Low-Velocity Non-Linear Numerical Simulation in Tight Sandstone Oil Reservoirs

Abstract Micro and nano throats are widely distributed in tight sandstone oil reservoirs and non-linear flow characteristics are obvious. However, no existing non-linear mathematical models and numerical simulations account for the effect of throat radius heterogeneity and fluid on non-linear flow characteristics. Additionally, they aslso do not account for the mutation of relative permeability curve resulted from non-linear flow characteristics. Therefore, in this paper, based on the method to characterize the non-linear flow characteristics and to calculate the relative permeability with non-linear flow characteristics, non-linear mathematical model is built. Then the numerical simulation module is developed. It is found that because of the effect of non-linear flow characteristics and quasi threshold pressure gradient, the early oil production of conventional model is largest and that of quasi threshold pressure gradient (QTPG) model and non-linear model are the same. Additionaly, QTPG model overestimates the threshold pressure gradient. Therefore, the sweep and cumulative oil production of conventional model is larger than that of non-linear model, larger than that of QTPG model. Becasuse the middle of the production well and injection well has the minimal pressure gradient, it has the minimal effective permeability. Accounting for the effect of non-linear flow characteristics and permeability stress sensitivity on relative permeability, the sweep area of injected water is small. Although the permeability is the same, the non-linear flow characteristics and permeability stress sensitivity are more obvious when throat distribution is narrower. As a result, the effective permeability is lower and sweep area become smaller. Therefore, oil rate and cumulative oil production is lower.