An advanced fractal-based well testing model capturing fracture complexity in low permeability tight gas reservoirs

Abstract

The study of heterogeneous and complex oil and gas reservoirs poses a significant challenge due to the problem of unstable seepage flow. This research investigates the non-linear seepage flow patterns in such reservoirs, with a particular focus on ultra-low permeability tight gas reservoirs, using fractal theory. By analysing the scale invariance in the seepage flow of ultra-low permeability tight gas reservoirs, we have derived a fractal geometric expression based on the capillary pressure curve. This expression was integrated with mercury intrusion porosimetry to study the fractal dimension of ultra-low permeability reservoirs. Our experimental results indicate the presence of fractal characteristics in ultra-low permeability tight gas reservoirs. Based on this, we have investigated the fractal nature of matrix porosity and fractures and their effect on the stress sensitivity of ultra-low permeability tight gas reservoirs. This led to the development of a new fractal model for seepage flow in these reservoirs, which takes into account the non-Darcy flow behaviour of gas in nanoscale pores. The mathematical model was simplified using point source solutions and regular perturbation methods. The analysis shows that the fractal parameters of the matrix and fractures, together with the adsorption coefficients and the permeability modulus, have a significant influence on the dynamic pressure behaviour. The effects of slip and diffusion coefficients and stress sensitivity on the dynamics were also investigated. The pressure dynamics curves of ultra-low permeability tight gas reservoirs show distinct differences from those of homogeneous reservoirs and conventional dual porosity reservoirs. This study not only reveals the unique dynamic pressure characteristics of ultra-low permeability tight gas reservoirs, but also shows that the traditional reservoir models are, under certain conditions, special cases of the model proposed in this paper.