Mathematical and numerical filtration–advection–dispersion model of miscible grout propagation in saturated porous media

The development of a predictive model of behaviour of porous media during injection of miscible grout, taking into account convection, dilution and filtration of grout solution with interstitial water, as well as consolidation aspects, is presented. Model assumptions are reviewed and discussed first. During the establishment of the model, we insist on surface terms and their physical relevance in expressing adsorption effects. Constitutive laws such as Fick's law for diffusive mass transport, hydrodynamic dispersion tensor dealing with miscibility, are modified by taking into account filtration effects. A new surface term appears in mass balance equations as a consequence of filtration. According to the filtration laws used, an initial filtration rate is estimated on the basis of a one‐dimensional experimental campaign. The field equations are discretized by using Galerkin finite element and θ‐scheme standard method. For transport equation, Streamline Upwind Petrov Galerkin method is employed to prevent numerical oscillations. Lastly, confrontation of numerical results with laboratory experiments constitutes a first step to validate the model on a realistic basis. Copyright © 2001 John Wiley & Sons, Ltd.     

Effective properties of a cemented or an injected granular material

In this paper the macroscopic elastic properties of injected or cemented sands are derived from the characteristics of the constituents and the analysis of the microstructure using a multi‐scale modelling approach. Particular interest is given to the choice of the representative elementary volume, by relying on existing microstructural data. The periodic homogenization is adopted and required numerical solutions are performed by the finite element method. An assessment of the validity of the multi‐scale approach is achieved through comparison with theoretical and experimental results on cemented and injected granular media reported in the literature. The capabilities of the model are also used to investigate the influence of geometrical and mechanical microscale parameters on the macroscopic behaviour of the treated materials. Copyright © 2004 John Wiley & Sons, Ltd.     

A Tortonian onset for the Algerian margin inversion: Evidence from low‐temperature thermochronology

In North Africa, the Algerian margin is made of basement blocks that drifted away from the European margin, namely the Kabylia, and docked to the African continental crust in the Early Miocene. This young margin is now inverted, as dated Miocene (17 Ma) granites outcrop alongshore, evidencing kilometre‐scale exhumation since their emplacement. Age of inversion is actually unknown, although Pliocene is often considered in the offshore domain. To decipher the exhumation history of the margin between 17 and 5 Ma, we performed a coupled apatite fission track (AFT) and (U–Th–Sm)/He (AHe) study in the Cap Bougaroun Miocene granite. AFT dates range between 7 ± 1 and 10 ± 1 Ma, and mean AHe dates between 8 ± 2 and 10 ± 1 Ma. These data evidence rapid and multi‐kilometre exhumation during Tortonian times. This event cannot be related to slab break‐off but instead to the onset of margin inversion that has since developed as an in‐sequence north‐verging deforming prism.     

An experimental study of dispersion of an interactive tracer in chemically heterogeneous medium at a column scale

This paper aims at examining the increase of phenol adsorption breakthrough curves spreading caused by the chemical heterogeneity of granular activated carbon fixed beds. The local and the thermodynamic equilibrium assumption, as well as the nonlinear adsorption obeying to Langmuir isotherm, are considered. This study particularly tempts to link the reduced variance of phenol breakthrough curves to a measurable quantifying parameter of the chemical heterogeneity. The investigated artificial heterogeneous media are prepared by alternating layers of two types of granular activated carbon, active and non-active ones, that have similar physical properties. On the one hand, the chemical heterogeneity is quantified by the active layer relative thickness of the column length, l₁/L. On the other hand, it is quantified by the mean value of the probability distribution γ. The latter also represents the mean active grains mass ratio of the total medium mass, hence the medium mean capacity. The obtained results show an increase in the reduced variance and thus the effective global dispersion with the heterogeneity; the increase is as important as the medium capacity decreases. However, the dispersion increase achieves a limit value, even when the heterogeneity increases. The results are statistically modelled using a regression equation function of the capacity variation in terms of γ and the chemical heterogeneity in terms of l₁/L. The relationship combining the medium capacity and the chemical heterogeneity is obtained. The relationship implicitly takes into account the effect of the column length.     

Multi-scale study of permeability evolution of a bentonite clay owing to pollutant transport: Part II. Application to an MG-bentonite

This paper is concerned with the application of a multi-scale model of permeability evolution to the simulation of permeation tests of lead nitrate solutions in a compacted natural bentonite. In a previous work, the weathered hydraulic conductivity has been measured for different pollutant concentrations. Textural and structural evolutions induced by heavy metal sorption have also been investigated, therefore giving us information about the various pore spaces that may be encountered during the process of pollutant leaching. Such knowledge has been exploited during the construction of the numerical microstructures. First of all, pure water permeability tests have been simulated, this has allowed us to ascertain the representation of compacted clay before pollutant permeation. For both Prrenjas and Wyoming clays, permeation tests after pollutant permeation have then been simulated, using connected and non-connected macro-voids configurations. Different conclusions have been drawn based on simulation results for the two different clays investigated, which are supported by experimental evidence.     

Multi-scale modelling of the permeability evolution of fine sands during cement suspension grouting with filtration

Fluid flow during permeation grouting of fine sands with a microcement-based grout is studied by assuming that the heterogeneous medium composed of the initial granular skeleton, filtered cement and the interstitial fluid phase can be replaced by a continuous equivalent medium at the macroscopic level. Consequently, the method of Homogenization of Periodic Structures (HPS) is used to identify the effective permeability tensor evolution under the effect of cement filtration. The expression of the macroscopic permeability tensor derived through the HPS procedure is shown to depend on the permeating fluid viscosity and the geometrical arrangement of the sand grains and cement deposit within the microstructure. Numerical computations are made using various two-dimensional and three-dimensional microstructures, and the model results are confronted with grouting experiments performed on small scale columns in the laboratory.     

Assessing the organic pollution of surface water of Medjerda watershed (NE Algeria)

Water quality in the Northern part of Mellegue-Medjerda watershed (East Algeria) has been adversely affected by important pollutants discharged into the Medjerda wadi without, in most cases, any treatment. Chemical and physical degradation are due to agricultural and industrial practices and domestic wastewaters. Over a three-month period, a study of the low-flow water quality characteristics throughout Medjerda wadi was undertaken. Longitudinal profiles of water quality were constructed using data from fourteen sites. All sewage, agricultural, and industrial inputs were included. Analyzed properties were nutrients (NO₃ ⁻, NO₂ ⁻, NH₄ ⁺, and PO₄ ³⁻), Biochemical oxygen demand after five days (BOD₅), chemical oxygen demand (COD), and dissolved oxygen (DO). Along Medjerda wadi, all values change because of conditions specific to each sampling station. Nitrate was the most important form of nitrogen-element load (94%). Its concentration reached 34.3 mg L⁻¹ at OM₄ point, downstream of domestic wastewater discharges. The spatial evolution of the organic pollution index (OPI) shows that the wastewater effluent constitutes the main source of pollution. Indeed, water quality goes from a moderate pollution state at some sampling stations not or slightly affected by wastewaters discharges to a very strong pollution state (OPI of about 1.75) downstream of the domestic effluents inputs of Souk-Ahras city.     

Micropaleontological study (foraminifera, ostracods) and characterization of the paleoenvironment of middle Cretaceous deposits (Djebel Chemla area, north-eastern Algeria)

The Djebel Chemla section is situated in the north-east of Algeria, close to the town of Tébessa and just a few kilometers from the Tunisian border. This section is composed mainly of a sequence of marl and marly limestone levels, alternating with recurring oyster levels which range in age from Vraconnian to the Early Turonian. Firstly, the micropaleontological study of the content (counting of foraminifera and ostracods, thin sections) allows the subdivision of the section into four biozones, with Rotalipora appenninica, Rotalipora globotruncanoides, Rotalipora cushmani, and Whiteinella archaeocretacea as bio-indicators; and, secondly, it provides the opportunity to specify the paleoenvironment. The supposed depositional environment is rather calm and deep, of an external platform type, with a maximum depth of 200 m. Bottom waters seem to be commonly poorly oxygenated. The end-Cenomanian anoxic crisis was also characterized by the presence of Bahloul facies levels, rich in TOC, in filaments and of globulous planktic foraminifera, including a considerable proportion of Heterohelix. The genus Rotalipora has disappeared a few levels lower down.