Stabilized Well Productivity in Double-Porosity Reservoirs

Abstract

Summary In this work, we present a simple1 analytical formula for the stabilized productivity index (PI) of an arbitrary well in an arbitrary closed, naturally fractured reservoir that can be modeled as a double-porosity reservoir. The formula relates the PI to the PI of a well in a single-porosity reservoir with permeability equal to the effective fracture permeability of the double-porosity reservoir. We have elaborated this formula for a vertical and a horizontal well in a rectangular reservoir made up of orthogonal matrix blocks. It appears that the double-porosity characteristics, along with reservoir flow capacity and reservoir volume, combine into a single factor, which plays the same role as the familiar skin factor. For small values of this double-porosity skin, well productivity is dominated by fracture permeability; for large values, the controlling parameter is matrix permeability. Inflow-performance relationship (IPR) curves of wells in double-porosity gas reservoirs can be created readily with the help of the new PI formula. An example is included showing the production profiles of a vertical and a horizontal well in a double-porosity gas reservoir with cubes and square pillars as matrix blocks. The results of this work are particularly relevant for the reservoir engineering of naturally fractured gas reservoirs.