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Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems, and inverse techniques play a fundamental role in modeling hydrogeological parameters and assessing their uncertainties. Nonetheless, the use of a forward model in these methods can be highly time-consuming, especially with an increasing number of model parameters. To address this issue, we propose a surrogate model based on a U-Net architecture that replaces the transient groundwater flow model, reducing runtime and enabling a fast quantification of uncertainties related to key parameters, including heterogeneous hydraulic conductivity, boundary conditions, specific storage, and pumping rate. The surrogate is trained using limited evaluations of the forward model to learn the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. The physical principles of the studied problem, including boundary conditions, specific storage, and source terms, are also mapped and introduced as inputs to the model to enhance its understanding of the governing equation of transient groundwater flow. To speed up learning using image–image regression, the previously predicted transient hydraulic heads also serve as an input to predict the transient heads at the current time step. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem, a pumping test of 12 h, using the surrogate model in place of the forward model. Our study demonstrates that the trained U-Net accurately reproduces the state variables corresponding to a specific parameter field, and in terms of computational demand, using U-Net as a surrogate model reduces the required computational time by approximately an order of magnitude for the defined problem. The proposed approach offers an efficient and accurate method for groundwater flow parameter characterization and uncertainty quantification in complex aquifer systems. [Display omitted] • A U-Net surrogate approach is developed for transient groundwater inverse problems. • Uncertainties are rapidly evaluated using a geostatistical spectral method. • Uncertain parameters include log(K), Q, Ss, and boundary conditions • Integrate time into image–image regression for capturing time-varying processes. • The surrogate model significantly reduces computation times for inverse problems. [ABSTRACT FROM AUTHOR]

• A new percolation-based model for unsaturated hydraulic conductivity is developed. • Weibull distribution is used in combination with critical path analysis and percolation theory. • Model validation using measured and simulated data confirms good performance. • Capillary pressure curve slightly outperforms pore-throat size in estimating K (S w). Accurate estimation of unsaturated hydraulic conductivity, K (S w), is crucial for modeling water and solute transport in variably-saturated soils. In this study, a new model for the estimation of K (S w) based on percolation theory and critical path analysis is presented, in which the pore-throat size distribution is described by the three-parameter Weibull probability density function. To evaluate the performance of the proposed K (S w) model, two datasets including more than three hundred samples are analyzed. The first dataset includes 240 pore-network simulations, while the second dataset consists of 101 soil samples from the UNSODA database. For the pore-network simulations, for which both pore-throat size distributions and capillary pressure curves are available, we estimate K (S w) from the capillary pressure curve with RMSLE = 0.54 slightly better than the estimations obtained from the pore-throat size distribution with RMSLE = 0.6. For the soil samples, since only the capillary pressure curve is measured, we estimate K (S w) from the capillary pressure curve and evaluate three previously proposed approaches for determining the exponent, α, in Poiseuille's law. We find that RMSLE = 0.98 for α = 3, RMSLE = 0.87 for α = 2(4 − D) − (3 − D)/(2 D − 3), and RMSLE = 1.06 for α = 4 − 0.74 D , in which D is the fractal dimension characterizing the pore space. Comparing the results with previous studies in which the power-law probability density function was used to characterize capillary pressure curve and pore sizes shows that the proposed three-parameter Weibull distribution, in conjunction with the CPA analysis, may more accurately estimate K (S w) for a wide variety of soils ranging from very fine to very coarse textures. [ABSTRACT FROM AUTHOR]

The incorporation of hard data in geostatistical modeling is crucial for enhancing the accuracy of interpolating or stochastically estimating subsurface spatial features. The hard data at specified points in the model domain serve as a guide in optimizing the unknown parameters to follow the patterns of the hard data. Recently, a novel approach to solving hydrogeologic/reservoir modeling problems has emerged by using deep generative models, specifically generative adversarial networks (GANs), to generate realistic and diverse images of channelized aquifers. This subsequently can be coupled with inverse models to solve parameter estimation problems. This study focused on using an improved GAN, called a progressive growing generative adversarial network (PGGAN), conditioned with hard data to perform parameter estimation of complex facies models by coupling an ensemble smoother with multiple data assimilation (ES-MDA). First, the PGGAN was trained to an image with 128 × 128 resolution. The trained PGGAN was used to generate hydraulic conductivity fields when fed an ensemble of latent variables and hard data. The ES-MDA then was used to update the latent variable with the help of hydraulic head data obtained from the groundwater model. The approach was tested on synthetic hydraulic conductivity data. Results show that this approach was able to perform efficient estimation of an unknown facies model domain. Additionally, the proposed method was applied to a different test case of a facies model exhibiting different statistical characteristics. The results were satisfactory, demonstrating that the method is not constrained to the particular hydraulic conductivity fields introduced in the generator's training. • Coupling deep learning with data assimilation for groundwater modeling. • Both hard data and soft data are conditioned. • Synthetic examples are used to demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

• A high-speed camera observed gravity-driven unstable finger formation. • At the fingertip, water advances intermittently one pore at a time. • Pore invasions occur at high velocities. • High velocities increase dynamic contact angles. • Greater contact angles reduce the matric potential at the front and cause instability. The imbibition of fluids in porous media has been studied widely. Still, processes of preferential flow under gravity due to instability at the wetting front, crucial in groundwater contamination, have yet to be fully understood. Recent theories using dynamic contact angles could describe unstable flow phenomena but have not been proven experimentally. Therefore, infiltration experiments in small sand-filled chambers were conducted to explore the effect of dynamic contact angles. A high-speed camera recorded pore invasion at the unstable imbibition liquid front. A tensiometer recorded the matric potential. The results show that water moved in milliseconds through a small pore at the wetting front, followed by a stationary period. The maximum observed pore water velocity was 25 cm/s, exceeding the saturated hydraulic conductivity by three orders of magnitude. The relationship between dynamic contact angle and water velocity found by Hoffman in glass tubes could describe which was observed in soils. [Display omitted] [ABSTRACT FROM AUTHOR]

• The variability of solute transport in heterogeneous confined aquifers of variable thickness is quantified by the variance of solute displacement. • Variability of solute displacement is caused by variability of the hydraulic conductivity and the thickness of the aquifer. • Even if the random fields of hydraulic conductivity and aquifer thickness are second-order stationary, the hydraulic head fields could be nonstationary. • The nonstationary hydraulic head fields lead to nonstationary flow fields and thus to nonstationary solute displacement fields. In this work, the variability of regional-scale transport of inert solutes in heterogeneous confined aquifers of variable thickness is quantified by the variance of the displacement of a solute particle. In the traditional stochastic approach to solute transport at the regional scale, the variability of solute displacement is attributed to the variability of the transmissivity fields. In this work, however, variability in solute displacement is attributed to variability in hydraulic conductivity and aquifer thickness fields. A general stochastic methodology for deriving the variance of the displacement of a solute particle based on the convection velocity of solute particles, developed from the relationship between the two-dimensional depth-averaged solute mass conservation equation and the Fokker-Planck equation, is given. Assuming that the fluctuations in log hydraulic conductivity and log thickness of the confined aquifer are second-order stationary processes, a closed-form expression for the solute displacement variance in the mean flow direction is obtained for the case of advection-dominated solute transport. The results show that variation in hydraulic conductivity and aquifer thickness can lead to nonstationarity in the covariance of flow velocity, making longitudinal macrodispersion anomalous and increasing linearly with travel time at large distances. [ABSTRACT FROM AUTHOR]

• Spatially variable, scale-dependent dispersivities are jointly estimated with hydraulic conductivity. • Joint inversion of tracer and ERT data improves aquifer characterization and transport predictions. • Spatially variable dispersivities outperform uniform dispersivities in transport prediction when adding ERT data. The hydraulic conductivity (K) has been recognized as one of the controlling parameters that significantly impact the transport behavior in groundwater systems. To improve the predictive ability of a transport model, concentration measurements are commonly used in inverse modeling to characterize the K distribution. In addition to K , the spread of the solute plume also depends on dispersion coefficients. The evolution of the plume morphology can only be satisfactorily reproduced with appropriate dispersivities. Dispersivity values or distributions rely on the resolution of the inferred K distribution. Dispersivities were typically treated as spatially uniform in inverse modeling and jointly estimated with K. Although employing spatially variable dispersivities may hold the potential to better capture the solute transport behavior, it may significantly increase the number of unknown parameters for inverse modeling. Solving such an ill-posed inversion problem is challenging, especially when the amount of intrusive borehole-based measurements is limited. As a non-intrusive, cost-effective, and high sampling density method, time-lapse geophysical technique (e.g. , electrical resistivity tomography, ERT) has not yet drawn much attention as a useful source of information for dispersivity estimation. In this study, we developed a joint hydrogeophysical inversion framework to simultaneously estimate spatially variable K and dispersivities by integrating tracer-concentration and ERT-derived potential data. We evaluated the proposed framework by conducting numerical tracer experiments in a highly heterogeneous aquifer. Results show that using limited tracer concentration data alone failed to resolve the fine structure in K field. In this case, there was little difference in the prediction performance of solute transport by considering spatially uniform or variable dispersivities. In contrast, the K distribution was estimated at a significantly higher resolution when integrating tracer-concentration and ERT data, contributing to a remarkable improvement in transport modeling. Powered by the sufficient amount of ERT measurements, jointly estimating spatially variable dispersivities further enhanced the reproduction of tracer plumes and breakthrough curves. [ABSTRACT FROM AUTHOR]

• An analytical model is developed for inter-aquifer, abandoned-well leakage. • A well injected to the confined aquifer is considered in the leakage model. • A thinner confined aquifer will lead to a higher abandoned well leakage rate. A non-plugged abandoned well may cause unwanted flows and solute transport between aquifers. This research provides a novel analytical model to calculate the leakage rate in an abandoned well between a confined aquifer and an unconfined aquifer under steady-state flow conditions. The abandoned well is treated as a passive preferential flow channel connecting a confined aquifer receiving injection from a separate well and an overlying unconfined aquifer; an impermeable aquiclude separates the two aquifers. A closed-form analytical solution for the steady-state leakage rate through an abandoned well is derived. The concerned abandoned well in this study fully penetrates the receiving unconfined aquifer but only penetrates the ceiling of the injecting confined aquifer with a very small screen length (with respect to the confined aquifer thickness). The injection well is sealed from the receiving unconfined aquifer and fully penetrating in the injecting confined aquifer. The solution developed in this study is compared with a previous solution by Avci (1994) (Avci, 1994. Evaluation of flow leakage through abandoned wells and boreholes. Water Resources Research, 30 (9), 2565–2578). Compared to Avci (1994), this research has two different assumptions: (1) The Avci solution assumed that the leakage effect occurs between two confined aquifers, and leakage concerned in this research occurs between an injecting confined aquifer and a receiving unconfined aquifer. (2) The abandoned well in the Avci (1994) solution fully penetrates both the receiving and injecting confined aquifers, while the abandoned well in this research fully penetrates the receiving unconfined aquifer but only penetrates the ceiling of the injecting confined aquifer with a minor screen length. In both this study and the Avci (1994), the injecting well is isolated from the receiving aquifer and fully penetrating in the injecting aquifer. The results show that the two solutions have similarities in thin confined aquifers but are much different in relatively thick confined aquifers (with thickness greater than 10 m). Using the Sobol method for global sensitivity analysis, we tested controls of the hydraulic conductivity ratio between confined and unconfined aquifers, the transmissivity of the confined aquifer over the injection rate per unit screen length, and the aquifer thickness on model performance. The results show that the model is most sensitive to the transmissivity of the confined aquifer over the injection rate per unit screen length. This research can be applied in multiple applications, such as modeling the leakage effect among two aquifers involving stormwater recharge and using a monitoring well to detect the existence of abandoned wells when the abandoned wells are not visible on the surface or not documented, among others. [ABSTRACT FROM AUTHOR]

• Preferential pathways at the Darcy scale can be characterized by their bifurcations, and USR formation formed by their tortuous path. • The bifurcation fraction, USR, tortuosity, and fractal dimension scale with the conductivity heterogeneity. • The same power law exponent captures the scaling of bifurcation fraction, USR, tortuosity, and fractal dimension. Transport in porous media on the Darcy scale can be both Fickian and non-Fickian, an outcome dependent on the degree of homogeneity of the hydraulic conductivity pattern, as well as the boundary conditions and flow rate. The non-Fickian manifestation is generally associated with heterogeneous media, which promotes the formation of preferential pathways that funnel the transport. Yet this funneling occurs in both weakly and strongly heterogeneous domains, through a mechanism that is yet to be fully characterized. We model Darcy-scale transport using a particle tracking code (PT) that samples a 2D, lognormally distributed conductivity field with a variance representing a range of homogeneous to heterogeneous domains. We find that the resulting preferential pathways tend to split into more pathways (bifurcations), leaving regions into which particles do not invade, which we refer to as "under sampled regions" (USR), while forming a tortuous path. The fraction of bifurcations decreases downstream, reaching an asymptotic value, with a trend that can be fitted as a power-law of the variance. We show that the same power-law exponent relating the bifurcations to the variance holds true for the USR fraction, tortuosity, and fractal dimension with the same variance. An extension of our work is also presented for varying correlation length of the conductivity spatial distribution. We further expand our analysis to a case of impermeable fraction in a uniform conductivity field and show that the power-law fit still holds. Key Points Preferential pathways at the Darcy scale can be characterized by their bifurcations, and USR formation formed by their tortuous path. The bifurcation fraction, USR, tortuosity, and fractal dimension scale with the conductivity heterogeneity. The same power law exponent captures the scaling of bifurcation fraction, USR, tortuosity, and fractal dimension. [ABSTRACT FROM AUTHOR]

• We solve low-velocity non-Darcian flow to a confined and partially penetrating well in a leaky aquifer system. • An analysis is conducted to examine the temporal and spatial changes in confined groundwater head differences between Darcian and non-Darcian flow conditions. • Non-Darcian flow in the aquitard needs to be considered under small confined aquifer hydraulic conductivity and large threshold pressure gradient of the aquitard. Previous studies on the flow dynamics of leaky aquifer systems have primarily relied on Darcy's law, assuming fully penetrating wells in confined aquifers. However, when dealing with aquitards dominated by clay, the flow behavior often deviates from Darcy's law. Moreover, in the majority of cases, this entails partially penetrating well pumping. This paper introduces a mathematical model for non-Darcian flow in a confined and partially penetrating well system within a leaky aquifer system. The model is based on the low-velocity non-Darcian flow equation, incorporating the threshold pressure gradient. In the confined aquifer, the flow exhibits two-dimensional Darcian flow behavior, while in the aquitard, the flow is characterized by one-dimensional non-Darcian flow in the vertical direction. In the shallow aquifer, the flow is one-dimensional Darcian flow in the radial direction. The mathematical model is solved using the finite difference method, and the obtained results are compared with calculations based on traditional Darcian flow theory. The findings indicate that the confined groundwater head difference, as predicted by the Darcian and non-Darcian flow theories, diminishes radially as the distance from the pumping well increases and vertically as one moves away from the top of the confined aquifer. As pumping progresses, the confined groundwater head difference initially rises and subsequently stabilizes gradually. Moreover, the magnitude of the confined groundwater head difference is more pronounced when the threshold pressure gradient, vertical hydraulic conductivity of the aquitard, pumping rate, hydraulic conductivity and specific yield of shallow aquifer are larger, or when the hydraulic conductivity and specific storage of the confined aquifer are smaller. The effect of well screen length on the confined groundwater head difference is minimal. [ABSTRACT FROM AUTHOR]

• The immiscible fluid flow with zero-velocity and continuity interface are simulated at pore scale. • A modified scaling model of non-wetting fluid conductance with zero-velocity interface is given. • The viscous coupling effect with fluid viscosity, wettability and wetting-film length is addressed. • An accurate scaling model of hydraulic conductance with viscous coupling effect is proposed. Viscous coupling effect on pore-scale flow capacity and its impact on macroscopic flow properties in porous media remain subjects of ongoing debate. This study employs the Stokes equation in conjunction with the zero-velocity interface and continuity interface to investigate viscous coupling effect during two-phase flow through a square capillary tube. Our findings substantiate the significance of the viscous coupling effect in angular pore multiphase flows. Enhanced fluid conductance is linked to fluid viscosity ratios, contact angles, and wetting-film lengths at the pore scale. Proposing a novel upscaling approach, we formulate hydraulic conductance in a square capillary tube for multiphase flows by incorporating a viscous coupling term, and its validation is accomplished through comparison with results from lattice Boltzmann method simulations. Our scaling model predicts hydraulic conductance with a mean relative error of less than 1%, outperforming prior viscous coupling models with errors reaching up to 19%. The derived scaling model, incorporating the viscous coupling effect, holds potential for integration within pore-network models, offering an efficient and precise simulation method for characterizing two-phase flow through porous media at a representative scale. [ABSTRACT FROM AUTHOR]

• Physics Informed Neural Networks (PINNs) is a promising technique. • Current implementation of PINNs face convergence issues in heterogeneous domains. • A new implementation is proposed based on the mixed formulation of the equations. • The new implementation simulate flow, regardless the level and type of heterogeneity. • It provide high accurate results without additional learning time. Current implementations of Physics Informed Neural Networks (PINNs) can experience convergence problems in simulating fluid flow in porous media with highly heterogeneous domains. The objective of this work is to develop an accurate implementation of PINNs to model fluid flow in heterogeneous porous media that avoids alternative approaches in the literature that tend to impose unphysical continuity of the hydraulic conductivity field. The proposed implementation is inspired by the mixed formulation of the governing equations, which separates the mass continuity equation and Darcy's law. This methodology has been used with the mixed finite element method and is known to provide accurate pressure and velocity fields in highly heterogeneous domains. In this work, a similar methodology is applied to PINNs, where the training loss function is based on the decoupled continuity equation and Darcy's law. The separation of the continuity equation and Darcy's law allows for calculating the residual term in the learning loss function without evaluating the spatial derivatives of the discontinuous hydraulic conductivity and associated non-differentiable functions. This approach provides more accurate automatic differentiation of the neural networks for pressure and velocity fields. The new implementation of PINNs can be applied to simulate flow in porous media, regardless of the type and level of heterogeneity with a discontinuous hydraulic conductivity distribution. A variety of structures of the new implementation are investigated. Numerical experiments show that the structure based on different neural networks for the pressure and each component of the velocity field provides the highest accuracy with equivalent training time as other structures. The proposed methodology presents a novel approach to broaden the scope of PINNs in modeling fluid flow in porous media, while preserving the precise representation of the domain's discontinuous features. [ABSTRACT FROM AUTHOR]

• Transient tidal overheight represented by phase-averaged tidal boundary condition. • Planar beach model successfully predicts overheight for complex coastal morphology. • Boundary condition performance is sensitive to coastal morphology representation. • Phase-resolved simulations and observed data can be replicated reasonably well. • Considerable reduction of coastal groundwater flow simulation runtimes achieved. Ocean tides cause water table overheight near the seaward boundary of coastal aquifers which can have a large impact on groundwater flows and saltwater intrusion. Despite this, regional-scale coastal groundwater flow models often neglect the effects of ocean tides or alternatively assume that the influences of ocean tides and sea level are constant over time. These simplifications are often required because simulation of the phase-resolved tidal signal at a coastal boundary is computationally demanding. Our objective was to derive a phase-averaged tidal boundary condition for application along gently sloping coastlines that enables simulation of real, complex tidal signals combined with sea-level changes due to meteorological effects. The boundary condition extends an existing analytical solution of tidal overheight by including an empirical correction function for conditions where the assumptions of the existing solution are violated. The correction function was developed by conducting a parametric study on an idealized two-dimensional cross-sectional coastal aquifer model and considering the effects of parameters including horizontal hydraulic conductivity, vertical anisotropy, specific yield, aquifer thickness, and beach slope. The performance of the new phase-averaged tidal boundary condition was assessed using a three-dimensional groundwater flow model of the island of Spiekeroog, Northwest Germany, which comprises complex coastal morphology with non-planar beach slopes. Simulations applying the new boundary condition were compared to simulations that adopted a phase-resolved tidal boundary condition and to observed groundwater levels. Accounting for time-varying changes in the tidal signal and sea level was found to be critical to simulate observed data and to adequately reproduce the transient tidal overheight simulated by the phase-resolved model. The performance of the new phase-averaged boundary condition in the regional-scale model varied depending on how the coastal morphology was represented in the boundary condition with local morphological features increasingly important for lower intertidal vertical infiltration capacity (low isotropic hydraulic conductivity or high vertical anisotropy) or specific yield. In conclusion, the new boundary condition presented overcomes current limitations in simulating transient tidal overheight in regional-scale groundwater models. [ABSTRACT FROM AUTHOR]

Contaminant source and aquifer characterization (CSAC) is critical in groundwater pollution evaluation and remediation. The ensemble smoother with multiple data assimilation (ES-MDA) is utilized to jointly identify contaminant source information and hydraulic conductivities by assimilating time-lapse electrical resistivity tomography (ERT) data. In a synthetic profile with a time-varying release history in a heterogeneous aquifer, we verify the performance of the proposed data assimilation framework. The results show that the CSAC problem could be handled by the proposed approach. The time-varying release history and the high permeability area can be identified with adequate time-lapse ERT measurements. Further reproduction of the evolution of the plume after CSAC also shows consistency with the reference plume. The poor conditioning inversion caused by the filter inbreeding is analyzed by comparing four scenarios with different apparent resistivity measurements. Furthermore, we also evaluate the impact of uncertainties in the petrophysical properties and geophysical observations on our data assimilation framework. The results show that the proposed ES-MDA data assimilation framework could provide a convincing inversion of the time-varying release history and hydraulic conductivities. • We propose a data assimilation framework including the coupling of the simulators of MODFLOW, MT3DS and ResIPy into the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) implementation. • The time-lapse electrical resistivity tomography (ERT) measurements are first employed for the joint identification of contaminant source information and hydraulic conductivities. • We analyze the influence of different bipole–bipole electrode array configurations on the ES-MDA data assimilation framework. [ABSTRACT FROM AUTHOR]

• Dispersion effects on offshore freshwater extent and discharge investigated. • Toe moves seaward monotonically with increased dispersion. • Tip-dispersion relationship is non-monotonic. • Dispersion increases fresh groundwater discharge to the sea. • Dominant control on the interface width at the tip is K:K z contrast. Recent recognition of the widespread occurrence of freshwater beneath the ocean has renewed interest in approaches to understand and predict its extent. The most straightforward methodologies are based on the sharp-interface approximation, which neglects dispersive mechanisms. The understanding of dispersion effects on freshwater extents in coastal aquifers is based almost entirely on onshore aquifer situations. This study explores dispersion in offshore coastal aquifers, in terms of the steady-state freshwater extent, seawater circulation and freshwater discharge, through numerical experimentation. Results show that increasing dispersion causes a seaward shift in the interface toe location, as expected, whereas the interface tip shows a non-monotonic relationship with dispersion that depends on the contrast between aquifer and aquitard hydraulic conductivities. Higher dispersion leads to enhanced seawater recirculation rates and freshwater discharge, as opposed to non-monotonic relationships obtained previously for onshore aquifers. The mixing zone at the toe widens as dispersion increases, similar to onshore cases, whereas the mixing zone at the tip has a surprisingly non-monotonic relationship with dispersion. The dispersion relationships revealed in this study can be explained by counteractions between dispersion, density and advective forces, and refraction across the aquifer-aquitard interface, which in combination produce offshore aquifer behaviour that differs, in some ways, to the manner in which onshore aquifers respond to dispersive processes. Consequently, previous empirical corrections to sharp-interface methods (to account for dispersive effects) applied to onshore coastal aquifers are ineffective in their application to offshore settings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze the statistical properties of non-reactive solute concentrations in natural aquifers, taking into account the hydraulic conductivity heterogeneity. Quantifying the uncertainty in the evaluation of solute concentrations in aquifers is an important issue for human health and in ecological risk analysis. In particular, the concentration Cumulative Distribution Function (CDF) is a key element, as it informs the decision makers of the probability that the concentration at an environmental target is below a maximum contaminant level. The analysis presented in this paper is performed in a Lagrangian framework. According to the "reverse formulation", the origin of the particle being sampled is sought instead of considering the destination of the injected particles. Based on this formulation, a closed form for the unconditioned concentration CDF is derived. The same procedure is applied to obtain a closed form for the concentration conditioned by measurements at sampling points in an aquifer. [ABSTRACT FROM AUTHOR]

• A novel approach combining an integrated surface/subsurface model and a groundwater parameter-estimation model, was able to better constrain the model. • The groundwater system may be nearing, if not exceeding, its sustainable groundwater production capacity and the speed of recovery is not indicative of sustainability. • Results from using conventionally-assumed uniform recharge distort calibrated K fields and impacts assessment The quantification of recharge and trans-valley underflow is needed in arid regions to estimate the impacts of new water withdrawals on the water table. However, for mountainous desert areas, such estimates are highly challenging, due to data scarcity, heterogeneous soils, and long residence times. Conventional assessment employs isolated groundwater models configured with simplified uniform estimates of recharge. Here, we employed a data-constrained surface-subsurface process model to provide an ensemble of spatially distributed recharge and underflow estimates using perturbed parameters. Then, the Model-Independent Parameter Estimation and Uncertainty Quantification (PEST) package was used to calibrate the aquifer hydraulic conductivity field in MODFLOW for this ensemble and reject implausible recharge values. This novel dual-model approach, broadly applicable to mountainous arid regions, was designed to maximally exploit available data sources. It can assimilate groundwater head observations, reject unrealistic parameters, and narrow the range of estimated drawdowns due to pumping. We applied this approach to the Chuckwalla basin in California, USA to determine natural recharge. Simulated recharge concentrates along alluvial fans at the mountain fronts and ephemeral washes where run-off water infiltrates. If an evenly distributed recharge was employed as in conventional studies, it would result in regional biases in estimated drawdown and larger uncertainty bounds. We also note that the speed of groundwater recovery does not guarantee sustainability: heavy pumping induces large hydraulic gradients that initially recover quickly when pumping is halted, but the system may not ultimately recover to pre-pumping levels. [ABSTRACT FROM AUTHOR]

The connectivity of the more conductive hydrofacies strongly determines flow and transport in heterogeneous media. Here we study solute transport in 3D binary isotropic samples with a proportion p of a high hydraulic conductivity facies (k +), and (1 − p) of a low (k −) one. The k + facies is characterized by two connectivity parameters: a connectivity structure type (no, low, intermediate and high), that controls how well the k + facies is connected, and an integral scale I b , that controls the heterogeneity characteristic lengthscale. Under ergodic conditions, and in the asymptotic Fickian regime that arises only very far from the injection plane, we analyze two transport quantities: the normalized mean solute arrival time 〈 t a ∗ 〉 , and the longitudinal dispersivity α L. As p reaches the percolation threshold p c (p c depends on the connectivity parameters), k + channels spanning the sample along the mean flow direction appear, giving rise to fast flow pathways. A sharp decrease of 〈 t a ∗ 〉 , and a sharp increase of α L , occur when p → p c . As p exceeds p c , a subsequent minimum of 〈 t a ∗ 〉 and a maximum of α L are observed. This result is in contrast with previous ones by other authors that found a maximum of α L at p = p c . On the other hand, p kept fixed, α L decreases as the connectivity of the k + facies increases. We conclude that the connectivity features sampled by the solute particles during their trajectories are retained in the transport quantities even after the asymptotic regime is attained. Also, that connectivity mainly affects α L through a shift or displacement of p c. Finally, the existence of a spatial connectivity structure may imply early, but also late, arrival times, compared with the absence of structure. • Solute transport in percolative binary media is studied, with focus on connectivity. • Media have a proportion p of a high conductivity facies and (1-p) of a low one. • The connectivity sampled by the solute particles is kept in the transport quantities. • Influence of connectivity is accounted for by a shift of the percolation threshold p c. • Solute dispersivity is not maximal at p = p c , but for p > p c . [ABSTRACT FROM AUTHOR]

• First to use superparamagnetic DNA tagged colloids (SiDNAmag) for hydraulic parameter estimation of a 3D sand aquifer, using monte carlo modelling approach at different ionic strengths. • Hydraulic parameter distributions estimated from sidnamag breakthrough curves through Monte Carlo simulation approach were statistically similar to salt tracer. • SiDNAmags are good candidate for determining hydraulic parameters of saturated 3D sand aquifer at short travel distance (50 cm). We investigated the applicability of Silica encapsulated, superparamagnetic DNA particles (SiDNAmag) in determining aquifer hydraulic parameters at different ionic strengths (1 mM, 5 mM, and 20 mM phosphate buffer) of injection suspension. Thereto, in a homogeneous, unconsolidated sand tank we pulse - injected two uniquely sequenced SiDNAmag at two injection points. At 0.5 m and 0.8 m downstream from the injection points, we measured the concentration of SiDNAmags at three vertically distributed and two horizontally distributed sampling locations. We estimated the hydraulic parameter distributions from the SiDNAmag breakthrough curves through a Monte – Carlo approach and compared the parameter distributions with salt tracer breakthrough curves. Our results indicated that at all the ionic strengths, the times of peak concentrations, and the shapes of the breakthrough curves were similar to the salt tracer. As compared to the salt, a 1 – 3 log units reduction in the maximum effluent concentration of SiDNAmag was due to kinetic attachment. The attachment rate reduced from 1 mM to 5 mM phosphate buffer possibly due to competitive adsorption of phosphate onto the favourable attachment sites. SiDNAmag attachment rate further increased in 20 mM buffer suspension, possibly due to the compression of electric double layer and reduction in energy barrier for attachment. The parameter distributions of hydraulic conductivity (k), effective porosity (n e), longitudinal dispersivity (α L), vertical transverse dispersivity (α TV /α L) and horizontal transverse dispersivity (α TH /α L) estimated from the SiDNAmag and the salt tracer breakthrough curves were statistically similar. Our work contributes to the applicability of colloidal SiDNAmags for determining hydraulic parameters at different ionic strength conditions. [ABSTRACT FROM AUTHOR]

• A multi-fidelity Gaussian process model was implemented to estimate the hydro-geological properties by different sources of data. • The accuracy of the model prediction is dependent on the locations and the distribution of both high- and low-fidelity data, especially when data points are sparse. • A Bayesian experimental design algorithm was coupled with the multi-fidelity Gaussian process model to determine future sampling locations. Enhanced water management systems depend on accurate estimation of subsurface hydraulic properties. However, geologic formations can vary significantly, so information from a single source (e.g., widely spaced boreholes) is insufficient in characterizing subsurface aquifer properties. Therefore, multiple sources of information are needed to complement the hydrogeology understanding of a region. This study presents a numerical framework in which information from different measurement sources is combined to characterize the 3D random field in a multi-fidelity prediction model. Coupled with the model, a Bayesian experimental design was used to determine the best future sampling locations. The Upper Sangamon watershed in east-central Illinois was selected as the case study site, where the multi-fidelity Gaussian process model was used to estimate the hydraulic conductivity in the region of interest. Multi-source observation data were obtained from electrical resistivity and borehole pumping tests. The accuracy of the model prediction is dependent on the locations and the distribution of both high- and low-fidelity data. Furthermore, the multi-fidelity model was compared with the single-fidelity model. The uncertainties and confidence in the measurements and parameter estimates were quantified and used to design future cycles of data collection to further improve the confidence intervals. [ABSTRACT FROM AUTHOR]

• Hydraulic conductivity is a key control of the way precipitation signals are filtered in the subsurface. • Hydrologic controls of the signal filtering depend on the timescale being investigated. • The filtering that occurs in streamflow, unsaturated storage, and saturated storage signals have varying physical controls. Watersheds act as low-pass filters, damping and attenuating climatic signals as water moves through the surface and subsurface. This is a well observed phenomenon; however, the ways in which watershed properties control the nature of this filtering are less well documented, especially with respect to groundwater surface water interactions. Here, we use a physically based groundwater surface water model to simulate idealized hillslope ensembles with varying watershed properties (hillslope slope, hydraulic conductivity, and precipitation magnitude) to quantitively explore the impact of watershed configuration on temporal filtering in both the surface and subsurface. To limit the complexities of this system an idealized titled-v domain is used. Multi-decadal simulations (95 years) are run, and then power spectral densities and transfer functions are used to quantify the temporal dynamics and damping of each simulation. Overall, we show that the degree of filtering and the degree of signal transformation is controlled by the total time spent in the subsurface and the degree of groundwater surface water exchanges. The ratio of precipitation to hydraulic conductivity controls the partitioning between infiltration and runoff. Greater infiltration results in less filtering in the subsurface and more filtering in streamflow. For a given precipitation conductivity ratio, deeper water table depths lead to greater streamflow filtering for periods less than 5 years. For time periods greater than 5 years the streamflow filtering is most strongly related to hydraulic conductivity which controls the baseflow dynamics. The majority of the input signal is filtered in the subsurface for short periods less than one year. For longer time scales, hydraulic conductivity is found to be the primary control of filtering and power shift taking place in the subsurface with larger conductivities correlated to less filtering and less of a signal transformation. Deeper water table depths lead to more signal transformation in saturated storage but are not correlated to filtering in unsaturated storage. This is likely due to counteracting effects of higher conductivity (which decreases filtering) and deeper water table depths (which increase filtering). [ABSTRACT FROM AUTHOR]

• A general BEST method is presented for estimating soil hydraulic parameters without the need for particle-size distribution data. • Estimation of soil hydraulic parameters can be performed directly by using the quasi-exact implicit formulation of Haverkamp et al. (1994). • Kosugi and van Genuchten soil hydraulic parameters are satisfactorily retrieved with the methodology. Soil hydraulic characterization is crucial to describe the retention and transport of water in soil, but current methodologies limit its spatial applicability. This paper presents a cost-effective general Beerkan Estimation of Soil Transfer parameters (BEST) methodology using single ring infiltration experiments to derive soil hydraulic parameters for any unimodal water retention and hydraulic conductivity functions. The proposed method relies on the BEST approach. The novelty lies in the use of Kosugi hydraulic parameters without need for textural information. In addition, the method uses a quasi-exact formulation that is valid for all times, which avoids the use of approximate expansions and related inaccuracy. The new BEST methods were tested against numerically generated data for several contrasting synthetic soils, and the results show that these methods provide consistent hydraulic functions close to the target functions. The new BEST method is accurate and can use any water retention and hydraulic conductivity functions. [ABSTRACT FROM AUTHOR]

• We proposed an analytical method for upscaling hydraulic conductivity using perturbation expansion techniques and Fourier analysis. • The proposed method generates the same results as from the numerical method in a finite difference scheme with periodic boundary conditions efficiently. • The proposed method is validated for various cases considering anisotropy, heterogeneity and geometry in general. Modern geological modeling techniques represent anisotropic heterogeneous formations by high-resolution grids, which can be computationally prohibitive. This motivates the upscaling process that scales-up properties defined at a fine-scale system to equivalent properties defined at a coarse-scale system. In general, analytical methods are very efficient but limited to assumptions and approximations, whereas numerical methods are more robust albeit more time-consuming. In this work, we developed an analytical method to approximate numerical solutions in a finite difference scheme with periodic boundary conditions for two-dimensional problem. Using perturbation expansion techniques and Fourier analysis, the method generates explicit formulas of tensorial equivalent conductivity considering heterogeneity and anisotropy of two-dimensional space, as well as geometry of gridblocks. It is applicable for various cases with different covariance/variagram models and a wide range of log-conductivity variances, correlation lengths, rotation angles, anisotropy ratios of fine grid conductivity, anisotropy ratios of fine grid size, and the number of fine gridblocks in a coarse gridblock. The analytical method matched well with the numerical method for the estimation of the conductivity tensor, hydraulic head, and discharge velocity. The coefficients in the analytical method need to be computed only once for any given statistics, which makes the proposed method much more efficient than the numerical method. [ABSTRACT FROM AUTHOR]

Characterization of flow topology is essential to understand the effects of the heterogeneity and dimensionality of geological formations on the mixing of inert solute clouds in these same geological formations. In this work, we numerically study two indicators of flow topology, the averaged vorticity magnitude | ω | av and the averaged positive second invariant Q av of the deformation tensor ∇ u , in steady Darcy flows through exponentially correlated lognormal hydraulic conductivity fields K. Our numerical results allow us to establish the relationships between the two indicators considered here and the hydraulic conductivity variance σ 2 in 2D and 3D, highlighting the role played by the spatial structure of these porous media on flow topology, and indirectly on mixing. This work leads us to assess the maximum dilution index E max , indicator of mixing, theoretically known to increase monotonically in steady Darcy flows through isotropic heterogeneous porous media. Our numerical results allow us to test this hypothesis by establishing the relationship between the slope a of maximum dilution index E max and the averaged positive second invariant Q av of deformation tensor ∇ u. The parameters of this relationship depend on molecular diffusion and dimensionality of problem considered. [ABSTRACT FROM AUTHOR]

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]

Highlights • The continuous adjoint state associated with the transport equation is derived. • Hydraulic conductivity and porosity fields are estimated by inverse modeling. • Concentration data complementing heads slightly improve inverse solutions to flow. Abstract A parameter estimation methodology has been developed on the basis of model inversion using a Quasi–Newton method and adaptive parameterization. The continuous adjoint state equations for both flow and transport in porous media are employed as the tool calculating the gradient components of the objective function with respect to parameters. Solving the continuous form of the adjoint equations can be implemented independently of the code used to solve the forward problem, which renders the technique non-intrusive. The developed methodology is applied to the identification of hydraulic conductivity and porosity fields conditioned by piezometric head data associated with steady-state flow and transient solute concentrations. Synthetic numerical experiments have been undertaken for test cases of increasing complexity, from an almost uniform flow sweeping the modeled domain with a prescribed uniform continuous injection of solute at the inflow boundary, to spatially highly variable flow conditions obtained through source/sink terms within the flow domain and a local stepwise solute injection. The results of inversions are analyzed using criteria based on the comparisons between estimated concentration and reference concentration values as well as comparisons between estimated hydraulic conductivity (and porosity for one test case) and reference hydraulic conductivity fields. The results show that employing a continuous adjoint state technique computed independently of the direct problem is an efficient option for parameter estimation relying jointly upon flow and transport data. In the reported numerical examples that are characterized by the identifiability of the flow problem on the basis of hydraulic head observations, concentration data from solute transport scenarios bring few added value to sought solutions of hydraulic conductivities. The spatial structure of the conductivity fields is slightly improved compared with the reference, but the overall system in terms of head distribution, identification of main flow paths, and solute transit times, only inherits cosmetics. [ABSTRACT FROM AUTHOR]

Highlights • Coastal aquifer filters out high-frequency tidal signals and leaves behind low-frequency signals to affect upper saline plume and lower saltwater wedge. • Upper saline plume and lower saltwater wedge are significantly affected by antecedent tidal conditions. • Effect of antecedent tidal conditions was enhanced by increased soil hydraulic conductivity or decreased beach slope. Abstract Subterranean estuary, as a saltwater-freshwater mixing zone in a coastal aquifer, is significantly affected by tides. While many studies have been conducted to examine the effects of tides on groundwater dynamics in subterranean estuaries in relation to submarine groundwater discharge and seawater intrusion, the focus of the investigation, particularly for those based on numerical modelling, has been on tides with few frequencies, e.g., monochromatic tide and spring-neap tides (bichromatic). In this study, we examine numerically effects of measured multi-constituent tides on a coastal unconfined aquifer. With the antecedent tidal conditions accounted for using the Gamma distribution function, we conducted regression analysis and quantified the effects of measured multi-constituent tides on coastal unconfined aquifers in a prolonged and cumulative fashion. The results showed that the response of submarine groundwater discharge to the tidal fluctuation is mostly instantaneous. The coastal aquifer behaved like a low-pass filter that smooths out high-frequency tidal signals and leaves behind low-frequency signals to affect upper saline plume and lower saltwater wedge. The upper saline plume and lower saltwater wedge were significantly affected by antecedent tidal conditions at monthly and yearly time scales, respectively. Sensitivity analysis showed that the low-pass filter capacity can be altered by soil hydraulic conductivity and beach slope. This study revealed the importance of antecedent tidal conditions for seawater intrusion and will help to improve our understanding of hydrological processes in natural coastal unconfined aquifers. [ABSTRACT FROM AUTHOR]

Highlights • Estimation of heterogeneous hydraulic conductivity and van Genuchten α and n fields • Iterative EnKF successfully estimated jointly the soil parameter fields. • In the 3D-case, soil parameter estimation is less improved than for 2D-case. • 1D parameter estimation at measurement locations plus kriging performs as good as 3D-IEnKF. Abstract The accurate modeling of flow and transport in the vadose zone for agricultural and environmental applications requires knowledge about soil parameters. Soil parameters vary in space depending on soil texture and structure. In the present synthetic study we considered spatial variation of permeability (k), inverse of capillary entry pressure head (α VG) and exponent (n) of the Mualem-van Genuchten model. The iterative Ensemble Kalman filter (IEnKF) can estimate the spatially variable soil parameters if measurements of water saturation at different locations and times are available. We used as input daily precipitation data from the Berambadi catchment (southern India). We first considered that the parameters vary horizontally but are constant in the vertical direction. In this case log (k) and log (α VG) can be estimated satisfactorily with 30%–40% reduction of RMSE (compared to open loop runs), if the initial guess of the spatial correlation lengths of the heterogeneous fields is equal to or larger than the unknown, true values. The estimation of exponent n is poorer as the reduction of RMSE is just 20%. If vertical heterogeneity of the parameters is considered the estimation of log (k) and log (α VG) is only improved for the upper 1.5 m and estimation of n is not improved. We also demonstrate that the estimation problem can be simplified when flow in the unsaturated zone is predominantly vertical. If in this case soil hydraulic parameters are estimated with IEnKF at measurement locations and afterwards interpolated with kriging, results are produced with a similar quality as with 3D-IEnKF. [ABSTRACT FROM AUTHOR]

Abstract A systematic understanding of hyporheic flux (HF) and residence times (RT) is important as they are a major control of biogeochemical processing in streambeds. Previous studies addressing the effect of heterogeneity in streambed hydraulic conductivity (K) on HF and RT have come to deviating conclusions depending on the specific study design and the selection of heterogeneity cases being investigated. To more systematically evaluate the effects of conductivity heterogeneity on HF and RT, we simulated hyporheic exchange induced by idealized streambed ripples over a large range of heterogeneities. Conductivity heterogeneity was represented in the simulations in terms of 10,000 different heterogeneity realizations from a geostatistical model based on continuous Gaussian and discrete indicator random fields. We demonstrate that any isotropic homogeneous K-field, as an average of a heterogeneous K-field, can only match RT or HF of the respective heterogeneous K-field, but never both. We found exponential correlations of RT and HF with the variance of heterogeneous conductivity. Based on these correlations, an equivalent anisotropic homogeneous conductivity tensor K can be derived. This equivalent anisotropic K efficiently accounts for the effects of small scale heterogeneity on HF and RT. It can be calculated from the median and variance of the hydraulic conductivity distribution of the targeted heterogeneous sediment, without explicitly characterizing the sediment texture. [ABSTRACT FROM AUTHOR]

• An analytical model is developed to handle horizontal aquifer/aquitard heterogeneity. • A high- K aquitard window tends to dampen tide-induced aquifer head fluctuations. • Aquifer head fluctuations may be dampened by a large-size high- S s aquitard window. • Sandbox experiments validated the effects of a high- K aquitard window. Low-permeability aquitards are important sedimentary units that protect the underlying confined aquifers from contamination by seawater and anthropogenic sources in coastal leaky aquifer systems. Therefore, the integrity of the aquitard is of crucial importance. However, the aquitard integrity may be vulnerable to horizontal heterogeneities in the form of aquitard windows. In this study, an innovative analytical model was developed to describe groundwater flow in a coastal leaky aquifer system with horizontal heterogeneities in hydraulic properties of either the aquitard or the confined aquifer. Consequently, the effects of aquitard windows, which manifest as horizontally local heterogeneities in hydraulic conductivity and/or specific storage, on the tidal wave propagation can be considered in the analysis. Analytical solutions were derived for tidal-head or constant-flux inland boundary conditions. The derivation process avoided previous methodologies that involved the assembly of large-size matrices. The newly developed analytical model can cover multiple existing analytical models that are associated with the assumptions of homogeneity in hydraulic properties of the aquifer and the aquitard, infinite horizontal extent of the coastal leaky aquifer system, impermeability of the aquitard, or ignorance of aquitard storativity. Analytical investigations revealed that high-permeability aquitard windows acting as preferential-flow conduits tended to dampen the tide-induced head propagation within the underlying confined aquifer. Moreover, an aquitard with a higher storativity (but the same permeability) and of considerable size can result in an apparent propagation bias. The newly developed analytical model in this study was further corroborated through sandbox experiments. Both piezometer measurements and parameter estimates indicated the non-negligible effects of high-permeability aquitard windows on the tidal wave propagation. The sandbox investigation also highlighted the importance of geostatistical inverse modeling in characterizing local heterogeneities within the confined aquifer and in detecting the location and size of aquitard windows, when measurement data of tide-induced aquifer head fluctuations were provided. [ABSTRACT FROM AUTHOR]

• Clogging risk assessment at managed aquifer recharge (MAR) sites. • Site characterization techniques to estimate model parameters for physical clogging. • The fines remobilization affects the formation of clogging patterns in the field. • Field spatial factors are included to estimate the evolution in the site's infiltration capacity. Managed aquifer recharge (MAR) techniques are in demand to cope with water scarcity challenges posed by climate change and groundwater overexploitation. One of the long-lasting technical issues associated with MAR systems is physical clogging. The intrusion and deposition of external fines during water recharge reduce the infiltration capacity of the site over time. Operation and maintenance (O&M) costs are experienced directly at the site to restore the original efficiency of infiltration rates. Thus, investors need reliable estimations of the risk of clogging during the planning of the site. As a rule, in MAR design, the main parameter of concern for physical clogging is the total suspended solids (TSS), and most clogging models rely on experiment calibrations in 1D sand columns. However, secondary processes can control the development and spatial distribution of physical clogging in field conditions. The proposed work aims to detect key clogging factors directly in the field and to model these processes for reproducibility at other sites. The fieldwork is conducted at the two-stage infiltration basin in Suvereto (Tuscany, Italy). Spatial factors are included in the analysis (i.e. basin topography) to explain clogging patterns in the field altered by erosion processes. The observed clogging profiles at two sampled locations exhibiting clogging are replicated by a mathematical model. Based on the computation of annual erosion rates in the pond and fines' redistribution, the exceeding fines' contents over depth are validated with an RMSE of 2.53% and 12.53%. The infiltration capacity of the site is estimated to reach a stable value of 90% of the initial infiltration capacity over 20 years, given the Suvereto basin features. The model's parameterisation from field measurements represents a great advantage over existing clogging models due to its transferability to other MAR sites. The assessment of the risk of clogging supported by field characterization and numerical modelling is cost-effective and assists the deduction of O&M schemes for MAR sites. [ABSTRACT FROM AUTHOR]

A deep learning technique called Physics Informed Neural Networks (PINNs) is adapted to study steady groundwater flow in unconfined aquifers. This technique utilizes information from underlying physics represented in the form of partial differential equations (PDEs) alongside data obtained from physical observations. In this work, we consider the Dupuit–Boussinesq equation, which is based on the Dupuit–Forchheimer approximation, as well as a recent, more complete model derived by Di Nucci (2018) as underlying models. We then train PINNs on data obtained from steady-state analytical solutions and laboratory based experiments. Using PINNs, we predict phreatic surface profiles given different input flow conditions and recover estimates for the hydraulic conductivity from the experimental observations. We show that PINNs can eliminate the inherent inability of the Dupuit–Boussinesq equation to predict flows with seepage faces. Moreover, the inclusion of physics information from the Di Nucci and Dupuit–Boussinesq models constrains the solution space and produces better predictions than training on data alone. PINNs based predictions are robust and show a little effect from added noise in the training data. Furthermore, we compare the PINNs solutions obtained via the Di Nucci and Dupuit–Boussinesq flow models to examine the effects of higher order flow terms that are included in the Di Nucci formulation but are neglected by the Dupuit–Boussinesq approximation. Lastly, we discuss the effectiveness of using PINNs for examining groundwater flow. • PINNs predict hydraulic conductivity and water table heights using experimental data. • PINNs eliminate inability of Dupuit–Boussinesq equation when predicting seepage face. • Inclusion of physics improves PINNs predictions compared to plain neural networks. [ABSTRACT FROM AUTHOR]

We explore how X-ray computed microtomography can be used to generate highly-resolved 3D biofilm datasets on length scales that span multiple pore bodies. The data is integrated into a study of the effects of flow rate on three-dimensional growth of biofilm in porous media. Three flow rates were investigated in model packed-bed columns. Biofilm growth was monitored during an 11-day growth period using a combination of differential pressure and effluent dissolved oxygen measurements. At the end of the growth period, all columns were scanned using X-ray computed microtomography and a barium sulfate-based contrast agent. The resulting images were prepared for quantitative analysis using a novel image processing workflow that was tailored to this specific system. The reduction in permeability due to biofilm growth was studied using both transducer-based pressure drop measurements and image-based calculations using the Kozeny–Carman model. In addition, a set of structural measures related to the spatial distribution of biofilms were computed and analyzed for the different flow rates. We generally observed 1 to 2 orders of magnitude decrease in permeability as a result of bioclogging for all columns (i.e, across flow rates). The greatest average permeability and porosity reduction was observed for the intermediate flow rate (4.5 ml/h). A combination of results from different measurements all suggest that biofilm growth was oxygen limited at the lowest flow rate, and affected by shear stresses at the highest flow rate. We hypothesize that the interplay between these two factors drives the spatial distribution and quantity of biofilm growth in the class of porous media studied here. Our approach opens the way to more systematic studies of the structure-function relationships involved in biofilm growth in porous media and the impact that such growth may have on physical properties such as hydraulic conductivity. [ABSTRACT FROM AUTHOR]

Quantifying the uncertainty in solute mass discharge at an environmentally sensitive location is key to assess the risks due to groundwater contamination. Solute mass fluxes are strongly affected by the spatial variability of hydrogeological properties as well as release conditions at the source zone. This paper provides a methodological framework to investigate the interaction between the ubiquitous heterogeneity of the hydraulic conductivity and the mass release rate at the source zone on the uncertainty of mass discharge. Through the use of perturbation theory, we derive analytical and semi-analytical expressions for the statistics of the solute mass discharge at a control plane in a three-dimensional aquifer while accounting for the solute mass release rates at the source. The derived solutions are limited to aquifers displaying low-to-mild heterogeneity. Results illustrate the significance of the source zone mass release rate in controlling the mass discharge uncertainty. The relative importance of the mass release rate on the mean solute discharge depends on the distance between the source and the control plane. On the other hand, we find that the solute release rate at the source zone has a strong impact on the variance of the mass discharge. Within a risk context, we also compute the peak mean discharge as a function of the parameters governing the spatial heterogeneity of the hydraulic conductivity field and mass release rates at the source zone. The proposed physically-based framework is application-oriented, computationally efficient and capable of propagating uncertainty from different parameters onto risk metrics. Furthermore, it can be used for preliminary screening purposes to guide site managers to perform system-level sensitivity analysis and better allocate resources. [ABSTRACT FROM AUTHOR]

To study subsurface microbial processes, a coupled model which has been developed within a Thermal-Hydraulic-Chemical-Mechanical (THCM) framework is presented. The work presented here, focuses on microbial transport, growth and decay mechanisms under the influence of multiphase flow and bio-geochemical reactions. In this paper, theoretical formulations and numerical implementations of the microbial model are presented. The model has been verified and also evaluated against relevant experimental results. Simulated results show that the microbial processes have been accurately implemented and their impacts on porous media properties can be predicted either qualitatively or quantitatively or both. The model has been applied to investigate biofilm growth in a sandstone core that is subjected to a two-phase flow and variable pH conditions. The results indicate that biofilm growth (if not limited by substrates) in a multiphase system largely depends on the hydraulic properties of the medium. When the change in porewater pH which occurred due to dissolution of carbon dioxide gas is considered, growth processes are affected. For the given parameter regime, it has been shown that the net biofilm growth is favoured by higher pH; whilst the processes are considerably retarded at lower pH values. The capabilities of the model to predict microbial respiration in a fully coupled multiphase flow condition and microbial fermentation leading to production of a gas phase are also demonstrated. [ABSTRACT FROM AUTHOR]

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment. [ABSTRACT FROM AUTHOR]

Accurate characterization of subsurface hydraulic conductivity is vital for modeling of subsurface flow and transport. The iterative ensemble smoother (IES) has been proposed to estimate the heterogeneous parameter field. As a Monte Carlo-based method, IES requires a relatively large ensemble size to guarantee its performance. To improve the computational efficiency, we propose an adaptive Gaussian process (GP)-based iterative ensemble smoother (GPIES) in this study. At each iteration, the GP surrogate is adaptively refined by adding a few new base points chosen from the updated parameter realizations. Then the sensitivity information between model parameters and measurements is calculated from a large number of realizations generated by the GP surrogate with virtually no computational cost. Since the original model evaluations are only required for base points, whose number is much smaller than the ensemble size, the computational cost is significantly reduced. The applicability of GPIES in estimating heterogeneous conductivity is evaluated by the saturated and unsaturated flow problems, respectively. Without sacrificing estimation accuracy, GPIES achieves about an order of magnitude of speed-up compared with the standard IES. Although subsurface flow problems are considered in this study, the proposed method can be equally applied to other hydrological models. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Modeling of uncertainty associated with subsurface dynamics has long been a major research topic. Its significance is widely recognized for real-life applications. Despite the huge effort invested in the area, major obstacles still remain on the way from theory and applications. Particularly problematic here is the confusion between modeling uncertainty and modeling spatial variability, which translates into a (mis)conception, in fact an inconsistency, in that it suggests that modeling of uncertainty and modeling of spatial variability are equivalent, and as such, requiring a lot of data. This paper investigates this challenge against the backdrop of a 7 km, deep underground tunnel in China, where environmental impacts are of major concern. We approach the data challenge by pursuing a new concept for Rapid Impact Modeling (RIM), which bypasses altogether the need to estimate posterior distributions of model parameters, focusing instead on detailed stochastic modeling of impacts, conditional to all information available, including prior, ex-situ information and in-situ measurements as well. A foundational element of RIM is the construction of informative priors for target parameters using ex-situ data, relying on ensembles of well-documented sites, pre-screened for geological and hydrological similarity to the target site. The ensembles are built around two sets of similarity criteria: a physically-based set of criteria and an additional set covering epistemic criteria. In another variation to common Bayesian practice, we update the priors to obtain conditional distributions of the target (environmental impact) dependent variables and not the hydrological variables. This recognizes that goal-oriented site characterization is in many cases more useful in applications compared to parameter-oriented characterization. [ABSTRACT FROM AUTHOR]

Hydrologic models are commonly over-smoothed relative to reality, owing to computational limitations and to the difficulty of obtaining accurate high-resolution information. When used in an inversion context, such models may introduce systematic biases which cannot be encapsulated by an unbiased “observation noise” term of the type assumed by standard regularization theory and typical Bayesian formulations. Despite its importance, model error is difficult to encapsulate systematically and is often neglected. Here, model error is considered for an important class of inverse problems that includes interpretation of hydraulic transients and contaminant source history inference: reconstruction of a time series that has been convolved against a transfer function (i.e., impulse response) that is only approximately known. Using established harmonic theory along with two results established here regarding triangular Toeplitz matrices, upper and lower error bounds are derived for the effect of model error on time series recovery for both well-determined and over-determined inverse problems. It is seen that use of additional measurement locations does not improve expected performance in the face of model error. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. A possible diagnostic criterion for blind transfer function characterization is also uncovered. [ABSTRACT FROM AUTHOR]

Geological heterogeneity, i.e. the spatial variability of discrete hydrogeological units, is investigated in an aquifer analog of glacio-fluvial sediments to determine how such a geological structure can be simplified for characterization needs. The aquifer analog consists of ten hydrofacies whereas the scarcity of measurements in typical field studies precludes such detailed spatial models of hydraulic properties. Of particular interest is the role of connectivity of the hydrofacies structure, along with its effect on the connectivity of mass transport, in site characterization for predicting early arrival times. Transport through three realizations of the aquifer analog is modeled with numerical particle tracking to ascertain the fast flow channel through which early arriving particles travel. Three simplification schemes of two-facies models are considered to represent the aquifer analogs, and the velocity within the fast flow channel is used to estimate the apparent hydraulic conductivity of the new facies. The facies models in which the discontinuous patches of high hydraulic conductivity are separated from the rest of the domain yield the closest match in early arrival times compared to the aquifer analog, but assuming a continuous high hydraulic conductivity channel connecting these patches yields underestimated early arrivals times within the range of variability between the realizations, which implies that the three simplification schemes could be advised but pose different implications for field measurement campaigns. Overall, the results suggest that the result of transport connectivity, i.e. early arrival times, within realistic geological heterogeneity can be conserved even when the underlying structural connectivity is modified. [ABSTRACT FROM AUTHOR]

Knowledge of sub-core permeability is necessary for accurate numerical modeling of coreflooding experiments and for investigation of sub-core flow phenomenon. A new method for estimating sub-core permeability geometric mean ( k G ) and log-permeability variance ( σ y 2 ) is presented. The method is based on matching coreflooding experiment measurements of wetting phase relative permeability with semi-analytical calculations of effective relative permeability. The semi-analytical solution is formulated assuming log-normal permeability ( k ), steady state and capillary-limit conditions. It is based on the geometric mean and log-phase-permeability variance for isotropic k and power law averaging for anisotropic correlations. The solution is validated on synthetic k realizations by comparison with numerical calculations. Then, the estimation method is tested on synthetic data assuming various types of core capillary pressure relationships, relative permeability functions and k anisotropies. Results demonstrate high accuracy in almost all of the cases except for small anisotropy ratios l h / l v between horizontal ( l h ) and vertical ( l v ) dimensionless correlation lengths, where flow is in the horizontal direction, and when σ y 2 is large. The method is also validated using data from CO 2 -brine coreflooding experiments conducted on two different cores. It is found that the estimation method remains accurate in these realistic settings, however, accuracy of k G is reduced when the core permeability departs from a log-normal distribution. [ABSTRACT FROM AUTHOR]

A merging procedure is applied to five daily rainfall estimates achieved via SM2RAIN applied to the soil moisture products obtained by the Advanced SCATterometer, the Advanced Microwave Scanning Radiometer 2, the Soil Moisture Active and Passive mission, the Soil Moisture and Ocean Salinity mission and backscattering observations of RapidScat. The precipitation estimates are evaluated against dense ground networks in the period ranging from April to December, 2015, in India and in Italy, at 0.25°/daily spatial/temporal resolution. The merged product derived by combining the different SM2RAIN rainfall products shows better results in term of statistical and categorical metrics with respect to the use of the single products. A good agreement with reference to ground observations is obtained, with median correlations equal to 0.65 and 0.77 in India and in Italy, respectively. The merged dataset is found to slightly outperform those of the IMERG product of the Global Precipitation Measurement mission underlying the large potential of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y * ( Y  = ln T ) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the ln T has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities ( σ Y 2 = 1.0 and σ Y 2 = 5.3 ). The estimated transmissivity fields were compared to the true one. The joint use of Y * and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds. [ABSTRACT FROM AUTHOR]

This paper demonstrates quantitative reasoning to separate the dataset of spatially distributed variables into different entities and subsequently characterize their geostatistical properties, properly. The main contribution of the paper is a statistical based algorithm that matches the manual distinction results. This algorithm is based on measured data and is generally applicable. In this paper, it is successfully applied at two datasets of saturated hydraulic conductivity (K) measured at the Borden (Canada) and the Lauswiesen (Germany) aquifers. The boundary layer was successfully delineated at Borden despite its only mild heterogeneity and only small statistical differences between the divided units. The methods are verified with the more heterogeneous Lauswiesen aquifer K data-set, where a boundary layer has previously been delineated. The effects of the macro- and the microstructure on solute transport behaviour are evaluated using numerical solute tracer experiments. Within the microscale structure, both Gaussian and non-Gaussian models of spatial dependence of K are evaluated. The effects of heterogeneity both on the macro- and the microscale are analysed using numerical tracer experiments based on four scenarios: including or not including the macroscale structures and optimally fitting a Gaussian or a non-Gaussian model for the spatial dependence in the micro-structure. The paper shows that both micro- and macro-scale structures are important, as in each of the four possible geostatistical scenarios solute transport behaviour differs meaningfully. [ABSTRACT FROM AUTHOR]

Models used for data interpretation of constant-rate tests (CRTs) are commonly derived with the assumption of Darcian flow in an idealized integer flow dimension, where the non-Darcian nature of fluid flow and the complexity of flow geometry are disregarded. In this study, a Forchheimer's law-based analytical model is proposed with the assumption of buildup (or drawdown) decomposition for characterizing the non-Darcian flow in a generalized radial formation where the flow dimension n may become non-integer. The proposed model immediately reduces to Barker's (1988) model for Darcian flow in the generalized radial formation and to Mathias et al.'s (2008) model for non-Darcian flow in a two-dimensional confined aquifer. A comparison with numerical simulations shows that the proposed model behaves well at late times for flow dimension n  > 1.5. The proposed model is finally applied for data interpretation of the constant-rate pumping tests performed at Ploemeur (Le Borgne et al., 2004), showing that the intrinsic hydraulic conductivity of formations will be underestimated and the specific storage will be overestimated if the non-Darcian effect is ignored. The proposed model is an extension of the generalized radial flow (GRF) model based on Forchheimer's law, which would be of significance for data interpretation of CRTs in aquifers of complex flow geometry in which non-Darcian flow occurs. [ABSTRACT FROM AUTHOR]

A new mathematical model is developed to describe the flow in response to a constant-head pumping (or constant-head test, CHT) in a leaky unconfined aquifer system of infinite lateral extent with considering unsaturated flow. The model consists of an unsaturated zone on the top, an unconfined aquifer in the middle, and a second aquifer (aquitard) at the bottom. The unsaturated flow is described by Richard's equation, and the flows in unconfined aquifer and second layer are governed by the groundwater flow equation. The well partially penetrates the unconfined aquifer with a constant head in the well due to CHT. The governing equations of the model are linearized by the perturbation method and Gardner's exponential model is adopted to describe the soil retention curves. The solution of the model for drawdown distribution is obtained by applying the methods of Laplace transform and Weber transform. Then the solution for the wellbore flowrate is derived from the drawdown solution with Darcy's law. The issue of the equivalence of normalized drawdown predicted by the present solution for constant-head pumping and Tartakovsky and Neuman's (2007) solution for constant-rate pumping is discussed. On the basis of the wellbore flowrate solution, the results of the sensitivity analysis indicate that the wellbore flowrate is very sensitive to the changes in the radial hydraulic conductivity and the thickness of the saturated zone. Moreover, the results predicted from the present wellbore flowrate solution indicate that this new solution can reduce to Chang’s et al. (2010a) solution for homogenous aquifers when the dimensionless unsaturated exponent approaches 100. The unsaturated zone can be considered as infinite extent in the vertical direction if the thickness ratio of the unsaturated zone to the unconfined aquifer is equal to or greater than one. As for the leakage effect, it can be ignored when the vertical hydraulic conductivity ratio (i.e., the vertical hydraulic conductivity of the lower layer over that of the unconfined aquifer) is smaller than 0.1. The present solution is compared with the numerical solution from FEMWATER for validation and the results indicate good match between these two solutions. Finally, the present solution is applied to a set of field drawdown data obtained from a CHT for the estimation of hydrogeologic parameters. [ABSTRACT FROM AUTHOR]

We investigate tracer transport on random discrete fracture networks that are characterized by the statistics of the fracture geometry and hydraulic conductivity. While it is well known that tracer transport through fractured media can be anomalous and particle injection modes can have major impact on dispersion, the incorporation of injection modes into effective transport modeling has remained an open issue. The fundamental reason behind this challenge is that—even if the Eulerian fluid velocity is steady—the Lagrangian velocity distribution experienced by tracer particles evolves with time from its initial distribution, which is dictated by the injection mode, to a stationary velocity distribution. We quantify this evolution by a Markov model for particle velocities that are equidistantly sampled along trajectories. This stochastic approach allows for the systematic incorporation of the initial velocity distribution and quantifies the interplay between velocity distribution and spatial and temporal correlation. The proposed spatial Markov model is characterized by the initial velocity distribution, which is determined by the particle injection mode, the stationary Lagrangian velocity distribution, which is derived from the Eulerian velocity distribution, and the spatial velocity correlation length, which is related to the characteristic fracture length. This effective model leads to a time-domain random walk for the evolution of particle positions and velocities, whose joint distribution follows a Boltzmann equation. Finally, we demonstrate that the proposed model can successfully predict anomalous transport through discrete fracture networks with different levels of heterogeneity and arbitrary tracer injection modes. [ABSTRACT FROM AUTHOR]

• Cross-gradients constraint inversion is fused into hydraulic tomography. • The method permits deterministic optimization of structural similarities. • Limited improvements are obtained from the cross-gradients constraint. The inclusion of a priori information is helpful to obtain high resolution parameter identifications. A common practice is to exploit structural information in the search for detailed hydrogeological characterizations of subsurface. In this study, we proposed to incorporate cross-gradients as a constraint in nonlinear inverse problems. The resultant inversion scheme is successfully applied to three synthetic experiments and one laboratory rock block experiment with structural similarities in hydraulic parameters and also compared to estimated results with a traditional method. Our results show similar estimated hydraulic parameters whether the objective function has the cross-gradients operator or not. The improvements are only enhanced when assuming one type of parameter is completely known. The limited improvement is proved by the small contribution from the cross-gradients term in the objective function. Therefore, the cross-gradients constraint is a weak structural constraint. The main reason is that drawdown data has already contained correlated hydrogeological parameter information. Estimated results substantiate the rationalization for a simplified assumption that hydraulic conductivity and specific storage are treated as mutual independent variables. [ABSTRACT FROM AUTHOR]

We consider non-linear Bayesian inversion problems targeting the geostatistical hyperparameters of a random field describing hydrogeological or geophysical properties given hydrogeological or geophysical data. This problem is of particular importance in the non-ergodic setting as there are no analytical upscaling relationships linking the data to the hyperparameters, such as, mean, standard deviation, and integral scales. Full inversion of the hyperparameters and the local properties of the field (typically involving many thousands of unknowns) brings substantial computational challenges, such that simplifying model assumptions (e.g., homogeneity or ergodicity) are typically made. To prevent the errors resulting from such simplified assumptions while also circumventing the burden of high-dimensional full inversions, we use a pseudo-marginal Metropolis–Hastings algorithm that treats the random field as latent variables. In this random effects model, the intractable likelihood of observing the data given the hyperparameters is estimated by Monte Carlo averaging over realizations of the random field. To increase the efficiency of the method, low-variance approximations of the likelihood ratio are obtained by using importance sampling and by correlating the samples used in the proposed and current steps of the Markov chain. We assess the performance of this correlated pseudo-marginal method by considering two representative inversion problems involving diffusion-based and wave-based physics, respectively, in which we infer the hyperparameters of (1) hydraulic conductivity fields using apparent hydraulic conductivity data in a data-poor setting and (2) fracture aperture fields using borehole ground-penetrating radar (GPR) reflection data in a more data-rich setting. For the first test case, we find that the correlated pseudo-marginal method generates similar estimates of the geostatistical mean as classical rejection sampling, while an inversion assuming ergodicity provides biased estimates. For the second test case, we find that the correlated pseudo-marginal method estimates the hyperparameters well, while rejection sampling is computationally unfeasible and a simplified model assuming homogeneity leads to biased estimates. [Display omitted] • Hyperparameters enable general descriptions of target property fields. • No analytical relation linking hyperparameters and data in the non-ergodic setting. • Correlated pseudo-marginal method accounts for the influence of sample realizations. • It avoids a high-dimensional target space and errors from simplified assumptions. [ABSTRACT FROM AUTHOR]

Pore-network models were found useful in describing important flow and transport mechanisms and in predicting flow properties of different porous media relevant to numerous fundamental and industrial applications. Pore-networks provide very fast computational framework and permit simulations on large volumes of pores. This is possible due to significant pore space simplifications and linear/exponential relationships between effective properties and geometrical characteristics of the pore elements. To make such relationships work, pore-network elements are usually simplified by circular, triangular, square and other basic shapes. However, such assumptions result in inaccurate prediction of transport properties. In this paper, we propose that pore-networks can be constructed without pore shape simplifications. To test this hypothesize we extracted 3292 2D pore element cross-sections from 3D X-ray microtomography images of sandstone and carbonate rock samples. Based on the circularity, convexity and elongation of each pore element we trained neural networks to predict the dimensionless hydraulic conductance. The optimal neural network provides 90% of predictions lying within the 20% error bounds compared against direct numerical simulation results. Our novel approach opens a new way to parameterize pore-networks and we outlined future improvements to create a new class of pore-network models without pore shape simplifications. [ABSTRACT FROM AUTHOR]