ABSTRACT
It is widely recognized now that borehole geophysical measurements are no less important than ground geophysical observations. Borehole geophysical logging is used for searching various economic minerals, fresh and hot water, tectonic-structural investigations and environmental and ecological analysis (Gretener 1981; Jorden and Campbell 1984; Bourdarot 1998). Temperature and pressure investigations fall within the domain of the most exploitable physical parameters (Serra 1984; Tittman 1986). The knowledge of thermal properties of formations (Kappelmeyer and Haenel 1974; Somerton 1992; Vosteen and Schellschmidt 2003) and initial formation temperature are needed to evaluate the energy capacity of geothermal reservoirs. The forecasting of fl uid fl ow rate of production and injection geothermal wells requires an estimation of mobility (formation permeability and fl uid viscosity ratio), porosity, total formation compressibility, skin factor, and initial reservoir pressure (Earlougher 1977; Elder 1981). In petroleum and geothermal reservoir engineering pressure and fl ow well tests are routinely conducted to determine these parameters (Earlougher 1977; Lee 1982; Prats 1982; Edwards et al. 1982; Sabet 1991; Horne 1995; Kutasov 1999). Due to the similarity in Darcy’s and Fourier’s laws the same differential diffusivity equation describes the transient fl ow of incompressible fl uid in porous medium and heat conduction in solids. As a result, a correspondence exists between the following parameters: volumetric fl ow rate, pressure gradient, mobility, hydraulic diffusivity coeffi cient and heat fl ow rate, temperature gradient, thermal conductivity and thermal diffusivity. Thus, it is reasonable to assume that similar to the techniques and data processing procedures of pressure well tests can be applied to temperature well tests (Muskat 1946; Carslaw and Jaeger 1959). However, as it will be shown below, this approach can be used only in some cases (large dimensionless times). Generally the mathematical model of pressure well tests is based on presentation of the borehole as an infi nite long linear source with a constant fl uid fl ow rate in an infi nite-acting
homogeneous reservoir. For this case the well-known solution of the differential diffusivity equation is expressed through the exponential integral (Carslaw and Jaeger 1959). At temperature well testing the borehole (or the cylindrical heater) cannot be considered as an infi nite long linear source of heat. This is due to low values of thermal diffusivity of formations (in comparison with the hydraulic diffusivity) and corresponding low values of dimensionless time. As was shown in (Kutasov 2003) the convergence of solutions of the diffusivity equation for cylindrical and linear sources occurs at dimensionless time of about 1000.
