Characterizations of Solutions in Geochemistry: Existence, Uniqueness and Precipitation Diagram

International audienceIn this paper, we study the properties of a geochemical model involving aqueous and precipitation-dissolution reactions at a local equilibrium in a diluted solution. This model can be derived from the minimization of the free Gibbs energy subject to linear constraints. By using logarithmic variables, we define another minimization problem subject to different linear constraints with reduced size. The new objective function is strictly convex, so that uniqueness is straightforward. Moreover, existence conditions are directly related to the totals, which are the parameters in the mass balance equation. These results allow us to define a partition of the totals into mineral states, where a given subset of minerals are present. This precipitation diagram is inspired from thermodynamic diagrams where a phase depends on physical parameters. Using the polynomial structure of the problem, we provide characterizations and an algorithm to compute the precipitation diagram. Numerical computations on some examples illustrate this approach

A Study of Reactive Transport Phenomena in Porous Media

This work was also published as a Rice University thesis/dissertation: http://hdl.handle.net/1911/19202The numerical modeling of reactive transport in a porous medium has important applications in hydrology, the earth sciences and in numerous industrial processes. However, realistic simulations involving a large number of chemical species undergoing simultaneous transport and chemical transformation present a significant computational challenge, particularly in multiple spatial dimensions. A framework for analyzing the chemical batch problem is first introduced, which is sufficiently general to allow for reaction of both equilibrium and kinetic type. The governing equations for reactive transport of a single flowing phase through a porous medium are presented next, and a classification based on the nature of the reactive system is established. A computer module for the equilibrium problem is developed, based on a novel application of the interior-point algorithm for nonlinear programming. Among its advantages are good global convergence and automatic selection of mineral phases. To handle kinetic reactions, the equilibrium module is embedded in a time-integration framework using explicit ODE integrators. Reactive transport of species is achieved through operator-splitting, which enables a straightforward incorporation of the batch module into the existing parallel, three-dimensional, single-phase flow and transport simulator PARSim1. Numerical results are presented which demonstrate the correctness of the computer program for major classes of geochemistry problems, including ion-exchange, precipitation/dissolution, adsorption, aqueous complexation and redox reactions

Basic Research Needs for Geosciences: Facilitating 21st Century Energy Systems

Executive Summary Serious challenges must be faced in this century as the world seeks to meet global energy needs and at the same time reduce emissions of greenhouse gases to the atmosphere. Even with a growing energy supply from alternative sources, fossil carbon resources will remain in heavy use and will generate large volumes of carbon dioxide (CO2). To reduce the atmospheric impact of this fossil energy use, it is necessary to capture and sequester a substantial fraction of the produced CO2. Subsurface geologic formations offer a potential location for long-term storage of the requisite large volumes of CO2. Nuclear energy resources could also reduce use of carbon-based fuels and CO2 generation, especially if nuclear energy capacity is greatly increased. Nuclear power generation results in spent nuclear fuel and other radioactive materials that also must be sequestered underground. Hence, regardless of technology choices, there will be major increases in the demand to store materials underground in large quantities, for long times, and with increasing efficiency and safety margins. Rock formations are composed of complex natural materials and were not designed by nature as storage vaults. If new energy technologies are to be developed in a timely fashion while ensuring public safety, fundamental improvements are needed in our understanding of how these rock formations will perform as storage systems. This report describes the scientific challenges associated with geologic sequestration of large volumes of carbon dioxide for hundreds of years, and also addresses the geoscientific aspects of safely storing nuclear waste materials for thousands to hundreds of thousands of years. The fundamental crosscutting challenge is to understand the properties and processes associated with complex and heterogeneous subsurface mineral assemblages comprising porous rock formations, and the equally complex fluids that may reside within and flow through those formations. The relevant physical and chemical interactions occur on spatial scales that range from those of atoms, molecules, and mineral surfaces, up to tens of kilometers, and time scales that range from picoseconds to millennia and longer. To predict with confidence the transport and fate of either CO2 or the various components of stored nuclear materials, we need to learn to better describe fundamental atomic, molecular, and biological processes, and to translate those microscale descriptions into macroscopic properties of materials and fluids. We also need fundamental advances in the ability to simulate multiscale systems as they are perturbed during sequestration activities and for very long times afterward, and to monitor those systems in real time with increasing spatial and temporal resolution. The ultimate objective is to predict accurately the performance of the subsurface fluid-rock storage systems, and to verify enough of the predicted performance with direct observations to build confidence that the systems will meet their design targets as well as environmental protection goals. The report summarizes the results and conclusions of a Workshop on Basic Research Needs for Geosciences held in February 2007. Five panels met, resulting in four Panel Reports, three Grand Challenges, six Priority Research Directions, and three Crosscutting Research Issues. The Grand Challenges differ from the Priority Research Directions in that the former describe broader, long-term objectives while the latter are more focused

On multicomponent reactive transports in porous media: from the natural complexity to analitycal solutions

El transporte de solutos no conservativos en medios porosos o fracturados es altamente influenciado por su heterogeneidad. Complejidad adicional se agrega al proceso de transporte, debido a la presencia de diferentes tipos de reacciones químicas que controlan la evolución de las concentraciones de las especies en el medio. Muchas de esas reacciones químicas están gobernadas por la mezcla de aguas con diferente calidad geoquímica. La mezcla produce desequilibrio químico instantáneo en el agua mezclada resultante, y las reacciones dan lugar para que se re-equilibre el sistema.Esta disertación doctoral estudia el transporte en medios heterogéneos cubriendo diferentes y tipos de acuíferos. Primero, el flujo y el transporte se analizan en rocas fracturadas, las cuales poseen baja permeabilidad. Estas formaciones son estudiadas usando como modelo conceptual las Redes Discretas de Fracturas, donde se considera el medio como una densa red de fracturas que se interconectan y conducen agua. Este modelo de es una alternativa válida para conceptualizar el transporte de solutos en el medio fracturado, pero tradicionalmente no se ha utilizado para analizar ni el transporte ni el flujo en una modelación de tipo problema inverso, debido a su alto costo computacional.El transporte de solutos conservativos en medios heterogéneos puede modelarse con una ecuación efectiva que involucre un término de transferencia de masa entre la zona móvil y la zona inmóvil. La segunda parte de la disertación explora la posibilidad de extender esta idea para tener en cuenta las especies reactivas. Se parte de la consideración de que las especies están en equilibrio químico local, el cual es alcanzado instantáneamente. El impacto de la heterogeneidad del medio en el transporte efectivo es representado por un modelo de tasa de transferencia múltiple de masa (MRMT), el cual aproxima el medio a un multicontinuo de una región móvil y varias regiones inmóviles, las cuales se relacionan por una transferencia de masa cinética. Partiendo del hecho de que todas las regiones están bien mezcladas, el equilibrio global no se preserva. Esta imposición implica que las reacciones tomen lugar en todo el dominio, y sean dominadas tanto por la dispersión local como por la transferencia de masa. Se derivaron expresiones explícitas para calcular las tasas de reacción en las regiones móvil e inmóvil y se estudió el impacto de la transferencia de masa en el transporte reactivo. Las tasas de reacción pueden cambiar significativamente comparadas con aquellas que se obtendrían en un medio homogéneo. Para una amplia distribución de tiempos de residencia en las zonas inmóviles, el sistema podría tomar mucho más tiempo para equilibrar globalmente el medio comparado que para un medio homogéneo.El último tema abordado en esta disertación es el análisis del transporte de especies bajo condiciones de cinética química o equilibrio no instantáneo. El transporte reactivo a escala local es analizado bajo dos situaciones: (i) con una reacción sencilla y (ii) con dos reacciones simultáneas: una considerada instantánea y la otra como lenta respecto al tiempo característico de transporte. En la primera situación de las dos planteadas, es posible concluir que el problema puede ser reescrito sólo en términos del estado inicial del sistema más una ecuación diferencial para la tasa de reacción. El resultado clave es que la tasa de reacción en equilibrio depende de un término relativo a la mezcla y a la reacción cinética, la cual es de hecho el factor que controla la disponibilidad de reactantes en el sistema, y la distribución de las combinaciones lineales de las concentraciones acuosas de las especies, llamadas componentes tanto conservativas como cinéticas. Desde un punto de vista operacional, estas expresiones permiten el cálculo directo de las tasas de reacción en equilibrio sin la necesidad de calcular las concentraciones de las especies acuosas.Transport of non-conservative species or solutes in porous or fractured media is highly influenced by heterogeneity. Additional complexity is added to the processes due to the presence of different types of chemical reactions that control the fate of species concentrations in the medium. Many of these chemical reactions are governed by mixing of waters with different geochemical signature. Mixing yields instantaneous chemical disequilibrium in the resulting mixed water, and reactions take place to re-equilibrate the system.This dissertation studies transport in heterogeneous media covering different problems (flow, conservative transport and reactive transport) and in different aquifer types. First, we analyze flow and transport in low permeable highly fractured massifs. These are studied using the Discrete Fracture Network (DFN) approach, where a dense network of water-conducting intersecting fractures is considered. The DFN approach traditionally has lacked the possibility of analyzing transport (as well as flow) in an inverse problem framework. The actual tracer test, performed with a conservative solute (deuterium), evidences Non-Fickian behavior, characterized by tailing in the breakthrough curve.As a consequence, transport of conservative solutes in heterogeneous media can be modeled with an effective equation involving a mass transfer term between the mobile and some immobile zones. In the second part of the thesis we explore the possibility of extending this idea to account for transport of reactive species. We start by considering species where local chemical equilibrium conditions are reached instantaneously. The impact of the medium heterogeneity on effective transport is represented by a multi rate mass transfer approach, which models the medium as a multiple continuum of one mobile and multiple immobile regions, which are related by kinetic mass transfer. Even though all regions (mobile and immobile) are assumed to be well mixed (local equilibrium), globally equilibrium is not preserved. The imposition of local equilibrium at all points implies the need for reactions to take place all through the domain, driven by both local dispersion and mass transfer. We derive explicit expressions for the reaction rates in the mobile and immobile regions and study the impact of mass transfer on reactive transport. The reaction rates can change significantly compared with the ones that would be obtained in a homogeneous media. For a broad distribution of residence times in the immobile zones, the system may take much more time to equilibrate globally than for a homogeneous medium.The last topic addressed in this Thesis is the analysis of transport of species undergoing non-instantaneous (kinetic) chemical equilibrium. Reactive transport at the local scale is analyzed under two situations: (i) with a single kinetic reaction and (ii) with two simultaneous reactions: one considered instantaneous and the other one being slow related to the transport characteristic time. In the first problem of these problems, we find that the problem can be rewritten only in terms of the initial state of the system plus a non-linear partial differential equation for the reaction rate.The key result is that the equilibrium reaction rate depends on a mixingrelated term, the kinetic reaction rate, which is actually controlling the availability of reactants in the system, and the distribution of (conservative and kinetic) linear combinations of aqueous species concentrations. From an operational standpoint, our expressions allow direct computation of equilibrium reaction rates without the need to calculate aqueous species concentrations. To illustrate the results, the dissolution of calcite in the presence of precipitating gypsum in a one-dimensional fully saturated system is analyzed. The example highlights the highly nonlinear and non monotonic response of the system to the controlling input parameters

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Modelling Bioremediation of Uranium Contaminated Aquifers

Radionuclide extraction, processing and storage have resulted in a legacy of radionuclide-contaminated groundwater aquifers worldwide. An emerging remediation technology for such sites is the in situ immobilisation of radionuclides via biostimulation of dissimilatory metal reducing bacteria. While this approach has been successfully demonstrated in experimental studies, advances in understanding and optimization of the technique are needed. Mass transfer processes in heterogeneous and structured porous media may significantly affect the geochemical and microbial processes taking place in contaminated sites, impacting remediation efficiency significantly. The objective of this work was to understand better how heterogeneous porous media may affect immobilisation efficiency through interactions with the dominant geochemical, microbial and transport processes. A biogeochemical reactive transport model was developed for uranium immobilisation by DMRB. Physical heterogeneity is conceptually represented by a two-region model. Simulations investigate the parameter sensitivities of the system over wide ranging geochemical, microbial and groundwater transport conditions. The simulations highlight the conditions under which optimal remediation occurs. The relative significance of regional microbial residence patterns, U(VI)-surface complexation, geochemical conditions such as mineralogy, and porous media characteristics such as porosity and regional mass transfer are identified. Additionally, low level radioactive waste disposal sites typically contain significant quantities of cellulose, whose hydrolysis can have a significant impact on the geochemical conditions in these sites. Those geochemical conditions, in turn, can affect radionuclide mobility and bioimmobilisation. To investigate the potentially critical role of cellulose, process-based predictive model was developed, which includes a novel approach to biomass transfer between a cellulose-bound biofilm and biomass in the bulk liquid. A sensitivity analysis of the system parameters revealed the significance of bacterial colonisation of cellulose particles by attachment through contact in solution. The thesis concludes that the processes involved in uranium bioimmobilisation are sensitive to regional residence characteristics, media porosity, surface complexation, microbial efficiency, and mass transfer under varying conditions. Careful characterisation of potential sites and use of a model that includes these processes in sufficient detail is therefore deemed necessary before the remediation effectiveness can be reliably predicted