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Highlights • Impact of positive porosity-conductivity correlation on probabilistic risk analysis. • Relevance of including porosity variability depends on the metric of interest, the control plane-source distance and the level of conductivity heterogeneity. • A heterogeneous porosity field leads to a reduction of the increased lifetime cancer risk uncertainty. Abstract Heterogeneities in natural porous formations, mainly manifested through the hydraulic conductivity (K) and, to a lesser degree, the porosity (ϕ), largely control subsurface flow and solute transport. The influence of the heterogeneous structure of K on transport processes has been widely studied, whereas less attention is dedicated to the joint heterogeneity of conductivity and porosity fields. Our study employs Monte Carlo simulations to investigate the coupled effect of K − ϕ spatial variability on the transport behavior (and uncertainty) of conservative and reactive plumes within a 3D aquifer domain. We explore multiple scenarios, characterized by different levels of heterogeneity of the geological properties, and compare the computational results from the joint K − ϕ heterogeneous system with the results originating from generally adopted constant ϕ conditions. In our study, the spatially variable K − ϕ fields are positively correlated. We statistically analyze key Environmental Performance Metrics: first arrival times and peak mass fluxes for non-reactive species and increased lifetime cancer risk for reactive chlorinated solvents. The conservative transport simulations show that considering coupled K − ϕ fields decreases the plume dispersion, increases both the first arrival times of solutes and the peak mass fluxes at the observation planes. A positive correlation between aquifer connectivity and peak mass fluxes is identified for both homogeneous and heterogeneous ϕ. Our conservative transport results indicate that the relevance of ϕ variability can depend on the metric of interest, the control plane-source distance as well as the level of heterogeneity of the conductivity field. The analysis on reactive transport shows that ϕ variability only slightly affects the mean increased lifetime cancer risk at the control planes but leads to a considerable reduction of the cancer risk uncertainty. We also see that the sensitivity of cancer risk towards ϕ heterogeneity can be influenced by the level of variability of the conductivity field, the source-to-control plane distance, but is not affected by the manner in which the contaminant concentration is computed. [ABSTRACT FROM AUTHOR]

• Log-conductivity (Y) is modeled as a generalized sub-Gaussian (GSG) field. • Average longitudinal spreading is smaller for GSG than for Gaussian Y fields. • Plume stretching in GSG fields is enhanced with respect to Gaussian fields. • Local dispersion masks identification of impacts of non-Gaussianity on transport. • The GSG nature of Y can be difficult to identify relying only on transport metrics. There are increasing evidences that probability distributions and associated statistical moments of a variety of hydrogeological and soil science variables and their spatial increments display distinctive scale-dependent features that are not captured by a typical Gaussian model. A Generalized Sub-Gaussian (GSG) model is able to capture key aspects of this pattern. We present the results of a suite of computational analyses set in a Monte Carlo framework and aimed at assessing the impact of a GSG structure of log hydraulic conductivity (Y) on transport of a conservative solute through a three-dimensional bounded porous medium under steady-state saturated Darcy flow. Our results indicate that the longitudinal spreading of a plume is on average significantly smaller for Sub-Gaussian than for Gaussian Y fields. Otherwise, the velocity field arising from a Sub-Gaussian Y field induces enhanced plume stretching with respect to what can be observed in a Gaussian Y setting, this aspect potentially influencing the strength of solute mixing within these two types of conductivity domains. We also find that, in some cases, it may be difficult to identify the nature of the underlying conductivity field relying solely on observations of solute concentrations migrating within the system. In this regard, we show that the action of local dispersion tends to mask the influence of Sub-Gaussianity on major transport metrics. [ABSTRACT FROM AUTHOR]

• Hyporheic mixing (inherit ensemble average concepts) is a scale-dependent phenomenon. • Flux variance at different scales is a proper metric to assess the hyporheic mixing. • Stream velocity, groundwater are the most dominant factors for hyporheic mixing. Hyporheic mixing plays a vital role in physical, biogeochemical, and thermal processes in river networks. While many studies have emphasized the role of streambed heterogeneity in hyporheic mixing processes, this study articulates the scale issues inherent in concentration, mixing, heterogeneity, and modeling approaches. It subsequently conducted simulations of hyporheic mixing in synthetic, heterogeneous, 2-D cross-sectional river beds based on prescribed hydraulic conductivity defined at the local-scale. It then investigated the flux variation distribution and the mixing zone under different degrees of heterogeneity and flow scenarios. Since the characterization of the heterogeneities in detail at the local scale is practically impossible, Monte Carlo simulation based on stochastic theory was used to demonstrate the hyporheic mixing under the large-scale control volume (macromixing). Afterward, a first-order stochastic analysis was undertaken to explore the relationship between local-scale flux variance distribution and the mixing zone under different heterogeneity and flow scenarios. The results of this study show that the flux variance in the streambed is an appropriate metric for assessing the magnitude of hyporheic mixing at all scales. Further, surface water velocity and upwelling groundwater are found to be the dominant controlling factors of the flux variance and in turn, the mixing process, followed by the streambed heterogeneity. In addition, it demonstrates that the hyporheic mixing process is significantly affected by the complex surface and groundwater circulation regimes and the stagnation zone under steady-state flow conditions. [ABSTRACT FROM AUTHOR]

• Classical aquitard drainage model COMPAC utilized for a heterogeneous aquitard. • Geostatistical model used to deal with aquitard heterogeneity. • To interpret the heterogeneity from multi-extensometer data. • Comparison between geostatistical and geological models in fitting observation data. • Both synthetic and field application cases implemented. The classical aquitard drainage model COMPAC was used to simulate the deformation of a one-dimensional vertically heterogeneous aquitard (i.e. Heter-COMPAC). By coupling Heter-COMPAC with the quasi-linear geostatistical inversion approach, the vertical heterogeneities of hydraulic conductivity (K v), elastic specific storage (S ske ) and inelastic specific storage (S skp ) fields could be characterized with the availability of long-term multi-extensometer data. The methodology was first tested through a group of ten synthetic cases with randomly generated K v , S ske and S skp fields. Results of the synthetic cases revealed that a geostatistical model could characterize the variability of aquitard hydraulic parameter fields, and yields improved fits of simulated versus observed zone deformation than a geological model that treats each zone to be homogeneous. Subsequently, the methodology was applied to a research site situated in Changzhou city, Jiangsu Province, China, where long-term deformation behaviors of the strata within the aquifer-aquitard system have been monitored. Vertical heterogeneities of K v , S ske and S skp fields of the investigated aquitard at the site were characterized using the quasi-linear geostatistical approach. The correlation length of the three fields that yielded the best-quality fit was assessed to be approximately 50 m, and the fitting quality was slightly improved in comparison with that produced from calibrating a geological or zonation model. Through Monte Carlo analysis of aquitard deformation utilizing the inversed parameters and corresponding uncertainties, the investigated aquitard is estimated to have compacted −914.8 ± (42.6) mm before the rise in groundwater levels in adjoining aquifers. [ABSTRACT FROM AUTHOR]