Flow of variable-density formation water in deep sloping aquifers: minimizing the error in representation and analysis when using hydraulic-head distributions

Although not fully adequate, freshwater hydraulic heads have been used historically to represent and analyze variable-density flow in sloping aquifers in sedimentary basins. The use of environmental heads is valid only for strictly vertical flow in unconfined aquifers, while using variable-density hydraulic heads contravenes Darcyʹs law. Although the use of hydraulic-head surfaces is the simplest and quickest means of flow analysis and interpretation, preceding other methods such as numerical modeling, it introduces some errors that should be assessed and minimized in order to provide the most accurate flow representation. A first error is introduced when approximating the potential and buoyancy components along aquifer slope of the flow-driving force with their projections onto the horizontal plane. This error is most probably negligibly small for sloping aquifers in undisturbed sedimentary basins, but may be significant for aquifers dipping at a significant angle, such as in folded strata. A second error is introduced when using only hydraulic heads in the representation and analysis, and neglecting the buoyancy component of the flow-driving force. The significance of this error can be assessed by performing a Driving Force Ratio (DFR) analysis. There is no single or critical value of the DFR, below which the error in using hydraulic heads alone is negligible, and above which it is not acceptable anymore; rather, the decision regarding the error acceptability should and can be made on a case by case basis. The DFR, hence the errors in flow direction and magnitude, can be minimized for any given aquifer by using an optimum reference density in hydraulic-head calculations that is the areally-weighted average density of formation water in that aquifer. In flow analyses based on potentiometric surfaces, the use of freshwater as the reference density actually maximizes the errors introduced by the neglect of the buoyancy component of the flow-driving force because it is either at the low end of the density-variation spectrum or outside it.