Well-Posedness Analysis of a Fractional Two-Phase Flow System in Porous Media

Geological carbon sequestration is an important technology for mitigating climate change by reducing atmospheric CO2 emissions. The geological storage process is governed by complex multiphase flow behaviors in porous media. Classical two-phase flow models are generally formulated using integer-order derivatives, which may not adequately capture the memory effects caused by complex porous media structures. In this work, a pressure–saturation coupled two-phase flow model with a fractional saturation equation is established. The normalized quasi-static pressure problem is first analyzed, while the fractional saturation problem is studied through a conditional fixed-point argument. Under explicitly assumed compatibility, uniform pressure regularity, L2-valued well-definedness and local Lipschitz continuity of the saturation operator, and truncation regularity, an invariant-region estimate ensures that the gas saturation remains in the physical interval [0,1]. These stronger operator properties are imposed as structural hypotheses rather than derived from the basic L2 saturation and H1 pressure spaces. The pressure and saturation solution operators are then composed, and a contraction argument on a sufficiently small time interval establishes conditional local existence and uniqueness within the prescribed admissible class KR(T)×DT, where DT⊂Xp(T). This work provides a conditional analytical framework for the fractional pressure–saturation system under explicit structural hypotheses.