Minimum Hydraulic Resistance and Least Resistance Path in Heterogeneous Porous Media

In this study, we focus on the electrical tortuosity‐based permeability model k = reff2/8F (reff is an effective pore size, and F is the formation factor) and analyze its applicability to rocks experiencing mineral precipitation and dissolution. Two limiting cases of advection‐dominated water‐rock reactions are simulated, that is, the reaction‐limited and transport‐limited cases. At the pore scale, the two precipitation/dissolution patterns are simulated with a geometrical model and a phenomenological model. The fluid and electric flows in the rocks are simulated by directly solving the linear Stokes equation and Laplace equation on the representative elementary volume of the samples. The numerical results show that evolutions of k and F differ significantly in the two limiting cases. In general, the reaction‐limited precipitation/dissolution would result in a smooth variation of k and F, which can be roughly modeled with a power function of porosity ϕ with a constant exponent. In contrast, the transport‐limited precipitation/dissolution mostly occurs near the pore throats where the fluid velocity is high. This induces a sharp change in k and F despite a minor variation in ϕ. The commonly used power laws with constant exponents are not able to describe such variations. The results also reveal that the electrical tortuosity‐based permeability prediction generally works well for rocks experiencing precipitation/dissolution if reff can be appropriately estimated, for example, with the electrical field normalized pore size Λ. The associated prediction errors are mainly due to the use of electrical tortuosity, which might be considerably larger than the true hydraulic tortuosity.

Section: Introductionmentioning

confidence: 99%

Permeability Prediction in Rocks Experiencing Mineral Precipitation and Dissolution: A Numerical Study

Niu

Zhang

2019

“…A series of static and dynamic connectivity metrics have been proposed (Fernàndez-Garcia et al, 2010;Fiori, 2014;Fiori & Jankovic, 2012;Freixas et al, 2017;Knudby & Carrera, 2005;Renard & Allard, 2013;Trinchero et al, 2008;Tyukhova & Willmann, 2016a, 2016bWillmann et al, 2008). In the recent work of Rizzo and de Barros (2017), for instance, the connectivity of the K field is quantified with a static metric based on the identification of paths of least resistance (Tyukhova & Willmann, 2016a), which is subsequently shown to be correlated to the early arrival times of a solute plume. Connectivity is closely related to the concepts of percolation and critical path analysis (e.g., Harter, 2005;Hunt & Sahimi, 2017;Stauffer & Aharony, 1994).…”

Section: Introductionmentioning

confidence: 99%

An Entrogram‐Based Approach to Describe Spatial Heterogeneity With Applications to Solute Transport in Porous Media

Bianchi

Pedretti

2018

The recently introduced geological entropy concept evaluates spatial order/disorder in the structure of the hydraulic conductivity (K) field to explain and predict certain characteristics of transport behavior. This concept is expanded in this work by introducing a novel tool for spatial analysis called entrogram from which a metric called entropic scale (HS) can be calculated to measure the overall persistency of patterns of spatial association in a distributed field and to allow robust comparisons between different spatial structures. The entrogram and the entropic scale concepts are applied here to investigate the link between solute transport behavior and the spatial structure of K fields modeled as the distribution of three hydrofacies in alluvial aquifers. Accurate empirical relationships are found between HS and key transport quantities confirming the clear correlation between transport and the structure of the K field described in terms of its entropic scale. The entrogram analysis is also applied to continuous 2‐D and 3‐D fields having identical lognormal K distributions, but with different connectivity. Comparisons between the entrograms and the calculated HS values for these fields, as well as for their corresponding flow velocity distributions, shed light on the key differences among these structures in 2‐D and in 3‐D, which in turn explain their dissimilar impact on solute transport. The entrogram‐based interpretation of the transport simulations seems to confirm that the geological entropy is a promising approach for predicting solute transport behavior simply from a description of the K field heterogeneity.

“…The effect of well‐connected paths on solute transport has been extensively studied in the hydrogeological community (e.g., Fiori et al, ; ; Fogg et al, ; Knudby & Carrera, ; Rizzo & de Barros, ; Sánchez‐Vila et al, ; Trinchero et al, ; Tyukhova et al, ; ; Western et al, ). Implications of aquifer connectivity in the probabilistic assessment of increased lifetime cancer risk due to the exposure of chlorinated solvents is also reported in the literature (Henri et al, ).…”

Section: Introductionmentioning

confidence: 99%

“…For additional details on different connectivity metrics, we refer the reader to Knudby and Carrera () and Renard and Allard (). In this paper, we focus on a static quantity denoted as the minimum hydraulic resistance ( MHR ) and the corresponding least resistance path ( LRP ; Rizzo & de Barros, ; Tyukhova & Willmann, ). The MHR and the LRP are solely based on the K ‐field.…”

Section: Introductionmentioning

confidence: 99%

Minimum Hydraulic Resistance Uncertainty and the Development of a Connectivity‐Based Iterative Sampling Strategy

Rizzo

Barros

2019

Self Cite

The presence of well‐connected paths is commonly observed in spatially heterogeneous porous formations. Channels consisting of high hydraulic conductivity (K) values strongly affect fate and transport of dissolved species in the subsurface environment. Several studies have established a correlation between connectivity properties of the spatially variable K‐field and solute first arrival times. However, due to limited knowledge of the spatial structure of the K‐field, connectivity metrics are subject to uncertainty. In this work, we utilize the concept of the minimum hydraulic resistance and least resistance path to evaluate the connectivity of a K‐field in a stochastic framework. We employ a fast graph theory‐based algorithm to alleviate the computational burden associated with stochastic computations in order to investigate both the impact of the hydrogeological structural conceptualization and domain dimensionality (2‐D vs. 3‐D) on the uncertainty of the minimum hydraulic resistance. Finally, we propose an iterative data acquisition strategy that can be utilized to identify the least resistance path (which is linked to preferential flow channels) in real sites. A synthetic benchmark test is presented, showing the advantages of the proposed sampling strategy when compared to a regular sampling strategy. By using the iterative data sampling strategy, we were able to reduce first arrival time uncertainty by 47% (when compared to the regular sampling strategy), while maintaining site characterization efforts constant.