A dynamic non-linear flow model coupling temperature influence

Abstract

The existing non-linear flow model does not consider the influence of temperature change on the non-linear flow law. Therefore， based on the capillary flow model， the Hagen-Poiseuille equation， and the boundary layer theory， as well as the influence of the temperature on the thickness of the boundary layer and the yield stress of the fluid， a dynamic non-linear flow model in low-permeability porous media considering the influence of temperature was derived. Then， the fitting verification was carried out according to the experimental data in published literature， and the calculated flow velocity curve and minimum start-up pressure gradient were highly consistent with the experimental data， which revealed the correctness of the dynamic non-linear flow model. Meanwhile， the comparative analysis with the static non-linear flow model and the Darcy flow model illustrated the rationality of the dynamic non-linear flow model. The sensitivity analysis of the flow velocity curve revealed that the increase in coefficients A and B made the flow velocity curve right-shift； the curvature degree of the non-linear flow section was weakened， and the minimum start-up pressure gradient was increased. The increase in the temperature had a much more significant effect on the flow velocity curve， which made the velocity curve move up obviously. The curvature degree of the non-linear flow section weakened， and the minimum start-up pressure gradient increased. The proposal of this dynamic non-linear flow model further enriches the development of the non-linear flow theory and can be extended to the numerical simulation of two-phase flow and high-temperature and high-pressure oil and gas reservoirs.

Keywords

• temperature
• non-linear flow
• model derivation
• model verification and comparison
• sensitivity parameter analysis