Numerical simulation of the steam-water flow instability as a mechanism of long-period ground vibrations at geothermal areas

Abstract

We present a model for the excitation of continuous ground vibration at geothermal areas and active volcanoes, which is based on the instability of water/steam two-phase flow. Through a series of numerical experiments, we evaluate the amplitude and period of ground vibrations excited by density wave oscillation (called 'DWO'), one of the flow-instability phenomena, which is known in the nuclear reactor engineering to occur under a wide variety of boundary conditions. We consider a vertical cylindrical pipe buried underground and 1-D flows through it driven by the lithostatic pressure gradient. Water flows into the pipe from below and is evaporated by the heat supplied from outside. When the heating rate is low, after a perturbation such as a change in heating rate is given to the flow system, a decaying oscillation of pressure, flow velocity and void fraction occurs being followed by a stationary flow. On the other hand, when the heating rate exceeds a threshold, the perturbation grows to a continuous oscillation with a fixed amplitude, forming a limit cycle DWO. We investigate how various parameters such as pipe length, pressure and heating rate, affect the stability of the two-phase flow. We then estimate the amplitudes of seismic waves excited by DWO, assuming that the pipe is embedded in a elastic half-space. We find that a longer pipe can excite a DWO of longer period and of larger maximum amplitude. For a pipe of length of 100 m with its bottom at the depth of 150 m, the DWO period is nearly 10 s. In this case the maximum pipe diameter for the excitation of limit cycle DWO for reasonable rates of stationary conductive heat supply from country rocks to the two-phase mixture inside the pipe (less than about 35 MW m-3) is 0.02 m. The maximum amplitudes of ground displacement due to DWO are of the order of 7 × 10-8 m 4 × 10-9 m at epicentral distances of 200 and 1000 m, respectively. Typical geothermal areas and active volcanoes can supply heat and discharged water mass, which are required to excite DWO larger than typical background noises. Therefore, DWO due to a shallow water/ steam flow could excite ground motions with periods longer than 10 s which is large enough to be observed with suitably designed broadband seismic experiments at geothermal fields. © 2005 RAS.