Basic mathematical model for the normal black smoker system and the hydrothermal megaplume formation

A tube model to simulate the normal black smoker system has been built,where the Darcy flow equation,the Ergun equation and the turbulent pipe flow equation are used respectively to describe the dynamic process of different key areas in the hydrothermal circulation system.At the same time,a convection-diffuse Equation for the temperature field is used for describe the exchange of thermal energy and the law of temperature variation.Combining the above facts and using efficient mathematical algorithms and programming with the MatLab programming language,the variation curves of temperature,pressure and mass flow rate are determined,while also the dynamic heat equilibrium and pressure equilibrium within the black smoker system are analyzed.On the basis of the model of the normal black smoker system,a megaplume formation model is further built.For instance,the hydrothermal venting plume on the Juan de Fuca Ridge has been simulated and the simulation results are fairly consistent with Baker's imputed data in 1986.On the basis of the above productive simulation,a series of factors for megaplume formation and the effectiveness of the main parameters of the periodicity of the megaplume formation,temperature and the maximum mass flow rate are systematically discussed.Main conclusions are as follows:The normal black smoker system can evolve into a megaplum eruption.In fact,the passageway of the hydrothermal discharge is blocked by the hydrothermal sediments during the black smoker period,which leads to a hydrothermal fluid accumulation,rise of temperature and increase of buoyancy pressure under the seabed.After a period of 2~3 a,the megaplume hydrothermal eruption will occur when the increasing buoyancy pressure is high enough to crack the blockage(cap).Meanwhile,the temperature of the heat source must exceed 500℃,while the highest temperature of the eruption fluid may be high up to 413℃,which is fairly consistent with the surveying data.If the temperature of the heat source were to be higher than 500℃,then the critical period for the megaplume formation could be obviously curtailed to be less than 1 a,while the critical temperature and the maximum mass flow rate are nearly invariable.As the permeability increases,the maximum mass flow rate increases gradually close to a steady value.