Probabilistic Modeling and Interpretation of Inaccessible Pore Volume in Polymer Flooding

Abstract

Inaccessible pore volume fraction (IPV) significantly affects polymer transport and retention in porous media during enhanced oil recovery. Conventional methods typically estimate IPV using deterministic or empirical models. These approaches often overlook the randomness in pore and polymer size distributions. This study introduces a probabilistic framework that redefines IPV as a stochastic outcome of size exclusion interactions between polymer molecules and pore throats. Ten mathematically equivalent formulations were developed based on the expectation or event probability logic, and from both polymer- and pore-centered perspectives. All models were analytically verified for consistency. Case studies using representative pore and polymer size distributions (0.1–20 μm and 1–5 μm) confirm that the models yield consistent IPV values across formulations. Sensitivity analysis shows that the results respond to the key parameters, such as the exclusion threshold. The results were computed from probability distributions, weighted based on exclusion rules derived from absolute size values. For instance, increasing the exclusion parameter from 3.0 to 5.0 led to a sharp rise in IPV from 0.0367 to 0.3713. Fundamentally, this framework offers a new perspective. It redefines IPVF as a derived probabilistic quantity governed by physically meaningful size distributions, rather than a fixed empirical input. By decoupling estimation from raw size data and emphasizing distribution-driven computation, the method improves robustness and interpretability and enables integration into uncertainty-aware simulators and data-driven workflows.