative model of a NFTR, with extension fractures to describe its pressure behavior. A discussion is also presented with field examples, regarding the effect of a quadratic gradient term and the difference between the nonlinear and linear pressure solutions, comparing the Darcy laminar flow equation, with the exact solution of the Navier-Stokes equation applied to the diffusion equation and boundary conditions in wellbore.
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Modeling of limestone reservoirs is traditionally developed applying tectonic fractures concepts or planar discontinuities and has been simulated dynamically without considering nonplanar discontinuities as sedimentary breccias, vugs, fault breccias, and impact breccias, assuming that all these nonplanar discontinuities are tectonic fractures, causing confusion and contradictions in reservoirs characterization. The differences in geometry and connectivity in each discontinuity affect fluid flow, generating the challenge to develop specific analytical models that describe quantitatively hydrodynamic behavior in breccias, vugs, and fractures, focusing on oil flow in limestone reservoirs. This paper demonstrates the differences between types of discontinuities that affect limestone reservoirs and recommends that all discontinuities should be included in simulation and static-dynamic characterization, because they impact fluid flow. To demonstrate these differences, different analytic models are developed. Findings of this work are based on observations of cores, outcrops, and tomography and are validated with field data. The explanations and mathematical modeling developed here could be used as diagnostic tools to predict fluid velocity and fluid flow in limestone reservoirs, improving the complex reservoirs static-dynamic characterization.
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