Thermal Modelling of Fluid Flow Effects In Thin-Dipping Aquifers

Abstract

Permeable structures such as aquifers or fault zones can focus the ground-water flow system and transfer heat by convection across the surrounding rocks where conduction dominates. In this paper, we describe a simple method to calculate both the steady- and transient-state temperature disturbance related to such a circulation. In the 2-D (x-z) model used, the flow is described by its flow rate q, the geometry of the channel [depth h(x)] and its thickness. Assuming that the horizontal conduction can be neglected, a semi-analytical solution is obtained when the temperature disturbance is described as a function of the Peclet number α=q(ρc)ƒ/λ − (ρc))ƒ is the heat capacity of the fluid and λ the conductivity of surrounding rocks-and of the slope of the channel ϕ and of the time since the flow duration. the case of an upward flow along a dipping channel is considered in detail but more complex cases with a channel composed of segments can be handled easily. The validity of the assumption of no horizontal conduction is carefully discussed by comparing to a numerical solution where both vertical and horizontal conductions are taken into account. For a value of slope which does not exceed 30°, the analytical solution gives quite acceptable results. Finally, we propose simple rules for estimating the transient and steady-state temperature disturbance generated by a given fluid flow.