T. N. Narasimhan

Modeling reactive transport of organic compounds in groundwater using a partial redox disequilibrium approach

The chemical transformation of organic contaminants in natural groundwater systems is clearly dependent upon local geochemistry which determines the thermodynamically favorable degradation reactions and the nature of local microbial populations. Conversely, groundwater geochemistry may be impacted significantly in terms of pH and redox couple speciation by the chemical transformation of sufficient quantities of organic compounds. Therefore an understanding of the coupling between degradation reactions, local geochemistry, and chemical transport is essential in predicting the chemical evolution of contaminated aquifers. Equilibrium-based reactive chemical transport models are usually not utilized for problems involving the transport of degradable organic compounds due to slow reaction kinetics and the persistence of intermediate degradation products. In this study we propose a reactive geochemical transport model which considers these types of degradation reactions. An expert system approach is used to postulate a set of sequential, first-order degradation reactions for the organic compounds based upon thermodynamic considerations and user-defined rules. Redox disequilibrium provides the driving force for the abiotic or microbially mediated transformation of the organic compounds as well as the associated response of groundwater geochemistry. Coupling between local inorganic geochemistry and reacting organic compounds is achieved by assuring conservation of operational valence and mass balance. The composite geochemical model is in turn coupled with an integral finite difference transport algorithm using a two-step sequential solution approach. The transport equation is solved separately for each inorganic aqueous species, complex, and dissolved organic species, allowing a high degree of flexibility in problem definition. We apply the model to an illustrative example problem concerning the introduction of aromatic hydrocarbons and chlorinated ethenes into an initially oxidizing aquifer. Modeling results agree well qualitatively with field and laboratory observations reported in the literature in terms of degradation patterns and the effects on groundwater geochemistry.

Transient flow of water to a well in an unconfined aquifer: Applicability of some conceptual models

Currently available methods for interpreting data from unconfined aquifers are based on analytical solutions which restrict attention to flow in the saturated zone and account for drainage of water from the unsaturated zone through a source term. The parameter, specific yield (Sy), is assumed to dictate the total quantity of water that is derivable through the desaturation process. It is commonly assumed that flow in the unsaturated zone has little effect on flow in the saturated zone and therefore that all the drainable water is instantly delivered at the water table as it declines in response to pumping. In a model proposed in 1954, Boulton empirically assumed that the drainable water associated with Sy is released gradually at the water table as an exponential function of time. This concept of Boulton is similar to the notion of first-order kinetics frequently used to handle chemical transformations. Boultons model is considered by some to have no physical basis. Numerical experiments performed on sand columns with reasonable properties suggest that vertical drainage of water at the water table due to a falling water table is a time-dependent process which is mathematically more complex than a simple exponential relation. Although Boulton did not provide a rational physical explanation, his exponential assumption has some merit in that it implicitly provides for a time dependent drainage process which seems to occur in the unsaturated zone. However, the simple exponential approximation is not adequate to account for what is seemingly a complex process. It appears that a physically comprehensive model of radial flow in an unconfined aquifer will combine time-dependent drainage from above the water table with vertical components of flow in the saturated zone. An additional assumption frequently made is that the well can be treated as a line source. Results from numerical experiments suggest that caution is in order before neglecting effects of well-bore storage in interpreting data from tests on unconfined aquifers.

An Evaluation of the Bouwer and Rice Method of Slug Test Analysis

The method of Bouwer and Rice (1976) for analyzing slug test data is widely used to estimate hydraulic conductivity (K). Based on steady state flow assumptions, this method is specifically intended to be applicable to unconfined aquifers. Therefore it is of practical value to investigate the limits of accuracy of the K estimates obtained with this method. Accordingly, using a numerical model for transient flow, we evaluate the method from two perspectives. First, we apply the method to synthetic slug test data and study the error in estimated values of K. Second, we analyze the logical basis of the method. Parametric studies helped assess the role of the effective radius parameter, specific storage, screen length, and well radius on the estimated values of K. The difference between unconfined and confined systems was studied via conditions on the upper boundary of the flow domain. For the cases studied, the Bouwer and Rice analysis was found to give good estimates of K, with errors ranging from 10% to 100%. We found that the estimates of K were consistently superior to those obtained with Hvorslevs (1951) basic time lag method. In general, the Bouwer and Rice method tends to underestimate K, the greatest errors occurring in the presence of a damaged zone around the well or when the top of the screen is close to the water table. When the top of the screen is far removed from the upper boundary of the system, no difference is manifest between confined and unconfined conditions. It is reasonable to infer from the simulated results that when the screen is close to the upper boundary, the results of the Bouwer and Rice method agree more closely with a “confined” idealization than an “unconfined” idealization. In effect, this method treats the aquifer system as an equivalent radial flow permeameter with an effective radius, Re, which is a function of the flow geometry. Our transient simulations suggest that Re varies with time and specific storage. Thus the effective radius may be reasonably viewed as a time-averaged mean value. The fact that the method provides reasonable estimates of hydraulic conductivity suggests that the empirical, electric analog experiments of Bouwer and Rice have yielded shape factors that are better than the shape factors implicit in the Hvorslev method.

A numerical investigation of free surface—Seepage face relationship under steady state flow conditions

The relationship between free surface and seepage face under steady conditions of flow has been analyzed for radial and planar flow configurations. The numerical studies, carried out with a saturated-unsaturated flow model, included the simulation of a series of experimental observations documented by Hall (1955). The numerical analysis took into consideration effects of capillary fringe, model geometry, as well as converging and diverging patterns of flow. For the control series of three cases studied, discharge rates, free surface location, seepage face height and the spatial distribution of potentials closely matched the experimental observations. Additional parametric studies showed that converging patterns of flow favor more pronounced development of seepage face than divergent flows. In two-dimensional planar flow, larger drawdowns tend to favor relatively more pronounced development of seepage face. Comparison of the detailed simulation results (taking unsaturated flow into consideration) with results generated using Dupuit-Forchheimer assumptions suggest that the latter may provide discharge estimates that are in error by 12 to 20% both for radial and for two-dimensional planar flows.

Reactive Transport of Petroleum Hydrocarbon Constituents in a Shallow Aquifer: Modeling Geochemical Interactions Between Organic and Inorganic Species

Dissolved organic contaminants such as petroleum hydrocarbon constituents are often observed to degrade in groundwater environments through biologically mediated transformation reactions into carbon dioxide, methane, or intermediate organic compounds. Such transformations are closely tied to local geochemical conditions. Favorable degradation pathways depend upon local redox conditions through thermodynamic constraints and the availability of appropriate mediating microbial populations. Conversely, the progress of the degradation reactions may affect the chemical composition of groundwater through changes in electron donor/acceptor speciation and pH, possibly inducing mineral precipitation/dissolution reactions. Transport of reactive organic and inorganic aqueous species through open systems may enhance the reaction process by mixing unlike waters and producing a state of general thermodynamic disequilibrium. In this study, field data from an aquifer contaminated by petroleum hydrocarbons have been analyzed using a mathematical model which dynamically couples equilibrium geochemistry of inorganic constituents, kinetically dominated sequential degradation of organic compounds, and advective-dispersive chemical transport. Simulation results indicate that coupled geochemical processes inferred from field data, such as organic biodegradation, iron reduction and dissolution, and methanogenesis, can be successfully modeled using a partial-redox-disequilibrium approach. The results of this study also suggest how the modeling approach can be used to study system sensitivity to various physical and chemical parameters, such as the effect of dispersion on the position of chemical fronts and the impact of alternative buffering mineral phases (e.g., goethite versus amorphous Fe(OH)3) on water chemistry.

A multiple species transport model with sequential decay chain interactions in heterogeneous subsurface environments

The spatial and temporal distribution of solutes in groundwater is controlled by several physical and chemical processes. Among the chemical processes, sequential degradation phenomena play an important role in determining the fate of radioactive materials and certain types of organic compounds. We present a numerical model designed to evaluate the simultaneous transport and kinetically controlled sequential degradation (straight and branched chains) of several dissolved components in groundwater systems. The model utilizes a two-step quasi-linearization algorithm to solve the equations of chemical transport and transformation. The transport equations are solved explicitly using the integral finite difference method. The chemical transformation equations are solved using an implicit finite difference (in time) algorithm for each volume element in the discretized flow domain. Although this algorithm is designed to solve problems involving first-order kinetics, it may be modified in certain instances to accommodate rate mechanisms other than first order. The chemical transformation module and the transport module are coupled via a source/sink term in the transport equation. This combination results in a numerical code that is computationally efficient. We have found that the model yields solutions which are in excellent agreement with available analytical solutions. Solution of a test problem based on the sequential degradation of the pesticide aldicarb demonstrates that the model can provide useful insights into the fate of solutes subject to certain degradation regimes in heterogeneous groundwater systems. Although the illustrative examples presented are one dimensional, the model itself is capable of handling two- and three-dimensional problems. In addition, the modular structure of the model is built upon user-specified chemical reactions. This allows for flexibility in problem definition, which may accommodate both reversible and irreversible reactions.

Hydraulic characterization of aquifers, reservoir rocks, and soils: A history of ideas

Estimation of the hydraulic properties of aquifers, petroleum reservoir rocks, and soil systems is a fundamental task in many branches of Earth sciences and engineering. The transient diffusion equation proposed by Fourier early in the 19th century for heat conduction in solids constitutes the basis for inverting hydraulic test data collected in the field to estimate the two basic parameters of interest, namely, hydraulic conductivity and hydraulic capacitance. Combining developments in fluid mechanics, heat conduction, and potential theory, the civil engineers of the 19th century, such as Darcy, Dupuit, and Forchheimer, solved many useful problems of steady state seepage of water. Interest soon shifted towards the understanding of the transient flow process. The turn of the century saw Buckingham establish the role of capillary potential in governing moisture movement in partially water-saturated soils. The 1920s saw remarkable developments in several branches of the Earth sciences; Terzaghis analysis of deformation of watersaturated earth materials, the invention of the tensiometer by Willard Gardner, Meinzers work on the compressibility of elastic aquifers, and the study of the mechanics of oil and gas reservoirs by Muskat and others. In the 1930s these led to a systematic analysis of pressure transients from aquifers and petroleum reservoirs through the work of Theis and Hurst. The response of a subsurface flow system to a hydraulic perturbation is governed by its geometric attributes as well as its material properties. In inverting field data to estimate hydraulic parameters, one makes the fundamental assumption that the flow geometry is known a priori. This approach has generally served us well in matters relating to resource development primarily concerned with forecasting fluid pressure declines. Over the past two decades, Earth scientists have become increasingly concerned with environmental contamination problems. The resolution of these problems requires that hydraulic characterization be carried out at a much finer spatial scale, for which adequate information on geometric detail is not forthcoming. Traditional methods of interpretation of field data have relied heavily on analytic solutions to specific, highly idealized initial-value problems. The availability of efficient numerical models and versatile spreadsheets of personal computers offer promising opportunities to relax many unavoidable assumptions of analytical solutions and interpret field data much more generally and with fewer assumptions. Currently, a lot of interest is being devoted to the characterization of permeability. However, all groundwater systems are transient on appropriate timescales. The dynamics of groundwater systems cannot be understood without paying attention to capacitance. Much valuable insights about the dynamic attributes of groundwater systems could be gained by long-term passive monitoring of responses of groundwater systems to barometric changes, Earth tides, and ocean tides.

Modeling of selenium transport at the Kesterson reservoir, California, U.S.A.

Abstract Field observations indicated that the vertical movement of a selenium plume from the pond into the selenium-free groundwater at the Kesterson reservoir lags significantly behind the hydrodynamic front. The movement of selenium was simulated using DYNAMIX, aredoxcontrolled, multiple species chemical transport model. The actual nature of the retardation mechanism, whether it is inorganically controlled or biologically controlled, is not yet clearly understood. In the present work, the observed retardation is treated equivalently by treating the organic layer of pond-bottom sediments as a medium of oxygen consumption. In addition, the dissolution of magnetite in the contaminated aquifer was treated as a kinetic process. The agreement between the observed and computed results suggests that the inorganic process could at least be a contributing factor in the retardation of the selenium front. Further research is needed to investigate the microbial effect on the movement of selenium.