稠油开采中非等温压强扩散方程的数学建模

Mathematical Modeling of Non-Isothermal Pressure Diffusion in Heavy Oil Recovery

摘要: 在常见的稠油开采技术建模中，往往忽略压强影响或者统一用等温压强扩散方程替代非等温压强扩散方程进行计算求解。本文针对蒸汽辅助重力泄油(SAGD)、温溶剂萃取采油(warm VAPEX)两种采油技术分别建立考虑温度影响的压强扩散方程和同时考虑温度和浓度影响的压强扩散方程。并以SAGD为例对比等温与非等温压强扩散方程计算得到的压强分布，发现随着温度升高，两者差异逐渐增大，说明在有温度作用的采油技术中，更应该建立非等温压强扩散模型。

Abstract: In common heavy oil recovery technology modeling, the impact of pressure is often neglected, or the isothermal pressure diffusion equation is used as a substitute for the non-isothermal pressure diffusion equation for calculation and solution. In this paper, pressure diffusion equations that account for the temperature effect and pressure diffusion equations that consider both temperature and concentration effects are established for two oil extraction techniques: Steam Assisted Gravity Drainage (SAGD) and warm VAPEX (Warm Solvent Extraction for Oil). Taking SAGD as an example, the pressure distributions obtained from the isothermal and non-isothermal pressure diffusion equations are compared. It is found that as the temperature increases, the differences between the two distributions gradually grow, indicating that in oil extraction techniques affected by temperature, a non-isothermal pressure diffusion model should be established.