Well head pressure in geothermal field generally increases to its maximum after shut-in valve. The maximum well head pressure, which is controlled by fluid temperature of the after flow from reservoir to well bore, is mathematically estimated based on energy balance and mass balance equations for well volume. Well head pressures measured in the Sumikawa geothermal field quite match to the vapor phase pressure simulated in upper part of well bore. Pressure fluctuation after shut-in valve is also explained by difference of fluid temperature and density between the bore hole and the reservoir in case of multiple feed point exist. This simulator is effective to design the flow casing and the well head equipments.
This paper describes a relationship between average saturation and relative permeabilities of which values are estimated by using a probability density function of saturation. The authors have already proposed the estimation method and discussed the relative permeabilities in a porous medium with saturation distribution. In the result, the relative permeabilities depend not only on average saturation, but also on the standard deviation and the skewness. However, it is difficult to estimate their detail values in analyses of two-phase flow in a geothermal reservoir. In this paper, the relative permeability of gas-phase is calculated for each average saturation, each standard deviation, and each skewness, under an assumption that ralative permeability of liquidphase is proportional to second-or third-power of average saturation in a porous medium with saturation distribution. The calculations indicate the upper limit and the lower limit values of the relative permeability of gas-phase in the relation to the average saturation. Also, this paper proposes the approximation equations to express the relative permeabilities. These equations successfully describe effects of the saturation distribution on heat flow rate in a porous medium.
A numerical model for a vertical two-phase flow in a geothermal well developed based on Ramirez's algorithm (1983) was applied to the data analysis of a certain well in the Sumikawa geothermal field and its applicability was discussed. It was concluded that the numerical model could simulate vertical two-phase fluid flow phenomena that could be considered as steady state. From the analysis of a certain well, following couclusions were also obtained. (1) There were two feed points in the analyzed well and they interfered each other. (2) The fluid at feed points of the analyzed well was already in two-phase. (3) It was estimated that approximately 80 percent of fluids was supplied from a deeper feed point during the interval that could be considered as steady state.
In the extraction of thermal energy from magma, it is expected that a fracture network would be created due to thermal contraction of the solidified magma formed around the wellbore during heat extraction and the fracture network is expected to work as the flow path of the working fluid for the heat extraction. In the present paper, the stress field in the solidified magma and its variation with respect to time were analyzed based on the creep theory, emphasizing the feasibility of formation of the fracture network for a various types of rocks, i.e., granite, olivine and anorthosite. As for the constitutive law for the creep, the usual incremental flow theory was employed, where the second invariant of the stress deviator is used as the creep potential. It was revealed that, due to the intense effect of creep deformation, the stress distribution for granite was completely different from the elastic stress field and was almost independent of time and growth of solidified region during the heat extraction. The effect of creep deformation is less intense in in the cases of olivine and anorthosite. It was also revealed that the stress on the well bore was compressive regardless of depth in the case of granite. On the contrary to this, it is tensile in the region shallower than 8km in the case of olivine and 6km in anorthosite, implying that, among the three, olivine would be the most potential candidate for the magma energy extraction from the view point of formation of the fracture network. Anorthosite comes next.