Equilibration times of gas-filled diffusion samplers in slow-moving ground water systems

The installation of gas-filled diffusion samplers into small-diameter boreholes results in a significant reduction of the dissolved gas concentration around the sampler. In aquifers where the diffusive flux of solutes outpaces advective transport, the process that governs the equilibration time of a sampler is the resupply of solutes by diffusion from the aquifer. We have derived a solution that can be used to estimate the time required for a diffusion sampler to reach equilibrium with the dissolved gas concentration in the aquifer, where diffusion is the only solute transport mechanism. Thus the solutions provide equilibration times for cells placed in aquifers where diffusion dominates and maximum equilibration times for cells placed in aquifers where advection can also resupply solutes. The solutions are generic and are functions of nondimensionalized variables, therefore providing estimates of equilibration times for any type of solute, sampler volume, bore dimensions, and aquifer porosity. Examples are given for various sized gas-filled helium samplers placed in boreholes of different radii.