A Model for the Transient Temperature Effects of Horizontal Fluid Flow in Geothermal Systems

Ziagos, J.P. and Blackwell, D.D., 1986. A model for the transient temperature effects of horizontal fluid flow in geothermal systems. J. Volcanol. Geotherm. Res., 27: 371-397. A characteristic temperature versus depth (T-D) profile is observed in various geothermal environments. Particular features of the T-D profile can be explained in terms of a simple time-dependent two-dimensional (x, z) hydrothermal model. In this model a hot fluid is constrained to flow along a thin aquifer buried at a depth l from the surface with conductive heat transfer into the rocks both above and below the aquifer. In many geothermal systems transient changes in the flow patterns occur whose thermal effects can be described in terms of this model. The mathematical representation is that of a layer of thickness l over a half-space with specified temperature on the surface and variable temperature along the interface. An approximate analytical solution is derived using the Laplace transform solution technique and compared to a numerical Fourier transform solution. This approximate analytical solution is computationally simple and can be expressed in terms of key parameters of the fluid flow system. These key parameters are useful in understanding and exploring the sometimes complex hydrology of geothermal systems. Because of the simple computational form, the solution is easily implemented in an inverse solution scheme. Two T-D profiles, one from the Oregon Cascade Range and one from Arizona, are forward and inverse modeled, respectively. Fluid flow, velocity, time since initiation of flow, and background gradient are estimated parameters.