Jacques Bodin

Simulation of solute transport in discrete fracture networks using the time domain random walk method

The time domain random walk (TDRW) method has been developed for simulating solute transport in discrete fracture networks. The following transport processes have been considered: advective transport in fractures, hydrodynamic dispersion along the fracture axis, sorption reactions on the fracture walls and decay reactions. The TDRW method takes advantage of both random walk and particle-tracking methods. It allows for the one-step calculation of the particle residence time in each bond of the network while avoiding mass balance problems at fracture intersections with contrasted dispersion coefficients. The accuracy of the TDRW method has been addressed by means of synthetic test problems into single fractures and into a 2D discrete fracture network. In each case, simulated and theoretical results compare very well.

From analytical solutions of solute transport equations to multidimensional time‐domain random walk (TDRW) algorithms

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Peclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

Biogeohydrodynamic in the forested humid tropical environment: the case study of the Nsimi small experimental watershed (south Cameroon)

This paper summarizes a six-year study of the Nsimi Small Experimental Watershed (SEW), considered as a model for the South Cameroon humid tropical ecosystem. When this small watershed was set up, no similar survey of input/output hydrobiogeochemical fluxes in granitoid rocks in stable cratonic environment was available, to our knowledge, on any site close to the Equator. Moreover, this is the first attempt, world-wide, to combine different approaches in hydrology, (bio)geochemistry, mineralogy, crystallography, microbiology, geophysics and pedology. Research is based on (1) regular hydrobiogeochemical surveys in various water reservoirs of the SEW ecosystem (atmospheric deposits, groundwater and stream), (2) surveys related either to the organisation and composition of different reservoirs in the superficial layers (basement rocks, saprolite, soils) or to various hydrological, biological and geochemical processes. These surveys aim at (1) finding the main parameters involved in the chemical and physical erosion processes of the humid tropical ecosystem, (2) understanding the source of a particular chemical composition in groundwater and rivers, (3) documenting accurately the different exportation processes of chemical elements in water and soil (4) investigating the possible relation between the biodegradation of soil organic matter and the leaching of metals (especially iron) and (5) comparing the long and short term weathering rates using mass balance calculations. Another important objective of this study is to provide a new scientific and engineering database for the future development of South Cameroon, which is still nowadays a relatively preserved ecosystem. One of the major results is the essential role played by the biological cycle (vegetation and soil organic matter) in the fractionation, exportation or storage of the chemical elements in humid tropical environments. Moreover we are able to propose a model of the current erosion for this SEW from the database obtained on (1) the mineralogy of the basement rocks and the soil layers, (2) the geochemistry of the soluble and colloidal phases of waters and (3) the hydrology within the different reservoirs of the hydrosystem. This model has been confirmed and extended on a regional scale (Nyong river basin). It emphasized the behaviour of the main elements of the tropical soil layers (Fe, Al, Si), the nutrients (C, Ca, Mg, K, Sr) and specific tracers of the weathering processes either with strong mobility (Cl, Na) or on the contrary with an extremely low mobility (Zr, Th, REEs). On the SEW scale, a strong geochemical contrast occurs between the different groundwater zones flooding (1) the hill slope lateritic profiles, (2) the weathering front (interface between the saprolite and the basement rocks), and (3) the swampy zone in which the Mengong brook flows. High DOC contents (15 mg/L) but also high Fe, Th, Al, Zr contents characterize the swampy zone waters. Na and Si have mainly a deep origin (exfiltration), Al, Th, Zr and REEs are strongly linked with colloidal organic matter located in the upper horizons of the swamp. Fe has a much more complex behaviour due to its change of redox state which can be independent of organic matter complexation. Concerning the major base cations, their origin can be constrained by the biological cycle (storage or leaching). K is typically influenced by the biological cycle. During the floods, Cl has the same behaviour as K: it is one of the most striking points of this study. However, the Cl annual budget is balanced. These characteristics can be understood as the consequence of the weathering of the minerals present in the saprolite (kaolinite, goethite, zircon, Th-oxide). This chemical weathering allows the leaching of base cations and also Al and Fe. It has been demonstrated that the microbial populations of the swampy zone can play an important role in the mobilization of transition metals (e.g. Fe). This study point out the role of humic acids in the transport and the weathering budget of elements usually considered as immobile in the superficial cycle (e.g. Al, Th, Zr, Fe). It must be mentioned that worldwide the SEW and even the Nyong network waters are among the least concentrated river waters. It means that even if the organic matter plays an important role in the mobilization and transport of some elements in the swampy zone, its action is limited in term of major cation fluxes on the SEW scale. The reason invoked is that the cation fluxes are directly linked to the pedological history and the geomorphology of the watershed. The presence of thick soil layers composed of saprolite and latosol on the hillsides and of hydromorphic soils in the swampy zone with constant mineralogy lead to isolating the bedrock. The long residence time of water close to the weathering front plays a major role in preserving the parent rock from the hydro-chemical outputs. Moreover, the topsoil layers are stabilized by the vegetation cover, which limits mechanical erosion. This should be taken into account for the carbon mass balance calculation because of the wide areas on stable shields concerned by the humid tropical ecosystems. Moreover, comparison between long and short-term weathering allows us to suggest that paleo-climatic conditions did not change since the Miocene (6-20 Ma) in this part of the world.

Continuous-time model identification of wells interaction on the Hydrogeological Experimental Site of Poitiers

In hydrogeology, estimating aquifer permeability is an important issue. This can be useful in understanding the flow of pollutants from one area of an aquifer to another. For this aquifer analysis sake, the Hydrogeological Experimental Site of Poitiers (France) covering a limestone aquifer is an appropriate instrumented test bed enabling measurement of hydraulic responses of a series of observation wells due to a step-type pumping out excitation at a given well. Given the input-output data, black-box continous-time modeling is quite a straight forward process as shown in this paper. The aim is then to be able to use the identified parameters to classify the different wells according to how sensitive they are to the one having been excited. A correlation between black-box parameters and hydrogeological ones is then established.