Flow equations in terms of piezometer levels for nonisothermal fluid in low-permeability porous medium

The Basalt Waste Isolation Project is investigating deep basalt flows for the disposal of high‐level nuclear wastes. The time spans of interest are so long that site performance must be projected by mathematical modeling. At great depths, velocity potentials determined simply by using the gradients of piezometric levels (i.e., neglecting the temperature dependence) may cause some errors. In this paper, flow equations are written in terms of the piezometric level as the dependent variable, so that model input and output are in terms of directly measured field data. For nonisothermal flow, a nonlinear governing equation is obtained. Under certain assumptions on the functional representation of fluid density, a scalar potential can be defined. A simple example is presented to demonstrate the methodology to obtain such a potential. Improvement in calculating the downhole pressures from water level data is also discussed.