Transition Probability/Markov Chain Analyses of DNAPL Source Zones and Plumes

Abstract

At sites where a dense nonaqueous phase liquid (DNAPL) was spilled or released into the subsurface, estimates of the mass of DNAPL contained in the subsurface from core or monitoring well data, either in the nonaqueous or aqueous phase, can be highly uncertain because of the erratic distribution of the DNAPL due to geologic heterogeneity. In this paper, a multiphase compositional model is applied to simulate, in detail, the DNAPL saturations and aqueous-phase plume migration in a highly characterized, heterogeneous glaciofluvial aquifer, the permeability and porosity data of which were collected by researchers at the University of Tübingen, Germany. The DNAPL saturation distribution and the aqueous-phase contaminant mole fractions are then reconstructed by sampling the data from the forward simulation results using two alternate approaches, each with different degrees of sampling conditioning. To reconstruct the DNAPL source zone architecture, the aqueous-phase plume configuration, and the contaminant mass in each phase, one method employs the novel transition probability/Markov chain approach (TP/MC), while the other involves a traditional variogram analysis of the sampled data followed by ordinary kriging. The TP/MC method is typically used for facies and/or hydraulic conductivity reconstruction, but here we explore the applicability of the TP/MC method for the reconstruction of DNAPL source zones and aqueous-phase plumes. The reconstructed geometry of the DNAPL source zone, the dissolved contaminant plume, and the estimated mass in each phase are compared using the two different geostatistical modeling approaches and for various degrees of data sampling from the results of the forward simulation. It is demonstrated that the TP/MC modeling technique is robust and accurate and is a preferable alternative compared to ordinary kriging for the reconstruction of DNAPL saturation patterns and dissolved-phase contaminant plumes.

Three-dimensional high resolution fluvio-glacial aquifer analog: Part 1: Field study

“…Meanwhile, several recent studies have used part of the data set for demonstration of geophysical forward (Kowalsky et al, 2001) or inverse modeling (Hu et al, 2009), for hydraulic or transport modeling (Maier et al, 2005;Maji et al, 2006;Werth et al, 2006), and for sedimentological analysis (Heinz et al, 2003). The developed dataset is provided as downloadable supplement and may be used in realistic 3D hydrogeological modeling studies.…”

A Markov chain model for characterizing medium heterogeneity and sediment layering structure

“…Outcrop data were also used by Dai et al [2005] for a better definition of transition probability. Recent studies [Maji et al, 2006;Lee et al, 2007] demonstrate that the TP/MC method outperforms conventional geostatistical methods by reconstructing the linkage between lithology and contaminant plumes.…”

“…Conventional geostatistical methods (e.g., kriging) use the two-point variogram (or covariance) to describe spatial structures; recently the three-point variogram has been advocated [Strebelle, 2002;Krishnan and Journel, 2003;Journel and Zhang, 2006;Feyen and Caers, 2006]. An alternate geostatistical method, one that does not use a variogram, uses transition probability and Markov chains (TP/MC) to describe spatial structures of categorical data [e.g., Carle andFogg, 1996, 1997;Fogg et al, 1998;Carle, 1999;Weissmann et al, 1999;Li et al, 1999;Ritzi, 2000;Elfeki and Dekking, 2001;Lu and Zhang, 2002;Park et al, 2004;Dai et al, 2005;Sivakumar et al, 2005;Maji et al, 2006;Zhang et al, 2006;Li, 2007aLi, , 2007bLee et al, 2007;Dai et al, 2007;Sun et al, 2008]. An advantage of the TP/MC method relative to the conventional geostatistical methods is that it can incorporate geological information such as mean lengths and directional orientation of lithofacies [Carle andFogg, 1996, 1997].…”

Three-dimensional high resolution fluvio-glacial aquifer analog – Part 2: Geostatistical modeling

“…1) are used both as hard conditioning data (268,000 points) to constrain the simulation and more generally as a source of information to develop the whole methodology. The discretization is identical to that used by Maji et al (2006). The simulation domain X is divided into 9 million (320 Â 201 Â 140) cubic cells having a side of 5 cm.…”

“…Among them, the most interesting for our purposes are the works of Maji (2005) and Maji et al (2006). These authors applied a transition-probability-based Markov chain approach (TP/MC, Carle, 1996), using the software TProgs, to reconstruct the complete 3D volume and to use it for analyzing the impact of heterogeneity on DNAPL transport.…”