# Effect of Pore Structure Heterogeneity of Sandstone Reservoirs on Porosity–Permeability Variation by Using Single–Multi-Fractal Models

## TL;DR

This study examines how pore structure heterogeneity in sandstone affects porosity and permeability using fractal models.

## Contribution

The study introduces the use of single- and multi-fractal models to quantify pore structure heterogeneity in sandstone reservoirs.

## Key findings

- The Sierpinski model's fractal dimension correlates strongly with pore volume percentage, making it effective for characterizing fracture distribution.
- Porosity and permeability decrease as a power function with increasing confining pressure, with significant changes at a critical pressure threshold.
- Permeability variation is more sensitive to confining pressure than porosity, and pore structure parameters do not directly influence compressibility.

## Abstract

Pore structure heterogeneity affects sandstone porosity
and permeability
and thus sandstone gas productivity. A total of 17 sandstone samples
collected from the northwestern margin of the Junggar Basin in Xinjiang
Province are investigated in this study. The pore-fracture system
distribution of target sandstones is studied by high-pressure mercury
injection tests. On this basis, single- and multi-fractal models are
used to characterize pore structure heterogeneity, and the applicability
of four models (Menger model, Sierpinski model, Thermodynamic model, multifractal model)
to characterize pore and fracture distribution heterogeneity are discussed.
Moreover, a correlation between fractal dimension, pore structure
parameters, and variation coefficient of porosity–permeability
is discussed based on overburden permeability test results. The results
are as follows. (1) DS (fractal dimension
of Sierpinski model) shows a significant correlation
with pore volume percentage, so the Sierpinski model could better
characterize fracture distribution heterogeneity quantitatively. Multifractal
dimensions are consistent with those of Sierpinski and Thermodynamic
models, which indicates that the single- and multiple-fractal models
are consistent. (2) The porosity and permeability decrease as a power
function with higher confining pressure. The porosity and permeability
behavior changes at a critical conversion pressure value. For a confining
pressure lower than this critical value, the porosity and permeability
decrease largely. For confining pressures higher than this critical
value, the porosity and permeability vary less. In contrast, permeability
has a larger variation rate and is more obviously affected by confining
pressure. (3) Pore compression space is affected by the permeability
variation coefficient. Compressibility, porosity, and permeability
variation coefficient have no relationship with pore structure parameters
since compressibility is affected by pore structure, mineral composition,
and other factors in sandstone samples.