Conditional stochastic mapping of transport connectivity

Abstract

[1] We present a method for the stochastic simulation of point-to-point transport connectivity honoring data from three types of information: (1) travel time estimates obtained from field tracer tests; (2) estimates of flow connectivity indicators obtained from the relatively fast or slow flow response that is observed at a point location given the flow impulse at another location, and (3) measurements of transmissivity at a local scale. The method thus efficiently integrates data obtained from different hydraulic tests, each sampling different areas within the aquifer. To achieve this, we first extend the concept of point-to-point flow connectivity and transport connectivity, mathematically formulated by Trinchero et al. (2008) for pumping conditions, to support a more general flow configuration. Interestingly, point-to-point flow connectivity can be generally seen as a weighted integral of transmissivity over the entire domain, the weighting function being proportional to the sensitivity of heads with respect to the natural log of transmissivity per unit of aquifer volume. On the contrary, point-to-point transport connectivity is a weighted integral along the particle path of the solute mass that involves two variables: transmissivity and flow connectivity. Each variable has its own distinct weighting function. The weighting function of transmissivity is inversely proportional to both the homogeneous travel time and the point velocity sampled along the travel path. On this basis, we show how to generate conditional point-to-point transport connectivity maps. The method avoids the inference of cross-covariance functions between variables measured over different scales and sampled areas (which cannot be otherwise estimated with a few data measurements) by expressing them as a function of the local transmissivity covariance function. An example of the method is provided to evaluate the worth of including tracer data to delineate capture zones of abstraction wells originally defined from local transmissivity measurements. Monte Carlo simulations reveal that the impact of including tracer data is a maximum when the travel time data are obtained at a location different than that of transmissivity measurements. The reason is that weighting functions give larger weights to the injection location, so introducing tracer test data at points where transmissivity is already known is somewhat redundant.

Connectivity metrics for subsurface flow and transport

“…This is extremely powerful since it does not require to solve explicitly any flow or transport equations with a numerical method. As shown by Fernandez-Garcia et al [151] this method allows to delineate accurately and in a very straightforward manner the capture zone of a well in a multi-Gaussian framework. But one of the very interesting part of their results is that it also allows to analyze theoretically the impact of data conditioning.…”

“…The tracer connectivity metric is expressed as line integral along the flow path between the two points. In that framework, Fernandez-Garcia et al [151] express analytically the cross covariances between the local transmissivity values, the flow connectivity metrics and the transport metrics (travel times) as a function of the covariance of the logarithm of the transmissivities. This allows them to generate directly simulations of the three variables conditional to field observations either of transmissivity, travel times, or flow connectivity.…”

“…Based on the work of Trinchero et al [58] who defined a connectivity metric for radial flow and one for transport, Fernandez-Garcia et al [151] extended those definitions to more general flow conditions. They express the point to point flow connectivity metric as a space integral of the transmissivity involving a weighting function proportional to the sensitivity of the heads with respect to the natural logarithm of the transmissivity.…”

“…How a general methodology including new experimental procedures and modeling approaches to quantify the connectivity in the field and to constrain the models will improve forecast? So far the research that is the closest to reach that aim is the work of Fernandez-Garcia et al [151].…”

Probabilistic human health risk assessment of degradation‐related chemical mixtures in heterogeneous aquifers: Risk statistics, hot spots, and preferential channels

“…Different metrics have been used to describe connectivity [Sanchez-Vila et al, 1999;Fernandez-Garcia et al, 2002;Carrera, 2005, 2006;Trinchero et al, 2008;Fernandez-Garcia et al, 2010]. In general, Renard and Allard [2013] distinguished two types of measures: Static connectivity metrics only depend on the spatial distribution of aquifer properties, and dynamic connectivity metrics depend on the flow and/or transport response to a given impulse.…”