Influence of pumping operational schedule on solute concentrations at a well in randomly heterogeneous aquifers

We investigate the way diverse groundwater extraction strategies affect the history of solute concentration recovered at a pumping well while taking into account random spatial variability of the system hydraulic conductivity. Considering the joint effects of spatially heterogeneous hydraulic conductivity and temporally varying well pumping rates leads to a realistic evaluation of groundwater contamination risk at the pumping well location. We juxtapose the results obtained when the pumping well extracts a given amount of water operating (a) at a uniform pumping rate and (b) under a transient regime. The analysis is performed within a numerical Monte Carlo framework. Our results show that contaminant concentration breakthrough curves (BTCs) at the well are markedly affected by the transient pumping strategy according to which the well is operated. Our results document the occurrence in time of multiple peaks in the mean and variance of flux-averaged concentrations at the extraction well operating at a transient rate. Our findings suggest that lowest and largest values of mean and variance of flux-averaged concentration at the well tend to occur at the same time. We show that uncertainty associated with detected BTCs at the well increases for pumping regimes displaying a high degree of temporal variability. As such, the choice of the type of engineering control to the temporal sequence of pumping rates could represent a key factor to drive quantification of uncertainty of the contaminant concentration detected at the well. It is documented that pumping rate fluctuations induce a temporally oscillating risk pattern at the well, thus suggesting that the selection of a dynamic pumping regime has a clear influence on the temporal evolution of risk at the well

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 = ln T, 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 Cpestimates is larger when operating under a transient extraction scheme than under the action of a uniform withdrawal schedule. The probability density function (PDF) of Cpdisplays 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 Cpdisplays a bimodal shape for all types of pumping schemes analyzed, independent of the type of heterogeneity considered

Continuum-scale characterization of solute transport based on pore-scale velocity distributions

We present a methodology to characterize a continuum-scale model of transport in porous media on the basis of pore-scale distributions of velocities computed in three-dimensional pore-space images. The methodology is tested against pore-scale simulations of flow and transport for a bead pack and a sandstone sample. We employ a double continuum approach to describe transport in mobile and immobile regions. Model parameters are characterized through inputs resulting from the micron-scale reconstruction of the pore space geometry and the related velocity field. We employ the outputs of pore-scale analysis to (i) quantify the proportion of mobile and immobile fluid regions, and (ii) assign the velocity distribution in an effective representation of the medium internal structure. Our results (1) show that this simple conceptual model reproduces the spatial profiles of solute concentration rendered by pore-scale simulation without resorting to model calibration, and (2) highlight the critical role of pore-scale velocities in the characterization of the model parameters

On the Quantization of the Chern-Simons Fields Theory on Curved Space-Times: the Coulomb Gauge Approach

We consider here the Chern-Simons field theory with gauge group SU(N) in the presence of a gravitational background that describes a two-dimensional expanding ``universe". Two special cases are treated here in detail: the spatially flat {\it Robertson-Walker} space-time and the conformally static space-times having a general closed and orientable Riemann surface as spatial section. The propagator and the vertices are explicitely computed at the lowest order in perturbation theory imposing the Coulomb gauge fixing.Comment: 15 pp., Preprint LMU-TPW 93-5, (Plain TeX + Harvmac

Adaptive POD model reduction for solute transport in heterogeneous porous media

We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (Pe), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasing Pe. This suggests that the effects of local-scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost

Physically meaningful and not so meaningful symmetries in Chern-Simons theory

We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift k \to k+\cv of the bare Chern-Simons parameter $k$ in conncection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS invariant regulators used as yet yield the same value for the shift.Comment: phyzzx, 21 pages, 2 figures in one PS fil

Local and Global Sensitivity Analysis of Cr (VI) Geogenic Leakage Under Uncertain Environmental Conditions

We focus on the joint application of local and global sensitivity analyses (SA) to characterize propagation of model parameter uncertainties to outputs of subsurface water geochemical models. The latter typically involve uncertain inputs, including environmental conditions, mineral rock composition and flow/transport features. In this context, implementation of sensitivity analysis techniques enables us to grasp the relative role of each model input. Here, we focus on the application of several sensitivity approaches to the assessment of Cr(VI) geogenic leakage due to water-rock interactions. We specifically target the impact of uncertain environmental conditions on the chemical composition of spring waters following water transfer through a host rock system with given mineral composition. We employ a reaction path modeling approach and represent uncertainties of environmental conditions through three parameters, i.e., oxygen fugacity (fO2), CO2 fugacity (fCO2), and temperature, which we consider as random quantities. We consider three diverse methodologies, i.e., (a) the Scatter Plots sensitivity analysis (SP) (b) the Distributed Evaluation of Local Sensitivity Analysis (DELSA); and (c) a moment-based global sensitivity analysis. Our results suggest that (a) the relative importance of a given model parameter in driving the uncertainty of the spring water composition may display remarkable variations across the sampled parameter space, and (b) parameter ranking through sensitivity metrics for geochemical applications in subsurface water resources requires a joint assessment of local and global sensitivity

Algebraic characterization of the Wess-Zumino consistency conditions in gauge theories

A new way of solving the descent equations corresponding to the Wess-Zumino consistency conditions is presented. The method relies on the introduction of an operator $\delta$ which allows to decompose the exterior space-time derivative $d$ as a $BRS$ commutator. The case of the Yang-Mills theories is treated in detail.Comment: 16 pages, UGVA-DPT 1992/08-781 to appear in Comm. Math. Phy

Chern-Simons as a geometrical set up for three dimensional gauge theories

Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge fieldComment: 26 pages, latex2

Renormalization Ambiguities in Chern-Simons Theory

We introduce a new family of gauge invariant regularizations of Chern-Simons theories which generate one-loop renormalizations of the coupling constant of the form $k\to k+2 s c_v$ where $s$ can take any arbitrary integer value. In the particular case $s=0$ we get an explicit example of a gauge invariant regularization which does not generate radiative corrections to the bare coupling constant. This ambiguity in the radiative corrections to $k$ is reminiscent of the Coste-L\"uscher results for the parity anomaly in (2+1) fermionic effective actions.Comment: 10 pages, harvmac, no changes, 1 Postscript figure (now included