A Nonisothermal Numerical Well Test Model for Multistage Fractured Horizontal Wells in Deep Shale Gas Reservoirs

Abstract

Reliable pressure-transient interpretation for deep shale gas wells requires the thermal response of fractured reservoirs to be considered. This study develops a fully coupled nonisothermal numerical well test model for multistage fractured horizontal wells (MFHWs). The model is formulated within the analytically enhanced embedded discrete fracture model (EDFM) framework. It couples mass and energy conservation, matrix-fracture and fracture-fracture transfer, temperature-dependent adsorption/desorption with the associated energy exchange, and pressure- and temperature-sensitive permeability. Methane properties are obtained from pressure-temperature lookup tables generated using CoolProp. The model is verified against the thermal numerical model in KAPPA Saphir. It reproduces the KAPPA pressure-transient responses while requiring only 0.366% of the KAPPA solution time for the verification case. A pressure-derivative deviation coefficient is introduced to quantify the error caused by neglecting temperature variations. The pressure-transient response is divided into seven flow periods. Thermal effects are limited during wellbore storage and early fracture flow, but accumulate as pressure depletion propagates into the matrix and fracture network. The deviation coefficient increases to approximately 0.08 during desorption, 0.11 during interfracture interference, and 0.65 at the end of boundary-dominated flow. Sensitivity analyses show that effective matrix permeability and hydraulic fracture spacing control the spatial extent and timing of thermal disturbances. Adsorption density, isosteric heat of adsorption, and rock specific heat capacity strongly affect the deviation magnitude, whereas rock thermal conductivity has a smaller influence. Increasing adsorption density from 5 kg/m³ to 50 kg/m³ increases the terminal deviation coefficient from 0.34 to 0.85. Increasing rock specific heat capacity from 500 J/(kg·K) to 2,000 J/(kg·K) reduces it from 0.80 to 0.30. Application to a pressure-buildup test in the Weiyuan Block provides a good match to field data. The field-case deviation coefficient reaches 0.44 at the end of shut-in, confirming that thermal history can materially affect shale gas pressure-transient interpretation.