  Transport in biological systems often occurs in complex spatial environments
involving random structures. Motivated by such applications, we investigate an
idealised model for solute transport past an array of point sinks, randomly
distributed along a line, which remove solute via first-order kinetics. Random
sink locations give rise to long-range spatial correlations in the solute field
and influence the mean concentration. We present a non-standard approach to
evaluating these features based on rationally approximating integrals of a
suitable Green's function, which accommodates contributions varying on short
and long lengthscales and has deterministic and stochastic components. We
refine the results of classical two-scale methods for a periodic sink array
(giving more accurate higher-order corrections with non-local contributions)
and find explicit predictions for the fluctuations in concentration and
disorder-induced corrections to the mean for both weakly and strongly
disordered sink locations. Our predictions are validated across a large region
of parameter space.
