Effect of tortuosity on the stress-dependent permeability of tight sandstones: Analytical modelling and experimentation

Accurately modelling stress-dependent permeability is of great significance to predicting the oil/gas production of unconventional tight sandstone reservoirs with time-dependent pressure depletion. The classic theory indicates that the porosity exponents of the capillary tube model and the fracture model are 2 and 3, respectively. However, experimental results demonstrate that the value of the porosity exponent usually varies greatly. The effect of the nonuniform distribution of tortuosity on stress-dependent permeability is rarely studied. Assuming that tight sandstones with natural microfractures can be represented by a bundle of tortuous capillary tubes and parallel plate fractures, a new stress-dependent permeability model of tight sandstones is proposed based on fractal theory considering the tortuosity effect. The research results show that the porosity exponents of the tortuous capillary tube model and the tortuous plate fracture model are (3 + D-T)/2 and 2 + D-T, respectively (here, D-T is the tortuosity fractal dimension). For the capillary tube model and the plate fracture model without tortuosity (D-T = 1), their porosity exponents can be simplified to 2 and 3, respectively. The tortuosity fractal dimension is one of the reasons causing the porosity exponent to deviate from the classic theoretical value. The newly developed stress-dependent permeability model is verified with experimental data determined using tight sandstone core samples from the Yanchang Formation in the Ordos Basin, China. The average error of the permeability prediction under different effective stresses is only 3.78%; thus, the newly developed model can accurately predict the stress-dependent permeability of tight sandstones.