Search

• Conductivity is employed in flow models upon averaged Monte Carlo fields. • A Monte Carlo volume of 10 % of that required for full numerical stability. • A 10 % volume returns stable outputs, i.e. heads and residuals at wells' locations. The knowledge of aquifer systems, their geological setting, their structure, and subsequent modeling is highly uncertain and is usually faced through Monte Carlo-based methods in hydrogeology. One of the most important uncertainty sources for groundwater models is represented by input hydraulic conductivities, related to the aquifer's structure. There are no specific rules when simulating hydraulic conductivity fields within Monte Carlo frameworks to instruct numerical models, and information about employed conductivity fields and their numerical convergence is often not given. This technical work aims to fill this gap by investigating the impact of employing conductivity information upon different volumes of Monte Carlo simulations applied to a real case study. Thus, this work estimates the minimum volumes of Monte Carlo hydraulic conductivity fields to be employed in groundwater flow models for achieving numerically stable (i) boundary conditions, (ii) global model performances, and (iii) local ones such as simulated hydraulic heads. The present results aim to be indicative of similar hydrogeological settings and will serve as a basis for more complex ones and for investigating transport problems. [ABSTRACT FROM AUTHOR]

• First hydrogeological model established for URL site of HLW disposal in China. • The effect of the hydraulic influence zones of faults is incorporated in the numerical model. • Different variations in the horizontal and vertical directions of hydraulic conductivity are considered. • A total of 120 stochastic parameterized models are presented. • Hydraulic conductivity < 10−9 m/s at high-level radioactive waste disposal depth. Deep geological disposal is internationally accepted as a feasible and safe approach for high-level radioactive waste (HLW) disposal. To evaluate hydrogeological conditions in support of safety assessments for HLW disposal at the Xinchang preselected site in China, stochastic inverse models of site-scale groundwater flow were developed in this study to generate highly parameterized hydraulic conductivity fields for the fractured medium by adopting pilot point and null-space Monte Carlo methods. The hydraulic influence zones of the faults were carefully considered to have homogenous parameter values across the zones. A total of 120 multiple random realizations were generated to characterize the 3D spatial variations in hydraulic conductivity by conditioning to 1218 fixed pilot points. The simulated hydraulic heads of the realizations were in good agreement with observational data. The hydraulic conductivity fields close to the boreholes could be characterized in detail and had relatively low uncertainties. Furthermore, the hydraulic conductivity (K) values around underground research laboratory (URL) at the HLW disposal zone depth were less than 10−9 m/s. The K values obtained for most of the influence zones of these faults at this depth were consistent with hydraulic test data and ranged from 10−10 to 10−9 m/s, thereby indicating that the surrounding rock has low permeability and is suitable for HLW disposal. These findings offer new insights into hydrogeological conditions by providing key information on the permeability characteristics that need further focus on HLW disposal. [ABSTRACT FROM AUTHOR]

Summary In this work, we design a series of benchmark problems for subsurface flow uncertainty quantification. Three basic subsurface flow problems with increasing complexity are selected, which are steady state groundwater flow, groundwater contamination, and multi-phase flow. For the steady state groundwater flow, hydraulic conductivity is assumed to be uncertain, and the uncertain model parameter is assumed to be Gaussian random constant, Gaussian random field, and facies field, respectively. For the other two flow problems, the uncertain model parameter is assumed to be Gaussian random field and facies field, respectively. The statistical property of the uncertain model parameter is specified for each problem. The Monte Carlo (MC) method is used to obtain the benchmark results. The results include the first two statistical moments and the probability density function of the quantities of interest. To verify the MC results, we test the convergence of the results and the reliability of the sampling algorithm. For any existing and newly developed uncertainty quantification methods, which are not (fully) verified, the designed benchmark problems in this work can facilitate the verification process of those methods. For illustration, in this work, we provide a verification of the probabilistic collocation method using the benchmark results. [ABSTRACT FROM AUTHOR]

Summary: Multi-scale heterogeneity of geological formations is a rule, which consists of random (local-scale) and systematic (large-scale) variability of hydraulic conductivity. The random variability and depth–decaying trend, a systematic variability, have different effects on subsurface flow, thus on groundwater discharge into tunnels. Little research has examined this problem in the past. Using Monte Carlo simulation and information of statistics of heterogeneity, we evaluate the most likely (ensemble average) discharge rate into a tunnel in geologic media with the multi-scale heterogeneity and uncertainty associated with this estimate. We find that the ensemble average discharge rate is larger than the discharge rate predicted by geometric mean of hydraulic conductivity, and smaller than the discharge rate predicted by arithmetic mean of hydraulic conductivity. Moreover, the ensemble average discharge rate decreases with the decay exponent of the depth–decaying trend, and increases with the standard deviation as well as the correlation scale of the stationary log-conductivity fields. We also find that the discharge rate of a tunnel is highly influenced by the hydraulic conductivity near the tunnel. Furthermore, deviation of the true discharge rate from the ensemble average can be large and increases with the decay exponent, standard deviation and correlation scale of log-conductivity fields. The largest uncertainty of discharge rate prediction in the shallow subsurface is controlled by the variability of conductivity fields and the uncertainty at the deep subsurface is by the depth–decaying trend of hydraulic conductivity. Therefore, accurate prediction of groundwater discharge into tunnels requires detailed characterization of multi-scale heterogeneity. [Copyright &y& Elsevier]

• 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]

• Variations in the support/observation scale of hydraulic conductivity induce changes in the information content of the associated Darcy fluxes. • Propagation of information about conductivity onto Darcy flux through the flow and mass balance equation can be quantified via information theory. • Flux data at large scales provide more information about fluxes at small scales than what can be observed with reference to conductivities. We rest on an Information Theory perspective and assess (i) the average information content and (i) the information shared between Darcy flux fields associated with fields of hydraulic conductivity (K) characterized by differing support (or measurement) scale. We treat hydraulic conductivity as a spatial random field, characterized by a given distribution and correlation structure. The latter is modeled through a truncated power law variogram (TPV), which explicitly takes into account a characteristic length scale of the support volume of K through a lower cutoff scale. We then frame our study in a numerical Monte Carlo context where groundwater flow is evaluated across a collection of realizations of hydraulic conductivity characterized by different values of the TPV parameters and subject to uniform in the mean flow. We quantify information through the Shannon entropy of the probability mass functions of the Darcy flux components as well as the mutual information and the multivariate mutual information respectively shared by pairs and triplets of Darcy flux components related to hydraulic conductivity fields evaluated at diverse scales and associated with various levels of heterogeneity. Partitioning of multivariate mutual information according to unique, redundant and synergetic contributions is also quantified. We found consistent trends (i) in the variation of the average information content with respect to the size of lower cutoff scale and (ii) in the way information is shared between pairs and triplets of Darcy flux components associated with diverse support scales of the underlying conductivities. [ABSTRACT FROM AUTHOR]