Scaling thermal effects in radial flow

Abstract

To adequately evaluate the environmental impact of siting nuclear waste repositories in basalt aquicludes, it is essential to know the effects on parameter identification algorithms of thermal gradients that exist in these basaltic aquicludes. Temperatures of approximately 60°C and pressures of approximately 150 atm can be expected at potential repository sites located at depths of approximately 1000 m. The phenomenon of over-recovery has been observed in some pumping tests conducted at the Hanford Nuclear Reservation located in the Pasco Basin adjacent to the Columbia River in the state of Washington, USA. This over-recovery phenomenon may possibly be due to variations in the fluid density caused by thermal gradients. To assess the potential effects of these thermal gradients on indirect parameter identification algorithms, a systematic scaling of the governing field equations is required in order to obtain dimensionless equations based on the principle of similarity. The constitutive relationships for the specific weight of the fluid and for the porosity of the aquiclude are shown to be exponentially dependent on the pressure gradient. The dynamic pressure is converted to the piezometric head and the flow equation for the piezometric head is then scaled in radial coordinates. Order-of-magnitude estimates are made for all variables in unsteady flow for a typical well test in a basaltic aquiclude. Retaining all nonlinear terms, the parametric dependency of the flow equation on the classical dimensionless thermal and hydraulic parameters is demonstrated. These classical parameters include the Batchelor, Fourier, Froude, Grashof, and Reynolds Numbers associated with thermal flows. The flow equation is linearized from order-of-magnitude estimates based on these classical parameters for application in parameter identification algorithms.