Equivalent Porous Medium Research Articles

Suitability evaluation of an equivalent porous medium method for characterizing 2-D flow based on the fracture fractal dimension

ABSTRACT An equivalent porous medium (EPM) method is widely utilized in various practical applications of hydrogeological engineering with areas of a fractured geological medium (FGM). However, the suitability of the EPM model still lacks sufficient scientific evaluation when considering the distribution of water head and flow velocity. In this study, the suitability of the EPM model to the fractal dimension of a discrete fracture network (DFN) is analyzed based on numerical simulation experiments. The simulation results of the EPM model are compared with those of the DFN model. Then, a formula is proposed to evaluate the suitability of the EPM model for characterizing two-dimensional flow distribution. The results show that with the increase of the fractal dimension, the suitability of the EPM model decreases first and then increases, and the inflection point gradually appears in advance with the increase of the length–width ratio of the simulation domain. The length–width ratio of the simulation domain has a linear relationship with the suitability of the EPM model, and the slope increases with the increase of the fractal dimension. Finally, a quantitative evaluation method is proposed to calculate the suitability of the EPM model based on the fractal dimension and the length–width ratio of the simulation domain.

Reversibility of seawater intrusion in a coastal aquifer: Insights from long-term field observation and numerical modeling

It is essential to understand basis processes affecting the reversibility of seawater intrusion (SWI) and the related timescale after groundwater pumping stopped for coastal groundwater management. Groundwater salinity variations presented by previous studies showed a fast SWI process and the following seawater retreat (SWR) process indicated by overall salinity decrease in the coast karst aquifer in the Dalian Peninsula, northeast China. Cross-sectional variable-density flow and transport simulations using equivalent porous medium (EPM) model, dual-domain (DDM) model and the EPM with a single discrete feature representative of conduit flow (EPM-DF) are conducted to understand the SWI reversibility related to the characteristics of the flow system, including aquifer parameters and seaside boundary conditions. Large dispersity combined with a low salinity concentration at the sea boundary are necessary in the EPM and DDM models to produce a fast SWI and low salinity concentration as observed. The enhanced dispersion in the DDM model enhances the mixing in the transition zone (TZ) and produces more obvious seasonal variation but longer SWR process compared to the EPM model. The EPM-DF model produces significant salinity seasonal variation during the SWI process and a fast decrease in the SWR process. The overall fast system response but low peak concentration during the SWI might be attributed to the highly heterogeneous characteristics of the karst aquifer system, which produces a wide front edge of TZ as observed. The dispersion-dominated EPM and DDM models produced higher degree of SWI reversibility compared to the EPM-DF model, as indicated by the weaker lag effects between groundwater levels and salinity concentration. Moreover, the SWI reversibility may arise not only from the heterogeneous characteristics of the karstic aquifer system but also from the rate for rise in the inland groundwater level during the seasonal variation cycle. An overall SWR process can be divided into two stages: the first stage with rapid decrease in salinity concentration but small changes in toe associated with TZ widening and the second stage with rapid toe retreat during aquifer flushing. The flushing of the brine leakage from the solar salt field may extend the SWR process. Considering this relatively longer water quality response time than the time span in general groundwater management plans, a reasonable objective and how maintain the hydraulic head during the SWI controlling have been of a great concern to the coastal groundwater management.

Groundwater flow modelling in Neoproterozoic carbonate karst based on dye tracer pathways

The current study consisted of the development of a hydrogeological numerical model in the Lagoa Santa Karst Environmental Protection region, in order to represent the conduit-flow karst springs in the most well-studied karst system in Brazil. Once carbonate aquifers are characterized by a complex 3D pattern with a combination of a double porosity of matrix and conduits, two different modelling approaches were used: Equivalent Porous Medium (EPM), based on Darcy’s law, to represent laminar flow in the fractured massif and Conduit Network (CN), using Manning-Stricker Law and the discrete feature tool, to represent the karst conduits with turbulent flow. Modeling was calibrated in a steady-state and simulations of groundwater flow and an evaluation of water exchanges between the karstic aquifer and the other hydrogeological units, were conducted. The model was developed based on data available for many studies carried out in the area, including tracer-derived route data. The calibration results for spring discharges, water levels and mass balance were satisfactory and aligned with modeling good practices. In turn, the hydraulic conductivities and recharge rates obtained by back-analysis were in agreement with literature references. The regional groundwater flow was well represented and indicated how external water entrances can be relevant to explain the higher discharge rates observed in some karstic springs. In addition, the representation of conduits allowed for the simulation of tracer pathways, enabling the inference of potential flow rates to the karstic springs from the particle simulations.

The effect of fracture aperture and matrix permeability on suitability of the equivalent porous medium model for steady-state flow in fractured porous media

The effect of fracture aperture and matrix permeability on suitability of the equivalent porous medium model for steady-state flow in fractured porous media

Accounting for mesoscale geometry and intra-yarn fiber volume fraction distribution on 3D angle-interlock fabric permeability

Understanding resin flows within 3D interlock fabrics involves addressing a dual-scale flow problem. Indeed, the fluid can flow through inter-yarn channels, characterized by a unit cell mesoscale morphology, but also within yarns considered as homogeneous equivalent porous media. The former is assumed to follow the Stokes’ law while the latter be related to the Darcy’s law, directly linked to the microscopic intra-yarn fiber volume fraction (FVF) field. In this work, a coupled Stokes–Darcy steady-state flow within a 3D woven textile, modeled at mesoscale, is solved through a finite element monolithic approach with a mixed velocity-pressure formulation, stabilized by the Variational MultiScale Method (VMS) and implemented in the Z-set software. The fabric permeability tensor is then computed without any assumptions on its nature and analyzed both through its diagonal components, its eigenvectors and eigenvalues. The main contribution of this study lies in examining the influence of variations of the inter-yarn porous medium morphology, through textile compaction and geometrical reduction to prevent edge flows, and the intra-yarn permeability (from complete field to unique value) on the overall fabric permeability.

Can effective porosity be used to estimate near-well protection zones in fractured chalk?

Protection of fractured carbonate aquifers is often based on a single-porosity description of a dual-porosity system. However, it is difficult to assess a trustworthy value of the effective porosity based on scientific principles; thus, a range of estimates is often suggested. The complexity of the problem is compounded by the fact that the effective porosity may be scale-dependent. This paper investigates whether it is possible to describe solute transport in fractured carbonate rocks with an equivalent porous medium model using a constant value of effective porosity. It is assumed that the dual-porosity model provides an acceptable description of transport mechanisms in fractured porous rock and that it is possible to estimate the parameters needed in the single-porosity models from results generated by the dual-porosity model. The effective porosity is estimated from the dual-porosity results that are used as targets. For Danish chalk, an effective porosity of 13% (11–17%) is estimated. However, it is demonstrated that the estimated effective porosity is only valid at the specific transport time (1 year) from which simulation results of the dual-porosity model were extracted. The effective porosity is shown to increase with travel time until equilibrium conditions are realised between the fractures and matrix, following which, the effective porosity equals the matrix porosity and will maintain this value at larger transport times. Assuming that the dual-porosity model provides a trustworthy description of solute transport in fractured chalk and limestone, a method to estimate the effective porosity of an equivalent porous medium model is presented.

High‐Resolution Characterization of Excavation‐Induced Fracture Network Using Continuous and Discrete Inversion Schemes

AbstractThe Meuse/Haute‐Marne Underground Research Laboratory provides the location for the experiment designed to investigate the induced fracture network around open or sealed galleries and drifts. The objective of this study is to investigate and reconstruct the hydraulic properties and the geometry of the induced fracture network to improve the insights and validate the conceptual model of the induced fracture network due to the stress redistribution during tunnel excavations. Within the presented study, the cross‐hole responses of the pneumatic tests were analyzed in the first step with an equivalent porous media—3D travel time‐based tomographic approach. In the next step selected 2D profiles of the 3D model domain were inverted using a discrete fracture network inversion approach. The database of the tomographic analysis is based on 18 gas injection tests and 151 pressure interferences, which were recorded between nine closely spaced boreholes. The travel time‐based inversion approach allowed for the reconstruction of the 3D gas diffusivity distribution between nine boreholes with high‐resolution. The applied discrete fracture network inversion approach is based on a transdimensional Markov Chain Monte Carlo (MCMC) methodology and it operates with reversible model updates (jumps) that change the problem dimensions, that is, the number, length and position of fractures within the model domain after each iteration step. The synthesis of the results between the reconstructed 3D diffusivity tomogram and the 2D fracture tomograms improved the insights into the spatial geometry of the induced fracture network around galleries.

Effect of Physical Properties on Mechanical Behaviors of Sandstone under Uniaxial and Triaxial Compressions.

Mechanical properties of sandstone, such as compressive strength and young's modulus, are commonly used in the design of geotechnical structures and numerical simulation of underground reservoirs using models such as the digital groundwater, equivalent porous medium, and Discrete Fracture Network (DFN) models. A better understanding of the mechanical behaviors of sandstone under different loading conditions is imperative when assessing the stability of geotechnical structures. This paper highlights the effect of the physical properties (i.e., porosity, mean grain size) and environmental conditions (i.e., water content and confining stress) on uniaxial compressive strength, triaxial compressive strength, and young's modulus of sandstone. A series of uniaxial and triaxial compression experiments are conducted on sandstone formations from Wyoming. In addition, experimental data on sandstones from the literature are compiled and integrated into this study. Prediction equations for the compressive strengths and young's modulus of sandstone are established based on commonly available physical properties and known environmental conditions. The results show that the mean Uniaxial Compressive Strength (UCS) decreases as the porosity, water content, and mean grain size increase. Furthermore, a predictive empirical relationship for the triaxial compressive strength is established under different confinements and porosity. The relationship suggests that the mean peak compressive strength increases at a higher confinement and decreases at a higher porosity. The results and recommendations provide a useful framework for evaluating the strength and deformation of most sandstone.

Pressure transient analysis to investigate a coupled fracture corridor and a fault damage zone causing an early thermal breakthrough in the North Alpine Foreland Basin

The heterogeneity of the Upper Jurassic carbonate reservoir (Malm reservoir) beneath the North Alpine Foreland Basin has a significant influence on the mass and heat flow processes during geothermal exploitation. Geophysical borehole data revealed that sub-seismic scale fractures and karstified fractures occur at the inflow zones of deep geothermal wells. However, pressure transient analysis (PTA) in some previous studies concluded that it is difficult to detect the influence of sub-seismic scale features, suggesting that radial flow regime is dominant. Accordingly, a regional thermal-hydraulic model adopted the equivalent porous medium (EPM) approach, homogenizing the sub-seismic scale reservoir heterogeneities; however, unable to detect an early thermal breakthrough (ETB) in a geothermal doublet located SE of Munich. We apply PTA on three buildup tests belonging to that doublet following a deterministic approach to constrain the reservoir type by interpreting the pressure derivative (PD) plots constrained by geophysical and geological data. We derive the magnitudes of the reservoir hydraulic parameters by matching the PD plots with the selected interpretation models. We find that clustered fractures have a significant influence on the reservoir hydraulics, evidenced by trough-shaped curves in the PD plots. Linear flow regime interpreted from the interference test between the two wells indicates permeability anisotropy, which may have caused the ETB. Geophysical data interpretations indicate that these fractures correspond to a coupled fault damage zone and a fracture corridor. Finally, we present a fit-for-purpose 2D discrete fracture network model utilizing the PTA results to match our analytically calibrated model. Our study offers a potential hydraulic explanation to the cause of the ETB highlighting the importance of integrating multi-scale/disciplinary data sets to improve the reliability of dynamic reservoir models, based on which, economic-related decisions are made.

Numerical study on thermal behaviors of parallel plate systems for sensible thermal energy storage with heat loss

A numerical study on thermal energy storage systems with parallel plates to collect sensible heat is conducted with porous and direct model approaches. The simulations in a two-dimensional domain are performed with COMSOL Multiphysics commercial software. For the equivalent porous medium, the permeability and effective thermal conductivity as well as the specific area, and interfacial convective coefficient are numerically evaluated, considering a thermally and hydrodynamically fully developed flow. A stack of parallel plates is the system with assigned length and height, and the external heat losses effect is considered. The analysis allows to evaluate an optimized configuration as Channels Per Length (CPL) by means of a balance in the channels between pressure drop and heat transfer. Moreover, the effect of CPL values and heat loss from the parallel plate system is estimated in terms of charging time and heating capacity. The results exhibit that as the CPL increases, the time required for the charging process decreases while heat accumulation inside the system increases significantly. In fact, at the highest CPL, charging time is 2.7 times faster and the amount of heat accumulation is approximately 20% higher in adiabatic case. It is illustrated that the amount of heat accumulation inside the system varies considerably for different heat loss values. Ultimately, this study shows that porous model is more practical and accurate to be used for higher CPL cases.

Evaluation method of underground water storage space and thermal reservoir model in abandoned mine

A large number of mines are closed or abandoned every year in China. Geothermal utilization is one of the important ways to efficiently reuse underground resources in abandoned mines. How to calculate the volume and distribution of underground water storage space is the key to accurately evaluate the sustainable geothermal production in abandoned mines. In this paper, according to the multi-scale characteristics of the underground space in abandoned mine, the flow and heat transfer equations in the multi-scale space are sorted out systematically, and the calculation methods of different secondary space volumes are derived in detail. Taking Jiahe abandoned mine as the background, the volume and distribution of underground secondary space are calculated, and three heat storage evaluation models considering different water storage spaces are established by using COMSOL. The simulation results show that there are great differences among different models, and the results of the equivalent porous media model considering the multi-scale space are most consistent with the reality. Sensitivity analyses of key parameters model results indicated that the heat production is closely related to not only the recharge flow rate but also the recharge temperature and operating time. Furthermore, the energy saving and emission reduction benefits of geothermal utilization in abandoned mines are calculated, the results show that geothermal utilization of abandoned mines can effectively reduce energy consumption and CO2 emissions, and it has great economic benefits.

Numerical Modeling of Hydrothermal System Circulation Beneath Asal Rift, Republic of Djibouti

Asal rift is an aerial rift segment resulting from the westward propagation of the Aden ridge into the Afar Depression. Geothermal manifestations such as hot springs and fumaroles, fault creep, conductivity anomaly, and high geothermal gradient were observed both at the surface and in the subsurface. Despite many scientific works conducted in Asal to understand the rifting mechanisms, the hydrothermal fluid circulation still needs to be evaluated since it is based on simplified conceptual models. To further contribute and progress toward a quantitative evaluation of fluid circulation, a 2D numerical model perpendicular to the rift axis was developed with the objective of better understanding the role of subsurface anisotropy in fluid flow and heat transfer in the Asal rift. Numerical modeling of multiphase flow and heat transfer was carried out with an equivalent porous medium intersected by fault zones having greater permeability. Horizontal anisotropic permeability and magmatic fluid release were taken into account with different simulation scenarios. The results indicate that fault zones act as recharge/discharge areas depending on their location, permeability, and number. Simulations considering horizontal anisotropic permeability allowed the reproduction of the thermal state observed in geothermal wells with the expected general pattern of fluid circulation in the Asal rift. Comparing our result with a recent study made with a 2D numerical modeling parallel to the rift axis, we suggest the presence of a saddle point where fluid flow is both to the northeast and to the southwest direction of the rift. Moreover, magmatic fluid release assumed in two simulation scenarios showed to have an impact on the hydrological behavior of fault zones and facilitate the development of super-critical flow at the center of the rift.

Multiscale fractures integrated equivalent porous media method for simulating flow and solute transport in fracture-matrix system

The fracture–matrix system, in which water is stored and transported, has a significant impact on the hydraulic behaviors of fractured geologic media (FGM). However, it is very challenging to accurately simulate flow behavior in FGM due to the difficulty of characterizing dual-permeability media, including multiscale fractures with high permeability and porous matrix with low permeability. In this study, a multiscale fracture integrated equivalent porous medium (MFEPM) method is proposed for simulating fluid flow and solute transport in a fracture–matrix system. The synthetic enhanced matrix (SEM) is compounded by integrating small-scale fractures into the porous medium, and the medium- and large-scale fractures are mapped to refined grids of the MFEPM to increase the characterization of the fracture geometry and orientation. Then, the equivalent hydraulic properties are calculated according to the properties of the fractures. Finally, a finite difference method (FDM) based on the MFEPM is used to simulate flow and solute transport in coupled multiscale fractures and rock matrix. The case study illustrates that compared with the traditional equivalent porous medium (EPM) method, the MFEPM manifests an efficient effect in the characterization of preferential flow; compared with the discrete fracture network (DFN) method, the MFEPM can characterize flow and solute transport in the SEM and represent mass interactions between the fractures and matrix. The results of the numerical case studies of flow and solute transport also show that the MFEPM method has a high computational accuracy and good reliability, while maintaining an appropriate computational burden.

Simulation Study on Nitrogen Pollution in Shallow Groundwater in Small Agricultural Watersheds in the Huixian Wetland

In this study, we investigated the influence of different simulations on the transport of shallow groundwater nitrogen in the Mudong River watershed of the Huixian Wetland, a karst wetland. Based on GMS (Groundwater Modeling System) software, the equivalent porous media model was used to simulate the transport of total nitrogen under different conditions in the study area. Two years of field monitoring data in the study area provided the input for the modeling. The SWAT (soil and water assessment tool) model was used to divide the study area into sub-basins. The initial concentration flux index W is first introduced in the equivalent porous medium model to calculate the initial concentration. The simulation results showed the difference between the simulated and monitored values of total nitrogen concentration was between 20% and 40% in 22.2% of the cases, and less than 20% in 66.7% of the cases, indicating that the solute transport model has good applicability in the Huixian Wetland. Parameter sensitivity analysis showed that fertilizer application was the main factor influencing total nitrogen. A 25% reduction in fertilizer application reduced total nitrogen emissions by 31.5% in sub-basin S3 and 22.5% in sub-basin S4. These reductions were greater than the abatement effect of changing land cover and managing river pollution. The pollution plume of total nitrogen was reduced by 38.5% in the southern part of sub-basin S3 (Mudong Lake) and by 40.2% in the western part of sub-basin S4 (Blacksmithing Village). The average concentration was reduced by 2.04 mg/L and 1.22 mg/L, respectively. This study shows that reasonable control of double-season rice nitrogen fertilizer application and appropriate land cover modification can help reduce total nitrogen emissions from wetlands in the Li River watershed and ensure the sustainable development of the local economy and groundwater.

Reply to discussion on ‘Review of groundwater flow and contaminant transport modelling approaches for the Sherwood Sandstone aquifer, UK; insights from analogous successions worldwide’ by Medici and West ( QJEGH , 55, qjegh2021-176)

Sandstone aquifers are challenging to characterize, model and review due to interplays between intergranular porosities, narrow fractures and rock discontinuities enlarged by the groundwater flow (Tellam and Barker 2006; Hitchmough et al. 2007, Bashar and Tellam 2011, Medici et al. 2019). New data collected, and advances in hydraulic testing and modelling techniques should guide the next steps on research on sandstone aquifers worldwide. The contribution of Medici and West (2022) is intended to point the hydrogeological community towards more novel modelling approaches that need to be integrated with all the previous practices for the Sherwood Sandstone aquifer, that have mostly focussed on the Equivalent Porous Medium (EPM), as this is the most widely accepted and practical solution. The focus of the review paper is thus novel approaches to modelling of the flow heterogeneities of the Sherwood Sandstone aquifer as a consequence of a hydraulic characterization project funded by TotalEnergies, which was specific to the Triassic comprising the Sherwood Sandstone Group rather than Permian strata. The flow heterogeneities of sedimentary origin and tectonic origin have also been reviewed in the UK Triassic Sandstone with no angle on groundwater flow modelling (Medici et al. 2019a, b).

Uncertainty and sensitivity analysis of radionuclide migration through fractured granite aquifer

The radionuclide migration in the high-level radioactive waste (HLW) disposal is usually predicted by numerical simulations for risk analysis of radionuclide contamination in a large scale of time and space. However, the uncertainties in radionuclide migration models and their associated parameters significantly affect the simulation results. In the present study, we first selected certain parameters and output data as independent parameters and risk metrics and performed a series of radionuclide transport models at a research site in Northwestern China. The models considered radionuclide migration in the equivalent porous medium with the mechanism of nuclide decay in an arbitrary-length decay chain, adsorption, advection, diffusion, and dispersion. Then 3000 Monte Carlo (MC) simulations were performed to carry out a set of uncertainty and global sensitivity analysis by coupling an uncertainty quantification tool with a radionuclide migration simulator. The results indicated that both hydraulic gradient and hydraulic conductivity significantly influenced the risk metrics. Thus, it is critical to obtain hydraulic gradient and hydraulic conductivity data under the same economic conditions. We applied the multivariate adaptive regression spline (MARS) method to generate response surface models representing the relationships among independent parameters and risk metrics. Calculations of the risk metric distribution ranges revealed that the peak release doses would appear at 0.40 and 0.79 million years, and their values will be in the range of 4.7 × 10−7–1.93 × 10−6 Sv/a. Uncertainty and sensitivity analysis results of radionuclide contamination in the fractured granite upon which HLW is disposed can improve simulation and prediction accuracy for radionuclide migration.

A Stepwise Modelling Approach to Identifying Structural Features That Control Groundwater Flow in a Folded Carbonate Aquifer System

This paper concerns a stepwise modelling procedure for groundwater flow simulation in a folded and faulted, multilayer carbonate aquifer, which constitutes a source of good quality water for human consumption in the Apennine Range in Central Italy. A perennial river acts as the main natural drain for groundwater while sustaining valuable water-related ecosystems. The spatial distribution of recharge was estimated using the Thornthwaite–Mather method on 60 years of climate data. The system was conceptualized as three main aquifers separated by two locally discontinuous aquitards. Three numerical models were implemented by gradually adding complexity to the model grid: single layer (2D), three layers (quasi-3D) and five layers (fully 3D), using an equivalent porous medium approach, in order to find the best solution with a parsimonious model setting. To overcome dry-cell problems in the fully 3D model, the Newton–Raphson formulation for MODFLOW-2005 was invoked. The calibration results show that a fully 3D model was required to match the observed distribution of aquifer outflow to the river baseflow. The numerical model demonstrated the major impact of folded and faulted geological structures on controlling the flow dynamics in terms of flow direction, water heads and the spatial distribution of the outflows to the river and springs.

Stochastic Modeling Approach to Identify Uncertainties of Karst Conduit Networks in Carbonate Aquifers

AbstractThe characterization of the karst conduit network is an essential task to understand the complex flow system within karst aquifers. However, this task is challenging and often associated with uncertainty. Equivalent porous media approaches for modeling flow in karst aquifers fall short of capturing the hydraulic effect of individual karst features, while process‐oriented karst evolution models imply major computational efforts. In this study, we apply the Stochastic Karst Simulator (SKS) developed by Borghi et al. (2012) to generate karst conduit networks at a regional scale of a highly karstified carbonate aquifer located in the Eastern Mediterranean region and extensively used for water supply. The SKS generates conduit network geometries reasonably quick, using a mathematical proxy that mimics conduit evolution. The conduit simulation is based on a conceptual model of the genesis of the aquifer, consisting of different karstification phases. The stochastic approach of the algorithm enables us to generate an ensemble of conduit network realizations and to represent the uncertainties of these simulations in a Karst Probability Map. With only soft input information to constrain conduit evolution, multiple equivalent realizations yield similar resulting network geometries, indicating a robust approach. The presented methodology is numerically efficient, and its input can be easily adjusted. Subsequently, the resulting stochastic spatial distribution of conductivities can be employed for the parametrization of regional karst groundwater models.

Bayesian inversion of laboratory experiments of transport through limestone fractures

In this study, a novel experimental setup is proposed for which a column filled with glass beads and parallelepiped-shaped limestone beams is used to reconstruct a multiple fracture limestone media. The proposed setup produces asymmetric breakthrough curves (BTCs) that are consistent with the shape expected from the past field and lab-scale studies. Three transport experiments have been conducted under fast, medium, and slow flow velocity conditions.The research focuses on parameter and state estimation using Bayesian inference via Markov Chain Monte Carlo (MCMC) sampler, investigating the degree to which three models of transport through fractured media can reproduce the experimental results under the three flow conditions. The first transport model, named ADE, is based on the equivalent porous medium (EPM) approach and corresponds to the linear advection dispersion equation (ADE). The second model, named FOMIM (first-order mobile immobile), is based on the mobile/immobile approach and uses the dual porosity model with a linear first-order transfer between mobile and immobile regions. The third model, named NLMIM (non-linear mobile-immobile), uses a nonlinear transfer function between these two regions.The results of the three models show that almost all the unknown model input parameters can be well-estimated with narrow confidence intervals using the MCMC method. With respect to state estimation, the ADE model fails to reproduce correctly the tail of the BTCs observed under slow and medium flow conditions. The FOMIM model improves the tailing of the BTCs, but significant discrepancies remain between simulated and measured concentrations. The NLMIM model with velocity-dependent parameters is the only model that captures BTCs under all three conditions of slow, medium, and fast flow velocities.

Review of groundwater flow and contaminant transport modelling approaches for the Sherwood Sandstone aquifer, UK; insights from analogous successions worldwide

Sandstones are characterized by different hydraulic behaviours and need to be modelled in various ways to represent groundwater flow and contaminant transport. This review shows how sandstone aquifers within the UK Triassic Sherwood Sandstone Group can be represented using three modelling approaches: the Conduit Network, Discrete Fracture Network and Equivalent Porous Medium. The Sherwood Sandstone aquifer is dominated by matrix flow in the Eastern England Shelf, Worcester, Needwood and Staffordshire basins. Here, the aquifers are modelled as Equivalent Porous Media at different spatial scales. Fractures represent the principal flow pathways in the Cheshire Basin. In this basin, Discrete Fracture Network models that account for diffusivity in the matrix can be used where the domain scale is small. The Sherwood Sandstone aquifer across northwestern England shows evidence of intense groundwater alteration and high flow velocities in solutionally enlarged fractures. Turbulent flowing pipe-elements can be inserted in the modelling domain represented by Equivalent Porous Medium at specific sites. The review shows how the Sherwood Sandstone aquifer as well as other siliciclastic deposits across the world need to be represented using a range of modelling approaches, as they behave as matrix or fracture flow aquifers, or in specific cases show a karst-like behaviour. Thematic collection: This article is part of the Hydrogeology of Sandstone collection available at: https://www.lyellcollection.org/cc/hydrogeology-of-sandstone