基于N-S方程的裂缝酸刻蚀数值模拟

Numerical Simulation of Fracture Acid Etching Based on N-S Equation

酸化压裂是碳酸盐岩储层增产改造的主要措施.通过酸压数值模拟预测碳酸盐岩裂缝的刻蚀形态对酸化压裂施工有指导意义.酸压数值模拟多以立方定律为基础,然而随着油气勘探技术进步,油气开采难度增加,酸压数值模拟需要更清晰的流场分布和更高的精度.针对此问题,以N-S方程为基础,推导裂缝酸刻蚀数学模型,随后采用有限差分求解速度场,迎风差分格式求解酸浓度场.结果显示,N-S方程构建的数学模型能较好地模拟裂缝刻蚀形态变化.

Acid fracturing is the main measure to increase production of carbonate reservoirs.Numerical simulation of acid etching is used to predict the etching morphology of carbonate rock fractures,which has guiding significance for acid fracturing construction.Numerical simulations of acid fracturing are mostly based on the cubic law.However,with the advancement of oil and gas exploration technology,the difficulty of oil and gas extraction has increased,and numerical simulation of acid fracturing requires clearer flow field distribution and higher accuracy.To solve this problem,based on the N-S equation,this paper derives the fracture acid etching mathematical model,and then uses the finite difference method to solve the velocity field and the upwind difference scheme to solve the acid concentration field.The results show that the mathematical model constructed by the N-S equation can simulate the acid etching in the fractures.