An Analytical Solution and Nonlinear Regression Analysis for Sandface Temperature Transient Data in the Presence of a Near-Wellbore Damaged Zone

Throughout this study, we present a dual-continuum model of transport of the natural gas in shale formations. The model includes several physical mechanisms such as diffusion, adsorption and rock stress sensitivity. The slippage has a clear effect in the low-permeability formations which can be described by the apparent permeability. The adsorption mechanism has been modeled by the Langmuir isotherm. The porosity-stress model has been used to describe stress state of the rocks. The thermodynamics deviation factor is calculated using the equation of state of Peng–Robinson. The governing differential system has been solved numerically using the mixed finite element method (MFEM). The stability of the MFEM has been investigated theoretically and numerically. A semi-implicit scheme is employed to solve the two coupled pressure equations, while the thermodynamic calculations are conducted explicitly. Moreover, numerical experiments are performed under the corresponding physical parameters of the model. Some represented results are shown in graphs including the rates of production as well as the pressures and the apparent permeability profiles.