Heat Extraction Rate and Growth and/or Contraction of Solidified Region in Magma Energy Extraction

Abstract

Three dimensional axisymmetric analysis on heat transfer is performed to examine heat extraction rate and behavior of the solidified magma region during heat extraction from molten magma by the so-called open heat extraction system. In the analysis, it is assumed that heat transfer in the solidified magma is almost horizontal, because the heat exchange system is expected to be very slender in the vertical direction. The variation of temperature of the solidified magma with respect to depth is mainly due to heat transfer from the solidified magma to water which is flowing in the vertical direction. It is revealed that the optimum heat extraction rate can be achieved for the flow rate of injected water of 10kg/s∼20kg/s depending on the value of coefficient of heat transfer between the solidified magma and water. The solidified region grows up with time after the onset of heat extraction, but the growth rate decreases with time and is very small after 3000 hours. If heat extraction is stopped, the solidified region would melt down. This phenomena of melting down is also examined.