A comprehensive mathematical model for spontaneous imbibition in oil-saturated fractured tight sandstones: Incorporating fracture distribution, displacement pressure, gravity, and buoyancy effects

Abstract

This paper presents a generalized mathematical model that comprehensively characterizes the flow behavior of matrix nanopores and natural/hydraulic fractures in tight oil reservoirs during spontaneous imbibition. The model incorporates various influencing factors such as fracture distribution, displacement pressure gradient, gravity, and buoyancy. The complex pore structure of tight oil reservoirs, including nanopores and natural microfractures, presents a challenge in developing an accurate mathematical model for predicting flow behavior. The proposed model considers the fractal characteristics of pores and fractures and accounts for many factors to predict cumulative oil production, oil flow rate, and oil recovery factor during imbibition flow. Experimental data on fractured tight sandstones are used to validate the model, and sensitivity analyses are conducted to assess the influence of pore structure parameters, fracture distribution, and fluid properties on imbibition behavior. The findings reveal that gravity and buoyancy effects become more prominent under low interfacial tension. Fracture distribution significantly impacts imbibition behavior, with critical values for fractal dimensions, fracture numbers, and apertures determining the extent of their influence. Higher contact angles and increased oil phase viscosity result in reduced imbibition efficiency. In pressure-driven displacement processes, larger fractures preferentially produce crude oil, and the higher pressure gradients result in shorter imbibition processes. The proposed model offers insights into the imbibition oil recovery mechanism in tight oil reservoirs and can contribute to improved recovery factors.