## 1. Introduction

[2] The Stanford-Waterloo (SW) experiment [*Mackay et al.*, 1986b; *Roberts et al.*, 1986] is one of a few well-characterized reactive solute transport field experiments that exist against which to test and develop our conceptual understanding of reactive contaminant transport [e.g., *Freyberg*, 1986; *Roberts et al.*, 1986a; *Sudicky*, 1986; *Goltz and Roberts*, 1988; *Rajaram and Gelhar*, 1991; *Quinodoz and Valocchi*, 1993; *Miralles-Wilhelm and Gelhar*, 1996; *Brusseau and Srivastava*, 1997; *Cushey and Rubin*, 1997]. In the SW experiment, conducted in the early 1980s, dissolved apolar organic solutes were injected below the water table as a pulse, creating a small plume within the unconfined sandy aquifer. Their concentrations were monitored in three dimensions relative to nonreactive chloride and bromide tracers over a period of approximately two years. A subset of the organic solutes were naturally transformed during the experiment. Perchloroethylene (PCE) and carbon tetrachloride (CT) were the persistent organic compounds. Of these two, PCE was the most retarded. The sorbing organic solute plumes exhibited two unexpected transport behaviors [*Roberts et al.*, 1986]: (1) the solute plumes decelerated with travel distance (apparent retardation factors increased) [*Roberts et al.*, 1986] exhibiting what has been termed a “macrokinetic” behavior [*Miralles-Wilhelm and Gelhar*, 1996]; and (2) the longitudinal spreading of the sorbing organic solutes was greater than for the nonreactive solutes at the same travel distance.

[3] Some uncertainty in the quantification of SW plume spreading has been expressed, for example because of incomplete plume capture for some compounds at some sampling events and because of the limitations inherent in the sampling and interpolation of heterogeneous concentrations [*Miralles-Wilhelm and Gelhar*, 1996; *Ball et al.*, 1997]. Solute spreading was estimated originally using two-dimensional depth-integrated data [*Freyberg*, 1986; *Roberts and Mackay*, 1986] and, more recently, using a fully three dimensional process [*Rajaram and Gelhar*, 1991; *Miralles-Wilhelm*, 1993; *Miralles-Wilhelm and Gelhar*, 1996]. Despite the uncertainties, both methods determined that the longitudinal organic solute spreading was greater than that of the conservative tracers at the same travel distance for distances greater than ∼5 m: by a factor of three in the two-dimensional analysis [*Brusseau and Srivastava*, 1997], and a factor between two and three for the nondegraded solutes (CT and PCE) in the three-dimensional analyses (i.e., compare longitudinal spreading presented by *Miralles-Wilhelm* [1993] for CT and PCE to that computed by *Rajaram and Gelhar* [1991] for the conservative tracer at the same distance). Importantly, the trends described for the first and second spatial moments above were: exhibited by both PCE and CT; identified by both methods of analysis; and exhibited for combinations of sampling date and compound that were deemed ‘reliable’ (complete plume capture) by *Miralles-Wilhelm and Gelhar* [1996] in their critical reevaluation of plume sampling completeness. Therefore, although the value of the increase in spreading for the sorbing solutes appears to differ between studies, the trend cannot be refuted.

[4] Laboratory studies have shown that sorption is rate limited at the grain scale; a process that can be simulated by intragranular diffusion [*Ball and Roberts*, 1991b]. Batch-measured sorption rates have been used successfully to predict transport in dynamic laboratory column experiments [*Young and Ball*, 1994]. However, several plume simulation studies have concluded that the macrokinetic behavior of the organic solutes in the field cannot be caused by the observed grain-scale rate-limited sorption alone [*Goltz and Roberts*, 1988; *Quinodoz and Valocchi*, 1993; *Miralles-Wilhelm and Gelhar*, 1996; *Brusseau and Srivastava*, 1997; *Ball et al.*, 1998; *Cushey and Rubin*, 1998].

[5] The importance of published Borden (or Borden-like) permeability heterogeneity [*Sudicky*, 1986; *Woodbury and Sudicky*, 1991] has been explored extensively. For example, *Cushey and Rubin* [1997] successfully matched measured with modeled plume behavior through simulation of transport with a heterogeneous permeability field combined with rate-limited sorption. However, their simulations did not incorporate sorption heterogeneity. Several studies have explored the effects of assumed correlation between the ln *k* and ln *K*_{d} in addition to heterogeneous ln *k* [*Quinodoz and Valocchi*, 1993; *Burr et al.*, 1994; *Miralles-Wilhelm and Gelhar*, 1996; *Brusseau and Srivastava*, 1997]. *Burr et al.* [1994] demonstrated that correlated ln *k* and ln *K*_{d} in a heterogenous aquifer can result in an apparent increasing (or decreasing) trend in the retardation factor with travel distance despite the fact that sorption was modeled as an instantaneous process. They and others [*Brusseau and Srivastava*, 1997; *Cushey and Rubin*, 1997] highlight the importance of ergodicity by showing that single realizations of heterogeneous ln *k* and ln *K*_{d} fields reproduced the SW plume deceleration when the contaminant was “injected” into a relatively low *K*_{d} zone in the simulation. However, *Brusseau and Srivastava* [1997] demonstrated that such a simulation cannot also match the second moment in the same realization unless a spatial trend in the *K*_{d} field is also assumed. (They assumed an increase in PCE *K*_{d} from 0.47 mL/g at the injection point to 0.79 mL/g at a distance of 10.5 m, the approximate travel distance experienced by the PCE plume center of mass in the field experiment.)

[6] There are two unproven assumptions about the aquifer underlying the simulations described above: (1) the studies that incorporated heterogeneity in the ln *K*_{d} field assumed that ln *K*_{d} is negatively correlated to ln *k* [*Burr et al.*, 1994; *Miralles-Wilhelm and Gelhar*, 1996; *Brusseau and Srivastava*, 1997]; and (2) a horizontal spatial trend in *K*_{d} is assumed [*Brusseau and Srivastava*, 1997]. The simulations showed that plume spreading is very sensitive to the spatial correlation between ln *k* and ln *K*_{d}, but because the spatial distribution of ln *K*_{d} for an organic solute in the Borden aquifer and its correlation to ln *k* were not known, these studies by necessity assumed spatial distributions for ln *K*_{d}. Assuming a negative correlation between the two attributes also results in an ln *K*_{d} field that has the same spatial statistical properties as the ln *k* field, a feature which also has not been demonstrated.

[7] The rationale supplied for assuming a negative ln *k*-ln *K*_{d} correlation was either the work of *Robin et al.* [1991], who observed a weak negative correlation between ln *k* and the Sr^{2+} ln *K*_{d} in the Borden aquifer, and/or theoretical arguments that assume greater surface area with smaller grain size [*Burr et al.*, 1994; *Miralles-Wilhelm and Gelhar*, 1996; *Brusseau and Srivastava*, 1997]. However, apolar organic solute sorption is controlled primarily by interactions with carbonaceous matter (noncarbonate, carbon containing material) [*Allen-King et al.*, 2002, and references reviewed therein] and not interactions with charged mineral surfaces in saturated (water wet) sediments in which organic mineral interactions are weak [*Schwarzenbach et al.*, 2003]. While carbonaceous matter content can be greater for more fine-grained sediment, it is not necessarily so. Therefore the expectation that the PCE *K*_{d} should be negatively correlated to grain size or behave similarly to a cation sorption behavior (Sr^{2+}) is not supported by geochemical principles. In fact, there exists evidence to the contrary for the Borden aquifer. *Ball and Roberts* [1991a] observed a positive trend between the PCE *K*_{d} and grain size for fine to very coarse sand size grains sieved from the Borden aquifer (location in Figure 1). More specifically, *Allen-King et al.* [1998] observed a weak positive correlation between ln PCE *K*_{d} and ln *k* (estimated by correlation to grain size) for high-resolution subsamples taken from a single core in the Borden aquifer. For the same data set, these workers [*Allen-King et al.*, 1998] also report that the vertical integral scale of ln *k* is larger (7 cm) than the value determined for ln *K*_{d} (5.2 cm). These studies [*Ball and Roberts*, 1991a; *Allen-King et al.*, 1998] imply that the negative correlation assumed in previous simulation studies is incorrect and suggest that the geostatistics that describe ln *K*_{d} may not be the same as those describing ln *k*. However, these studies provide a limited data set from which to draw insights on vertical ln *K*_{d} variability and no information on the horizontal geostatistical properties of ln *K*_{d}.

[8] Assumption (2), that there is a positive horizontal trend in *K*_{d} with travel distance, is related but not identical to the finding of importance of ergodicity on plume transport. *Brusseau and Srivastava* [1997] derive support for this assumption by reinterpreting *Durant*'s [1986] depth-integrated core sample data from the approximate centerline of the initial 12 m of SW plume travel. In these data they [*Brusseau and Srivastava*, 1997, p. 128] identify a trend of increasing *K*_{d} that is “of sufficient magnitude to potentially influence the transport of the organic solutes.” Later work by *Ball and Roberts* [1991b] showed that the time required for Borden sand grains of various sizes to equilibrate ranges from days to months, thus equilibrium can require much longer than the 3 day contact time used by *Durant* [1986]. Therefore the apparent variability between core samples reported by Durant includes differences in the *K*_{d} that would have been measured at equilibrium and the degree to which these data represent nonequilibrium. Because the latter is not known, a significant aquifer trend in *K*_{d} cannot be supported by *Durant*'s [1986] data.

[9] Finally, the decomposition of HCA to PCE during the SW experiment [*Curtis*, 1991] also contributed to the apparent PCE spreading in the experiment. *Ball et al.* [1997] used a one-dimensional homogenous approximation of the aquifer incorporating field-derived sorption mass transfer rates (greater than the laboratory-observed values) to show that HCA decomposition contributed very modestly to the zeroth and first PCE plume moments. This result arises from the relatively rapid half-life of HCA transformation, estimated as 40 days [*Ball et al.*, 1997]. During 40 days, the PCE plume would have traveled a distance less than the initial pulse width of the experiment. However, because HCA is more retarded than PCE [*Mackay et al.*, 1986a; *Roberts et al.*, 1986], decomposition of the remaining HCA contributed to apparent tailing in the PCE plume [*Ball et al.*, 1997]. This process has not been incorporated into quantitative simulations of the PCE plume that also model aquifer heterogeneity.

[10] Because the assumptions about the ln *K*_{d} field required to simulate both the first and second moments of the field experiment accurately are not supported by available observations, the conclusions concerning the importance of various processes on plume transport are also drawn into question. This situation highlights a significant knowledge gap and underscores a need for more complete information about the chemical property heterogeneity of the reference Borden aquifer. Aquifer attributes differing from those assumed will produce different plume transport effects. For example, a positive ln *k*-ln *K*_{d} correlation diminishes spreading for sorbing compared to nonreactive tracers [*Bosma et al.*, 1993; *Rabideau and Miller*, 1994], opposite the result observed in the SW experiment. Additionally, imperfect correlation diminishes spreading to a greater extent than perfect positive correlation [*Bellin and Rinaldo*, 1995]. Therefore understanding of plume spreading processes must include accurate representation of the heterogeneity of ln *K*_{d} and its correlation to ln *k*.

[11] The goal of this study was to examine the natural distributions of reactive transport properties, *K*_{d} and *k*, for PCE in the Borden aquifer. Specific tasks in our study were to characterize and model the univariate distribution of values for PCE ln *K*_{d}, the regression-based correlation between PCE ln *K*_{d} and ln *k*, and the two-point bivariate autocorrelation and cross correlation of the PCE ln *K*_{d} and ln *k* in the Borden aquifer. For expediency, the *k* values were determined using air permeametry. Our samples were purposefully collected adjacent to the location of the SW experiment (Figure 1) to facilitate consideration of the potential impact of our findings on its interpretation.