Nuclear Waste Disposal Simulations: Couplex Test Cases

We give some results obtained for the Couplex test cases proposed by the ANDRA. In this paper our aim is twofold. Firstly, to compute the release of nuclides out of the repository by concentrating on the 3D near field (Couplex 2). The simulation of the transport phenomena takes into account the dissolution of the glass containers and congruent emissions of the radio-nuclides including filiation chains and some simplified chemistry. Secondly, it is to use the near field computations in order to simulate the nuclide migrations in a 2D far field (Couplex 3). Coupling in between the two simulations takes into consideration the periodicity of the disposal modules and the geometry of the repository described in Couplex 1. The mixed finite element and discontinuous Galerkin methods are used to solve the convection–diffusion equations. In order to handle the nonlinear precipitation/dissolution term, we developed a new iterative technique that combines Picard and Newton–Raphson methods.     

Under stress permeability determination of the Meuse/Haute-Marne mudstone

In the underground waste isolation projects such as the ANDRA'one in the site of Bure, the transport properties of the surrounding rock mass is of fundamental importance. To measure very low permeability, we use the modified version of the pulse test proposed by Hsieh et al. [Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D., Silliman, S.E., 1981. A transient laboratory method for determining the hydraulic properties of ‘tight’ rocks — I. Theory. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. Vol. 18, pp. 245-252] which enables the intrinsic permeability, k, and the specific storage coefficient, S_s, of rocks such as mudstone to be characterized. In this paper, the special effort performed on the laboratory apparatus design, to ensure a good sensitivity of the rock response with respect to both parameters, k and S_s, is presented. In addition, two parameters identification procedures are proposed: the graphical method given by Hsieh et al. [Hsieh, P.A., Tracy, J.V., Neuzil, C.E., Bredehoeft, J.D., Silliman, S.E., 1981. A transient laboratory method for determining the hydraulic properties of ‘tight’ rocks — I. Theory. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. Vol. 18, pp. 245-252] and a parameter identification based on the solution of an inverse problem. The efficiency of the apparatus design and the parameters identification procedures is then demonstrated though some pulse tests performed on the Meuse/Haute-Marne mudstone.     

Sedimentological and stratigraphic evolution of northern Lebanon since the Late Cretaceous: implications for the Levant margin and basin

This paper presents an updated review of the Upper Mesozoic and Cenozoic sedimentological and stratigraphic evolution of the Levant margin with a focus on the northern Lebanon. Facies and microfacies analysis of outcrop sections and onshore well cores (i.e., Kousba and Chekka) supported by nannofossil and planktonic foraminifers biostratigraphy, allowed to constrain the depositional environments prevailing in the Turonian to Late Miocene. The “Senonian” (a historical term used to define the Coniacian to Maastrichtian) source rock interval was subdivided into four sub-units with related outer-shelfal facies: (1) Upper Santonian, (2) Lower, (3) Upper Campanian, and (4) Lower Maastrichtian. This Upper Cretaceous rock unit marks the major drowning of the former Turonian rudist platform. This paper confirms the Late Lutetian to Late Burdigalian hiatus, which appears to be a direct consequence of major geodynamic events affecting the Levant region (i.e., the continued collision of Afro-Arabia with Eurasia), potentially enhanced by regressional cycles (e.g., Rupelian lowstand). The distribution of Late Burdigalian–Serravallian rhodalgal banks identified in northern Lebanon was controlled by pre-existing structures inherited from the pulsating onshore deformation. Reef barriers facies occur around the Qalhat anticline, separating an eastern, restricted back-reef setting from a western, coastal to open marine one. The acme of Mount Lebanon’s uplift and exposure is dated back to the Middle–Late Miocene; it led to important erosion of carbonates that were subsequently deposited in paleo-topographic lows. The Late Cretaceous to Cenozoic facies variations and hiatuses show that the northern Lebanon was in a higher structural position compared to the south since at least the Late Cretaceous.     

Variability of water exchanges through the Strait of Hormuz

Ocean Dynamics - The variability of the water mass exchange between the Arabian Gulf and the Indian Ocean is investigated using a high-resolution (1/36°) ocean model. We focus on the period...     

Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures

Contrast in capillary pressure of heterogeneous permeable media can have a significant effect on the flow path in two-phase immiscible flow. Very little work has appeared on the subject of capillary heterogeneity despite the fact that in certain cases it may be as important as permeability heterogeneity. The discontinuity in saturation as a result of capillary continuity, and in some cases capillary discontinuity may arise from contrast in capillary pressure functions in heterogeneous permeable media leading to complications in numerical modeling. There are also other challenges for accurate numerical modeling due to distorted unstructured grids because of the grid orientation and numerical dispersion effects. Limited attempts have been made in the literature to assess the accuracy of fluid flow modeling in heterogeneous permeable media with capillarity heterogeneity. The basic mixed finite element (MFE) framework is a superior method for accurate flux calculation in heterogeneous media in comparison to the conventional finite difference and finite volume approaches. However, a deficiency in the MFE from the direct use of fractional flow formulation has been recognized lately in application to flow in permeable media with capillary heterogeneity. In this work, we propose a new consistent formulation in 3D in which the total velocity is expressed in terms of the wetting-phase potential gradient and the capillary potential gradient. In our formulation, the coefficient of the wetting potential gradient is in terms of the total mobility which is smoother than the wetting mobility. We combine the MFE and discontinuous Galerkin (DG) methods to solve the pressure equation and the saturation equation, respectively. Our numerical model is verified with 1D analytical solutions in homogeneous and heterogeneous media. We also present 2D examples to demonstrate the significance of capillary heterogeneity in flow, and a 3D example to demonstrate the negligible effect of distorted meshes on the numerical solution in our proposed algorithm.     

Efficiency of reduced-order, time-dependent adjoint data assimilation approaches

Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reduced-order optimization methods that reduce the size of the control vector by projecting it onto a limited number of basis functions were suggested. In this paper, we show that such order reduction can indeed speed up the initial convergence rate of an assimilation effort in the eastern subtropical North Atlantic using in situ and satellite data as constraints. However, an improved performance of the optimization was only obtained with a hybrid approach where the optimization is started in a reduced subspace but is continued subsequently using the full control space. In such an experiment about 50% of the computational cost can be saved as compared to the optimization in the full control space. Although several order-reduction approaches seem feasible, the best result was obtained by projecting the control vector onto Empirical Orthogonal Functions (EOFs) computed from a set of adjusted control vectors estimated previously from an optimization using the same model configuration.     

Assessing 4D-VAR for dynamical mapping of coastal high-frequency radar in San Diego

The problem of dynamically mapping high-frequency (HF) radar radial velocity observations is investigated using a three-dimensional hydrodynamic model of the San Diego coastal region and an adjoint-based assimilation method. The HF radar provides near-real-time radial velocities from three sites covering the region offshore of San Diego Bay. The hydrodynamical model is the Massachusetts Institute of Technology general circulation model (MITgcm) with 1 km horizontal resolution and 40 vertical layers. The domain is centered on Point Loma, extending 117 km offshore and 120 km alongshore. The reference run (before adjustment) is initialized from a single profile of T and S and is forced with wind data from a single shore station and with zero heat and fresh water fluxes. The adjoint of the model is used to adjust initial temperature, salinity, and velocity, hourly temperature, salinity and horizontal velocities at the open boundaries, and hourly surface fluxes of momentum, heat and freshwater so that the model reproduces hourly HF radar radial velocity observations. Results from a small number of experiments suggest that the adjoint method can be successfully used over 10-day windows at coastal model resolution. It produces a dynamically consistent model run that fits HF radar data with errors near the specified uncertainties. In a test of the forecasting capability of the San Diego model after adjustment, the forecast skill was shown to exceed persistence for up to 20 h.     

Numerical Reliability for Mixed Methods Applied to Flow Problems in Porous Media

This paper is devoted to the numerical reliability and time requirements of the Mixed Finite Element (MFE) and Mixed-Hybrid Finite Element (MHFE) methods. The behavior of these methods is investigated under the influence of two factors: the mesh discretization and the medium heterogeneity. We show that, unlike the MFE, the MHFE suffers with the presence of badly shaped discretized elements. Thereat, a numerical reliability analyzing software (Aquarels) is used to detect the instability of a matrix-inversion code generated automatically by a symbolic manipulator. We also show that the spectral condition number of the algebraic systems furnished by both methods in heterogeneous media grows up linearly according to the smoothness of the hydraulic conductivity. Furthermore, it is found that the MHFE could accumulate numerical errors if large jumps in the tensor of conductivity take place. Finally, we compare running-times for both algorithms by giving various numerical experiments.     

Simultaneous perturbation stochastic approximation for tidal models

The Dutch continental shelf model (DCSM) is a shallow sea model of entire continental shelf which is used operationally in the Netherlands to forecast the storm surges in the North Sea. The forecasts are necessary to support the decision of the timely closure of the moveable storm surge barriers to protect the land. In this study, an automated model calibration method, simultaneous perturbation stochastic approximation (SPSA) is implemented for tidal calibration of the DCSM. The method uses objective function evaluations to obtain the gradient approximations. The gradient approximation for the central difference method uses only two objective function evaluation independent of the number of parameters being optimized. The calibration parameter in this study is the model bathymetry. A number of calibration experiments is performed. The effectiveness of the algorithm is evaluated in terms of the accuracy of the final results as well as the computational costs required to produce these results. In doing so, comparison is made with a traditional steepest descent method and also with a newly developed proper orthogonal decomposition-based calibration method. The main findings are: (1) The SPSA method gives comparable results to steepest descent method with little computational cost. (2) The SPSA method with little computational cost can be used to estimate large number of parameters.