Productivity Prediction of Fractured Horizontal Wells in Shale Gas Reservoirs: A Comparative Study of Analytical Models

Abstract

Accurate productivity prediction of multi-stage fractured horizontal wells in shale gas reservoirs remains a critical challenge in petroleum engineering. Due to ultra-low permeability and complex storage mechanisms, conventional gas well analysis methods require significant revision for shale gas extraction. Traditional evaluations assign constant fracture conductivity values and overlook time-dependent diversion capacity changes, causing substantial forecasting errors. This study presents a comparative assessment of analytical productivity prediction models for fractured horizontal wells in shale gas reservoirs. Based on the classical Guo Genliang model, an improved productivity equation is derived by introducing pseudo pressure functions for gas-phase behavior. Additionally, a novel productivity equation is established using a capsule flow model that conceptualizes drainage area as two hemispheroids connected by a cylinder, explicitly accounting for matrix-to-fracture transport, linear flow, radial flow, and spherical centripetal flow through equivalent seepage resistance methodology. Both models are validated against field data from a Sichuan Basin horizontal shale gas well. Comparative analysis confirms the capsule flow model delivers superior accuracy, attributed to fewer restrictive assumptions and realistic stimulated reservoir volume representation. Comprehensive sensitivity analysis evaluates effects of formation parameters, well geometry, fracturing design, and desorbed gas steady diffusion rate. Results demonstrate that wellbore radius, fracture half-length, and desorbed gas diffusion rate dominate productivity control, while horizontal well length and fracture number show diminishing returns beyond optimal thresholds. The derived formulas provide practical guidance for predicting fractured horizontal well productivity and optimizing completion strategies in shale gas reservoirs.

Keywords: Shale gas reservoirs; fractured horizontal wells; productivity prediction; capsule flow model; Guo Genliang model; desorbed gas diffusion; pseudo pressure; equivalent seepage resistance