Numerical Simulation of Scale Formation for Injection–Production Units in Oil Reservoirs

Water injection is one of the most economical and effective methods of ensuring the continuous and stable production of an oil field and improving oil recovery. However, scale formation is unavoidable in long-term water injection, and this seriously affects and restricts oil field development. Our research on scale formation in injection–production units was based on the dissolution–precipitation equilibrium, thermodynamics, ionic association theory, the solubility product rule, and the common ion effect. Considering formation temperature, pressure, scale ion concentration, and rate of flow as influencing factors, we established a formation pressure field model, a temperature field model, a porosity model, a scale formation model, and a scale inhibition model, which together constitute a numerical model of scale formation in an injection–production unit. We then used MATLAB software to analyze the influence of various factors on the total amount of scale, the scale range, and the scale distribution, as well as the influence of scale formation on the apparent injectivity index and permeability. To verify the reliability of our model, we introduced a scale inhibition rate, and we compared the scale inhibition rate that we calculated with the scale inhibition rate measured by experiment. The simulation shows that scale formation is mainly affected by formation temperature and scale ion concentration distribution, but that formation pressure has relatively little influence on it. Formation pressure decreases gradually along the direction of water flooding in an injection–production unit, and formation temperature changes mainly near the wellbore of the injection well. Along the direction of water flooding, scale formation first increases rapidly and then decreases rapidly. The reason for this trend is that with low formation temperature near the injection well, a small dissolution equilibrium constant and a high flow rate make scale formation difficult. Radially outward, the formation temperature increases and the flow rate decreases greatly, making it easier for scale to form. Even further out, the scale ion concentration is lower than the minimum scale concentration and scale can no longer form.