Measurement network design including traveltime determinations to minimize model prediction uncertainty

Traveltime determinations have found increasing application in the characterization of groundwater systems. No algorithms are available, however, to optimally design sampling strategies including this information type. We propose a first-order methodology to include groundwater age or tracer arrival time determinations in measurement network design and apply the methodology in an illustrative example in which the network design is directed at contaminant breakthrough uncertainty minimization. We calculate linearized covariances between potential measurements and the goal variables of which we want to reduce the uncertainty: the groundwater age at the control plane and the breakthrough locations of the contaminant. We assume the traveltime to be lognormally distributed and therefore logtransform the age determinations in compliance with the adopted Bayesian framework. Accordingly, we derive expressions for the linearized covariances between the transformed age determinations and the parameters and states. In our synthetic numerical example, the derived expressions are shown to provide good first-order predictions of the variance of the natural logarithm of groundwater age if the variance of the natural logarithm of the conductivity is less than 3.0. The calculated covariances can be used to predict the posterior breakthrough variance belonging to a candidate network before samples are taken. A Genetic Algorithm is used to efficiently search, among all candidate networks, for a near-optimal one. We show that, in our numerical example, an age estimation network outperforms (in terms of breakthrough uncertainty reduction) equally sized head measurement networks and conductivity measurement networks even if the age estimations are highly uncertain

Inverse modeling of multimodal conductivity distributions

We present a method for the calibration of multimodal hydraulic conductivity distributions and apply this method to the particular case of confining layers with a complex geological architecture. The basis of our technique is the transformation of the original multimodal conductivity distribution to the standard normal distribution, thus fulfilling the condition of normality which is required by the used representer-based inverse algorithm (Valstar et al., 2004). Using this transformation, a calibration that starts from a homogeneous prior field is shown to radically improve the estimation of the protective properties of the confining layer compared to a unimodal approach to the calibration. The method is also used for the calibration of multimodal heterogeneous prior fields. The inevitable distortion of the original parameter covariances in the posterior fields that results from the transformation process is absorbed by an iterative postprocessing procedure, in which lithologic information obtained from the distorted calibrated fields is used to condition the generation of a new multimodal field that complies again with the original geostatistics. After transformation, this new field can be calibrated again, and this process is repeated until the newly generated field agrees with the measurement information sufficiently well. Then, the lithologic distribution of this new field is fixed, and the intrafacies conductivity distributions are calibrated. This approach is shown to preserve the original geostatistics, both of the lithology field and of the intralithology hydraulic conductivity distributions

Inverse modeling of groundwater flow and transport

Civil Engineering and Geoscience

Inverse modeling of groundwater flow using model reduction

Numerical groundwater flow models often have a very high number of model cells (greater than a million). Such models are computationally very demanding, which is disadvantageous for inverse modeling. This paper describes a low?dimensional formulation for groundwater flow that reduces the computational burden necessary for inverse modeling. The formulation is a projection of the original groundwater flow equation on a set of orthogonal patterns (i.e., a Galerkin projection). The patterns (empirical orthogonal functions) are computed by a decomposition of the covariance matrix over an ensemble of model solutions. Those solutions represent the behavior of the model as a result of model impulses and the influence of a chosen set of parameter values. For an interchangeable set of parameter values the patterns yield a low?dimensional model, as the number of patterns is often small. An advantage of this model is that the adjoint is easily available and most accurate for inverse modeling. For several synthetical cases the low?dimensional model was able to find the global minimum efficiently, and the result was comparable to that of the original model. For several cases our model even converged where the original model failed. Our results demonstrate that the proposed procedure results in a 60% time reduction to solve the groundwater flow inverse problem. Greater efficiencies can be expected in practice for large?scale models with a large number of grid cells that are used to compute transient simulations.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

The impact of aquifer heterogeneity on the performance of aquifer thermal energy storage

Heterogeneity in hydraulic properties of the subsurface is not accounted for in current design calculations of aquifer thermal energy storage (ATES). However, the subsurface is heterogeneous and thus affects the heat distribution around ATES wells. In this paper, the influence of heterogeneity on the performance of a doublet well system is quantified using stochastic heat transport modeling. The results show that on average, thermal recovery decreases with increasing heterogeneity, expressed as the lognormal standard deviation of the hydraulic conductivity field around the doublet. Furthermore, heterogeneity at the scale of a doublet ATES system introduces an uncertainty in the amount of expected thermal interference between the warm and cold storage. This results in an uncertainty in thermal recovery that also increases with heterogeneity and decreases with increasing distance between ATES wells. The uncertainty in thermal balance due to heterogeneity can reach values near 50 percent points in case of regional groundwater flow in excess of 200 m/yr. To account for heterogeneity whilst using homogeneous models, an attempt was made to express the effect of heterogeneity by an apparent macrodispersivity. As expected, apparent macrodispersivity increases with increasing heterogeneity. However, it also depends on well-to-well distance and regional groundwater velocity. Again, the uncertainty in thermal recovery is reflected in a range in the apparent macrodispersivity values. Considering the increasing density of ATES systems, we conclude that thermal interference limits the number of ATES systems that can be implemented in a specific area, and the uncertainty in the hydraulic conductivity field related to heterogeneity should be accounted for when optimizing well-to-well distances

Sensitivity analysis on parameters and processes affecting vapor intrusion risk

A one-dimensional numerical model was developed and used to identify the key processes controlling vapor intrusion risks by means of a sensitivity analysis. The model simulates the fate of a dissolved volatile organic compound present below the ventilated crawl space of a house. In contrast to the vast majority of previous studies, this model accounts for vertical variation of soil water saturation and includes aerobic biodegradation. The attenuation factor (ratio between concentration in the crawl space and source concentration) and the characteristic time to approach maximum concentrations were calculated and compared for a variety of scenarios. These concepts allow an understanding of controlling mechanisms and aid in the identification of critical parameters to be collected for field situations. The relative distance of the source to the nearest gas-filled pores of the unsaturated zone is the most critical parameter because diffusive contaminant transport is significantly slower in water-filled pores than in gas-filled pores. Therefore, attenuation factors decrease and characteristic times increase with increasing relative distance of the contaminant dissolved source to the nearest gas diffusion front. Aerobic biodegradation may decrease the attenuation factor by up to three orders of magnitude. Moreover, the occurrence of water table oscillations is of importance. Dynamic processes leading to a retreating water table increase the attenuation factor by two orders of magnitude because of the enhanced gas phase diffusio