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

Abstract

Abstract. 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 Iv 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 tim, e and of the various parameters of the problem, i.e., o-• (the logconductivity variance), l = l/I (l is the distance between wells), and e = IvI (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 vand of radius r w much smaller than I, (2) a first-order solution in o-• 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, mean and variance, the mean flux-averaged concentration is found by assuming that, 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. IntroductionWe consider steady aquifer flow between a recharging well and a pumping one (briefly a doublet, Figure 1), operating under a constant head difference. A solute is injected either for a short period (pulse) or continuously in the recharging well, and the concentration is monitored in the pumping one. Such a configuration is quite common in many applications, for example, as a testing method to determine aquifer properties or in remediation schemes. Therefore it is of interest to model the flow and transport for this type of application. The simplest case is that of a homogeneous formation, which was investigated in the past. Thus, in the recent work of Koplik et al. [1994], the problem is solved for transport of a tracer by advection and by pore-scale dispersion. For the high Peclet numbers characterizing natural formations, the spread of the pulse in the pumping well is dominated by the advective effect. This large effect is due to the nonuniformity of the flow, resulting in differences in the travel times along the streamlines connecting the two wells, the quickest and slowest paths being the ones in the wells plane [Kurowski et al., 1994]. With neglect of pore-scale dispersion, the transport problem can be solved In reality, natur...

On the use of peak concentration arrival times for the inference of hydrogeological parameters

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“…[67] When evaluated at the extraction well (h = 1/2), equations (C10) and (C11) reduce to the expressions (32) for the central streamline q = 0 and (33) given by Dagan and Indelman [1999].…”

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Macrodispersivity for transport in arbitrary nonuniform flow fields: Asymptotic and preasymptotic results

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