普通黑烟囱热液系统及巨羽流形成的基本数学模型

The basic mathematic model for normal black smoker system and hydrothermal megaplume

建立了一种新的管状模型来模拟普通黑烟囱体的热液循环系统，分别用达西方程、湍流方程、Ergun方程和“浮压力差”方程来描述热液循环不同关键环节处的动力学系统，用一个温度场的对流一扩散方程来描述反应区的热能交换及系统的温度变化规律．在联立几个方程并用有效的数值算法及Matlab语言编程求解后，得出了系统中温度、压力及物质流速随时间的变化曲线，并对黑烟囱体内部的动态热平衡和压力平衡进行了分析．在普通黑烟囱体系统模型的基础上进一步建立了巨型羽状流（巨羽流）生成的数学模型．选择胡安·德富卡（Juan de Fuca）洋脊热液喷口对巨羽流的形成进行了模拟，其结果与Baker根据实测数据估算的近似值吻合很好．在上述模型的基础上进一步探讨了巨羽状流形成的一系列条件及主要参数对巨羽流生成周期、温度和最大物质流速等的影响．主要结论如下：巨羽流系统可以由普通黑烟囱系统发展演化而成，其实际过程是普通黑烟囱流系统活动所形成的热液沉积在一定程度上会堵塞热液喷溢通道（相当于形成盖层），造成热液在海底之下积蓄和升温，从而导致浮压力差增大，经过2～3a（浮压力差达到盖层破裂极限值）则可形成巨羽流系统，巨羽流产生时的热源温度必须超过500℃，喷出热液的最高温度为413℃左右（与实际观测到的海底热液的最高温度一致）．当反应区热源温度增大时，产生巨羽流的临界时间明显变短（可能不到1a），而临界温度（巨羽流生成时的温度）及巨羽流的最大物质流速几乎不随其变化；随着渗透率的增大，巨羽流的最大物质流速也随之增大，但其增速随渗透率的进一步增大而变缓，并逐渐趋向一个相当于下渗流无摩擦阻力时的极限稳定值．

The tube model to simulate a normal black smoker system has been built. Darcy flow equation, Ergun equation and turbulent pipe flow equation are respectively used to describe the dynamic processes of different key parts in a hydrothermal circulation system. Meanwhile, a convection-diffuse equation for a temperature field is used to describe the exchange of heat energy and temperature variety. Combining those equations, using efficient mathematic algorithms and programming in Matlab language, the variation curves of temperature, pressure and mass fluid rate by the time are achieved. Then, developing hot and pressure balances in the black smoker system are analyzed. On the basis of the model of normal black smoker system, a megaplume formation model is further built. As an instance, the hydrothermal venting plume on the Juan de Fuca Ridge has been simulated and the simulated results are fairly consistent with Baker＇s imputed data on surveying. On the basis of the above productive simulations, a series of conditions for megaplume＇s formation and the effect of main parameters on the megaplume-forming period, temperature and maximum mass fluid rate were systemly discussed. Main conclusions are as follows： The normal black smoker system can evolve to a megaplume eruption. In fact, hydrothermal discharge pass way can be blocked up with hydrothermal sediments during black smoker period, leading to hydrothermal fluid accumulating, temperature rising and the buoyancy pressure increasing under the seafloor. After 2-3 a, the megaplume hydrothermal eruption will occur if the buoyancy pressure increase is high enough to break through the blockage. At the same time, the highest temperature of eruption fluid may be high up to 413℃, fairly consisting with the surveyed data, and the temperature of the heat source must exceed 500℃. If the temperature of the heat source increases higher 500 ℃ ,the critical period for the megaplume＇s formation can be obviously curtailed to be less than 1 a, while the critical temperature and the maximum mass fluid rate are nearly invariable. As the permeability increases, the maximum mass fluid rate increases gradually close to a steady value.