Mathematical Model for the Mechanism of Profile Control and Water Shutoff by Gel Particles in Porous Media and...

With the large-scale application of profile control and water shutoff technology in the oil reservoir development process, high-water-cut oil reservoirs face a core challenge during the profile control and water shutoff process: the balance mechanism between the selective plugging of high-permeability channels by gel particles and the residual seepage capacity remains unclear. In particular, there is a lack of quantitative characterization methods for the multiscale coupling effects between gel particles and porous media, which leads to inaccurate cross-scale coordinated regulation of plugging strength and flow conductivity and further causes engineering problems such as plugging agent channeling failure and excessive plugging. In response to this, based on the theory of seepage mechanics, this study takes the pore-throat structure of medium-high-permeability/low-permeability reservoirs as the prototype and establishes a multiscale physical and mathematical model for the dynamic plugging of gel particles in annular seepage channels. Through theoretical derivation and boundary condition verification, the global analytical solutions for the axial seepage velocity field v _z (r), seepage flow rate Q, effective permeability K, and seepage resistance R _f were obtained. This study quantitatively reveals the nonlinear regulation law of the gel particle radius r _c and pore-throat size ratio λ = r _c/R (where R is the pore-throat radius) on seepage parameters and clarifies the formation mechanism of micronano-scale residual seepage channels. The results show that gel particles form local plugging bodies through the synergistic effect of deformation and jamming, and the gap between these plugging bodies and the pore-throat wall constitutes the residual seepage channel. When λ ∈ [0.4, 0.8], the seepage resistance R _f increases nonlinearly sharply (with an increase of 2-5 orders of magnitude), while the permeability K decays following a power-law rule dominated by R ⁴. This study establishes a quantitative characterization method for the action mechanism of gel particles from the microscopic scale and constructs a correlation model between plugging agent parameters and seepage response, thereby providing a theoretical basis for the particle size optimization of profile control and water shutoff systems in heterogeneous reservoirs, as well as the design of balance between plugging and flow conductivity.