Solute flux approach to transport through spatially nonstationary flow in porous media

Abstract

Abstract. A theoretical framework for solute flux through spatially nonstationary flows in porous media is presented. The flow nonstationarity may stem from medium nonstationarity (e.g., the presence of distinct geological layers, zones, or facies), finite domain boundaries, and/or fluid pumping and injecting. This work provides an approach for studying solute transport in multiscale media, where random heterogeneities exist at some small scale while deterministic geological structures and patterns can be prescribed at some larger scale. In such a flow field the solute flux depends on solute travel time and transverse displacement at a fixed control plane. The solute flux statistics (mean and variance) are derived using the Lagrangian framework and are expressed in terms of the probability density functions (PDFs) of the particle travel time and transverse displacement. These PDFs are given with the statistical moments derived based on nonstationary Eulerian velocity moments. The general approach is illustrated with some examples of conservative and reactive solute transport in stationary and nonstationary flow fields. It is found based on these examples that medium nonstationarities (or multiscale structures and heterogeneities) have a strong impact on predicting solute flux across a control plane and on the corresponding prediction uncertainty. In particular, the behavior of solute flux moments strongly depends on the configuration of nonstationary medium features and the source dimension and location. The developed nonstationary approach may result in non-Gaussian (multiple modal) yet realistic behaviors for solute flux moments in the presence of flow nonstationarities, while these non-Gaussian behaviors may not be reproduced with a traditional stationary approach. IntroductionPredicting the migration of contaminants in subsurface flows is a major conceptual and practical challenge. The subsurface flow consists of tortuous and unpredictable flow pathways that result from natural geologic heterogeneity. As a consequence, the contaminant concentration is a random field that can be described only in the statistical sense. Since geologic media are heterogeneous and the medium heterogeneity generally cannot be described deterministically, it becomes quite common to treat medium properties as spatial random variables. That is, they are unpredictable deterministically and have to be described in statistical terms. In turn, subsurface flow and transport are treated as stochastic processes. Most efforts in studying subsurface contaminant transport in random porous media have been focused on quantifying the expected concentration and the associated uncertainty

Ensemble Kalman filter versus ensemble smoother for assessing hydraulic conductivity via tracer test data assimilation

“…The color bar indicates log-transformed hydraulic conductivity in ln(L/T ). 2005), the log-normal pdf is easier to handle and often represents a reasonable assumption (e.g., Bellin et al, 1994;Zhang et al, 2000). Figure 5 shows the Y fields estimated by the EnKF and the ES when assimilating log-transformed concentration measurements.…”

On stochastic modeling of groundwater flow and solute transport in multi-scale heterogeneous formations

“…For the case study, we used a bimodal heterogeneous formation, which composed of two different materials, as an example to show how to apply the general theory to analyze the conductivity correlation in a specific case. Based on this analysis, we applied a numerical method of moment developed recently [Zhang et al, 2000;Wu et al, 2003] to investigate the influences of the two stochastic processes of heterogeneity on groundwater flow and transport. One specific case was chosen in this study, bimodal medium.…”

“…In some cases, the large-scale features, such as the locations of geological layers (or zones), can be identified from measurements, only the spatial variability of medium properties, such as the hydraulic conductivity, within each layer (or zone) need to be treated as random processes. Solute transport in this kind of medium has been studied [Zhang et al, 2000;Wu et al, 2003]. But in other cases, the geometries or BILL X. HU, JICHUN WU and CHANGMING HE 123 boundaries of the large-scale features cannot be very well defined due to incomplete knowledge about them, they also need to be treated as random variables.…”

“…Solute transport in a nonstationary permeability field is a relatively new research area. Recently, a theoretical framework for solute flux through spatially nonstationary flows in porous media has been developed [Zhang et al, 2000;Wu et al, 2003]. The solute flux depends on the solute travel time and transverse displacement at a fixed control plane.…”

A numerical method of moments for solute transport in physically and chemically nonstationary formations: linear equilibrium sorption with random K d

“…Recently, a numerical method of moment for solute transport in a nonstationary, heterogeneous medium has been developed (Zhang et al, 2000;Wu et al, 2003), where a Lagrangian perturbation method is applied to develop the framework for solute transport in a nonstationary flow field and a numerical method is implemented to obtain the solution. For this method, the first three assumptions listed above for most stochastic theories are not required.…”