层流—紊流共存流场中岩溶裂隙网络演化过程的数值模拟方法

Numerical simulation method for the karst development of carbonate fracture networks with both laminar and turbulent flow

研究岩溶水系统的演化过程对许多资源与环境问题有着重要意义。岩溶地区水资源、油气资源的预测与开发、水土流失成因及防治等课题都与此密切相关。岩溶管道是地下水对裂隙的逐渐溶蚀扩展形成的,岩溶演化初期,所有裂隙宽度不大,流场整体成层流状态。随着溶蚀的进行,一部分裂隙优先扩大使其中的水流进入紊流状态,而另一部分裂隙中水流仍呈层流状态。文章提出一种数值方法,能够模拟层流-紊流共存流场的岩溶演化过程。利用蒙特卡洛(Monte-Carlo)方法模拟初始裂隙网络,通过非连续介质方法模拟裂隙网络中的渗流。裂隙扩展的速度通过岩石表面溶蚀速度经验公式计算,使用迭代方法求解层流-紊流共存条件下的水头非线性方程。构建了能够利用解析法求解的模型,把数值解和解析解的结果进行对比,验证了本研究的数值法及软件的可行性。

The development process of karst water systems is of great significance to many resource and environmental problems.The issues such as the prediction and exploitation of water resource,oil and gas resources,and the prevention of soil erosion are all closely related to this process.Karst conduits are formed by the gradual dissolution of fractures by groundwater.In the early stage of karstification,the width of the fractures is small and the whole flow field is laminar flow.With the progress of karstification,the flow in some fractures becomes turbulent because of preferential dissolution,and the flow in other fractures remains laminar.This paper presents a numerical method to simulate the karst development of fracture networks with both laminar and turbulent flow.The initial fracture networks are constructed by Monte-Carlo simulation.The groundwater flow is simulated by the discrete fracture network method.The dissolution enlargement of fractures is calculated by the empirical equations of dissolution rate of carbonate rock surface.The nonlinear equation system for the water heads of the flow field,with both laminar and turbulent flow,is solved using the iteration method.The numerical method and software of this work are proved by comparing the calculation results of the analytical and numerical methods.