Semi-analytical prediction of critical oil rate in naturally fractured reservoirs with water coning

Abstract

Naturally fractured reservoirs (NFRs) with bottom water are generally produced above their critical oil rate (maximum possible oil production rate without water breakthrough) that is difficult to determine as it varies between wells, depending on the well's location in the fracture network. In principle, wells can either be completed in matrix or fractures. Present formulas of critical-rate in NFR are oversimplified ignoring the network heterogeneity and anisotropy ratio of fractures, and they also do not consider the difference between on-fracture/off-fracture well completion placements. Presented is development of a new semi-analytical formula that considers these effects– with emphasis given to well placement assessment.The critical rate model is derived from mechanistic principles and then improved with statistical calibration. The mechanistic approach (Chaperon (1986)) considers vertical equilibrium of viscous and gravity forces for a hemispherical flow to a point-source well in a dual porosity/dual permeability model of naturally fractured reservoirs. The model considers the water cone instability, and anisotropy ratio of NFR only for a short-perforated completion interval. The model is tested for wide variety of NFRs for short completions. The model is then statistically calibrated to including the effect of long penetration ratio, using a designed matrix of simulated experiments covering wide ranges of NFR properties. This statistical approach allows the model to consider any change in flow regime from semi-spherical to non-radial distorted flow.The comparison of Chaperon's analytical model and NFR simulations shows that the model is good for NFRs for penetration ratio smaller than 0.35. For penetration ratio greater than 0.35, a new semi-analytical model of critical-rate for NFR is developed by statistically calibrating the Chaperon's analytical model. The new model considers the parameters ignored in the previous models of NFR. Finally, a new mechanistic derivation of critical rate for wells completed in matrix block of NFR is determined by analytically including the effect of well's distance to fracture in a critical rate formula for NFR. The model matches well with the simulated data when compared with it. The model shows that the wells accidently completed off-fractures may display higher values of critical rates and the difference relates to their distance to the nearest fractures. It is also shown that the off-fracture well's formula reduces to the on-fracture well's formula when the distance is reduced to zero.