Influence of initial fractures on the occurrence of karst turbulent flow

In karst areas of China, there are many karst caves and underground river conduits in the underground aquifer. The development of large cave and conduit are controlled by many factors and it is not every karst aquifer would develop into conduit system, for example, the southern karst area with ample rainfall has many underground rivers, but in the northern arid and semi-arid karst area, underground rivers are relatively rare. The flow states in conduits may be laminar or turbulent. Turbulent flow is an important condition of forming large-scale caves and conduits. In turbulent state, the water flow begin to have the ability of mechanical transportation, which would carry the solid granule and cause the impact and erosion into surrounding rock. The powerful mechanical erosion of turbulence is very important for karst aquifer to develop into large scale conduits and caves. Furthermore, the dissolution rate of carbonate rock in turbulent flow is at least one order of magnitude faster than laminar flow condition. Therefore, the mechanical erosion and chemical dissolution in turbulent flow make the development of conduit and cave more possible. However, the occurrence of turbulent flow is rigidly affected by the hydraulic condition and the initial medium of the aquifer, such as the initial rock fracture, including the aperture, direction, length and density of initial fractures. So we designed different statistic features of fractures and different hydraulic gradients to study the flow state and dissolution widening rates of fractures by numerical simulation. The cubic law and Lomize equation were used to model the laminar and turbulent flow state in fracture. The Newton-Raphson iteration is high-performance to solve the nonlinear flow equation system of laminar and turbulent flow. Then the dissolution rate equation and the Ca²⁺ concentration equation system was employed to model the widening of the fractures. The simulation results and discussions were all under given outer environment with P_CO2 0.8% and hydraulic gradient 0.02. The modeling results of fracture aperture showed that when the standard deviation of aperture was 0.0005 cm and the mean of aperture is 0.006, there was no turbulence in the modeling period of 5,000 thousand years. But when the standard deviation was increased to 0.001 cm, the turbulent flow emerged on 189 thousand year and the time was greatly shorten. In the 8 modeling aperture statistic situations, as the mean and the standard deviation of aperture increased and the heterogeneity of fractures was more intensive, the turbulent flow began to appear and the time of turbulence became earlier. The existence of primary fractures led to much heterogeneous aquifer and earlier turbulent time. The results of fracture direction modeling scenes showed that when the angle between the direction of primary fractures and the direction of main hydraulic gradient was smaller, the turbulence time would be shorter. If the mean of fracture length is too little, the connectivity of fracture would become poor and the karst dissolution would be heavily restricted. The fracture density, especially the primary fracture density, had much influence on the karst development. Compared with the secondary fractures, if the density of primary fractures was too smaller, the turbulence time would largely increase, and even no turbulence in the whole simulation. We also discussed the influence of hydraulic gradient on the turbulent time. The hydraulic gradient varied from 0.001 to 1 and the mean of aperture was from 0.001 to 0.005. The results showed that for each aperture, it had the corresponding smallest hydraulic gradient to the occurrence of turbulence and the greater gradient the turbulent time would become earlier. Below the smallest hydraulic gradient the turbulence would never occur. If the mean of aperture is less than 0.001cm, no matter how the hydraulic gradient is increased, the flow state in fractures remained laminar and no turbulence occurred, in which karst is nearly not developed in the aquifer. In conclusion, the occurrence time of turbulent flow reflects the possibility of forming large karst conduits and caves in present aquifer. The shorter the time is, the greater the possibility will be.