Sten Berglund

Injection mode implications for solute transport in porous media: Analysis in a stochastic Lagrangian Framework

The effect of solute injection mode is examined in the stochastic-advective framework. For three-dimensional heterogeneous aquifers, uniform resident injection of solute results in nonlinear propagation of mass arrival time mean and variance with distance. Injection in flux results in a linear propagation of mean mass arrival time and mass arrival time variance that is both lower and appears to reach a linear regime more rapidly than uniform resident injection. Implementation of instantaneous injections for both modes as boundary conditions for mathematical and numerical models is discussed.

Aquifer remediation by pumping: A model for stochastic-advective transport with nonaqueous phase liquid dissolution

The coupled effects of advection and rate-limited mass transfer to the aqueous phase from residual dense nonaqueous phase liquid (DNAPL) in the saturated zone are investigated within an analytical stochastic-advective framework. The transport domain is assumed to consist of a source zone where mass transfer takes place and a down-gradient plume zone where transport is by advection only. The mass flux in the aquifer is evaluated from an analytical solution to coupled advection-reaction and nonlinear mass transfer equations. The results emphasize the importance of the parameters associated with the source zone: its length in the mean flow direction, the residual DNAPL saturation, and the mass transfer rate coefficient. The sensitivity to the hydraulic conductivity variance is low for significantly rate-limited mass transfer. It is found that advection in the plume zone has small effect on mass fluxes and cleanup times for the considered lengths of the source and plume regions.

Stochastic analysis of oxygen- and nitrate-based biodegradation of hydrocarbons in aquifers

A Lagrangian stochastic framework was used to analyze field-scale aerobic biodegradation in a heterogeneous aquifer, using Monod-kinetics based reactions between the contaminant, oxygen and microbes. Subsurface heterogeneity was represented by closed-form travel time distributions, derived from a spatially correlated random hydraulic conductivity field with a log-normal distribution. The solution to the coupled and nonlinear, one-dimensional Lagrangian transport equations was obtained using the operator-splitting technique. The presence of nitrate, and considering nitrate as a second electron acceptor, produced significantly different results under intrinsic conditions for different scales of heterogeneity and sorption. In general, nitrate as a second electron acceptor can substantially lower the peak contaminant concentration and increase the maximum remediation under various conditions of heterogeneity and sorption. There exists a critical value for retardation coefficients of both contaminant and microbes that produce complete degradation of mass, and this value depends on the availability of the electron acceptor(s) and is independent of the heterogeneity. Maximum remediation and peak contaminant concentration were sensitive to half-saturation constants. Enhanced remediation using oxygen and nitrate showed that maximum remediation can be increased by approximately 15% when oxygen or nitrate concentration was increased by 50%, but a further increase may be obtained if injection occurred at a more effective location. The proposed stochastic methodology is capable of analyzing field-scale biodegradation using multiple electron acceptors in a simple and computationally attractive manner, producing useful results on design parameters. The key contributions arising from the Lagrangian stochastic framework in field-scale analysis, its limitations and potential approaches for overcoming these limitations are also discussed.

Contaminant Displacement in Aquifers: Coupled Effects of Flow Heterogeneity and Nonlinear Sorption

An analytical solution is developed for displacement of a nonlinearly sorbing solute in a three-dimensional heterogeneous aquifer. Nonlinear sorption is modeled by means of different isotherm equations including the commonly used Langmuir and Freundlich isotherms, but also the Langmuir-Freundlich, Toth, and two-site Langmuir isotherms. Evaluation of cleanup times, defined as the times required to reduce the concentration to a given fraction of its initial value, for different isotherms and combinations of input parameters demonstrate the effects of the properties of the isotherms. In particular, the asymptotic behavior as the aqueous concentration approaches zero is important for transport predictions, where Freundlich sorption leads to infinitely increasing cleanup times as the initial plume concentration decreases. The effect of the choice of sorption isotherm, evaluated by using “best-fit”parameters for four different isotherms, is found to be large and dependent on heterogeneity for the particular data set considered.

Influence of transverse mixing on the breakthrough of sorbing solute in a heterogeneous aquifer

The temporal moments associated with the breakthrough of a sorbing solute in a heterogeneous aquifer are investigated assuming an anisotropic distribution of hydraulic conductivity and deterministic linear sorption kinetics. The expressions for the temporal moments are based on a solution to the advection-dispersion equation with constant coefficients which implies that they are valid in the large-time regime. For the evaluation of the “macrodispersion” coefficient we use the asymptotic results of Fiori [1996], who quantified the effect of pore-scale dispersion on nonreactive solute and showed that porescale dispersion affects field-scale transport primarily through transverse mixing between flow paths. The present study shows that linear sorption kinetics decrease the effect of transverse mixing on the temporal moments as compared to the nonreactive case. It is concluded that in the considered large-time regime, the pure-advection approach to quantify field-scale spreading is appropriate under the conditions encountered in most natural formations.

The effect of Langmuir sorption on pump-and-treat remediation of a stratified aquifer

An analytical solution is derived for the mass flux during remediation of a perfectly stratified aquifer by pumping. The idealized plume and the flow field are defined in a circular-cylinder geometry, where the aquifer is assumed to display spatial variability in the hydraulic conductivity, K, in the vertical direction only. The interaction between the solute in the mobile and immobile phases is described by the nonlinear Langmuir equation, which for a remediation case introduces additional dispersion to that caused by the heterogeneous flow conditions. Calculations for the case of variable K and constant sorption parameters show that the parameters expressing heterogeneity (σY2) and sorption capacity (N0) may cause changes of one order of magnitude, or more, in the time periods needed to fulfill the goals of remediation operations. For a given concentration, increased values of σY2 and/or N0 lead to prolonged cleanup times. Furthermore, the effects of different cleanup goals, expressed as the mass fraction needed to be recovered, and the concentration-dependent effect, i.e. the variation in cleanup time with concentration for given natural conditions, are found to be important. Simultaneous spatial variability in K and N0 is modeled assuming different degrees of negative correlation between these parameters. Calculation results based on very limited field data that spatial variability in N0 may have relatively small impact on cleanup times. The degree of negative correlation is found to be an important factor for determining whether spatial variability in N0 needs to be included in the analysis.

Effect of injection mode on the spatial moments of a non-reactive solute plume

The effects of solute injection mode on the spatial moments of instantaneously injected, non-reactive solute plume are examined in the stochastic-advective framework. Two different modes for the introduction of a solute in a heterogeneous aquifer are considered, namely injection of solute in the resident fluid and in fluid flux. The first and second spatial moments for the two injection modes are quantified using closed-form expressions.

Significance of Pore-Scale Dispersion and Sorption Kinetics for Solute Flux in Heterogeneous Aquifers

Analytical expressions for the statistics of mass fluxes of nonreactive and reactive solutes in presence of pore-scale dispersion are presented, where the reactive solutes undergo first-order sorption kinetics. The developments which lead to the analytical formulation of the solute flux are rigorous in the first-order analysis framework. The methodology is illustrated for a two-dimensional aquifer, assuming that the source is of small transverse extent compared to the heterogeneity length scales. The examples show that pore-scale dispersion has a small effect on the mean point flux, whereas the point flux variance shows much larger sensitivity to the Peclet number. The variance reduction first decreases as the reaction rate increases from the nonreactive limit, but for equilibrium reactions it is of the same order as for nonreactive solutes.