Reactive solute transport in flow between a recharging and a pumping well in a heterogeneous aquifer

Steady flow between a fully penetrating recharging and pumping well (doublet) takes place in a heterogeneous aquifer. The spatially variable hydraulic conductivity is modeled as a lognormal stationary random function, of anisotropic two-point covariance. The latter is characterized by the horizontal and vertical integral scales I and I(v), respectively. A tracer, or a reactive solute obeying first-order kinetics, is injected as a pulse or continuously in the recharging well. Our aim is to determine the flux-averaged concentration (the breakthrough curve) in the pumping well as a function of time and of the various parameters of the problem, i.e., σ(Y)/² (the logconductivity variance), l' = l/I (l is the distance between wells), and e = I(v)/I (the anisotropy ratio). A simple solution of this difficult problem is achieved by adopting a few simplifying assumptions: (1) the wells are fully penetrating, of length much larger than I(v) and of radius r(w) much smaller than I, (2) a first-order solution in σ(Y)/² of the flow and transport equations is sought, (3) the anisotropy ratio is small, say e < 0.2, and (4) neglect of the effect of pore-scale dispersion. After determining the travel time τ mean and variance, the mean flux-averaged concentration is found by assuming that τ is lognormal. In a homogeneous medium there is a large spreading of the solute signal in the pumping well owing to the variation of the travel time among the streamlines connecting the two wells. The effect of heterogeneity is similar to that of pore-scale dispersion; that is, it leads to enhanced spreading and in particular to an early breakthrough. The solution has potential applications to aquifer tests and to evaluation of efficiency of remediation schemes and may serve as a benchmark for numerical models.