#### Fractal Prediction Model of Gas-Liquid Sulfur Phase Permeability Curve with Boundary Layer Considered Jian-Yi Liu, Lu Jiang, Miao Liu, Shan Yi, Zhi-Bin Liu, Xue-Ni Dai, Yang Xie, Yi-Zhao Chen

Abstract

The liquid sulfur precipitated from high-sulfur gas reservoir will change the situation of only single-phase gas permeability. Moreover, the continuous accumulation of precipitated liquid sulfur will bring certain damages to the reservoir, reduce the productivity and affect the development of gas well. In order to define the law of gas-liquid sulfur phase permeability, this paper sets up a flow resistance model considering the liquid sulfur boundary layer at the pore scale including the capillary force, gas phase viscosity force and liquid sulfur phase viscosity force. Then in combination with the fractal theory of porous media, this paper establishes the prediction model of gas-liquid sulfur relative permeability and compares the prediction curve calculated by the model with the result of real core gas-liquid sulfur phase permeability experiment in non-steady state. According to the comparison result, the mathematical model of gas-liquid sulfur phase permeability can reflect the features of gas-liquid sulfur phase permeability, but there is a certain error with the experimental results, for instance, the sulfur saturation of isotonic point is 5% less than the experimental result while the relative permeability of isotonic point is 10% higher than the experimental result. This is because the mathematical model of phase permeability is deduced based on the steady state theory while in the experiment the non-steady state method is adopted. The two methods are based on different assumptions, which naturally results in a certain error.

Keywords flow resistance, gas-liquid sulfur phase permeability, liquid sulfur adsorption boundary layer