Heterogeneous Transmissivity Field Research Articles

Multitasking neural network to jointly map discrete fracture structures and matrix transmissivity by inverting hydraulic data acquired in 2D fractured aquifers. XNET-fracture

In this paper, we propose a new approach to simultaneously map the fracture/conduit network and the equivalent transmissivity of the rock matrix from hydraulic head measurements acquired during pumping/injection tests in fractured aquifers. The algorithm relies on the use of a multitask neural network to directly approximate the joint inversion operator that links hydraulic head data to aquifer hydraulic properties. In which, the hydraulic head responses are used as input data while the output consists of the fracture structure and matrix transmissivity field. The multitasking is formed by fusing two single-task neural networks, both based on convolutional encoder-decoder architectures, one of which processes the fracture map inversion and the other the transmissivity map. Training neural network then relies on a large database, which consists of thousands of synthetic aquifers characterized by the presence of the fracture/conduit network and a heterogeneous transmissivity field attributed to the rock matrix, both randomly generated. In these aquifer models, the groundwater flow equation is solved in a discrete-continuum concept to numerically simulate the hydraulic head responses associated with sequential pumping/injection tests.Multitasking succeeds in reconstructing the fracture architecture and matrix transmissivity field with higher accuracy in comparison to conventional single-task networks. The difference is due to the transfer mechanism involved in the multi-task network, where the information shared between the tasks effectively enhances the accuracy of both reconstructions. However, as with other inversion techniques, the result accuracy depends on the quality and quantity of the hydraulic head data used in the inversion, as well as the prior information involved in featuring the training models.

Integration of moment equations in a reduced-order modeling strategy for Monte Carlo simulations of groundwater flow

We illustrate and test an approach grounded on embedding moment equations (MEs) of groundwater flow within a Monte Carlo based modeling strategy to yield a Reduced-Order Model (ROM) that enables the efficient and accurate evaluation of probability distributions of hydraulic heads in randomly heterogeneous transmissivity fields. The projection space determining the accuracy of the ROM solution is typically computed through the principal component analysis of a selected number of full system model solutions (the so-called snapshots). Computationally expensive sensitivity analyses are then required to assess the independence of the ROM from the snapshots. Here, we propose to compute the projection vectors upon relying on the hydraulic head covariance evaluated from the solution of corresponding MEs of groundwater flow.Our workflow to compute hydraulic head distributions is organized according to the following steps: (i) approximation of mean hydraulic head and head covariance matrix through (second-order accurate) solutions of MEs; (ii) computation of the leading eigenvectors of the head covariance matrix to form the basis set for the ROM projection space; and (iii) construction of the ROM. Sample probability density functions of hydraulic heads are then efficiently obtained via Monte Carlo simulations relying on the developed ROM. The proposed methodology is compared against snapshot-based ROMs and the full system model in a two- and a three-dimensional steady-state groundwater flow setting where pumping from a point source is superimposed to a mean uniform flow. Our results show that the projection space computed by relying on MEs provides a more accurate ROM solution than the one resulting from reliance on snapshots.

Mutual information analysis to approach nonlinearity in groundwater stochastic fields

In heterogeneous porous media, transmissivity can be regarded as a spatial stochastic variable. Transmissivity fluctuations induce stochasticity in the groundwater velocity field and transport features. In order to model subsurface phenomena, it is important to understand the relationships that exist between the variables that characterize flow and transport. Linear relationships are easier to deal with. Nevertheless, it is well known that flow and transport variables exhibit interdependences that become more and more nonlinear as the heterogeneity increases. The aim of this work is to draw attention to the information contained in nonlinear linkages, and to show that it can be of great relevance with respect to the linear information content. Information theory tools are proposed to detect the presence of nonlinear components. By comparing the cross-covariance function and mutual information, the amount of linear linkage is compared with nonlinear linkage. In order to avoid analytical approximations, data from Monte Carlo simulations of heterogeneous transmissivity fields have been considered in the analysis. The obtained results show that the presence of nonlinear components can be relevant, even when the cross-covariance values are nil.

Solute concentration at a well in non-Gaussian aquifers under constant and time-varying pumping schedule

Our study is keyed to the analysis of the interplay between engineering factors (i.e., transient pumping rates versus less realistic but commonly analyzed uniform extraction rates) and the heterogeneous structure of the aquifer (as expressed by the probability distribution characterizing transmissivity) on contaminant transport. We explore the joint influence of diverse (a) groundwater pumping schedules (constant and variable in time) and (b) representations of the stochastic heterogeneous transmissivity (T) field on temporal histories of solute concentrations observed at an extraction well. The stochastic nature of T is rendered by modeling its natural logarithm, Y=lnT, through a typical Gaussian representation and the recently introduced Generalized sub-Gaussian (GSG) model. The latter has the unique property to embed scale-dependent non-Gaussian features of the main statistics of Y and its (spatial) increments, which have been documented in a variety of studies. We rely on numerical Monte Carlo simulations and compute the temporal evolution at the well of low order moments of the solute concentration (C), as well as statistics of the peak concentration (Cp), identified as the environmental performance metric of interest in this study. We show that the pumping schedule strongly affects the pattern of the temporal evolution of the first two statistical moments of C, regardless the nature (Gaussian or non-Gaussian) of the underlying Y field, whereas the latter quantitatively influences their magnitude. Our results show that uncertainty associated with C and Cp estimates is larger when operating under a transient extraction scheme than under the action of a uniform withdrawal schedule. The probability density function (PDF) of Cp displays a long positive tail in the presence of time-varying pumping schedule. All these aspects are magnified in the presence of non-Gaussian Y fields. Additionally, the PDF of Cp displays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered.

Cokriging Transmissivity, Head and Trajectory Data for Transmissivity and Solute Path Estimation.

In practical situations concerning aquifers, time and/or economic restraints often make it impossible to construct numerical models, and in these cases simple methodologies could be useful, at least for feasibility studies. In this context, the present manuscript deals with the use of a straightforward cokriging method to use data acquired from a monitoring network (transmissivity, piezometric head and trajectory data) in order to obtain useful information about the characteristics of the aquifer. Two issues have been addressed: estimation of the solute path and estimation of the transmissivity. This manuscript, compared with previous works that have applied cokriging, considers that the solute transit data originate from a source of unknown intensity and from an unknown location. The proposed cokriging systems are implemented through already developed covariance and cross-covariance functions, considering a first-order approximation in the log-transmissivity variance. For this reason, numerical Monte Carlo experiments have been performed to test the accuracy of the results of the proposed cokriging procedures in both weakly (σY2=0.16) and mildly (σY2=2) heterogeneous transmissivity aquifers. Since a prerequisite of cokriging is a linear relationship among the involved quantities, more accurate results can be expected in weakly heterogeneous transmissivity fields, where the trajectory, transmissivity and hydraulic head data relations are almost linear. Comparing the numerical results with the analytical solutions, it in fact emerges that cokriging can be very useful for the estimation of a solute path and transmissivity when a limited set of data is available for weakly heterogeneous aquifers.

Dimensionality reduction for efficient Bayesian estimation of groundwater flow in strongly heterogeneous aquifers

We focus on the Bayesian estimation of strongly heterogeneous transmissivity fields conditional on data sampled at a set of locations in an aquifer. Log-transmissivity, Y, is modeled as a stochastic Gaussian process, parameterized through a truncated Karhunen–Loeve (KL) expansion. We consider Y fields characterized by a short correlation scale as compared to the size of the observed domain. These systems are associated with a KL decomposition which still requires a high number of parameters, thus hampering the efficiency of the Bayesian estimation of the underlying stochastic field. The distinctive aim of this work is to present an efficient approach for the stochastic inverse modeling of fully saturated groundwater flow in these types of strongly heterogeneous domains. The methodology is grounded on the construction of an optimal sparse KL decomposition which is achieved by retaining only a limited set of modes in the expansion. Mode selection is driven by model selection criteria and is conditional on available data of hydraulic heads and (optionally) Y. Bayesian inversion of the optimal sparse KLE is then inferred using Markov Chain Monte Carlo (MCMC) samplers. As a test bed, we illustrate our approach by way of a suite of computational examples where noisy head and Y values are sampled from a given randomly generated system. Our findings suggest that the proposed methodology yields a globally satisfactory inversion of the stochastic head and Y fields. Comparison of reference values against the corresponding MCMC predictive distributions suggests that observed values are well reproduced in a probabilistic sense. In a few cases, reference values at some unsampled locations (typically far from measurements) are not captured by the posterior probability distributions. In these cases, the quality of the estimation could be improved, e.g., by increasing the number of measurements and/or the threshold for the selection of KL modes.

Extending Theis' solution: Using transient pumping tests to estimate parameters of aquifer heterogeneity

AbstractA framework for interpreting transient pumping tests in heterogeneous transmissivity fields is developed to infer the overall geostatistical parameters of the medium without reconstructing the specific heterogeneous structure point wise. The methodology of Radial Coarse Graining is applied to deduce an effective radial description of multi‐Gaussian transmissivity. It was used to derive an Effective Well Flow Solution for transient flow conditions including not only the storativity, but also the geometric mean, the variance, and the correlation length of log‐transmissivity. This solution is shown to be appropriate to characterize the pumping test drawdown behavior in heterogeneous transmissivity fields making use of ensembles of simulated pumping tests with multiple combinations of statistical parameters. Based on the Effective Well Flow Solution, a method is developed for inferring heterogeneity parameters from transient pumping test drawdown data by inverse estimation. Thereby, the impact of statistical parameters on the drawdown is analyzed, allowing to determine the dependence of reliability of parameter estimates on location and number of measurements. It is shown, that the number of measurements can be reduced compared to steady state pumping tests. Finally, a sampling strategy for single aquifer analysis is developed, which allows to estimate the statistical parameters, in particular variance and correlation length for individual heterogeneous transmissivity fields making use of transient pumping test measurements at multiple locations.

Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

Abstract. A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: mean, variance, and correlation length. Such a model is provided by the upscaling procedure radial coarse graining, which describes the transition of near-well to far-field transmissivity effectively. Based on this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.

Predicting field-scale dispersion under realistic conditions with the polar Markovian velocity process model

In most groundwater aquifers, dispersion of tracers is dominated by flow-field inhomogeneities resulting from the underlying heterogeneous conductivity or transmissivity field. This effect is referred to as macrodispersion. Since in practice, besides a few point measurements the complete conductivity field is virtually never available, a probabilistic treatment is needed. To quantify the uncertainty in tracer concentrations from a given geostatistical model for the conductivity, Monte Carlo (MC) simulation is typically used. To avoid the excessive computational costs of MC, the polar Markovian velocity process (PMVP) model was recently introduced delivering predictions at about three orders of magnitude smaller computing times. In artificial test cases, the PMVP model has provided good results in comparison with MC. In this study, we further validate the model in a more challenging and realistic setup. The setup considered is derived from the well-known benchmark macrodispersion experiment (MADE), which is highly heterogeneous and non-stationary with a large number of unevenly scattered conductivity measurements. Validations were done against reference MC and good overall agreement was found. Moreover, simulations of a simplified setup with a single measurement were conducted in order to reassess the model’s most fundamental assumptions and to provide guidance for model improvements.

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting--both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

FASTREACT – An efficient numerical framework for the solution of reactive transport problems

In the framework of safety assessment studies for geological disposal, large scale reactive transport models are powerful inter-disciplinary tools aiming at supporting regulatory decision making as well as providing input to repository engineering activities. Important aspects of these kinds of models are their often very large temporal and spatial modelling scales and the need to integrate different non-linear processes (e.g., mineral dissolution and precipitation, adsorption and desorption, microbial reactions and redox transformations). It turns out that these types of models may be computationally highly demanding. In this work, we present a Lagrangian-based framework, denoted as FASTREACT, that aims at solving multi-component-reactive transport problems with a computationally efficient approach allowing complex modelling problems to be solved in large spatial and temporal scales. The tool has been applied to simulate radionuclide migration in a synthetic heterogeneous transmissivity field and the results have been successfully compared with those obtained using a standard Eulerian approach. Finally, the same geochemical model has been coupled to an ensemble of realistic three-dimensional transport pathways to simulate the migration of a set of radionuclides from a hypothetical repository for spent nuclear fuel to the surface. The results of this modelling exercise, which includes key processes such as the exchange of mass between the conductive fractures and the matrix, show that FASTREACT can efficiently solve large-scale reactive transport models.

Assessing radial transmissivity variation in heterogeneous aquifers using analytical techniques

AbstractPumping tests are one of the most commonly used in situ testing techniques for assessing aquifer hydraulic properties. Numerous researches have been conducted to predict the effects of aquifer heterogeneity on the groundwater levels during pumping tests. The objectives of the present work were as follows: (1) to predict drawdown conditions and to estimate aquifer properties during pumping tests undertaken in radially symmetric heterogeneous aquifers, and (2) to identify a method for assessing the transmissivity field along the radial coordinate in radially symmetric and fully heterogeneous transmissivity fields. The first objective was achieved by expanding an existing analytical drawdown formulation that was valid for a radially symmetric confined aquifer with two concentric zones around the pumping well to an N concentric zone confined aquifer having a constant transmissivity value within each zone. The formulation was evaluated for aquifers with three and four concentric zones to assess the effects of the transmissivity field on the drawdown conditions. The specific conditions under which aquifer properties could be identified using traditional methods of analysis were also evaluated. The second objective was achieved by implementing the inverse solution algorithm (ISA), which was developed for petroleum reservoirs to groundwater aquifer settings. The results showed that the drawdown values are influenced by a volumetric integral of a weighting function and the transmissivity field within the cone of depression. The weighting function migrates in tandem with the expanding cone of depression. The ability of the ISA to predict radially symmetric and log‐normally distributed transmissivity fields was assessed against analytical and numerical benchmarks. The results of this investigation indicated that the ISA method is a viable technique for evaluating the radial transmissivity variations of heterogeneous aquifer settings. Copyright © 2013 John Wiley & Sons, Ltd.

Calibrating transmissivities from piezometric heads with the gradual deformation method: An application to the Culebra Dolomite unit at the Waste Isolation Pilot Plant (WIPP), New Mexico, USA

Summary The gradual deformation method (GDM) is a geostatistical parameterization technique introduced in reservoir engineering for compelling reservoir models to respect production history. It makes it possible to adjust the spatial distribution of the hydraulic properties populating the reservoir model so that the flow responses simulated for the modified model closely replicate the production data collected on the field. The work presented in this paper investigates the potential of the GDM to solve inverse problems in hydrogeology, or subsurface hydrology, and produce heterogeneous transmissivity fields conditional to both transmissivity and piezometric head measurements within a stochastic context. It focuses on the calibration of the Culebra Dolomite unit, which lies approximately 450 m above the repository horizon of the Waste Isolation Pilot Plant (WIPP) in southeastern New Mexico, USA. Results show that the proposed version of the GDM, with a local deformation in each sub-domain neighboring a well, is efficient and competitive compared to other geostatistical-based inverse methods such as the pilot point method.

A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments

Inverse modelling is a key step in groundwater-related hydrological studies. Several inversion techniques were developed during the last decades, but hardly any comparison between them was presented. We compare seven modern inverse methods for groundwater flow: the Regularised Pilot Points Method (both the estimation, RPPM-CE, and the Monte Carlo ( MC) simulation variants, RPPM-CS), the MC variant of the Representer Method ( RM), the Sequential Self-Calibration Method ( SSC), the Moment Equations Method ( MEM), the Zonation Method ( ZM) and a non-iterative Semi-Analytical Method ( SAM). These methods are applied to a two-dimensional synthetic example, depicting steady-state groundwater flow around a pumping well. Their relative performance is assessed in terms of their ability to characterise the log-transmissivity and hydraulic head fields and to predict the extent of the well catchment, both for a mildly and a strongly heterogeneous transmissivity field. The main conclusions drawn from the comparison are: (1) MC-based methods ( RPPM-CS, SSC and RM) yield very similar results, regardless the degree of heterogeneity and despite they use different parameterisation schemes and objective functions; (2) statistical moments of the target quantities provided by MEM and RPPM-CE are similar to those of MC-based methods; (3) ZM and SAM are negatively affected by strong heterogeneity; and (4) in general, observed differences between the performances of all methods are not very large. MC-based inverse methods need considerably more CPU time than the other tested approaches. An advantage of MC-based methods is that they allow computing the posterior probability distribution of the target quantities, which can be directly fed to probabilistic risk-assessment procedures.

Geostatistical inversing for large-contrast transmissivity fields

The estimation of field parameters, such as transmissivity, is an important part of groundwater modeling. This work deals with the quasilinear geostatistical inverse approach to the estimation of the transmissivity fields from hydraulic head measurements. The standard quasilinear approach is an iterative method consisting of successive linearizations. We examine a synthetic case to evaluate the basic methodology and some modifications and extensions. The first objective is to evaluate the performance of the quasilinear approach when applied to strongly heterogeneous (or “high-contrast”) transmissivity fields and, when needed, to propose improvements that allow the solution of such problems. For large-contrast cases, the standard quasilinear method often fails to converge. However, by introducing a derivative-free line search as a polishing step after each Gauss–Newton iteration, we have found that convergence can be practically assured. Another issue is that the quasilinear procedure, which uses linearization about the best estimate to evaluate estimation variances, may lead to inaccurate estimation of the variance of the estimated variable. Our numerical results suggest that this may not be a particularly serious problem, though it is hard to say whether this conclusion will apply to other cases. Nevertheless, since the quasilinear approach is an approximation, we propose a potentially more accurate but computer-intensive Markov Chain Monte Carlo (MCMC) procedure based on conditional realizations generated through the quasilinear approach and accepted or rejected according to the Metropolis–Hastings algorithm. Six transmissivity fields with increasing contrast were generated and one thousand conditional realizations were computed for each studied case. The MCMC procedure proposed in this work gives an overall more accurate picture than the quasilinear approach but at a considerably higher computational cost.

Beyond Thiem: A new method for interpreting large scale pumping tests in heterogeneous aquifers

The heterogeneous character of aquifers prevents a consistent interpretation of pumping tests based on Thiem's formula which has been developed for homogeneous aquifers. We present a new mathematical method for interpreting an ensemble and single large scale pumping tests in heterogeneous confined isotropic aquifers. By combining a multiscale technique called Coarse Graining with Renormalization Group analysis, we derive an explicit formula for the coarse grained aquifer transmissivity. The coarse grained transmissivity is dependent on the radial distance from the well. Close to the well, it equals the local transmissivity in single pumping tests and the harmonic mean of the heterogeneous transmissivity field in ensemble pumping tests. In the far field of the well the coarse grained transmissivity approaches the geometric mean. The transition between both regimes is mainly determined by the transmissivities correlation length. This relation is used for an inversely estimate of the statistical properties of the transmissivity such as its geometric mean. In addition, this method allows for determining aquifer structures characterized by a correlation length from a single pumping test, while the variance can be estimated from pumping tests with ensemble averaged hydraulic heads.

Sustainability of the Bedrock Aquifer Systems in South-Central Manitoba: Implications for Large-Scale Modelling

A three-dimensional density dependent flow and transport model was developed for the Carbonate and Sandstone Aquifers in a 60,000 square-kilometre area of south-central Manitoba. Hydrogeological properties, such as transmissivity, and aquifer response data, were collected for both aquifers. Bayesian Updating was used to determine the heterogeneous transmissivity field of each aquifer. Other parameters were designated based on collected data or typical values from the literature. The resulting model was used to evaluate several water resources scenarios within the Province of Manitoba. The sustainability over 20 years with constant pumping rates was examined. Within both aquifers, hydraulic heads declined in some regions and on average a decline in head was predicted. Model simulations were also conducted to observe the effect of flooding as this is an issue of concern in southern Manitoba. A pseudo-flood was assumed to last for a period of one month. The model was run for a period of 50 years to observe the long-term effects. The solute transport results show a concentration increase in the region south of the City of Winnipeg after one-month, indicating a decline in water quality. Drought simulations were incorporated by reducing recharge rates to the aquifers. The hydraulic heads within the Carbonate Aquifer decline within the Interlake region with a maximum decline within the Sandilands region southeast of the City of Winnipeg. As might be expected, the effects of reduced recharge on the entire aquifer sequence are significant.

Controls of mass recovery rates in single‐well injection‐withdrawal tracer tests with a single‐porosity, heterogeneous conceptualization

A single‐well injection‐withdrawal (SWIW) test is evaluated as a tool to assess a single‐porosity conceptualization for a transport system. We have shown that there are cases in which matrix diffusion cannot be proven definitively from the results of SWIW tests owing to uncertainties of aquifer properties. Drift during the resting phase of the test can carry a plume to areas where the flux is lower during the withdrawal phase, leading to decreased mass recovery rates. Results of sensitivity studies on multiple, stochastically generated, heterogeneous transmissivity fields indicate that variance in transmissivity has a strong effect on drift and consequently mass recovery rates. In addition to impacting drift directly, the regional gradient has the potential to influence mass recovery rates by interfering with the pumping‐induced fluxes toward the well during withdrawal. The Kolmogorov‐Smirnov test is used to evaluate whether simulated data using a single‐porosity conceptualization with plume drift significantly differ from SWIW tracer test data from a fractured dolomite unit at the Waste Isolation Pilot Plant. Given the uncertainty in the variance of transmissivity, it is unlikely that a single‐porosity conceptualization can match the field data. Matrix diffusion is a likely explanation for the observed gradual mass recovery rates.

Convergent-flow tracer tests in heterogeneous media: combined experimental–numerical analysis for determination of equivalent transport parameters

In modeling transport within naturally heterogeneous aquifers, it is usually assumed that the transport equations valid at local scales can also be applied at larger scales. At larger scales, the heterogeneous domain is represented by an equivalent homogeneous medium. Convergent-flow tracer tests constitute one of the most frequently used field tests to estimate effective input parameters of equivalent homogeneous aquifers. Traditionally, statistical approaches applied to groundwater flow and solute transport have provided tools to estimate these equivalent parameters. These approaches are based on a number of simplifications including the assumption that the point transmissivity values follow a multilog-normal random function. Several investigators have found that this assumption may not be valid in many field cases. In order to study the applicability of the equivalent homogeneous formulation in a nontraditional stochastic field, a number of experimental and numerical studies were conducted. The results are used to determine the apparent values of porosity and dispersivity that would be obtained if convergent-flow tracer tests were conducted in a deterministically generated heterogeneous transmissivity field displaying anisotropy in the correlation structure. It is shown that in this particular heterogeneous media, apparent porosity strongly depends on connectivity rather than on transmissivity. This dependence on connectivity questions the theoretical results obtained in continuum equivalent fields to estimate effective porosity.

Determining Karst Transmissivities with Inverse Modeling and an Equivalent Porous Media

AbstractFlow simulation is difficult to implement in heterogeneous media such as karst aquifers, primarily because the structure of the rock is extremely complex and usually unknown. The aim of this study was to verify the possibility of using inverse modeling and an equivalent porous media to identify transmissivities in a slightly karstified aquifer, the La Rochefoucauld karst (Charente, France). Different simulation scenarios were tested: using two spatial discretizations with different finite‐element cell sizes and using measured or interpolated heads. The inverse modeling was performed with the downscaling parameterization procedure, using a finite‐element representation of bidimensional ground water flow. The inverse modeling converged satisfactorily with all scenarios: head residuals were small and spring flow rates and the river/aquifer exchanges were adequately simulated. The scenario using small cells and measured heads generated a highly heterogeneous transmissivity field, indicating an overpa‐rameterization of the problem. The calibrated transmissivities and simulated heads of this scenario proved less reliable overall than those of the other scenarios. The use of interpolated heads generated more uniform transmissivities as a result of the head smoothing. A rotation of the initial parameter mesh showed that the scenarios using interpolated heads generate the most stable and reliable results. The scenarios with interpolated heads could therefore be used when head measurements are limited or are unevenly distributed over the aquifer. Overall, the calibrated transmissivities reproduced the entire range of transmissivities measured in the field using different methods. The results indicate that inverse modeling and an equivalent porous media can be used to determine transmissivities in a moderately karstified aquifer.