A thermodynamics-based coupled model for multi-phase flowback in deformable dual-porosity shale gas reservoirs

•Thermodynamics-based model for multi-phase flow in deformable double-porosity media.•New unified adsorptive multi-phase Hydro-Mechanical constitutive equations.•New fully coupled numerical insights into the flowback process of shale reservoirs. Over the past decades, there has been growing interest in modelling multi-phase flowback in shale gas reservoirs during hydraulic fracturing, primarily due to the significant risk of groundwater pollution. However, the lack of fully coupled simulations and a unified theoretical model has hindered the study of coupled adsorptive hydro-mechanical behaviour and its influence on fluid flowback prediction. In this paper, we have extended the non-equilibrium thermodynamics-based Mixture Coupling Theory to derive the constitutive relationship and governing equation for adsorptive multi-phase fluid flows in deformable dual-porosity media. Helmholtz free energy density has been used to establish the relationship between solids and fluids. The interaction of adsorptive fluids in the pore and fracture space has been fully considered, leading to a new form of constitutive equation, which obtained the molecular adsorptive effect on the rock by introducing adsorption entropy production. The proposed governing equations determine the fully coupled evolution of solid deformation and multi-phase flow, with the consideration of adsorption as well as pore and fracture porosity change. Numerical simulation is then performed to study the flowback of a real shale gas well and the influence of coupled behaviour on model prediction. The simulation shows that the flowback flux is mainly by the fracture (more than 99.9 %) and the overall cumulative volume is 2427.1 m3 within 225 h which accounts for about 5.3 % of the total injected fracturing fluid, and the sensitivity analysis reveals that the manual fracture porosity is the most sensitive factor to the cumulative flowback. This work provides new insights into the flowback process of shale reservoirs in a fully coupled view and the proposed theoretical tool should contribute to the modelling of other adsorptive multi-phase flow problem in deformable dual-porosity media such as carbon storage and coalbed methane production.