Equivalent Porous Medium Research Articles

Equivalent porous medium for modeling of the elastic and the sonic properties of sandstones

This study is devoted to model the elastic and the sonic properties of sandstones. The main difficulty in modeling granular materials like sandstones is the effect of grain-to-grain contacts. A new concept of an equivalent porous medium (EPM), which is a porous medium of a continuous solid matrix and pore-inclusions with an equivalent porosity that is higher than the porosity of the initial medium, is proposed to avoid this difficulty. A combination of the classical Hashin–Shtrikman (HS) approach and EPM provides an efficient simulation of the elastic properties of aggregate materials like sandstones, in comparison with experimental and numerical data in literature. The porosity of EPM of clean sandstones, that is calibrated using laboratory data, is about two times greater than that of the initial medium. The effects of clay and organic contents in shaly sandstones are also taken into account by introducing a notion of an un-supporting soft-phase. Similarly to the case of clean sandstones, the volumetric fraction of the soft-phase of EPM is about two times greater than that of the initial rock. The stress sensitivity and a comparison of this model to the heuristic modified Hashin–Shtrikman model are also discussed at the end of the paper. A power law is proposed for the dependence of the volumetric fraction of the EPM's soft-phase on the effective confining pressure. The proposed concept of EPM is proved to have many practical applications for the interpretation of sonic and seismic data of reservoir rocks.

Evaluation of two conceptual approaches for groundwater flow simulation for a rock domain at the block-scale for the Olkiluoto site, Finland

To evaluate conceptual approaches for simulating a rock domain, which is a rock unit outside a fracture zone, the block-scale groundwater flow system of the radioactive waste disposal site in Olkiluoto, Finland, was simulated using two approaches: the equivalent porous medium (EPM) approach and the hybrid approach. For the EPM approach, the rock domain was considered to be a homogeneous continuum with an equivalent hydraulic conductivity, while in the hybrid approach, it was conceptualized as a heterogeneous continuum from the stochastically generated background fracture network. In both approaches, several large fracture zones were included in the simulation models, which were calibrated by comparing the simulated hydraulic heads to the observed ones. The results showed that the simulated heads were in good agreement with the observed ones in both approaches, although the root mean square errors of the EPM approach were smaller than those of the hybrid approach. The estimated groundwater flow pathways in the hybrid approach generally had more complex geometries and longer travel times than those from the EPM approach. The simulations were evaluated by comparing the simulated flow rates at the boreholes in the site to the observed ones from the flow loggings, and the results show that the hybrid approach reproduced the observations more similarly than did the EPM approach.

Modelling and management of a Mediterranean karstic coastal aquifer under the effects of seawater intrusion and climate change

The study and management of the groundwater resources of a large, deep, coastal, karstic aquifer represent a very complex hydrogeological problem. Here, this problem is successfully approached by using an equivalent porous continuous medium (EPCM) to represent a karstic Apulian aquifer (southern Italy). This aquifer, which is located on a peninsula and extends to hundreds of metres depth, is the sole local source of high-quality water resources. These resources are at risk due to overexploitation, climate change and seawater intrusion. The model was based on MODFLOW and SEAWAT codes. Piezometric and salinity variations from 1930 to 2060 were simulated under three past scenarios (up to 1999) and three future scenarios that consider climate change, different types of discharge, and changes in sea level and salinity. The model was validated using surveyed piezometric and salinity data. An evident piezometric drop was confirmed for the past period (until 1999); a similar dramatic drop appears to be likely in the future. The lateral intrusion and upconing effects of seawater intrusion were non-negligible in the past and will be considerable in the future. All phenomena considered here, including sea level and sea salinity, showed non-negligible effects on coastal groundwater.

A numerical study of EGS heat extraction process based on a thermal non-equilibrium model for heat transfer in subsurface porous heat reservoir

With a previously developed numerical model, we perform a detailed study of the heat extraction process in enhanced or engineered geothermal system (EGS). This model takes the EGS subsurface heat reservoir as an equivalent porous medium while it considers local thermal non-equilibrium between the rock matrix and the fluid flowing in the fractured rock mass. The application of local thermal non-equilibrium model highlights the temperature-difference heat exchange process occurring in EGS reservoirs, enabling a better understanding of the involved heat extraction process. The simulation results unravel the mechanism of preferential flow or short-circuit flow forming in homogeneously fractured reservoirs of different permeability values. EGS performance, e.g. production temperature and lifetime, is found to be tightly related to the flow pattern in the reservoir. Thermal compensation from rocks surrounding the reservoir contributes little heat to the heat transmission fluid if the operation time of an EGS is shorter than 15 years. We find as well the local thermal equilibrium model generally overestimates EGS performance and for an EGS with better heat exchange conditions in the heat reservoir, the heat extraction process acts more like the local thermal equilibrium process.

Simulation of Regional Karst Aquifer System and Assessment of Groundwater Resources in Manatí-Vega Baja, Puerto Rico.

The North Coast karst aquifer system of Puerto Rico, the most productive aquifer of the island, is a vital water source for drinking water and local ecosystems. High freshwater demands alter the coastal groundwater system that impacts both human populations and coastal ecosystems of the island. To predict how this system might respond to rainfall events and high pumping demands, we used the equivalent porous medium (EPM) technique to develop a three-dimensional ground-water flow model to estimate hydrogeological parameters and assess groundwater resources in the Manatí-Vega Baja karst aquifer. The approach is based on the hypothesis that the simplified EPM approach will reproduce groundwater hydrodynamics in this complex karst environment. The steady-state model was calibrated with trial and error and parameter estimation methods using an observed groundwater table of 1995 (r = 0.86, p < 0.0001, n = 39). The large-scale simulation suggested that groundwater flow roughly follows the elevation slope [i.e. south to north). Calibrated hydraulic conductivities range from 0.5 to 86 m/d, whereas the hydro-geologic data strongly suggest higher permeability in the middle karst section of the study area. The transient model adequately estimates the observed groundwater fluctuations in response to rainfall events from 1980 until 2014. The transient results indicate that the conceptual model accuracy is more acceptable with a mean error (ME) of −0.132 m, mean absolute error (MAE) of 0.542 m and root mean square (RMSE) error of 0.365 m. The results of water budget simulation show that the total recharge satisfies the total groundwater withdrawal rate in the past, but continuous closure of more contaminated wells causes groundwater levels to increase in the future. The results indicate that the assumption of applicability of EPM approach is sustained and supported by measured data in the study area. Taking future water demands into account, this model could be applied further to predict the changes of groundwater levels and mass balance under different exploitation scenarios.

Experimental and numerical flow investigation of Stirling engine regenerator

This paper presents both preliminary experimental and numerical studies of pressure drop and heat transfer characteristics of Stirling engine regenerators. A test bench is designed and manufactured for testing different regenerators under oscillating flow conditions, while three-dimensional (3-D) numerical simulations are performed to numerically characterize the pressure drop phenomena through a wound woven wire matrix regenerator under different porosity and flow boundary conditions.The test bench operating condition range is initially determined based on the performance of the commercial, well-known Stirling engine called WhisperGen™. This oscillating flow test bench is essentially a symmetrical design, which allows two regenerator samples to be tested simultaneously under the same inflow conditions. The oscillating flow is generated by means of a linear motor which moves a piston in an oscillatory motion. Both the frequency and the stroke of the piston are modified to achieve different test conditions.In the numerical study, use of a FVM (finite volume method) based CFD (computational fluid dynamics) approach for different configurations of small volume matrices leads to a derivation of a two-coefficient based friction factor correlation equation, which could be later implemented in an equivalent porous media with a confidence for future regenerator flow and heat transfer analysis.

Impact of fracture network geometry on free convective flow patterns

The effect of fracture network geometry on free convection in fractured rock is studied using numerical simulations. We examine the structural properties of fracture networks that control the onset and strength of free convection and the patterns of density-dependent flow. Applicability of the equivalent porous medium approach (EPM) is also tested, and recommendations are given, for which situations the EPM approach is valid. To date, the structural properties of fracture networks that determine free convective flow are examined only in few, predominantly simplified regular fracture networks. We consider fracture networks containing continuous, discontinuous, orthogonal and/or inclined discrete fractures embedded in a low-permeability rock matrix. The results indicate that bulk permeability is not adequate to infer the occurrence and magnitude of free convection in fractured rock. Fracture networks can inhibit or promote convection depending on the fracture network geometry. Continuous fracture circuits are the crucial geometrical feature of fracture networks, because large continuous fracture circuits with a large vertical extent promote convection. The likelihood of continuous fracture circuits and thus of free convection increases with increasing fracture density and fracture length, but individual fracture locations may result in great deviances in strength of convection between statistically equivalent fracture networks such that prediction remains subject to large uncertainty.

Structural controls on groundwater flow in a fractured bedrock aquifer underlying an agricultural region of northwestern New Brunswick, Canada

A hydrogeological study was conducted in northwestern New Brunswick, Canada, to improve the predictability of fracture-dominated groundwater flow within folded bedrock composed of fine-grained turbidites. Borehole televiewer logging and outcrop mapping, integrated with hydraulic packer tests revealed enhanced hydraulic conductivity associated with northeasterly striking bedding-plane fractures formed during folding and flexural slip. These fractures impart azimuthal anisotropy to the aquifer because of moderately dipping fold limbs. High-angle fractures form a well-developed non-stratabound network, comprising two open fracture sets striking NNE parallel to the current direction of principal stress, and WNW parallel to the direction of principal stress that dominated during the Acadian orogeny. The subset of fractures showing significant oxidation, deemed most important to the groundwater flow system, is dominated by bedding-plane and high-angle fractures striking near-parallel to the maximum principal stress direction, resulting in extensional opening and enhanced hydraulic conductivities. An equivalent porous media model, incorporating anisotropy and varying hydraulic conductivity with depth, indicates that horizontal flow dominates the aquifer with relatively minor exchange between different model layers. These findings have implications for understanding flow directions in the Black Brook Watershed and elsewhere in the Matapedia Basin where fractures formed under similar stress conditions.

A computational study of flow mal-distribution on the thermal hydraulic performance of an intermediate heat exchanger in LMFBR

The flow and thermal non-uniformities occurring in the intermediate heat exchanger (IHX) of a liquid metal-cooled fast breeder reactor have been characterized through numerical simulations. For modeling the primary and secondary sodium flow through the IHX, an equivalent anisotropic porous medium approach has been used. The pressure drop in the equivalent porous medium is accounted through the inclusion of additional pressure drop terms in the Navier–Stokes equations, with the help of standard correlations for cross flow or parallel flow over tubes. For secondary sodium flow, the effects of a flow distributor device with orifices and baffles at the inlet have also been included, in addition to axial flow through the tubes. The heat exchange between primary and secondary streams is incorporated in the form of a volumetric heat source or sink term, which is corrected iteratively. The resulting flow distributions are in reasonable agreement with available experimental results. The study shows that the temperature of the secondary sodium flow at the exit can be made more uniform by exchanging less heat near the inner wall of IHX, as compared to the region close to the outer wall, using suitable flow distribution devices.

Lepini Mountains Carbonatic Ridge: try of springs recharge areas verification and water exchange quantification with Pontina Plain by use of a numerical model (Central Italy)

The study area of this work is represented by the Lepini Mountains carbonatic ridge and by the Pontina Plain foothills area, on which in the past, within quantitative hydrogeological characterizations, models were developed for calculating the groundwater flow, but only referred to the ridge. The most recent studies (Teoli, 2012) have done their best, instead, to represent the underground water exchanges between the ridge and the Pontina Plain foothill area. The new model (developed using computer code MODFLOW 2005) has been implemented to simulate steady-state underground flow using equivalent porous media approach even for the ridge; attention has been particularly directed to the proper tectonic ridge schematic, which the authors had previously defined, together with others (Alimonti et al., 2010), on detailed structural-geological survey basis, integrated by hydrogeological analysis. So, it’s been possible to determine partitioning effects on groundwater flowpaths and on springs recharge areas extent, whose total average discharge is about 10m3/s. Model calibration main goal has been the recharge areas permeability definition, posing the correspondence of calculated flows with measured springs’ flows; as a consequence, it’s been possible to improve the model reliability (uncertainty reduction) quantifying the flow residuals’ standard deviation offset.

Workflow for fast and efficient integration of Petrel-based fault models into coupled hydro-mechanical TOUGH2-MP - FLAC3D simulations of CO2 storage

Abstract We discuss a workflow implemented for coupling arbitrary numerical simulators considering complex geological models with discrete faults. This includes grid conversion of geological model grids generated with the Petrel software package to different simulator input formats within a few minutes for multi-million element models. We introduce the conceptual workflow design and tools required for the workflow realization. In this context, different fault representations can be realized including discrete fault planes supported by a virtual element concept in the multiphase flow simulator or an equivalent porous media approach using the mechanical ubiquitous joint model.

Fluid flow numerical experiments of faulted porous carbonates, Northwest Sicily (Italy)

A methodology to assess the effects of structural heterogeneities below seismic resolution in porous carbonate grainstones on reservoir performance during production is developed by integrating structural analysis, power law distributions, up-scaling, and numerical techniques. The novelty of the methodology consists of accounting for the buffering effects on permeability caused by compactive and cataclastic deformation bands. By using this methodology, a 3D deterministic field analogue and a 3D Discrete Fracture Network (DFN) representations of the reservoir/aquifer were built first, and then single-phase, steady-state fluid flow numerical experiments in an equivalent porous medium framework were performed. The field analogue is located along the Northwestern coast of Sicily (Italy) where Lower Pleistocene porous carbonate grainstones are crosscut by a strike-slip fault system. This fault system is made up of two conjugate sets of strike-slip shear structures recognized as single compactive shear bands (CSB), zones of compactive shear bands (ZB) and well-developed faults (DF), with discrete slip surfaces and cataclastic material. The permeability of these structures is up to three orders of magnitude less than the surrounding porous carbonate rocks. The fluid flow numerical experiments have been performed on the two aforementioned reservoir/aquifer descriptions to assess the effect of Sub-Seismic Resolutions Faults (SSRF), such as those observed in the outcrops, on fluid flow during production from a well, injection production in Enhanced Oil Recovery (EOR), and up-scaling to large cell size for regional flow simulation. Comparison of draw-down modeling in the DFN and the deterministic models show that results are similar with the exception of wells located in areas of intense strain localization with ZB and DF. The use of the DFN model is therefore an acceptable representation of the heterogeneities induced by SSRF in a reservoir/aquifer. Results of numerical computations show that, in structurally complex areas, SSRF-related ZB and DF might represent a drilling risk because they can enhance draw-down during production and EOR activities.

Comparison of a karst groundwater model with and without discrete conduit flow

Karst aquifers exhibit a dual flow system characterized by interacting conduit and matrix domains. This study evaluated the coupled continuum pipe-flow framework for modeling karst groundwater flow in the Madison aquifer of western South Dakota (USA). Coupled conduit and matrix flow was simulated within a regional finite-difference model over a 10-year transient period. An existing equivalent porous medium (EPM) model was modified to include major conduit networks whose locations were constrained by dye-tracing data and environmental tracer analysis. Model calibration data included measured hydraulic heads at observation wells and estimates of discharge at four karst springs. Relative to the EPM model, the match to observation well hydraulic heads was substantially improved with the addition of conduits. The inclusion of conduit flow allowed for a simpler hydraulic conductivity distribution in the matrix continuum. Two of the high-conductivity zones in the EPM model, which were required to indirectly simulate the effects of conduits, were eliminated from the new model. This work demonstrates the utility of the coupled continuum pipe-flow method and illustrates how karst aquifer model parameterization is dependent on the physical processes that are simulated.

Can electrical conductivity data from a single pumping test provide information about the location of a neighboring mixing zone between two aquifers? An example from Aix-les-Bains/Marlioz (Savoie, France)

Summary Pumping tests were first developed to interpret observed drawdown in wells. Analyses of drawdown and temperature profiles now help petroleum geologists and geothermal-energy specialists improve production rates, and numerous hydrogeological studies have combined drawdown data with measures of electrical conductivity or a chemical parameter (often a pollutant). The present study used electrical conductivity data from a pumping test in a single well to obtain information about the position of the hydrothermal plume that feeds Aix-les-Bains’ Thermes de Marlioz spa. Applying this data to a 3D model of an equivalent porous medium showed that the plume at the bottom of the subsurface aquifer must be downstream from the well. In the present study, combining drawdown data for a single well with electrical-conductivity measurements provided an efficient method for determining the position of a mixing zone near pumped wells. This method may well be generalizable to other situations.

Combined MODFLOW‐FRACTRAN Application to Assess Chlorinated Solvent Transport and Remediation in Fractured Sedimentary Rock

AbstractDetailed field investigations and numerical modeling were conducted to evaluate transport and fate of chlorinated solvent contamination in a fractured sedimentary bedrock aquifer (sandstone/siltstone/mudstone) at a Superfund site in central New Jersey. Field investigations provided information on the fractured rock system hydrogeology, including hydraulic gradients, bulk hydraulic conductivity, fracture network, and rock matrix, and on depth discrete contaminant distribution in fractures (via groundwater sampling) and matrix (via detailed subsampling of continuous cores). The numerical modeling endeavor involved application of both an equivalent porous media (EPM) model for flow and a discrete fracture network (DFN) model for transport. This combination of complementary models, informed by appropriate field data, allowed a quantitative representation of the conceptual site model (CSM) to assess relative importance of various processes, and to examine efficacy of remedial alternatives. Modeling progressed in two stages: first a large‐scale (20 km x 25 km domain) 3‐D EPM flow model (MODFLOW) was used to evaluate the bulk groundwater flow system and contaminant transport pathways under historic and current aquifer stress conditions and current stresses. Then, results of the flow model informed a 2‐D DFN transport model (FRACTRAN) to evaluate transport along a 1,000‐m flowpath from the source represented as a 2‐D vertical cross‐section. The combined model results were used to interpret and estimate the current and potential future extent of rock matrix and aqueous‐phase contaminant conditions and evaluate remedial strategies. Results of this study show strong effects of matrix diffusion and other processes on attenuating the plume such that future impacts on downgradient well fields under the hydraulic stresses modeled should be negligible. Results also showed futility of source remediation efforts in the fractured rock, and supported a technical impracticability (TI) waiver for the site. © 2013 Wiley Periodicals, Inc.

Comparison of digital outcrop and conventional data collection approaches for the characterization of naturally fractured reservoir analogues

Abstract In this study, fracture systems developed within faulted, high-porosity sandstones in the decommissioned mines of Alderley Edge, Cheshire, UK are characterized using lidar (Light Detection And Ranging)-based analysis. The geometry of the mine workings prove to be conducive to the extraction of fracture attributes, whilst providing a degree of exposure of a notable Triassic-aged reservoir outcrop analogue (Helsby Sandstone Formation) not afforded at the surface. To test the fidelity of the approach, fracture statistics generated from lidar-derived digital outcrop models are compared to an equivalent dataset collected using conventional manual surveys, with digital outcrop and manually acquired fracture attributes used to populate discrete fracture network models. These are upscaled to provide equivalent porous medium properties, enabling the impact of uncertainties introduced into fracture modelling workflows by lidar-based techniques to be assessed. Whilst broadly comparable to fracture attributes obtained using manual surveys, the systematic underrepresentation of fracture properties is observed within lidar-derived dataset, resulting in the underestimation of fracture network flow capacity. The study results suggest that, whilst enhancing data acquisition rates and coverage of exposure surfaces, the use of digital discontinuity analysis may introduce additional biases into fracture datasets, increasing the level of uncertainty within resultant modelled networks.

Modeling the effects of pumping wells in spring management: The case of Scirca spring (central Apennines, Italy)

Summary One of the techniques used to increase the water yield of springs during dry seasons and droughts is drilling wells close to them. Where there is a low-hydraulic conductivity boundary close to a spring (the case considered here), this technique implies low well efficiency, high drawdown, and high cost of withdrawals. In addition, a set of pumping wells close to a spring can cause both it and the stream originating from it to dry up - a situation which is not always acceptable from an environmental point of view. In order to study better management strategies, this paper presents a finite difference model of the Scirca spring (Umbria – Marche Apennines, Italy), which originates from a limestone massif in which some formations are karstified. The model, built with Modflow using the equivalent porous media (EPM) approach, simulated the effects of pumping wells at various distances from the spring. Hydraulic Conductivity and Storativity were calibrated and validated on discharge data during recession, when recharge is nil. “Inverse modeling” was then used to estimate the daily recharge of the hydro-geological system of the Scirca spring for a period of several years. Lastly, the efficiency of various management schemes was evaluated by simulating the reaction of the spring, in terms of discharge, to a series of pumping scenarios, all guaranteeing a certain imposed withdrawal during summer, much larger than the natural spring discharge, given by spring discharge and well drawdown. The wells were located between 2850 and 100 m from the spring, the pumping time-span was set at 90 days, and pumping rates of 60, 90 and 120 l/s were applied. Results show that the maximum discharge at which spring drainage is avoided and that minimum vital flow is guaranteed is 90 l/s. The higher water volumes extracted during summer (dry season) are balanced by a lowering of the maximum natural discharges in winter and spring (recharge seasons). Simulations indicate that, by drilling pumping wells far from the spring, the efficiency of the whole system can be optimized in terms of total withdrawal, drilling and management costs, with reduced environmental impact. The mathematical model also shows how long the system takes to regain its “undisturbed” state, with a tolerance of 0.5 l/s. The model highlights the possibility of forcing the system to supply a smaller amount of water in winter, in order to increase the summer yield. Such a management scheme, which can be applied to other springs, may be useful in better meeting the demand for water during dry seasons.

Comparing Discrete Fracture and Continuum Models to Predict Contaminant Transport in Fractured Porous Media

We used the FRAC3Dvs numerical model (Therrien and Sudicky 1996) to compare the dual-porosity (DP), equivalent porous medium (EPM), and discrete fracture matrix diffusion (DFMD) conceptual models to predict field-scale contaminant transport in a fractured clayey till aquitard. The simulations show that the DP, EPM, and DFMD models could be equally well calibrated to reproduce contaminant breakthrough in the till aquitard for a base case. In contrast, when groundwater velocity and degradation rates are modified with respect to the base case, the DP method simulated contaminant concentrations up to three orders of magnitude different from those calculated by the DFMD model. In previous simulations of well-characterized column experiments, the DFMD method reproduced observed changes in solute transport for a range of flow and transport conditions comparable to those of the field-scale simulations, while the DP and EPM models required extensive recalibration to avoid high magnitude errors in predicted mass transport. The lack of robustness with respect to variable flow and transport conditions suggests that DP models and effective porosity EPM models have limitations for predicting cause-effect relationships in environmental planning. The study underlines the importance of obtaining well-characterized experimental data for further studies and evaluation of model key process descriptions and model suitability.

A novel three-dimensional transient model for subsurface heat exchange in enhanced geothermal systems

Understanding the subsurface heat exchange process in enhanced geothermal systems (EGS) is crucial to the efficiency of heat extraction and the sustainable utilization of geothermal reservoir. In the present work we develop a novel three-dimensional transient model for the study of the subsurface heat exchange process in EGS. The novelty of this model is embodied by a couple of salient features. First, the geometry of interest physically consists of multiple domains: open channels for injection and production wells, the artificial heat reservoir, and the rock enclosing the heat reservoir, while computationally we treat it as a single-domain of multiple sub-regions associated with different sets of characteristic properties (porosity and permeability etc.). This circumvents typical difficulties about matching boundary conditions between sub-domains in traditional multi-domain approaches and facilitates numerical implementation and simulation of the complete subsurface heat exchange process. Second, the heat reservoir is treated as an equivalent porous medium of a single porosity, while we consider thermal non-equilibrium between solid and fluid components and introduce two sets of heat transfer equations to describe the heat advection and conduction for fluid in rock apertures and the heat conduction in rock matrix, respectively, thus enabling the simulation and analysis of convective heat exchange between rock matrix and fluid flowing in the apertures. Case study with respect to an imaginary EGS demonstrates the validity and capability of the developed model.

Studying the Flow Dynamics of a Karst Aquifer System with an Equivalent Porous Medium Model

The modeling of groundwater flow in karst aquifers is a challenge due to the extreme heterogeneity of its hydraulic parameters and the duality in their discharge behavior, that is, rapid response of highly conductive karst conduits and delayed drainage of the low-permeability fractured matrix after recharge events. There are a number of different modeling approaches for the simulation of the karst groundwater dynamics, applicable to different aquifer as well as modeling problem types, ranging from continuum models to double continuum models to discrete and hybrid models. This study presents the application of an equivalent porous model approach (EPM, single continuum model) to construct a steady-state numerical flow model for an important karst aquifer, that is, the Western Mountain Aquifer Basin (WMAB), shared by Israel and the West-Bank, using MODFLOW2000. The WMAB was used as a catchment since it is a well-constrained catchment with well-defined recharge and discharge components and therefore allows a control on the modeling approach, a very rare opportunity for karst aquifer modeling. The model demonstrates the applicability of equivalent porous medium models for the simulation of karst systems, despite their large contrast in hydraulic conductivities. As long as the simulated saturated volume is large enough to average out the local influence of karst conduits and as long as transport velocities are not an issue, EPM models excellently simulate the observed head distribution. The model serves as a starting basis that will be used as a reference for developing a long-term dynamic model for the WMAB, starting from the pre-development period (i.e., 1940s) up to date.