Sealed containers in Z

Physical means of securing information, such as sealed envelopes and scratch cards, can be used to achieve cryptographic objectives. Reasoning about this has so far been informal. We give a model of distinguishable sealed envelopes in Z, exploring design decisions and further analysis and development of such models

Hydrologic Transport of Dissolved Inorganic Carbon and Its Control on Chemical Weathering

Chemical weathering is one of the major processes interacting with climate and tectonics to form clays, supply nutrients to soil microorganisms and plants, and sequester atmospheric CO2. Hydrology and dissolution kinetics have been emphasized as factors controlling chemical weathering rates. However, the interaction between hydrology and transport of dissolved inorganic carbon (DIC) in controlling weathering has received less attention. In this paper, we present an analytical model that couples subsurface water and chemical molar balance equations to analyze the roles of hydrology and DIC transport on chemical weathering. The balance equations form a dynamical system that fully determines the dynamics of the weathering zone chemistry as forced by the transport of DIC. The model is formulated specifically for the silicate mineral albite, but it can be extended to other minerals, and is studied as a function of percolation rate and water transit time. Three weathering regimes are elucidated. For very small or large values of transit time, the weathering is limited by reaction kinetics or transport, respectively. For intermediate values, the system is transport controlled and is sensitive to transit time. We apply the model to a series of watersheds for which we estimate transit times and identify the type of weathering regime. The results suggest that hydrologic transport of DIC may be as important as reaction kinetics and dilution in determining chemical weathering rates

Reactive transport modelling of cement-groundwater-rock interaction at the Grimsel Test Site

An in situ experiment at the Grimsel Test Site (Switzerland) to study water-cement-rock interaction in fractured granite was modelled. It consisted of a hardened cement source in a borehole intersecting a water conducting fracture. Grimsel groundwater was injected into this borehole. Two other boreholes at about 0.56 m and 1.12 m from the emplacement borehole were used to monitor the evolution of water composition for 5 years. The modelling approach was based on a 1D radial model for the emplacement borehole and a small volume of rock (fault gouge) around it, and a 2D model for the rest of the domain. The results of the 1D model were used as input for the 2D model. Both models showed dissolution of the fault gouge minerals. Results from the 1D model showed dissolution of portlandite in the cement with an increase in porosity. The 2D model showed a reduction in porosity in the fault gouge due to mineral precipitation. Near the emplacement borehole ettringite precipitated. At the centre of the plume there was precipitation of C-A-S-H and hydrotalcite. At the edge of the hyperalkaline plume calcite, hydrotalcite and illite precipitated.Peer ReviewedPostprint (author's final draft

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection-diffusion PDE's coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton-Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that on be able to solve chemical equilibrium problems (and compute derivatives), without having to know the solution method. An additional advantage of the Newton-Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009) http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1

Modeling the influence of MgSO4 invariant points on multiphase reactive transport process during saline soil evaporation

In the present work, we modeled a laboratory experiment where a sand column saturated with a MgSO4 solution is subject to evaporation. We used a compositional formulation capable of representing the effect of geochemistry on flow and transport for concentrated solutions under extreme dry conditions. The model accounts for the water sink/sources terms due to hydrated mineral dissolution/precipitation and the occurrence of invariant points, which prescribe the water activity. Results show that the occurrence of the invariant points at the top of the domain could affect the vapor flux at the column top and salt precipitation along the column. In fact, the invariant points occurrence could explain the spatial fluctuation on the salt precipitates formation. Results also suggest that the complex hydrochemical interactions occurring during soil salinization, including osmotic effects, are crucial not only to understand the salt precipitation, but also the evaporation rate.Fil: Gamazo, P.. Universidad de la Republica; Uruguay. Universidad Politecnica de Catalunya; EspañaFil: Saaltink, M. W.. Universidad Politecnica de Catalunya; EspañaFil: Carrera, J.. Instituto de Diagnóstico Ambiental y Estudios del Agua; EspañaFil: Slooten, L. J.. Instituto de Diagnóstico Ambiental y Estudios del Agua; EspañaFil: Bea, Sergio Andrés. Universidad Nacional del Centro de la Provincia de Buenos Aires. Rectorado. Instituto de Hidrología de Llanuras - Sede Azul; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Tandil; ArgentinaFil: Gran, M.. Universidad Politecnica de Catalunya; Españ

Lagrangian modeling of reactive transport in heterogeneous porous media with an automatic locally adaptive particle support volume

The particle support volume is crucial for simulating reactive transport with Lagrangian methods as it dictates the interaction among particles. Assuming that it is constant in space, the particle support volume can be selected by means of kernel density estimation theory, an approach that has been shown to provide accurate estimates in simple setups. However, the particle support volume should intuitively vary with the particle position and evolve with time so as to mimic the local behavior of the solute plume. In this paper, we present a new approach to select a locally optimal particle support volume in reactive transport simulations. We consider that each particle has a different support volume that can locally adapt its shape and size with time based on the nearby particle distribution. By introducing a new optimality criterion, closed-form expressions of the particle support volume are presented under certain assumptions. In advection-dominated transport, we propose to orient the support volume along the local velocities. Numerical simulations of solute transport in a randomly heterogeneous porous medium demonstrate that the new approach can substantially increase accuracy with a more rapid convergence to the true solution with the number of particles. The error reduction seen in local approaches is particularly important in regions with extreme (high and low) density of particles. The method is shown to be computationally efficient, displaying better results than traditional histogram or global kernel methods for the same computational effort.Peer ReviewedPostprint (published version

Reactive transport modelling of a high-pH infiltration test in concrete

A laboratory-scale tracer test was carried out to characterize the transport properties of concrete from the Radioactive Waste Disposal Facility at El Cabril (Spain). A hyperalkaline solution (K-Ca-OH, pH = 13.2) was injected into a concrete sample under a high entry pressure in order to perform the experiment within a reasonable time span, obtaining a decrease of permeability by a factor of 1000. The concentrations of the tracers, major elements (Ca2+, SO42-, K+ and Na+) and pH were measured at the outlet of the concrete sample. A reactive transport model was built based on a double porosity conceptual model, which considers diffusion between a mobile zone, where water can flow, and an immobile zone without any advective transport. The numerical model assumed that all reactions took place in the immobile zone. The cement paste consists of C-S-H gel, portlandite, ettringite, calcite and gypsum, together with residual alite and belite. Two different models were compared, one with portlandite in equilibrium (high initial surface area) and another one with portlandite reaction controlled by kinetics (low initial surface area). Overall the results show dissolution of alite, belite, gypsum, quartz, C-S-H gel and ettringite and precipitation of portlandite and calcite. Permeability could have decreased due to mineral precipitation.Peer ReviewedPostprint (author's final draft

Modeling evaporation processes in a saline soil from saturation to oven dry conditions

Thermal, suction and osmotic gradients interact during evaporation from a salty soil. Vapor fluxes become the main water flow mechanism under very dry conditions. A coupled nonisothermal multiphase flow and reactive transport model was developed to study mass and energy transfer mechanisms during an evaporation experiment from a sand column. Very dry and hot conditions, including the formation of a salt crust, necessitate the modification of the retention curve to represent oven dry conditions. Experimental observations (volumetric water content, temperature and concentration profiles) were satisfactorily reproduced using mostly independently measured parameters, which suggests that the model can be used to assess the underlying processes. Results show that evaporation concentrates at a very narrow front and is controlled by heat flow, and limited by salinity and liquid and vapor fluxes. The front divides the soil into a dry and saline portion above and a moist and diluted portion below. Vapor diffusses not only upwards but also downwards from the evaporation front, as dictated by temperature gradients. Condensation of this downward flux causes dilution, so that salt concentration is minimum and lower than the initial one, just beneath the evaporation front. While this result is consistent with observations, it required adopting a vapor diffusion enhancement factor of 8

An open extensible tool environment for Event-B

Abstract. We consider modelling indispensable for the development of complex systems. Modelling must be carried out in a formal notation to reason and make meaningful conjectures about a model. But formal modelling of complex systems is a difficult task. Even when theorem provers improve further and get more powerful, modelling will remain difficult. The reason for this that modelling is an exploratory activity that requires ingenuity in order to arrive at a meaningful model. We are aware that automated theorem provers can discharge most of the onerous trivial proof obligations that appear when modelling systems. In this article we present a modelling tool that seamlessly integrates modelling and proving similar to what is offered today in modern integrated development environments for programming. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

Formal Proof from UML Models

Abstract. We present a practical approach to a formal analysis of UMLbased models. This is achieved by an underlying formal representation in Z, which allows us to pose and discharge conjectures to analyse models. We show how our approach allows us to consistency-check UML models, and model analysis by simply drawing snapshot diagrams