  We investigate the transport of a solute past isolated sinks in a bounded
domain when advection is dominant over diffusion, evaluating the effectiveness
of homogenization approximations when sinks are distributed uniformly randomly
in space. Corrections to such approximations can be non-local, non-smooth and
non-Gaussian, depending on the physical parameters (a P\'eclet number Pe,
assumed large, and a Damk\"ohler number Da) and the compactness of the sinks.
In one spatial dimension, solute distributions develop a staircase structure
for large Pe, with corrections being better described with credible intervals
than with traditional moments. In two and three dimensions, solute
distributions are near-singular at each sink (and regularized by sink size),
but their moments can be smooth as a result of ensemble averaging over variable
sink locations. We approximate corrections to a homogenization approximation
using a moment-expansion method, replacing the Green's function by its
free-space form, and test predictions against simulation. We show how, in two
or three dimensions, the leading-order impact of disorder can be captured in a
homogenization approximation for the ensemble mean concentration through a
modification to Da that grows with diminishing sink size.
