A novel fully implicit method for calculating fluid saturation distribution in immiscible gas flooding and its application.

Compared with water-flooding reservoirs, gas-flooding reservoirs exhibit more complex characteristics, primarily attributed to the significant viscosity difference between the displacing phase and the displaced phase. Under the influence of the equation of state, gas viscosity and deviation factor are binary functions of temperature and pressure. As the reservoir recovery degree increases, regardless of the injection strategy employed, the reservoir pressure will present a complex heterogeneous spatial distribution. When analyzing the variation of gas saturation at different positions during the production process, it is necessary to consider the effects of reservoir pressure at the corresponding location on gas viscosity and compressibility. An extensive literature review reveals that most publicly published studies on fluid saturation in gas-flooding reservoirs are based on numerical reservoir simulation methods, where the gas state equation is introduced for quantitative description. Based on the Buckley-Leverett water-flooding equation, this study proceeds as follows: ① Firstly, a one-dimensional homogeneous radial flow tube model is established. Considering that the fractional flow curve is an S-shaped nonlinear function, a novel fully implicit method is adopted to automatically search and calculate the optimal water saturation value at each spatial step and time step. ② Secondly, considering the heterogeneity of the actual model, a multi-flow tube model accounting for permeability variation is further constructed; the fingering phenomenon of the displacing phase considering heterogeneity can be obtained by averaging the saturation distribution changes of different flow tubes. ③ Thirdly, considering the compressibility and viscosity variation of gas, the volume conservation in the water-flooding mode is converted into the mass conservation in the gas-flooding mode. Subsequently, combined with the Buckley-Leverett equation and the fully implicit solution applied to the multi-flow tube model, the fluid saturation distribution of immiscible gas flooding can be derived. The proposed method in this paper is applied to interpret and analyze the field data of an actual restricted channel gas-flooding case, and the theoretically calculated gas breakthrough time of the oil well is in high agreement with the actual data. This research method features rigorous theoretical derivation and has been verified to be feasible through practical application, thereby providing certain practical guidance and reference significance for reservoir engineering researchers.