Spatial Distribution Of Hydraulic Conductivity Research Articles

Innovative hydrogeophysical approach for detecting the spatial distribution of hydraulic conductivity in Bahri city, Sudan: A comparative study of Csókás and Heigold methods

Hydraulic conductivity is one of the crucial parameters used to identify the potentiality and productivity of groundwater aquifers. This research employs an integrated approach using geophysical well logging, exploratory factor analysis and surface electrical resistivity methods to detect the vertical and horizontal variation of hydraulic conductivity in Bahri city, Sudan. Based on the geophysical well logs of Spontaneous potential (SP), natural gamma ray (GR), and electrical resistivity (RS), Csókás method is used to determine the continuous variation of hydraulic conductivity along the aquifer. Csókás method is an experimentally modified version of the Kozeny–Carman equation and is based on the formation factor of the groundwater aquifer and the effective grain size. This approach is performed in three groundwater boreholes, and the obtained hydraulic conductivities showed a close agreement with that of the pumping test analysis. Furthermore, the hydraulic conductivity is measured using multivariate statistical factor analysis. This statistical approach relies on the correlation between the extracted factors and petrophysical and hydrogeological parameters. In this research, a strong negative linear correlation between the first factor and hydraulic conductivity is indicated. Consequently, a site-specific equation is suggested for continuous estimation of hydraulic conductivity along the aquifer. In the last stage, the results obtained from the Csókás method are interpolated with vertical electrical sounding (VES) measurements using to detect the horizontal variation of hydraulic conductivity throughout the studied area. This was achieved by combining the hydraulic conductivities of geophysical well logging and vertical electrical soundings to obtain a consistent estimation. As a result, the variation of hydraulic conductivity is obtained, and the average was 1.9 m/day which shows a close agreement with the average of the previous investigations (1.5 m/day). This approach is highly recommended since it can enhance data coverage, cutting down the expense of hydrogeological investigations and lowering the uncertainty of the hydrogeological models.

A Short‐Term Pumping Strategy for Hydraulic Tomography Based on the Successive Linear Estimator

AbstractIn this study, the random finite element method, a finite element method with random field generation techniques, was applied to investigate the cross correlations between the observed head and hydraulic conductivity and specific storage at different locations and different times in pumping tests. The results show that the two cross correlations between the pumping well and the observation well reach their maximums before pumping reaches a steady state. Specifically, the cross correlation between the observed head and hydraulic conductivity is the greatest when the temporal derivative of the observed head does not change significantly, and that between the observed head and specific storage is the greatest when the temporal derivative (the rate) of the observed head is maximum. Based on the results of cross‐correlation analysis, a short‐term pumping strategy for hydraulic tomography is proposed to obtain the spatial distribution of hydraulic conductivity and specific storage using the successive linear estimator. Furthermore, this strategy was validated by Monte Carlo simulations. This paper points out that the sensitivity and cross‐correlation analyses report the ensemble (averaged) behaviors of any heterogeneous aquifers, which is not necessarily suitable for one realization. Furthermore, Monte Carlo simulation is suggested for validating any groundwater inverse modeling result.

Mapping conduits in two-dimensional heterogeneous karst aquifers using hydraulic tomography

Hydraulic tomography (HT) is a well-established approach to yield the spatial distribution of hydraulic conductivity of an aquifer. This work explores the potential of HT for the characterization of the distribution and connectivity of conduits in a two-dimensional sandbox and its corresponding synthetic aquifer. Two inversion techniques were implemented and compared: the geostatistics-based inversion which uses the simultaneous successive linear estimator (SimSLE) algorithm to conduct stochastic inversions on the transient hydraulic heads, and the travel time-based inversion which employs the simultaneous iterative reconstruction technique (SIRT) algorithm on the hydraulic travel times for tomography reconstructions. Four artificial karst conduits of different geometries were placed in an aquifer of layer with different hydraulic conductivities. We conducted 6 pumping tests at 6 different locations, and the resultant pressure responses were recorded at 42 observation points in both the sandbox and the corresponding synthetic aquifer. The measured data were then used for the inversion of hydraulic diffusivity using the SimSLE and SIRT algorithms. Our results show that both algorithms were able to approximately identify the embedded karst conduits and yield similar hydraulic diffusivity distribution. Statistically, the travel time-based inversion re-constructed high-contrast diffusivities which clearly differentiate the karst structures from the surrounding matrix. The geostatistics-based SimSLE algorithm yields a better agreement on the positions and the shapes of the embedded karst structures, compared to those obtained by the travel time-based SIRT algorithm. Uncertainties and limitations of our results are also discussed in this work, followed by recommendations on hydraulic tests in karst aquifers.

Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

AbstractKnowledge of the spatial distribution characteristics of hydraulic parameters is essential for the management and protection of karst groundwater resources. In this study, we propose a workflow integrating the transition probability geostatistics (T‐PROGS) and the discrete cosine transform (DCT) with the ensemble smoother with multiple data assimilation (ES‐MDA) method to map the hydraulic conductivity of karst aquifers that usually follow a multimodal distribution. The priori parameter ensemble is constructed from the T‐PROGS and transformed into an approximately Gaussian distributed coefficient field containing critical spatial structural features about the aquifer using DCT. The ES‐MDA method is employed to update the DCT coefficients by assimilating the measurements. In addition, a postprocessing process based on cumulative distribution function (CDF) mapping is used to address the problem of parameters gradually tending to a Gaussian distribution after updating using the ES‐MDA and the inappropriate selection of initial parameter values. In practice, the limited amount of available data makes it difficult to fully capture the spatial distribution of the parameters in the initial ensemble of a single realization. Therefore, we suggest a new strategy for structuring the initial ensemble by mixing samples from multiple realizations. We then apply the proposed approach to four single realization models and a combined multiple realizations model in a field hydraulic tomography investigation of a real karst aquifer. The computed results show that this method can effectively identify the characteristics of the spatial distribution of hydraulic conductivity in karst aquifers. Compared with an individual realization model, the uncertainty of the hydraulic conductivity estimated by the combined multiple realizations model is significantly reduced. Therefore, including more uncertainty of the aquifer in the initial ensemble is beneficial to improve the accuracy of the parameter estimation.

Novel approach to predicting the spatial distribution of the hydraulic conductivity of a rock mass using convolutional neural networks

Characterizing the spatial distributions of the hydraulic conductivity of a rock mass is important in geoscience and engineering disciplines. In this paper, the architecture of convolutional neural networks (CNNs) is proposed to predict the spatial distributions of hydraulic conductivity based on limited geological factors. The performance of the CNN model is evaluated using the new data of hydraulic conductivity. A comparative study with the empirical method is performed to validate the reliability of the CNN model. The effect of weathering and unloading on the spatial distributions of hydraulic conductivity is studied using the CNN model. The results show that the hydraulic conductivity predicted by the CNN model is within an error range of 5% compared to Lugeon borehole tests. The predictive accuracy of the CNN method is higher than the estimations made using empirical relationships. The spatial distributions of hydraulic conductivity v. depth can be divided into three stages. In the first stage, the hydraulic conductivity is slightly reduced with increasing depth. Increasing in the depth range of 300–600 m (second stage), the hydraulic conductivity is slightly reduced as a function of the lower degree of weathering. In the final stage, the hydraulic conductivity is not changed by weathering and values gradually converge to a constant as depth increases.

Imaging hydraulic conductivity in near-surface aquifers by complementing cross-borehole induced polarization with hydraulic experiments

Precise information about the spatial distribution of hydraulic conductivity (K) in an aquifer is essential for the reliable modeling of groundwater flow and transport processes. In this study, we present results of a new inversion procedure for induced polarization (IP) data that incorporates petrophysical relations between electrical and hydraulic parameters, and therefore allows for the direct computation of K. This novel approach was successfully implemented for the Bolstern aquifer analog by performing synthetic IP experiments with a combined surface and cross-borehole setup. From these data, the distribution of K was retrieved with high accuracy and resolution, showing a similar quality compared to images achieved by hydraulic tomography. To further improve the quantitative estimates of K, we use synthetic pumping test data to inform two novel calibration strategies for the IP inversion results. Both calibrations are especially helpful for correcting a possible bias of the IP inversion, e.g., due to resolution limitations and/or to bias in the underlying petrophysical relations. The simulation of tracer experiments on the retrieved tomograms highlights the accuracy of the inversion results, as well as the significant role of the proposed calibrations.

Geostatistics of the Borden Aquifer: High‐Resolution Characterization Using Direct Groundwater Velocity Measurements

AbstractIn 1986, a seminal data set from the Canadian Forces Base (C.F.B.) Borden aquifer, Ontario, Canada, was published, illustrating, in unprecedented detail, the spatial distribution of hydraulic conductivity (K). Among many contributions attached to that data set was a geostatistical examination of field‐based data for comparison with theoretical predictions of macro‐dispersivity. However,that work treatedKas a static parameter and the sole source of flow variability. Here, point velocity probes (PVPs) are used to extend the earlier work by collecting a novel high‐resolution data set of groundwater velocity (v) measurements in the C.F.B. Borden aquifer. Velocity is a dynamic parameter of fundamental importance, closely tied to solute dispersion. Over 400 velocity measurements were collected along a transect perpendicular to flow, analyzed geostatistically, and compared with the analysis of the B‐B′ cross‐section ofKreported by Sudicky (1986),https://doi.org/10.1029/wr022i013p02069. The PVP measurements exhibited geostatistics similar to those previously estimated by Sudicky (1986),https://doi.org/10.1029/wr022i013p02069. This finding suggests, as implicitly assumed in the previous work, the distribution ofvis primarily controlled byK. PVPs also provided a novel, high‐resolution data set of groundwater flow directions. Since the ultimate objective of aquifer characterization includes the definition of velocity fields, this work not only extends the 1986 work, but also demonstrates a viable alternative for characterizing flow patterns in aquifers—with the advantage thatdirect vmeasurements reflect variability in porosity and hydraulic gradient, as well asK. This could ultimately be advantageous at sites with greater heterogeneity or other dynamic hydrogeological variabilities more pronounced than those at the Borden site.

A Case Study Using Seismic Reflection and Well Logs to Reduce and Quantify Uncertainty During a Hydrogeological Assessment

Building a representative three-dimensional conceptual model of the hydrostratigraphic units is the critical first step when undertaking a hydrogeological assessment. The construction of such conceptual model requires integrating all geological data available for reducing the uncertainty of the conceptual model. In addition, the different types of data collected do not have the same level of uncertainty, and this has to be considered during the modeling. This manuscript presents a geostatistical workflow developed to integrate high resolution seismic reflection data with geological well markers and well logs. The proposed workflow allows reducing and quantifying the uncertainty when developing the conceptual model of hydrostratigraphic units and estimating the spatial distribution of hydraulic conductivity needed to simulate groundwater flow. The study involves the field investigation and numerical modeling for understanding the hydraulic connection between a local sand and gravel esker aquifer overlying a fractured bedrock regional aquifer. Seismic reflection data recorded in 2019 and 2021 significantly modify the conceptual model originally envisioned at site by discovering unknown deep esker extensions. Seismic data also help reducing the spatial uncertainty by delimiting the lateral extents, thickness, and depth of the esker aquifer between existing boreholes. Thickness maps of major hydrostratigraphic units are computed by first interpolating the data with higher uncertainty, which are then locally deformed by successive kriging with external drift to honor data with lower uncertainty. Well logs are then combined with seismic reflection data to better represent the spatial distribution of hydrofacies within the esker aquifer, and identify subunits in the bedrock aquifer. These modifications in the conceptual model of hydrostratigraphic units and the better understanding of the vertical heterogeneity of the hydraulic conductivity significantly impact the simulation of groundwater flow, both regionally and locally at site.

Groundwater Flow Modeling: A Case Study of the Lower Rusizi Alluvial Plain Aquifer, North-Western Burundi

The study area, in northwestern Burundi, is an alluvial plain consisting of fine clayey sands and coarse sands with mixed lithology. The aquifer of the lower Rusizi plain could be considered as confined under a clay layer. A 2D horizontal groundwater flow model was developed under steady-state conditions using the Modflow software. The study aims to determine the most productive areas of this confined alluvial aquifer and the main aquifer inflow and outflow values together with the recharge and river–aquifer interactions. The groundwater potential is dependent on the spatial distribution of hydraulic conductivity and aquifer thickness values providing the local transmissivity values. The calibrated model made it possible to assess the spatial distribution of the hydraulic conductivity values at the regional scale, which ranged from 6 × 10−6 (contact between alluvial plain and Precambrian basement) to 7.5 × 10−3 m/s (coastal barriers). The results also provided the computed groundwater flow directions, and an estimation of the groundwater levels in areas not yet investigated by drilling. The results of the computed groundwater flow budget allowed us to deduce that recharge and river–aquifer interaction constitute the main inflow while the downwards boundaries (where piezometric heads could be prescribed) are the main zones where outflows occur. The results of this model can be used in the planning of pumping test programs, locating areas with high groundwater potential to plan water supply for different private and public users. This predictive tool will contribute to the resolution of problems related to the use and integrated management of the groundwater resource in this part of Burundi.

Stochastic nitrate simulation under hydraulic conductivity uncertainty of an agricultural basin aquifer at Eastern Thessaly, Greece.

Lake Karla Watershed is an agricultural basin characterized by intense agricultural activities, which lead to quantitative and qualitative aquifer degradation. The exploitation of non-renewable groundwater resources and nitrate contamination are the major threats to aquifer sustainability. Groundwater resources cover mainly irrigation and domestic water needs. Hence, the simulation of groundwater resources is necessary to (a) determine the quantity available for water supply and (b) estimate probable nitrate contamination to propose subsequent remediation techniques to protect public health. Furthermore, the aquifer's heterogeneity as well as the lack of hydraulic conductivity data, in a large-scale study area, creates uncertainty regarding groundwater flow and nitrate transport simulation. Deterministic modelling approaches for spatially distributed nitrate concentration simulation could not estimate the contamination risk, since it can address only one realization of the aquifer. This study estimates the effect of hydraulic conductivity uncertainty on the simulation of groundwater nitrate concentration. The proposed framework uses Geostatistical Sequential Gaussian Simulation (SGSIM) for the generation of equally probable realizations of the spatial distribution of hydraulic conductivity. It includes the application of a modelling system based on the following inter-linked models: a rainfall-runoff model, a reservoir operation model, a lake-aquifer interaction model, a groundwater flow model, and a nitrate transport and dispersion model. The last two models simulate the multiple realizations of aquifer's groundwater flow and nitrate concentration. Furthermore, two analyses (a statistical and a threshold analysis) are employed to estimate the exceedance probability of the nitrate concentrations and their spatial extent. The results indicate that hydraulic conductivity uncertainty does affect the simulation of nitrate concentration and that nitrate concentrations will most probably exceed the thresholds in areas where groundwater is extracted for domestic use.

Estimation of hydraulic conductivity by using pumping test data and electrical resistivity data in faults zone

Obtaining hydraulic properties is crucial for describing the transport of groundwater and pollutants in the faults area. In this way, the spatial distribution of hydraulic conductivity plays a major role in expressing the heterogeneous flow and non‐Fickian behavior of solute transport which both are common in nature. However, the existing methods are focusing on obtain the mean value (1D) of the aquifer’s hydraulic conductivity, and there are certain challenges in obtaining the spatial distribution (2D) of the hydraulic conductivity. Thus, in this study, a novel method was proposed that combines electrical resistivity tomography (ERT) with pumping test data to obtain the spatial distribution of hydraulic conductivity for metamorphic rock and granite fault zone in the Xinchang region of Beishan, China. The hydraulic conductivity of an aquifer was obtained using data from 30 pumping tests for seven pumping wells, and the results were fitted using the ERT and used to determine the aquifer resistivity at the respective positions. The measured resistivity and hydraulic conductivity were fitted to obtain a correlation (R-K). The hydraulic conductivity for metamorphic rock with a small hydraulic conductivity was better fit by an exponential (R2 = 0.97) than a linear or power law. The hydraulic conductivity calculated using the R-K correlation has an error of less than 10.50% compared with that measured by pumping tests, and the Nash-Sutcliffe efficiency coefficient is 0.96. The superior accuracy of the results obtained using the proposed method was confirmed by comparison with the results obtained using two established methods. The 2-D hydraulic conductivity distribution of the fault zone is potential for accurate and low-cost descriptions of groundwater and pollutant transport in the fault zone with strong heterogeneity.

A comparison between ES-MDA and restart EnKF for the purpose of the simultaneous identification of a contaminant source and hydraulic conductivity

Understanding a contaminant source may help in a better management and risk assessment of a polluted aquifer. However, contaminant source information may not be available when a pollutant is detected in a drinking well. The restart ensemble Kalman filter (restart EnKF, also named r-EnKF) has been demonstrated in synthetic and laboratory experiments as an efficient solution for the identification of a contaminant source. Recently, the ensemble smoother with multiple data assimilation (ES-MDA) has been proposed as an alternative to the r-EnKF as a more efficient solution given that the r-EnKF needs to restart the simulation of the state equation from time zero after each data assimilation step. An analysis, in a synthetic aquifer, of the accuracy of the ES-MDA for the simultaneous identification of a contaminant source and the spatial distribution of hydraulic conductivity by assimilating both piezometric head and concentration observations is carried out using the r-EnKF as a benchmark. The conclusion is that the ES-MDA can outperform the r-EnKF, but the expected speed advantage, associated with the possibility of assimilating all data at once, does not exist. For the ES-MDA to reach the same level of accuracy as the r-EnKF, the number of multiple data assimilations must be large, and final computing time is similar for both approaches. However, the ES-MDA can do much better than the r-EnKF if the number of iterations increases even further, with the consequent increase of computational cost.

Spatial estimation of aquifer’s hydraulic parameters by a combination of borehole data and inverse solution

A combination of borehole data interpretation and inverse solution method used to estimate the spatial distribution of hydraulic conductivity (K) and specific yield (Sy) for the Bandar-e Gaz unconfined aquifer located in Northern Iran considering no access to pumping test data. A numerical model used to simulate the behavior of the aquifer in two 12-month calibration and validation periods. The Nash-Sutcliffe criterion in calibration and validation periods indicates a completely appropriate accuracy and reliability of the combined method. The values of calibrated K and Sy by the inverse solution method are in accordance with their initial estimated values based on boreholes logs data. The estimated K and Sy are in the ranges of 5–15 and 0.024–0.036 m/day and their spatial distribution pattern shows a decreasing trend in the south-to-north direction, which is well suited to the spatial pattern of aquifer sediment’s type and size.

Hydrogeological Model Selection Among Complex Spatial Priors

AbstractHydrogeological field studies rely often on a single conceptual representation of the subsurface. This is problematic since the impact of a poorly chosen conceptual model on predictions might be significantly larger than the one caused by parameter uncertainty. Furthermore, conceptual models often need to incorporate geological concepts and patterns in order to provide meaningful uncertainty quantification and predictions. Consequently, several geologically realistic conceptual models should ideally be considered and evaluated in terms of their relative merits. Here, we propose a full Bayesian methodology based on Markov chain Monte Carlo to enable model selection among 2‐D conceptual models that are sampled using training images and concepts from multiple‐point statistics. More precisely, power posteriors for the different conceptual subsurface models are sampled using sequential geostatistical resampling and Graph Cuts. To demonstrate the methodology, we compare and rank five alternative conceptual geological models that have been proposed in the literature to describe aquifer heterogeneity at the MAcroDispersion Experiment site in Mississippi, USA. We consider a small‐scale tracer test for which the spatial distribution of hydraulic conductivity impacts multilevel solute concentration data observed along a 2‐D transect. The thermodynamic integration and the stepping‐stone sampling methods were used to compute the evidence and associated Bayes factors using the computed power posteriors. We find that both methods are compatible with multiple‐point statistics‐based inversions and provide a consistent ranking of the competing conceptual models considered.

Geologic controls on hydraulic conductivity in a karst-influenced carbonate bedrock groundwater system in southern Ontario, Canada

A large set of hydraulic conductivity values has been integrated with the geologic characterization of a Paleozoic-age carbonate groundwater system to assess the relative influence of specific geologic features on hydraulic conductivity. Three geologic controls are investigated: (1) proximity to bedrock valleys within a regional stress field; (2) carbonate rock texture; and (3) sequence stratigraphic breaks. Results demonstrate that high hydraulic conductivity values do not correlate with a single geological feature, but are associated with various features that have been enhanced by carbonate dissolution. Predicting the spatial distribution of hydraulic conductivity in carbonate rocks requires a regional understanding of the geological history with a conceptualization of where and when waters have interacted with the rocks to dissolve and enhance porosity through geologic time. This investigation focused on a region in southern Ontario, Canada, and concludes with a map identifying the area with the greatest probability of encountering high hydraulic conductivities in the main hydrostratigraphic unit, the Gasport Formation. The map supports the selection of groundwater resource exploration targets for a local municipality. Beyond the local benefits of this work, this investigation offers an approach that can be adopted by practitioners exploring for bedrock groundwater resources or characterizing contaminant transport pathways in complex karst-influenced, carbonate bedrock groundwater systems.

Characterization of spatially variable riverbed hydraulic conductivity using electrical resistivity tomography and induced polarization

The spatial distribution of hydraulic conductivity (K) in riverbeds is essential to understand and model river–groundwater interactions. However, K in riverbeds varies over several orders of magnitude and its spatial distribution is closely linked to complex geological and fluvial processes. Investigating the local distribution and spatial heterogeneity of K is therefore a challenging task. The use of direct current (DC) and time-domain-induced polarization (IP) geoelectrical methods to map qualitatively the spatial distribution of K within riverbeds is described. The approach is demonstrated for a test site situated in a typical lowland river in Belgium. Inverted geophysical parameters (resistivity, chargeability and normalized chargeability) are compared with estimates of K obtained through slug tests. In general, high values of K are observed in the middle of the river and lower values towards the banks, while the opposite is true for chargeability and normalized chargeability. Therefore, there exists an inverse correlation between K and IP geophysical parameters. Furthermore, geostatistical analyses using variograms show that all parameters have ranges of similar magnitudes. The strong correlation between K and chargeability or normalized chargeability can be explained by the fact that all three parameters are mainly controlled by clay and organic matter content.

Numerical Groundwater Modeling of an Eogenetic Karst Catchment Using Analytical Head-Guided Zonation Method: A New Analytical Approach

In parameterisation step, implementing suitable calibration methods that accurately represents the actual system is crucial in developing a dependable groundwater model in data-scarce areas. In this study, the Head-Guided Zonation (HGZ) method was applied to accommodate the limitation of subsurface data, such as the lack of comprehensive spatial distribution of hydraulic conductivity and specific yield values. This study demonstrated that the spatial distribution of groundwater heads can be used to assume the spatial distribution of sub-surface parameters, hence, hydraulic conductivity zones in the model domain can be established using the distribution of hydraulic gradient. We conclude that the HGZ method is practical and applicable for development of a physically-based groundwater model.

Simultaneous identification of a contaminant source and hydraulic conductivity via the restart normal-score ensemble Kalman filter

Detecting where and when a contaminant entered an aquifer from observations downgradient of the source is a difficult task; this identification becomes more challenging when the uncertainty about the spatial distribution of hydraulic conductivity is accounted for. In this paper, we have implemented an application of the restart normal-score ensemble Kalman filter (NS-EnKF) for the simultaneous identification of a contaminant source and the spatially variable hydraulic conductivity in an aquifer. The method is capable of providing estimates of the spatial location, initial release time, the duration of the release and the mass load of a point-contamination event, plus the spatial distribution of hydraulic conductivity together with an assessment of the estimation uncertainty of all the parameters. The method has been applied in synthetic aquifers exhibiting both Gaussian and non-Gaussian patterns. The identification is made possible by assimilating in time both piezometric head and concentration observations from an array of observation wells. The method is demonstrated in three different synthetic scenarios that combine hydraulic conductivities with unimodal and bimodal histograms, and releases in high and low conductivity zones. The results prove that the specific implementation of the EnKF is capable of recovering the source parameters with some uncertainty and of recovering the main patterns of heterogeneity of the hydraulic conductivity fields by assimilating a sufficient number of state variable observations. The proposed approach is an important step towards contaminant source identification in real aquifers, which may have logconductivity spatial distributions with either Gaussian or non-Gaussian features, yet, it is still far from practical applications since the transport parameters, the external sinks and sources and the initial and boundary conditions are assumed known.

Space-time mesh adaptation for solute transport in randomly heterogeneous porous media

We assess the impact of an anisotropic space and time grid adaptation technique on our ability to solve numerically solute transport in heterogeneous porous media. Heterogeneity is characterized in terms of the spatial distribution of hydraulic conductivity, whose natural logarithm, Y, is treated as a second-order stationary random process. We consider nonreactive transport of dissolved chemicals to be governed by an Advection Dispersion Equation at the continuum scale. The flow field, which provides the advective component of transport, is obtained through the numerical solution of Darcy's law. A suitable recovery-based error estimator is analyzed to guide the adaptive discretization. We investigate two diverse strategies guiding the (space-time) anisotropic mesh adaptation. These are respectively grounded on the definition of the guiding error estimator through the spatial gradients of: (i) the concentration field only; (ii) both concentration and velocity components. We test the approach for two-dimensional computational scenarios with moderate and high levels of heterogeneity, the latter being expressed in terms of the variance of Y. As quantities of interest, we key our analysis towards the time evolution of section-averaged and point-wise solute breakthrough curves, second centered spatial moment of concentration, and scalar dissipation rate. As a reference against which we test our results, we consider corresponding solutions associated with uniform space-time grids whose level of refinement is established through a detailed convergence study. We find a satisfactory comparison between results for the adaptive methodologies and such reference solutions, our adaptive technique being associated with a markedly reduced computational cost. Comparison of the two adaptive strategies tested suggests that: (i) defining the error estimator relying solely on concentration fields yields some advantages in grasping the key features of solute transport taking place within low velocity regions, where diffusion-dispersion mechanisms are dominant; and (ii) embedding the velocity field in the error estimator guiding strategy yields an improved characterization of the forward fringe of solute fronts which propagate through high velocity regions.

Simulation of the Spatial Distribution of Hydraulic Conductivity in Porous Media through Different Methods

Seepage problems exist in water conservancy projects, groundwater research, and geological research, and hydraulic conductivity is an important factor that affects the seepage field. This study investigates the heterogeneity of hydraulic conductivity. Kriging methods are used to simulate the spatial distribution of hydraulic conductivity, and the application of resistivity and grain size is used to obtain hydraulic conductivity. The results agree with the experimental pumping test results, which prove that the distribution of hydraulic conductivity can be obtained economically and efficiently and in a complex and wide area.