Productivity Prediction in Deflagration-Fractured Wells: A Novel Approach Based on Fractal Fracture Medium

Deflagration fracturing can create complex near-wellbore fracture networks whose contribution to well productivity remains difficult to describe analytically. We develop a flow-resistance model that represents the stimulated zone as a fractal fracture medium. A dual radial-flow framework separates reservoir flow from local flow around perforation tunnels and yields closed-form expressions for vertical, horizontal, and deviated wells. One-factor sensitivity analyses show increasing productivity with perforation length, shot density, horizontal-well length, and well inclination over the tested ranges. In these cases, where stimulated-zone permeability exceeds that of the original reservoir, increasing the fractured-zone radius increases vertical-well productivity. Perforation radius and phasing have smaller effects over their respective ranges. These expressions relate completion geometry to regional flow resistance and provide an analytical method for evaluating productivity responses in different well types.