Semi-analytical Solution for Brine Leakage Through Passive Abandoned Wells Taking Account of Brine Density Differences

Abstract

Both $\hbox {CO}_{2}$ storage and disposal of waste fluid (e.g., co-produced brine) in deep saline aquifers of sedimentary basins create large scale over-pressurization and tend to displace brine upwards if a vertical connection (e.g., an abandoned well) is present. This raises groundwater pollution issues of brine intrusion into shallower potable water aquifers. When saline brine from the deep aquifer is displaced upwards it lifts and replaces the a priori less saline, less dense water initially filling the connection, resulting in a weight increase that counters leakage. This article presents and explains an innovative semi-analytical solution to this problem of leakage between two aquifers connected by a passive well (represented by a porous column and/or an open wellbore) taking account of the effect of the density difference between lifting and lifted brines during both upward and downward flow. It is based on the linearization of brine density profiles against depth and on two improvements made to the approximate evaluation of convolution products introduced in Nordbotten et al. (Water Resour Res 40:W04204, 2004) for calculation of the pressurization induced by transient flows in open aquifers. The comparison with numerical simulations shows good agreement of results. Since the solution uses time discretization but no spatial grid, computation time is reduced by 3–4 orders of magnitude compared to numerical resolution. It does, however, require considering homogeneous aquifers of constant thickness and brine properties.