Pressure Stress Coupled Deterministic Modeling of Multiphase Flow in Fractured Reservoirs

Abstract

Fractured reservoirs exhibit complex flow behavior due to strong coupling between fracture matrix interaction, multiphase transport, and pressure induced geo mechanical effects. This study develops a deterministic dual porosity multiphase model that explicitly incorporates poroelastic stress coupling and stress dependent permeability. Analytical results establish the positivity and boundedness of solutions, ensuring physical admissibility of saturations, pressures, stress, and porosity. Equilibrium states are derived and their local stability is examined through linearization and eigenvalue analysis. The results show that system Dynamics are governed by real eigenvalues and that stress induced permeability degradation leads to steady state bifurcations associated with loss or exchange of fracture matrix connectivity, while oscillatory instabilities are excluded. Numerical simulations using representative literature-based parameters are compared with published coupled reservoir geo mechanical studies. The predicted fracture and matrix pressure ranges (20–27 MPa and 18–24 MPa, respectively) and effective stress evolution (15–22 MPa) agree well with reported values. Permeability reductions of one to two orders of magnitude are reproduced, and saturation dynamics demonstrate rapid fracture response and delayed matrix behavior. These results confirm that the proposed reduced order model reliably captures key features of stress coupled fractured reservoir systems.

Keywords

• Rock Matrix
• Geo-Mechanical
• Positivity and Boundedness
• Permeability
• Dual Porosity

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